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One of two Stanford plaintiffs to drop out of admissions lawsuit, lawyer says
Several students to be added in amended complaint to be filed later today
Courtesy of Stanford Photo
By Erin Woo on March 14, 2019
Erica Olsen '21, one of two Stanford students who have filed a class-action suit against Stanford University and seven other universities implicated in the college admissions bribery scandal, will be dropping out of the suit, lawyer John Medler told The Daily on Thursday morning. Medler and two other lawyers are representing the plaintiffs in the lawsuit.
Medler also wrote that "several" other plaintiffs will be added when an amended complaint is filed later today.
Olsen declined to comment.
Medler and Kalea Woods '20 — the only other plaintiff currently on the suit — could not be immediately reached by The Daily for comment.
The suit alleges that Olsen and Woods — along with all students who between 2012 and 2018 were rejected from one of the eight colleges named after paying an application fee — were denied a "fair admissions consideration process" due to defendant William Singer's multimillion-dollar admissions cheating scheme. With the help of Singer, wealthy parents across the country paid proctors to inflate their children's standardized test scores or, in some cases, bribed college athletic coaches to act as if their children were recruited athletes.
Contact Erin Woo at erinkwoo 'at' stanford.edu.
This story will be updated as more details come to light.
Erin Woo
Erin Woo '21 is a senior staff writer. She was previously managing editor of news during Vol. 254 and 255, and she has also reported for The Mercury News and WNYC. Contact her at erinkwoo 'at' stanford.edu.
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{
"redpajama_set_name": "RedPajamaCommonCrawl"
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est un genre d'insectes hyménoptères de la famille des Apidae (les abeilles). .
Systématique
Le genre Euglossa a été créé en 1802 par l'entomologiste français Pierre-André Latreille (1762-1833).
Répartition
. .
Liste d'espèces
Selon :
Notes et références
Liens externes
Apidae
Genre d'Abeilles (nom scientifique)
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
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Read Kudos Online
Authors: Rachel Cusk
BOOK: Kudos
Rachel Cusk
She got up and went away
Should she not have? Not have what?
Got up and gone away.
Yes, I think she should have
Because it was getting darker.
Getting what? Darker. Well,
There was still some
Day left when she went away, well,
Enough to see the way.
And it was the last time she would have been able …
Able? … to get up and go away.
It was the last time the very last time for
After that she could not
Have got up and gone away any more.
'She Got Up and Went Away', Stevie Smith
'The man next to me on the plane was so tall…'
'The hotel was completely round…'
'I had been told that the interviewer was waiting for…'
'The party was being held at a venue in the city centre…'
'There was a long queue for food at the bar…'
'The conference was being held in a suburb by the sea…'
'The next morning the wind had dropped and the…'
'The hotel where Paola had asked me to meet her…'
'After the heat and light of outside,'
'The taxi driver had pointed the way to the beach…'
Also by the Author
'The man next to me on the plane was so tall…'
The man next to me on the plane was so tall he couldn't fit in his seat. His elbows jutted out over the armrests and his knees were jammed against the seat in front, so that the person in it glanced around in irritation every time he moved. The man twisted, trying to cross and uncross his legs, and inadvertently kicked the person to his right.
'Sorry,' he said.
He sat motionless for a few minutes, breathing deeply through his nostrils with his hands clenched in his lap, but before long he became restless and tried to move his legs again so that the whole bank of seats in front of him was jolted back and forth. Finally I asked him if he wanted to change seats, since mine was on the aisle, and he accepted with alacrity, as if I had offered him a business opportunity.
'Usually I travel in executive class,' he explained, while we got up and changed places. 'There's a lot more legroom.'
He stretched out into the aisle and his head fell against the back of the seat in relief.
'Thank you very much,' he said.
The plane began to move slowly out over the tarmac. My neighbour gave a contented sigh and appeared almost instantly to fall asleep. An air hostess came up the aisle and stopped at his legs.
'Sir?' she said. 'Sir?'
He jerked awake and folded himself awkwardly back into the narrow space in front so that she could pass. The plane paused for a few minutes and then lurched forward and then paused again. Through the window a queue of planes could be seen ahead, waiting their turn. The man's head began to nod and soon his legs were splayed once more across the aisle. The air hostess returned.
'Sir?' she said. 'We need to keep the aisle clear for take-off.'
He sat up.
She moved away and gradually his head began to nod again. Outside a haze stood over the flat grey landscape so that it seemed to merge with the overcast sky in horizontal bands of such subtle variation that it almost resembled the sea. In the seats in front a woman and a man were talking. It's so sad, the woman said, and the man grunted in reply. It's just really sad, she repeated. There was a pounding of footsteps up the carpeted aisle and the air hostess
reappeared. She put her hand on my neighbour's shoulder and shook it.
'I'm afraid I'm going to have to ask you to keep your legs out of the way,' she said.
'I'm sorry,' the man said. 'I can't seem to stay awake.'
'I'm going to have to ask that you do,' she said.
'I didn't actually get to bed last night,' he said.
'I'm afraid that's not my problem,' she said. 'You're putting other passengers at risk by obstructing the aisle.'
He rubbed his face and rearranged himself in his chair. He took out his phone and checked it and put it back in his pocket. She waited, watching him. Finally, as though satisfied that he had genuinely obeyed her, she went away. He shook his head and made a gesture of incomprehension, as though to an unseen audience. He was somewhere in his forties, with a face that was both handsome and unexceptional, and his tall frame was clad with the clean, well-pressed neutrality of a businessman's weekend attire. He wore a heavy silver watch on his wrist and new-looking leather shoes on his feet; he exuded an air of anonymous and slightly provisional manliness, like a soldier in uniform. By now the plane had made its halting progress up the queue and was slowly turning in a wide arc towards the runway. The haze had turned to rain and droplets ran down the window pane.
The man looked out with an exhausted stare at the gleaming tarmac. The clamour of the engines was rising around us and the plane finally surged forward, then rose tipping and rattling through layers of thick wadded cloud. For a while the dull green network of fields beneath us with its block-like houses and huddled groups of trees returned to sight through sporadic rents in the grey before it closed over them. The man emitted another deep sigh and in a few minutes had gone back to sleep, his head lolling forward over his chest. The cabin lights flickered on and the sounds of activity began. Before long the air hostess was at our row, where the sleeping man had once more stretched his legs out into the aisle.
'Sir?' she said. 'Excuse me? Sir?'
He lifted his head and looked around himself, bewildered. When he saw the air hostess standing there with her trolley he slowly and effortfully withdrew his legs so that she could pass. She watched with pursed lips, her eyebrows arched.
'Thank you,' she said, with barely concealed sarcasm.
'It's not my fault,' he said to her.
Her painted eyes fell on him momentarily. Their expression was cold.
'I'm just trying to do my job,' she said.
'I realise that,' he said. 'But it's not my fault that
the seats are too close together.'
There was a pause in which the two of them looked at one another.
'You'll have to take that up with the airline,' she said.
'I'm taking it up with you,' he said.
She folded her arms and lifted her chin.
'Most of the time I travel business,' he said, 'so it isn't usually a problem.'
'We don't offer business class on this flight,' she said. 'But there are plenty of other carriers who do.'
'So your suggestion is that I fly with someone else,' he said.
'That's right,' she said.
'Brilliant,' he said. 'Thank you very much.'
He gave a sour bark of laughter at her departing back. For a while he continued to smile self-consciously, like someone who has mistakenly wandered out onstage, and then, apparently to disguise his feelings of exposure, he turned to me and asked the reason for my trip to Europe.
I said I was a writer and was on my way to speak at a literary festival.
Immediately his face assumed an expression of polite interest.
'My wife's a big reader,' he said. 'She belongs to one of those book clubs.'
A silence fell.
'What kind of thing do you write?' he said, after a while.
I said it was hard to explain and he nodded his head. He drummed his fingers on his thighs and tapped a disjointed rhythm with his shoes on the carpeted floor. He shook his head from side to side and rubbed his fingers vigorously over his scalp.
'If I don't talk,' he said finally, 'I'll just go to sleep again.'
He said it pragmatically, as though he was used to solving problems at the expense of personal feeling, but when I turned to look at him I was surprised to see a pleading expression on his face. His eyes were red-rimmed with yellow whites and his neatly cut hair stood on end where he had rubbed it.
'Apparently they lower the oxygen levels in the cabin before take-off to make people sleepy,' he said, 'so they shouldn't really complain when it works. I have a friend who flies these things,' he added. 'He was the one who told me that.'
The strange thing about this friend, the man went on, was that despite his profession he was a fanatical environmentalist. He drove a tiny electric car and ran his household entirely on solar panels and windmills.
'When he comes to our place for dinner,' he said, 'you'll find him out by the recycling bins while everyone else is four sheets to the wind, sorting the food
packaging and the empties. His idea of a holiday,' he said, 'is carrying all his own gear up a Welsh mountainside and sitting in a tent in the rain for two weeks talking to the sheep.'
Yet this same man regularly donned a uniform and climbed into the cockpit of a fifty-ton smoke-spewing machine and flew a cabin-load of drunken holidaymakers to the Canary Islands. It was hard to think of a worse route to fly, yet his friend had flown it for years. He worked for a budget airline that practised the most brutal economies, and apparently the passengers behaved like zoo animals. He took them out white and he brought them back orange, and despite earning less than anyone else in their circle of friends, he gave half his income to charity.
'The thing is,' he said perplexedly, 'he's just a really nice guy. I've known him for years, and it's almost like the worse things are, the nicer he becomes. He told me once,' he said, 'that in the cockpit they have a screen where they can watch what's going on in the cabin. He said that at first he couldn't stand looking at it because it was so depressing seeing the way these people conducted themselves. But after a while he started to become sort of obsessed with it. He's watched hundreds of hours of it. It's a bit like meditation, he says. Even so,' he said, 'I wouldn't be able to stand working in that world. The first thing I did
when I retired was cut up my frequent flyer's card. I swore I'd never get on one of these things again.'
I said he seemed very young to be retired.
'I kept a spreadsheet on my desktop called "Freedom",' he said, with a sideways grin. 'It was basically just columns of figures that had to add up to a certain number, and when they did I could leave.'
He had been the director of a global management company, he said, a job that involved being constantly away from home. For example, it wasn't unusual for him to visit Asia, North America and Australia all in the space of two weeks. He had once flown to South Africa for a meeting and flown back again as soon as the meeting was over. Several times, he and his wife had worked out where the halfway point was between their two locations and then met there for a holiday. Once, when the company's Australasian branch had gone into meltdown and he'd had to stay over there to sort it out, he hadn't seen his children for three months. He'd started work at eighteen and now he was forty-six, and he hoped he would have enough time to live the whole of his working life in reverse. He had a house in the Cotswolds he'd barely set foot in and a whole garage full of bikes and skis and sporting equipment he'd never had time to use; he had friends and family he'd spent the past two decades mostly saying hello and goodbye to, since he
was usually either going away and had to prepare and go to bed early, or coming back exhausted. He had read somewhere about a medieval method of punishment that involved incarcerating the prisoner in a space specially designed to prevent him from being able to fully extend his limbs in any direction, and though just thinking about it made him break out in a sweat, it pretty much summed up the way he had lived.
I asked him whether his release from that prison had lived up to the title of his spreadsheet.
'It's funny you should say that,' he said. 'Since I left work I find that I'm constantly getting into arguments with people. My family complain that now I'm at home all the time, I'm trying to control them. They haven't actually said,' he added, 'that they wish we could go back to how things were. But I know they're thinking it.'
He couldn't believe, for example, how late they slept in the morning. All those years that he'd left the house before dawn, the thought of their slumbering forms in the darkness had often made him feel purposeful and protective. If he'd realised how idle they were he might not have seen it the same way. Sometimes he had to wait until lunchtime for them to get up: he had started going into their rooms and opening the curtains, as his father used to do every morning
when he was growing up, and was astonished by the hostility this action elicited. He had tried to schedule their mealtimes – they all, he had discovered, ate different foods at different times of day – and to institute an exercise routine, and was trying hard to believe that the full-scale revolt these measures provoked was proof of their necessity.
'I spend a lot of time talking to the cleaner,' he said. 'She turns up at eight. She says she's been dealing with these issues for years.'
He recounted all this with an abashed and easy confidentiality that made it clear he spoke for the purposes of entertainment rather than to arouse consternation. A deprecating smile played around his mouth, showing an even row of strong white teeth. He had grown more animated while he spoke, and his desperate, wild-eyed demeanour had softened into the genial mask of the raconteur. I had the impression that these were stories he had told before and liked to tell, as though he had discovered the power and pleasure of reliving events with their sting removed. The skill, I saw, lay in skirting close enough to what appeared to be the truth without allowing what you actually felt about it to regain its power over you.
I asked him how, given his oath, he had come to find himself on an aeroplane again.
He smiled again somewhat shamefacedly and ran a hand through his fine brown hair.
'My daughter's playing in a music festival over there,' he said. 'She plays for her school orchestra. The – ah – oboe.'
He had been supposed to fly out with his wife and children yesterday but their dog had been taken ill and he'd had to let them go on without him. It might sound ridiculous, but the dog was probably the most important member of their family. He'd had to sit up with him all night and then drive straight to the airport.
'To be honest I shouldn't have been behind the wheel of a car,' he said in a low voice, leaning his elbow on the armrest between us. 'I could hardly see straight. I kept passing these signs by the road with the same words on them over and over again and I started to think they'd been put there for me. You know the ones I mean – they're everywhere. It took me ages to work out what they were. I did wonder,' he said, with his abashed smile, 'if I was actually going mad. I couldn't understand who had chosen them, or why. They seemed to be addressing me personally. Obviously,' he said, 'I read the news, but I've got a bit behind since leaving work.'
I said it was true that the question of whether to leave or remain was one we usually asked ourselves in private, to the extent that it could almost be said to
constitute the innermost core of self-determination. If you were unfamiliar with the political situation in our country, you might think you were witnessing not the machinations of a democracy but the final surrender of personal consciousness into the public domain.
In Ecstasy by Kate McCaffrey
League of Dragons by Naomi Novik
Little Fingers! by Tim Roux
The Headless Huntsman by Benjamin Hulme-Cross
Ghost Dancer (A Modern Magics Story) by Maer Wilson
Summer on Blossom Street by Debbie Macomber
Reckless (Wrecked) by Casey, Elle
Mosaic by Leigh Talbert Moore
Fragile by Chris Katsaropoulos
The Vampire Book of the Month Club by Rusty Fischer
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 263
|
\section{Introduction}
\label{sec:Introduction}}
In the past three decades considerable efforts have been devoted to understanding
the rich structure and functions of complex networks, be they technologically engineered,
found in nature or generated through social interactions.
These developments have been recorded in surveys,
e.g., \cite{AlbertBarabasiReview, DorogovstevMendes, NewmanSurvey},
research monographs, e.g.,
\cite{BarratBarthelemyVespignani, CohenHavlinBook, Durrett_Book, JacksonBook, NewmanBook},
and anthologies of research papers, e.g., \cite{NewmanBarabasiWatts}.
The questions of interest often relate to a collection of entities (alternatively called nodes,
agents, etc.) and to a set of relationships between them.
The pairings can be physical, logical or social in nature; when pictured
as links or edges between nodes, they naturally give rise to {\em graphs} and
graph-like structures (customarily referred to as networks) on the set of nodes. Often the pairwise
relationships are best viewed as inherently random, suggesting that
random graph models be used to frame the relevant issues -- Here we understand a random graph to be a
graph-valued random variable (rv).
A popular research direction has been concerned with designing
random graph models that exhibit key properties observed in real networks.
Historically attention has been given
to the simplest of network properties, namely the degree of nodes and their various distributions.
The discussion invariably starts with the work
of Erd\H{o}s and R\'enyi \cite{ER1960}: With $n$ nodes and link probability $p$,
the (binomial) Erd{\H{o}}s-R{\'e}nyi graph $\mathbb{G}(n;p)$ postulates that
the $\frac{n(n-1)}{2}$ potential undirected links between these $n$ nodes
are each created with probability $p$, independently of each other.
The degree distribution in Erd{\H{o}}s-R{\'e}nyi graphs is announced to be Poisson-like, the justification going roughly as follows:
(i) With $D_{n,k} (p)$ denoting the degree rv of node $k$ in $\mathbb{G}(n;p)$,
the rvs $D_{n,1} (p), \ldots , D_{n,n} (p)$
are identically distributed, each distributed according to
a binomial rv ${\rm Bin}(n-1;p)$;
(ii) If the link probability scales with $n$ as $p_n \sim \frac{\lambda}{n}$ for some $\lambda > 0$, then
Poisson convergence ensures the distributional
convergence
\begin{equation}
D_{n,1}(p_n) \Longrightarrow_n D
\label{eq:PoissonConvergenceER}
\end{equation}
with $D$ denoting a Poisson rv with parameter $\lambda$.
A rich asymptotic theory has been developed
for Erd\H{o}s-R\'enyi graphs in the many node regime; see the monographs
\cite{Bollobas_Book, DraiefMassoulieLMMS, Durrett_Book, JansonLuczakRucinski}.
However, in many networks the data tells a different story: If the network
comprises a large number $n$ nodes and $N_n(d)$ is the number of nodes with degree $d$ in the network,
then statistical analysis suggests a power-law behavior of the form
\begin{equation}
\frac{ N_n(d) }{n} \simeq C d^{-\alpha}
\label{eq:PowerLaw}
\end{equation}
for some $\alpha$ in the range $[2,3]$ (with occasional exceptions) and $C>0$.
See \cite[Section 4.2]{Durrett_Book} for an introductory discussion and references,
and the paper by Clauset et al. \cite{ClausetShaliziNewman} for a principled statistical framework.
Statements such as (\ref{eq:PowerLaw})
are usually left somewhat vague as the range of $d$ is never carefully specified;
networks where (\ref{eq:PowerLaw}) was observed are often called {\em scale-free} networks.
On account of this observation, Erd{\H{o}}s-R{\'e}nyi graphs were deemed inadequate for
modeling scale-free networks (as well as other networks of interest).
As a result, new classes of random graph models have been proposed in an attempt to capture the
behavior (\ref{eq:PowerLaw}) (and other properties),
e.g., the configuration model \cite{BenderCaulfield_1978, Bollobas_1980, MolloyReed_1995, MolloyReed_1998},
generalized random graphs \cite{BrittonDeijfenMartinLof_2006}, and exponential random graphs
\cite{HollandLeinhardt_1981, Strauss_1986} to name some of the possibilities.
The Barab\'asi-Albert network model came to prominence
for its ability to formally \lq\lq explain" the existence of power law degree distributions in large networks
via the mechanism of preferential attachment \cite{BarabasiAlbert}.
The statement (\ref{eq:PowerLaw})
concerns an {\em empirical} degree distribution computed {\em network-wide}, whereas the convergence
(\ref{eq:PoissonConvergenceER}) addresses the behavior of the (generic) degree of a {\em single} node,
its distribution being identical across nodes.
A natural question is then whether these two different points of view are compatible with each other and
can be reconciled, at least asymptotically, in large networks, and if so, under what conditions.
The purpose of this paper is to explore this issue in some details.
What follows is an outline of some of the contributions along these lines:
\noindent
{\bf 1.} In Section \ref{sec:Framework} a general framework to investigate this discrepancy
is introduced in terms of a sequence of random graphs $\{ \mathbb{G}_n, \ n=1,2, \ldots \}$
whose size goes to infinity with $n$. Two different settings of increasing generality are considered.
\noindent
{\bf 2.} The {\em homogeneous} setting
captures situations where an asymptotic nodal degree distribution exists, and is presented in Section \ref{sec:HomogeneousAssumptions}.
It is defined in terms of the following three assumptions:
\begin{enumerate}
\item[(i)] A weak form of distributional homogeneity (hence the terminology homogeneous networks):
In particular, for each $n=1,2, \ldots $, the degree rvs in $\mathbb{G}_n$
are identically distributed across nodes -- Let $D_n$ denote
the generic degree rv in $\mathbb{G}_n$;
\item[(ii)] Existence of an asymptotic (nodal) degree distribution: In analogy with (\ref{eq:PoissonConvergenceER}),
there exists an $\mathbb{N}$-valued rv $D$ such that
\begin{equation}
D_n \Longrightarrow_n D.
\label{eq:ConvergenceGeneric}
\end{equation}
Let $( p(d), \ d=0,1, \ldots )$ denote the pmf of $D$; and
\item[(iii)] Asymptotic uncorrelatedness: The degree rvs $\{ D_n, \ n=1,2, \ldots \}$
display a weak form of asymptotic \lq\lq pairwise independence."
\end{enumerate}
\noindent
{\bf 3.} The relevant results for the homogeneous case are discussed in Section \ref{sec:HomogeneousLittleTheory}.
Under the aforementioned assumptions, Proposition \ref{prop:ConvergenceEmpirical+PMF} states that
if $( P_n(d), \ d=0,1, \ldots )$ is the empirical degree distribution
in $\mathbb{G}_n$ (with $P_n(d)$ denoting the fraction of nodes with degree $d$ in $\mathbb{G}_n$), then
\begin{equation}
P_n (d) \mbox{~$\stackrel{P}{\longrightarrow}$}_n ~ p(d), \quad d=0,1, \ldots
\label{eq:AsymptoticEmpiricalPMF}
\end{equation}
where the pmf $( p(d), \ d=0, 1, \ldots )$ on $\mathbb{N}$ is as postulated in (ii) above.
A strengthening of this result in terms of total variation distance
is provided as Proposition \ref{prop:ConvergenceEmpirical+TotalVariation}.
\noindent
{\bf 4.} A more general setting is considered in Section \ref{sec:GeneralSettingLittleTheory} where degree homogeneity, namely (i) above,
is replaced by a {\em random sampling} procedure over pairs of nodes.
Many situations are easily fitted into this more general framework. They include
the {\em non}-homogeneous Barab\'asi-Albert model (and other growth models), sequences of
deterministic graphs and sequences which are {\em locally weakly convergent} \cite{AldousSteele}
(or weakly convergent in the sense of Benjamini and Schramm \cite{BenjaminiSchramm}).
\noindent
{\bf 5.} In Section \ref{sec:CommonSetting} we introduce a broad class of models where the underlying assumptions (i)--(iii) can be checked;
this provides a natural and convenient setting for applying Proposition \ref{prop:ConvergenceEmpirical+PMF}.
Erd{\H{o}}s-R{\'e}nyi graphs (under the scaling yielding (\ref{eq:PoissonConvergenceER})) are readily subsumed in this framework,
as are many other homogeneous networks of interest in applications; see \cite{SPal_Thesis} for details.
This resolves the discrepancy mentioned earlier in that the appropriate version of
(\ref{eq:AsymptoticEmpiricalPMF}) does hold for both Erd{\H{o}}s-R{\'e}nyi graphs
(by virtue of Proposition \ref{prop:ConvergenceEmpirical+PMF})
\cite{SPal_Thesis} and for the Barab\'asi-Albert model (for which (\ref{eq:AsymptoticEmpiricalPMF}) holds
with limiting pmf satisfying $p(d) \sim d^{-3}$ ($d \rightarrow \infty)$ \cite{Bollobas_BAmodel}).
\noindent
{\bf 6.} Next we turn our attention to the proposition, too often taken for granted,
that in homogeneous random graphs the convergence (\ref{eq:ConvergenceGeneric}) of the generic degree distribution
{\em automatically} implies the convergence (\ref{eq:AsymptoticEmpiricalPMF}) of the empirical degree distribution.
In Section \ref{sec:CounterExample} we provide a counterexample drawn from
the class of random threshold graph models \cite{CCDM, FIKMMU, MakowskiYagan-JSAC, SC}.
For this class of models under {\em exponentially} distributed fitness,
although (\ref{eq:ConvergenceGeneric}) is known to take place with $p(d) \sim d^{-2}$ ($d \rightarrow \infty)$ \cite{FIKMMU},
we show that (\ref{eq:AsymptoticEmpiricalPMF}) fails to hold.
This fact, contained in Proposition \ref{prop:NonConvergenceInProbability}, constitutes an easy byproduct of Proposition \ref{prop:AssumptionC+fails}.
Proofs occupy Section \ref{sec:ProofPart+1} to Section \ref{sec:ProofsAsymptoticsOrderStatistics},
and rely on the asymptotics of
order statistics for i.i.d. variates \cite{EKM, LeadbetterLindgrenRootzen}.
We illustrate this failure through limited simulation results in Section \ref{sec:SimulationResults}.
\noindent
{\bf 7.} One implication of this last finding is that random threshold graphs with exponentially distributed fitness
{\em cannot} be used as an alternative scale-free model to the Barab\'asi-Albert model (see below) as claimed by some authors
\cite{CCDM,SC}. Indeed, only the convergence (\ref{eq:AsymptoticEmpiricalPMF}) has meaning
in the preferential attachment model
while (\ref{eq:ConvergenceGeneric}) is meaningless there, with the situation being reversed for random threshold graphs. In other words,
leaving aside the issue of which value of $\alpha$ is appropriate,
the two models cannot be compared in terms of their degree distributions!
This highlights the fact that {\em even} in homogeneous graphs,
the network-wide degree distribution and the nodal degree distribution may capture vastly different information.
Some of the results discussed in this paper were announced in the conference paper \cite{PalMakowski_CDC2015}, mostly
without proofs. Different proofs to establish Proposition \ref{prop:NonConvergenceInProbability}.
were originally given in the Ph.D. thesis of the first author \cite{SPal_Thesis}.
\section{A simple framework}
\label{sec:Framework}
First some notation and conventions:
The random variables (rvs) under consideration are all
defined on the same probability triple $(\Omega, {\cal F}, \mathbb{P})$.
The construction of a probability triple sufficiently large to carry all the required rvs is standard,
and omitted in the interest of brevity.
All probabilistic statements are made with respect to the probability
measure $\mathbb{P}$, and we denote the corresponding expectation
operator by $\mathbb{E}$.
The notation $\mbox{~$\stackrel{P}{\longrightarrow}$}_n$ (resp. $\Longrightarrow_n$)
is used to signify convergence in probability
(resp. convergence in distribution) (under $\mathbb{P}$) with $n$ going to infinity;
see the monographs \cite{BillingsleyBook, ChungBook} for definitions and properties.
If $E$ is a subset of $\Omega$, then $\1{E}$ is the indicator rv
of the set $E$ with the usual understanding that $\1{E}(\omega) = 1$ (resp. $\1{E}(\omega) = 0$) if $\omega \in E$
(resp. $\omega \notin E$).
The symbol $\mathbb{N}$ (resp. $\mathbb{N}_0$) denotes the set
of non-negative (resp. positive) integers.
The discussion is carried out in the following framework often encountered in the literature; see Section \ref{sec:CommonSetting} for examples:
Given is a sequence of random graphs $\{ \mathbb{G}_n , \ n=2,3, \ldots \}$ defined
on the probability triple $(\Omega, {\cal F}, \mathbb{P})$ -- We interchangeably use the terms random graphs and random networks.
Fix $n=2,3, \ldots$. The random graph $\mathbb{G}_n$ is then an ordered pair
$(V_n, \mathbb{E}_n)$ defined on the set of nodes $V_n $ with random edge set $\mathbb{E}_n \subseteq V_n \times V_n$.
Throughout the deterministic set $V_n$ is assumed to be non-empty and finite.
The random edge set $\mathbb{E}_n$ is equivalently determined by
a set of $\{0,1\}$-valued edge rvs $\{ \chi_n (k,\ell), \ k,\ell \in V_n \}$ -- Thus,
$\chi_n(k,\ell) =1$ (resp. $\chi_n(k,\ell) =0$) if there is a directed edge (resp. no edge) {\em from} node $k$ {\em to} node $\ell$,
so that
$ \mathbb{E}_n = \{ (k,\ell) \in V_n \times V_n: \ \chi_n (k,\ell) = 1 \}$.
We do not necessarily assume that $\mathbb{G}_n$ is an {\em undirected} graph, and we allow {\em self-loops}.
There is no loss in generality in taking $V_n = \{ 1, \ldots , k_n \}$ for some positive integer $k_n$.
In most cases of interest $V_n = \{ 1, \ldots , n \}$ so that $k_n = n $.
For each $k$ in $V_n$, the degree of node $k$ in the random graph $\mathbb{G}_n$ is the rv $D_{n,k}$ given by
\begin{equation}
D_{n,k} = \sum_{\ell \in V_n} \chi_n (k,\ell).
\label{eq:Out-degreeDefinition}
\end{equation}
For each $d=0,1, \ldots $, the rv $N_n(d)$ defined by
\begin{equation}
N_n(d) = \sum_{k\in V_n} \1{ D_{n,k}= d }
\label{eq:NumberNodes}
\end{equation}
counts the number of nodes in $V_n$ which have degree $d$
in $\mathbb{G}_n$. The fraction of nodes in $V_n$ with degree $d$ in
$\mathbb{G}_n$ is then given by
\[
P_n(d) = \frac{ N_n(d) }{ |V_n| } = \frac{1}{|V_n|} \sum_{k\in V_n} \1{ D_{n,k}= d }.
\]
This defines the random pmf
\[
\myvec{P}_n = \left ( \frac{ N_n(d) }{ |V_n| }, \ d=0,1, \ldots \right )
\]
on $\mathbb{N}$ with support contained in $V_n \cup \{ 0 \}$.
Strictly speaking, the expression (\ref{eq:Out-degreeDefinition}) defines the {\em out}-degree of a node.
However, everything said for out-degrees can also be developed for in-degrees with no substantive changes.
In what follows the term degree will refer interchangeably to either out-degree or in-degree,
the point being moot when considering undirected graphs as is the case in many situations.
For each $d=0,1, \ldots $, we explore the convergence (in probability) of the random sequence $\{ P_n(d), \ n=2, \ldots \}$
to a deterministic limit, say $L(d)$ in $\mathbb{R}$, when the graph size becomes infinitely large, namely
$\lim_{n \rightarrow \infty} |V_n| = \infty$.
For sequences of bounded rvs, convergence in probability and mean-square convergence are equivalent by standard
facts concerning modes of convergence for rvs \cite{BillingsleyBook, ChungBook}.
Therefore, the convergence
\begin{equation}
P_n(d) \mbox{~$\stackrel{P}{\longrightarrow}$}_n ~ L(d)
\label{eq:LIMIT}
\end{equation}
occurs if and only if
\begin{equation}
\lim_{n \rightarrow \infty} \bE{ \left | P_n(d) - L(d) \right |^2 } = 0.
\label{eq:MSConvergence}
\end{equation}
For each $n=2,3, \ldots $, standard properties of the variance give
\begin{eqnarray}
\lefteqn{ \bE{ \left | P_n(d) - L(d) \right |^2 } } & &
\nonumber \\
&=&
{\rm Var} \left [ P_n(d) \right ]
+
\left | \bE{ P_n(d) } - L(d) \right |^2 ,
\label{eq:VARIANCE}
\end{eqnarray}
and the following characterization is readily obtained.
\begin{fact}
{\sl With $d=0,1, \ldots$, the convergence in probability (\ref{eq:LIMIT}) occurs
to some scalar $L(d)$ if and only if we simultaneously have
$\lim_{n \rightarrow \infty} \bE{P_n(d) } = L(d)$
and $\lim_{n \rightarrow \infty} {\rm Var} \left [ P_n(d) \right ] = 0$.
}
\label{fact:BasicFact}
\end{fact}
To exploit this observation we begin by computing the first two moments $\bE{ N_n(d) }$ and $\bE{ N_n(d)^2 } $.
The definition (\ref{eq:NumberNodes}) of the rv $N_n(d)$ yields the expressions
\begin{equation}
\bE{ N_n(d) }
= \sum_{k \in V_n} \bP{ D_{n,k} = d }
\label{eq:MEAN}
\end{equation}
and \begin{eqnarray}
\lefteqn{ \bE{ N_n(d)^2 } } & &
\nonumber \\
&=&
\sum_{k \in V_n} \bP{ D_{n,k} = d }
\label{eq:SECOND} \\
& &
+~ \sum_{k \in V_n } \left ( \sum_{\ell \in V_n : \ \ell \neq k} \bE{ \1{ D_{n,k} = d } \1{ D_{n,\ell} = d } } \right )
\nonumber
\end{eqnarray}
by the binary nature of the involved rvs.
We leverage Fact \ref{fact:BasicFact} in two different settings:
The {\em homogeneous} setting, introduced in Section \ref{sec:HomogeneousAssumptions},
captures situations already mentioned in the introduction where an asymptotic nodal degree distribution exists; the relevant results are
presented in Section \ref{sec:HomogeneousLittleTheory}.
A more general setting is considered in Section \ref{sec:GeneralSettingLittleTheory}.
\section{The homogeneous case -- Assumptions}
\label{sec:HomogeneousAssumptions}
First we specify what we mean by a random network (or interchangeably,
a random graph) to be {\em homogeneous} for the purpose of this paper.
\begin{assumption}
{\sl (Homogeneity) For each $n=2,3, \ldots$, the degree rvs
in $\mathbb{G}_n$ are equidistributed in the sense that
\begin{equation}
D_{n,k} =_{st} D_{n,1},
\quad k \in V_n
\label{eq:GenericDegreeRV}
\end{equation}
and
\begin{equation}
(D_{n,k}, D_{n,\ell} ) =_{st} ( D_{n,1},D_{n,2} )
\quad
\begin{array}{c}
k \neq \ell \\
k,\ell \in V_n .\\
\end{array}
\label{eq:GenericDegreeRV_Pair}
\end{equation}
}
\label{ass:A}
\end{assumption}
Obviously condition (\ref{eq:GenericDegreeRV_Pair}) implies condition (\ref{eq:GenericDegreeRV}).
In many settings (see Section \ref{sec:CommonSetting}),
Assumption \ref{ass:A} follows from the stronger structural assumption that
for each $n=1,2, \ldots $, the edge rvs $\{ \chi_n (k,\ell) , \ k, \ell \in V_n \}$ (or a subset thereof in the undirected case)
are {\em exchangeable} -- Random networks with this property are traditionally called homogeneous.
Under Assumption \ref{ass:A}, for each $n=2,3, \ldots $,
it is appropriate to speak of {\em the} degree distribution of a node in $\mathbb{G}_n$,
namely the distribution of $D_{n,1}$.
In many cases of interest the degree rvs $\{ D_{n,1}, \ n=2,3, \ldots \}$ converge in the following sense.
\begin{assumption}
{\sl (Existence of an asymptotic degree distribution)
Assume that Assumption \ref{ass:A} holds and that there exists an $\mathbb{N}$-valued rv $D$ such that
\begin{equation}
D_{n,1} \Longrightarrow_n D.
\label{eq:ConvergenceToLittleP}
\end{equation}
Let $ \myvec{p} = ( p(d), \ d =0,1, \ldots )$ denote the pmf of the limiting rv $D$.
}
\label{ass:B}
\end{assumption}
Assumption \ref{ass:B} can be rephrased as
\begin{equation}
\lim_{n \rightarrow \infty} \bP{ D_{n,1} = d } = p(d),
\quad
d=0,1, \ldots
\label{eq:ConvergenceDegreeDistribution}
\end{equation}
Even in well-structured settings where Assumption \ref{ass:A} holds,
the convergence (\ref{eq:ConvergenceToLittleP}) may fail. For instance,
in large homogeneous binary multiplicative attribute graph (MAG) models introduced by Kim and Leskovec \cite{KimLeskovec},
although (\ref{eq:ConvergenceToLittleP}) occurs, it does so only with a trivial limiting pmf $\myvec{p}$,
say $D=0$ a.s. or $D=\infty$ a.s. depending on the parameter values;
see \cite{QuMakowski} for an extended discussion.
In the homogeneous setting, the motivating issue driving the discussion is whether under Assumptions \ref{ass:A} and \ref{ass:B},
the convergence
\begin{equation}
P_n(d) \mbox{~$\stackrel{P}{\longrightarrow}$}_n ~ p(d),
\quad d=0,1, \ldots
\label{eq:ConvergenceFractionNodes}
\end{equation}
takes place where the pmf $\myvec{p} = ( p(d), \ d =0,1, \ldots )$
is the pmf postulated in Assumption \ref{ass:B}.
The next assumption turns out to be key.
\begin{assumption}
{\sl (Asymptotic uncorrelatedness)
Assume that Assumption \ref{ass:A} holds, and that for each $d=0,1, \ldots $,
the identically distributed rvs $\1{ D_{n,1} = d }$ and $\1{ D_{n,2} = d }$ are asymptotically uncorrelated
in the sense that
\begin{equation}
\lim_{n \rightarrow \infty}
{\rm Cov} \left [ \1{ D_{n,1} = d }, \1{ D_{n,2} = d } \right ] = 0.
\label{eq:C}
\end{equation}
\label{ass:C}
}
\end{assumption}
Assumption \ref{ass:C} amounts to the convergence statement
\begin{align}
&\lim_{n \rightarrow \infty}
\big ( \bP{ D_{n,1} = d, D_{n,2} = d }
\nonumber \\
& \hspace{3mm}
-
\bP{ D_{n,1} = d } \bP{ D_{n,2} = d }
\big ) = 0
\label{eq:ExplicitFormAssC}
\end{align}
for each $d=0,1, \ldots $. It is implied by the following stronger assumption which is easier to check in
practice; see Section \ref{sec:CommonSetting} for some examples in a commonly occurring setting.
\begin{assumption}
{\sl (Pairwise asymptotic independence)
Assume Assumptions \ref{ass:A} and \ref{ass:B} to hold. Furthermore,
the degree rvs $D_{n,1}$ and $D_{n,2}$ are asymptotically independent
in the sense that
\begin{equation}
(D_{n,1}, D_{n,2} ) \Longrightarrow_n (D_1,D_2)
\label{eq:JointConvergenceD}
\end{equation}
where $D_1$ and $D_2$ are independent $\mathbb{N}$-valued rvs,
each distributed according to the pmf $ \myvec{p} $
postulated in Assumption \ref{ass:B}.
\label{ass:D}
}
\end{assumption}
While Assumption \ref{ass:D} reads
\[
\lim_{n \rightarrow \infty} \bP{ D_{n,1} = d, D_{n,2} = d^\prime }
= p(d)p(d^\prime),
\quad
d,d^\prime=0,1, \ldots
\]
Assumption \ref{ass:C} does not require the joint convergence (\ref{eq:JointConvergenceD}) to hold.
However, if (\ref{eq:JointConvergenceD}) were known to hold (but with {\em no} further characterization of the {\em joint} limit),
then under Assumption \ref{ass:B} it is easy to check
that Assumption \ref{ass:C} is equivalent to the independence of the {\em binary} rvs
$\1{ D_{1} = d }$ and $\1{ D_{2} = d }$ for each $d=0,1, \ldots $.
However, the lack of independence of the rvs $D_1$ and $D_2$ does not preclude
the possibility that the rvs $\1{ D_{1} = d }$ and $\1{ D_{2} = d }$ are independent -- It is possible to have
$\bP{ D_{1} = d , D_{2} = d } = \bP{ D_{1} = d } \bP{ D_{2} = d }$ for {\em all} $d=0,1, \ldots$ without the rvs $D_1$ and $D_2$ being independent.
\section{A little theory -- The homogeneous case}
\label{sec:HomogeneousLittleTheory}
We return to Fact \ref{fact:BasicFact}. Fix $d=0,1, \ldots $ and $n=2,3, \ldots $.
Under Assumption \ref{ass:A}, the expressions (\ref{eq:MEAN}) and (\ref{eq:SECOND}) become
\begin{equation}
\bE{ N_n(d) } = |V_n| \cdot \bP{ D_{n,1} = d }
\nonumber
\end{equation}
and
\begin{eqnarray}
\bE{ N_n(d)^2 }
&=& |V_n| (|V_n| - 1 ) \cdot \bP{ D_{n,1} = d , D_{n,2} = d }
\nonumber \\
& &
~+ |V_n|\cdot \bP{ D_{n,1} = d } ,
\nonumber
\end{eqnarray}
respectively.
It follows that
\begin{equation}
\bE{ P_n(d) } = \bP{ D_{n,1} = d }
\label{eq:Homogeneous1}
\end{equation}
and
\begin{eqnarray}
\lefteqn{ {\rm Var} \left [ P_n(d) \right ] } & &
\nonumber \\
&=&
\bE{ \left ( \frac{N_n(d)}{|V_n|} \right )^2 }
-
\left ( \bE{ \frac{N_n(d)}{|V_n|} } \right )^2
\nonumber \\
&=&
\frac{ |V_n| - 1 }{ |V_n|} \cdot \bP{ D_{n,1} = d , D_{n,2} = d }
\nonumber \\
& &
~+ \frac{ \bP{ D_{n,1} = d } }{|V_n|} - \left ( \bP{ D_{n,1} = d } \right )^2
\nonumber \\
&=&
\frac{ {\rm Var} \left [ \1{ D_{n,1} = d } \right ] }{|V_n|}
\label{eq:Homogeneous2} \\
& &
+~ \frac{|V_n|-1}{|V_n|} \cdot
{\rm Cov} \left [ \1{ D_{n,1} = d }, \1{ D_{n,2} = d } \right ]
\nonumber
\end{eqnarray}
since $ \bP{ D_{n,1} = d } = \bP{ D_{n,2} = d } $ under Assumption \ref{ass:A}.
Let $n$ go to infinity in (\ref{eq:Homogeneous1}) and (\ref{eq:Homogeneous2})
with $\lim_{n \rightarrow \infty} |V_n| = \infty$.
It is plain that $\lim_{n \rightarrow \infty} \bE{ P_n(d) } $ exists if and only if $\lim_{n \rightarrow \infty} \bP{ D_{n,1} = d }$ exists,
and that $\lim_{n \rightarrow \infty} {\rm Var} \left [ P_n(d) \right ] $ exists if and only if
the limit
\begin{equation}
C(d)
\equiv
\lim_{n \rightarrow \infty} {\rm Cov} \left [ \1{ D_{n,1} = d }, \1{ D_{n,2} = d } \right ]
\label{eq:LimitC(d)Exists}
\end{equation}
exists.
Fact \ref{fact:BasicFact} translates into the following equivalence.
\begin{proposition}
{\sl
Assume Assumption \ref{ass:A}.
With $d=0,1, \ldots $, we have the convergence (\ref{eq:LIMIT})
for some constant $L(d)$ in $\mathbb{R}$ if and only if
\begin{equation}
\lim_{n \rightarrow \infty} \bP{ D_{n,1} = d } = L(d)
\label{eq:LimitFirst}
\end{equation}
and
\begin{equation}
\lim_{n \rightarrow \infty} {\rm Cov} \left [ \1{ D_{n,1} = d }, \1{ D_{n,2} = d } \right ] = 0.
\label{eq:LimitCovariance}
\end{equation}
}
\label{prop:Stationary+A}
\end{proposition}
Under Assumption \ref{ass:A}, Assumption \ref{ass:B} and Assumption \ref{ass:C}
imply that the conditions (\ref{eq:LimitFirst}) (with $L(d)=p(d)$) and (\ref{eq:LimitCovariance})
hold for {\em all} $d=0,1, \ldots $, respectively.
Applying Proposition \ref{prop:Stationary+A} we then obtain the following compact conclusion.
\begin{proposition}
{\sl
Under Assumptions \ref{ass:A}-\ref{ass:C}, the convergence (\ref{eq:ConvergenceFractionNodes}) holds
for all $d=0,1, \ldots $
where the pmf $\myvec{p} = ( p(d), \ d =0,1, \ldots )$
is the pmf postulated in Assumption \ref{ass:B}.
}
\label{prop:ConvergenceEmpirical+PMF}
\end{proposition}
To formulate a converse to Proposition \ref{prop:ConvergenceEmpirical+PMF},
assume Assumption \ref{ass:A} to hold. The mere existence of the limit (\ref{eq:LimitFirst}) for {\em all} $d=0,1, \ldots$
does not guarantee that the limiting values $\{ L(d), \ d =0,1, \ldots \}$ constitute a pmf on $\mathbb{N}$.
Without any additional assumption, it only holds that $\sum_{d=0}^\infty L(d) \leq 1$: Indeed, for each $n=2,3, \ldots $,
we have $\sum_{d \in V} P_n(d) \leq 1$ for every finite subset $V \subseteq \mathbb{N}$, hence
$\sum_{d \in V} \bE{ P_n(d) } \leq 1$. By virtue of (\ref{eq:Homogeneous1})
this is equivalent to $\sum_{d \in V} \bP{ D_{n,1} = d } \leq 1$. Letting $n$ go to infinity we get
$\sum_{d \in V} p(d) \leq 1$, and the desired conclusion follows.
\begin{proposition}
{\sl
Under Assumption \ref{ass:A}, assume that for every $d=0,1, \ldots $, there exists a scalar $L(d)$ such that
\begin{equation}
P_n(d) \mbox{~$\stackrel{P}{\longrightarrow}$}_n ~ L(d).
\label{eq:ConvergenceEmpirical+Converse}
\end{equation}
If the limiting values $\{ L(d), \ d =0,1, \ldots \}$ constitute a pmf $\myvec{p} = ( p(d), \ d=0,1, \ldots )$ on $\mathbb{N}$, then both
Assumption \ref{ass:B} (with pmf $\myvec{p}$) and Assumption \ref{ass:C} must hold.
}
\label{prop:ConvergenceEmpirical+Converse}
\end{proposition}
\myproof
By Proposition \ref{prop:Stationary+A}, the validity of (\ref{eq:ConvergenceEmpirical+Converse}) for all $d=0,1, \ldots $
implies (\ref{eq:LimitCovariance}) for all $d=0,1, \ldots $, hence
Assumption \ref{ass:C} holds.
By Proposition \ref{prop:Stationary+A}, the validity of (\ref{eq:ConvergenceEmpirical+Converse}) for all $d=0,1, \ldots $
also implies that (\ref{eq:LimitFirst}) holds for all $d=0,1, \ldots$.
If additionally the limiting values $\{ L(d), \ d =0,1, \ldots \}$ constitute a pmf $\myvec{p}$ on $\mathbb{N}$, then there exists
an $\mathbb{N}$-valued rv $D$ distributed according to the pmf $\myvec{p}$ such that $D_{n,1} \Longrightarrow_n D$, and Assumption \ref{ass:B} holds.
\myendpf
As we survey the discussion so far, it is plain that under Assumptions \ref{ass:A}-\ref{ass:B},
the convergence (\ref{eq:LIMIT})
necessarily takes the form (\ref{eq:ConvergenceFractionNodes}). Furthermore, whenever we have
\begin{equation}
\lim_{n \rightarrow \infty}
{\rm Cov} \left [ \1{ D_{n,1} = d }, \1{ D_{n,2} = d } \right ] > 0,
\label{eq:LimInfCondition1}
\end{equation}
then (\ref{eq:ConvergenceFractionNodes}) cannot hold.
\section{A little theory -- The general setting}
\label{sec:GeneralSettingLittleTheory}
Proposition \ref{prop:Stationary+A} is a special case of a more general fact that does not require any homogeneity assumption.
We devote this section to a presentation of this more general viewpoint:
Fix $n=2,3, \ldots $.
In the context of the random graph $\mathbb{G}_n$, let $\Sigma_n$
denote the set $\{ (k,\ell) \in V_n \times V_n : \ k \neq \ell \}$ that comprises all ordered pairs drawn from $V_n$
without repetition.
Let also the rv $(\nu_n,\mu_n): \Omega \rightarrow \Sigma_n$ be {\em uniformly} distributed over $\Sigma_n$, i.e.,
\[
\bP{ \nu_n= k, \mu_n = \ell }
= \frac{1}{|V_n|(|V_n|-1)},
\quad
\begin{array}{c}
k \neq \ell \\
k,\ell \in V_n. \\
\end{array}
\]
Thus, the rv $(\nu_n,\mu_n)$ models the randomly uniform selection of two nodes in $V_n$ (without repetition);
the rvs $\nu_n$ and $\mu_n$ are both {\em uniformly} distributed over $V_n$.
The selection rv $(\nu_n,\mu_n)$ is assumed to be {\em independent} of the random graph $\mathbb{G}_n$.
Fix $d=0,1, \ldots $. Under the enforced independence assumptions, we note from (\ref{eq:MEAN}) that
\begin{eqnarray}
\bE{ \frac{N_n(d)}{|V_n|} }
&=& \frac{1}{|V_n|} \cdot \sum_{k \in V_n } \bP{ D_{n,k} = d }
\nonumber \\
&=& \sum_{k \in V_n } \bP{ \nu_n = k, D_{n,k} = d },
\nonumber
\end{eqnarray}
and it follows that
\begin{equation}
\bE{ P_n(d) } = \bP{ D_{n,\nu_n} = d } .
\label{eq:AAA}
\end{equation}
Using (\ref{eq:SECOND}) we also conclude from (\ref{eq:AAA}) that
\begin{eqnarray}
\lefteqn{ \bE{ N_n(d)^2 } } & &
\nonumber \\
&=& |V_n | \cdot \bP{ D_{n,\nu_n} = d }
\nonumber \\
& &
+~
|V_n| \left ( |V_n| - 1 \right ) \cdot \bP{ D_{n,\nu_n} = d , D_{n,\mu_n} = d },
\nonumber
\end{eqnarray}
whence
\begin{eqnarray}
\lefteqn{
{\rm Var} \left [ P_n(d) \right ]
} & &
\nonumber \\
&=& \bE{ \left ( \frac{N_n(d)}{|V_n|} \right ) ^2 }
-
\left ( \bE{ \frac{N_n(d)}{|V_n|} } \right )^2
\nonumber \\
&=& \frac{ \bP{ D_{n,\nu_n} = d } }{|V_n|} + \frac{|V_n|-1}{|V_n|} \cdot \bP{ D_{n,\nu_n} = d , D_{n,\mu_n} = d }
\nonumber \\
& & -~ \bP{ D_{n,\nu_n} = d } \bP{ D_{n,\mu_n} = d }
\nonumber \\
&=& \frac{ {\rm Var } \left [ \1{ D_{n,\nu_n} = d } \right ] }{ |V_n|}
\label{eq:DAA} \\
& &
+~ \frac{ |V_n|-1}{|V_n|} \cdot {\rm Cov} \left [ \1{ D_{n,\nu_n} = d } , \1{ D_{n,\mu_n} = d } \right ].
\nonumber
\end{eqnarray}
To obtain the variance term in (\ref{eq:DAA}) we used the obvious equality
$\bP{ D_{n,\mu_n} = d } = \bP{ D_{n,\nu_n} = d }$.
Let $n$ go to infinity in (\ref{eq:AAA}) and (\ref{eq:DAA})
with $\lim_{n \rightarrow \infty} |V_n|=\infty$.
Appealing again to Fact \ref{fact:BasicFact} we obtain the following analog of Proposition \ref{prop:Stationary+A}.
\begin{proposition}
{\sl
Under the foregoing assumptions, with $d=0,1, \ldots $, the convergence (\ref{eq:LIMIT}) holds
for some scalar $L(d)$ in $\mathbb{R}$ if and only if
\begin{equation}
\lim_{n \rightarrow \infty } \bP{ D_{n,\nu_n} = d } = L(d)
\label{eq:LBAA}
\end{equation}
and
\begin{equation}
\lim_{n \rightarrow \infty } {\rm Cov} \left [ \1{ D_{n,\nu_n} = d } , \1{ D_{n,\mu_n} = d } \right ] = 0 .
\label{eq:LBBA}
\end{equation}
}
\label{prop:GeneralSetting}
\end{proposition}
Under Assumption \ref{ass:A}, for each $n=1,2, \ldots $ the distributional equalities
$D_{n,\nu_n} =_{st} D_{n,1}$, $D_{n,\mu_n} =_{st} D_{n,1}$,
and $( D_{n,\nu_n}, D_{n,\mu_n} )=_{st} ( D_{n,1}, D_{n,2})$ hold, in which case the
conditions (\ref{eq:LBAA}) and (\ref{eq:LBBA}) reduce to
conditions (\ref{eq:LimitFirst}) and (\ref{eq:LimitCovariance}) of Proposition \ref{prop:Stationary+A}, respectively --
Proposition \ref{prop:Stationary+A} is plainly subsumed by Proposition \ref{prop:GeneralSetting}.
While the latter holds under {\em no} assumption on the sequence $\{ \mathbb{G}_n , \ n=2,3, \ldots \}$, unfortunately in that generality it does
not retain the operational ability of Proposition \ref{prop:Stationary+A} of {\em equating} the two different degree distributions
available in the homogeneous case.
Proposition \ref{prop:GeneralSetting} also applies when the graphs $\{ \mathbb{G}_n, \ n=2,3, \ldots \}$ are deterministic.
The {\em non}-homogeneous Barab\'asi-Albert model
(and other growth models) are easily fitted into this more general framework.
In particular, Proposition \ref{prop:GeneralSetting} offers the possibility
of establishing the convergence (\ref{eq:LIMIT}) through (\ref{eq:LBAA}) and (\ref{eq:LBBA}).
These two properties follow if the sequence $\{ \mathbb{G}_n, \ n=2,3, \ldots \}$ is {\em locally weakly convergent}
(or weakly convergent in the sense of Benjamini and Schramm \cite{BenjaminiSchramm}); see
the reference \cite{AldousSteele} for an introduction to these ideas.
The Barab\'asi-Albert model (and some of its variants) were shown to be locally weakly convergent by Berger et al.
\cite{BergerBorgsChayesSaberi}.
However, in the Barab\'asi-Albert model, Bollob\'{a}s et al. have shown the convergence (\ref{eq:LIMIT})
by direct Hoeffding-Azuma bounding arguments \cite{Bollobas_BAmodel},
thereby implying (\ref{eq:LBBA}) (as well as (\ref{eq:LBAA}) trivially by bounded convergence).
\section{Convergence in total variation distance}
\label{sec:Totalvariation}
The weak convergence of $\mathbb{N}$-valued rvs is equivalent to convergence
in the total variation distance of their corresponding pmfs (on $\mathbb{N}$); this is a well-known consequence
of Scheff\'e's Theorem \cite[App. II, p. 224]{BillingsleyBook} when applied to discrete rvs. Here we show an analogous
equivalence when the convergence in {\em probability} (\ref{eq:ConvergenceFractionNodes}) holds for all $d=0,1, \ldots$:
If $\myvec{\mu} = ( \mu(x), \ x=0,1, \ldots )$ and $\myvec{\nu} = ( \nu(x), \ x=0,1, \ldots )$ are two
pmfs on $\mathbb{N}$, the {\em total variation distance} between them is given by
\[
d_{\rm TV} ( \myvec{\mu}, \myvec{\nu} )
=
\frac{1}{2} \sum_{x=0}^\infty \left | \mu(x) - \nu(x) \right |.
\]
This quantity can alternatively be expressed as
\[
d_{\rm TV} ( \myvec{\mu}, \myvec{\nu} )
= \sum_{x=0}^\infty \left ( \mu(x) - \nu(x) \right )^+ = \sum_{x=0}^\infty \left ( \nu(x) - \mu(x) \right )^+ .
\]
\begin{proposition}
{\sl
Under Assumptions \ref{ass:A}-\ref{ass:C}, we have
\begin{equation}
d_{\rm TV}
\left ( \myvec{P}_n , \myvec{p} \right )
\mbox{~$\stackrel{P}{\longrightarrow}$}_n ~ 0
\label{eq:TotalVariationConvergenceInProbability}
\end{equation}
where the pmf $\myvec{p} = ( p(d), \ d =0,1, \ldots )$
is the pmf postulated in Assumption \ref{ass:B}.
}
\label{prop:ConvergenceEmpirical+TotalVariation}
\end{proposition}
\myproof
Pick $V \subseteq \mathbb{N}_0$ arbitrary with $|V| < \infty$.
Using the alternate representation above, we get
\begin{eqnarray}
\bE{ d_{\rm TV} \left ( \myvec{P}_n , \myvec{p} \right ) }
\leq
\sum_{x \in V} \bE{ \left ( p(x) - P_n(x) \right )^+ }
+ \sum_{x \notin V} p(x)
\nonumber
\end{eqnarray}
for each $n=1,2, \ldots $. Let $n$ go to infinity in this last inequality.
By Proposition \ref{prop:ConvergenceEmpirical+PMF} we have $P_n (x) \mbox{~$\stackrel{P}{\longrightarrow}$}_n ~ p(x)$ for each $x=0,1, \ldots$, whence
$\lim_{n \rightarrow \infty} \bE{ \left ( p(x) - P_n(x) \right )^+ } = 0$ by bounded convergence.
It follows that
\[
\limsup_{n \rightarrow \infty} \bE{ d_{\rm TV} \left ( \myvec{P}_n , \myvec{p} \right ) } \leq \sum_{x \notin V} p(x).
\]
The set $V$ being an arbitrary finite subset of $\mathbb{N}$ and $\myvec{p}$ being a pmf on $\mathbb{N}$ (hence tight), we readily obtain
$\lim_{n \rightarrow \infty} \bE{ d_{\rm TV} \left ( \myvec{P}_n , \myvec{p} \right ) } = 0$,
and the desired conclusion
(\ref{eq:TotalVariationConvergenceInProbability}) follows by Markov's inequality.
\myendpf
\section{A commonly encountered setting}
\label{sec:CommonSetting}
In many situations of interest the sequence of random graphs $\{ \mathbb{G}_n, \ n=1,2, \ldots \}$
arises in the following natural manner:
Given is an {\em underlying} parametric family of random graphs, say
\begin{equation}
\{ \mathbb{G}(n;\alpha), \ n=2,3, \ldots \},
\quad \alpha \in A \subseteq \mathbb{R}^r
\label{eq:UnderlyingFamily}
\end{equation}
where $A$ is some parameter set and $r$ is a positive integer.
With $\alpha$ in $A$, for each $n=2,3, \ldots $, the random graph
$\mathbb{G}(n;\alpha)$ is a random graph on $V_n$ whose statistics depend on the parameter $\alpha$.
For each $k$ in $V_n$, let $D_{n,k}(\alpha)$ denote the degree of node $k$ in $\mathbb{G}(n;\alpha)$;
it is often the case that the rvs $\{ D_{n,k} (\alpha) , \ k \in V_n \}$ constitute an {\em exchangeable} family,
as we assume thereafter in this section.
Thus, there is no ambiguity when speaking of {\em the} (nodal) degree distribution in $\mathbb{G}(n;\alpha)$
because {\em all} nodes have the same degree distribution, namely that of the rv $D_{n,1} (\alpha)$.
We construct the collection $\{ \mathbb{G}_n, \ n=2,3, \ldots \}$ by setting
\begin{equation}
\mathbb{G}_n \equiv \mathbb{G}(n;\alpha_n),
\quad n=2,3, \ldots
\label{eq:SettingWithUnderlyingFamily}
\end{equation}
for some scaling $\alpha: \mathbb{N}_0 \rightarrow A$, in which case $D_{n,k} = D_{n,k} (\alpha_n)$ for each $k$ in $V_n$ --
Scalings are sequences which we view as mappings defined on $\mathbb{N}_0$; the mapping itself is denoted by
the same symbol used for the generic element of the sequence.
The scaling $\alpha: \mathbb{N}_0 \rightarrow A$ appearing in (\ref{eq:SettingWithUnderlyingFamily})
is the (usually unique) scaling which ensures the convergence
\begin{equation}
D_{n,1}(\alpha_n) \Longrightarrow_n D
\label{eq:ConvergenceToD}
\end{equation}
for some non-degenerate $\mathbb{N}$-valued rv $D$;
this scaling is often the critical scaling associated with the emergence of a maximal component.
Under these circumstances, Assumptions \ref{ass:A} and \ref{ass:B} are automatically satisfied,
and only Assumption \ref{ass:C} needs to be verified.
The setting outlined above applies to a number of examples routinely
discussed in the literature: Here for each $n=1,2, \ldots $, we take $V_n = \{1, \ldots , n \}$. With $c > 0$,
\begin{enumerate}
\item
Erd\H{o}s-R\'enyi graphs $\mathbb{G}(n;p)$ ($0 \leq p \leq 1$)
with scaling $p: \mathbb{N}_0 \rightarrow [0,1]$ such that $p_n \sim \frac{c}{n}$
\cite{Bollobas_Book,DraiefMassoulieLMMS,ER1960};
\item
Geometric random graphs $\mathbb{G}(n;\rho)$ on a unit square
($\rho > 0$) with scaling $\rho: \mathbb{N}_0 \rightarrow \mathbb{R}_+ $ such that $ \pi \rho_n^2 \sim \frac{c}{n}$
\cite{PenroseBook}; and
\item
Random key graphs $\mathbb{K}(n;K,P)$ ($K < P$ in $\mathbb{N}_0$)
with scalings $K,P: \mathbb{N}_0 \rightarrow \mathbb{N}_0$ such that $\frac{K^2_n}{P_n} \sim \frac{c}{n}$
\cite{YaganMakowskiConnectivity}.
\end{enumerate}
Assumption \ref{ass:A} is readily satisfied in these homogeneous situations.
In each case, Poisson convergence can be invoked to validate Assumption \ref{ass:B} with the rv $D$ in (\ref{eq:ConvergenceToD})
being a Poisson rv with parameter $c$.
In all cases, the stronger Assumption \ref{ass:D} is established, thereby implying Assumption \ref{ass:C}.
While it is elementary to do so for Erd\H{o}s-R\'enyi graphs,
the calculations become increasingly tedious as we move from geometric random graphs to random key graphs;
see \cite{SPal_Thesis} for details.
Finally, despite an abundance of situations where Assumptions \ref{ass:A}-\ref{ass:C} are satisfied (beyond the ones discussed above),
it is nevertheless possible to find homogeneous random networks in the sense of Assumption \ref{ass:A}
where (\ref{eq:ConvergenceToLittleP}) occurs but where the convergence (\ref{eq:ConvergenceFractionNodes}) fails.
This is taken on in the remainder of the paper starting with the next section.
\section{A counterexample}
\label{sec:CounterExample}
\subsection{Random threshold graphs}
The setting is that of \cite{CCDM, FIKMMU, MakowskiYagan-JSAC, SC}:
Let $\{ \xi, \xi_k, \ k=1,2, \ldots \}$
denote a collection of i.i.d. $\mathbb{R}_+$-valued rvs defined on
the probability triple $(\Omega, {\cal F}, \mathbb{P})$,
each distributed according to a given
(probability) distribution function
$F: \mathbb{R} \rightarrow [0,1]$ with
$F(x) = 0$ for $x\leq 0$.
With $\xi$ acting as a generic representative for this sequence of i.i.d. rvs,
we have
\[
\bP{ \xi \leq x } = F(x),
\quad x \in \mathbb{R}.
\]
Once $F$ is specified, random thresholds graphs are characterized by two parameters,
namely a positive integer $n$ and a threshold value $\theta > 0$:
The network comprises $n$ nodes, labelled $k=1, \ldots , n$,
and to each node $k$ we assign a {\em fitness} variable
(or weight) $\xi_k$ which measures its importance or rank.
For distinct $k,\ell =1, \ldots , n$,
the nodes $k$ and $\ell$ are declared to be adjacent if
\begin{equation}
\xi_k + \xi_\ell > \theta ,
\label{eq:AdjacencyDefnRTGs}
\end{equation}
and a bidirectional edge exists between nodes $k$ and $\ell$.
The adjacency notion (\ref{eq:AdjacencyDefnRTGs}) defines the {\em random threshold} graph
$\mathbb{T}(n;\theta)$ on the set of vertices $V_n = \{ 1, \ldots , n \}$.
The degree $D_{n,k}(\theta)$ of node $k$ in $\mathbb{T}(n;\theta)$ is clearly given by
\[
D_{n,k}(\theta) = \sum_{\ell=1, \ \ell \neq k}^n \1{ \xi_k + \xi_\ell > \theta },
\quad k=1, \ldots , n.
\]
Under the enforced assumptions, the rvs $D_{n,1}(\theta), \ldots , D_{n,n}(\theta)$
are exchangeable, thus equidistributed.
\subsection{Applying Proposition \ref{prop:ConvergenceEmpirical+PMF} under exponential fitness}
From now on we focus on the special case
when $\xi$ is exponentially distributed
with parameter $\lambda > 0$, written $\xi \sim {\rm Exp}(\lambda)$, that is
\begin{equation}
\bP{ \xi \leq x }
= 1 - e^{-\lambda x^+},
\quad x \in \mathbb{R}
\label{eq:CDF=Exponential}
\end{equation}
where we have used the standard notation $x^+ = \max(x,0)$.
While other distributions could be considered to develop counterexamples to Proposition \ref{prop:ConvergenceEmpirical+PMF},
the exponential distribution was selected for two main reasons:
This situation was considered in the references \cite{CCDM, FIKMMU, SC}
in making the case that scale-free networks can be generated through the fitness-based mechanism used
in random threshold graphs; more on that later.
Moreover, calculations are greatly simplified in the exponential case.
With random threshold graphs as the underlying family (\ref{eq:UnderlyingFamily}),
the definition (\ref{eq:SettingWithUnderlyingFamily}) here takes the form
\begin{equation}
\mathbb{G}_n = \mathbb{T}(n; \theta^\star_n),
\quad n=2,3, \ldots
\label{eq:G=RTG}
\end{equation}
with scaling $\theta^\star : \mathbb{N}_0 \rightarrow [0,\infty)$ given by
\begin{equation}
\theta^\star _n = \lambda^{-1} \log n,
\quad n=2, 3, \ldots .
\label{eq:FujiharaScaling}
\end{equation}
We are in the setting of Section \ref{sec:CommonSetting}.
Having in mind to apply Proposition \ref{prop:ConvergenceEmpirical+PMF} to the random graphs
$\{ \mathbb{G}_n, \ n=1,2, \ldots \}$, we recover the notation of Section \ref{sec:Framework} by setting
\[
D_{n,k} = D_{n,k}(\theta^\star_n),
\quad
\begin{array}{c}
k=1, \ldots , n\\
n=2,3,\ldots \\
\end{array}
\]
Assumption \ref{ass:A} is obviously satisfied in light of the aforementioned exchangeability.
It was shown by Fujihara et al. \cite[Example 1, p. 366]{FIKMMU} that
$D_{n,1} \Longrightarrow_n D$
where the $\mathbb{N}$-valued rv $D$ is a conditionally Poisson rv with pmf
$\myvec{p}_{\rm Fuj} = ( p_{\rm Fuj} (d) , \ d=0,1, \ldots )$ given by
\begin{eqnarray}
p_{\rm Fuj} (d)
= \bP{ D=d }
= \bE{ \frac{ (e^{\lambda \xi})^d }{d!} e^{-e^{\lambda \xi}} },
\quad d=0,1, \ldots
\label{eq:Fujihara}
\end{eqnarray}
Therefore, Assumption \ref{ass:B} holds with
\begin{equation}
\lim_{n \rightarrow \infty} \bP{ D_{n,1} =d } = p_{\rm Fuj} (d) ,
\quad d=0,1, \ldots
\label{eq:ConvergenceToFuj}
\end{equation}
\subsection{Assumption \ref{ass:C} fails}
The remainder of the paper is devoted to showing the following convergence result.
\begin{proposition}
{\sl
Assume $\xi \sim {\rm Exp}(\lambda)$ for some $\lambda > 0$. For each $d=0,1, \ldots $, the limit
\begin{align}
C(d)
\equiv
\lim_{n \rightarrow \infty}
{\rm Cov} \left [ \1{ D_{n,1} (\theta^\star_n) = d } , \1{ D_{n,2} (\theta^\star_n) = d } \right ]
\label{eq:AssumptionC+fails}
\end{align}
exists and $C(d) > 0$.
}
\label{prop:AssumptionC+fails}
\end{proposition}
Proposition \ref{prop:AssumptionC+fails} is established from Section \ref{sec:ProofPart+1} to Section \ref{sec:ProofPart+2} where
expressions are given for the limits (\ref{eq:AssumptionC+fails}):
For instance, we show at (\ref{eq:C(0)}) that
\[
C(0)
=
\bE{ e^{ -\max( e^{\lambda \xi_1}, e^{\lambda \xi_2} ) } } - \bE{ e^{ - ( e^{ \lambda \xi_1 } + e^{ \lambda \xi_2 } ) } } > 0.
\]
The expression (\ref{eq:C(d)}) of the limit $C(d) $ for $d \neq 0$ is rather cumbersome and is omitted at this point.
However, the fact that $C(d) > 0$ on the entire range suffices to establish the desired counterexample
by virtue of the observation following Proposition \ref{prop:ConvergenceEmpirical+Converse}.
\begin{proposition}
{\sl Assume $\xi \sim {\rm Exp}(\lambda)$ for some $\lambda > 0$. For each $d=0,1, \ldots $, the sequence of rvs
\begin{equation}
\left \{
\frac{1}{n}
\sum_{k=1}^n \1{ D_{n,k} (\theta^\star_n) = d },
\ n= 2, 3, \ldots
\right \}
\label{eq:NonConvergenceInProbability}
\end{equation}
does not converge in probability to any constant.
}
\label{prop:NonConvergenceInProbability}
\end{proposition}
In fact, for each $d=0,1, \ldots $, there exists
a non-degenerate $[0,1]$-valued rv $\Pi(d)$ with $\bE{ \Pi (d) } = p_{\rm Fuj}(d)$ and ${\rm Var} \left [ \Pi(d) \right ] > 0$
such that
\[
\frac{1}{n}
\sum_{k=1}^n \1{ D_{n,k} (\theta^\star_n) = d } \Longrightarrow_n ~ \Pi(d).
\]
Details are available in \cite{SPal_Thesis}.
The failure of the convergence (\ref{eq:ConvergenceFractionNodes}) in the
context of random threshold graphs with exponentially distributed fitness is noteworthy for the following reason:
Caldarelli et al. \cite{CCDM,SC} have proposed this class of random graph models
as an alternative scale-free model to the preferential attachment model of Barab\'{a}si and Albert \cite{BarabasiAlbert}.
The basis for their proposal was the provable power-law behavior
\begin{equation}
p_{\rm Fuj}(d) \sim d^{-2}
\quad (d \rightarrow \infty).
\label{eq:TailFujihara}
\end{equation}
See Fujihara et al. \cite[Example 1, p. 366]{FIKMMU} for details.
However, a meaningful comparison between the two models would have required at minimum
the validity of the convergence
\[
\frac{1}{n}
\sum_{k=1}^n \1{ D_{n,k} (\theta^\star_n) = d } \mbox{~$\stackrel{P}{\longrightarrow}$}_n ~p_{\rm Fuj} (d) ,
\quad d=0,1, \ldots
\]
By Proposition \ref{prop:NonConvergenceInProbability}
this last convergence fails to happen, and the two models cannot be meaningfully compared
since for the Barab\'{a}si-Albert model it only holds that
\[
\frac{1}{n}
\sum_{k=1}^n \1{ D_{n,k} (\theta^\star_n) = d } \mbox{~$\stackrel{P}{\longrightarrow}$}_n ~ p_{\rm BA} (d),
\quad d=0,1, \ldots
\]
with $p_{\rm BA}(d) \sim d^{-3}$ $(d \rightarrow \infty)$ \cite{Bollobas_BAmodel}.
Although the Barab\'asi-Albert model has attracted much attention as a network model,
its tree-like structure does not make it a particularly good fit for the empirical data coming from large real-life networks.
Similar comments apply to the class of random threshold graph models due to a propensity to produce star-like structures.
\section{Simulation Results}
\label{sec:SimulationResults}
Through a limited set of simulation experiments, we now demonstrate the failure of the convergence
(\ref{eq:ConvergenceFractionNodes}) established for random threshold graphs in Proposition \ref{prop:NonConvergenceInProbability}.
Throughout, the fitness variable $\xi$ is taken to be exponentially distributed with parameter $\lambda=1$,
and the threshold is scaled in accordance to (\ref{eq:FujiharaScaling}), namely $\theta _n ^\star = \log n$ for each $n=2,3,\ldots$.
The number $n$ of nodes being given,
we generate $R$ mutually independent realizations of the random threshold graph $\mathbb{T}(n;\theta _n ^\star)$;
they are denoted $\mathbb{T}^{(1)}(n;\theta_n^\star), \mathbb{T}^{(2)}(n;\theta_n^\star), \ldots, \mathbb{T}^{(n)}(n;\theta _n ^\star)$, respectively.
For each $k=1,2,\ldots,n$ and $r=1,2,\ldots,R$, let $D_{n,k} ^{(r)}(\theta _n^\star)$ denote the degree of node $k$ in the random graph
$\mathbb{T}^{(r)}(n;\theta_n^\star)$.
\begin{figure}[h]
\centering
\subfloat[$n=10000$, $R=100$\label{fig:Stripplot_10000nodes]}]{\includegraphics[width=\linewidth]{Stripplot_10000_nodes100_runs.png}}
\hfill
\subfloat[$n=30000$, $R=100$\label{fig:Stripplot_30000nodes}]{\includegraphics[width=\linewidth]{Stripplot_30000_nodes100_runs.png}}
\caption{
\label{fig:Stripplot_EmpiricalVsNodal}
\end{figure}
We explore the behavior of the empirical degree distribution along the scaling (\ref{eq:FujiharaScaling})
(with $\lambda=1$) as generated through a single network realization. We do so by plotting the histograms
\begin{equation}
\frac{N_n ^{(r)}(d;\theta_n ^\star)}{n} = \frac{1}{n} \sum_{k=1}^n \1{ D^{(r)}_{n,k} (\theta^\star_n) = d },
\quad
\begin{array}{c}
d=0,1,\ldots \\
r=1, \ldots , R \\
\end{array}
\label{eq:SingleRealization}
\end{equation}
for various values of $d$ and $r$, and large $n$, and comparing against the corresponding value for
the limiting nodal distribution $p_{\rm Fuj} (d)$ given in (\ref{eq:Fujihara}).
Using this expression we numerically evaluate $p_{\rm Fuj} (d)$ as
\begin{equation}
p_{\rm Fuj} (d)
= \frac{1}{d!} \int_0^\infty \frac{e^{d x} }{d!} e^{-e^{x} } e^{-x} dx
\nonumber
\end{equation}
for each $ d=0,1, \ldots$.
In Figure \ref{fig:Stripplot_EmpiricalVsNodal} we plot the histogram $\frac{N_n ^{(r)}( . ;\theta_n ^\star)}{n}$
for different runs $r=1,2,\ldots,R$ and varying graph sizes $n=10000,30000$. Observe the high variability
with respect to the nodal degree distribution $\myvec{p}_{\rm Fuj}$ which does not change as the graph size is increased.
We smooth out the variability observed in Figure \ref{fig:Stripplot_EmpiricalVsNodal}
by averaging the empirical degree distributions (\ref{eq:SingleRealization}) over the $R$ i.i.d. realizations
$\mathbb{T}^{(1)}(n; \theta ^\star _n), \mathbb{T}^{(2)}(n; \theta ^\star _n) , \ldots , \mathbb{T}^{(R)}(n; \theta ^\star _n)$.
This results in the statistic
\begin{equation}
\frac{1}{R} \sum _{r=1} ^R \frac{N_n ^{(r)}(d;\theta_n ^\star)}{n},
\ d=0,1,\ldots .
\label{eq:Run_averaged_empirical_distribution}
\end{equation}
Fix $d=0,1, \ldots $. The Strong Law of Large Numbers yields
\begin{eqnarray}
\lim_{R \rightarrow \infty} \frac{1}{R} \sum _{r=1} ^R \frac{N_n ^{(r)}(d;\theta_n ^\star)}{n}
= \bE{ \frac{N_n (d;\theta_n ^\star)}{n} }
\quad \mbox{a.s.}
\end{eqnarray}
with
\[
\bE{ \frac{N_n (d;\theta_n ^\star)}{n} } = \bP{ D_{n,1} (\theta^\star_n) = d }
\]
by exchangeability. On the other hand, by virtue of (\ref{eq:ConvergenceToFuj}) we have
$\lim_{n \rightarrow \infty} \bP{ D_{n,1} (\theta^\star_n) = d } = p_{\rm Fuj}(d)$.
Combining these observations yields the approximation
\begin{equation}
\frac{1}{R} \sum _{r=1} ^R \frac{N_n ^{(r)}(d;\theta_n ^\star)}{n} =_{\rm Approx} p_{\rm Fuj}(d)
\label{eq:Approx4}
\end{equation}
for large $n$ and $R$.
The goodness of the approximation (\ref{eq:Approx4}) is noted in Figure \ref{fig:Stripplot_EmpiricalVsNodal},
where the empirical distribution averaged over $R=100$ runs is observed to be very close to the nodal degree distribution.
However, the accuracy of the approximation (\ref{eq:Approx4}) does in no way imply the validity of (\ref{eq:ConvergenceFractionNodes}).
In fact the mistaken belief that (\ref{eq:ConvergenceFractionNodes}) holds,
implicitly assumed in the papers \cite{CCDM,SC}, might have stemmed from using the smoothed estimate (\ref{eq:Approx4}).
\section{Preparing the proof of Proposition \ref{prop:AssumptionC+fails}}
\label{sec:ProofPart+1}
For every $n=2,3, \ldots $ and $\theta > 0$, the decomposition
\begin{equation}
D_{n,j}(\theta) = \1{ \xi_1 + \xi_2 > \theta } + D^\star_{n,j}(\theta),
\quad j=1,2
\label{eq:DegreeDecomposition}
\end{equation}
holds where we have set
\[
D^\star_{n,j}(\theta)
= \sum_{k=3}^n \1{ \xi_j + \xi_k > \theta }.
\]
Fix $d=0,1, \ldots $. It is a simple matter to check that
\begin{eqnarray}
\lefteqn{ \left | \bP{ D_{n,j} (\theta) = d }
-
\bP{ D^\star_{n,j} (\theta) = d }
\right | } & &
\nonumber \\
&\leq& 2 \bP{ \xi_1 + \xi_2 > \theta } ,
\quad j=1,2
\label{eq:BoundOnDifference1}
\end{eqnarray}
and
\begin{eqnarray}
& &
\left | \bP{ D_{n,j} (\theta) = d , \ j=1,2 } - \bP{ D^\star_{n,j} (\theta) = d , \ j=1,2 } \right |
\nonumber \\
& & \leq 2 \bP{ \xi_1 + \xi_2 > \theta } .
\label{eq:BoundOnDifference2}
\end{eqnarray}
Next, for each $n=2,3, \ldots$ we substitute $\theta$ by $\theta^\star_n$ in
the bound (\ref{eq:BoundOnDifference2})
and let $n$ go to infinity in the resulting inequality.
Since $\lim_{n \rightarrow \infty} \theta^\star_n = \infty$, we conclude that
$ \lim_{n \rightarrow \infty}
\big | \bP{ D_{n,1} (\theta^\star_n) = d , D_{n,2} (\theta^\star_n) = d }
-
\bP{ D^\star_{n,1} (\theta^\star_n) = d , D^\star_{n,2} (\theta^\star_n) = d }
\big | =0$,
whence
\begin{eqnarray}
& &
\lim_{n \rightarrow \infty}
\bP{ D_{n,1} (\theta^\star_n) = d , D_{n,2} (\theta^\star_n) = d }
\nonumber \\
&=&
\lim_{n \rightarrow \infty}
\bP{ D^\star_{n,1} (\theta^\star_n) = d , D^\star_{n,2} (\theta^\star_n) = d }
\label{eq:TwoDimConvergence}
\end{eqnarray}
provided either limit exists. The same argument applied to the bounds
(\ref{eq:BoundOnDifference1}) readily yields
\begin{align}
\lim_{n \rightarrow \infty}
\bP{ D_{n,j} (\theta^\star_n) = d }
&=
\lim_{n \rightarrow \infty}
\bP{ D^\star _{n,j} (\theta^\star_n) = d }
\nonumber \\
&= p_{\rm Fuj}(d) ,
\quad j=1,2
\label{eq:OneDimConvergence}
\end{align}
in light of (\ref{eq:ConvergenceToFuj}).
It then follows from
(\ref{eq:TwoDimConvergence}) and (\ref{eq:OneDimConvergence}) that
\begin{eqnarray}
\lefteqn{ C(d) } & &
\label{eq:LimitGivesC(d)} \\
&=& \lim_{n \rightarrow \infty}
{\rm Cov} \left [ \1{ D^\star_{n,1} (\theta^\star_n) = d } , \1{ D^\star_{n,2} (\theta^\star_n) = d } \right ]
\nonumber
\end{eqnarray}
provided either limit at
(\ref{eq:TwoDimConvergence}) exists.
As we now turn to evaluating (\ref{eq:LimitGivesC(d)}), it will be notationally
convenient to introduce a second collection of $\mathbb{R}_+$-valued rvs
$\{ \eta_\ell, \ \ell=1,2, \ldots \}$. We assume that the rvs $\{ \eta_\ell, \ \ell=1,2, \ldots \}$ are also i.i.d. rvs,
each of which is exponentially distributed with parameter $\lambda > 0$.
The two collections $\{ \xi, \xi_k, \ k=1,2, \ldots \}$
and $\{ \eta_\ell, \ \ell =1,2, \ldots \}$ are assumed to be mutually independent.
For each integer $p=2,3, \ldots $, let $\eta_{p|1} , \ldots , \eta_{p|p}$ denote the values of the
rvs $\eta_1, \ldots , \eta_{p}$ arranged in decreasing order, namely
$\eta_{p|p} \leq \ldots \leq \eta_{p|1}$,
with a lexicographic tiebreaker when needed. The rvs $\eta_{p|1} , \ldots , \eta_{p|p}$
are the {\em order statistics} associated with the collection $\eta_{1} , \ldots , \eta_{p}$,
so that for each $s=1, \ldots , p$, the rv $\eta_{p|s}$ denotes the $s^{th}$ largest value amongst $\eta_{1} , \ldots , \eta_{p}$;
in particular $\eta_{p|1} $ and $\eta_{p|p}$ are the maximum and minimum of the rvs
$\eta_{1} , \ldots , \eta_{p}$, respectively \cite{DavidNagaraja, EKM}.
The evaluation of the limiting covariances (\ref{eq:LimitGivesC(d)}) proceeds with the following observation:
Fix $d=0,1, \ldots $ and take $n=3,4, \ldots $ such that $d \leq n-2$.
Under the enforced i.i.d. assumptions, for each $\theta > 0$ we get
\begin{eqnarray}
\lefteqn{
\left ( D^\star_{n,1}(\theta) , D^\star_{n,2}(\theta) \right )
} & &
\nonumber \\
&=&
\left (
\sum_{k=3}^n \1{ \xi_1 + \xi_k > \theta }, \sum_{k=3}^n \1{ \xi_2 + \xi_k > \theta }
\right )
\nonumber \\
&=_{st}&
\left (
\sum_{\ell=1}^{n-2} \1{ \xi_1 + \eta_\ell > \theta }, \sum_{\ell=1}^{n-2} \1{ \xi_2 + \eta_\ell > \theta }
\right )
\nonumber \\
&=&
\left (
\sum_{\ell=1}^{n-2} \1{ \xi_1 + \eta_{n-2|\ell} > \theta }, \sum_{\ell=1}^{n-2} \1{ \xi_2 + \eta_{n-2|\ell} > \theta }
\right )
\nonumber
\end{eqnarray}
where $=_{st}$ denotes distributional equality between rvs.
Two different cases arise:
First, with $d=0$ we find
\begin{eqnarray}
\bP{ D^\star _{n,1} (\theta) = 0 }
&=&
\bP{ \sum_{\ell=1}^{n-2} \1{ \xi_1 + \eta_{n-2|\ell} > \theta } = 0 }
\nonumber \\
&=&
\bP{ \xi_1 + \eta_\ell \leq \theta, \ \ell =1, \ldots , n-2 }
\nonumber \\
&=&
\bP{ \xi_1 + \eta_{n-2|1} \leq \theta }
\nonumber \\
&=&
\bP{ \eta_{n-2|1} - \theta \leq -\xi_1 }
\label{eq:CaseD=0ForOne}
\end{eqnarray}
and
\begin{eqnarray}
\lefteqn{\bP{ D^\star _{n,1} (\theta) = 0 , D^\star _{n,2} (\theta) = 0 } } & &
\nonumber \\
&=&
\bP{
\sum_{\ell=1}^{n-2} \1{ \xi_j + \eta_{n-2|\ell} > \theta } = 0, \ j=1,2
}
\nonumber \\
&=&
\bP{ \xi_1 + \eta_\ell \leq \theta , \xi_2 + \eta_\ell \leq \theta, \ \ell =1, \ldots , n-2 }
\nonumber \\
&=&
\bP{ \xi_1 + \eta_{n-2|1} \leq \theta , \xi_2 + \eta_{n-2|1} \leq \theta }
\nonumber \\
&=&
\bP{ \eta_{n-2|1} - \theta \leq - \max \left ( \xi_1 , \xi_2 \right ) }.
\label{eq:CaseD=0ForTwo}
\end{eqnarray}
Next we consider the case $d=1,2, \ldots $.
Under the enforced independence assumptions we have
\begin{eqnarray}
\lefteqn{\bP{ D^\star _{n,1} (\theta) = d } } & &
\nonumber \\
&=&
\bP{ \sum_{\ell=1}^{n-2} \1{ \xi_1 + \eta_{n-2|\ell} > \theta } = d }
\nonumber \\
&=&
\bP{ \xi_1 + \eta_{n-2|d+1} \leq \theta < \xi_1 + \eta_{n-2|d} }
\nonumber \\
&=&
\bP{ \theta - \eta_{n-2|d} < \xi_1 \leq \theta - \eta_{n-2|d+1} }
\nonumber \\
&=&
\bE{
e^{- \lambda ( \theta - \eta_{n-2|d} )^+} - e^{- \lambda ( \theta - \eta_{n-2|d+1} )^+ }
} \hspace{10mm}
\label{eq:CaseDforOne}
\end{eqnarray}
and
\begin{eqnarray}
\lefteqn{\bP{ D^\star _{n,1} (\theta) = d , D^\star _{n,2} (\theta) = d } } & &
\nonumber \\
&=&
\bP{
\sum_{\ell=1}^{n-2} \1{ \xi_j + \eta_{n-2|\ell} > \theta } = 0, \ j=1,2
}
\nonumber \\
&=&
\bP{ \xi_j + \eta_{n-2|d+1} \leq \theta < \xi_j + \eta_{n-2|d}, \ j=1,2 }
\nonumber \\
&=&
\bP{ \theta - \eta_{n-2|d} < \xi_j \leq \theta - \eta_{n-2|d+1} , \ j=1,2 }
\nonumber \\
&=&
\bE{
\left (
e^{- \lambda ( \theta - \eta_{n-2|d} )^+} - e^{- \lambda ( \theta - \eta_{n-2|d+1} )^+ }
\right )^2
}.
\label{eq:CaseDforTwo}
\end{eqnarray}
In the next step, carried out in Section \ref{sec:ProofPart+2},
we replace $\theta$ by $\theta^\star_n$ in the expressions above, and let $n$ go to infinity in the resulting expressions.
To evaluate these limits we shall rely on asymptotic properties of the order statistics
which are discussed next.
\section{Asymptotic results for order statistics}
\label{sec:AsymptoticTheoryOrderStatistics}
We begin with a one-dimensional result.
For each $s=1, 2, \ldots $, consider the mapping
$G_s: \mathbb{R} \rightarrow \mathbb{R}_+$ defined by
\begin{equation}
G_s(x_s)
\equiv \left ( \sum_{m=0}^{s-1} \frac{e^{-mx_s}}{m!} \right ) G(x_s),
\quad x_s \in \mathbb{R}
\label{eq:GeneralizedGumbel}
\end{equation}
where $G: \mathbb{R} \rightarrow \mathbb{R}_+$ denotes the well-known
{\em Gumbel} distribution given by
\begin{equation}
G(x)
= e^{-e^{-x}},
\quad x \in \mathbb{R}.
\label{eq:GumbelCDF}
\end{equation}
The next result is well known \cite[Thm. 2.2.1, p. 33]{LeadbetterLindgrenRootzen}, and takes the following form when
applied to exponential distributions.
\begin{lemma}
{\sl For each $s=1,2, \ldots $, it holds that
\begin{equation}
\lim_{p \rightarrow \infty}
\bP{ \lambda \left ( \eta_{p|s} - \theta^\star_p \right ) \leq x_s }
= G_s (x_s),
\quad x_s \in \mathbb{R}
\label{eq:ConvergenceGeneralizedGumbelB}
\end{equation}
where the scaling $\theta^\star: \mathbb{N}_0 \rightarrow \mathbb{R}$ is given by (\ref{eq:FujiharaScaling}).
}
\label{lem:ConvergenceGeneralizedGumbel}
\end{lemma}
With $s=1$, Lemma \ref{lem:ConvergenceGeneralizedGumbel} expresses
the well-known membership of exponential distributions in the maximal domain of attraction of the Gumbel distribution \cite{EKM}
\cite[Example 1.7.2, p. 21]{LeadbetterLindgrenRootzen}.
We now turn to the two-dimensional result we need:
For each $s=1, 2, \ldots $, define the mapping $J_s: \mathbb{R}^2 \rightarrow \mathbb{R}_+$ given by
\begin{eqnarray}
J_s(x_{s+1},x_s)
\equiv
\sum_{k_s=0}^{s-1}
\left ( \ldots \right )
\times
\frac{ e^{ -k_s x_s } }{k_s!} \cdot
e^{- e^{- \min ( x_s , x_{s+1} ) } }
\label{eq:TwoDimLimitCDF+a}
\end{eqnarray}
with
\begin{equation}
\ldots = \sum_{k_{s+1}=k_s}^{s}
\frac{ \left ( e^{ -\min ( x_s , x_{s+1} ) } - e^{ -x_s } \right )^{k_{s+1} - k_s } }{ (k_{s+1} - k_s )!}
\label{eq:TwoDimLimitCDF+b}
\end{equation}
as $x_s$ and $x_{s+1}$ range over $\mathbb{R}$.
In these expressions we use the convention $0^0=1$.
\begin{lemma}
{\sl For each $s=1,2, \ldots$, we have
\begin{eqnarray}
& &\lim_{p \rightarrow \infty}
\bP{ \lambda ( \eta_{p|s+1} - \theta^\star_p ) \leq x_{s+1}, \lambda ( \eta_{p|s} - \theta^\star_p ) \leq x_s }
\nonumber \\
&=&
J_s(x_{s+1}, x_s),
\quad x_{s+1}, x_{s} \in \mathbb{R}
\label{eq:KeyTwoDimAsymptotics}
\end{eqnarray}
with mapping $J_s: \mathbb{R}^2 \rightarrow \mathbb{R}_+$ given by (\ref{eq:TwoDimLimitCDF+a})-(\ref{eq:TwoDimLimitCDF+b}),
and scaling $\theta^\star: \mathbb{N}_0 \rightarrow \mathbb{R}$ given by (\ref{eq:FujiharaScaling}).
}
\label{lem:KeyTwoDimAsymptotics}
\end{lemma}
This result is a consequence of Theorem 2.3.1 in \cite[p. 34]{LeadbetterLindgrenRootzen}.
As only the case $s=1$ was discussed in \cite[Thm 2.3.2, p. 34]{LeadbetterLindgrenRootzen},
we provide in Section \ref{sec:ProofsAsymptoticsOrderStatistics} a proof for arbitrary
values of $s$ when the variates $\{ \eta_k, \ k=1,2, \ldots \}$ are exponentially distributed.
By inspection we note from (\ref{eq:TwoDimLimitCDF+a})-(\ref{eq:TwoDimLimitCDF+b}) that
\begin{equation}
J_s(x_{s+1},x_s) = G_s( x_{s}) ,
\quad
\begin{array}{c}
x_s \leq x_{s+1} \\
x_s, x_{s+1} \in \mathbb{R} \\
\end{array}
\label{eq:TwoX_sBelowX_s+1}
\end{equation}
so that
\begin{align}
J_s(\infty ,x_s) &= \lim_{x_{s+1} \rightarrow \infty} J_s(x_{s+1},x_s)
\nonumber \\
&= G_{s} (x_{s}),
\quad x_{s} \in \mathbb{R}
\label{eq:Marginal1}
\end{align}
while
\begin{align}
J_s(x_{s+1},\infty)
&=
\lim_{x_s \rightarrow \infty} J_s(x_{s+1},x_s)
\nonumber \\
&= G_{s+1} (x_{s+1}),
\quad x_{s+1} \in \mathbb{R} .
\label{eq:Marginal2}
\end{align}
This confirms that the probability distributions $G_{s+1}$ and $G_s$ are the one-dimensional marginal distributions of $J_s$ (as expected).
For use in Section \ref{sec:ProofPart+2} we find it convenient to give
Lemma \ref{lem:ConvergenceGeneralizedGumbel} and Lemma \ref{lem:KeyTwoDimAsymptotics}
the following probabilistic (and more compact) formulation:
For any given $s=1, 2, \ldots $, there exists a pair of $\mathbb{R}$-valued rvs $\Lambda_{s+1}$ and $\Lambda_{s}$ defined on
$(\Omega , \mathcal{F}, \mathbb{P})$ such that
\begin{equation}
\lambda \left ( \eta_{p|s+j} - \theta^\star_p \right ) \Longrightarrow_p \Lambda_{s+j},
\quad j=0,1
\label{eq:oneDimConvergence}
\end{equation}
and
\begin{equation}
\left ( \lambda \left ( \eta_{p|s+1} - \theta^\star_p \right ), \lambda \left ( \eta_{p|s} - \theta^\star_p \right ) \right )
\Longrightarrow_p ( \Lambda_{s+1}, \Lambda_{s})
\label{eq:JointConvergence}
\end{equation}
with $(\Lambda_{s+1}, \Lambda_{s})$ jointly distributed according to $J_s$,
and the $\mathbb{R}$-valued rvs $\Lambda_{s+1}$ and $\Lambda_{s} $
distributed according to $G_{s+1}$ and $G_{s}$, respectively.
\section{Completing the proof of Proposition \ref{prop:AssumptionC+fails}}
\label{sec:ProofPart+2}
We return to the expressions obtained in Section \ref{sec:ProofPart+1}:
With $d=0,1, \ldots $ held fixed, for each $n=2,3, \ldots$ we substitute $\theta$ by $\theta^\star_n$ in
these expressions according to (\ref{eq:FujiharaScaling}),
and let $n$ go to infinity in the resulting expressions.
\subsection{The case $d=0$}
For each $n=3,4,\ldots $, with the aforementioned substitution,
we rewrite (\ref{eq:CaseD=0ForOne}) and (\ref{eq:CaseD=0ForTwo}) as
\[
\bP{ D^\star _{n,1} (\theta^\star_n) = 0 }
=
\bP{ \lambda ( \eta_{n-2|1} - \theta^\star_{n} ) \leq - \lambda \xi_1 }
\]
and
\begin{eqnarray}
\lefteqn{ \bP{ D^\star _{n,1} (\theta^\star_n) = 0 , D^\star _{n,2} (\theta^\star_n) = 0 } } & &
\nonumber \\
&=&
\bP{ \lambda ( \eta_{n-2|1} - \theta^\star_{n} ) \leq - \lambda \max ( \xi_1, \xi_2 ) }
\nonumber
\end{eqnarray}
where by construction the rv $ \eta_{n-2|1} $ is independent of the i.i.d. rvs $\xi_1$ and $\xi_2$.
Let $\Lambda_1$ denote a rv which is distributed according to the Gumbel distribution (\ref{eq:GumbelCDF}),
and which is independent of the i.i.d. rvs $\xi_1$ and $\xi_2$.
By Lemma \ref{lem:ConvergenceGeneralizedGumbel} (for $s=1$ and $p=n-2$),
since $\lim_{n \rightarrow \infty} \left ( \theta^\star_n - \theta^\star_{n-2} \right ) = 0$, it is now plain that
\begin{eqnarray}
p_{\rm Fuj}(0)
&=&
\lim_{n \rightarrow \infty} \bP{ D^\star _{n,1} (\theta^\star_n) = 0 }
\nonumber \\
&=&
\bP{ \Lambda_1 \leq - \lambda \xi_1 } = \bE{ e^{ -e^{ \lambda \xi_1 } } }
\nonumber
\end{eqnarray}
and
\begin{eqnarray}
\lefteqn{\lim_{n \rightarrow \infty}
\bP{ D^\star _{n,1} (\theta^\star_n) = 0 , D^\star _{n,2} (\theta^\star_n) = 0 } }
& &\nonumber \\
&=&
\bP{ \Lambda_1 \leq - \lambda \max ( \xi_1, \xi_2) }
= \bE{ e^{ -e^{ \lambda \max ( \xi_1, \xi_2 ) } } }
\nonumber
\end{eqnarray}
under the independence assumptions.
Collecting these facts, we find
\begin{eqnarray}
\lefteqn{\lim_{n \rightarrow \infty}
{\rm Cov} \left [ \1{ D^\star_{n,1} (\theta^\star_n) = 0 } , \1{ D^\star_{n,2} (\theta^\star_n) = 0 } \right ] }
& &
\nonumber \\
&=&
\bE{ e^{ -e^{ \lambda \max ( \xi_1, \xi_2 ) } } } - \bE{ e^{ -e^{ \lambda \xi_1 } } } \bE{ e^{ -e^{ \lambda \xi_2 } } }.
\end{eqnarray}
As we make use of the reduction step (\ref{eq:LimitGivesC(d)}) discussed in Section \ref{sec:ProofPart+1}.
It follows that
\begin{eqnarray}
C(0)
&=&
\lim_{n \rightarrow \infty}
{\rm Cov} \left [ \1{ D^\star_{n,1} (\theta^\star_n) = 0 } , \1{ D^\star_{n,2} (\theta^\star_n) = 0 } \right ]
\nonumber \\
&=&
\bE{ e^{ -e^{ \lambda \max ( \xi_1, \xi_2 ) } } } - \bE{ e^{ -e^{ \lambda \xi_1 } } } \bE{ e^{ -e^{ \lambda \xi_2 } } }
\nonumber \\
&>& 0
\label{eq:C(0)}
\end{eqnarray}
since $\max( e^{\lambda \xi_1}, e^{ \lambda \xi_2} ) < e^{ \lambda \xi_1 } + e^{ \lambda \xi_2 } $.
\myendpf
\subsection{The case $d=1,2, \ldots $}
Pick $n=3,4,\ldots $ such that $d < n-2$.
Under the aforementioned substitution, we can rewrite
(\ref{eq:CaseDforOne}) and (\ref{eq:CaseDforTwo}) as
\begin{eqnarray}
\lefteqn{\bP{ D^\star _{n,1} (\theta^\star_n ) = d } } & &
\nonumber \\
&=&
\bE{
e^{- \lambda ( \theta^\star_n - \eta_{n-2|d} )^+} - e^{- \lambda ( \theta^\star_n - \eta_{n-2|d+1} )^+ }
}
\label{eq:CaseDforOneB}
\end{eqnarray}
and
\begin{eqnarray}
\lefteqn{ \bP{ D^\star _{n,1} (\theta^\star_n ) = d , D^\star _{n,2} (\theta^\star_n) = d } } & &
\nonumber \\
&=&
\bE{
\left (
e^{- \lambda ( \theta^\star_n - \eta_{n-2|d} )^+} - e^{- \lambda ( \theta^\star_n - \eta_{n-2|d+1} )^+ }
\right )^2
}.
\label{eq:CaseDforTwoB}
\end{eqnarray}
Applying Lemma \ref{lem:ConvergenceGeneralizedGumbel} and Lemma \ref{lem:KeyTwoDimAsymptotics} (for $s=d$ and $p=n-2$)
we conclude that
\[
\left ( \lambda \left ( \eta_{n-2|d+1} - \theta^\star_{n-2} \right ), \lambda \left ( \eta_{n-2|d} - \theta^\star_{n-2} \right ) \right )
\Longrightarrow_n ( \Lambda_{d+1}, \Lambda_{d})
\]
in the notation used at (\ref{eq:JointConvergence}).
Because $\lim_{n \rightarrow \infty} \left ( \theta^\star_n - \theta^\star_{n-2} \right ) = 0$,
we obtain
\begin{eqnarray}
\lefteqn{ \left ( \lambda \left ( \theta^\star_{n} - \eta_{n-2|d+1} \right )^+, \lambda \left ( \theta^\star_{n} - \eta_{n-2|d} \right )^+ \right ) }
& & \nonumber \\
& &\Longrightarrow_n ( (-\Lambda_{d+1})^+ , (- \Lambda_{d})^+ ) \hspace{32mm}
\nonumber
\end{eqnarray}
by the Continuous Mapping Theorem for weak convergence, whence
\begin{eqnarray}
\lefteqn{
e^{- \lambda ( \theta^\star_n - \eta_{n-2|d} )^+} - e^{- \lambda ( \theta^\star_n - \eta_{n-2|d+1} )^+ }
} & &
\nonumber \\
& & \Longrightarrow_n
e^{-(-\Lambda_{d})^+ } - e^{-(-\Lambda_{d+1})^+ }
\nonumber
\end{eqnarray}
by applying the Continuous Mapping Theorem once more.
Let $n$ go to infinity in (\ref{eq:CaseDforOneB}) and (\ref{eq:CaseDforTwoB}): The Bounded Convergence Theorem yields
\begin{eqnarray}
\lefteqn{ \lim_{n \rightarrow \infty}
\bE{
\left (
e^{- \lambda ( \theta^\star_n - \eta_{n-2|d} )^+} - e^{- \lambda ( \theta^\star_n - \eta_{n-2|d+1} )^+ }
\right )^a
} } & &
\nonumber \\
&=&
\bE{
\left (
e^{-(-\Lambda_{d})^+ } - e^{-(-\Lambda_{d+1} )^+ }
\right )^a } \hspace{20mm}
\end{eqnarray}
for each $a=1,2$ upon observing the obvious bounds
\[
\left | e^{- \lambda ( \theta^\star_n - \eta_{n-2|d} )^+} - e^{- \lambda ( \theta^\star_n - \eta_{n-2|d+1} )^+ } \right |
\leq 1,
\quad n=3,4, \ldots
\]
It follows that
\begin{eqnarray}
\lefteqn{ \lim_{n \rightarrow \infty}
{\rm Cov} \left [ \1{ D^\star _{n,1} (\theta^\star_n) = d}, \1{ D^\star _{n,2} (\theta^\star_n) = d } \right ]
} & &
\nonumber \\
&=&
\bE{
\left (
e^{-(-\Lambda_{d})^+ } - e^{-(-\Lambda_{d+1} )^+ }
\right )^2
}
\nonumber \\
& &-
\left ( \bE{
e^{-(-\Lambda_{d})^+ } - e^{-(-\Lambda_{d+1} )^+ }
}
\right )^2 \hspace{15mm}
\nonumber
\end{eqnarray}
and the reduction step (\ref{eq:LimitGivesC(d)}) leads to
\begin{eqnarray}
C(d)
&=&
\lim_{n \rightarrow \infty}
{\rm Cov} \left [ \1{ D^\star _{n,1} (\theta^\star_n) = d}, \1{ D^\star _{n,2} (\theta^\star_n) = d } \right ]
\nonumber \\
&=&
{\rm Var}
\left [
e^{-(-\Lambda_{d})^+ } - e^{-(-\Lambda_{d+1})^+ }
\right ] .
\label{eq:C(d)}
\end{eqnarray}
Note that $C(d) > 0$ as the variance of the non-degenerate rv
$e^{-(-\Lambda_{d})^+ } - e^{-(-\Lambda_{d+1})^+ } $.
\myendpf
\section{A Proof of Lemma \ref{lem:KeyTwoDimAsymptotics}}
\label{sec:ProofsAsymptoticsOrderStatistics}
First some preliminaries.
Fix $p=1,2, \ldots $ and $u \geq 0$. The rv $S_p(u)$ given by
\[
S_p(u) = \sum_{\ell=1}^p \1{ \xi_\ell > u }
\]
counts the number of {\em exceedances} of level $u$ by the rvs $\xi_1, \ldots , \xi_p$.
The proof of Lemma \ref{lem:KeyTwoDimAsymptotics} relies on the well-known equivalence
\begin{equation}
\eta_{p|s} \leq u
\quad \mbox{if and only if} \quad
S_p(u) < s,
\quad s=0, 1, \ldots , p
\label{eq:equivalence1}
\end{equation}
given in \cite[Section 2.2, p. 33]{LeadbetterLindgrenRootzen}; see also \cite[Theorem 2.3.2, p. 36]{LeadbetterLindgrenRootzen}
for the case $s=1$.
Throughout we shall write
\begin{equation}
u_p (x) = \lambda^{-1} \left ( \log p + x \right )^+ ,
\quad x \in \mathbb{R}.
\label{eq:u_p(x)}
\end{equation}
Fix $s=1, 2, \ldots $, and pick $x_s$ and $x_{s+1}$ in $\mathbb{R}$. Two cases are possible:
(i) If $x_s \leq x_{s+1}$ in $\mathbb{R}$, then for each $p=s+1,s+2, \ldots $, it holds that $u_p(x_s) \leq u_p(x_{s+1}) $, whence
\begin{eqnarray}
\lefteqn{\bP{ \eta_{p|s+1} \leq u_p(x_{s+1}) , \eta_{p|s} \leq u_p(x_s) } } & &
\nonumber \\
&=&
\bP{ \eta_{p|s+1} \leq u_p(x_s) , \eta_{p|s} \leq u_p(x_s) }
\nonumber \\
&=&
\bP{ \eta_{p|s} \leq u_p(x_s) }
\nonumber
\end{eqnarray}
since $\eta_{p |s+1} \leq \eta_{p|s} $.
From Lemma \ref{lem:ConvergenceGeneralizedGumbel} it follows that
\begin{eqnarray}
& &
\lim_{p \rightarrow \infty}
\bP{ \lambda ( \eta_{p|s+1} - \theta^\star_p ) \leq x_{s+1}, \lambda ( \eta_{p|s} - \theta^\star_p ) \leq x_s }
\nonumber \\
&=&
\lim_{p \rightarrow \infty}
\bP{ \lambda ( \eta_{p|s} - \theta^\star_p ) \leq x_{s} }
\nonumber \\
&=&
G_{s} (x_s)
\nonumber
\end{eqnarray}
and (\ref{eq:KeyTwoDimAsymptotics}) holds as seen through (\ref{eq:TwoX_sBelowX_s+1}).
(ii) If $x_{s+1} \leq x_s$ in $\mathbb{R}$, then for each $p=s+1,s+2, \ldots $,
the equivalence (\ref{eq:equivalence1}) yields
\begin{eqnarray}
\lefteqn{
\bP{ \eta_{p|s+1} \leq u_p(x_{s+1}) , \eta_{p|s} \leq u_p(x_s) }
} & &
\nonumber \\
&=&
\bP{ S_p(u_p(x_{s+1})) < s+1, S_p(u_p(x_s)) < s }
\label{eq:equivalence2} \\
\nonumber \\
&=&
\sum_{k_s=0}^{s-1}
\left ( \sum_{k_{s+1}=0}^{s}
\bP{
\begin{array}{c}
S_p(u_p(x_{s+1})) = k_{s+1} \\
\\
S_p(u_p(x_s)) = k_s \\
\end{array}
}
\right )
\label{eq:AA} \\
&=&
\sum_{k_s=0}^{s-1}
\Bigg( \sum_{k_{s+1}=k_s}^{s}
\bP{
\begin{array}{c}
\sum_{\ell =1}^p \1{ \xi_\ell > u_p(x_{s+1}) } = k_{s+1} \\
\\
\sum_{\ell =1}^p \1{ \xi_\ell > u_p(x_s) } = k_s
\end{array}
}
\nonumber
\end{eqnarray}
upon noting the fact $S_p(u_p(x_{s})) \leq S_p(u_p(x_{s+1}))$ since $u_p(x_{s+1}) \leq u_p(x_{s}) $.
For arbitrary $k_s, k_{s+1} =0,1, \ldots $ with $k_s \leq k_{s+1}$, standard counting arguments give
\begin{eqnarray}
& &
\bP{ \begin{array}{c}
\sum_{\ell =1}^p \1{ \xi_\ell > u_p(x_{s+1}) } = k_{s+1} \\
\\
\sum_{\ell =1}^p \1{ \xi_\ell > u_p(x_s) } = k_s
\end{array}
}
\nonumber \\
&=&
{ p \choose k_s } e^{- \lambda k_s u_p(x_s)} \left ( e^{- \lambda u_p(x_{s+1})} - e^{- \lambda u_p(x_{s})} \right )^{k_{s+1} - k_s }
\nonumber \\
& & \times { p-k_s \choose k_{s+1} - k_s } \left ( 1 - e^{- \lambda u_p(x_{s+1})} \right )^{p-k_{s+1}}
\nonumber \\
&=&
\frac{1}{k_s! ( k_{s+1} - k_s ) !} \cdot \frac{p! \cdot p^{- k_{s+1} } }{ (p-k_{s+1})!}
\cdot e^{ -k_s x_s }
\nonumber \\
& &
\times
\left ( e^{ -x_{s+1} } - e^{ -x_s } \right )^{k_{s+1} - k_s }
\cdot
\left ( 1 - \frac{e^{-x_{s+1} } }{p} \right )^{p-k_{s+1}}
\label{eq:BB}
\end{eqnarray}
where the last step holds whenever $p$ is large enough so that $\log p + x_s > 0$ and $\log p + x_{s+1} > 0$.
Let $p$ go to infinity in (\ref{eq:AA}): From (\ref{eq:BB}) the limit of each term in (\ref{eq:AA}) is given by
\begin{eqnarray}
\lefteqn{
\lim_{p \rightarrow \infty}
\bP{
\begin{array}{c}
\sum_{\ell =1}^p \1{ \xi_\ell > u_p(x_{s+1}) } = k_{s+1} \\
\\
\sum_{\ell =1}^p \1{ \xi_\ell > u_p(x_s) } = k_s \\
\end{array}
}
} & &
\nonumber \\
&=&
\frac{ e^{ -k_s x_s } }{k_s!}
\cdot
\frac{ \left ( e^{ -x_{s+1} } - e^{ -x_s } \right )^{k_{s+1} - k_s } }{ (k_{s+1} - k_s )!}
\cdot
e^{- e^{-x_{s+1} } }
\nonumber
\end{eqnarray}
for $k_s \leq k_{s+1}$ in $\mathbb{N}$,
as we note that
\[
\lim_{p \rightarrow \infty}
\frac{p! }{ (p-k_{s+1})! \cdot p^{ k_{s+1} }} =1
\]
and
\[
\lim_{p \rightarrow \infty} \left ( 1 - \frac{e^{-x_{s+1} } }{p} \right )^{p-k_{s+1}} = e^{- e^{-x_{s+1} } } .
\]
The convergence (\ref{eq:KeyTwoDimAsymptotics}) follows upon using the equivalence (\ref{eq:equivalence2})
together with the observation that $u_p (x_{s}) = \lambda^{-1} \left ( \log p + x_{s} \right )$ and
$u_p (x_{s+1}) = \lambda^{-1} \left ( \log p + x_{s+1} \right )$ for $p$ sufficiently large.
\myendpf
\section*{Acknowledgment}
The authors thank the anonymous referee from the first round of reviews for pointing out reference \cite{LeadbetterLindgrenRootzen} which lead to
a much shorter proof of Proposition \ref{prop:AssumptionC+fails}, and for additional comments which greatly improved the presentation of the paper.
They also would like to thank another anonymous referee which indicated the possibility of extending the original results
to a more general setting without homogeneity assumptions as was done in Section \ref{sec:GeneralSettingLittleTheory}.
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 7,937
|
I am Native Brazilian living in Finland and will be have to assists you! In addtition, You help me make some money too! What would you say? Do we have a deal?
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|
{
"redpajama_set_name": "RedPajamaC4"
}
| 6,922
|
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The brokers are counting on it, but as Louis Pasteur once said, \u201cChance favors only the prepared mind.\u201d\n\nIf we denote by S the FOR\/DOM exchange rate (i.e., 1 unit of foreign currency is worth S units of domestic currency) we can observe that paying out 1 unit of the domestic currency if the spot at maturity is above or below the strike is exactly like a cash-or nothing call and put respectively. Similarly, paying out 1 unit of the foreign currency if the spot at maturity is above or below the strike is exactly like an asset-or nothing call and put respectively. Hence if we now take {\\displaystyle r_{\\mathrm {FOR} }} , the foreign interest rate, {\\displaystyle r_{DOM}} , the domestic interest rate, and the rest as above, we get the following results.","date":"2019-01-21 04:31:29","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.17154742777347565, \"perplexity\": 1892.9164866622116}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 20, \"end_threshold\": 5, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2019-04\/segments\/1547583755653.69\/warc\/CC-MAIN-20190121025613-20190121051613-00027.warc.gz\"}"}
| null | null |
\section{Introduction and outline}
In this paper we are concerned with systems of interacting particles
moving on the real line. The models of interest can be
described as follows: Let $x_i \in \Bbb{R}$ denote the position of
the $i$-th particle. In an elementary move particle $i$ jumps to
the right to a position $x_i + \delta_i$ between $x_i$ and
$x_{i+1} > x_i$.
In the absence of a lattice spacing, there are two natural
ways of setting the scale for the jump distance $\delta_i$:
It can be imposed externally through the choice of a fixed
probability density $f_i(\delta_i)$, in which case moves with
$\delta_i > x_{i+1} - x_i$ have to be rejected, or the scale
can be set by the gap or ``headway''
\begin{equation}
\label{ui}
u_i = x_{i+1} - x_i
\end{equation}
in front of particle $i$ by letting $f_i$ depend on the
configuration ${\cal U} \equiv \{u_i \}_{i \in \Bbb{Z}}$
as
\begin{equation}
\label{pdf}
f_i(\delta_i \vert {\cal U}) = u_i^{-1} \phi(\delta_i/u_i),
\end{equation}
where $\phi(r)$ is a probability density with support on the unit interval.
Equation (\ref{pdf}) implies that the jump length $\delta_i$ is a random
fraction $r$ of the headway $u_i$.
The rate for the move is a function $\gamma(u_i)$ of the headway.
The moves are executed in continuous time (in which
case each particle is equipped with an exponential clock) or
in discrete time; in the latter case the particle positions are updated
either in parallel, or sequentially by going through the system against the
direction of particle motion. A model is defined by specifying the functions
$f_i(\delta)$
and $\gamma(u)$ as well as the type of dynamics (continuous time,
parallel or sequential).
Two equivalent representations of the dynamics will prove to be useful.
In terms of the headway
variables $u_i$ the particle configuration
may be visualized as a system of
sticks located at the sites $i$ of the
integer lattice, $u_i$ being the length of stick $i$. In an elementary
move a fraction $\delta_i$ of stick $i$ is broken off and added to stick
$i-1$ \cite{timo96,rajesh}. Alternatively, the particle positions
$x_i(t)$ can be taken to define the height of a one-dimensional
interface above the point $i$. The asymmetric particle motion translates
into a growth process, and the fact that particles cannot pass each
other implies that the interface is a monotonically increasing
staircase ($x_{i+1} - x_i > 0$) at all times. We will refer to these
two viewpoints as the stick representation and
the interface representation, respectively.
For continuous time dynamics, a jump length distribution of the
type (\ref{pdf}) with $\phi$ uniform,
and $\gamma(u) = u$ the model reduces to
the Hammersley process discussed in \cite{aldous95}. In this case
the invariant distribution of particle positions is Poisson.
Here we are interested in obtaining similar
results for other choices of $f_i$ and
$\gamma$, and other types of dynamics.
Our motivation is mainly conceptual: While a wealth of results
\cite{liggett,spohn,kipnis99,liggett99,spohn}
are available for particle systems on the integer lattice
such as the asymmetric simple exclusion process \cite{spitzer},
little is known analytically for the case of continuous
particle positions, although motion on the real line
appears naturally e.g. in applications to highway traffic
\cite{krauss96,krauss97,krauss98}.
An important simplifying feature of the asymmetric exclusion process
is the existence of stationary product measures. Here the analogous
desirable property is the product form
\begin{equation}
\label{product}
{\cal P}({\cal U}) = \prod_i P(u_i)
\end{equation}
for the stationary probability of a configuration
${\cal U}$ of particle headways. Therefore a
primary goal will be to find nontrivial examples of
asymmetric particle systems on $\Bbb{R}$ for which (\ref{product})
holds.
We provide an outline of the paper. In the next section we
explore the conditions for a Poisson distribution of
particle positions (corresponding to an exponential distribution
of interparticle spacings in (\ref{product})) to be
invariant
for continuous time dynamics.
Our strategy is to consider a finite number $N$ of particles moving
on a ring of length $L$, and to demand that the stationary
measure gives the same weight to all allowed configuration;
this then implies a Poisson measure for $N,L \to \infty$
at fixed density $\rho = N/L$.
Provided the jump rate $\gamma$ is independent
of the headway, we find that the Poisson measure is invariant
for {\em arbitrary} externally imposed (i.e., configuration
and particle
independent) jump length distributions $f(u)$.
On the other hand, if the jump length is scaled to the headway
as in (\ref{pdf}), the Poisson measure is stationary
only for a one-parameter family of
power law functions $\phi$ and $\gamma$, which have been identified
previously in the context of (symmetric) stick models \cite{feng96}.
Sections 3 and 4, which constitute the main part of the
paper, are devoted to models with constant jump rate,
$\gamma \equiv 1$ independent of the headway, and jump length
distributions of the type (\ref{pdf}).
In the interface representation these belong to the class
of random average processes (RAP) studied by
Ferrari and Fontes \cite{ferrari98}:
The particle position $x_i'$ after the
move is an average
\begin{equation}
\label{rap}
x_i' = r x_i + (1-r) x_{i+1}
\end{equation}
of the previous positions $x_i$, $x_{i+1}$, with a random
weight $r \in [0,1]$ drawn from the probability
density $\phi(r)$.
We therefore refer
to these models as Asymmetric Random Average Processes (ARAP).
Discrete time ARAP's have been introduced previously
to model force fluctuations in random bead packs
\cite{liu95,coppersmith96,claudin98}. In that context the headway $u_i(t)$
represents the (scaled) force supported by bead $i$ at depth
$t$ below the surface of a two-dimensional packing (see
Section 3.2.1).
In Section 3.1.1 we show, for the
case of continuous time dynamics, that the two-point correlation
function of particle headways $\langle u_i u_j \rangle$ factorizes
in the stationary state for any choice of $\phi(r)$, and obtain
the expression
\begin{equation}
\label{varu}
\langle u^2 \rangle - \langle u \rangle^2 = \frac{\mu_2}{\rho^2(\mu_1 - \mu_2)}
\end{equation}
for the stationary variance of headways in terms of
the moments
\begin{equation}
\label{mn}
\mu_n = \int_0^1 dr \; r^n \phi(r)
\end{equation}
of $\phi(r)$ and the particle density $\rho$. Similar results
for the discrete time models are derived in Section 3.2.
More detailed information about the stationary headway
distribution can be obtained when $\phi(r)$ is the uniform
distribution on $[0,1]$. Assuming that the factorization property
of the two-point function implies pairwise independence of
the $u_i$, we
derive and solve
stationarity conditions for their moments,
which show that the invariant density of
headways (normalized to $\langle u_i \rangle = 1$)
takes the form of a gamma distribution,
\begin{equation}
\label{Gamma}
P_\nu(u) = \frac{\nu^\nu}{\Gamma(\nu)}
u^{\nu - 1}
e^{-\nu u}
\end{equation}
where the parameter $\nu$ depends on the dynamics:
For continuous time dynamics $\nu = 1/2$, while
sequential and parallel dynamics yield $\nu = 1$ and
2, respectively. The result for parallel dynamics
has been previously derived by Coppersmith {\em et al.}
\cite{coppersmith96}, who also gave an explicit proof of
the factorization property (\ref{product}).
Equation (\ref{Gamma}) implies {\em bunching} of particles
(enhanced density fluctuations compared to the
Poisson measure) for continuous time
dynamics ($\nu = 1/2$) and {\em antibunching} for parallel
dynamics ($\nu = 2$).
The associated
nontrivial particle-particle correlations are explicitly
computed in Section 3.3.
Based on numerical simulations, we conjecture
that the stationary single particle headway distribution is
exactly given by (\ref{Gamma}) for all three
types of dynamics. For continuous time dynamics
and a finite number of particles on a ring
the assumption of an invariant product measure is
examined in Section 3.1.2. Surprisingly,
we find that the product measure is {\em not} invariant
for the ARAP, although it {\em is} invariant for a related
symmetric stick model. This conclusion agrees with recent
results for the infinite system obtained by Rajesh and Majumdar
\cite{rajesh}.
Section 4
is devoted to the large scale, long time behavior of the ARAP.
We derive a hydrodynamic equation of singular diffusion type, and
compute the tracer diffusion coefficient using a Langevin approach.
Since these results depend only on the stationary two-point function
of headways, they are valid for any choice of the jump
length distribution $\phi(r)$.
Finally, some conclusions and
open questions are formulated in Section 5.
\section{Models with invariant Poisson measures}
\label{Poisson}
\subsection{Constant invariant measure on the ring}
In this section we want to identify continuous time
dynamics which leave a Poisson distribution of
particle positions invariant. For this purpose we
first consider $N$ particles moving in continuous time
on a ring of length $L$, with density $\rho = N/L$.
Allowed headway configurations then satisfy the constraint
\begin{equation}
\label{constraint}
\sum_{i=1}^N u_i = L
\end{equation}
and the product measure (\ref{product}) is required
to hold on the set of configurations
defined by (\ref{constraint}). For an exponential
distribution $P(u) \sim e^{- \rho u}$ this implies
that all allowed headway configurations carry the same
weight $\Omega(N,L)^{-1}$, where
\begin{equation}
\label{omega}
\Omega(N,L) = \frac{L^{N-1}}{(N-1)!}
\end{equation}
denotes the volume of the set, i.e. the invariant
measure is {\em constant} on allowed configurations.
It is straightforward
to check that this implies Poisson measure
in the limit $N,L \to \infty$ at fixed density $\rho$.
For example, the distribution of a single headway on
the ring is given by
\begin{equation}
\label{PNL}
P_{N,L}(u) = \frac{\Omega(N-1,L-u)}{\Omega(N,L)}
\to \rho e^{-\rho u}, \;\;\;\; N,L \to \infty
\end{equation}
while the joint distribution of the headways of
two neighboring particles is
\begin{equation}
\label{PNL2}
P_{N,L}(u_i, u_{i+1}) =
\frac{\Omega(N-2,L-u_i - u_{i+1})}{\Omega(N,L)}
\to \rho^2 e^{-\rho(u_i + u_{i+1})}, \;\;\;\; N,L \to \infty.
\end{equation}
A similar argument can be carried out for the probability distribution
of the particle positions on the ring.
Invariance of the constant measure requires
the total transition rates for going into and out of any configuration
to balance. This yields the condition
\begin{equation}
\label{invariant}
\sum_{i=1}^N \int_0^{u_{i-1}} dw \; f_i(w \vert {\cal U}^{(i)}(w))
\gamma(u_i+w) =
\sum_{i=1}^N \int_0^{u_i} dw f_i(w \vert {\cal U}) \gamma(u_i)
\end{equation}
for any configuration ${\cal U}$,
with the configuration ${\cal U}^{(i)}(w) = \{ u_j^{(i)}(w)
\}_{j \in \Bbb{Z}}$ defined through
\begin{equation}
\label{uprime}
u_j^{(i)}(w) = \left\{ \begin{array}{l@{\quad:\quad}l}
u_i + w & j = i \\
u_{i-1} - w & j = i-1 \\
u_j & {\rm else}
\end{array} \right.
\end{equation}
and periodic boundary conditions implied
in the summation over $i$.
Note the upper integration limits, which ensure that
particles cannot pass each other ($\delta_i \leq u_i$).
Two examples of dynamics which satisfy (\ref{invariant}) will
be given in the following.
\subsection{Configuration-independent jump length distributions}
If the jump rate $\gamma$ is independent of headway, the
invariance condition (\ref{invariant}) is seen to hold for
{\em any} jump length distribution $f(w)$ which is independent
of the configuration and of the particle label $i$. The stationary
speed $\overline v$ of particles at density $\rho$ is
then computed from
\begin{equation}
\label{speed}
\overline v = \gamma \rho \int_0^\infty du \; e^{-\rho u}
\int_0^u dw \; w f(w),
\end{equation}
and the current follows from $j(\rho) = \rho {\overline v}(\rho)$. For example,
for jump lengths chosen uniformly in the unit interval one finds
\begin{equation}
\label{juni}
j(\rho) = \frac{\gamma}{\rho} [1 - (1 + \rho)e^{-\rho} ].
\end{equation}
It should be noted that in general the Poisson distribution is not
the unique invariant measure. For example, if $f(w) = 0$ for
$w$ less than some minimum jump length $a$, then all configurations
with $u_i < a$ for all $i$ are trivially invariant. Numerical simulations
indicate, however, that such ``absorbing'' states are typically
not reached,
even if the system is started very close to them. If $f(w) =
\delta(w - 1)$ {\em and} the particles are started on the integer lattice,
the model reduces to the asymmetric exclusion process, which has
a geometric (rather than exponential) headway distribution.
\subsection{Scale-invariant models}
When the scale of the jumps is set by the headways, inserting
(\ref{pdf}) into (\ref{invariant})
and requiring the terms on both sides to cancel pairwise
yields
the following integral equation connecting
the functions $\phi$ and $\gamma$,
\begin{equation}
\label{integral}
\int_0^u dw \;\gamma(u'+w) \frac{\phi(w/(u'+w))}{u'+w} = \gamma(u),
\end{equation}
which should be true for all $u$, $u'$. Taking the derivative with
respect to $u$ this becomes a differential equation for $\gamma$,
\begin{equation}
\label{diffgamma}
\frac{d \gamma}{du} = \frac{\gamma(v) \phi(u/v)}{v}
\end{equation}
with $v = u + u' \geq u$. Setting in particular $v = u$ we see that
$\gamma$ has to be a power law function,
\begin{equation}
\label{powergamma}
\gamma(u) = \gamma_0 u^{\alpha - 1},
\end{equation}
where $\gamma_0 > 0$ is a constant and $\alpha = 1 + \phi(1)$.
Using (\ref{diffgamma}) the jump length distribution is then found
to be also a power law,
\begin{equation}
\label{powerphi}
\phi(v) = (\alpha - 1) v^{\alpha - 2}.
\end{equation}
Normalizability of $\phi$ requires $\alpha > 1$.
Equations (\ref{powergamma},\ref{powerphi}) define a one-parameter
family of models for which the Poisson distribution of positions
is invariant for an arbitrary number of particles $N$, the Hammersley
process being given by $\alpha = 2$. The corresponding
{\em symmetric} stick models, in which the broken-off piece is
distributed with equal probability to the left or right neighbor,
were considered by Feng {\em et al.} \cite{feng96}. Since $\gamma$
is a power law, these models are {\em scale invariant} in the
sense that the average particle spacing $\langle u_i \rangle =
1/\rho$ is the only
length scale in the problem. Therefore also the stationary
particle current $j$ is a power law function of the density.
To compute it, we note that the average particle
speed is given by
\begin{equation}
\label{speed2}
{\overline v} = \langle \gamma(u_i) \delta_i \rangle =
\rho \int_0^\infty du \, e^{-\rho u} \gamma(u) u \int_0^1 dv \; v \phi(v) =
\gamma_0 (1 - 1/\alpha) \Gamma(\alpha + 1) \rho^{-\alpha}
\end{equation}
and therefore
\begin{equation}
\label{j}
j(\rho) = \rho {\overline v} = \gamma_0 (1 - 1/\alpha)
\Gamma(\alpha + 1) \rho^{1 - \alpha}.
\end{equation}
\section{Asymmetric Random Average Processes}
\label{ARAP}
The asymmetric random average process is a
scale-invariant model characterized by a
jump length distribution of type (\ref{pdf}),
and a constant jump rate
$\gamma \equiv \gamma_0 = 1$.
The discussion is phrased most naturally in the stick representation,
and begins with the continuous time models.
\subsection{Continuous time dynamics}
\subsubsection{Stationary headway correlations}
Consider first
the time evolution of the second moment $\langle u_i^2 \rangle$.
In a small
time interval $\Delta t$ two processes affecting $u_i$ may occur:
A random fraction $\delta_i$ of $u_i$ may be lost to $i-1$,
and a random fraction $\delta_{i+1}$ of $u_{i+1}$ may be gained from
$i+1$. Both processes occur with probability $\Delta t$. Thus
\begin{equation}
\label{Deltat}
\langle u_i^2 \rangle (t + \Delta t) =
\Delta t [\langle (u_i - \delta_i)^2 \rangle + \langle (u_i +
\delta_{i+1} )^2 \rangle ] + (1 - 2 \Delta t)
\langle u_i^2 \rangle (t).
\end{equation}
Stationarity then implies
\begin{equation}
\label{delta}
- 2 \langle \delta_i u_i \rangle + \langle \delta_i^2 \rangle +
2 \langle \delta_{i+1} u_i \rangle + \langle \delta_{i+1}^2 \rangle = 0.
\end{equation}
Since $\delta_j = r_j u_j$ where $r_j$ is an independent random
variable with mean $\mu_1$ and second moment $\mu_2$,
we have that
$\langle \delta_i u_i \rangle = \mu_1 \langle u_i^2 \rangle$,
$\langle \delta_i^2 \rangle = \langle \delta_{i+1}^2 \rangle =
\mu_2 \langle u_i^2 \rangle$ and
$\langle \delta_{i+1} u_i \rangle =
\mu_1 \langle u_i u_{i+1} \rangle$. Thus (\ref{delta}) becomes
\begin{equation}
\label{corr0}
(\mu_1 - \mu_2) \langle u_i^2 \rangle = \mu_1 \langle u_i u_{i+1} \rangle.
\end{equation}
Similarly for the general two-point function $C_k \equiv \langle u_i u_{i+k}
\rangle$ we obtain the stationarity condition
\begin{equation}
\label{Ck}
\mu_1 (C_{k+1} + C_{k-1} - 2 C_k ) = \mu_2 C_0(\delta_{k,1} + \delta_{k,-1} -
2 \delta_{k,0}),
\end{equation}
where translational invariance and symmetry ($C_k = C_{-k}$) of the
correlations has been used. Solving eq.(\ref{Ck}) starting from
$k=0$ one finds
\begin{equation}
\label{Ck2}
C_k = [1 - (\mu_2/\mu_1)(1 - \delta_{k,0})] C_0.
\end{equation}
Imposing the boundary condition
$\lim_{k \to \infty} C_k =
\langle u_i \rangle^2 = 1/\rho^2$
for an infinite system of density $\rho$, eq.(\ref{Ck2}) then
shows that the two-point function factorizes for any $k \geq 1$ and
the variance of headways is given by (\ref{varu}).
\subsubsection{Stationary headway distribution for uniform
$\phi(r)$}
We now specialize to the case when the distribution of scaled
jump lengths $\phi(r)$ is uniform in $[0,1]$, and assume that the
factorization property which was verified above for the two-point
function implies the pairwise independence of the
$u_i$.
Then the stationarity condition for the $n$-th moment
\begin{equation}
\label{statn}
\langle (u_i + \delta_{i+1})^n \rangle + \langle (u_i - \delta_i)^n \rangle =
2 \langle u_i^n \rangle.
\end{equation}
yields (the index $i$ of $u_i$ is now dropped)
\begin{equation}
\label{sumn}
\sum_{k=0}^n \left( {n \atop k} \right) \frac{1}{k+1}
[\langle u^{n-k} \rangle \langle u^k \rangle + (-1)^k \langle u^n \rangle ]
= 2 \langle u^n \rangle
\end{equation}
which can be rewritten as a recursion relation,
\begin{equation}
\label{recursion}
\langle u^n \rangle = \frac{n+1}{n-1} \sum_{k=1}^{n-1}
\left( {n \atop k} \right) \frac{1}{k+1}
\langle u^{n-k} \rangle \langle u^k \rangle.
\end{equation}
Evaluating this expression for $n=1,...,5$ we find that the relation
\begin{equation}
\label{moments}
\langle u^n \rangle = \left[\prod_{k=1}^n (2k-1) \right]
\langle u \rangle^n
\end{equation}
appears to hold, which is characteristic of the gamma distribution
(\ref{Gamma}) with parameter $\nu = 1/2$.
To prove it, we first
insert (\ref{moments}) into (\ref{recursion}),
and obtain
\begin{equation}
\label{binom1}
\left( {2n \atop n} \right)= \frac{n+1}{n-1} \sum_{k=1}^{n-1}
\frac{1}{k+1} \left( {2k \atop k} \right) \left( {2(n-k) \atop n-k} \right).
\end{equation}
This can be verified using the binomial expansion
\begin{equation}
\label{binom2}
\frac{1}{2} (1 - 4x)^{-1/2} = \frac{1}{2} + \sum_{k=1}^\infty
\left( {2k-1} \atop {k-1} \right) x^k.
\end{equation}
Integrating with respect to $x$ we also have
\begin{equation}
\label{binom3}
-\frac{1}{4} (1 - 4x)^{1/2} = - \frac{1}{4} + \frac{x}{2} +
\sum_{k=1}^\infty \frac{1}{k+1} \left( {2k-1} \atop {k-1} \right)
x^{k+1}.
\end{equation}
Since the product of the left hand sides is a constant,
all coefficients of $x^m$ with $m > 0$ in the series obtained by multiplying
(\ref{binom2}) and (\ref{binom3}) must vanish. After rearranging terms
this is seen to imply (\ref{binom1}).
In fact the relation (\ref{moments}) was first guessed on the basis
of numerical simulations. Rather accurate numerical estimates
for the stationary
moments of $u_i$ can be obtained by
starting from an ordered initial condition
($u_i = 1$ for all $i$) and fitting the finite time
data to the form
\begin{equation}
\label{finitetime}
\langle u^n \rangle(t) = A_n + B_n \; t^{-1/2}
\end{equation}
which is suggested by the fluctuation theory of Section 4.2
(see eq.(\ref{G1})).
The results shown in Table I
strongly
indicate that the stationary single particle
headway distribution is exactly
given by the $\nu = 1/2$ gamma distribution.
To test the assumption of an invariant product measure
underlying the derivation of (\ref{recursion}), we proceed
as in Section 2 and consider
a finite number $N$ of particles on a ring.
The condition for the product measure (\ref{product}),
restricted
to the set (\ref{constraint}) of allowed configurations,
to be invariant now
reads
\begin{equation}
\label{invariantrap}
\sum_{i=1}^N \int_0^{u_{i-1}}
\frac{dw}{u_{i} + w} \frac{P(u_i + w) P(u_{i-1} - w)}{
P(u_i) P(u_{i-1})} =
\sum_{i=1}^N \gamma(u_i) = N.
\end{equation}
Inserting the gamma distribution with parameter $\nu = 1/2$
(eq.(\ref{Gamma}))
and noting that
\begin{equation}
\label{integral2}
\int_0^v dw (u+w)^{-3/2} (v - w)^{-1/2} =
\frac{2 \sqrt{v/u}}{u + v}
\end{equation}
the condition (\ref{invariantrap}) becomes
\begin{equation}
\label{invariant2}
\sum_{i=1}^N \frac{2 u_{i-1}}{u_i + u_{i-1}} = N,
\end{equation}
with periodic boundary
conditions, $u_{-1} = u_N$.
Equation (\ref{invariant2}) is satisfied for $N=2$, but not for
general $N$. We conclude that the product measure (\ref{product})
is {\em not} invariant for
$N$ different from 2. It is however the exact invariant measure for
the {\em symmetric} stick process obtained by transferring the
piece broken off stick $i$ to $i-1$ or $i+1$ with equal probability.
Indeed, in that case the left hand side of (\ref{invariant2}) becomes
\begin{equation}
\label{invariant3}
\sum_{i=1}^N \frac{u_{i-1}}{u_i + u_{i-1}} +
\frac{u_{i+1}}{u_i + u_{i+1}} = N.
\end{equation}
While these arguments are restricted to finite systems, the conclusions
agree with calculations carried out for the infinite system by Rajesh and Majumdar
\cite{rajesh}. Specifically, they show that the product measure ansatz
for the continuous time ARAP breaks down at the level of
three-point correlations,
but is exact for the symmetric stick model.
\subsection{Discrete time dynamics}
\subsubsection{Parallel update}
\label{parup}
A discrete time version of the ARAP is obtained by writing
\begin{equation}
\label{parallel}
u_i(t+1) = u_i(t) - \delta_i(t) + \delta_{i+1}(t)
\end{equation}
where $\delta_j = r_j u_j$ with independent random numbers
$r_j$ distributed according to the density
$\phi(r)$. This is closely related
to a model introduced by Coppersmith, Liu, Majumdar, Narayan and Witten
for the description of force fluctuations in bead packs
\cite{coppersmith96}. To see the connection, let $W(i,t)$ denote the
weight supported by bead $i$ in the $t$-th layer below the (free) surface
of the packing. The key assumption of the model is that the beads are
arranged on a regular lattice, and that each bead transfers its weight
to exactly $M$ beads in the layer below. The fraction $q_{ij}(t) \in [0,1]$ of
the weight of bead $i$ in layer $t$ which is transferred to bead $j$ in
layer $t+1$ defines a matrix with random entries subject to the
constraint $\sum_{j} q_{ij}(t) = 1$. Assigning unit mass to each bead,
the weights evolve according to
\begin{equation}
\label{q-model}
W(j,t+1) = 1 + \sum_i q_{ij}(t) W(i,t).
\end{equation}
For large $t$ all weights increase linearly with $t$, which suggests
to introduce normalized variables $U(i,t) = W(i,t)/t$.
Specializing to a two-dimensional lattice where the beads are labeled such
that bead $i$ is connected to beads $i$ and $i+1$ in the layer below,
we see that for $t \to \infty$ the evolution of the $U(i,t)$ reduces
to (\ref{parallel}) with the identification $q_{ii} = 1 - r_i$ and
$q_{i+1 i} = r_{i+1}$. In the context of beak packs $q_{ii}$ and
$q_{i+1 i}$ should have the same distribution, and hence strict equivalence
between the two models holds only when $\phi(r)$ is symmetric around
$r=1/2$.
Let us first show that the stationary two-point headway correlations
factorize for any $\phi(r)$. Proceeding as above in Section 3.1.1, we
obtain the stationarity condition
\begin{equation}
\label{Ckpar}
(\mu_1 - \mu_1^2) (C_{k+1} + C_{k-1} - 2 C_k ) =
(\mu_2 - \mu_1^2) C_0(\delta_{k,1} + \delta_{k,-1} -
2 \delta_{k,0}),
\end{equation}
with the solution
\begin{equation}
\label{Ckpar2}
C_k = [1 - (\mu_2-\mu_1^2)/(\mu_1-\mu_1^2)(1 - \delta_{k,0})] C_0.
\end{equation}
As in the continuous time case
this implies factorization
for $k \geq 1$ in the infinite system, with the stationary variance
of headways given by
\begin{equation}
\label{varupar}
\langle u^2 \rangle - \langle u \rangle^2 =
\frac{\mu_2 - \mu_1^2}{\rho^2(\mu_1 - \mu_2)}.
\end{equation}
For the case of a uniform distribution $\phi(r)$, Coppersmith {\em et al.}
\cite{coppersmith96} (see also \cite{majumdar99,rajesh})
have shown explicitly that the stationary measure takes
the product form (\ref{product}), with the headway distribution $P(u)$
given by the gamma distribution (\ref{Gamma}) with $\nu = 2$. The latter
is easily derived along the lines of Section 3.1.2.
Under the assumption of pairwise independence, the
stationarity condition for general moments $\langle u_i^n \rangle$
now reads
\begin{equation}
\label{parrecursion}
\langle u^n \rangle = \frac{1}{(n-1)(n+2)} \sum_{k=1}^{n-1}
\left( {n+2 \atop k+1} \right)
\langle u^{n-k} \rangle \langle u^k \rangle.
\end{equation}
A straightforward computation shows that this
is solved by the expression
\begin{equation}
\label{parmom}
\langle u^n \rangle = 2^{-n} (n+1)! \langle u \rangle^n
\end{equation}
for the moments of the gamma distribution (\ref{Gamma}) with
parameter $\nu = 2$.
\subsubsection{Ordered sequential update}
\label{ordered}
In the context of traffic modeling \cite{evans97,raj98}
it has been found useful
to implement a different kind of discrete time dynamics, in which
the particles are moved one by one, in the order of their positions in
the system. This {\em ordered sequential update} can proceed either in
the direction of particle motion (forward update) or against it (backward
update). For the ARAP it is easy to see that
the forward update is equivalent to the parallel dynamics discussed in
Section 3.2.1, however the backward update is not.
In the stick representation, backward sequential update implies that
stick $i$ first receives a random fraction of stick $i+1$, placing it
in an intermediate state of length $u_i'$, and subsequently transfers
a random fraction $\delta_i'$ of $u_i'$ to stick $i-1$. It is important
to note that, at the time of transfer of mass to stick $i$, stick $i+1$
has already received mass from $i+2$ and thus the amount transferred from
$i+1$ to $i$ is a random fraction of $u_{i+1}' > u_{i+1}$. The dynamics
therefore proceeds in two steps,
\begin{equation}
\label{seq1}
u_{i}'(t) = u_i (t) + \delta_{i+1}'(t)
\end{equation}
\begin{equation}
\label{seq2}
u_{i}(t+1) = u_i' (t) - \delta_{i}'(t),
\end{equation}
where $\delta_j'$ is a random fraction of $u_j'$.
Taking the average of both sides of (\ref{seq1}) or
(\ref{seq2}) the stationary mean of $u_i'$ is seen to be
\begin{equation}
\label{meanu'}
\langle u' \rangle = \frac{\langle u \rangle}{1 - \mu_1} =
\frac{1}{\rho(1 - \mu_1)}.
\end{equation}
Equation (\ref{seq2}) implies the relation
\begin{equation}
\label{C'}
C_k = [(1 - \mu_1)^2 + (\mu_2 - \mu_1^2)\delta_{k,0}] C_k'
\end{equation}
between the stationary two-point functions $C_k$ of $u_i$ and
$C_k'$ of $u_i'$. Using (\ref{seq1}) it is easy to show that
the stationarity condition for $C_k'$ is identical to the
condition (\ref{Ckpar}) obtained in the case of parallel update.
Therefore also $C_k'$ factorizes in the infinite system, and
through (\ref{C'}) this property carries over to $C_k$.
For the stationary variance of the backward sequential update
model we find the expression
\begin{equation}
\label{varseq}
\langle u^2 \rangle - \langle u \rangle^2 =
\frac{\mu_2 - \mu_1^2}{\rho^2(1-\mu_1)(\mu_1 - \mu_2)}.
\end{equation}
Turning to the stationary headway probability distribution $P(u)$,
we again assume pairwise independence and note the
functional
equation
\begin{equation}
\label{functional}
P(u) = \int_0^1 dr \; r^{-1} \phi(1-r) P'(u/r)
\end{equation}
relating $P(u)$ to the distribution $P'(u')$ of the intermediate
state headway. For uniform $\phi(r)$ the stationarity condition
for the $n$-th moment of $u_i'$ then reads
\begin{equation}
\label{statu'}
\langle (u_i')^n \rangle = \langle (u_i + \delta_{i+1}')^n
\rangle = \sum_{k=0}^n \left( n \atop k \right)
\frac{1}{k+1} \langle (u_i')^k \rangle \langle u_i^{n-k} \rangle.
\end{equation}
Using the relation $\langle (u')^n \rangle = (n+1) \langle u^n \rangle$
obtained from (\ref{functional}) this reduces to
\begin{equation}
\label{statuseq}
\langle u^n \rangle = \frac{1}{n+1} \sum_{k=0}^n
\left( n \atop k \right) \langle u^k \rangle
\langle u^{n-k} \rangle,
\end{equation}
which is solved by setting $\langle u^n \rangle = n! \langle u \rangle^n$.
We conclude that $P(u)$ is an exponential distribution (a gamma
distribution (\ref{Gamma}) with $\nu = 1$). This is confirmed by the
numerical data shown in Table I.
From (\ref{functional}) the distribution of the intermediate state headway
is found to be a $\nu=2$ gamma distribution with mean $2\langle u \rangle =
2/\rho$,
\begin{equation}
\label{primedist}
P'(u) = \rho^2 u e^{-\rho u}.
\end{equation}
Given the equivalence between the intermediate state headway and
the headway for parallel update which we found on the level of the two-point
function, it is no surprise that (\ref{primedist}) is identical, up to
a scale factor, to the headway distribution $P(u)$ for parallel dynamics.
\subsection{Particle-particle correlations}
In this section we illustrate how the product measure
(\ref{product}) with the headway distribution (\ref{Gamma})
translates into nontrivial particle-particle correlations when
$\nu \neq 1$.
For example, the probability density $g(x)$ for finding
a particle at $x$, conditioned on having a particle at the origin,
can be written as
\begin{equation}
\label{g}
g(x) = \sum_{n=1}^\infty P_n(x),
\end{equation}
where $P_n(x)$ is the probability density for the $n$-th particle
to be at $x$ when the $0$-th is at the origin or, equivalently,
the probability that $\sum_{i=0}^{n-1} u_i = x$. The $P_n$ are obtained
iteratively from $P_1(x) = P(x)$ through the convolution
\begin{equation}
\label{convolve}
P_n(x) = \int_0^x dy \; P_{n-1}(y) P(x-y).
\end{equation}
Inserting the gamma distributions (\ref{Gamma}) with parameters
$\nu = 1/2$ and $\nu = 2$, one finds that
\begin{equation}
\label{Pncont}
P_n(x) = \rho (\Gamma(n/2) 2^{n/2})^{-1} (\rho x)^{n/2 -1}
e^{- \rho x/2}
\end{equation}
for the continuous time case, and
\begin{equation}
\label{Pnpar}
P_n(x) = \frac{2^{2n} \rho}{(2n-1)!}(\rho x)^{2n-1}
e^{-2 \rho x}
\end{equation}
for parallel dynamics.
In the parallel case the evaluation of the sum
(\ref{g}) is straightforward, and yields the expression
\begin{equation}
\label{gpar}
g(x) = \rho (1 - e^{-4 \rho x})
\end{equation}
for the correlation function, which explicitly displays the
tendency of particles to avoid each other at distances short compared
to $1/\rho$.
To compute (\ref{g}) with the $P_n$
given by (\ref{Pncont}), it is useful to write $g$ as the sum of
two contributions $g_{\rm even}$ and $g_{\rm odd}$ from even and
odd $n$, respectively. One finds that $g_{\rm even}(x) = \rho/2$
independent of $x$, while the odd part can be brought into the form
\begin{equation}
\label{godd}
g_{\rm odd}(x) = P_1(x) + \frac{\rho }{2 \sqrt{\pi}}
e^{-\rho x/2} \sum_{m=1}^\infty \frac{(m-1)!}{(2m-1)!}
(\sqrt{2 \rho x})^{2m-1}.
\end{equation}
To sum the series we write $(m-1)! = \int_0^\infty dz \; z^{m-1}
e^{-z}$ and interchange the summation over $m$ with the integration
over $z$. This yields finally
\begin{equation}
\label{gcont}
g(x) = \sqrt{\frac{\rho}{2 \pi x}} e^{-\rho x/2} +
\frac{\rho}{2}(1 + {\rm erf}{\sqrt{\rho x/2}})
\end{equation}
with the error function ${\rm erf}(z) = (2/\sqrt{\pi})
\int_0^z dt \; e^{-t^2}$.
For $x \to 0$ the correlation function is dominated by $P_1(x)$
and correspondingly diverges as $1/\sqrt{x}$, reflecting the
tendency of particles to bunch together in the continuous time case.
For $x \to \infty$ $g(x)$ decays somewhat faster than exponentially,
as
\begin{equation}
\label{largex}
g(x) - \rho \approx \frac{\rho}{\sqrt{2 \pi} (\rho x)^3}
e^{-\rho x/2}.
\end{equation}
Alternatively the correlations between particles can be
characterized through the variance $(\Delta N_L)^2$ of the
number of particles $N_L$ in an interval of size $L$. When
$L$ is small compared to the mean interparticle spacing
$N_L$ is either 0 or 1, and $(\Delta N_L)^2 = \rho L$.
For $L \gg 1/\rho$ a central limit argument shows that
\begin{equation}
\label{DeltaN}
(\Delta N_L)^2 \approx \chi L
\end{equation}
where the ``compressibility'' $\chi$ (defined in analogy with
equilibrium systems \cite{spohn}) is given by
\begin{equation}
\label{chi}
\chi(\rho) = \rho^3 (\langle u^2 \rangle - \langle u \rangle^2) =
\rho/\nu,
\end{equation}
with the parameter $\nu$ of the headway distribution (\ref{Gamma}).
Thus the slope of $(\Delta N_L)^2$ versus $L$ changes from
unity for $L \ll 1/\rho$ to $1/\nu$ for $L \gg 1/\rho$, reflecting
the increase (decrease) of particle number fluctuations for
continuous time (parallel) dynamics, respectively.
The compressibility is related to the pair correlation function
(\ref{g}) through
\begin{equation}
\label{chig}
\chi = \rho ( 1 + \int_{- \infty}^\infty dx \; (g(x) - \rho)).
\end{equation}
\section{Large scale dynamics of the ARAP}
\label{hydro}
\subsection{Hydrodynamic equation}
The average particle speed ${\overline v}$
in the ARAP is inversely proportional
to the density, hence the current
$j = \rho {\overline v}$ is independent of $\rho$.
The dynamics on the Euler scale $x \sim t$
is therefore trivial, and one expects a hydrodynamic equation of diffusion
type \cite{spohn}. A simple derivation will be given below.
Throughout this section we consider a general scaled jump length
distribution $\phi(r)$.
\subsubsection{Continuous time dynamics}
In the continuous time case the ensemble averaged
particle positions $X_i \equiv \langle x_i \rangle$
evolve according
to the {\em linear} equations
\begin{equation}
\label{Xi}
\frac{d X_i}{dt} = \mu_1 (X_{i+1} - X_i).
\end{equation}
This problem has been studied previously in the context of crystal growth
\cite{wed97}, and the procedure can be directly applied to the present
context.
To extract the long wavelength behavior,
we introduce a scaling parameter \cite{spohn,kipnis99} $\epsilon$ and a smooth
function $\xi(y,\tau)$ such that
\begin{equation}
\label{scale}
X_i(t) = \xi(\epsilon i, \epsilon t).
\end{equation}
Inserting this into (\ref{Xi}) and expanding to second order in $\epsilon$
we obtain
\begin{equation}
\label{hydro1}
\mu_1^{-1}
\frac{\partial \xi}{\partial \tau} = \frac{\partial \xi}{
\partial y} + \frac{\epsilon}{2} \frac{\partial^2 \xi}{\partial y^2}.
\end{equation}
In the scaling limit $\epsilon \to 0$ this becomes a first order
equation which describes simple translation to the left
\cite{ferrari98}.
Here we will however postpone to take the limit,
and first carry out a Lagrange
transformation \cite{rosenau95,wed97},
which relates the Lagrangian description in terms of
the particle positions $X_i(t)$ to the Eulerian evolution of the density
field. The local density $\rho$ near the position of particle $i$ is
estimated as $(X_{i+1} - X_i)^{-1}$, so using (\ref{scale}) we
have the relation
\begin{equation}
\label{rhoxi}
\rho(\xi(y,\tau), \tau) = \epsilon^{-1} (\partial \xi/\partial y)^{-1}.
\end{equation}
Differentiating this equation with respect to $\tau$ and using
the evolution equation (\ref{hydro1}) for $\xi(y,\tau)$ one obtains,
after some algebra,
\begin{equation}
\label{hydro2}
\frac{\partial \rho}{\partial t} =
\epsilon \frac{\partial \rho}{\partial \tau} =
\frac{\partial}{\partial x}
\left(\frac{\mu_1}{2 \rho^2} \right) \frac{\partial \rho}{\partial x}.
\end{equation}
The scaling factor $\epsilon$ cancels, and
the {\em collective} diffusion coefficient is identified to be
\begin{equation}
\label{Dcoll}
D_{\rm c}(\rho) = \frac{\mu_1}{2 \rho^2}.
\end{equation}
The $\rho^{-2}$-dependence is dictated by scale invariance: The typical
jump length in a region of density $\rho$ is ${\overline \delta} =
\mu_1/\rho$, and $D_{\rm c} \sim \gamma {\overline \delta}^2 \sim \rho^{-2}$.
\subsubsection{Discrete time dynamics}
For discrete parallel update eq.(\ref{Xi}) is replaced by
\begin{equation}
\label{Xidis}
X_i(t+1) - X_i(t) = \mu_1 [X_{i+1}(t) - X_i(t)].
\end{equation}
In the scaling limit $\epsilon \to 0$ this results in the same
coarse grained evolution equation (\ref{hydro1}), and thus also
the nonlinear diffusion equation (\ref{hydro2}) is the same as in
the continuous time case.
In the case of ordered sequential update
one has to take into account that the new position of particle $i$
is a random average of its old position and the {\em new} position
of particle $i+1$, hence
\begin{equation}
\label{Xiseq}
X_i(t+1) - X_i(t) = \mu_1 [X_{i+1}(t+1) - X_i(t)].
\end{equation}
Making the ansatz $X_i(t) = i/\rho + {\overline v} t$, we see that
the average particle speed is
\begin{equation}
\label{speedseq}
{\overline v} = \frac{\mu_1}{\rho(1-\mu_1)} > \frac{\mu_1}{\rho}.
\end{equation}
The speedup compared to continuous time and
parallel dynamics is due to
the decrease of the local density near the update site, see
\cite{raj98} for a discussion of similar effects in the asymmetric
exclusion process. For the derivation of the hydrodynamic equation
it is useful to incorporate the expected diffusive scaling from the
outset and replace (\ref{scale}) by
\begin{equation}
\label{scaleseq}
X_i(t) = \xi(\epsilon i, \epsilon^2 t).
\end{equation}
The expansion of (\ref{Xiseq}) to second order in $\epsilon$ then yields
\begin{equation}
\label{hydro1seq}
\left(
\frac{1-\mu_1}{\mu_1}
\right)
\frac{\partial \xi}{\partial \tau} = \epsilon^{-1} \frac{\partial \xi}{
\partial y} + \frac{1}{2} \frac{\partial^2 \xi}{\partial y^2}.
\end{equation}
As before, the drift term disappears under the Lagrange transformation
based on the relation (\ref{rhoxi}), and one obtains
\begin{equation}
\label{hydro2seq}
\frac{\partial \rho}{\partial t} =
\epsilon^2 \frac{\partial \rho}{\partial \tau} =
\frac{\partial}{\partial x}
\left(\frac{\mu_1}{2(1-\mu_1)\rho^2} \right) \frac{\partial \rho}{\partial x}.
\end{equation}
As far
as the hydrodynamics is concerned, the different types of dynamics
are seen to be equivalent up to a rescaling of time.
\subsection{Tracer diffusion}
Hydrodynamic equations of diffusion type are usually associated
with symmetric (unbiased) particle systems \cite{spohn}. In one
dimension the tracer diffusion coefficient in such systems
typically vanishes, and the mean square displacement of a tagged
particle grows subdiffusively as $t^{1/2}$ \cite{arratia83,vB83}. By contrast,
the biased random average process shows normal tracer diffusion when started
from a random initial condition and subdiffusive behavior when
the initial configuration is ordered \cite{ferrari98}. Here we
provide a compact derivation of the two cases and compute the
coefficient of the asymptotic law for different types of dynamics.
\subsubsection{Langevin approach for continuous time dynamics}
We start the system in an initial condition without long wavelength
fluctuations, such as $x_i(0) = i/\rho$, $i \in \Bbb{Z}$, and
denote the positional fluctuation of particle $i$ by
\begin{equation}
\label{zetai}
\zeta_i(t) = x_i(t) - \langle x_i \rangle = x_i(t) - x_i(0) -
{\overline v} t.
\end{equation}
For the purpose of extracting the long time behavior of fluctuations,
a Langevin approximation \cite{vankampen92}
to the dynamics of $\zeta_i$ is sufficient.
Thus we add a phenomenological noise term $\eta_i(t)$ to the
linear equation (\ref{Xi}),
\begin{equation}
\label{Langevin}
\frac{d \zeta_i}{dt} = \mu_1 (\zeta_{i+1} - \zeta_i) +
\eta_i.
\end{equation}
The noise is taken Gaussian with zero mean and covariance
\begin{equation}
\label{eta}
\langle \eta_i(t) \eta_j(t') \rangle = \sigma \delta_{ij} \delta(t - t').
\end{equation}
The noise strength $\sigma$ will eventually be matched to the variance
of particle headways.
Equation (\ref{Langevin}) is solved by introducing the Fourier transformed
fluctuations
\begin{equation}
\label{ft}
\hat \zeta(q,t) = \sum_{n \in \Bbb{Z}} e^{i q n} \zeta_n(t)
\end{equation}
with wave numbers $q$ in the first Brillouin zone $[-\pi, \pi]$, and
the corresponding Fourier transformed noise
\begin{equation}
\label{ftnoise}
\hat \eta(q,t) = \sum_{n \in \Bbb{Z}} e^{i q n} \eta_n(t)
\end{equation}
with covariance
\begin{equation}
\label{etaq}
\langle \hat \eta(q,t) \hat \eta(q',t') \rangle =
2 \pi \sigma \delta(q + q') \delta(t - t').
\end{equation}
The most general
quantity of interest is the variance of the displacement
between particle $i$ at time $t$ and particle $j$ at time $t'$.
By translational invariance this depends only on $n = i - j$ and
is given by the correlation function
\begin{equation}
\label{Gn}
G_n(t, t') = \langle (\zeta_0(t) - \zeta_n(t'))^2 \rangle.
\end{equation}
Inserting (\ref{ft}) into (\ref{Langevin}), solving the equation
for $\hat \zeta(q,t)$ and averaging over the noise according to
(\ref{etaq}) one arrives at the expression
$$
G_n(t,t') =
$$
\begin{equation}
\label{Gn2}
\frac{\sigma}{2 \pi} \int_{0}^\pi
\frac{dq}{\omega(q)}(2 - e^{-2 \omega t} - e^{-2 \omega t'} -
2 \cos[qn - \mu(q) T] (e^{-\omega \vert T \vert} - e^{-\omega T'}))
\end{equation}
with $\omega(q) = \mu_1(1 - \cos(q))$, $\mu(q) = \mu_1 \sin(q)$,
$T = t' - t$ and $T' = t' + t$.
The evaluation is straightforward in the relevant limiting cases.
Consider first the
variance of the headways at time $t = t'$. For large $t$ (\ref{Gn2}) yields
\begin{equation}
\label{G1}
G_1(t,t) \approx \frac{\sigma}{\mu_1} \left(
1 - \frac{1}{2 \sqrt{\pi \mu_1 t}}
\right).
\end{equation}
This allows us to identify
the noise strength $\sigma$ as
\begin{equation}
\label{sigmau}
\sigma = \mu_1 (\langle u^2 \rangle - \langle u \rangle^2),
\end{equation}
and explicitly demonstrates the $1/\sqrt{t}$-approach to the stationary
headway distribution alluded to in (\ref{finitetime}).
Next we focus on the dynamics of a single particle and
set $n=0$ in (\ref{Gn2}). If we fix the time increment $T = t' - t$
and let both $t$ and $t' \to \infty$, $G_0$ represents the mean square
displacement of a particle in the stationary regime. Evaluation of
(\ref{Gn2}) gives $G_0(t,t') \approx \sigma \vert T \vert$, which
shows that $\sigma$ is precisely the tracer diffusion coefficient
$D_{\rm tr}$. Combining this with (\ref{sigmau}) and (\ref{varu})
we obtain
\begin{equation}
\label{tracer}
D_{\rm tr} = \mu_1 (\langle u^2 \rangle - \langle u \rangle^2) =
\frac{\mu_1 \mu_2}{\rho^2(\mu_1 - \mu_2)}.
\end{equation}
In fact the first relation in
(\ref{tracer}) is easy to understand.
The linear equation (\ref{hydro1}) shows that fluctuations in the particle
positions drift backwards
in ``label space'' $y = \epsilon i$.
This translates the stationary distance fluctuations into
temporal fluctuations, with a conversion factor given by the drift
speed $\mu_1$.
As was mentioned already,
the existence of a nonvanishing tracer diffusion coefficient
for models with a hydrodynamic equation of diffusion type is unusual
in one dimension, since generically such an equation implies
symmetric particle jumps, in which case the tracer particle
displacement grows only subdiffusively
due to the single file constraint \cite{arratia83,vB83}.
Here $D_{\rm tr}$ is nonzero because the particles move, at speed
${\overline v}$, relative to the (stationary) density fluctuations.
A rigorous derivation of (\ref{tracer}) has recently been presented
by Sch\"utz \cite{schuetz99}.
Since the hydrodynamic equations in the two cases are identical,
the argument leading to first relation in (\ref{tracer})
carries over directly to discrete parallel update, and using
(\ref{varupar}) we conclude that the tracer diffusion coefficient
in this case is given by
\begin{equation}
\label{tracerpar}
D_{\rm tr}^{\rm par} = \frac{\mu_1(\mu_2 - \mu_1^2)}{\rho^2(\mu_1 - \mu_2)}.
\end{equation}
Similarly the expression
\begin{equation}
\label{tracerseq}
D_{\rm tr}^{\rm seq} =
\frac{\mu_1(\mu_2 - \mu_1^2)}{\rho^2(1-\mu_1)^2(\mu_1 - \mu_2)}.
\end{equation}
is obtained for the backward sequential case
by combining eqs.(\ref{varseq}) and (\ref{speedseq}).
Both (\ref{tracerpar}) and (\ref{tracerseq}) have been verified
numerically for the case of uniform $\phi(r)$.
Subdiffusive behavior is found in the
mean square displacement of a particle
starting from an initial configuration without long wavelength
disorder \cite{ferrari98}. This is given by (\ref{Gn2}) with
$n = t'= 0$. For large $t$ one obtains
\begin{equation}
\label{subdiff}
\langle \zeta_0^2 (t) \rangle = G_0(t,0) \approx \sigma
\sqrt{\frac{t}{\pi \mu_1}}
=
\frac{\mu_2}{\rho^2(\mu_1 - \mu_2)} \sqrt{\frac{\mu_1 t}{\pi}}.
\end{equation}
Using (\ref{chi}) and (\ref{Dcoll}) this is seen to agree with the
expression
\begin{equation}
\label{subdiff2}
\langle \zeta_0^2 (t) \rangle =
\sqrt{2/\pi} (\chi/\rho^2) \sqrt{D_{\rm c} t}
\end{equation}
derived from hydrodynamic arguments \cite{vB83}.
\subsubsection{The independent jump approximation}
For the totally asymmetric simple exclusion process it is known
\cite{spitzer,arratia83,ferrari96}
that the motion of a tagged particle in the
stationary state follows a Poisson process, and therefore the
tracer diffusion coefficient is simply equal to the mean speed
$1 - \rho$. Here we show that the expressions (\ref{tracer} -
\ref{tracerseq}) for the ARAP are consistent with a similar
independent jump picture.
Consider first the case of discrete time dynamics, where
the random choice of the jump length $\delta_i$ is the only
source of disorder, and therefore the tracer diffusion coefficient
for independent jumps is equal to the variance of $\delta_i$.
For parallel update $\delta_i$ is a
uniform random fraction of the particle headway $u_i$, hence
$
\langle \delta^2 \rangle - \langle \delta \rangle^2 = \mu_2
\langle u^2 \rangle - \mu_1^2/\rho^2$, which is easily checked to
coincide with (\ref{tracerpar}). For the backward sequential case
$\delta_i$ is a random fraction of the intermediate state headway
$u_i'$. Therefore, using eqs. (\ref{C'}), (\ref{meanu'}) and (\ref{varseq}),
\begin{equation}
\label{deltaseq}
\langle \delta^2 \rangle - \langle \delta \rangle^2 =
\mu_2 \langle (u')^2 \rangle - \mu_1^2 \langle u' \rangle^2 =
\frac{1}{(1-\mu_1)^2} \left(\frac{\mu_2 \langle u^2 \rangle}{
1 - 2 \mu_1 + \mu_2} - \frac{\mu_1^2}{\rho^2} \right),
\end{equation}
which is also found to agree with (\ref{tracerseq}).
In the continuous time case the random timing of jumps introduces an
additional source of disorder. It is natural to assume, in analogy
with the asymmetric exclusion process, that the
jumps occur according to a Poisson process. In the independent jump
approximation the particle displacement $\Delta x$ in time $t$ is then
given by
\begin{equation}
\label{deltax}
\Delta x (t) = \sum_{l=1}^{n(t)} \delta^{(l)}
\end{equation}
where $n(t)$ is a Poisson random variable with mean $t$ and the jump lengths
$\delta^{(l)}$ are independent random fractions of the
(independent, random) particle headways.
It is straightforward to show that the variance of $\Delta x$
is
\begin{equation}
\label{deltaxvar}
\langle (\Delta x)^2 \rangle -
\langle \Delta x \rangle^2 = \langle \delta^2 \rangle t,
\end{equation}
thus in this case the independent jump approximation to
$D_{\rm tr}$ is
$
\langle \delta^2 \rangle = \mu_2 \langle u^2 \rangle $
in agreement with (\ref{tracer}).
\section{Summary and outlook}
\label{open}
We have presented results for two classes of particle systems on
$\Bbb{R}$. The models considered in Section 2. have
Poisson invariant measures and nonlinear current-density relations
(see eqs.(\ref{juni}, \ref{j})). Time-dependent fluctuations in these
models are therefore expected \cite{bks85,ks91}
to be governed by the noisy Burgers
(or Kardar-Parisi-Zhang \cite{kpz86}) equation, which is not
amenable to simple analysis. By contrast, the asymmetric random
average processes introduced in
Section 3. have nontrivial invariant measures, but
the linearity of the jump rules allows for a detailed
study of dynamic properties (Section 4.).
A central result for the ARAP is the dependence of the
headway distribution (\ref{Gamma})
on the type of dynamics.
The idea that parallel update reduces density fluctuations
is familiar from earlier work on the asymmetric exclusion process
and related models for traffic flow, however in that case
the ordered sequential update produces the same (Bernoulli) invariant
measure as the continuous time process \cite{raj98}.
Our study suggests that the invariant measure of the continuous time
ARAP displays an unusual combination of features: The two-point headway
correlations factorize, the single particle
headway distribution appears to be exactly
given by the expression (\ref{Gamma})
derived under the assumption of pairwise independence,
but nevertheless the product measure (\ref{product})
is {\em not} invariant. Rajesh and
Majumdar have found the same features in a larger class of models which
interpolate between continuous time and parallel update \cite{rajesh}.
It would be most interesting to find a simple ``deformation'' of the product
measure which explains this behavior. The status of the product measure
assumption for the ordered sequential update also remains to be clarified.
The considerations of Section 3.2.2 indicate that it might be possible
to exactly reduce this case to that of parallel update, for which the
product measure is known to be invariant \cite{coppersmith96}.
Another interesting direction for future work is the introduction
of quenched random inhomogeneities.
In asymmetric
exclusion models it is possible to find invariant product measures
also in the presence of random jump rates associated with particles
\cite{benjamini96,kf,evans96,evans97}.
For the continuous time ARAP with jump rates $\gamma_i$ depending on the
particle label $i$ (the position $i$ in the stick representation)
preliminary numerical
simulations indicate that the product measures discussed above do not
persist. It is possible to write down a closed set of linear equations
for the two-point function $\langle u_i u_j \rangle$ which depends on the
disorder configuration $\{ \gamma_i \}$ and which should yield insight
into the emergence and nature of correlations.
Here we merely remark that, since the
mean speed of particle $i$ is
$\gamma_i \langle u_i \rangle$, stationarity implies
$
\langle u_i \rangle = C/\gamma_i
$
where the constant $C$ is fixed by the average headway. If the distribution
of jump rates is chosen such that $\langle 1/\gamma_i \rangle$ exists,
$C \to \langle 1/\gamma_i \rangle^{-1}$ in the limit
of infinite system size, and all headways have a finite mean.
Otherwise (e.g. for a uniform distribution of jump rates)
arbitrarily large headways will open in front of the slowest particles, similar to the
low density phase of asymmetric exclusion models with particlewise
disorder \cite{kf,evans96,evans97}.
\vspace{0.5cm}
{\bf Acknowledgements.} We are much indebted to
Bernard Derrida, Pablo Ferrari,
Herve Guiol, Satya Majumdar, Gunter Sch\"utz and Timo
Sepp\"al\"ainen for useful discussions
and remarks. This work was supported by DAAD and CAPES within the PROBRAL programme. J.K. acknowledges the hospitality of IME/USP,
S\~{a}o Paulo, and the Erwin Schr\"odinger Institute
for Mathematical Physics, Vienna, where part of the paper was written.
J.G. acknowledges the hospitality of Universit\"at GH
Essen during the early stages of the project.
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
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/**
* @file: react
* @author: Cuttle Cong
* @date: 2017/11/9
* @description:
*/
module.exports = require('../lib/lib/utils/Error').default
|
{
"redpajama_set_name": "RedPajamaGithub"
}
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La lechera (en neerlandés: Het melkmeisje o también De keukenmeid o De melkmeid) es uno de los cuadros más famosos del artista holandés Johannes Vermeer, cuya datación, como casi toda la obra de Vermeer, solo puede ser aproximada. Se trata de un óleo sobre lienzo de reducidas dimensiones, custodiado en el Rijksmuseum de Ámsterdam desde su adquisición en 1908.
Descripción de la obra
En la esquina de una habitación iluminada por una ventana se ve una mujer, probablemente una criada, haciendo su trabajo con la leche de cabra que estaba en una jarra en un recipiente de barro que descansa sobre una mesa. En esta, y en un primer plano, hay una cesta de mimbre, varios pedazos de pan y una jarra azulada.
El resto de la habitación es bastante austera; casi desnuda, vacía y sola. Apenas alberga más decoración que un sencillo cesto colgado de una de las paredes. Destacan los sencillos dibujos de los azulejos del fondo de la escena.
Análisis
Esta pintura consigue unir de un modo magistral dos conceptos que en principio parecen antagónicos: una sensación de monumentalidad y un gran sosiego. La criada se encuentra en su universo particular, en un interior casi desnudo, con la presencia de unos pocos objetos sencillos. El gesto inmortalizado por Vermeer tiene algo de estatua antigua; está de pie, bañada en luz. El pintor ha utilizado sus colores: el azul (realizado con un pigmento, el azul de ultramar, derivado del lapislázuli), y el amarillo, en sorprendente armonía.
Los objetos de la mesa constituyen, como tantas veces en Vermeer, una auténtica naturaleza muerta, donde el pintor hace gala de su excelente técnica para la plasmación de lo sencillo, consiguiendo resultados vivos y limpios.
Características estilísticas
Es una escena de la vida cotidiana, donde se presenta a una mujer trabajadora. En este caso Vermeer quería poner a la mujer como un ser fuerte y que da ejemplo. Este cuadro tiene realismo, teatralidad y dinamismo y está hecho con un contraste de luces y sombras. Es un óleo sobre lienzo y los trazos son finos.
Referencias
Bibliografía
BLANKERT, Albert; MONTIAS, John Michael; AILLAUD, Gilles. Vermeer. Obra completa. Ediciones Polígrafa. Pág. 183. ISBN 978-84-343-1121-3
RERAT, Alain. Vermeer. Editorial Debate ISBN 84-7444-972-39879867
Enlaces externos
La página del Rijksmuseum dedicada a esta obra
Análisis de La Lechera
Escenas de género
Colecciones del Rijksmuseum
Cuadros de los años 1650
Pinturas de comida y bebida
Leche en la cultura
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{
"redpajama_set_name": "RedPajamaWikipedia"
}
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One of the greatest benefits of living in San Antonio is the variety of "things" to see and do. In fact, there are so many San Antonio attractions and events on any given weekend that it can seem overwhelming to choose just one. In this series, all pressure is off! Ten fun things to do in San Antonio will be chosen each week to make researching for the next Friday celebration, date night, or family outing a little more simple. Specifically, during this time, we're here to make your holiday season more exciting with plenty of activities that are sure to spread holiday cheer!
You probably can't make it through the holiday season without watching the classic Christmas movie, Home Alone. This year, take it up a notch by reliving the iconic movie through the music of the San Antonio Symphony. The music will be performed live as you enjoy the movie in a whole new perspective. Taking place in the Majestic Theatre, you'll feel especially spirited getting dressed up for a movie night out. Don't miss out on this fun evening for the entire family!
Whatever you do for the holidays, the common ground among everyone is a delicious meal. This year, you can have a festive holiday brunch on Christmas morning at the beautiful Hotel Contessa. Traditional dishes will be served, as well as breakfast items and delicious desserts. If you're looking for a way to get out of cooking this Christmas, this brunch is the perfect excuse! Sip on hot chocolate, fill up on turkey, and enjoy the time spent with your family or friends. The hotel does recommend that you make a reservation ahead of time to ensure your seat.
The beautiful house, Steves Homstead, is located in the King William district of San Antonio. This year, the home is decorated with gorgeous authentic German Christmas decorations from over 100 years ago. You can stop by and look at the fresh greenery, traditional Christmas tree, and lovely lights anytime until January 6. Additionally, the home will have a Victorian style flair with its furniture and decorations. The King William area is beautiful at this time of year and after looking at The Steves Homestead, take some time to explore and walk around the other historic homes.
The San Antonio Museum of Art is pleased to share a collection of art from Carlos Merida. As an assistant to Diego Rivera, Merida lived and worked in Mexico City, making most of his work influenced by the Mexican culture, politics, and heritage. Mayan influences can be noticed in his work, as well as abstract art. The exhibit has been open since July and closes in January. Don't miss this exhibit while it is in town. From murals to small images, the large collection will have you studying art and contemplating the different messages that Merida portrays.
Merry Gentlemen is an original play, written by the San Antonio-based playwright Sheila Rinear. While the play has elements that are inspired by Dickens' A Christmas Carol, it is a modern Christmas play that is sure to leave you wanting more! Full of laughs and Christmas spirit, it is the perfect activity for this Christmas weekend. Grab a ticket to see this original production and you won't be sorry! Plan ahead and get any out of town family or guests a ticket as well.
Christmas is the time when as adults, we usually grow nostalgic for our favorite childhood memories and traditions. The classic holiday tale, A Charlie Brown Christmas is brought to life this season through the Magik Theatre troop. You'll love getting to see this cartoon favorite on the stage as beloved characters come to life. This is the perfect holiday event for children and family, young or old. The catchy music, memorable lines, and heart-warming moments will have you feeling the holiday spirit.
Celebrate the season and all of its holidays: Christmas, Hanukkah, Kwanzaa, and more! Paramour is opening its doors for a holiday celebration that is non-denominational and open to everyone. Holiday attire is encouraged and guests will have endless options of cocktails to choose from as they raise a glass and drink to the different traditions and religions of the season. Meet new people, socialize, and have a drink as a kick off to Christmas weekend. Don't forget to dress accordingly!
Ugly Christmas sweaters have become quite the trend this year. Whether it belonged to your grandma, is bedazzled, or has actual flashing lights, ugly Christmas sweaters come in a large variety. Dust yours off this season and head to 151 Saloon for an Ugly Sweater party. There will be judges to see whose sweater is the tackiest. Enjoy live music, drinks, dancing, and appetizers during the course of the evening. Don't miss out on a festive opportunity to get some wear out of that awesome sweater!
9. Cheer the Spurs to Victory!
While Tim Duncan may have played his last game, the spurs are just kicking off their season and need your support! Duncan was a crowd favorite and an amazing player; however, there are new team members and outstanding wins to watch! This Christmas, after finishing all of your family festivities, head down to the AT&T Center for a home game! The Spurs will be taking on the Chicago Bulls and need as many supporters as they can get. The season may be young, but the Spurs are ready to play and need their die-hard fans to cheer them to victory this Christmas!
Have your Christmas dinner out on the town and enjoy a delicious steak at Perry's Steakhouse at La Cantera this year. The beautiful restaurant has floor to ceiling wine storage, an amazing bar, and an "open concept" kitchen where you can see the chef prepare your food as you dine. Whether you want the famous filet mignon or the surf and turf pasta, Perry's is the perfect choice for holiday ambiance and exceptional food. Be sure to save room for the flaming bananas foster dessert or the rocky road bread pudding. Whatever your choice is for the evening, you won't regret going out!
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{
"redpajama_set_name": "RedPajamaC4"
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\section{Introduction}
Pulsars are highly magnetized rotating neutron stars,
which emit coherent beamed electromagnetic emission
at the expense of their rotational energy,
effectively slowing down the star. Their pulsed emission
varies from pulse to pulse. Absence of this pulsed emission
for several pulsar rotations was first noted by \cite{Backer1970}
in four pulsars. This phenomenon, called pulse nulling, has since
been seen in more than 100 pulsars to date
\citep{Wang2007,Biggs1992,Ritchings1976,Burke2012,gjk12,gjw14}.
The duration of nulls varies not only from one pulsar to other,
but also for a given pulsar. The percentage of pulses without
detectable emission is called nulling fraction (NF), which
ranges from few percent to more than 90 percent. While pulsars such as
PSR B0835$-$41 and B2021+51 show mostly single pulse nulls
\citep{gjk12}, no emission is seen in PSR B0826$-$34 for
15000 pulses \citep{dll+79}. Previously discovered intermittent
pulsars such as PSR B1931+24 \citep{klo+06}, PSR J1841$-$0500
\citep{crc+12}, PSR J1832$+$0029 \citep{llm+12}, PSR J1107$-$5907 \citep{yws+14},
PSR J1910+0517 and J1929+1357 \citep{lsf+16}, where no pulsed emission
is observed from few days to several years, can also
be considered as neutron stars with an extreme form of nulling.
Interestingly, the rate of slowdown ($\dot{\nu}$) is reduced
in these intermittent pulsars during their inactive phase
suggesting changes in torque \citep{klo+06,Lyne2009}. Changes
in magnetosphere state were proposed to explain the inactive phase
in these pulsars as this steers the emission beam away
from the line of site in addition to a change in slowdown
rate \citep{Timokhin2010}. Hence, some form of rotation rate
irregularities are expected in pulsars, which fall
in between classical nullers and intermittent pulsars.
In recent years, there is a growing class of such intermediate
nullers with nulling time scales of a few hours. Good examples
are PSRs like B0823+26 \citep{Young2012},
PSR J1717$-$4054 \citep{Johnston1992}, PSR J1634$-$5107
\citep{OBrien2006} and PSR J1853+0505 \citep{Young2015}.
Frequent emission of
long nulls results in high NFs ($> 70\%$) for all these
pulsars. Unlike the intermittent pulsars, where the change
in $\dot{\nu}$ can be estimated during the absence of emission
for several days, it is difficult to estimate the slowdown
rates for intermediate nullers as the duration of null phase
is not long enough to see a significant difference through
pulsar timing.
In this paper, detailed single pulse observations of
PSR B1706$-$16 (PSR J1709$-$1640), discovered in one of the initial
Molonglo {\bf surveys} \citep{Large1969}, are presented. It is like
any other normal pulsar with a period of 653 ms and
dispersion measure (DM) of 24.8733 pc/cm$^3$ (Table \ref{psrparam}). While no nulling
was reported even 4 decades after its discovery,
it was identified as nuller in a single pulse follow
up study of High Time Resolution Universe
survey \citep{Burke2012}. Its single pulse studies
are also relatively undocumented. The pulsar also shows
an interesting red noise distribution of the timing
residuals as reported by \cite{Baykal1999}. In our
study, PSR B1706$-$16 has shown long nulls ($>$ 2 hrs)
about once in a week making this a unique addition
to the class of intermediate nullers. In Section
\ref{observations}, the observations are described.
The description of analysis and results is in
Section \ref{analysis} followed by discussions
and conclusions in Section \ref{discussion} and
Section \ref{conclusion} respectively.
\begin{table*}
\caption{The known parameters for PSR B1706$-$16}
\label{psrparam}
\centering
\begin{tabular}{|l|c|c|c|c|c|c|c}
\hline
JNAME & Right Ascension & Declination &Period & DM & S$_{400 MHz}$ & Surface Magnetic field & Characteristic Age \\
& (h:m:s) & (d:m:s) &(s) &(pc\,cm$^{-3}$)& (mJy ) & (10$^{12}$ G) & (Myr) \\
\hline
J1709$-$1640&17:09:26.44&-16:40:57.73&0.653054&24.89&47&2.05 & 1.64 \\
\hline
\end{tabular}
\end{table*}
\begin{figure}
\includegraphics[width=1.0\columnwidth]{nullingplot.pdf}
\centering
\caption{Histogram showing the date of observations,
duration of observations (bars in the histogram) and
corresponding nulling fractions. The dotted line represents
the nulling fraction at each epoch and the solid line
represents the cumulative nulling fraction with
error bars. The ordinate on the left represents {\bf the}
nulling fraction and that on the right represents
duration of observations at each epoch.}
\label{nulling}
\end{figure}
\section{Observations}
\label{observations}
All the 325 MHz observations were carried out using the
Ooty Radio Telescope [ORT,\cite{Swarup1971}], which is
a single dish cylindrical parabolic reflector with
linearly polarized dipole feed. Data were recorded
by using the newly commissioned pulsar receiver
PONDER \citep{Naidu2015}. The frequency of observations
was 326.5 MHz with a bandwidth of 16 MHz.
The ORT has a capability to track PSR
B1706$-$16 for about 9.5 hours. A total of 15 long
duration observations were carried out for this
pulsar. The duration of observations varied from
2 hours to 9.5 hours (see Figure \ref{nulling}).
All the data were recorded after incoherent
dedispersion at the pulsar's nominal DM of
24.873 pc/cm$^{-3}$ and timeseries was provided
in SIGPROC\footnote{http://sigproc.sourceforge.net}
format. Further, daily short observations were
carried out over a period of four months to
check for any timing irregularities and to obtain
an updated timing solutions for the analysis.
In addition, simultaneous multi-frequency
observations were carried out using the
Giant Meterwave Radio Telescope (GMRT) \citep[]{sak+91}
and the ORT for this pulsar. The data at
the GMRT were obtained using the GMRT
Software Backend (GSB) \citep{Roy2010} in a
phased array mode, where closely spaced 15
antennas were phased to form a single beam
in the sky. The GMRT observations were carried
out at 610 MHz with a bandwidth of 33 MHz.
The data obtained with the GMRT were channelized
(512 channels) total intensity data sampled at
122 $\mu$s. These data were further analyzed
offline using the SIGPROC pulsar analysis software.
\section{Analysis and Results}
\label{analysis}
\subsection{Single pulse sequences and long nulls}
\label{analsp}
The dedispersed data from the ORT observations
was folded using the predictors generated with
the TEMPO2\footnote{http://tempo2.sourceforge.net/}
software to produce the single pulse sequences as
shown in the Figure \ref{singlepulses}. Figure
\ref{singlepulses}(a) shows the typical sequence
obtained in 11 of the 15 long observing sessions.
The pulsar is usually in an active state with
short nulls of null duration not more than 150
periods, which are easy to identify as the
single pulses can be seen with high signal
to noise ratio (S/N). Figure \ref{singlepulses}(b), (c) and (d)
show 3 out of 4 observing sessions, where long nulls
were observed, with each long null lasting between
1 hour to 4.5 hours. This nulling behaviour is
rare, with the pulsar exhibiting two different
phases, an Active Phase (AP), with pulsed
emission seen in most periods, interspersed by short nulls,
and an Inactive Phase (IP), where it switches
off for few hours with no pulsations at all,
similar to other intermediate nulling pulsars
\citep{Young2015}. However, unlike the other
intermediate nullers, the pulsar is in AP most
of the time and rarely switches to the IP.
\begin{figure*}
\includegraphics[width=1.0\textwidth]{smoothed_plots.pdf}
\caption{Single pulse plots of PSR B1706$-$16 for four
different observations. The top panel in each figure is
the single pulse sequence and the bottom panel is the
integrated profile. The ordinate on the left-hand axis
in each pulse sequence plot denotes the pulse number,
whereas the ordinate on the right-hand axis gives
time in minutes. Figure (a) shows the typical single pulses
observed with out any significant long nulls.
Figures (b), (c) and (d) shows the long nulls observed
at three different epochs.}
\label{singlepulses}
\end{figure*}
The nulling analysis was performed using the methods
devised by \cite{Ritchings1976,gjk12}. These methods, used for estimating
the NF and identifying null and burst pulses are briefly described below
\citep[For details see][]{gjk12}. We visually identified two
windows of equal width in the average profile, namely, a window with
phase bins, where the pulsed emission is present (on-pulse window)
and another window, away from the pulsed emission (off-pulse window).
Two sequences of energies, integrated over on-pulse and off-pulse
windows for each pulse, were formed after normalizing with the
mean pulse energy. The NF, which represents the percentage of
pulses with on-pulse energy distribution similar to that of
off-pulse energy, was estimated from the distributions
of on-pulse and off-pulse energies
\citep[See][for details]{gjk12}.
A threshold energy separating the zero energy excess
in the on-pulse distribution was used to separate null and burst
pulses. An overlap in the peak
of zero energy excess and the burst energy in the on-pulse distribution
can lead to a mis-identification of nulled (burst) pulses.
A total of approximately 100 hours of data were
obtained on B1706$-$16 in 15 separate long
observing sessions. The NF was estimated for
each observation and is shown in Figure \ref{nulling}.
The bars in the plot represent the duration of
observations indicated in hours on the right
side of the plot. The dotted line represents
the variation of the NF for each observation
and the solid line represents the cumulative NF
calculated for the total duration of the observations.
NF varies from 15 \% to 70 \% between observations.
This variation is mainly due to presence of long nulls
in some observations. The four long nulls detected
during our observations are listed in the
Table \ref{nullvalues}. The relatively large NF for
the other observations is due to the presence of
several 5 to 20 minute nulls during the AP,
where the NF is estimated to be 15$\pm$2 \%.
The cumulative NF, considering nulls in AP as
well as IP from all observations, is calculated
to be 31$\pm$2 \%. It is to be noted that the
pulsar rarely switches to the IP, which makes
it difficult to get an accurate NF from short
observations. Indeed, the nulling fraction was never reported
in the previous studies of this pulsar.
\begin{table}
\caption{The four epochs, where long nulls were
observed in PSR B1706$-$16. In three of these epochs,
the null was not bounded by burst pulses on both
sides. Hence, only a lower limit on the null
duration is listed}
\label{nullvalues}
\centering
\begin{tabular}{|l|c|r|}
\hline
MJD of & Length of null& Duration of null\\
observations & (Rotations) & (hours) \\
\hline
56515.5 & $\ge$ 6393 & $\ge$1.16 \\
56519.4 & $\ge$ 6194 & $\ge$1.12 \\
56520.5 & 15825 & 2.87 \\
56535.5 & $\ge$ 25850 & $\ge$4.68 \\
\hline
\end{tabular}
\end{table}
\begin{figure}
\centering
\includegraphics[width=\columnwidth]{simul.pdf}
\caption{Single pulse sequences, observed during the
simultaneous observations of PSR B1706$-$16 using the
ORT at 326.5 MHZ and the GMRT at 610 MHz}
\label{simul}
\end{figure}
\begin{figure}
\centering
\includegraphics[width=1\columnwidth]{energy.pdf}
\caption{Normalized energy in the on-pulse window
during 325/610 simultaneous observations shown
in the Figure \ref{simul}. The on-pulse energy at 610
MHz is shown by the blue solid lines, whereas the red lines
show the on-pulse energy at 326.5 MHz. The energy integrated
over off-pulse window is also shown by solid black line for
comparison and identification of nulls.}
\label{energy}
\end{figure}
\subsection{Is nulling broadband in PSR B1706$-$16?}
\label{bbnull}
The single pulses in PSR B1706$-$06 were observed
simultaneously with the ORT at 326.5 MHz and the GMRT
at 610.0 MHz for a duration of 1 hour (Figure \ref{simul}).
A short stretch of these observations, shown in this plot,
clearly shows the burst and null pulses. All the nulls,
including those lasting a single period
(not seen in the figure), are observed to be simultaneous.
Likewise, the transition from the burst emission to
null (and vice versa) is also observed
to be simultaneous at both the frequencies.
Figure \ref{energy} shows the on-pulse energy sequence
for both the observations for a stretch of 500 periods.
The sharp dips in the on-pulse energy in this figure
represent the nulls. Again, it is evident that the
nulls occur at both frequencies simultaneously. Results from a more
quantitative analysis confirming this conclusion
are presented below.
Null and burst pulses were identified after
a careful visual examination of single pulse sequences
at both the frequencies. A one-bit sequence, representing
the null and burst pulses (0 and 1 respectively), was derived
from both the observations for 2844 pulses, excluding
all the periods affected by radio frequency interference.
These one-bit sequences
for both the observations of the pulsar were compared
using contingency table analysis, where a 2 X 2 table is
formed from the two one-bit sequences, giving the statistics
of nulls and bursts in the two simultaneous one-bit sequences
(Table \ref{stats}.) In this analysis,
the strength of correlation is computed using a $\phi$-test
and uncertainty tests \citep{press}. The estimated Cramer-V
was 0.97 indicating a high significance of correlation,
while uncertainty coefficient was estimated to be 0.9,
consistent with simultaneity of nulling pattern across
frequencies. Moreover,
the NF calculated for the ORT and
the GMRT observations are 14$\pm$3 \% and 12$\pm$1 \%
respectively. During the simultaneous observations,
no long null was observed. The null and burst length
histograms at both the frequencies
(Figure \ref{nullbursthist}) were compared using a
Kolmogorov-Smirnov test, which rejected, at a high
significance ($\ge$96.9\%), the hypothesis that
these two distributions are different. Clearly,
nulling is simultaneous at both frequencies, similar
to broadband behaviour of nulling demonstrated in
a previous studies \citep{Gajjar2014,njm+17}, increasing
the sample of such pulsars.
\begin{figure}
\centering
\includegraphics[width=\columnwidth]{simul_kstest.pdf}
\caption{Null and burst length histograms of the simultaneous observations.}
\label{nullbursthist}
\end{figure}
\begin{table}
\caption{Statistics of null and burst pulses in the
simultaneous 326.5 and 610 MHz observations of PSR B1706$-$16.}
\label{stats}
\centering
\begin{tabular}{|l|c|c|}
\hline
& Null @ 325 MHz& Burst @ 325 MHz\\
\hline
Null @ 610 MHz & 332 & 2 \\
\hline
Burst @ 610 MHz & 14 & 2496 \\
\hline
\end{tabular}
\end{table}
\begin{figure*}
\includegraphics[width=\textwidth]{modes_f.pdf}
\caption{Profile modes of PSR B1706$-$16. Top left plot
shows the profile in mode A and corresponding single
pulse sequence, which is boxcar averaged with a window
size of 20 pulses. The corresponding S2DFS plot
is shown in bottom. Top middle plot is profile of
mode B with corresponding boxcar averaged pulse sequence
and corresponding S2DFS plots at the bottom. The right top
plot shows an observed mode change in the pulsar. The pulsar
is in mode A in the first 5500 pulses and switches to mode
B beyond. This manifests as a drifting signature appearing
after 5500 pulses in the corresponding S2DFS
plots in the bottom. }
\label{modes}
\end{figure*}
\subsection{Average profile of PSR B1706$-$16}
\label{avprofanal}
The 610 MHz GMRT observations of PSR B1706$-$16 show
a single component (see Figure \ref{simul}), which
according to the EPN pulsar data
base\footnote{http://www.jb.man.ac.uk/research/pulsar/Resources/epn/}
shows a steep linear polarization position angle swing
and a circular polarization sense reversal at the center
of the component. Thus, this component appears to be
a core component \citep{Rankin1983}. The corresponding
profile at 326.5 MHz in the simultaneous ORT observations
shows two components. This extra component is absent from
archival profile in EPN pulsar data base, which suggests
that we may have observed a profile mode change in our
simultaneous ORT observations. The EPN archival profile at
408 MHz shows circular polarization sense reversal
towards the trailing dominant component. Hence, it
appears that the extra leading component is a conal
component. Subpulse drift, manifested as
a fluctuation periodicity, is expected in this
leading component as this is usually seen in
conal components \citep{Rankin1983}. Indeed, we see
evidence for this, as discussed in Section \ref{profmodanal},
alongwith changes in average profile.
\subsection{Profile modes of PSR B1706$-$16}
\label{profmodanal}
As mentioned above, this pulsar seems to exhibit two
different profile modes at 325 MHz. In mode A, a single
component profile is seen, while a two component profile
is observed in mode B (Figure \ref{modes}). One way to
check if the two profiles are not similar is to treat them
as histograms and perform a Kolmogorov-Smirnov shape comparison test
described in \cite{p08}. Results are shown in Table \ref{kstest},
which imply that the profiles for the two modes are distinct from each
other. The two modes are characterized by distinct
fluctuation properties. As can be seen in Figure
\ref{modes}, mode B is accompanied by subpulse
drifting, which is associated with the leading component
in mode B, while no significant drift feature is detected
in mode A (Figure \ref{modes}). The rightmost plots in
Figure \ref{modes} shows such Sliding window two
dimensional fluctuation spectra \citep[S2DFS,][]{ssw,njm+17}
plot, where this transition from mode A to mode B is
clearly visible at about 5500 periods.
\begin{table}
\caption{Results of Kolmogorov-Smirnov shape comparison test
\citep{p08} between the profiles shown in Figure \ref{modes}.
A significance close to 1 indicates that the two profiles are similar
and vice-versa}
\label{kstest}
\centering
\begin{tabular}{|c|l|c|}
\hline
No & profiles & Significance \\
\hline
1 & mode A and mode B & 0.13 \\
2 & before null and after null & 0.23\\
3 & mode A and before null & 0.99\\
4 & mode A and after null & 0.34\\
5 & mode B and before null & 0.25\\
6 & mode B and after null & 0.94 \\
\hline
\end{tabular}
\end{table}
It should be noted that the ORT is a single polarization
instrument. If a pulsar is highly polarized and has
small rotation measure (RM), the profile shape can change
due to rotation of polarization angle (PA) with respect
to the telescope feed. PSR B1706$-$16 has a small degree
of linear polarization and circular polarization
[11 and 6 \% \citep{gl98}]. It has a small
RM of $- 1.3~rad/m^2$ \citep{hl87} resulting in a
swing in polarization angle across 16 MHz band of
about 6 degrees. Thus, the effect of change in PA
cannot produce as significant profile change as seen
in Figure \ref{modes} as most of the emission is
unpolarized. Moreover, it is evident from S2DFS in
Figure \ref{modes} that the fluctuation properties of
profile also change when a profile mode change
takes place with variable but clear drifting
seen in the mode B. Thus, the profile change
between the two modes in PSR B1706$-$16 is not due to
instrumental effects, but is real. The two profile
modes accompanied by changes in drift mode for
this pulsar are being reported for the first
time in this paper.
\begin{figure*}
\centering
\includegraphics[width=\textwidth]{profiles.pdf}
\caption{Plot on the left shows profiles for 4 different
sections of data, 1) Average profile after integrating
all the observations (blue), 2) Average profile after
integrating 10 pulses just before every null for 15
long observations with about 7500 nulls (green), 3)
Average profile after integrating 10 pulses just
after every null for the 15 long observations (red),
4) Average null profile for all the nulled pulses (black).
Plot on right shows average null profiles for nulls with
different null duration 1) null profile obtained
after averaging nulls (black). 2) Null profile obtained after
averaging all nulls which are less that 10 periods (blue).
3) Null profile obtained after averaging all the intermediate nulls
($>$ 10 periods) shown in green. 4) Null profile obtained after
averaging the 4 long nulls in Table \ref{nullvalues} (red).}
\label{on_off_profiles}
\end{figure*}
\subsection{Average profile before and after null and during nulls}
\label{banullprofanal}
The visual examination of the emission from PSR B1706$-$16
before a typical null suggests that the emission seems
to diminish gradually (Figure \ref{energy}). The mean
pulse intensity just before the null is less than that
for the full data suggesting that the pulsar switches
off to the null state gradually. This behaviour appears
similar to PSR J1752+2359, where differences in profiles
between last pulse before a null and the one after the null
were reported by \cite{gjw14}. Hence, we investigated the
emission before and after nulls. We selected 10 pulses
before and after every null. The left plot in Figure
\ref{on_off_profiles} shows the profile just after
the null (red) and before the null (green)
along with the total average profile (blue) and
the null profile (cyan) for all 15 observations.
This behaviour is observed in all individual data
sets of PSR B1706$-$16. The pulses just after the
null were observed to be of much higher intensity
than those observed on an average in this pulsar.
Moreover, the before null profile seems to be similar
to mode A and profile just after the null is similar to
mode B. An analysis using K-S shape comparison test also confirms
this conclusion (See Table \ref{kstest}).
Nulls are usually defined as pulses with no detectable
emission. However, this does not seem to be strictly
true for all nulls in PSR B1706$-$16. The right plot in
the Figure \ref{on_off_profiles} shows the average
profiles for nulls with various null duration
using all observations. The average null profile
for all nulls shows a weak pulse, which is probably
due to nulls with duration less than one hour (blue
and green). On the other hand, no emission is seen
for long nulls ($>$ 1 hour). The ratio of total
energy in average profile to null profile is
about $\sim$ 1420. To the best of our knowledge,
this is the largest drop in the pulsed emission
during the nulls ever reported
[see \cite {vj97, gjk12, Gajjar2014}].
\begin{figure*}
\centering
\includegraphics[width=1\textwidth]{on_off_length.pdf}
\caption{Burst length (left plot) and null length (right plot)
distributions.}
\label{on_off_length}
\end{figure*}
\subsection{Distribution of burst and null duration}
\label{bndistanal}
\subsubsection{Burst duration distribution}
\label{bldistanal}
The distribution of the duration for which the pulsar
is in the on state (burst) is shown in Figure
\ref{on_off_length}. This distribution is exponential
(black line fit), indicating that the pulsar does not
have memory about the burst duration after the
previous null. The slight excess of the short
bursts may be due to mis-identification of a few
short nulls as bursts. As discussed in Section
\ref{analsp}, such mis-identification results from the
overlap between the zero excess and the burst part of
on-pulse energy distributions.
\subsubsection{Null duration distribution}
\label{nldistanal}
The distribution of the null duration of the pulsar,
shown in the right plot of the Figure
\ref{on_off_length}, is bimodal.
Short nulls of few rotations
significantly out number the longer nulls
extending to tens of rotations. This is
partially due to mis-identification of weak low S/N
burst pulses as nulls, which could
also be the most probable explanation for the
weak profile seen after averaging all nulls of duration less
than 10 periods
(Figure \ref{on_off_profiles}).
However, very few pulses are likely to be
mislabeled with most of these being single period
nulls. Thus, the bi-modality appears to be genuine.
A similar behavior was reported for PSR B0031$-$07
\citep{Vivekanand1995}
\section{Discussion}
\label{discussion}
Our observations show that PSR B1706$-$16 has a NF of
15$\pm$2\% during the AP and shows sporadically
very long nulls. The longest null duration
identified is at least 4.68 hours. Its overall
NF is 31$\pm$2\%. Simultaneous two frequency
observations show that nulling in this pulsar
is broadband. We have, for the first time,
identified two profile modes in this pulsar,
which are accompanied by difference in the
fluctuation properties of single pulses. While the
emission during the long nulls drops by a factor of
1420, weak emission is seen in an average profile
of short nulls. We also report for the first
time a change in profile before and after nulls,
with the profile before the null similar to mode
A profile and that after a null similar to mode B.
Finally, a bimodal distribution for null length is
reported.
This interesting nulling behaviour is reported for
the first time for this pulsar. The variability in
NF from one observing session to other (Figure
\ref{nulling}) implies that NF, at best, provides a
qualitative description of nulling and is not an appropriate parameter
to look for correlation with other pulsar parameters
as was done in some previous studies [e.g. see \cite{Biggs1992}].
Nulling is likely to be better characterized by
the nulling pattern or null length distribution, as
was also shown by \cite{gjk12}. This motivates
longer than usual 1 hour observations to determine
these distributions before a comparison with pulse
period, magnetic field or spin-down energy loss
can be done.
The simultaneity of nulling at 326.5 MHz and 610 MHz, seen in
PSR B1706$-$06, is consistent with the previous multi-frequency
studies of three pulsars, where the nulling was reported
to be broadband \citep{Gajjar2014}. Broadly, there are two
different explanation for pulse nulling. The first class
of models invokes intrinsic changes in the magnetospheric
physics to explain nulling, whereas the second class
invokes geometry as explained in \cite{Gajjar2014}. Our result
further strengthens the possibility that intrinsic changes
are responsible for nulling rather than
the geometrical effects, such as traverses of the
line-of-sight through the gaps between the sub
beams (pseudo-nulls).
The difference in pulse profile shape with different
drift modes has been reported in a couple of previous
studies in PSR B0031$-$07 and B2319+60
\citep{wf81,vj97,jos13b}. Similar behaviour in PSR B1706$-$06
further strengthens the possibility that the profile
mode changes alongwith the nulls are probably related to
changes in pulsar magnetosphere.
Most pulsars show exponential or log-normal distributions
for their null duration. The notable exceptions are
PSR B0031$-$07 \citep{Vivekanand1995}, J1717$-$4054
\citep{Kerr2014}, J1649+2533 and
B2310+42 \citep{wwr+12}, where bimodal nulling distributions
have been reported. PSR B1706$-$06 also shows a bimodal
distribution representing short as well as long nulls. Together
with the on-state (or more precisely two different on-states
if the two profile modes are taken into account), this represents
a multi-state Markov process for such state switching as
proposed recently \citep{gjk12,c13}, which could arise
from a combination of modulation of ion and electron
currents within a range of extreme vacuum and
force-free state \citep{lst12b,lst12a}.
The non-white distribution in the timing analysis
of the PSR B1706$-$16 \citep{Baykal1999,Hobbs2010}
suggests that this pulsar exhibits varying slowdown
rates ($\dot{\nu}$) with time. If the pulsar undergoes
changes in slowdown rate during the nulls with
random null duration, it manifests as timing noise
in the residuals for the pulsar. We also see
evidence for such timing noise in our data. Such variable
$\dot{\nu}$ was attributed to switching between
distinct magnetospheric states for intermittent pulsars
\citep{Timokhin2010}. While the intermediate nature of nulls
in PSR B1706$-$16 does not permit establishing this clearly,
a higher timing noise is certainly expected in this model.
Classical nullers are known to have off-state
ranging upto several minutes in contrast to
intermittent pulsars (which null for several days) and
Rotating Radio transients (RRATs, which show
isolated single period bursts separated by several
periods). Long nulls reported by us place PSR
B1706$-$16 in the growing class of intermediate
nullers which lie between the classical nullers
and intermittent pulsars. The intermediate nullers and
intermittent pulsars are a useful way to probe the
effect of magnetospheric changes on pulsar timing
\citep{lhk+10}. While the latter require a several
years to study their timing behaviour, intermediate
nullers provide a tool for such studies in a smaller
time-scale.
It is useful to compare and contrast the nulling
behaviour of PSR B1706$-$06 with that of other known
intermediate nullers. While the NF for PSR B0823+26 in its
AP is estimated to be 15$\pm$1 \% \citep{Sobey2015}, estimates
for other intermediate nullers range from 67$\pm$8 \% in PSR J1853+0505
to
90$\pm$5 \% in
PSR J1634$-$5107 \citep{Young2015}. It may
be noted that these may be overestimates as the NF were
mostly inferred from non-detection/detection statistics in these
pulsars. Thus, the NF for PSR B1706$-$06 is much smaller in contrast
with majority of intermediate nuller. Bimodal null
distribution was reported for PSR J1717$-$4054
\citep{Kerr2014}, while it is not well determined
for other intermediate nuller. Thus, more detailed observations
of other intermediate nuller are needed to check if this property
is shared by this class as a whole. PSRs B0823$+$26,
J1634$-$5107 and PSR J1853$+$0505 all show weak emission
during longer nulls \citep{Young2015}, whereas we do not
detect any weak emission in PSR B1706$-$16 after
integrating all long nulls, although weak emission is
seen for shorter nulls in AP. It may be noted that no
weak emission was detected in the PSR J1717$-$4054
\citep{Kerr2014,Young2015}. Lastly, high timing noise
or non-white timing residuals have been noted for
PSR J1634$-$5107 and PSR J1717$-$4054, while such
behaviour is not very apparent in PSR J1853+0505
and B0823+26. The constraints on time scales
for IP for the latter two pulsars
are not very stringent at the moment and short
IP time-scale may explain this difference.
Longer (8$-$10 hrs) and more frequent
observations (with a cadence of 1$-$2 days) of an enhanced sample
of intermediate nullers is therefore motivated to investigate
a correlation between timing noise and long nulls
in these pulsars. Future
multi-beam telescopes, such as the SKA, MWA and LOFAR, will be very useful
in such studies as they will not only provide higher
sensitivity for unambiguous classifications of nulls,
but also a commensal way of observing with other pulsar
programs, such as search and timing, due to availability
of multiple beams.
\section{Conclusions}
\label{conclusion}
This paper presents the results from the nulling analysis of over 100 hours data on the PSR B1706$-$16 observed using the ORT. This pulsar is observed in 15 long observations with the duration of observations varying from 2 to 7.5 hours. It exhibits long nulls (null duration of $>$ 2 hours) suggesting that it is an intermediate nuller. Typical intermediate nullers have large nulling fractions ($>$ 70 \%) due to the frequent long nulls. However, long nulls are seen infrequently, typically once in a week, in this pulsar making it a unique addition to the intermediate nullers list. The over all nulling fraction is estimated to be $31\pm2$ \%. It shows a bimodal distribution for null duration. The pulsar's integrated profile is observed to switch from one mode to another with different fluctuation properties in the two modes.
\section*{Acknowledgments}
We thank the staff of the Ooty Radio Telescope and the Giant Meterwave
Radio Telescope for making these observations possible. Both these
telescopes are operated by National Centre for Radio Astrophysics (TIFR).
This work made use of PONDER backend, built with TIFR XII plan grants
12P0714 and 12P0716. We like to thank the anonymous referee for his/her useful
comments and suggestions. BCJ, PKM and MAK acknowledge support for this work
from DST-SERB grant EMR/2015/000515.
\bibliographystyle{mnras}
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 4,716
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Beautiful You: Moving to Uni? My 5 Tips For Freshers!
Moving to Uni? My 5 Tips For Freshers!
This week's video on my YouTube channel is about my tips that I would give to freshers for their first year at university. Seen as that is going up on there I thought that I would write a blog post alongside it for any of you guys that are about to start your first years!
I can't really talk when it comes to this because I didn't do anything during freshers fortnight but that's because I have anxiety when it comes to going out and I'd rather avoid that! However, many of my flat mates that did go out and participate in the activities had a better experience than I did, I'm not saying I didn't enjoy myself because I had an amazing time but you get more of a well rounded experience if you participate!
When you move in I know it is quite an intermediating and nervous time but you have to talk to your flat mates, your going to be living with these people for a whole year so it's not like you can't not talk to each other! It will be no time at all before you all are the best of friends, trust me I didn't think so but now some of my flat mates from last year are some of my bestest friends!
Buying shopping for yourself and cooking by yourself can be expensive and boring so like me and my flat mates decided that we would cook together most weekends! I really got on with my flat mates so it was easy for us but just make the effort with them and they will make the effort with you. It definitely makes it feel more homely when you eat all together.
Obviously this is going to be a hard one because you have only just met you new flat mates and you have to live with them for the next year so you want to fit in but a text now and again isn't hard. You are going to go home from time to time and you'll want people at home to go and see and for your friend to come and see you at uni because at the end of the day your friends from home have know you longer!
I don't know if this will apply to all of you but when I moved to uni we lived in a flat where we all had our own bedroom and bathroom but then we shared a kitchen/lounge. If it is the same then I would definitely say keep your door open when you can because having it shut all the time makes you seem like you don't want to be included. Buy a door stop and wedge your door open and it makes you seem more approachable, people will still knock on your door before they come in but it makes it more homely. Someone maybe feeling a little down and all they need is a friendly face and a chat so it could make all the difference!
I hope these tips are useful to some of you if you are moving of to uni, I know I will definitely be taking on board some of my own advice this year! If you are moving I would love if you would leave a comment below telling me what university your going to and I hope you all have an amazing time! I have also made a video on this over on my YouTube channel and there is a link at the bottom of this blog post if you want to go over, watch and subscribe! I will see you all tomorrow for my last blog post of me blogging everyday and we will be back to the normal schedule on Monday!
I am going to move next month! So excited!!
even though i finished uni last august, this is such a helpful post for new uni people!
I need to link this to my best friend who's suffering with freshers flu! She's not coping well! I'm going to uni next year so I'll need to revise these before I go!
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{
"redpajama_set_name": "RedPajamaC4"
}
| 2,522
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const gani = require('../../');
module.exports = gani.ocon([
gani.uipartial
], o => {
o.type = 'uidropdown';
o.getvnode = (sess, cfg, graph, node, subj) => {
const { label, select, option, span } = o.h(o, node),
{ disabled,
labelprimary,
labelsecondary,
labeltertiary,
labelhint,
isemptyvalue } = subj;
return (
label('.:ui', {
for: o.docencodekey(node.get('key'))
}, [
labelprimary &&
span('.:ui-label-primary', labelprimary),
labelsecondary &&
span('.:ui-label-secondary', labelsecondary),
select('.:ui-select#:key', {
name: node.get('name'),
disabled: disabled ? 'disabled' : ''
}, [
isemptyvalue &&
option('.:ui-select-option', {
value: ''
}, labelhint || '---'),
o.mapparts(node, false, ({ isactive, partkey, labelprimary }) => (
option('.:ui-select-option', {
value: partkey,
selected: isactive ? 'selected' : ''
}, labelprimary)
))
]),
labeltertiary &&
span('.:ui-label-tertiary', labeltertiary)
])
);
};
o.onchange = (sess, cfg, graph, node) =>
o.getlivekeys(sess, cfg, graph, node, (err, keyarr) => (
o.getpartkeysasdata(sess, cfg, graph, node, keyarr, (err, graph, value) => (
gani.publish.subj(sess, cfg, node.get('key'), {
value
}, (err, graph) => (
o.postevactionopt(sess, cfg, graph, node, 'onchange')))
))
));
o.setactive = (sess, cfg, graph, node, partkey) => {
let elem = o.gEBId(node);
[].map.call(elem.options, option => {
option.selected = option.value === partkey;
});
};
o.onsubj = (sess, cfg, graph, node, prev, { value }) => {
o.getkeysaspartarr(sess, cfg, graph, node, [ value ], (err, [ newpartial ]) => {
if (err) return console.error(err);
o.setactive(sess, cfg, graph, node, newpartial && newpartial.partkey);
});
};
o.getlivekeys = (sess, cfg, graph, node, fn) => {
let elem = o.gEBId(node);
fn(null, [ elem.value || '' ]);
};
});
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 623
|
Q: JFileChooser check if really a File is selected? I noticed the following: If I start my application and go to open a file, then the JFileChooser appears. I tried writing a filename and I did not get an error, even though the file does not exist. What I get is a file path.
JFileChooser fileChooser = new JFileChooser();
int values = fileChooser.showOpenDialog(null);
File file = fileChooser.getSelectedFile();
if (values == JFileChooser.APPROVE_OPTION) {
System.out.println(file.getPath());
} else if (values == JFileChooser.CANCEL_OPTION) {
System.out.println("No file is selected");
} else if (values == JFileChooser.ERROR_OPTION) {
System.out.println("Error!");
} else if (file == null) {
System.out.println("No File is chosen");
}
I hope you guys can help. I hope my question is clear because I have problems with explanations and with the English language.
A: you can check if a file exists with: file.exists(). Already answered in another post.
The creation of a file object does not garuantee that a file at your path does exist.
...
if (values == JFileChooser.APPROVE_OPTION) {
if(file.exists()){
System.out.println(file.getPath());
}else{
System.out.println("file does not exist");
}
}
...
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 513
|
Q: Copying the file from docker container to host when we are running the docker image I want to copy one file from a Docker container to localhost.
I know the command is
docker cp <container id>:<container path> <host path>
but this command will only work when you are outside the container.
I want to copy the file from Docker container while its image is being run: what would I can include in an entry point script which copies the file from the Docker container to the host machine?
A: Docker container instances are being isolated from the docker hosts. Container instances are not supposed to access data on the docker hosts. So that's why only the opposite direction is supposed to work.
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 1,112
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JoCo election commissioner hired to U.S. election commission
Nov 4, 2015 | News |
The United States Election Assistance Commission (EAC) announced the hiring of a new executive director and general counsel for the agency earlier this week.
Brian D. Newby is the agency's new executive director. Newby served as the Election Commissioner in Johnson County, Kan., for the last 11 years.
"It's difficult to leave a job I've loved for 11 years, but to say I'm thrilled to be going to the EAC is an understatement," Newby said.
In his role as Johnson County Election Commissioner, Newby oversaw more than 60 local, state and federal elections. He was first appointed to the position by former Secretary of State Ron Thornburgh, a Republican, in 2005. He was reappointed in 2010 by then Secretary of State Chris Biggs, making Newby the only election commissioner in state history to be appointed by both Republican and Democratic Secretaries of State. He was most recently reappointed in 2014 by Secretary of State Kris Kobach.
"Brian has been a tremendous leader for Johnson County and the state of Kansas," Kobach said. "I'm grateful for his many years of service to Kansas and wish him the very best in his new endeavor."
Newby serves on the Election Center Legislative Committee, is a member of the International Association of Clerks, Recorders, and Election Officials, The California Association of Voting Officials, The National Association of Voting Officials, and is a former board member of the National Association of County Records, Election Officials, and Clerks. Newby holds a Master's Degree in Public Administration from the University of Missouri-Kansas City and a bachelor's degree in communications studies from the same school.
In addition, the EAC announced the hiring of Cliff Tatum of Washington, DC as its new General Counsel.
"Brian and Cliff are leaders and innovators in the election community. We are thrilled to add their passion, creativity and management experience to the EAC as we push the agency forward to fulfill its mission under HAVA," EAC Chair Christy McCormick said.
EAC Vice-Chair Tom Hicks added, "Having Brian and Cliff as our leadership team is a tremendous positive for the EAC. These are two of the most well respected election officials in the country. This is an important step as we continue to establish the EAC as a national resource on elections."
"I can't wait to be part of the energy that is building at the EAC and be part of high-powered, responsive resource to the election administration community in this important presidential election cycle and in the years ahead," Newby added.
The EAC is an independent bipartisan commission created by the Help America Vote Act (HAVA) of 2002. HAVA was passed by the U.S. Congress to make sweeping reforms to the nation's voting process, address improvements to voting systems and voter access that were identified following the 2000 election, and to provide federal funding to states for new voting equipment. HAVA mandates that the EAC test and certify voting equipment, maintain the National Voter Registration form, conduct research, and administer a national clearinghouse on elections that includes shared practices, information for voters and other resources to improve elections. More information is available at EAC.gov.
PreviousNOV. 4 CLASSIFIEDS
NextWMS Mustangs open wrestling season well
Residents participate in Earth Day events
Blazers finish well at league events
Prairie Punisher set for July 12 at local park
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 5,703
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Q: Getting PayloadTooLargeError and Cors error simultaneously while sending a large file data through post request from client to server I am working on a project which has an upload file feature. The text data from this file is to be send to the backend Node js server through axios post request and then uploaded to the database.
While using a smaller file (around 4 kb), it is working fine. But when I upload a large sized file (~10000 kb), I am getting two error simultaneously.
CORS error at the client side (React Js).
PayloadTooLargeError at the server side (Node Js).
I tried using the soluyion given in the post: Error: request entity too large, but it is not working.
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 4,863
|
\section*{Many-body Hamiltonian for polar molecules in two dimensions}
We consider an ensemble of polar molecules confined
in a plane perpendicular to an external electromagnetic field that sets the quantisation axis $z$,
Fig.~\ref{fig:Schematic}(a). The rotational spectrum of each molecule can be indexed by the rotational
angular momentum $N$ and its projection $M$ onto the $z$ axis, Fig.~\ref{fig:Schematic}(b).
Throughout the paper we set $\hbar=k_{\mathrm{B}}=1$, and measure all lengths in units of the lattice constant $a$,
unless specified otherwise.
We assume that most molecules are in the ground rotational state ($N=0$),
and only the lowest-energy states,
those with $N=0$ and $N=1$, participate in the dynamics. The $N=1$ states are separated
from $N=0$ by a large gap $2B_N$ ($\sim$ GHz) which significantly exceeds the characteristic
interaction energy $E_{\mathrm{d}}$ ($\sim$ kHz). In addition,
the $\ket{1,0}$ state is separated from the $\ket{1,\pm1}$ states
by an energy scale $E_1$, $E_{\mathrm{d}}\ll E_1\ll B_N$, e.g., due to the presence of external electric field ${\bf E}$;
more details on realising such level structure will be given below.
Large lifetimes of the $N=1$ states ($\gtrsim10\,$s) allow us to neglect relaxation between the $N=1$ and $N=0$
manifolds.
The Hamiltonian for the system of polar molecules can be written as
\begin{align}
\hat{H}&=\sum_{i}\hat{H}_0\left(\mathbf{r}_i\right)+\frac{1}{2}\sum_{i\ne j}\hat{H}_{\mathrm{dip}}\left(\hat{\mathbf{d}}_i,\hat{\mathbf{d}}_j,\mathbf{r}_i-\mathbf{r}_j\right)\, ,
\end{align}
where the sums run over all particles in the system and $\hat{H}_0\left(\mathbf{r}_i\right)=\hat{\mathbf{p}}_i^2/2m+U(\mathbf{r}_i)+\hat{H}_{\mathrm{rot}}$ is the single-particle Hamiltonian. Here, $m$ is the mass of a molecule,
$U(\mathbf{r})$ is the external periodic potential, and $\hat{H}_{\mathrm{rot}}=B_N\hat{{\bf N}}^2-E_1 \hat{N}_z^2$ is the Hamiltonian of the internal degrees of freedom giving the spectrum in Fig.~\ref{fig:Schematic}(b). The dipole-dipole interaction between two molecules $i$ and $j$ with dipole moments
$\hat{{\bf d}}_i$ and $\hat{{\bf d}}_j$ and separated by vector ${\bf R}_{ij}$, Fig.~\ref{fig:Schematic}(a), is given by
\begin{align}
\hat{H}_{\mathrm{dip}}(\hat{{\bf d}}_i,\hat{{\bf d}}_j,{\bf R}_{ij})=\frac{\hat{{\bf d}}_i\cdot \hat{{\bf d}}_j}{R_{i,j}^3}-3\frac{(\hat{{\bf d}}_i\cdot {\bf R}_{ij})(\hat{{\bf d}}_j\cdot {\bf R}_{ij})}{R_{i,j}^5},
\label{DipHam}
\end{align}
Introducing polar coordinates $\mathbf{R}_{i,j}=({R}_{i,j},\phi_{ij})$, the interaction Hamiltonian \eqref{DipHam}
can be decomposed as
\begin{align}
&\hat{H}_{\mathrm{dip}}(\hat{\mathbf{d}}_i,\hat{\mathbf{d}}_j,{\bf R}_{ij})=\hat{H}^{q=0}_{ij}+
\hat{H}_{ij}^{q=\pm2},
\\
&\hat{H}^{q=0}_{ij}=
\frac{1}{R_{ij}^3}\left(\frac{\hat{d}_i^{-1}\hat{d}_j^{1}+\hat{d}_i^{1}\hat{d}_j^{-1}}{2}+{\hat{d}_i^z \hat{d}_j^z}\right),
\label{eq:q=0}
\\ &\hat{H}^{q=\pm2}_{ij}=-\frac{3}{2}\frac{1}{R_{ij}^3}\left(\hat{d}_i^{1}\hat{d}_j^{1}e^{-2i\phi_{ij}}
+\hat{d}_i^{-1}\hat{d}_j^{-1}e^{2i\phi_{ij}}\right),
\label{eq:q=pm2}
\end{align} where $\hat{d}^{\pm1}_i=\mp(\hat{d}^x_i\pm id_i^y)/\sqrt{2}$ are spherical components of the dipole operator of molecule $i$.
The operator $\hat{H}^{q=0}_{ij}$, Eq.~(\ref{eq:q=0}), conserves both the total
internal angular momentum of the interacting molecule and its $z$-component.
As shown in Fig.~\ref{fig:Schematic}(c), $\hat{H}^{q=0}_{ij}$
exchanges the states $|1,\pm1\rangle$ and $|0,0\rangle$ of two molecules while preserving $M_i+M_j$. Such ``spin-exchange'' dipolar interactions have been observed in recent
experiments on polar molecules \cite{Yan_Moses}, Rydberg atoms\cite{Weidemueller,PhysRevA.70.042703}, and magnetic atoms \cite{Laburthe}.
In contrast, the operator $\hat{H}^{q=\pm2}_{ij} $ transfers angular momentum between the internal and external orbital motion of the molecules, while preserving the total projection onto the $z$ axis.
Namely, the operator $\hat{d}_i^{-1}\hat{d}_j^{-1}$
decreases the internal angular momentum by $2$, while $e^{2i\phi_{ij}}$ increases the orbital angular momentum
of a molecule by 2, thus preserving the total angular momentum, cf. Fig.~\ref{fig:Schematic}(d). As we shall show, this transfer of angular momentum is responsible for the generation of the effective SOC of the elementary excitations.
\begin{figure}[h]
\centering
\includegraphics[width=1.0\columnwidth]{Fig1}
\caption{\label{fig:Schematic} {\bf The setup.} (a) Geometry: molecules confined in the $xy$ plane,
perpendicular to the quantisation axis $z$; $(R_{ij};\phi_{ij})$
are the polar coordinates of the vector $\mathbf{R}_{ij}$ joining molecules $i$ and $j$.
(b) Rotational levels of a molecule. The small icons mimic
the angular distributions of the rotational states and are coloured according to their phase, the arrows showing
the direction of the phase winding in the $|1,\pm1\rangle$ states.
(c)-(d) Processes involving dipolar exchange interactions.
In (c) molecules exchange rotational levels while preserving both their total internal angular
momentum and its $z$-component.
In (d) the internal angular momentum decreases by 2, while the orbital momentum of the two molecules
increases by 2.
}
\end{figure}
\section*{Phenomenological analysis}
\label{PhenomAnal}
Let us assume that almost all the molecules are initially in their lowest rotational level $|0,0\rangle$
and are in a spatially uniform, not necessarily equilibrium state, but with a relaxation time
sufficiently long to be considered stationary. We then suppose that this state is slightly perturbed
by a resonant microwave pulse which excites a small number of molecules from $|0,0\rangle$ to $|1,\pm 1\rangle$.
In what follows we show that the density and angular momentum dynamics of the $|1,\pm1\rangle$ rotational levels after such excitation is equivalent to that of an ideal gas of spin $1/2$ chiral quasiparticles (chirons).
The emergence of the excitations can be phenomenologically understood as follows.
Due to the translational invariance of the Hamiltonian of the system, the (quasi)momentum ${\bf k}$
(in the presence of an optical lattice),
with polar coordinates $(k,\phi_{\bf k})$, Fig.~\ref{fig:Dispersion}(a), is a
good quantum number.
In the long-wave limit ${\bf k}\rightarrow0$, there is a degeneracy
between the excitations carrying molecules in the rotational states $\ket{\uparrow}\equiv\ket{1,1}$
and $\ket{\downarrow}\equiv\ket{1,-1}$ due to the symmetry
with respect to inverting the dipole moment. Note that the other excited rotational states
are separated from $\ket{\uparrow}$ and $\ket{\downarrow}$ by large energy gaps and do not participate in the dynamics.
This allows us to consider a reduced space $\{\ket{\uparrow},\ket{\downarrow}\}$
of rotational states. Each of these states can be obtained from the other by acting with the operators $(\hat{{d}}^{\pm1})^2$.
Hence, the most general form of the excitation Hamiltonian in the reduced space reads
\begin{eqnarray}
{\hat{h}}({\bf k})=
\left(
\begin{array}{cc}
\xi_{\bf k} & \alpha(k)(k^{-})^2 \\
\alpha(k)(k^{+})^2 & \xi_{\bf k}
\end{array}
\right),
\label{SpinOrbitHam}
\end{eqnarray}
where $k^{\pm}=k_x\pm ik_y$, and
$\alpha(k)$ and $\xi_{\bf k}$ are some functions of $k$.
The Hamiltonian in Eq.~(\ref{SpinOrbitHam}) describes quasiparticles with a two-branch spectrum with energies
\begin{eqnarray}
E_\pm({\bf k})=\xi_{\bf k}\pm \alpha(k)k^2\, ,
\label{ChironSpectra}
\end{eqnarray}
corresponding to the eigenstates
\begin{eqnarray}
\psi_\pm({\bf k})=\left(\pm e^{-i\phi_{\bf k}}\quad e^{i\phi_{\bf k}}\right)^T/\sqrt{2}
\end{eqnarray}
respectively,
and a Berry phase of $2\pi$. In a system with an inversion-symmetric Hamiltonian, ${\hat{h}}({\bf k})={\hat{h}}(-{\bf k})$, the Berry phase
can be defined\cite{BPdefinition} modulo $4\pi$ as an integral ${\it \Phi}_{\mathrm{BP}}=
-2i\int_C\bra{{\it \Psi}_{\bf q}^\pm}{\boldsymbol \nabla}_{\bf q}\ket{{\it \Psi}_{\bf q}^\pm}d{\bf q}$
along a contour $C$ connecting two points ${\bf k}$ and $-{\bf k}$ in momentum space.
Thus, the Berry phase $2\pi$ of chirons is {\it non-trivial}.
As is necessary in a system with time-reversal symmetry\cite{BlountBook,HaldaneBP}, ${\it \Phi}_{\mathrm{BP}}$ is a multiple of $\pi$.
Let us notice that if $\alpha(k)=const$ the Hamiltonian~(\ref{SpinOrbitHam})
coincides with that of the low-energy excitations in bilayer graphene~\cite{McCannFalko:bilayer,Novoselov}
in the wavelength limit ${\bf k}\rightarrow0$.
In the next section we demonstrate that such Hamiltonian is indeed realised in the case of weak interactions
between the molecules.
\section*{Microscopic calculation of the Hamiltonian}
In the previous section we have shown phenomenologically that the effective Hamiltonian of long-wave
excitations in a system of polar molecules has the form given by Eq.~(\ref{SpinOrbitHam}). In what immediately
follows, we demonstrate that the Hamiltonian can be explicitly evaluated microscopically in the two opposite limits:
when the kinetic energy is negligible compared to the characteristic interaction strength
and when the interactions are small compared to the kinetic energy. While the first regime can be achieved by pinning the molecules in a deep optical lattice and is thus relevant for current experiments with reactive molecules \cite{Yan_Moses}, the second regime could be in principle realised in the future with molecules which are non-reactive and less susceptible to {\"u}berresonant processes~\cite{Mayle_13}.
To address the first limit,
we consider molecules in a deep, unit-filled square optical lattice. In this setting, the translational degrees of freedom are frozen and dynamics occurs only in the internal degrees of freedom. The dynamics can be mapped to that of a gas of bosons with spin $\sigma\in\left\{\uparrow,\downarrow\right\}$ and long-range hopping. The vacuum corresponds to all molecules being in the $|0,0\rangle$ state. The {effective} Hamiltonian describing the rotational excitations can be expressed in terms of the bosonic creation $\hat{b}_{\mathbf{i}\sigma}^{\dagger}$ and annihilation $\hat{b}_{\mathbf{i}\sigma}$ operators of rotational excitations with $\sigma$ character at lattice site $\mathbf{i}=\{i_x,i_y\}$, as
\begin{align}
\nonumber \hat{H}&=-{J_0}\sum_{\mathbf{i}\ne \mathbf{j};\sigma}\frac{\hat{b}_{\mathbf{i}\sigma}^{\dagger}\hat{b}_{\mathbf{j}\sigma}}{ |{\bf r}_\mathbf{i}-{\bf r}_\mathbf{j}|^3}-{J_2}\sum_{\mathbf{i}\ne \mathbf{j}}\frac{e^{-2i\phi_{ij}}\hat{b}_{\mathbf{i}\uparrow}^{\dagger}\hat{b}_{\mathbf{j}\downarrow}+
e^{2i\phi_{ij}}\hat{b}_{\mathbf{i}\downarrow}^{\dagger}\hat{b}_{\mathbf{j}\uparrow}}{|{\bf r}_\mathbf{i}-{\bf r}_\mathbf{j}|^3}\\
&\label{eq:HCHami}
\end{align} Here,
the hopping constants $J_0$ and $J_2$ are determined by dipole matrix elements. We work in the hard core limit, which restricts the occupation number on each site to $0$ or $1$. The hard-core constraint encapsulates that there is at most one molecule per lattice site and each molecule can harbour at most one $N=1$ rotational excitation. Physically, the hard-core constraint can stem either from strong elastic interactions or rapid inelastic loss rates, e.~g. two-body chemical losses, at short range~\cite{Yan_Moses,Zeno}.
\begin{figure}[t]
\centering
\includegraphics[width=0.55\columnwidth]{Fig2}
\caption{\label{fig:Dispersion} {\bf Chiron states.} (a) Chiron state on the Bloch sphere.
(b) Chiron dispersion in a deep optical lattice
in the first Brillouin zone for $J_2=3J_0$. The lower (upper) surface corresponds to $E_+({\bf k})$ [$E_-({\bf k})$].
The base of the plot shows the orientation of the $E_+$ branch Bloch vector in the equatorial plane.
}
\end{figure}
The dispersions of a single rotational excitation are given by
\begin{align}
\label{eq:lattenergy}E_{\pm}\left(\mathbf{k}\right)&=-J_0F^{(0)}\left(\mathbf{k}\right) \mp {J_2} |F^{(2)}\left(\mathbf{k}\right)|,
\end{align} and shown in Fig.~\ref{fig:Dispersion}. Here, $F^{(n)}(\mathbf{k})=\sum_{\mathbf{j}\ne 0}\exp(-i \mathbf{k}\cdot {\bf r}_\mathbf{j}+ i n\phi_{\mathbf{j}})|{\bf r}_\mathbf{j}|^{-3}$ with ${\bf r}_\mathbf{j}$ a vector connecting sites in the square lattice and $\phi_{\mathbf{j}}$ the polar angle of ${\bf r}_\mathbf{j}$.
The phase $\varphi_{\mathbf{k}}$ of $F^{(2)}$, {\it i.e.} $F^{(2)}(\mathbf{k})=|F^{(2)}\left(\mathbf{k}\right)| e^{i \varphi_{\mathbf{k}}}$ determines the polar angle of the Bloch vector, Fig.~\ref{fig:Dispersion}(a).
In the long-wave limit, ${\bf k}\rightarrow0$, we obtain in accordance with Eq.~\eqref{SpinOrbitHam} that
$\varphi_{\mathbf{k}}\approx2\phi_{\mathbf{k}}$, $\xi_{\mathbf{k}}/J_0\approx A +2\pi/k$ and $\alpha\left(k\right)=2\pi J_2/(3k)$, with $A\approx 9.03$. For general ratios $J_2/J_0$, both branches have a conical dispersion for small $k$. For the case $J_2=3J_0$, as results from the geometry of Fig.~\ref{fig:Schematic}(a), there is a cancellation of the linear $k$ component in the $E_{+}$ branch. This leads to a locally flat dispersion $E_{+}(\mathbf{k})/J_0\approx A+\mathcal{O}(k^2)$ and a conical dispersion $E_{-}(\mathbf{k})/J_0\approx A +4\pi k+\mathcal{O}(k^2)$, Fig.~\ref{fig:Dispersion}(b).
\begin{figure*}[t]
\centering
\includegraphics[width=1.8\columnwidth]{Fig3}
\caption{\label{fig:ChironDynam} {\bf Chiron spin dynamics. } Spatial distributions of the spin coherences in a gas of polar
molecules after applying a focused resonant pulse.
(a) Density profile of $\hat{S}_x$ in a weakly-interacting Fermi liquid.
(b) Density profile of $\hat{S}_x$ in a deep optical lattice.
(c) The density of $\hat{S}_x$, analogous to (b) but for a lattice of 10\% filling, averaged over disorder realisations (overbar denotes disorder average). The peak magnitude of $\bar{\rho}_{\hat{S}_x}$ is reduced by a factor of $\sim 20$ compared to unit filling, but the symmetry is the same. }
\end{figure*}
In the case of {\it a sufficiently shallow optical lattice} or {\it weak interactions},
the kinetic energy of the molecules can dominate over the mean interaction energy.
In this case, the dynamics can be analysed perturbatively in the interactions.
By explicitly evaluating the Hamiltonian of the excitations, the details of which are provided in the Supplementary Methods,
we reproduce Eq.~(\ref{SpinOrbitHam}) with the off-diagonal entry
\begin{eqnarray}
{\hat{h}}_{\downarrow\uparrow}({\bf k})=\pm\frac{\pi|{\bf d}|^2}{6}\int_{\bf q}\: \frac{(q^+)^2}{q} f_{00}({\bf q}+{\bf k}),
\label{AlphaPert}
\end{eqnarray}
where the upper and the lower signs apply to bosonic and fermionic molecules respectively;
$f_{00}({\bf q})$ is the distribution function of the molecules in the $\ket{0,0}$ state. It is
assumed to be stationary and independent of the molecule position but it is not restricted to be in thermal equilibrium;
$q^+=q_x+ iq_y$, and $\int_{\bf q}\ldots=\int(2\pi)^{-2}\ldots d^2{\bf q}$. Due to the smallness of the interactions, the diagonal elements of the matrix in Eq. (\ref{SpinOrbitHam})
are close to the kinetic energy of a single molecule and are only slightly modified by the interactions,
$\xi_{\bf k}\approx k^2(2m)^{-1}\left[1+\mathcal{O}(|{\bf d}|^2)\right]$. This calculation is performed explicitly in the Supplementary Methods.
The long-time dynamics is dominated by small momenta. For an isotropic distribution
function $f_{00}({\bf q})=f_{00}(q)$,
from Eq.~(\ref{AlphaPert}) we find the value of the spin-orbital coupling in the limit ${\bf k}\rightarrow0$ to be
\begin{eqnarray}
\label{eq:alphaIso} \alpha=\pm\frac{|{\bf d}|^2}{32}\int_0^{\infty}
f_{00}(q) \:dq.
\end{eqnarray}
For a Fermi liquid of fermionic molecules at zero temperature [$f_{00}(q)=\theta(k_{\mathrm{F}}-q)$] Eq.~\eqref{eq:alphaIso} yields
\begin{equation}
\alpha=-|{\bf d}|^2 k_{\mathrm{F}}/32,
\end{equation}
where $k_{\mathrm{F}}$ is the Fermi momentum. At sufficiently high temperatures $T\gg n/m$, where $n$ is the density of the molecules
(per nuclear spin), the distribution function is close to that of a Boltzmann gas,
$f_{00}(q)\approx\frac{2\pi n}{mT}e^{-\frac{q^2}{2mT}}$, and
\begin{equation}
\alpha=\pm\frac{\pi\sqrt{\pi}|{\bf d}|^2 n}{ 16\sqrt{ 2 m T}}.
\end{equation}
For cold atoms in a quadratic trapping potential, the density of the molecules depends on temperature
as $n(T)\propto T^{-1}$, resulting in the temperature dependency of the SOC
$\alpha(T)\propto T^{-3/2}$.
\section*{Chirality manifestations : Spin and density dynamics}
The chirality of the excitations can be observed in the dynamics of the spin-1/2 operator, ${\bf S}=\{\hat{S}_x,{\hat S}_y,{\hat S}_z\}$, in the reduced space of the rotational levels $\ket{\uparrow}$ and $\ket{\downarrow}$. Let us assume that a short laser pulse excites
a group of molecules in a small region of characteristic
size $\Lambda$ around ${\bf r}=0$, $\ket{0,0}\rightarrow\ket{\uparrow}$
(the results of this paper can be easily generalised to include more general
excitation protocols, $\ket{0,0}\rightarrow A_{\uparrow}\ket{\uparrow }+A_{\downarrow}\ket{\downarrow}$). The internal state $|\uparrow\rangle$ corresponds to excitation by light with right-circular polarisation $x+iy$, and has a definite phase winding, as shown in Fig.~\ref{fig:Schematic}(b). Hence, for a spatially isotropic distribution of excitations, the laser polarisation is what determines the spatial phase pattern emerging during the dynamics.
For sufficiently small $\Lambda$ chirons leave the excited region quickly, reaching sufficiently low density,
so that interactions between them can be neglected,
and their dynamics is described by the kinetic equation for free particles, see Methods.
In principle, chiron-chiron interactions may be important for hard-core particles in a deep optical lattice
in the beginning of the dynamics, which, however, will not affect the results qualitatively.
In the limit of pinned molecules
we additionally check that chiron-chiron interactions can be neglected by numerically
simulating the dynamics of two excitations, see the Supplementary Methods and Supplementary Figures 2,3.
\begin{figure*}[t]
\centering
\includegraphics[width=1.5\columnwidth]{Fig4}
\caption{\label{fig:DenDynamics} {\bf Chiron density dynamics. } Densities of $|\uparrow\rangle$ (panel (a)) and $|\downarrow\rangle$ (panel (b)). The vortex structure is clearly visible in the $|\downarrow\rangle$ density. The density dip $n_{\downarrow}\left(\mathbf{r},t\right)\propto r^4$ in the centre of the vortex structure is a manifestation of the Berry phase $2\pi$. (c) Dynamics of the total spin populations in a deep optical lattice. The population of the two spin components undergo a single oscillation before monotonically approaching 1/2. }
\end{figure*}
The chiral nature of the excitations is clearly visible in the density of $\hat{S}_x$
\begin{equation}
\rho_{\hat S_x}({\bf r},t)=
\frac{1}{2}\sum_\pm
\pm\int_{\bf q}
f_{\uparrow\uparrow}\left[{\bf r}-t{\bf v}_\pm({\bf q}),{\bf q}\right]
\cos(2\phi_{\bf q}),
\label{rhoS}
\end{equation}
where $f_{\uparrow\uparrow}({\bf r},{\bf q})$ is the distribution function
of the molecules in the $\ket{\uparrow}$ state at time $t=0$, ${\bf v}_\pm({\bf q})$ are the velocities of the
two chiron branches, and $\phi_{{\bf q}}$ is the polar angle of the vector ${\bf q}$.
In the long-wave limit (see Eq.~(\ref{ChironSpectra}))
\begin{equation}
{\bf v}_\pm({\bf q})={\boldsymbol \nabla}_{\bf q}\xi\pm\left(2\alpha(q){\bf q}+q^2{\boldsymbol \nabla}_{\bf q}\alpha(q) \right).
\end{equation}
Eq.~(\ref{rhoS}) describes the spin distribution at sufficiently long times,
when it is dominated by long-wave
chirons ($q\ll a^{-1}$). In this limit the phase factor $\cos(2\phi_{\bf q})$ originates from the off-diagonal element of Eq. \ref{SpinOrbitHam}. To account for arbitrary-momenta excitations, $2\phi_{\bf q}$ in Eq.~(\ref{rhoS})
has to be replaced by the polar angle $\varphi_{\bf q}$ of a chiron state on the Bloch sphere, Fig.~\ref{fig:Dispersion}(a). For the small $\Lambda$ under consideration, the distribution has a $d$-wave symmetry
$\rho_{\hat S_x}\propto \cos(2\phi)$ at long times, Figs.~\ref{fig:ChironDynam}(a-b),
which is a manifestation of the non-trivial Berry phase $2\pi$ of the excitations. The radial distribution of the spin component $\rho_{\hat S_x}$ after applying a narrow laser
pulse depends on the molecular statistics, interaction strength, optical lattice depth, etc., while its
$d$-wave symmetry is universal, being a consequence of the
Berry phase $2\pi$.
The spatial distribution of the spin coherences can be particularly easily understood in the case
of a Fermi liquid (fermionic molecules at low temperatures) with weak interactions.
In this case, the excitations propagate at the maximal speed $v_+(k_{\mathrm{F}})$, $k_{\mathrm{F}}$ being the Fermi momentum.
At a distance $r$ away from the initial excitation pulse, the spin distribution remains unaltered
until time $t=r/v_+(k_{\mathrm{F}})$ when it is reached by the quickest branch of chirons with the
angular distribution of spins $\rho_{{\hat S}_x}\propto\cos(2\phi)$.
At a slightly later moment of
time $t=r/v_-(k_{\mathrm{F}})$ the same point is reached by a wave of slower chirons with opposite spin,
after which the spin density remains very small. The resulting distribution
is shown in Fig.~\ref{fig:ChironDynam}(a).
In the case of a deep optical lattice, the branch of chirons with the dispersion $E_-({\bf q})$
is significantly faster than the other branch, leading to a quick spatial
separation of the two branches, Fig.~\ref{fig:ChironDynam}(b), after applying the laser pulse.
The outer circular density front corresponds to the faster chirons, which propagate at a nearly
constant speed, while the more complex
inner pattern comes from the slower branch of chirons. Despite different dispersions of the chirons,
the angular distribution of the spin is again $\propto\cos(2\phi)$.
Because of the SOC spin is not conserved
and the total numbers of molecules
in the rotational states $\ket{\uparrow}$ and $\ket{\downarrow}$,
{\small\begin{align}
&N_{\uparrow}(t)
\int d{\bf r}\int_{\bf q} f_{\uparrow\uparrow}({\bf r},{\bf q})\cos^2[{(E_+({\bf q})-E_-({\bf q}))t}/{2}],
\\
&N_{\downarrow}(t)
\int d{\bf r}\int_{\bf q} f_{\uparrow\uparrow}({\bf r},{\bf q})\sin^2[{(E_+({\bf q})-E_-({\bf q}))t}/{2}],
\end{align}}
are time-dependent.
At long times $t\rightarrow\infty$,
both $N_\uparrow(t)$ and $N_\downarrow(t)$
saturate at a half of the number $N_{\mathrm{ex}}$ of the initially excited molecules,
Fig.~\ref{fig:DenDynamics}(c), regardless of the details of the
distribution function $f_{\uparrow\uparrow}({\bf r},{\bf q})$.
The total number of molecules in excited rotational states is conserved, $N_\uparrow(t)+N_\downarrow(t)=N_{\mathrm{ex}}$.
Thus, the SOC transfers the internal angular momentum of the molecules, all of which are in the
$\ket{\uparrow}$ state at $t=0$, to their orbital motion, leading to the formation of a
{\it vortex structure} around ${\bf r}=0$. This manifests itself, for instance, in a dip in the density of
molecules in the $\ket{\downarrow}$ rotational state, $n_\downarrow({\bf r})\propto r^{2{\it \Phi}_{\mathrm{BP}}/\pi}=r^4$,
around the centre of the vortex structure, Fig.~\ref{fig:DenDynamics}(b). In particular, if the chiron spectrum
has a branch with quadratic dispersion $E({\bf k})\sim k^2(2M)^{-1}$,
which is realised, for example, for weak interactions in a shallow optical lattice or
for strong interactions in a deep optical lattice, the density of the spin-down molecules close
to the centre of the vortex estimates $n_\downarrow({\bf r},t)\sim\left(M^2r^2/t^2\right)^2N_{\mathrm{ex}}/\Lambda^2$
at sufficiently long times. Far from the centre of the vortex the density profile is described by freely propagating chirons which
do not interfere with each other:
\begin{eqnarray}
n_{\uparrow}({\bf r},t)= n_{\downarrow}({\bf r},t)= \frac{1}{4}\sum_\pm\int_{\bf q}
f_{\uparrow\uparrow}\left[{\bf r}-t{\bf v}_\pm({\bf q}),{\bf q}\right].
\label{density}
\end{eqnarray}
The two contributions in the sum in Eq.~(\ref{density}) correspond to the two branches of chirons
propagating with velocities $v_+({\bf q})$ and $v_-({\bf q})$, which leads to their spatial separation.
\section*{Experimental Accessibility}
\label{ExpAcc}
In this section, we discuss some details related to the observation of dipolar SOC in present cold polar molecule experiments, taking as a representative example the KRb experiment at JILA~\cite{Yan_Moses}. To prevent chemical reactions, KRb polar molecules are pinned in a deep 3D optical lattice. The relevant energy scales for Eq.~\eqref{eq:HCHami} are $J_0=|\langle 1,1|\hat{d}^1|0,0\rangle|^2/(2a^3)\sim 100 h\,$Hz and $J_2=3J_0$. Trapping in a deep optical lattice may also be required for molecular species which are chemically stable, as the presence of a very high density of resonances at ultracold energies has been proposed to lead to long-lived collision complexes which are highly susceptible to three-body loss~\cite{Mayle_13}.
The chirons' spectra in the entire Brillouin zone (BZ) can be measured by means of Rabi spectroscopy provided the probe beam can transfer the required quasi-momentum $k_{\mathrm{R}} \simeq 1/a$ to the molecules. Direct microwave transitions are insufficient since they have $k_{\mathrm{R}} a\ll 1$, but $k_{\mathrm{R}}a \simeq 1$ can be achieved using optical Raman pulses. Here, $k_{\mathrm{R}}=|\mathbf{k}_1-\mathbf{k}_2|$, with $\mathbf{k}_i$ the wavevector of the $i^{th}$ Raman beam. Raman transitions between internal states are already a key part of the production of ground-state molecules through STIRAP~\cite{KRb}; our proposal requires only minor modifications of this well-established procedure.
Due to the inherent difficulty of directly cooling molecules, present experiments are not quantum degenerate, leading to a sparse lattice filling fraction near 10\%~\cite{Yan_Moses,Zeno,Hazzard_Gadway_14}. Fig.~\ref{fig:ChironDynam}(c) displays the density of $\hat{S}_x$ in a lattice with 10\% filling, averaged over disorder realisations. The $d$-wave symmetry of the distribution is still visible, albeit with reduced contrast compared to the unit-filled case (Fig.~\ref{fig:ChironDynam}(b)). The $d$-wave symmetry is a consequence of the Berry phase, a topological property, and so is robust against disorder. In contrast, disorder smears the vortex structure.
In the rotational structure of KRb, nuclear quadrupole interactions cause the states with predominant $|1,-1\rangle$ and $|1,1\rangle$ character to be non-degenerate by about 70$h$kHz at the $545$G magnetic fields used for magneto-association~\cite{AnisotropicPol}. These states can be made degenerate and out of resonance with the $|1,0\rangle$ level by increasing the strength of the magnetic field $B$, even at zero electric field. In this scenario, the $B$ field determines the quantisation axis. For $^{40}$K$^{87}$Rb, where the nuclear quadrupole moments are $(eqQ)_{\mathrm{Rb}}=-1.308h\,$MHz and $(eqQ)_{\mathrm{K}}=0.452h\, $MHz~\cite{AnisotropicPol}, the levels cross near $B\simeq $1260G, well within experimental feasibility. The energy difference between these levels close to the crossing is nearly linear, with a slope of roughly 40Hz$\,$G$^{-1}$. Stabilisation of magnetic fields at the 10mG level, which is routine in ultracold gas experiments, would correspond to non-degeneracy on the order of 0.4Hz, and will not significantly affect our results. Similar comments apply for the other alkali metal dimers. The level structure in Fig.~\ref{fig:Schematic}(b) also results for $^1\Sigma$ molecules without hyperfine structure, for example bosonic SrO, in the presence of a uniform electric field.
Finally, we note that several knobs can be used to manipulate the Hamiltonian, Eq.~\eqref{eq:HCHami}. For example, by changing the angle of the quantisation axis with respect to the space-fixed $z$ axis one can tune the ratio $J_2/J_0$ and remove the cancelation seen in the $E_+$ branch. This can be used in turn to control the propagation velocity of the two branches of chirons. Chiron-chiron interactions which fall off as $1/r^3$ can also be controllably introduced by turning on an external static electric field.
\section*{Discussion}
We have demonstrated that
a 2D system of polar molecules behaves as a gas of chiral excitations with a Berry phase $2\pi$. We have shown that signatures of those excitations, which resemble the low-energy excitations exhibited by bilayer graphene, manifest in both the dynamics of the
density and spin coherences.
The implementation of SOC in polar molecules presented here can open other exciting research
avenues. In particular, by superimposing an effective magnetic field to the chirons via light-generated synthetic gauge fields \cite{Galitski2013} it might be possible to simulate the unconventional quantum Hall effect of bilayer graphene and to see its intriguing consequences \cite{McCannFalko:bilayer} in the lowest Landau levels in the limit of low
chiron density and high synthetic magnetic fields. Such an effect would require fermionic statistics of the excitations, which can be realised with fermionic molecules in a shallow optical lattice.
Although so far the system in consideration is an ideal or nearly ideal gas of chirons and interactions between them can be neglected, chiron-chiron interactions tunable by
the duration of the laser pulse, the size of the excited region or an external electric field
may lead to very rich physics. For example, chiron-chiron interactions together with non-stationary background $N=0$ molecules or microwave dressing can give rise to interesting dynamic structures, new types of transport phenomena and even to
fractional quantum Hall phases when combined with synthetic gauge fields \cite{Yao2013,PhysRevLett.110.185301}.
Finally, we expect our predictions to be extendable to
other dipole-dipole interacting systems such as Rydberg
atoms, magnetic atoms, and magnetic defects
in solids. \Notes{}
{\it Acknowledgements.} We appreciate useful discussions with M.~Hermele, M. Lukin, N. Yao, K.R.A.~Hazzard, T. Pfau, and the KRb JILA experimental group.
This work has been financially supported by
NIST, JILA-NSF-
PFC-1125844, NSF-PIF-1211914, NSF-PHY11-25915, ARO, ARO-DARPA-OLE,
AFOSR, AFOSR-MURI, and the NSF grants DMR-1001240 and PHY-1125844. M.L.W thanks the NRC postdoctoral
fellowship program for support. S.V.S. has been also partially supported by the Alexander
von Humboldt Foundation
through the Feodor Lynen Research Fellowship. A.M.R. and V.G.
thank the Aspen Center for Physics and KITP.
{\it Author contributions.}
All authors contributed significantly to the work presented in this paper.
{\it Competing financial interests.}
The authors declare no competing financial interests.
\section*{Methods}
\subsection*{Kinetic equation for polar molecules}
To characterise the dynamics of a system of polar molecules, we introduce
the non-equilibrium Green's functions
\begin{eqnarray}
G^<_{\sigma\sigma^\prime}({\bf r}_1,t_1;{\bf r}_2,t_2)=
\mp i\langle\hat \Psi^\dagger_{\sigma^\prime}({\bf r}_2,t_2)\hat \Psi_\sigma({\bf r}_1,t_1)\rangle,
\label{Glesser}
\\
G^>_{\sigma\sigma^\prime}({\bf r}_1,t_1;{\bf r}_2,t_2)=
-i\langle\hat \Psi_\sigma({\bf r}_1,t_1)\hat \Psi^\dagger_{\sigma^\prime}({\bf r}_2,t_2)\rangle,
\label{Glarger}
\end{eqnarray}
where $\sigma$ and $\sigma^\prime$ label the internal states of the molecules [$\sigma$ corresponds to $(|1,-1\rangle,|0,0\rangle,|1,1\rangle)$].
The upper (lower) sign applies to bosonic (fermionic) particles.
The distribution functions of the molecules are defined as
\begin{equation}
f_{\sigma_1\sigma_2}(t,{\bf r},{\bf p})=
\pm(2\pi i)^{-1}\int G_{\sigma_1\sigma_2}^<(t,{\bf r},{\bf p},E)dE,
\label{f}
\end{equation}
where the upper and the lower signs apply to bosonic and fermionic particles respectively,
and $G_{\sigma_1\sigma_2}^<(t,{\bf r},{\bf p},E)$ is the result of the
Wigner-transformation\cite{RammerSmith,Kamenev:book} of
$G^<_{\sigma\sigma^\prime}({\bf r}_1,t_1;{\bf r}_2,t_2)$.
Using the functions (\ref{Glesser}) and (\ref{Glarger}),
we define a $2\times 2$ matrix in the Keldysh space\cite{Kamenev:book,RammerSmith},
\begin{eqnarray}
\underline G=\left(
\begin{array}{cc}
G^{\mathrm{R}} & G^{\mathrm{K}} \\
0 & G^{\mathrm{A}}
\end{array}
\right).
\label{Gunderline}
\end{eqnarray}
Each of the Green's functions in Eq.~(\ref{Gunderline}) is a matrix in the space of the
internal rotational levels of the molecules.
The function (\ref{Gunderline}) satisfies the equation
\begin{eqnarray}\label{Dyson}
[(\underline G_0^{-1}-\underline\Sigma) \otimes \underline
G]=0
\end{eqnarray}
(Dyson equation minus its conjugate), where
$G_0^{-1}(1,2)=[i\partial_{t_1}-\hat H({\bf r}_1)]\delta(1-2)$;
$1=(t_1,{\bf r}_1)$, $2=(t_{2},{\bf r}_{2})$, and $\underline\Sigma$
is the self-energy part, determined by the dipole-dipole interactions.
In terms of the distribution functions $f_{\sigma_1\sigma_2}$ the kinetic equation reads
\begin{align}
&\partial_t f_{\sigma_1\sigma_2}-{\boldsymbol \nabla} U\:\partial_{\bf p} f_{\sigma_1\sigma_2}
\nonumber\\
&+\partial_{\bf p}(E_{\bf p}\delta_{\sigma_1\sigma}+\Sigma_{\sigma_1\sigma}){\boldsymbol \nabla} f_{\sigma\sigma_2}
=\left(\mathrm{St}f\right)_{\sigma_1\sigma_2},
\label{kingenmol}
\end{align}
where $U({\bf r})$ is the external smooth (trapping) potential, $E_{\bf p}$ is the kinetic
(quasi)energy, the summation over repeated indices is implied,
and $\mathrm{St}f$ is the collision integral, which accounts for the relaxation of the distribution
function due to molecular collisions.
In this paper we consider a model with a small relaxation rate, which can be neglected on the characteristic
times of interest, so that the excitations propagate ballistically. Also, we assume
that chirons reach sufficiently low density shortly after they are excited, so that chiron-chiron interactions
can be neglected, and the problem becomes effectively single-particle.
Introducing the chiron annihilation operator
\begin{equation}
\hat \Psi{({\bf k})}_\pm=\left[e^{i\phi_{\bf k}}\hat \Psi_\downarrow{({\bf k})}\pm e^{-i\phi_{\bf k}}\hat \Psi_\uparrow{({\bf k})}\right]/\sqrt{2},
\end{equation}
where $\hat \Psi_{\uparrow,\downarrow}{({\bf k})}$ are the annihilation operators for the plane-wave states in
the reduced space $\{\ket{\downarrow},\ket{\uparrow}\}$ of the rotational levels of the molecules, the kinetic
equation (\ref{kingenmol}) is reduced, under the assumptions made above, to that for a single-particle problem with
the dispersion $E_\pm({\bf k})$:
\begin{align}
&\partial_t f_{\pm}-{\boldsymbol \nabla} U\:\partial_{\bf p} f_{\pm}
+{\bf v}_\pm({\bf p}){\boldsymbol \nabla} f_{\pm}
=0.
\label{KineticChiron}
\end{align}
In the case $U=0$, considered in this paper, the most general solution of Eq.~(\ref{KineticChiron}) reads
\begin{equation}
f_\pm(t,{\bf r},{\bf p})=G_\pm[{\bf r}-t{\bf v}_\pm({\bf p}),{\bf p}],
\end{equation}
$G_\pm({\bf r},{\bf p})$ being arbitrary functions of two arguments.
|
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Pierre Brice (verdadeiro Pierre-Louis Baron de Bris; Brest, - Paris, ) foi um ator francês. Ganhou celebridade por sua interpretação de Winnetou, que faz parte do filme de maior sucesso alemão do pós-guerra.
Brice interpretou "Winnetou" em onze filmes juntamente com Lex Barker, em 7 filmes como Old Shatterhand), Stewart Granger (em tres filmes como Old Surehand) e Rod Cameron (num filme como Old Firehand. Repetiu a personagem em duas séries televisivas, em 1979 e 1997, que contudo não foram baseadas na obra de Karl May. Apesar de participar em inúmeros filmes e séries televisivas, Pierre Brice será sempre recordado como o Eterno Winnetou.
Pierre Brice esteve envolvido em 2010, no Luxemburgo, para uma retrospectiva no Utopolis. Ele então explicou longamente as suas alegrias, mas também as suas decepções de ser confinado a uma única função ao longo de sua carreira. Foi voluntário do exército francês, combatendo na Indochina. Após, fez cursos de atuação, e teve um pequeno papel no filme "Ça va Barder" em 1955.
Em 1962 foi escolhido pelo produtor Horst Wendlandt, que o conheceu no Festival de Filmes de Berlim para interpretar "Winnetou", personagem do autor alemão Karl May, o que o fez numa série de dez filmes ao lado dos atores Lex Barker (Old Shatterhand), Stewart Granger (Old Surehand) e Rod Cameron (Old Firehand).
Seu grande sucesso o transformou num astro na Alemanha, ganhando muitos prêmios como o Bambi ou o Golden Otto. Entretanto, aparecendo em outros filmes, ele será sempre relembrado como "Winnetou".
Filmografia
Ça va barder (1955)
Le septième ciel (1958)
Les tricheurs (1958)
Le miroir à deux faces (1958)
L'ambitieuse (1959)
I cosacchi (Os cossacos) 1960
Il rossetto (1960)
I piaceri del sabato notte (1960)
Il mulino delle donne di pietra (O moinho das mulheres de pedra) 1960
L'homme à femmes (1960)
La donna dei faraoni (A mulher do Faraó) 1960
Akiko (1961)
Le baccanti (1961)
Un alibi per morire (1962)
Los atracadores (1962)
Douce violence (1962)
Der Schatz im Silbersee (O tesouro dos renegados) 1962
Pacto de silencio (1963)
Il giorno più corto (1963)
L`invincibile cavaliere mascherato (O invencível cavaleiro mascarado) 1963
Col ferro e col fuoco (1963)
Zorro contro Maciste (Sansão e a rainha escrava) 1963
Winnetou 1. Teil (A lei dos apaches) 1963
Old Shatterhand (A batalha final dos apaches) 1964
Die goldene Göttin vom Rio Beni (Os selvagens) 1964
Winnetou 2. Teil (br.: Winnetou) 1964
Unter Geiern (Carne para abutres) 1964
Schüsse im Dreivierteltakt (1965)
Die Hölle von Manitoba (Duelo em Glory City) 1965
Der Ölprinz (Flechas ardentes) 1965
Winnetou 3. Teil (A Trilha dos Desalmados) 1965
Old Surehand (O Mão de Ferro) 1965
Carnaval des barbouzes (Carnaval de ladrões) 1966
Winnetou und das Halbblut Apanatschi (Apanatschi) 1966
Winnetou und sein Freund Old Firehand (Trovões na fronteira) 1966
Dacii (Os guerreiros) 1967
Le 13ème caprice (Seu corpo por um capricho) 1967
Winnetou und Shatterhand im Tal der Toten (No vale da morte) 1968
Un giorno, una vita (1970)
Les coups pour rien (1970)
La notte dei dannati (1971)
Erika (1971)
Una cuerda al amanecer (1972)
Féminin-féminin 1973
La pupa del gangster (A garota do gangster) 1975
Zärtliche Chaoten 1987
Der letzte Ritt 2009
The Columbia story de Clive Hirschhorn - The Internet Movie Database (IMDB)
Ligações externas
Homepage of Pierre Brice (em alemão)
Winnetou on WWW.ALMISSA.COM (em croata/inglês)
Pierre Brice, French Chieftain of the Mescalero Apaches - A Biography
Atores da França
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Administrative Resume Objectives Administrative Assistant Resume of Curriculum Vitae Examples For Administrative Assistant , Source image: http://giabotsan.com/resume-objective-for-office-job/administrative-resume-objectives-administrative-assistant-resume/.
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layout: post
title: "Blackberry picking + Swimming hole + Giants = Epic weekend"
date: 2018-09-13
author: Coloma Farré
backgrounds:
- /img/blackberry/0000_IMG_8908.JPG
thumb: /img/blackberry/0000_IMG_8869.JPG
categories: Family Parenting Traditions Summer Outdoors Video
comments: true
---
<a href="/img/blackberry/0000_IMG_8846.JPG"> <img border="0" src= "/img/blackberry/0000_IMG_8846.JPG" width="200"></a>
A few weeks ago we had an **unplanned amazingly fun weekend**. Some times the last minute plans are the best, and this time it really was.
<a href="/img/blackberry/0000_IMG_8869.JPG"> <img border="0" src= "/img/blackberry/0000_IMG_8869.JPG" width="200"></a>
Friday afternoon we went on a little hike with a little basket and we picked **1 kg of wild blackberries**, that later we turned out into blackberry delicious jam! Ramona was very into it! Into picking blackberries, but also into etaing them!
<a href="/img/blackberry/0000_IMG_8900.JPG"> <img border="0" src= "/img/blackberry/0000_IMG_8900.JPG" width="200"></a>
<a href="/img/blackberry/0000_IMG_8859.JPG"> <img border="0" src= "/img/blackberry/0000_IMG_8859.JPG" width="200"></a>
<a href="/img/blackberry/0000_IMG_8852.JPG"> <img border="0" src= "/img/blackberry/0000_IMG_8852.JPG" width="200"></a>
<a href="/img/blackberry/0000_IMG_8962.JPG"> <img border="0" src= "/img/blackberry/0000_IMG_8962.JPG" width="200"></a>
<a href="/img/blackberry/0000_IMG_8882.JPG"> <img border="0" src= "/img/blackberry/0000_IMG_8882.JPG" width="200"></a>
<a href="/img/blackberry/0000_IMG_8941.JPG"> <img border="0" src= "/img/blackberry/0000_IMG_8941.JPG" width="200"></a>
<a href="/img/blackberry/0000_IMG_8984.JPG"> <img border="0" src= "/img/blackberry/0000_IMG_8984.JPG" width="200"></a>
<a href="/img/blackberry/0000_IMG_9004.JPG"> <img border="0" src= "/img/blackberry/0000_IMG_9004.JPG" width="200"></a>
<a href="/img/blackberry/0000_IMG_8951.JPG"> <img border="0" src= "/img/blackberry/0000_IMG_8951.JPG" width="200"></a>
<a href="/img/blackberry/0000_IMG_9068.JPG"> <img border="0" src= "/img/blackberry/0000_IMG_9068.JPG" width="200"></a>
<a href="/img/blackberry/0000_IMG_8992.JPG"> <img border="0" src= "/img/blackberry/0000_IMG_8992.JPG" width="200"></a>
<a href="/img/blackberry/0000_IMG_8979.JPG"> <img border="0" src= "/img/blackberry/0000_IMG_8979.JPG" width="200"></a>
The next morning we went to the pool. Even if it was not so hot, we did read some magazines and chill in the hammock.
<a href="/img/blackberry/0000_IMG_9095.JPG"> <img border="0" src= "/img/blackberry/0000_IMG_9095.JPG" width="200"></a>
<a href="/img/blackberry/0000_IMG_9094.JPG"> <img border="0" src= "/img/blackberry/0000_IMG_9094.JPG" width="200"></a> Those little teeth!!!
<a href="/img/blackberry/0000_IMG_9097.JPG"> <img border="0" src= "/img/blackberry/0000_IMG_9097.JPG" width="200"></a>
In the afternoon we went to Santa Perpètua de Gaià, a town with a cool castle tower and church on top of a hill. Then we found this **hidden swimming hole** and we swam! It was fantstic to feel the cold water and to be in the middle of nature, so disconnected but yet so close to home!
<a href="/img/blackberry/0000_IMG_9189.JPG"> <img border="0" src= "/img/blackberry/0000_IMG_9189.JPG" width="200"></a>
<a href="/img/blackberry/0000_IMG_9153.JPG"> <img border="0" src= "/img/blackberry/0000_IMG_9153.JPG" width="200"></a>
<a href="/img/blackberry/0000_IMG_9194.JPG"> <img border="0" src= "/img/blackberry/0000_IMG_9194.JPG" width="200"></a>
<a href="/img/blackberry/0000_IMG_9161.JPG"> <img border="0" src= "/img/blackberry/0000_IMG_9161.JPG" width="200"></a>
<a href="/img/blackberry/0000_IMG_9141.JPG"> <img border="0" src= "/img/blackberry/0000_IMG_9141.JPG" width="200"></a>
<a href="/img/blackberry/0000_IMG_9212.JPG"> <img border="0" src= "/img/blackberry/0000_IMG_9212.JPG" width="200"></a>
<a href="/img/blackberry/0000_IMG_9185.JPG"> <img border="0" src= "/img/blackberry/0000_IMG_9185.JPG" width="200"></a>
On Sunday we took a day trip to **Prades**, this cute red moutain town, an hour from Santa Coloma, where my aunt and uncle live! We had an amazing lunch and then in the afternoon there was a giants parade!! Ramona's favorite!! Music, giants dancing and ice-cream, what else do you need ;-)
<a href="/img/blackberry/0000_IMG_9271.JPG"> <img border="0" src= "/img/blackberry/0000_IMG_9271.JPG" width="200"></a>
<a href="/img/blackberry/0000_IMG_9298.JPG"> <img border="0" src= "/img/blackberry/0000_IMG_9298.JPG" width="200"></a>
<a href="/img/blackberry/0000_IMG_9278.JPG"> <img border="0" src= "/img/blackberry/0000_IMG_9278.JPG" width="200"></a>
<a href="/img/blackberry/0000_IMG_9327.JPG"> <img border="0" src= "/img/blackberry/0000_IMG_9327.JPG" width="200"></a>
<a href="/img/blackberry/0000_IMG_9344.JPG"> <img border="0" src= "/img/blackberry/0000_IMG_9344.JPG" width="200"></a>
And here is a fun video so you can see how much fun we had!! Anybody else ready for another epic rural Catalunya weekend!?!
<iframe width="100%" height="315" src="https://www.youtube.com/embed/CjC23q6AJ7I" frameborder="0" allow="autoplay; encrypted-media" allowfullscreen></iframe>
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Timogenes dorbignyi je jedním z největších druhů celé čeledi štírů Bothriuridae. Větší je pouze Timogenes elegans.
Popis
Dorůstá velikosti 60-90 mm. Zbarvení je světle žluté až světložluté.
Areál rozšíření
Vyskytuje se v Argentině, Bolívii, Brazílii a Paraguayi.
Chov
Počet mláďat ve vrhu činil 18 larev. Jed není nebezpečný a štír není příliš agresivní.
Bothriuridae
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<p>specdisp —
Displays the magnitude values of the spectrum.
</p>
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<a id="idm47161588261872"></a>
<h2>Description</h2>
<p>
Displays the magnitude values of the spectrum.
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<h2>Syntax</h2>
<pre class="synopsis"><span class="command"><strong>specdisp</strong></span> wsig, iprd [, iwtflg]</pre>
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<a id="idm47161588193840"></a>
<h2>Initialization</h2>
<p>
<span class="emphasis"><em>iprd</em></span> -- the period, in seconds, of each new display.
</p>
<p>
<span class="emphasis"><em>iwtflg</em></span> (optional, default=0) -- wait flag. If non-zero, hold each display until released by the user. The default value is 0 (no wait).
</p>
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<div class="refsect1">
<a id="idm47161588191328"></a>
<h2>Performance</h2>
<p>
<span class="emphasis"><em>wsig</em></span> -- the input spectrum.
</p>
<p>
Displays the magnitude values of spectrum <span class="emphasis"><em>wsig</em></span> every <span class="emphasis"><em>iprd</em></span> seconds (rounded to some integral number of <span class="emphasis"><em>wsig</em></span>'s originating <span class="emphasis"><em>iprd</em></span>).
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ksum <span class="opc">specsum</span> wsig, 1 <span class="comment">; sum the spec bins, and ksmooth</span>
<span class="octrl">if</span> ksum <span class="op"><</span> 2000 <span class="octrl">kgoto</span> <span class="olabel">zero</span> <span class="comment">; if sufficient amplitude</span>
koct <span class="opc">specptrk</span> wsig <span class="comment">; pitch-track the signal</span>
<span class="octrl">kgoto</span> <span class="olabel">contin</span>
<span class="olabel">zero:</span>
koct <span class="op">=</span> 0 <span class="comment">; else output zero</span>
<span class="olabel">contin:</span></pre>
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\section{Introduction}
\label{sec:intro}
With the advent of deep neural network architectures as the prominent machine learning paradigm \cite{NIPS2012_4824} for human-centric applications a common issue that has plagued their application is the lack of interpretability of these models. As the spectrum of domains where deep learning replaces traditional and orthodox methods expands, and deep learning methods percolate to areas of immediate applicability to daily life, like self driving cars\cite{DBLP:journals/corr/BojarskiTDFFGJM16}, understanding what networks do takes on a more central role than aspiring performance gains. Future challenges that machine learning engineers face, are not just limited to improving model accuracy, but also debugging\cite{Tan_2018} and training networks in order to make them conform to ever evolving regulations concerning ethics\cite{IR} and privacy\cite{doi:10.1098/rsta.2016.0118}.
Most literature in the area of explainable AI focuses on providing explanations for pre-trained networks\cite{lime},\cite{ghorbani2019automatic}. While some methods focus on designed models which have explainability as a part of their design philosophy\cite{alvarezmelis2018robust}. Our work belongs to the former category and focuses on providing explanation for already trained models, or what is colloquially called post-hoc explanation. Within the strata of post-hoc explanations, there exist multiple evolutionary branches, some focus on interpreting the features\cite{SanityNIPS2018}, and\cite{Zhou2018InterpretableBD} interprets the network by breaking down an input prediction into semantically interpretable components and works like \cite{8417924} focus on interpreting neurons based on their behaviour when they activate for entities like different textures, colours and images.\\
We focus on unsupervised discovery of concepts learned by the network by trying to cluster the neurons, input features and inputs themselves in the same latent space. The motivation for doing so comes from works like\cite{DBLP:journals/corr/GardnerKLUWH15} where it has been conjectured that natural images usually lie on a manifold and that a neural network embeds this manifold as a subspace in it's feature space. The work most similar in spirit to ours is ACE\cite{ghorbani2019automatic} where the goal is to explain the prediction of neural networks not in terms of individual neurons, but rather, by focusing on learning the concepts utilized by the network that are most sensitive for a successful prediction, and learning of such concepts is a supervised process. Unlike our work, ACE\cite{ghorbani2019automatic} utilizes existing algorithms or manual annotation to curate a set of concepts, feed it to the network and measure the sensitivity of the network to those concepts using TCAV\cite{kim2017interpretability}. This solution, though elegant relies heavily on domain expert annotators or supervised tools, while we learn these concepts from the activations of the network and try to determine concepts learned by the network by probing it input examples. Another line of work in \cite{kim2017interpretability} focuses on learning vectors which when measured for their effects on class prediction, align with high-sensitivity directions in the latent space of the network. We also utilize \cite{kim2017interpretability} as a means to validate our approach in \autoref{sec:ext}.
Our approach aims to find a latent representation for neurons, input features and examples in a common subspace, where clustering them aims to elicit meaningful insights about the networks ability to discern between examples. Using such a tri-factor clustering, we can analyze intersections between groups of neurons which fire for different classes, focus on which input features provide a basic structure upon which the model correctly classify its inputs and analyze an individual example based on their similarity and differences to other examples, as determined by the network's embeddings of them. We model our problem as a coupled matrix factorization, where the model is constrained to appropriate constraints like non negativity, which aid in interpretability \cite{5c8e335ac9274d0aad4b96178bf24394} and the possibility of adding regularizations like group sparsity, orthogonality etc. to encode meaningful priors into the model. We conduct our analysis by observing the behaviour of a network on a set of images it has previously not seen, for the purpose of this study, we experiment with CIFAR-10 and CIFAR-100 as our datasets of choice. Our raison d'etre is to approach the problem of concept discovery in an unsupervised manner, in order to bridge a gap unfulfilled by \cite{ghorbani2019automatic} and \cite{8417924}. In doing so develop a methodology which can seed or supplement other interpretability methods.
\section{Related Work}
\label{sec:RelatedWork}
In our work we aim to interpret a learned model using a set of images which may or may not have been a part of the set of training classes of the network. Our work comes in stark contrast with most existing literature, since the goal in this work is not to evaluate the network on a feature by feature or on a sample by sample basis as in \cite{zeiler2013visualizing},\cite{koh2017understanding}, \cite{smilkov2017smoothgrad},\cite{simonyan2013deep}. Additionally, there are other works, such as \cite{zeiler2013visualizing} which visualize a network based on images that maximize the activation of hidden units or works like \cite{mahendran2014understanding} which use back-propagation to generate salient features of an image. \\
Works like \cite{alvarezmelis2018robust} focus on explaining a network by proposing a new framework where the network is forced to learn concepts and demonstrate their relevance towards a prediction. This framework relies on prior constraining and encoding for what is thought to be a concept. In \cite{Zhou2018InterpretableBD} the focus is on explaining each prediction made by the network by decomposing the activations of a layer in the network into a basis of pre-defined concepts, where each explanation a weighted sum of these concepts, where the weights determine the impact each concept has towards prediction.
Our work has similarities of philosophy with the previous 2 works, but unlike \cite{alvarezmelis2018robust} we don't focus on learning an interpretable model, instead we focus on unsupervised explanation of an already trained network. And unlike \cite{8417924} we do not have a pre-made notion of concepts, instead we let the model learn underlying concepts based on the set of examples fed in the analysis. This way our approach is application agnostic.
Recent work on Network Dissection \cite{DBLP:journals/corr/BauZKOT17} tries to provide a framework where they can tie up a neuron in the network to a particular concept for which the neuron activates. These concepts can be simple elements like colour, to compound entities like texture. They accomplish this through a range of curated and labeled semantic concepts whereas our work doesn't need user labeled data.
Another work which relies on interpreting the network through the lens of abstract concepts is TCAV \cite{kim2018interpretability}. This work tries to provide an interpretation into network's workings in terms of human interpretable concepts. Like our work, they too rely on the internal representation of the network to determine the network's behaviour, but unlike us they utilize manual/pre-defined concepts and test the network's sensitivity towards it.
The work presented in \cite{raghu2017svcca} uses a variant of canonical co-relational analysis and focuses on learning the complexity of the representations learned by the network to determine the dynamics of learning, our work differs as we use the structure of the learned representation as a guideline for our factorization framework and don't comment on the inherent complexity.\\
The work most in line with our goals is \cite{ghorbani2019automatic}, here the authors seek to automatically discover concepts learned by the network which are of high predictive value, as measured by their TCAV score \cite{kim2018interpretability}.\\
In \autoref{fig:comp} we compare our work to other works in the area, some of which relevant and others more tangential to our approach. While the axioms of interpretable machine learning are an ever evolving set of principles, we enlist a few features that help us highlight the differences between our work and it's closest neighbours in this space. Our work is the only unsupervised method in this space of model interpretability which helps us discover concepts learned by the network in terms of the examples clustered by the network. ACE \cite{ghorbani2019automatic}, SeNN\cite{alvarezmelis2018robust} learn concepts but either by utilizing explicit supervision or by employing pre-existing trained models, whereas works like \cite{8417924} require detailed human labeling of neurons and image pixels and patches, thus making the process slow and sluggish for adaptation to a new domain. LIME \cite{lime} on the other hand tries to visualize a linear decision boundary across an input, which we approximate by the input's K-Nearest Neighbours but unlike our work it cannot discover abstract concepts learned by the network without significant modifications.
\begin{figure*}
\caption{Relevant Work Comparison}
\label{fig:comp}
\centering
\begin{tabular}{|c|c|c|c|c|c|}
\hline
Model Features & ACE\cite{ghorbani2019automatic} & LIME\cite{lime} & SeNN\cite{alvarezmelis2018robust} & Net Dissection \cite{8417924} & Our work \\
\hline
Post-Hoc Interpretability & \cmark & \cmark & \xmark & \cmark &\cmark \\
\hline
Unsupervised & \xmark & \xmark & Partial & \xmark & \cmark \\
\hline
Insights on Inputs & \cmark & \cmark & \cmark & \cmark & \cmark \\
\hline
Insights on Neurons & \xmark & \xmark &\xmark & \cmark & \cmark \\
\hline
Insights on Features & \xmark & \cmark & \cmark & \cmark & \cmark \\
\hline
Collective Analysis of Inputs & \xmark & \xmark & \xmark & \xmark & \cmark \\
\hline
Individual Analysis of Inputs & \cmark & \cmark & \cmark & \cmark & Partial \\
\hline
Analysis of Representation Space & \xmark & \xmark & \xmark & \xmark & \cmark \\
\hline
\end{tabular}
\end{figure*}
\section{Proposed Method}
\label{sec:method}
In this section we begin by outlining the motivation for our methodology, we then proceed to outline the implementation schema and optimization problem for our model. Subsequently we present the model details and lay down the groundwork for evaluation protocols suited for this method.
\subsection{Motivation}
Our goal is to visualize the latent representation space learned by a Neural Network by comparing and contrasting the behaviour of the network on different types of inputs. We want to accomplish this in a framework where we can explain the concepts learned by the network in terms of the inputs that are used to probe the network. In doing so we can assess the generalization ability of the network, both to familiar and unseen datasets, thus providing insights to human evaluators about the health of the trained network and it's suitability to a particular domain. This is possible because there are no restrictions on what qualifies as a legitimate dataset for evaluating network behaviour, thus in theory, we can evaluate a network on a dataset which is different from it's training dataset and assess the suitability of the architecture to learn atomic concepts (which may be valid across domains) from the training data instead of learning it's idiosyncrasies.
\subsection{Proposed Model}
Given these goals in mind, we lay down the model principles aligned with our objectives. Our approach is a method that relies on a coupled matrix factorization framework where we compute embeddings of test examples and individual neurons in probed layers in a shared latent space. Our method relies on only having access to activations of internal layers of a network for a given input. Additionally, for ease of modelling, we assume that these activations are non-negative in nature, for instance ReLU and Sigmoid non-linearities are used in the network. In doing so our model does not introduce any external learning constraints while training the network, thus lending it universality. We probe various layers of a network with a set of test examples, and for each test example, we store the network's response across all (observed) layers. We do so with an aim to breakdown the process of interpretability into a process of finding common local structures across various test/evaluation examples, where each feature in the latent representation hopefully captures a latent semantic concept. Thus, through the lens of our model, we can, hopefully view individual concepts in an amalgam of constituents of a test example. In the following subsections we describe model construction and provide mathematical details of implementation.
\subsubsection{Model Construction}
For our analysis we need construct a set of matrices where each matrix $A_i$ in the set is a matrix $\in$ $ \mathbb{R}^{a_i \times N}_{+}$, where $a_i$ is the number of neurons in layer $i$ of the network, and $N$ is the number of examples on which our analysis is conducted. Each column $k$ of matrix $A_i$, is a vectorized activation of layer $i$ of the network for a given test sample $k$. Thus, to reiterate, a column $k$ of this matrix $A_i$, denoted by $A_i[:,k]$, is the activation of layer $i$ of the network when the $k^{th}$ test example is passed as an input to it.
Along similar lines we construct another set of matrices where each Matrix $D_i$ $\in$ $ \mathbb{R}^{S_i \times N}_{+}$ where $S_i$ is number of pixels in the $i^{th}$ channel of input images and $N$ is the same as earlier. On the same lines as before, each column $k$ of matrix $D_i$, is the $k^{th}$ test sample's $i^{th}$ channel vectorized.
\subsubsection{Model}
The objective function for our proposed method is as follows:
\begin{equation}\begin{split}J(\textbf{P},F,\textbf{O}) = \sum_{i = 0}^{C-1} \lVert D_i - P_iF\rVert_{F}^{2} + \sum_{j = 0}^{L-1} \lVert A_j - O_jF\rVert_{F}^{2} +\\ \sum_{i = 0}^{C-1}\lambda_P\lVert P_i \rVert^{2}_{p} + \sum_{j = 0}^{L-1}\lambda_O\lVert O_j \rVert^{2}_{p} + \lambda_F\lVert F \rVert^{2}_{p} \\ \ni P_{i}, O_{j}, F, \in \mathbb{R}^{S_i \times d}_{+},\mathbb{R}^{N_j \times d}_{+},\mathbb{R}^{d \times N}_{+}\\ ||P[:,i]||^{2}_{2} = 1 , ||O[:,i]||^{2}_{2} = 1 \forall i \end{split}\label{eq:1}\end{equation}
In \autoref{eq:1}, C is the number of channels in input data, L is the number of layers of the network that are part of analysis - as we can select the non-negative layers we want to analyze and are not obligated to include all the layers of any architecture. $p$ is usually 2 for $2-Norm$ regularization although for the purposes of some experiments we instead set the column norms of the Pixel and Neural Factor matrices to 1 \\
For each matrix $D_i$ in \autoref{eq:1}, it's $k^{th}$ column is the input data's channel $i$ vectorized as input. Thus for instance, for a 3-channel image, with image number $j$ of the test set, $D_0[:,j]$ is the vectorized $0^{th}$ channel of the $j^{th}$ image and so on. \\
As mentioned earlier, each $D_i$ is thus a matrix of Pixel-by-Example. Each $P_i$ in the first term of the summation in equation \ref{eq:1} is a latent representation matrix for each pixel. That is, Each row of $P_i$, for instance $P_i[k,:]$ is the latent representation of the $k^{th}$ pixel in the input space. \\
For each matrix $A_j$ in \autoref{eq:1}, it's $k^{th}$ column is the activation of layer $j$ of the network for $k^{th}$ test input. Thus for instance, image number $j$ of the test set, $A_0[:,j]$ is the activation of layer $0$ of the network for image $j$, $A_1[:,j]$ is the activation of layer $1$ of the network for image $j$, $A_2[:,j]$ is the activation of layer $2$ of the network for image $j$, as a point of caution we would like to mention that $A_0$,$A_1$,$A_2$ and so on, do not necessarily correspond to layers 0,1,2 of the network, they instead correspond to the $0^{th}$,$1^{st}$,$2^{nd}$ analyzed layers of the network, as our model offers the ability to skip layers of the network, in our convention, the higher index of the layer, the deeper we are in the network.\\
Each matrix $A_j$ encodes the activity of neurons of layer $j$ for a given training example. Therefore, each $O_j$ in the factorization encodes the latent representation of neurons of layer $j$ in it's rows. That is, $O_j[k,;]$ is the latent representation of $k^{th}$ neuron of layer $j$.
Similarly, the matrix $F$ encodes in it's columns, the latent representation of each test example fed to the network. That is, $F[:,k]$ is a d-dimensional latent representation of test sample $k$.
Each factor matrix in the objective function obeys non-negativity constraints, and we use multiplicative update rules as described in \cite{Lee:2000:ANM:3008751.3008829} to solve for the factor matrices.
Update Steps for solving the factor matrices in Equation \ref{eq:1} are as presented in the following Equation \autoref{fig:UpdateSteps} :-
\begin{eqnarray*}\label{fig:UpdateSteps}
F &\leftarrow& F * \frac{\sum\limits_i P_{i}^TD_{i} +\sum\limits_j O_{j}^TA_{j}}{\sum\limits_i P_{i}^TP_{i}F +\sum\limits_j O_{j}^TO_{j}F + \lambda_{F}F} \\
P_i &\leftarrow& P_i * \frac{D_{i}F^T}{P_iFF^T+ \lambda_{P}P_i} \\
O_j &\leftarrow& O_j * \frac{A_jF^T}{O_jFF^T + \lambda_{O}O_j}
\end{eqnarray*}
\subsubsection{Model Intuition}
We now provide some intuition for our modeling choices. Our goal is to identify hidden patterns or concepts that the network learns in order to classify data. To achieve this our model clusters the test examples, neurons and pixels in the same inner product space. We achieve this clustering by incorporating a coupled non-negative matrix factorization framework.
In our learned vector representation of these 3 types of objects, a high value along a latent dimension indicates that a particular latent concept participates in explaining the behaviour of the object. By constraining the model to adhere to a non negative framework, we encourage an interpretable sum-of-concepts based representation\cite{5c8e335ac9274d0aad4b96178bf24394}.
Further elaborating on the learned factor matrices, Each column $j$ of Matrix $P_i$ $\in$ $ \mathbb{R}^{S_i \times d}_{+}$ is the activation of the pixels of channel $i$ for the concept discovered in latent factor $j$. Collecting such information over all input channels $i$ for a given $j$ in the respective factor matrices we can uncover the average activation of pixels across channels for a given concept. This representation can be thought of as a channel-wise mask over features in the input, similar to LIME \cite{lime}, but instead we discover a latent concept level mask as opposed to an input level mask.
Matrix $F$ $\in$ $ \mathbb{R}^{d \times N}_{+}$ is the input representation matrix where each column $k$ of $F$ is a vector in $\mathbb{R}^{d}_{+}$ representing the $k^{th}$ example in the same latent space as Pixels and Neurons. For any input $k$, A high value along any component $j$ of it's d-dimensional representation indicates a high affinity of this input towards the latent concept encoded in the dimension $j$ and $P_0[:j]$,$P_1[:j]$,$P_2[:j]$ together will us visualize the pixel activation mask for this latent concept $j$ as discussed earlier. Collecting all the highest affinity inputs for each latent factor, we obtain a visual approximation of the concept learned in this latent dimension. Given the unsupervised nature of this model, it extremely well suited for concept discovery for neural networks, akin to a similar role played by ACE \cite{ghorbani2019automatic} for TCAV \cite{kim2017interpretability}.
Matrices $O_j$'s embed neurons of a layer $j$ in the same latent space as inputs and features and help us visualize which neurons in a layer activate for which concept, we do this by demonstrating the similarity of latent concepts when measured w.r.t. neurons of a layer. We can also look at the behaviour of neurons across layers by observing the cohesiveness of latent space as the neurons go deeper in the network.
\section{Experimental Evaluation}
\label{sec:experiments}
In the following subsections we will present the analysis of the latent space learned by a ResNet-18 \cite{DBLP:journals/corr/HeZRS15} when trained on CIFAR-100 images \cite{Krizhevsky09learningmultiple}. Our analysis touches all the modalities captured by our model, i.e. Analysis of Pixels, Analysis of Neurons and Analysis of Examples. We present this analysis in 3 subsections for a given network. We also released the code\footnote{Code: https://github.com/23Uday/Project1CodeSDM2021} for verification.
\subsection{Analysis of A ResNet-18 on CIFAR-100 Dataset:}
In the following subsections we analyze the behaviour of a ResNet-18\footnote{https://github.com/kuangliu/pytorch-cifar} trained and analyzed on CIFAR-100. Each subsection represents a modality of analysis, namely, inputs, Neurons, and input features or pixels themselves.
\subsubsection{Analysis of Input representations:}
\label{sec:concepts}
In this section we present the analysis of representations learned in the input representation Matrix $F$. For each latent dimension $i$ we compute the total class-wise activation score of inputs in the row $F[i,:]$ and present the top 3-4 activated classes along that latent dimension, the images which had the highest affinity in this latent dimension and most activated super-class in Table \ref{tab:Table1}. The motivation behind analyzing super class labels is to validate the assertion that each latent factor captures an abstract concept that is predominantly present in the member images. We reiterate that these super class labels were not used in training of the network but only used as a means to assign a pseudonym to each latent factor, the validity of which can be verified by looking at the topmost activated images and the group of top most activate classes in Table \ref{tab:Table1}.
\begin{table*}[!ht]
\caption{Matrix-$F$ Latent Factor Analysis For ResNet-18} \label{tab:Table1}
\begin{tabular}
{l|c|c} \hline Factor: Top Classes & Top Images & Top 1-2 Super Class\\
\hline 0: bed,television,wardrobe & \includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-0/1.png}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-0/2.png}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-0/3.png}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-0/4.png}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-0/5.png}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-0/6.png}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-0/7.png}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-0/8.png}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-0/9.png}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-0/10.png}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-0/11.png}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-0/12.png}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-0/13.png}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-0/14.png}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-0/15.png}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-0/16.png}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-0/17.png} & household furniture\\
\hline 1: kangaroo,beaver,bear & \includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-1/1.png}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-1/2.png}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-1/3.png}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-1/4.png}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-1/5.png}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-1/6.png}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-1/7.png}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-1/8.png}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-1/9.png}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-1/10.png}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-1/11.png}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-1/12.png}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-1/13.png}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-1/14.png}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-1/15.png}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-1/16.png}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-1/17.png}&large omnivores and herbivores\\
\hline 2: mountain,castle,bridge & \includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-2/1.png}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-2/2.png}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-2/3.png}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-2/4.png}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-2/5.png}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-2/6.png}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-2/7.png}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-2/8.png}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-2/9.png}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-2/10.png}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-2/11.png}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-2/12.png}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-2/13.png}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-2/14.png}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-2/15.png}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-2/16.png}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-2/17.png}&large man made outdoor things\\
\hline 3: willow, maple, pine, oak & \includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-3/1}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-3/2}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-3/3}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-3/4}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-3/5}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-3/6}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-3/7}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-3/8}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-3/9}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-3/10}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-3/11}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-3/12}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-3/13}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-3/14}
\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-3/15}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-3/16}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-3/17}&trees\\
\hline 4: shark,dolphin,whale & \includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-4/1}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-4/2}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-4/3}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-4/4}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-4/5}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-4/6}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-4/7}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-4/8}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-4/9}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-4/10}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-4/11}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-4/12}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-4/13}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-4/14}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-4/15}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-4/16}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-4/17}&fish and aquatic mammals\\
\hline 5: bee,beetle,spider & \includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-5/1}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-5/2}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-5/3}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-5/4}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-5/5}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-5/6}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-5/7}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-5/8}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-5/9}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-5/10}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-5/11}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-5/12}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-5/13}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-5/14}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-5/15}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-5/16}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-5/17}&insects\\
\hline 6: tulip,rose,poppy & \includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-6/1}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-6/2}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-6/3}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-6/4}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-6/5}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-6/6}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-6/7}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-6/8}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-6/9}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-6/10}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-6/11}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-6/12}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-6/13}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-6/14}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-6/15}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-6/16}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-6/17}&flowers\\
\hline 7: oak, willow, maple, pine & \includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-7/1}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-7/2}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-7/3}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-7/4}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-7/5}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-7/6}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-7/7}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-7/8}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-7/9}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-7/10}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-7/11}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-7/12}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-7/13}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-7/14}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-7/15}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-7/16}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-7/17}&trees\\
\hline 8: telephone,cockroach,cup & \includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-8/1}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-8/2}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-8/3}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-8/4}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-8/5}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-8/6}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-8/7}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-8/8}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-8/9}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-8/10}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-8/11}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-8/12}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-8/13}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-8/14}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-8/15}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-8/16}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-8/17}&household electrical devices\\
\hline 9: hamster,cockroach,mouse & \includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-9/1}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-9/2}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-9/3}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-9/4}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-9/5}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-9/6}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-9/7}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-9/8}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-9/9}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-9/10}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-9/11}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-9/12}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-9/13}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-9/14}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-9/15}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-9/16}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-9/17}&small mammals\\
\hline 10: boy,woman,girl,baby & \includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-10/1}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-10/2}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-10/3}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-10/4}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-10/5}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-10/6}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-10/7}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-10/8}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-10/9}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-10/10}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-10/11}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-10/12}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-10/13}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-10/14}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-10/15}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-10/16}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-10/17}&people\\
\hline 11: aquarium fish,trout & \includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-11/1}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-11/2}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-11/3}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-11/4}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-11/5}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-11/6}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-11/7}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-11/8}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-11/9}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-11/10}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-11/11}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-11/12}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-11/13}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-11/14}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-11/15}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-11/16}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-11/17}&fish\\
\hline 12: lawn mover,camel & \includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-12/1}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-12/2}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-12/3}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-12/4}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-12/5}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-12/6}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-12/7}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-12/8}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-12/9}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-12/10}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-12/11}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-12/12}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-12/13}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-12/14}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-12/15}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-12/16}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-12/17}&large omnivores and herbivores\\
\hline 13: motorcycle,bicycle,tiger & \includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-13/1}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-13/2}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-13/3}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-13/4}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-13/5}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-13/6}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-13/7}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-13/8}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-13/9}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-13/10}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-13/11}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-13/12}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-13/13}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-13/14}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-13/15}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-13/16}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-13/17}&vehicles1\\
\hline 14: sea,plain,could,mountain & \includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-14/1}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-14/2}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-14/3}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-14/4}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-14/5}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-14/6}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-14/7}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-14/8}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-14/9}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-14/10}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-14/11}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-14/12}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-14/13}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-14/14}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-14/15}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-14/16}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-14/17}&large natural outdoor scenes\\
\hline 15: caterpillar,skunk,worm & \includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-15/1}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-15/2}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-15/3}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-15/4}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-15/5}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-15/6}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-15/7}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-15/8}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-15/9}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-15/10}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-15/11}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-15/12}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-15/13}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-15/14}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-15/15}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-15/16}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-15/17}&reptiles\\
\hline 16: apple,orange,pear & \includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-16/1}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-16/2}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-16/3}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-16/4}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-16/5}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-16/6}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-16/7}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-16/8}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-16/9}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-16/10}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-16/11}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-16/12}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-16/13}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-16/14}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-16/15}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-16/16}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-16/17}&fruit and vegetables\\
\hline 17: hamster,raccoon,wolf & \includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-17/1}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-17/2}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-17/3}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-17/4}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-17/5}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-17/6}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-17/7}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-17/8}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-17/9}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-17/10}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-17/11}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-17/12}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-17/13}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-17/14}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-17/15}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-17/16}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-17/17}&medium mammals\\
\hline 18: castle,house,wardrobe & \includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-18/1}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-18/2}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-18/3}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-18/4}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-18/5}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-18/6}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-18/7}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-18/8}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-18/9}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-18/10}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-18/11}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-18/12}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-18/13}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-18/14}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-18/15}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-18/16}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-18/17}&large man made outdoor things\\
\hline 19: plate,cup,bowl & \includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-19/1}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-19/2}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-19/3}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-19/4}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-19/5}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-19/6}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-19/7}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-19/8}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-19/9}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-19/10}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-19/11}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-19/12}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-19/13}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-19/14}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-19/15}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-19/16}\includegraphics[width=0.4cm]{ResNet18Graphs/pt1/Raw/LatentFactor-19/17}&food containers\\
\hline
\end{tabular}
\end{table*}
\subsubsection{Layer-wise Analysis of Neuron representations:}
\label{sec:activations}
In this section we try to quantify the behaviour of neurons as a cluster and across layers. We utilize the neuron embedding matrix for a given layer $j$, as denoted by $O_j$ $\in$ $ \mathbb{R}^{N_j \times d}_{+}$, where $N_j$ is the number of neurons in layer $j$, whereas $d$ is the number of latent factors in the factorization. Next we compute pairwise cosine similarity between the columns of a matrix $O_j$ and we do this $\forall j$ as shown in Figure \ref{fig:resnetcos0}, Figure \ref{fig:resnetcos1} and Figure \ref{fig:resnetcos2}. Here Layer 0,1,2 refer to 3 layers analyzed in the ResNet-18 in increasing order of depth and are not necessarily the first,second and third layers of the network. In these plots a high value at any entry $(i,j)$ indicates a higher overlap between the number of neurons which fire for inputs belonging in the 2 super classes best approximated by latent factor $i$ and latent factor $j$.
As indicated in Figures \ref{fig:resnetcos0},\ref{fig:resnetcos1} and \ref{fig:resnetcos2} the activations tend to be more intra-superclass, a result similar in nature to one observed by SVCCA\cite{raghu2017svcca} , i.e. more concentrated along the diagonal of the Similarity Matrix as we go deeper down the layers. This is also borne out by the eigen values of these Similarity Matrices, as the matrices tend to get closer to Identity, the lower the mean of first-K eigen-values as shown in \ref{fig:resneteig}.
\begin{figure*}[t!]
\begin{subfigure}{0.3\textwidth}
\centering
\includegraphics[width=\linewidth]{ResNet18Graphs/pt2/LayerLatentCosineSimilarity0.jpg}
\caption{Cosine Similarity: Layer 0}
\label{fig:resnetcos0}
\end{subfigure}
\begin{subfigure}{0.3\textwidth}
\centering
\includegraphics[width=\linewidth]{ResNet18Graphs/pt2/LayerLatentCosineSimilarity1.jpg}
\caption{Cosine Similarity: Layer 1}
\label{fig:resnetcos1}
\end{subfigure}
\begin{subfigure}{0.3\textwidth}
\centering
\includegraphics[width=\linewidth]{ResNet18Graphs/pt2/LayerLatentCosineSimilarity2.jpg}
\caption{Cosine Similarity: Layer 2}
\label{fig:resnetcos2}
\end{subfigure}
\caption{Plots of Cosine Similarity of Latent Factors in Layers 0,1,2 of ResNet-18. This highlighits the layerwise learning dynamics of the network and helps us visualize with concepts and classes occupy similar neural regions in a given layer of a network and how they evolve as we go deeper into the network. In fact, we observe that as we go deeper into the network, the similarity bcomes diagonal, showing higher separation of the latent concepts}
\label{fig:figResnet1b}
\end{figure*}
\begin{figure*}[thb!]
\begin{subfigure}{0.5\textwidth}
\centering
\includegraphics[width=0.8\linewidth]{ResNet18Graphs/pt2/EVALvsLayersPlot.png}
\caption{Eigenvalues of Similarity Matrices of ResNet-18}
\label{fig:resneteig}
\end{subfigure}\hfill
\begin{subfigure}{0.5\textwidth}
\centering
\includegraphics[width=0.8\linewidth]{VGG11Graphs/pt2/EVALvsLayersPlot.png}
\caption{Eigenvalues of Similarity Matrices of VGG-11}
\label{fig:vgg11eig}
\end{subfigure}
\caption{Plots of Eigenvalues of Similarity Matrix for ResNet-18 and VGG-11. This plot shows increasing independence of learned latent concepts w.r.t. neurons as we go deeper in the non-classification layers of the network. The closer the a matrix is to Identity the closer the average of it's eigen values is to 1 and vice versa. The last layer in each of the 2 figures is the output of pre log softmax of the network, which is usually a much lower dimensional space than the previous layers}
\label{fig:resnet18vgg11eig}
\end{figure*}
We also show similar results for a VGG-11\cite{simonyan2014deep} Trained and analyzed on CIFAR-100 in Figure \ref{fig:vgg11eig}.
\subsubsection{Co-Analysis of Pixels and Inputs:}
\label{sec:pixels}
In this section we analyze the pixel space along with inputs. The Matrices $P_i$'s $\in$ $ \mathbb{R}^{S_i \times d}_{+}$ hold the input representation of pixels in the input channel $i$ where $S_i$ is the number of Pixels in Input Channel-$i$, or the vectorized size of the channel. Each column of a matrix $P_i$ represents a feature activation score of all the pixels in channel $i$ for the given latent factor. Therefore by collecting information from column 2 of $P_0$,$P_1$ and $P_2$ and resizing them appropriately we get an average pattern of activation across the pixel space for all the images that belong to Latent Factor 2, as shown in Figure \ref{fig:LF2}a, and for Latent-Factor-3 in \ref{fig:LF3}a. This functionality is very similar to LIME \cite{lime}, but instead of individual images we can operate on pixel representations which represent learned concepts. We then take these Latent-Factor-Images, and create a mask where we assign a value of 1 at a pixel location if it's activation value is above the median activation value for the Latent Image and 0 other wise and overlay it with the topmost images of the Latent Factor as found in our analysis of Matrix-$F$ in Table \ref{tab:Table1}. We also take around 30 Nearest Neighbours of the Image as determined by the Latent Space of Matrix-$F$ and give a distribution of the Latent Concepts those Neighbours have their highest affinity for, thereby helping us achieve interpretability on an input-by-input basis by being able to say that a given image is close to another. Next, via 2 examples we present a per example case study of interpretability possible by the use of this model.\\
In Figures \ref{fig:LF2}a,\ref{fig:LF2}b,\ref{fig:LF2}c and \ref{fig:LF2}d For Latent Factor-2 we present the Latent Representations of Pixels, The topmost Image in that Latent Factor, The top 50\% activated pixels super imposed on the original image, and the Latent Concept Distribution of top-30 Nearest Neighbours of the image, respectively. As noted previously in Table\ref{tab:Table1}, Latent Factor 2 Represents classes like mountain, bridge, castles, skyscrapers etc, leading to it's topmost super class being "large man-made outdoor things". On average, the most activated pixels for images belonging to this superclass tend to be blue pixels towards the top, green towards the middle and red towards the bottom. And the set of top-30 nearest neighbours for this particular image of a Mountain also has members belonging to Latent Factor 3 and 7, 2 concepts which have a high affinity for inputs belonging to super class of trees.\\
In Figures \ref{fig:LF3}a,\ref{fig:LF3}b,\ref{fig:LF3}c and \ref{fig:LF3}d we present a similar analysis for Latent Factor-3. As shown in Table\ref{tab:Table1}, Latent Factor 3 Represents classes like willow tree, maple tree , oak trees, pine trees etc, leading to it's topmost super class being "trees". In this case, the most activated set of pixels is on the right half of the pixel space with a higher affinity in green and red channels of the image, as shown in Figure \ref{fig:LF3}a. In Figure \ref{fig:LF3}c we see the effects of applying this latent image as a filter to the image of a willow tree \ref{fig:LF3}b and we see that the right half of the image is redundant and the left half captures basic underlying features about the image like contours, shapes colours etc.
\begin{figure} [!htb]
\begin{subfigure}[b]{0.3\linewidth}
\centering
\includegraphics[width=0.9\textwidth]{ResNet18Graphs/pt3/LatentFactor_2.jpg}
\label{fig:lf2a}
\caption{Latent-Factor:2}
\end{subfigure}
\begin{subfigure}[b]{0.3\linewidth}
\centering
\includegraphics[width=0.9\textwidth]{ResNet18Graphs/pt3/lf2/raw/1-large-natural-outdoor-scenes-mountain-test-index-03710.png}
\label{fig:lf2b}
\caption{Image:Mountain}
\end{subfigure}
\begin{subfigure}[b]{0.3\linewidth}
\centering
\includegraphics[width=0.9\textwidth]{ResNet18Graphs/pt3/lf2/masked/1-masked.png}
\label{fig:lf2c}
\caption{Filtered Image}
\end{subfigure}
\begin{subfigure}{0.4\textwidth}
\centering
\includegraphics[width=0.8\linewidth]{ResNet18Graphs/pt3/lf2/raw/1-ImgNum-2133.png}
\caption{Top-30 Nearest Neighbours of this Image}
\label{fig:lf2d}
\end{subfigure}
\caption{Analysis of Topmost Image from Latent-Factor:2}
\label{fig:LF2}
\end{figure}
\begin{figure} [!htb]
\begin{subfigure}[b]{0.3\linewidth}
\centering
\includegraphics[width=0.9\textwidth]{ResNet18Graphs/pt3/LatentFactor_3.jpg}
\label{fig:3a}
\caption{Latent-Factor:3}
\end{subfigure}
\begin{subfigure}[b]{0.3\linewidth}
\centering
\includegraphics[width=0.9\textwidth]{ResNet18Graphs/pt3/lf3/raw/1-trees-willow-tree-test-index-05303.png}
\label{fig:3b}
\caption{Image: Willow-Tree}
\end{subfigure}
\begin{subfigure}[b]{0.3\linewidth}
\centering
\includegraphics[width=0.9\textwidth]{ResNet18Graphs/pt3/lf3/masked/1-masked.png}
\label{fig:3c}
\caption{Filtered Image}
\end{subfigure}
\begin{subfigure}{0.4\textwidth}
\centering
\includegraphics[width=0.8\linewidth]{ResNet18Graphs/pt3/lf3/raw/1-ImgNum-2612.png}
\caption{Top-30 Nearest Neighbours of this Image}
\label{fig:3d}
\end{subfigure}
\caption{Analysis of Topmost Image from Latent-Factor:3}
\label{fig:LF3}
\end{figure}
\section{Extensions and Applications of the Model}
\label{sec:ext}
We modify the model in \autoref{eq:1} by imposing a group sparse regularization \cite{doi:10.1137/1.9781611972825.73} on the factor Matrix-$F$ and only including the neural activations in the objective function. In \autoref{tab:Table2}, we present a case study where a ResNet-18 is trained on CIFAR-10 \cite{Krizhevsky09learningmultiple} and evaluated on CIFAR-100, we omit some latent factors for brevity. The goal here is to visualize the generalization ability of the network to cluster and distinguish between natural images based on an observation of similar but out of sample data distribution during training. In order to validate the result we then take the latent concepts learned by the model and evaluate TCAV\cite{kim2017interpretability} scores \footnote{https://github.com/rakhimovv/tcav} for each combination of latent concept and input class, the results for which are shown in \autoref{fig:threePlusfour}.
\begin{table*}[!ht]
\caption{Latent Factor Analysis Group Sparsity - Activations Only} \label{tab:Table2}
\begin{tabular}
{lllll} \hline Factor: Top Classes & Top Images\\
\hline 1: kangaroo,rabbit,fox,squirrel & \includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-1/1}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-1/2}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-1/3}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-1/4}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-1/5}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-1/6}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-1/7}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-1/8}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-1/9}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-1/10}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-1/11}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-1/12}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-1/13}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-1/14}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-1/15}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-1/16}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-1/17}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-1/18}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-1/19}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-1/20}\\
\hline 2: woman,boy,girl,baby,man & \includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-2/1}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-2/2}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-2/3}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-2/4}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-2/5}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-2/6}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-2/7}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-2/8}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-2/9}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-2/10}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-2/11}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-2/12}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-2/13}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-2/14}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-2/15}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-2/16}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-2/17}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-2/18}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-2/19}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-2/20}\\
\hline 4: pickup-truck,motorcycle,bus,tank & \includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-4/1}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-4/2}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-4/3}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-4/4}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-4/5}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-4/6}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-4/7}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-4/8}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-4/9}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-4/10}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-4/11}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-4/12}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-4/13}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-4/14}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-4/15}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-4/16}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-4/17}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-4/18}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-4/19}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-4/20}\\
\hline 5: cattle,elephant,camel,chimpanzee & \includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-5/1}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-5/2}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-5/3}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-5/4}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-5/5}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-5/6}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-5/7}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-5/8}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-5/9}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-5/10}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-5/11}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-5/12}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-5/13}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-5/14}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-5/15}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-5/16}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-5/17}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-5/18}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-5/19}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-5/20}\\
\hline 6: porcupine,possum,squirrel,raccoon & \includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-6/1}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-6/2}
\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-6/3}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-6/4}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-6/5}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-6/6}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-6/7}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-6/8}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-6/9}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-6/10}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-6/11}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-6/12}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-6/13}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-6/14}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-6/15}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-6/16}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-6/17}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-6/18}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-6/19}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-6/20}\\
\hline 7: willow,maple,oak,palm -all trees & \includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-7/1}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-7/2}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-7/3}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-7/4}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-7/5}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-7/6}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-7/7}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-7/8}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-7/9}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-7/10}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-7/11}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-7/12}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-7/13}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-7/14}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-7/15}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-7/16}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-7/17}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-7/18}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-7/19}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-7/20}\\
\hline 9: apple,sweet-pepper,rose,orange & \includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-9/1}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-9/2}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-9/3}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-9/4}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-9/5}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-9/6}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-9/7}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-9/8}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-9/9}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-9/10}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-9/11}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-9/12}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-9/13}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-9/14}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-9/15}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-9/16}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-9/17}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-9/18}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-9/19}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-9/20}\\
\hline 10: plate,bowl,can,clock & \includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-10/1}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-10/2}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-10/3}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-10/4}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-10/5}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-10/6}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-10/7}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-10/8}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-10/9}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-10/10}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-10/11}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-10/12}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-10/13}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-10/14}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-10/15}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-10/16}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-10/17}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-10/18}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-10/19}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-10/20}\\
\hline 12: whale,rocket,dolphin,sea & \includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-12/1}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-12/2}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-12/3}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-12/4}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-12/5}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-12/6}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-12/7}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-12/8}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-12/9}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-12/10}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-12/11}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-12/12}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-12/13}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-12/14}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-12/15}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-12/16}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-12/17}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-12/18}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-12/19}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-12/20}\\
\hline 13: girl,snail,boy,spider,crab & \includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-13/1}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-13/2}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-13/3}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-13/4}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-13/5}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-13/6}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-13/7}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-13/8}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-13/9}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-13/10}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-13/11}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-13/12}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-13/13}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-13/14}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-13/15}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-13/16}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-13/17}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-13/18}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-13/19}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-13/20}\\
\hline 16: lion,hamster,wolf,mouse & \includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-16/1}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-16/2}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-16/3}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-16/4}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-16/5}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-16/6}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-16/7}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-16/8}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-16/9}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-16/10}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-16/11}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-16/12}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-16/13}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-16/14}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-16/15}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-16/16}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-16/17}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-16/18}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-16/19}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-16/20}\\
\hline 18: streetcar,train,bridge,bus & \includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-18/1}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-18/2}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-18/3}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-18/4}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-18/5}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-18/6}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-18/7}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-18/8}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-18/9}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-18/10}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-18/11}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-18/12}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-18/13}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-18/14}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-18/15}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-18/16}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-18/17}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-18/18}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-18/19}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-18/20}\\
\hline 19: oak,maple,poppy,sunflower & \includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-19/1}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-19/2}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-19/3}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-19/4}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-19/5}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-19/6}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-19/7}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-19/8}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-19/9}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-19/10}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-19/11}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-19/12}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-19/13}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-19/14}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-19/15}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-19/16}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-19/17}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-19/18}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-19/19}\includegraphics[width=0.4cm]{Sec5/Table3/LatentFactor-19/20}\\
\hline
\end{tabular}
\end{table*}
\begin{figure*}[!h]
\centering
\includegraphics[width=\linewidth]{Sec5/TCAVHEATMAPS/GRPSPARSEACT.png}
\caption{TCAV scores for Group Sparsity based model}
\label{fig:threePlusfour}
\end{figure*}
\section{Conclusions}
\label{sec:conclusions}
In this paper, we introduced an unsupervised framework for exploration of the representations learned by a CNN, based on constrained and regularized coupled matrix factorization. Our proposed method is unique and novel in that it is the first such framework to allow for {\em joint} exploration of the representations that a CNN has learned across features (pixels), activations, and data instances. This is in stark contrast to existing state-of-the-art works, which are typically restricted to one of those three modalities, as summarized in Fig. \ref{fig:comp}. Furthermore, owing to the simplicity of the factorization model, our method can provide easily interpretable insights. As a result, our proposed framework offers maximum flexibility and bridges the gap between existing works, while producing comparable results to state-of-the-art, when used for the same (albeit limited) purpose of existing work. Case in point, in this paper, we demonstrate a number of applications of our framework drawing parallels to what existing work can offer compared to our results, including the extraction of instance-based interpretable concepts (Sec. \ref{sec:concepts}), and based on those concepts we provide insights on the the behavior of neurons in different layers (Sec. \ref{sec:activations}), and instance-level pixel-based insights (Sec. \ref{sec:pixels}). In future work, we will investigate the adaptation to our framework to different architectures (e.g., RNN and GCN) and different applications (e.g., NLP, Graph Mining, and Recommendation Systems).
\subsubsection{Literature survey}}
\newcommand{\current} {\subsubsection{Current and Proposed Work}}
\section{Acknowledgements}
{\scriptsize
Research was supported by the National Science Foundation Grant No. XXXXXX. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the funding parties.
}
}
\balance
\bibliographystyle{plain}
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 6,111
|
Glarona Sud (toponimo italiano; in tedesco e ufficialmente Glarus Süd, in francese Glaris Sud) è un comune svizzero di 9 494 abitanti del Canton Glarona; è il comune più esteso del cantone.
Geografia fisica
Glarona Sud si estende su una superficie di 430,11 km²; il territorio del comune è attraversato dal fiume Linth e dal suo affluente Sernf. La Linth sfocia a Glarona Nord nel lago di Walenstadt.
Il comune confina con quattro cantoni svizzeri: Grigioni a sud, San Gallo a est, Svitto e Uri a ovest. Il punto più elevato del comune è il monte Tödi (3 614 m s.l.m.) al confine con i Grigioni; sul territorio si trovano le dighe Garichte West, Garichte Ost e Limmern.
Storia
Il comune di Glarona Sud è stato istituito il 1º gennaio 2011 con la fusione dei comuni soppressi di Betschwanden, Braunwald, Elm, Engi, Haslen, Linthal, Luchsingen, Matt, Mitlödi, Rüti, Schwanden, Schwändi e Sool; capoluogo comunale è Schwanden. In precedenza il comune di Luchsingen aveva inglobato i comuni soppressi di Diesbach e Hätzingen (1º gennaio 2004) e quello di Haslen i comuni soppressi di Leuggelbach e Nidfurn (1º gennaio 2006).
Geografia antropica
Frazioni
Le frazioni di Glarona Sud sono:
Betschwanden
Braunwald
Bergeten
Elm
Müsli
Obmoos
Schwändi
Steinibach
Sulzbach
Töniberg
Untertal
Vogelsang
Wald
Engi
Dörfli
Hinterdorf
Vorderdorf
Haslen
Büel
Leu
Leuggelbach
Steinigen
Mülibächli
Nidfurn
Oberhaslen
Zussigen
Linthal
Auen
Dorf
Ennetlinth
Matt
Luchsingen
Adlenbach
Diesbach
Dornhaus
Hätzingen
Tschuepis
Matt
Weissenberge
Mitlödi
Ennetlinth
Rüti
Schwanden
Thon
Tschachen
Schwändi
Lassigen
Oberschwändi
Unterschwändi
Sool
Obersool
Untersool
Wart
Infrastrutture e trasporti
Il comune è servito dalla ferrovia Ziegelbrücke-Linthal (linea S25 della rete celere di Zurigo).
Note
Altri progetti
Collegamenti esterni
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 4,029
|
Q: Rxjava2 - how to cache Observable I am thinking the best way to cache a retrofit2 api response observable is with behaviorSubject. This would emit the last item that was sent. so i am trying to make a function that would take a boolean cache paramter to know if the response should be retrieved from cache or from retrofit2 call. The retrofit2 call just returns an observable. But lets see what i want:
Here is the function before i implemented caching it just simply made a retrofit2 call to get a api response and someone subscribed to it somewhere else:
public Observable<List<CountryModel>> fetchCountries() {
CountriesApi countriesService = mRetrofit.create(CountriesApi.class);
return countriesService.getCountries();
}`
and here is what i want to achieve but having a hard time implementing a behaviorsubject to do it ? or how else can i cache the response at will ?
public Observable<List<CountryModel>> fetchCountries(boolean cache) {
CountriesApi countriesService = mRetrofit.create(CountriesApi.class);
if(!cache){
//somehow here i need to wrap the call in a behaviorsubject incase next time they want a cache - so need to save to cache here for next time around but how ?
return countriesService.getCountries();
} else{
behaviorsubject<List<CountryModel>>.create(countriesService.getCountries())
//this isnt right. can you help ?
}
}`
A: I'd suggest you to just cache the response (List) like this:
List<CountryModel> cachedCountries = null;
public Observable<List<CountryModel>> fetchCountries(boolean cache) {
if(!cache || cachedCountries == null){
CountriesApi countriesService = mRetrofit.create(CountriesApi.class);
return countriesService
.getCountries()
.doOnNext(new Action1<List<CountryModel>>() {
@Override
public void call(List<CountryModel> countries) {
cachedCountries = countries;
}
});
} else {
return Observable.just(cachedCountries);
}
}
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 6,920
|
Ruth Sandhoff is a German classically trained mezzo-soprano. Her concert repertory ranges from early Baroque to contemporary music, with a special fondness for lieder.
Biography
Ruth Sandhoff was born in Aachen, Germany. She studied singing at the Hochschule für Musik und Tanz Köln and then studied with Ingeborg Most at the Hochschule für Musik Freiburg, graduating in 1993. Sandhoff has continued training in master classes with Elisabeth Glauser, Sena Jurinac, Cornelia Kallisch and Anna Reynolds.
In 1996 and 1997 Sandhoff sang at notable music festivals in both Europe and the United States, including: the Oregon Bach Festival, Internationale Maifestspiele Wiesbaden, Musique en Picardie, Festival of Flanders, Bach Festival of Philadelphia and European Musikfest Stuttgart. Recent festival appearances include the Melbourne International Arts Festival, the La Folle Journée in Nantes and Folles Journées de Lisbon.
Sandhoff has sung as a soloist with Oper Leipzig, Hessisches Staatstheater Wiesbaden, Oper Köln, and Stadttheater Aachen. With Rilling, she performed in the United States with Bach's Mass in B minor and Matthäus-Passion. She has also performed with the conductors Jos van Immerseel and . She sang Schubert's lieder for choreographer Sasha Waltz in performances in Barcelona, Berlin, Lyon, Rome, Stockholm, among others.
Her repertoire ranges from early Baroque to contemporary music and has included many television, radio and recording performances. She recorded the first version of Bach's Magnificat, singing the soprano II part, with Helmuth Rilling in 2000, Ezio with Michael Hofstetter, and Carl Philipp Emanuel Bach's Magnificat with Michael Schneider, singing the alto part.
References
Living people
German opera singers
German sopranos
Hochschule für Musik und Tanz Köln alumni
Hochschule für Musik Freiburg alumni
People from Aachen
Year of birth missing (living people)
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 5,703
|
package io.github.mzmine.modules.io.projectload.version_2_5;
import com.google.common.collect.Range;
import io.github.mzmine.datamodel.MassList;
import io.github.mzmine.datamodel.PolarityType;
import io.github.mzmine.datamodel.RawDataFile;
import io.github.mzmine.datamodel.Scan;
import io.github.mzmine.datamodel.impl.DDAMsMsInfoImpl;
import io.github.mzmine.datamodel.impl.SimpleScan;
import io.github.mzmine.datamodel.msms.ActivationMethod;
import io.github.mzmine.datamodel.msms.DDAMsMsInfo;
import io.github.mzmine.main.MZmineCore;
import io.github.mzmine.project.impl.RawDataFileImpl;
import io.github.mzmine.util.RangeUtils;
import java.io.File;
import java.io.IOException;
import java.io.InputStream;
import java.util.ArrayList;
import java.util.TreeMap;
import java.util.logging.Logger;
import javax.xml.parsers.ParserConfigurationException;
import javax.xml.parsers.SAXParser;
import javax.xml.parsers.SAXParserFactory;
import org.xml.sax.Attributes;
import org.xml.sax.SAXException;
import org.xml.sax.helpers.DefaultHandler;
public class RawDataFileOpenHandler_2_5 extends DefaultHandler {
private Logger logger = Logger.getLogger(this.getClass().getName());
private StringBuffer charBuffer;
private RawDataFileImpl newRawDataFile;
private int scanNumber;
private int msLevel;
private int[] fragmentScan;
private int numberOfFragments;
private double precursorMZ;
private int precursorCharge;
private float retentionTime;
private int dataPointsNumber;
private int fragmentCount;
private int currentStorageID;
private int storedDataID;
private int storedDataNumDP;
private TreeMap<Integer, Long> dataPointsOffsets;
private TreeMap<Integer, Integer> dataPointsLengths;
private ArrayList<MassList> massLists;
private PolarityType polarity = PolarityType.UNKNOWN;
private String scanDescription = "";
private Range<Double> scanMZRange = null;
private boolean canceled = false;
/**
* Extract the scan file and copies it into the temporary folder. Create a new raw data file using
* the information from the XML raw data description file
*
* @param is
* @param scansFile
* @param isIMSRawDataFile this parameter is ignored in project version 2.3
* @throws SAXException
* @throws ParserConfigurationException
*/
public RawDataFile readRawDataFile(InputStream is, File scansFile, boolean isIMSRawDataFile,
boolean isImagingRawDataFile) throws IOException, ParserConfigurationException, SAXException,
UnsupportedOperationException {
if (isIMSRawDataFile) {
throw new UnsupportedOperationException(
"Ion mobility is not supported in projects created before MZmine 3.0");
}
if (isImagingRawDataFile) {
throw new UnsupportedOperationException(
"Imaging is not supported in projects created before MZmine 3.0");
}
charBuffer = new StringBuffer();
massLists = new ArrayList<>();
newRawDataFile = (RawDataFileImpl) MZmineCore.createNewFile("DUMMYNAME", null, null);
// newRawDataFile.openDataPointsFile(scansFile);
// dataPointsOffsets = newRawDataFile.getDataPointsOffsets();
// dataPointsLengths = newRawDataFile.getDataPointsLengths();
// Reads the XML file (raw data description)
SAXParserFactory factory = SAXParserFactory.newInstance();
SAXParser saxParser = factory.newSAXParser();
saxParser.parse(is, this);
// Adds the raw data file to MZmine
// RawDataFile rawDataFile = newRawDataFile.finishWriting();
return newRawDataFile;
}
public void cancel() {
canceled = true;
}
/**
* @see org.xml.sax.helpers.DefaultHandler#startElement(java.lang.String, java.lang.String,
* java.lang.String, org.xml.sax.Attributes)
*/
@Override
public void startElement(String namespaceURI, String lName, String qName, Attributes attrs)
throws SAXException {
if (canceled) {
throw new SAXException("Parsing canceled");
}
// This will remove any remaining characters from previous elements
getTextOfElement();
if (qName.equals(RawDataElementName_2_5.QUANTITY_FRAGMENT_SCAN.getElementName())) {
numberOfFragments =
Integer.parseInt(attrs.getValue(RawDataElementName_2_5.QUANTITY.getElementName()));
if (numberOfFragments > 0) {
fragmentScan = new int[numberOfFragments];
fragmentCount = 0;
}
}
if (qName.equals(RawDataElementName_2_5.SCAN.getElementName())) {
currentStorageID =
Integer.parseInt(attrs.getValue(RawDataElementName_2_5.STORAGE_ID.getElementName()));
}
if (qName.equals(RawDataElementName_2_5.STORED_DATA.getElementName())) {
storedDataID =
Integer.parseInt(attrs.getValue(RawDataElementName_2_5.STORAGE_ID.getElementName()));
storedDataNumDP = Integer
.parseInt(attrs.getValue(RawDataElementName_2_5.QUANTITY_DATAPOINTS.getElementName()));
}
if (qName.equals(RawDataElementName_2_5.MASS_LIST.getElementName())) {
String name = attrs.getValue(RawDataElementName_2_5.NAME.getElementName());
int storageID =
Integer.parseInt(attrs.getValue(RawDataElementName_2_5.STORAGE_ID.getElementName()));
// todo: what was this supposed to do?
// MassList newML = new SimpleMassList(null, null, null, null);
// massLists.add(newML);
}
}
/**
* @see org.xml.sax.helpers.DefaultHandler#endElement(java.lang.String, java.lang.String,
* java.lang.String)
*/
@Override
public void endElement(String namespaceURI, String sName, String qName) throws SAXException {
if (canceled) {
throw new SAXException("Parsing canceled");
}
// <NAME>
if (qName.equals(RawDataElementName_2_5.NAME.getElementName())) {
// Adds the scan file and the name to the new raw data file
String name = getTextOfElement();
logger.info("Loading raw data file: " + name);
newRawDataFile.setName(name);
}
if (qName.equals(RawDataElementName_2_5.QUANTITY_SCAN.getElementName())) {
// number of scans - actually not used for anything
Integer.parseInt(getTextOfElement());
}
if (qName.equals(RawDataElementName_2_5.SCAN_ID.getElementName())) {
scanNumber = Integer.parseInt(getTextOfElement());
}
if (qName.equals(RawDataElementName_2_5.STORED_DATA.getElementName())) {
// need to multiply the offsets by 2 to account for the fact that the old projects used floats
// but now we use doubles
// TODO is this still necessary? @tomas
long offset = Long.parseLong(getTextOfElement()) * 2;
dataPointsOffsets.put(storedDataID, offset);
dataPointsLengths.put(storedDataID, storedDataNumDP);
}
if (qName.equals(RawDataElementName_2_5.MS_LEVEL.getElementName())) {
msLevel = Integer.parseInt(getTextOfElement());
}
if (qName.equals(RawDataElementName_2_5.PARENT_SCAN.getElementName())) {
Integer.parseInt(getTextOfElement());
}
if (qName.equals(RawDataElementName_2_5.POLARITY.getElementName())) {
String txt = getTextOfElement();
try {
polarity = PolarityType.valueOf(txt);
} catch (Exception e) {
polarity = PolarityType.fromSingleChar(txt);
}
}
if (qName.equals(RawDataElementName_2_5.SCAN_DESCRIPTION.getElementName())) {
scanDescription = getTextOfElement();
}
if (qName.equals(RawDataElementName_2_5.SCAN_MZ_RANGE.getElementName())) {
final String text = getTextOfElement();
scanMZRange = RangeUtils.parseDoubleRange(text);
}
if (qName.equals(RawDataElementName_2_5.PRECURSOR_CHARGE.getElementName())) {
precursorCharge = Integer.parseInt(getTextOfElement());
}
if (qName.equals(RawDataElementName_2_5.PRECURSOR_MZ.getElementName())) {
precursorMZ = Double.parseDouble(getTextOfElement());
}
if (qName.equals(RawDataElementName_2_5.RETENTION_TIME.getElementName())) {
// Before MZmine.6 retention time was saved in seconds, but now we
// use minutes, so we need to divide by 60
retentionTime = (float) (Double.parseDouble(getTextOfElement()) / 60d);
}
// if (qName.equals(RawDataElementName_2_5.ION_MOBILITY.getElementName())) {
// mobility = Double.parseDouble(getTextOfElement());
// }
if (qName.equals(RawDataElementName_2_5.QUANTITY_DATAPOINTS.getElementName())) {
dataPointsNumber = Integer.parseInt(getTextOfElement());
}
if (qName.equals(RawDataElementName_2_5.FRAGMENT_SCAN.getElementName())) {
fragmentScan[fragmentCount++] = Integer.parseInt(getTextOfElement());
}
if (qName.equals(RawDataElementName_2_5.SCAN.getElementName())) {
final DDAMsMsInfo info =
msLevel != 1 && precursorMZ != 0d ? new DDAMsMsInfoImpl(precursorMZ, precursorCharge,
null, null, null, msLevel, ActivationMethod.UNKNOWN, null) : null;
Scan storableScan = new SimpleScan(newRawDataFile, scanNumber, msLevel, retentionTime,
info, /* fragmentScan, */ null, null, null, polarity,
scanDescription, scanMZRange);
try {
newRawDataFile.addScan(storableScan);
} catch (IOException e) {
throw new SAXException(e);
}
for (MassList newML : massLists) {
// newML.setScan(storableScan);
storableScan.addMassList(newML);
}
// Cleanup
massLists.clear();
currentStorageID = -1;
dataPointsNumber = -1;
scanNumber = -1;
msLevel = -1;
retentionTime = -1;
precursorMZ = -1;
precursorCharge = -1;
fragmentScan = null;
polarity = PolarityType.UNKNOWN;
scanDescription = "";
scanMZRange = null;
}
}
/**
* Return a string without tab an EOF characters
*
* @return String element text
*/
private String getTextOfElement() {
String text = charBuffer.toString();
text = text.replaceAll("[\n\r\t]+", "");
text = text.replaceAll("^\\s+", "");
charBuffer.delete(0, charBuffer.length());
return text;
}
/**
* characters()
*
* @see org.xml.sax.ContentHandler#characters(char[], int, int)
*/
@Override
public void characters(char buf[], int offset, int len) throws SAXException {
charBuffer = charBuffer.append(buf, offset, len);
}
}
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 2,291
|
using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.ComponentModel;
using Newtonsoft.Json;
namespace OptimalPayments.Common
{
/// <summary>
/// This is the base class for all objects within the sdk.
/// It is used to allow generic assignment of fields and properties.
/// </summary>
public abstract class JSONObject
{
/// <summary>
/// fieldTypes must be passed into the constructor in order to allow generic validation
/// </summary>
protected Dictionary<string, object> fieldTypes;
/// <summary>
/// this dictionary will store all set properties within the final object
/// </summary>
private Dictionary<string, object> properties = new Dictionary<string,object>();
/// <summary>
/// optionalFields will be used by the api client to determine which of the set fields
/// should be sent to the api
/// </summary>
private List<string> optionalFields;
/// <summary>
/// requiredFields will be used by the api client to determine which of the fields must
/// be set before sending a request to the api
/// </summary>
private List<string> requiredFields;
protected static Type STRING_TYPE = typeof(string);
protected static Type INT_TYPE = typeof(int);
protected static Type BOOL_TYPE = typeof(bool);
protected static Type URL_TYPE = typeof(Url);
protected static Type EMAIL_TYPE = typeof(Email);
protected static Type FLOAT_TYPE = typeof(float);
/// <summary>
/// The object will be json serialized using only the optional and required properties
/// </summary>
/// <returns>string</returns>
public override string ToString()
{
return JsonConvert.SerializeObject(this.jsonSerialize());
}
/// <summary>
/// This method will serialize only the required or optional properties within this
/// and any nested JSONObjects. or if no required/optional properties are set, then
/// all properties will be returned
/// </summary>
/// <returns></returns>
private Dictionary<string, object> jsonSerialize()
{
this.checkRequiredFields();
Dictionary<string, object> toJSON;
if ((null == this.optionalFields || 0 == this.optionalFields.Count) &&
(null == this.requiredFields || 0 == this.requiredFields.Count))
{
toJSON = this.properties;
}
else
{
toJSON = new Dictionary<string, object>();
if (requiredFields != null)
{
foreach (string key in requiredFields)
{
if (properties.ContainsKey(key))
{
toJSON.Add(key, properties[key]);
}
}
}
if (optionalFields != null)
{
foreach (string key in optionalFields)
{
if (properties.ContainsKey(key))
{
toJSON.Add(key, properties[key]);
}
}
}
}
return this.filterJSON(toJSON) as Dictionary<string, object>;
}
/// <summary>
/// Throws an exception if any required fields have not been set
/// </summary>
public void checkRequiredFields()
{
if (requiredFields != null)
{
List<string> missingFields = new List<string>();
foreach (string key in requiredFields)
{
if (!properties.ContainsKey(key))
{
missingFields.Add(key);
}
}
if (missingFields.Count > 0)
{
throw new OptimalException("Missing required properties: " + string.Join(", ", missingFields));
}
}
}
/// <summary>
/// This method is used by jsonSerialize, and will filter all non required/optional
/// from any nested objects
/// </summary>
/// <param name="result">Dictioanry<string,object></param>
/// <returns>Dictionary<string,object></returns>
private dynamic filterJSON(dynamic result)
{
if (result is Dictionary<string, object>)
{
Dictionary<string, object> @return = new Dictionary<string, object>();
foreach (string key in ((Dictionary<string, object>)result).Keys)
{
@return[key] = this.filterJSON(result[key]);
}
return @return;
}
else if (((object)result).GetType().IsGenericType
&& ((object)result).GetType().GetGenericTypeDefinition() == typeof(List<>))
{
return this.filterList(result);
}
else if (result is JSONObject)
{
return ((JSONObject)result).jsonSerialize();
}
return result;
}
private List<object> filterList<T>(List<T> list)
{
List<object> @return = new List<object>();
foreach (T item in list)
{
@return.Add(this.filterJSON(item));
}
return @return; ;
}
/// <summary>
/// Set the optional fields to be consumed by the api client
/// </summary>
/// <param name="fields">List<String></param>
public void setOptionalFields(List<string> fields)
{
List<string> invalidKeys = new List<string>();
foreach (string key in fields)
{
if (!this.fieldTypes.ContainsKey(key))
{
invalidKeys.Add(key);
}
}
if (invalidKeys.Count > 0)
{
throw new OptimalException("Invalid optional fields. Unknown fields: " + string.Join(", ", invalidKeys));
}
this.optionalFields = fields;
}
/// <summary>
/// Set the required fields to be consumed by the api client
/// </summary>
/// <param name="fields"></param>
public void setRequiredFields(List<string> fields)
{
List<string> invalidKeys = new List<string>();
foreach (string key in fields)
{
if (!this.fieldTypes.ContainsKey(key))
{
invalidKeys.Add(key);
}
}
if (invalidKeys.Count > 0)
{
throw new OptimalException("Invalid required fields. Unknown fields: " + string.Join(", ", invalidKeys));
}
this.requiredFields = fields;
}
/// <summary>
/// Initialize the Object, setting the internetal properties from parameters based on the types
/// </summary>
/// <param name="types">Dictioanry<string,string></param>
/// <param name="parameters">Dictionary<string,object></param>
public JSONObject(Dictionary<string, object> types, Dictionary<string, object> parameters = null)
{
this.fieldTypes = types;
if (!Object.ReferenceEquals(parameters, null))
{
foreach (string key in parameters.Keys)
{
var tmp = getFieldInfo(key);
if (!Object.ReferenceEquals(tmp, null))
{
KeyValuePair<string, object> info = (KeyValuePair<string, object>)tmp;
this.setProperty(info.Key, parameters[key]);
}
}
}
}
/// <summary>
/// Set the property name with value cast based on the fieldTypes dictionary
/// </summary>
/// <param name="name">string</param>
/// <param name="value">dynamic</param>
protected void setProperty(string name, dynamic value) {
var tmp = getFieldInfo(name);
if (Object.ReferenceEquals(tmp, null))
{
throw new OptimalException("Invalid property " + name + " for class " + this.GetType().ToString());
}
KeyValuePair<string, object> info = (KeyValuePair<string, object>)tmp;
if (Object.ReferenceEquals(value, null))
{
this.properties.Remove(info.Key);
}
else
{
this.properties[info.Key] = this.cast(info.Key, value, info.Value);
}
}
/// <summary>
/// Get the pproperty name fromt he properties dictionary
/// </summary>
/// <param name="name">string</param>
/// <returns></returns>
protected dynamic getProperty(string name)
{
var tmp = getFieldInfo(name);
if (Object.ReferenceEquals(tmp, null))
{
throw new OptimalException("Invalid property " + name + " for class " + this.GetType().ToString());
}
KeyValuePair<string, object> info = (KeyValuePair<string, object>)tmp;
if (this.properties.ContainsKey(info.Key))
{
return this.properties[info.Key];
}
return null;
}
/// <summary>
/// Checks if a specfic property has been set
/// </summary>
/// <param name="name">string</param>
/// <returns></returns>
public bool hasProperty(string name)
{
var tmp = getFieldInfo(name);
if (null == tmp)
{
return false;
}
KeyValuePair<string, object> info = (KeyValuePair<string, object>)tmp;
return this.properties.ContainsKey(info.Key);
}
/// <summary>
/// Get the validation rules for a given field
/// </summary>
/// <param name="name">string</param>
/// <returns>KeyValuePair<string, string> or null</returns>
private dynamic getFieldInfo(string name)
{
if (null == this.fieldTypes)
{
throw new OptimalException("field types must be initialized");
}
if (this.fieldTypes.ContainsKey(name))
{
return new KeyValuePair<string, object>(name, this.fieldTypes[name]);
}
name = name.ToLower();
foreach (string key in this.fieldTypes.Keys)
{
if (key.ToLower() == name)
{
return new KeyValuePair<string, object>(key, this.fieldTypes[key]);
}
}
return null;
}
/// <summary>
/// Casts property value to type validation
/// </summary>
/// <param name="name">string</param>
/// <param name="value">dynamic</param>
/// <param name="validation">string</param>
/// <returns></returns>
public dynamic cast(string name, dynamic value, dynamic validation)
{
string valueString = null;
if (value is string)
{
valueString = (string)value;
}
if (validation is List<string>)
{
List<string> validationList = (List<string>)validation;
if (null == valueString || !validationList.Contains(valueString))
{
throw new OptimalException("Invalid value for property " + name + " for class " + this.GetType().ToString() + ". Expected one of: " + string.Join(", ", validationList) + ".");
}
return value;
}
else if (validation is Type)
{
Type validationType = validation as Type;
if (validationType.Equals(STRING_TYPE))
{
if (null == valueString)
{
throw new OptimalException("Invalid value for property " + name + " for class " + this.GetType().ToString() + ". String expected.");
}
return value;
}
else if (validationType.Equals(EMAIL_TYPE))
{
if (null == valueString|| valueString.IndexOf("@", StringComparison.CurrentCulture) <= 0)
{
throw new OptimalException("Invalid value for property " + name + " for class " + this.GetType().ToString() + ". Email expected.");
}
return value;
}
else if (validationType.Equals(URL_TYPE))
{
System.Uri uriResult;
if (null == valueString || (Uri.TryCreate(valueString, UriKind.Absolute, out uriResult) && null == uriResult))
{
throw new OptimalException("Invalid value for property " + name + " for class " + this.GetType().ToString() + ". URL expected.");
}
return value;
}
else if (validationType.Equals(INT_TYPE))
{
try
{
return Convert.ToInt32(value);
}
catch (Exception)
{
//format exception or overflow exception
throw new OptimalException("Invalid value for property " + name + " for class " + this.GetType().ToString() + ". Integer expected.");
}
}
else if (validationType.Equals(FLOAT_TYPE))
{
decimal decVal;
if (value is decimal)
{
decVal = ((decimal)value);
}
else if (valueString != null || !decimal.TryParse(((string)value), out decVal))
{
throw new OptimalException("Invalid value for property " + name + " for class " + this.GetType().ToString() + ". Decimal expected.");
}
return decVal;
}
else if (validationType.Equals(BOOL_TYPE))
{
bool boolVal;
if (value is bool)
{
boolVal = ((bool)value);
}
else if (null == valueString || !bool.TryParse(valueString, out boolVal))
{
throw new OptimalException("Invalid value for property " + name + " for class " + this.GetType().ToString() + ". Boolean expected.");
}
return boolVal;
}
else if (validationType.IsGenericType &&
validationType.GetGenericTypeDefinition() == typeof(List<>))
{
Type subType = validationType.GetGenericArguments()[0];
if (!(value is System.Collections.IList))
{
throw new OptimalException("Invalid value for property " + name + " for class " + this.GetType().ToString() + ". List expected.");
}
Type T = null;
for (int i = 0; i < ((System.Collections.IList)value).Count; i++)
{
value[i] = this.cast(name, value[i], subType);
T = ((object)((System.Collections.IList)value)[i]).GetType();
}
if (T != null && value is List<object>)
{
//convert list of subtype object to a list of the required subtype
dynamic newList = typeof(List<>)
.MakeGenericType(T)
.GetConstructor(new Type[] { })
.Invoke(new object[] { });
for (int i = 0; i < ((List<dynamic>)value).Count; i++)
{
newList.Add(value[i]);
}
return newList;
}
return value;
}
else
{
Type valueType = value.GetType();
if ((value is Dictionary<string, object>))
{
Object[] args = { value };
return Activator.CreateInstance(validationType, args);
}
else if (valueType == validationType)
{
return value;
}
else if (valueType.GetMethod("Build") != null && valueType.IsSubclassOf(typeof(GenericJSONBuilder)))
{
dynamic returnValue = value.Build();
if (returnValue.GetType() as Type == validationType)
{
return returnValue;
}
}
throw new OptimalException("Invalid value for property " + name + " for class " + this.GetType().ToString());
}
}
throw new OptimalException("Invalid validation rule for property " + name + " for class " + this.GetType().ToString());
}
}
}
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 2,392
|
import os
from ...grids import utils as gutils
from .constants import _NP_TO_NC_TYPE, open_netcdf
_OPENED_FILES = {}
def close_all():
for path in _OPENED_FILES:
close(path)
def close(path):
try:
_OPENED_FILES[path].close()
except KeyError:
pass
else:
del _OPENED_FILES[path]
class NetcdfField(object):
def __init__(
self, path, field, fmt="NETCDF4", append=False, time=None, keep_open=False
):
path = os.path.abspath(path)
self._path = path
self._field = field
if path in _OPENED_FILES and not os.path.isfile(path):
close(path)
if path in _OPENED_FILES:
self._root = _OPENED_FILES[path]
else:
self._root = open_netcdf(path, mode="w", fmt=fmt, append=append)
self._set_mesh_topology()
self._set_node_variable_data()
self._set_face_variable_data()
self._set_time_variable(now=time)
if keep_open:
_OPENED_FILES[path] = self._root
else:
self.close()
def _set_mesh_dimensions(self):
raise NotImplementedError("_set_mesh_dimensions")
def _set_mesh_coordinate_data(self):
raise NotImplementedError("_set_mesh_coordinate_data")
@property
def node_data_dimensions(self):
raise NotImplementedError("node_data_dimensions")
@property
def face_data_dimensions(self):
raise NotImplementedError("face_data_dimensions")
def close(self):
if self._path in _OPENED_FILES:
del _OPENED_FILES[self._path]
self._root.close()
@property
def type(self):
return "unknown"
@property
def field(self):
return self._field
@property
def root(self):
return self._root
@property
def topology_dimension(self):
return len(gutils.non_singleton_shape(self.field))
@property
def field_axes(self):
return gutils.non_singleton_axes(self.field)
@property
def node_coordinates(self):
return ""
@property
def face_connectivity(self):
return "face_nodes_connectivity"
@property
def face_node_connectivity(self):
return "face_nodes"
@property
def node_count(self):
return self.field.get_point_count()
@property
def face_count(self):
return self.field.get_cell_count()
@property
def vertex_count(self):
return self.field.get_vertex_count()
@property
def time_count(self):
try:
return len(self._root.variables["time"])
except KeyError:
return 0
def has_dimension(self, name):
return name in self._root.dimensions
def has_variable(self, name):
return name in self._root.variables
def create_dimension(self, name, dim_len):
try:
if not self.has_dimension(name):
self._root.createDimension(name, dim_len)
except IndexError:
pass
def create_variable(self, name, *args, **kwds):
if not self.has_variable(name):
self._root.createVariable(name, *args, **kwds)
def set_variable(self, name, *args, **kwds):
if len(args) not in (0, 1):
raise ValueError("number of arguments must be 0 or 1")
attrs = kwds.pop("attrs", {})
variable = self.data_variable(name)
for (attr, value) in attrs.items():
variable.setncattr(attr, value)
if len(args) > 0:
array = args[0]
if "time" in variable.dimensions:
n_times = self.time_count
if array.size > 1:
variable[n_times, :] = array.flat
else:
variable[n_times] = array[0]
else:
variable[:] = array.flat
def data_variable(self, name):
return self.root.variables[name]
def _set_mesh_topology(self):
self._set_topology()
self._set_mesh_dimensions()
self._set_time_dimension()
self._set_mesh_coordinate_data()
self._set_face_node_connectivity_data()
def _set_topology(self):
self.create_variable("mesh", "i8")
self.set_variable(
"mesh",
attrs={
"cf_role": "mesh_topology",
"topology_dimension": self.topology_dimension,
"node_coordinates": " ".join(self.node_coordinates),
"face_connectivity": self.face_connectivity,
"face_node_connectivity": self.face_node_connectivity,
"type": self.type,
},
)
def _set_time_dimension(self):
if not self.has_dimension("time"):
self.create_dimension("time", None)
def _set_coordinate_data(self):
self._set_mesh_coordinate_data()
self._set_face_node_connectivity_data()
def _set_time_variable(self, now=None, units="days", reference="00:00:00 UTC"):
self.create_variable("time", "f8", ("time",))
time = self.data_variable("time")
time.units = " ".join([units, "since", reference])
time.long_name = "time"
if now is not None:
time[self.time_count - 1] = now
else:
time[self.time_count - 1] = self.time_count - 1
def _set_variable_data(self):
self._set_node_variable_data()
self._set_face_variable_data()
def _set_node_variable_data(self):
point_fields = self.field.get_point_fields()
for (var_name, array) in point_fields.items():
self.create_variable(
var_name,
_NP_TO_NC_TYPE[str(array.dtype)],
["time"] + list(self.node_data_dimensions),
)
self.set_variable(
var_name,
array,
attrs={
"units": self.field.get_field_units(var_name),
"standard_name": var_name,
"long_name": var_name,
"location": "node",
"coordinates": " ".join(self.node_data_dimensions),
},
)
def _set_face_variable_data(self):
face_fields = self.field.get_cell_fields()
for (var_name, array) in face_fields.items():
self.create_variable(
var_name,
_NP_TO_NC_TYPE[str(array.dtype)],
["time"] + list(self.face_data_dimensions),
)
self.set_variable(
var_name,
array,
attrs={
"units": self.field.get_field_units(var_name),
"standard_name": var_name,
"long_name": var_name,
"location": "face",
"coordinates": " ".join(self.node_data_dimensions),
},
)
def _set_face_node_connectivity_data(self):
pass
class NetcdfRectilinearField(NetcdfField):
@property
def type(self):
return "rectilinear"
@property
def node_coordinates(self):
return gutils.non_singleton_dimension_names(self.field)
@property
def topology_dimension(self):
return len(gutils.non_singleton_shape(self.field))
@property
def node_data_dimensions(self):
return gutils.non_singleton_dimension_names(self.field)
@property
def axis_coordinates(self):
return gutils.non_singleton_dimension_names(self.field)
def _set_mesh_dimensions(self):
field_shape = self.field.get_shape()
for (name, axis) in zip(self.axis_coordinates, self.field_axes):
self.create_dimension(name, field_shape[axis])
def _set_mesh_coordinate_data(self):
for (name, axis) in zip(self.axis_coordinates, self.field_axes):
self.create_variable(name, "f8", (name,))
self.set_variable(
name,
self.field.get_axis_coordinates(axis=axis),
attrs={
"units": self.field.get_coordinate_units(axis),
"standard_name": self.field.get_coordinate_name(axis),
"long_name": self.field.get_coordinate_name(axis),
"name": self.field.get_coordinate_name(axis),
},
)
class NetcdfStructuredField(NetcdfRectilinearField):
@property
def type(self):
return "structured"
@property
def node_data_dimensions(self):
return gutils.non_singleton_dimension_names(self._field)
@property
def node_coordinates(self):
return gutils.non_singleton_dimension_names(self._field)
# names = gutils.non_singleton_dimension_names(self._field)
# return ['node_' + name for name in names]
def _set_mesh_dimensions(self):
NetcdfRectilinearField._set_mesh_dimensions(self)
for name in self.node_coordinates:
self.create_dimension(name, self.node_count)
def _set_mesh_coordinate_data(self):
dims = self.node_data_dimensions
# for (name, axis) in zip(self.node_coordinates, self.field_axes):
for (name, axis) in zip(self.node_data_dimensions, self.field_axes):
self.create_variable(name, "f8", dims)
self.set_variable(
name,
self.field.get_coordinate(axis),
attrs={
"units": self.field.get_coordinate_units(axis),
"standard_name": self.field.get_coordinate_name(axis),
"long_name": self.field.get_coordinate_name(axis),
},
)
class NetcdfUnstructuredField(NetcdfStructuredField):
@property
def type(self):
return "unstructured"
@property
def node_coordinates(self):
names = []
for axis in range(self.field.get_dim_count()):
names.append("node_" + self.field.get_coordinate_name(axis))
return names
@property
def topology_dimension(self):
return self.field.get_dim_count()
@property
def node_data_dimensions(self):
return ("n_node",)
# dimensions = []
# for name in self.node_coordinates:
# dimensions.append((name, ))
# return dimensions
@property
def face_data_dimensions(self):
return ("n_face",)
def _set_mesh_dimensions(self):
# for name in self.node_coordinates:
# self.create_dimension(name, self.node_count)
self.create_dimension("n_node", self.node_count)
self.create_dimension("n_face", self.face_count)
self.create_dimension("n_vertex", self.vertex_count)
self.create_dimension("n_max_face_nodes", self.field.get_max_vertices())
def _set_mesh_coordinate_data(self):
dims = self.node_data_dimensions
# for (name, axis) in zip(self.node_data_dimensions, self.field_axes):
# for (name, axis) in zip(self.node_coordinates, self.field_axes):
for (axis, name) in enumerate(self.node_coordinates):
self.create_variable(name, "f8", dims)
self.set_variable(
name,
self.field.get_coordinate(axis),
attrs={
"units": self.field.get_coordinate_units(axis),
"standard_name": self.field.get_coordinate_name(axis),
"long_name": self.field.get_coordinate_name(axis),
},
)
def _set_face_node_connectivity_data(self):
self.create_variable("face_nodes_connectivity", "i8", ("n_vertex",))
self.set_variable(
"face_nodes_connectivity",
self.field.get_connectivity(),
attrs={
"cf_role": "face_node_connectivity",
"long_name": "Maps every face to its corner nodes.",
"start_index": 0,
},
)
self.create_variable("face_nodes_offset", "i8", ("n_face",))
self.set_variable(
"face_nodes_offset",
self.field.get_offset(),
attrs={
"cf_role": "face_node_offset",
"long_name": "Maps face index into connectivity array",
},
)
(connectivity, fill_val) = self.field.get_connectivity_as_matrix()
self.create_variable(
"face_nodes", "i8", ("n_face", "n_max_face_nodes"), fill_value=fill_val
)
self.set_variable(
"face_nodes",
connectivity,
attrs={
"cf_role": "face_node_connectivity",
"long_name": "Maps every face to its corner nodes.",
"start_index": 0,
},
)
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 3,282
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Next on In The Studio with Elson and the Soul Barkada, Larry Feldman records some guitar tracks!
Welcome to In The Studio with Elson and the Soul Barkada! It's our video documentation of the completion of our album, Brand New Thing. Today, you'll get to see Keith Dasalla overdub some percussion tracks and me overdub some fretless bass. Enjoy!
Manila, Manila, Manila, Manila Machiiiiiine!
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 3,006
|
Bruna Surfistinha (bürgerlich Raquel Pacheco, * 28. Oktober 1984 in São Paulo) ist eine ehemalige brasilianische Prostituierte und Bestseller-Autorin.
Leben
Die Publikation ihres Weblogs, in dem sie ihre Erfahrungen mit Freiern freizügig schilderte, sicherte ihr die Aufmerksamkeit der brasilianischen Massenmedien.
Pacheco wuchs als Adoptivkind bei einer zur brasilianischen Oberschicht gehörenden Familie auf. Familiäre Probleme bewogen sie dazu, sich im Alter von 17 Jahren zu prostituieren. Ihre Schilderungen in ihrem Bestseller O Doce Veneno do Escorpião (Das süße Gift des Skorpions) und auf ihrem Blog zeigen die Prostitution, in die viele brasilianische Jugendliche aus Armut gezwungen werden, von einer sehr positiven Seite.
Ihre Bücher haben Bruna Surfistinha zu großer Popularität in Brasilien verholfen.
Mit dem Erlös aus dem Verkauf ihres Bestsellers hat sich Bruna Surfistinha aus der Prostitution zurückziehen können. Sie benutzt ihren Blog als Tagebuch, in dem sie ihre Erfahrungen als Prominente festhält.
Ihr Buch wurde 2011 in dem brasilianischen Film Bruna Surfergirl – Geschichte einer Sex-Bloggerin (Bruna Surfistinha - O Doce Veneno do Escorpião) unter der Regie Marcus Baldini verfilmt.
Der fiktionale Nachname Surfistinha bedeutet auf Portugiesisch wörtlich "kleine Surferin" oder "kleines Surfermädchen"; im Film beschreibt ein Freier das Aussehen der Prostituierten mit diesen Worten, worauf sie diese Beschreibung ihrem Künstlernamen hinzufügt.
Werke
Das süsse Gift des Skorpions. Mein Leben als brasilianische Sexgöttin. Ullstein, Berlin 2007, ISBN 3-548-36919-7.
Weblinks
Brunas Blog wird zum Buch (portugiesisch)
Einzelnachweise
Prostituierter
Blogger
Autor
Pseudonym
Brasilianische Literatur
Literatur (Portugiesisch)
Literatur (21. Jahrhundert)
Brasilianer
Geboren 1984
Frau
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 9,000
|
Promo age
"[Vicki Hinze's] ingenious concept of time and time-travel will captivate readers who crave the unusual, intelligent, and fresh approach to an old idea. [Hinze] brings a refreshing, clever and intriguing concepts to readers and then adds three enthralling romances to craft an unforgettable reading experience."
—RT BookClub
———
They've lost each other time and again.
Now is their last chance.
A lonely eternity awaits New Orleans computer analyst Kevan Buchanan and businesswoman Alyssa Cameron unless they can overcome the problems that kept them apart in their past lives.
The amulet at his neck vibrated.
Kevan Buchannan vacillated, turned off his computer, then stared at its blank screen. Muted sounds drifted in through his office window; a blues band belting out jazz, people laughing and dancing in the French Quarter street below. Though tempted to kick back and relax, he couldn't. Soon he'd be "gifted" with yet another glimpse of the future, a gift natural to him . . . frightening to others.
But not to Alyssa.
Again the amulet vibrated at the hollow of his throat. After months of waiting and wondering
Surrounded by darkness, he stood alone. A slight wind ruffled his hair and breezed lazily across his skin. On the horizon, light flickered and gnarled fingers of mist swirled together, thickening to fog and descending on him.
The fog parted, revealing the bumpy stone path. He walked down to its end. When the fog merged into a solid wall in front of him, he stopped and waited, feeling hollow, empty, and alone–emotions he wouldn't have recognized before Alyssa came into his life. He'd loved her. He still loved her. He always would.
An uneasy shiver crept up his spine. A funeral had just been held here. He'd never before envisioned a funeral . . .
Concentrating, his vision of it grew more focused, more clear.
It was Alyssa's.
Other Vicki Hinze Titles from Bell Bridge Books
Novella
Before The White Rose
Military Romances
Shades of Gray
Acts of Honor
All Due Respect
Metaphysical Romantic Suspense
Legend of the Mist
Maybe This Time
The Seascape Trilogy
Beyond The Misty Shore
Beside A Dreamswept Sea
Upon A Mystic Tide
Maybe This Time
by
Vicki Hinze
Bell Bridge Books
Copyright
This is a work of fiction. Names, characters, places and incidents are either the products of the author's imagination or are used fictitiously. Any resemblance to actual persons (living or dead), events or locations is entirely coincidental.
Bell Bridge Books
PO BOX 300921
Memphis, TN 38130
Ebook ISBN: 978-1-61194-264-4
Print ISBN: 978-1-61194-248-4
Bell Bridge Books is an Imprint of BelleBooks, Inc.
Copyright © 1996 by Vicki Hinze
Printed and bound in the United States of America.
All rights reserved. No part of this book may be reproduced in any form or by any electronic or mechanical means, including information storage and retrieval systems, without permission in writing from the publisher, except by a reviewer, who may quote brief passages in a review.
A mass market edition of this book was published in1996 by Pinnacle Books, NY
We at BelleBooks enjoy hearing from readers.
Visit our websites – www.BelleBooks.com and www.BellBridgeBooks.com.
10 9 8 7 6 5 4 3 2 1
Cover design: Debra Dixon
Interior design: Hank Smith
Photo credits:
Background (manipulated) © David M. Schrader | Dreamstime.com
Locket (manipulated) © Natalia Siverina | Dreamstime.com
Castle (manipulated) © Holger Karius | Dreamstime.com
:Etmt:01:
Prologue
Contemporary New Orleans
THE AMULET at his neck vibrated.
Kevan Buchannan vacillated, turned off his computer, then stared at its blank screen. Muted sounds drifted in through his office window; a blues band belting out jazz, people laughing and dancing in the French Quarter street below. Though tempted to kick back and relax, he couldn't. Soon he'd be "gifted" with yet another glimpse of the future, a gift natural to him . . . frightening to others.
But not to Alyssa.
A dull pain lodged in his chest. Had it really only been three days since they'd argued over her refusal to marry him? It seemed forever.
He stared at his desk lamp's distorted reflection in the computer screen. They'd been good together. Better than good. How could he understand her reasoning? How could any man? She wouldn't make a lousy wife. And she wasn't just his lover. She was also his love. His . . . love.
The woman was driving him insane.
Again the amulet vibrated at the hollow of his throat. After months of waiting and wondering when the next vision would come, when he would again image the Elder, it was finally time.
Kevan closeted his thoughts until his pulse leveled, until the tick of his office clock grew to a steady thump inside his head. Then he opened his mind to the vision.
The ticking sound faded.
The vision started.
Surrounded by darkness, he stood alone. A slight wind ruffled his hair and breezed lazily across his skin. On the horizon, light flickered and gnarled fingers of mist swirled together, thickening to fog and descending on him.
As a boy, how many times had he imagined a giant face behind him, mouth puckered, cheeks hollowed, sucking at the fog until it engulfed him?
When the familiar cool mist gathered on his skin, he lifted his face to it. Maybe here he would find peace–if there was any.
The fog parted, revealing the bumpy stone path. He walked down to its end. When the fog merged into a solid wall in front of him, he stopped and waited, feeling hollow, empty, and alone–emotions he wouldn't have recognized before Alyssa came into his life. He'd loved her. He still loved her. He always would.
A low hum sounded. The fog retreated to the horizon then weakened to misty trails that disappeared.
Cold rain soaked his jacket. Kevan squinted, helping his eyes to adjust. Pale moonlight streaked through a lattice fence, casting weak shadows on the ground. Beyond the fence, tombs blackened with mold and cracked by age stretched up toward the sky like unwelcoming sentries.
Hesitant, he followed the weed-ridden path and entered the crumbling cemetery, then followed the scent of roses to a freshly dug grave. An uneasy shiver crept up his spine. A funeral had just been held here. He'd never before envisioned a funeral . . .
Concentrating, his vision of it grew more focused, more clear.
It was Alyssa's funeral.
Holding a black umbrella, Kevan stood alone beside her rain-swept grave, staring at the gaping black hole, at the lone spray of thorny white roses stripped naked of leaves. Heavy raindrops pelted his umbrella and pinged off her silver coffin, now suddenly inside the hole.
Sensing movement, he looked left. Two men in black, hooded coats appeared near a sagging gate, their chins dipped low, obscuring their faces. Mocking the rain, a twisted oak limb stretching out over their heads ignited and burned. The fire sizzled. Crackled and hissed. Its bright flames licked at the bark, the leaves, and glinted on something shiny in the men's hands. What were they carrying?
Treading to Alyssa's grave, they made sucking sounds with their shoes in the mud. They carried shovels. "Good evening," Kevan said. Golden shovels.
They moved past him without a word or a glance. Why were they ignoring him? Others encountered in his visions conversed openly. And why were they hiding their faces?
The men stabbed their tools into the mound of wet dirt, then dumped mud onto Alyssa's coffin. The clods splattered, then thunked hollowly. And with each clump that fell, the pain searing Kevan's chest intensified. His breathing shallowed. His pulse thrummed. He tried to look away and couldn't. Adrenaline, terror, regret, gushed through his veins.
Squeezing his eyes shut, he forced himself to accept the inevitable. He couldn't stop the ground from swallowing her, but he couldn't watch it. Dear God, he couldn't . . . watch.
The steady rain grew to a thunderous downpour. His tears, his anger at her leaving him, knotted in his throat. He lifted his collar against the icy chill seeping into his bones, and blinked, allowing himself no other release of the pain clawing holes in his stomach. He had to hold on to the pain. It was all he had left now. She didn't love him. Why didn't she love him?
Lightning flashed, setting blaze to mighty oaks, to vines smothering the tombs, to rocks that logically could not burn, conjuring visions that flickered through his mind like snapshots. Alyssa, angry and spattered with mud, clinging to him even as she cursed him. Alyssa, bold and defiant, glaring down at him from the back of a white mare, a pre-tartan Scottish plaid draped across her shoulder. Alyssa, proud and challenging, standing at the altar of a candlelit church, dressed in an eighteenth-century wedding gown and about to marry an English lord she didn't love. And then Alyssa–just as he'd seen her three days ago, when she'd refused to marry him. Beautiful, sitting in her sterile office, absorbed by the only thing capable of absorbing her: a computer.
The storm raged to a tempest. "Leave!" A male stranger screamed inside Kevan's mind. "Run! Hurry!"
A violent wind whipped up. Howling through the trees, it carried a portentous warning and plastered Kevan's eyelids shut. Panic seized his stomach and, furious because he'd yielded to panic, he clenched his jaw, shielded his eyes, and forced them to open. Immediately irritated by flying debris, they began to tear and ache.
"You must leave!" The stranger insisted.
An image of Kevan running down the stone path flooded his mind. Deep in his soul, he sensed eternal danger. Black and bleak and lethal. He fought the urge to heed the warning and escape before it was too late. But Alyssa was here. "No! I can't! I won't leave her like this!"
The wind whistled a high-pitched shriek. Cringing, Kevan dropped the umbrella and cupped his hands over his ears to block out the sound. Rain drove into him, stinging his arms, his legs, his back. Lightning lashed at the sky; deadly streaks that ripped through the darkness, slammed into the ground, then exploded in flaming balls of fire. Heat scorched his skin. His eyes stung, his throat felt raw, and the warning voice inside his head grew deafeningly loud. Kevan bellowed. "I'm not leaving her!"
Pain stabbed through his chest. He bent double and sank to his knees in the mud. "Do what you will!" he rasped out. "I'm not going without her!"
An ominous whisper pierced the roaring wind. "Affix time."
The pain stopped as abruptly as it had started. The rain gentled to a fine mist. Gasping, drained and weak, Kevan tried to make sense of this. Affix time. Was the moment of Alyssa's death the key to this vision?
He mentally collected his energy, focused, then studied the image of himself beside her grave. No gray streaked his black hair, no new lines creased the skin at his eyes. The suit was one he wore often–the one he wore now–and his were the only footsteps near her grave-site.
Her death would come soon.
Fear slithered through his pores. The visions always had been like a jigsaw puzzle; never this simple or clear. Now he understood her refusal to marry him, but the knowing made her rejection harder to accept, not easier. Harder, and more terrifying.
Alyssa hadn't loved him. But she hadn't loved anyone else. Demanding perfection in others, her pride, her lack of humility and modesty–all had rendered her incapable of loving.
Incapable. His heart hammered, sweat slid down his temples, his ribs. Her snapshot images proved his worst fears. She hadn't elected not to love him; she couldn't love him! Him–or anyone else!
He collapsed on the ground, venting the tears clogging his throat. The fear he'd worn like a shroud died. Despair replaced it. Until now, he'd hoped she would change her mind. But she hadn't learned that love is pure, people aren't; she couldn't change her mind. Not now. Not ever.
God help them both.
Kevan bowed his head and prayed. Hopeless, fervored prayers born of grief. Alyssa couldn't love. She was going to die never having known life's greatest joy. To die! And there was nothing he could do . . . wait.
Wait! He scrambled to his feet. Was that the message in this vision? That there was something he could do? He scanned the tops of the tombs, the shadows between them, and shouted, "Elder? Elder, I need guidance."
No answer.
Frowning at that unexpected result, Kevan again focused on the snapshot images. But he couldn't hold on to any of them. Instead, a new image formed. One of him as a ghostlike apparition, kneeling in a puddle beside Alyssa's grave. A crystal amulet–different from his, more like the one the Elder wore–hung from his neck, a silver sword from his side. He touched the cold mound of dirt covering Alyssa's coffin and whispered something he couldn't hear. A rumbling started deep within the ground. The mound glowed, cracked and split. Alyssa rose from within the gaping hole, then followed Kevan's apparition down a golden stone path.
Where were they going? Kevan tried to follow, but couldn't lift his feet. "Elder!" he called out. "Elder, where am I taking her? Why am I here?"
Pain ravaged Kevan's chest. In a cold sweat, he watched helplessly as the image disappeared. The pain was a signal as familiar to him as his amulet vibrating. Nothing more would be disclosed; his grace, the Elder of the Council of Perfection, was summoning.
Kevan closed his eyes. When he again opened them, he was standing on the stone path, surrounded by dense fog. No mud sullied his hands, his clothes were dry, and no wind rustled. All was still. Silent. Reverent.
He straightened his shoulders, responding to the summons with the respect the Elder had earned over the years, with the decorum due his visionary master of time and destiny.
Enveloped in a shimmering silver mist, the Elder appeared on the path. The brown stones beneath his feet turned golden. Small and robed in white, he might have been seventy, or seven hundred, or seventy thousand. No telling lines marred his smooth, translucent skin and the crystal amulet at his neck glowed, but his eyes, flat and colorless, reflected no light.
"It has been some time, Kevan."
"Yes, your grace." Kevan bowed his head, crossed his chest with his right hand. "It's good to see you. Though I don't understand the–"
The Elder interrupted in the raspy whisper Kevan never felt certain truly had been spoken or heard. "Acknowledgement is the first step toward enlightenment."
"She must die, then?"
"That depends on you."
"On me?" Kevan failed to keep his surprise from his voice.
"Your love for this woman has remained steadfast throughout time."
Where was this leading? "Yes."
"But only now have you seen the vision." His carriage regal, the Elder stepped closer, out of the mist. "Have your feelings for her changed?"
Acid poured into Kevan's stomach. In all their years together, the Elder never had been less cryptic or more blunt. That he was now, worried and alerted Kevan. This was no ordinary vision. "Yes, your grace, my feelings for Alyssa have changed. They've deepened."
"Even though you now are aware of her inability to love . . . ?"
Kevan swore he'd give everything he owned if he could honestly deny that truth. "Because of her inability. She's been denied–"
"No." Elder frowned. "Without acceptance, acknowledgement–"
"Is useless." Kevan's stomach sank. Drawing in a shuddery breath, he squared his shoulders and met the Elder's empty gaze. "She hasn't yet become a universal woman."
Nodding, a shadow fell across the Elder's eyes. "But she also rejected you and denied your love of value to her." He fingered his amulet. "During the tempest, you realized that your soul was in eternal jeopardy, yet you refused to leave her." The Elder pursed his lips. "I would know why."
"I love her." A warning bell clanged in the deep recesses of his mind. The Elder had heard him call. Why hadn't he answered? He'd always responded . . .
The reason hit with the force of a sledge. This wasn't about time! "Only a foolish man denies his destiny, your grace. Alyssa is mine."
"And you are not foolish."
Kevan mustered a thread of a smile. "Perhaps I am. I fell in love with a woman never capable of loving me back."
"Mmm. Unlike forever, never is a relative term." The Elder stepped back into the mist.
Perplexed, Kevan looked up, afraid to blink, afraid to breathe. "Elder?"
Quiet authority filled the Elder's voice. He lifted his chin. "Your devotion and perseverance have not escaped the recognition of the Council, Kevan. Thus, you have earned this reward: cast out the past from the Great Book. Remold your history, your destiny–if you dare. Your gift is to love Alyssa again, as you have loved her before."
Shock bolted through Kevan. He tensed against it. "And my trial?"
The Elder's expression grew intense. "To guide her to love's light."
Kevan's shock doubled. "The Council has interceded."
"On your behalf, yes." The Elder sounded resigned . . . and concerned. "Accomplish this mission, and Alyssa Cameron will be yours for eternity."
Reeling, Kevan forced himself to think. Nothing came without cost. Nothing in life, or in death. His heart began a slow hard beat that pounded in his temples. "And if I fail?"
"If you fail, you shall not fail. Seek your destiny and win."
He paused to decipher the message, in a sense relieved that it was cryptic. Loving Alyssa was his destiny. If he led her to love's light, he hadn't failed, but won her eternal love. If he wasn't successful, then she, not he, had failed. Though both of them would suffer the consequences.
Narrowing his colorless gaze, the Elder plundered Kevan's soul. "Do you accept the Council's challenge?"
All or nothing. Eternal love, or its absence. And in the case of failure, for him, an eternity trapped in the Hell of unrequited love. He would never know peace. The risk, like the reward, was high.
Solemn, Kevan looked up at the Elder. "I accept."
"Very well." The Elder tipped his head slightly. His beard grazed his chest, and pity laced his voice. "Henceforth, you shall be known to the Council as the Prophet."
Sensing the Elder's fear, Kevan stepped forward. "I need to know–"
"I can say nothing more." He raised his hand and turned his palm upward. "May wisdom realized through your gift serve you now in following your heart."
The Elder's silvery image faded. The golden stones on the path again turned brown, and the faint sounds of the ticking clock grew distinct, loud.
The vision was over.
Kevan opened his eyes. Bathed in sweat, his hands trembling, he tugged his tie loose from his throat and took in a deep, steadying breath. His quest would begin soon. And, for the first time in his life, he wouldn't have his visions to guide him . Only love. And fear.
Never before had the Elder doubted Kevan's success. But this vision was different from the hundreds he'd had in his twenty-seven years. It required no interpretation; its message was vivid and clear. This vision was of Alyssa.
And it, like all the others, would come to pass.
Shaking, his heart jackhammering, he took one last look at the familiar furnishings in his Canal Street office then stared at his blank computer screen. Again, he concentrated on the ticking clock. Waiting. Feeling stripped bare and frightened. Knowing that the visions wouldn't come to him again. Knowing that his love for Alyssa would be his only guide in pursuing his quest. And praying that his love would be enough. Alyssa's destiny, his destiny, depended on it.
Unbidden words filled his mind. "Have faith in your humble servant."
Pain split his chest. Kevan Buchannan slumped forward and died.
His quest had begun.
One
THE DEATH-WAIT would soon be over.
Alyssa Cameron had lain for days, feeling her strength shrivel and the pain that throbbed in her head mushroom. Fifty. So young to die.
Fifty? Fifty? She touched her hand to her temple. No, not fifty. Twenty-two.
Twenty-two, and she would die alone.
Few would attend her funeral. They said she'd killed him. Had she?
Poor Kevan. She should have married him. Love, that alien emotion, had plagued poor Kevan. He'd loved her and yet he, too, had died alone.
Shifting on the damp sheets beneath her, she plucked at her hospital gown, sticking to her skin. She'd allow herself that regret with Kevan, but no others. She'd been given time to put her affairs in order and couldn't complain about her life. She'd had financial comfort, her computers to fascinate her, and more men than she cared to recall. Had she been married three times, or four?
Droopy-eyed, she stared up at the white ceiling, at the blue and white dots dancing along the tiles. So hard to remember. So hard . . .
Pain shot through her skull and bolted down her spine. She sucked in a sharp breath, grabbed the handrail and squeezed, praying for the throbbing to ease, for death to come and make the pain stop.
Married? Had she been married? Fuzzy. Her memory grew more and more fuzzy.
She concentrated hard. She'd worked. Computers. Twenty-two and never married. No. No, she'd never married. Poor, poor, Kevan.
Another pain sliced through her temples, spiked down her spine, and set fire to her limbs. Stiffening, she sank her teeth into her lip and bit down until her mouth filled with the iron taste of blood. Done was done; tears wouldn't help. Kevan was gone. She would greet death alone.
And no one would mourn.
Anger trickled through her like fizzling sparks on a dampened fuse. Every life lost deserved mourning, didn't it? What mistakes had she made that not a single soul would grieve for her? What god-awful crime had she committed? What had she done wrong?
The pain in her head exploded.
Her blood seeped, no longer rushing through her veins.
Her heart stopped.
This was what it felt like to die. But she didn't want to die! She didn't want to feel her body grinding to a halt! Shouldn't someone be with her? Kevan! Where was Kevan?
She fought to concentrate. Nooo! Oh God! Oh God . . . Kevan was dead. Poor, poor Kevan.
She couldn't stand it. She couldn't go through this alone. Someone should know. Yes. Someone. Anyone. Fumbling with the cord tangling with her IV, she pressed the nurse's call button. Had she mashed it down? So weak. So . . . incredibly weak. Panic set in, she silently screamed. Kevvvvaaan!
Her body went limp.
She couldn't move. Couldn't feel the needle in her arm that had her skin an angry swollen red or the tube shoved down her once raw throat. The nauseating smell of antiseptic that had tortured her for days faded. Her vision dimmed to ink black. And the sounds of rushing feet disappeared.
Silence. Sweet silence.
Peace.
Dead.
Dead?
She couldn't be dead. Dead people don't exist. And she did exist!
Her thoughts, emotions, and ideas were still with her. Maybe she hadn't died. Maybe she'd gone crazy!
A sensation of movement surrounded her. Oh God, she was the object moving! She floated up, hovered at the ceiling, and looked down at the nurses and doctors crowded around her bed. Shouting orders, their voices were anxious, their movements jerked and frenzied. A jolt rammed through her body, shoving her out of the room, out of Tulane Medical Center. Darkness enshrouded her and she accelerated, speeding into the unknown.
Clutching at her chest, she drew in a sharp breath. She could breathe and move again, but the darkness . . . Why the darkness?
Warm air rushed past her hands, spreading her fingers. She reached out, stretching into the sinister pitch, trying to slow her speed. But her hands met nothing solid. She couldn't focus. Her stomach lurched, and dizzy, she cried out. "Slow down! Would you please slow me down?"
There seemed nothing present to cause an echo, yet her voice bounced back to her. No sights. No scents. Only the sensations of warm air rushing over her skin and her speeding along. Was this some sort of wind tunnel? Where was this place? What was this place? Where—what—was she? She crossed her chest with her arms, and strained to see, but only the darkness was out there. Only the . . . darkness.
The sense of speed lessened to a smooth glide. She lifted her hands and shifted her weight, trying to steer, but nothing altered her course. Odd. And even more odd, she wasn't afraid. Anyone in their right mind experiencing this would be terrified. She should be terrified. So why wasn't she?
For a long moment she felt nothing. Then it struck her. That nothing was the absence of pain. She pressed her fingers against her arm where the IV had been. No knots or swelling—and her head didn't hurt. She wasn't suffering any of the symptoms from the tumor that had caused her death—if she had died. For the first time in days, her memory was sharp and clear. She vividly remembered dying. Yet, if she were dead, would she be here? Wouldn't she just be . . . dead?
"Hello?" she called out. Pinching herself, she winced. New pain was possible then. "Hello?"
No one answered. But finding her own voice comforting, she called out again. "Where am I going? Did I die? Is this the way to Heaven? Hell? Some other place I haven't heard of? Hello?"
Still, no answer.
Supposing she had died. Was this what came after a lifesearch, then? An eternity of floating through this darkness? She shivered. She'd always hated the dark, and now she was engulfed in it. What if this was eternity? What if she did nothing more than float, isolated and alone, forever?
Her heart began a slow hard beat and her skin crawled. She rubbed hard at her arms until the gooseflesh disappeared. Panicking wouldn't help her now. Would anything?
In her distant path, a brilliant light appeared. Its rays spilled into the darkness in glistening shimmers that were warm and appealing. Anticipating being enveloped in it, her limbs tingled and alien feelings of safety and security welled in her stomach. Poignant tears stung her eyes. Feeling them fall, she touched her cheeks, then touched her wet fingertips, confused, awed. But she never cried. Never . . .
Tiny pastel bubbles depicting her life's joys and sorrows flickered in perfect miniature around her. Her parents, who had died years ago, were together, smiling at her from inside a pale pink sphere. Beside it, encapsulated in a translucent blue globe, she saw her own funeral, the empty pews inside the church.
Her heart pounded. Once she crossed the threshold, she'd never again be alone. Certainty filled her. Happiness, contentment such as she'd never known, would greet her in the light. So close now that the radiating heat warmed her, she cried out to move faster; eager, longing.
A massive and flowing shadow loomed ahead. A sentry? Her throat went dry. Would it refuse to let her pass? Tensing, she called out to it. "Move. Do you hear me? You have to move out of my way!"
The ominous shadow grew larger, blocking the heat from the light's rays. Chilled and desperate to again feel that wonderful warmth, she screamed. "Move! Damn it, you have to move!"
Her forward momentum slowed to a near halt. Squinting, she just made out the shadow's silhouette. An image began to form—a man.
Near him now, the wind died, and she stopped. She tried reaching for walls, but there were none. A ray of soft light beamed down the tunnel and shone on the sentry. He was a magnificent giant, standing on a crystal platform. Firm, muscular, and heavy-boned, he stood statue still. His hair, thick and glossy black, curled low on his strong neck. His eyes were closed; his mouth, wide and set in a firm line that didn't welcome or shun her. A crystal amulet hung at the hollow of his throat from a strip of leather coiling around his neck. A belt riding low on his hips embraced a gleaming silver sword, its hilt encrusted with fat emeralds and rubies the size of plump cherries. And his broad chest, bare and covered with a soft-looking down, showed no evidence of his breathing.
Her heartbeat sped to a canter, and she expelled a soft swoosh of breath. He was totally masculine. The epitome of manhood. Beautiful.
Then he looked at her.
"Dear God!" she gasped. "Your eyes . . ."
Glinting flecks of the coolest gray, his eyes whispered secrets of wisdom, purpose, and authority. His force, raw and unearthly, withered her, somehow draining her strength, yet she couldn't look away. She didn't want to look away.
Why didn't she? What power did he hold in those eyes? Without touching her, he'd imprisoned her. Was he an idol? God?
"Alyssa Cameron." His tone, rich and smooth, comforted her like a warm cloak on a wintry night.
He spoke a language she'd never heard, yet she understood him. "Yes."
He touched the hilt of his sword, and a crystal platform like his formed beneath her. Warmth radiated from it, crept up through her feet to her thighs, then spread through her body to her head. For some reason she didn't understand, she smiled. When he smiled back, she felt dazzled. Something strange was happening inside her; she was being molded into someone else. But that was impossible, wasn't it?
Compelled by an overwhelming urge to touch him, she stepped forward. But the dark distance between them didn't shrink, it expanded to a full three feet. Quickly, she stepped back.
The giant looked down at her, his face shadowed. "I've waited for you."
Her stomach fluttered. "Waited?" She'd never seen him before in her life. If she had, she definitely would have remembered. "Who are you?"
Prophet paused. She didn't know him. He'd known that she wouldn't, but it still hurt. He'd loved her throughout time. "I am the Prophet, Alyssa."
"You're a psychic?" Alyssa asked, her expression perplexed.
"Of sorts," he hedged.
The color drained from her smooth cheeks. "Am I . . . dead?"
Her voice being steady worried him. Where was her fear? Without it, their mission would be impossible. "You died two days ago."
She shut her eyes, shielding from him the green that rivaled his emeralds. God, how he hated it that he must put fear in her eyes.
"I thought I'd lost my mind." She looked up at him from under her silver-tipped lashes. "That was bad enough. But dead . . ."
His stomach churned. He swallowed and softened his tone. "It takes getting used to. But once you accept it, you'll do fine."
Wary, she licked at her lips. "What do you want from me?"
His heart twisted. He wanted everything. Her humor and temper, her quirks and faults—all of her, good and bad. But most of all, he wanted her love. "I'm your guide. My mission is to help you."
"To do what?"
"On your journey." Again he hedged, unable to put her mind at ease and unwilling to reveal what he could until she was prepared to listen to it.
She stepped out of one of her high heels and rubbed her arch over her other foot. "Where am I going?"
This wouldn't sit well with her. But he had no choice. "I can't say."
"If you can't tell me, then how are you going to guide me?"
Still no fear. And none of her usual tenacity. This wasn't good. "We'll manage." He rubbed at his temple. What would spur the old Alyssa into surfacing? Ah . . . "You've no reason to fear me. I won't harm you."
She frowned and swiped at a wrinkle in her skirt. "I don't fear you. And I'm capable of helping and protecting myself." She tilted back her head. "Are you new at this guiding business?"
"New?" Better. With little reassurance, she was handling the shock of her death well. But then Alyssa would; she looked within to fulfill her needs, not to outsiders. That truth hurt, but it was also why they were here and not on Earth; living out their lives.
"If you were more experienced," she said in a haughty tone that was transparently forced, "you'd know that the dead don't need guiding. They need burying."
He swallowed a chuckle. "Didn't you see your funeral in the sphere?" He pointed to her jacket. "Look at your clothes. Aren't they the same?"
She glanced down and fingered her lapel. "This is the cream suit I saw." Again frowning, she looked back up at him. "Where are we? And if I'm dead, then why do I still feel and look like . . . like me?"
How like her to accept that proven without qualm or emotion. Part of him was glad, but another part of him wished she'd needed consoling. God knew he could use a little. Where in blazes was her fear? That facet of her character clearly needed restructuring, too. "You feel like you, because you are you, Angel."
"Angel?" Her skin paled even more. "I'm an—an angel?"
She sounded torn between elation and despair. Now what should he make of that? "Not as you picture an angel, no."
"I didn't think so." She slid him a look laced with doubt. "You're not very accomplished, are you? No offense, but even a new guide shouldn't see me as an angel." She slid her foot back into her high heel. "Don't you know what to do with a corpse?"
"You aren't a corpse. And, though you have much to discover, you are an angel, Alyssa." He crossed his arms over his chest. "Have you heard the saying that a rose can't deny its petals?"
"Hasn't everyone?"
He rubbed at his temple. "Here, you're the rose, and your destiny is the petals. You can't deny your destiny."
"Wait a second." She lifted a hand. "Look, I appreciate a smooth line just as much as the next woman, but aren't you stretching this? I mean, roses? And angels are pure and gentle, aren't they?" She smiled her skepticism. "I don't think I'm a likely candidate for wings."
"You aren't—now." He watched her pulse throb at her throat. She was nervous. Not afraid, but nervous. Well, that settled it. A detour before they began their mission was necessary. "And, yes, angels are pure and gentle."
"That proves my point." She smoothed her hair back. Its long silvery strands captured the light and sparkled. "I'm far from pure or gentle, and I'm even further from soft, so let's get down to the real business—"
With a zipping whistle, the platform under her feet cracked. Yellow, green, and blue prisms streaked wildly through the tunnel. Alyssa's mouth rounded in an "oh" and, hunching her shoulders, she cupped her ears.
Wincing up at him, she crowded her feet onto the small section of crystal that didn't float away. "What happened?"
Weak fear lit in her eyes. He hated it. But she had to learn not to dispute him. She wasn't slow. She'd figure it out. "It is of no consequence."
That remark earned him a frown he'd be feeling for a week. She licked her lips with a smooth, pink tongue. "Now, look, Prophet."
He sighed and tapped his fingers against his bicep. "Yes?"
She nodded. "I've tried to be patient, but I want some answers—without the cryptic nonsense. And I'd appreciate it if you'd can the drivel."
"Drivel?"
"Me being soft and gentle—and I resent being compared to a rose. A thorn, maybe, but never a rose." She shot him a warning look. "It's been tried by the best. My petals don't crush."
True enough, he admitted. But, one way or another, she was going to bend, and hopefully to blossom. "I see."
"It's clear by your expression that you don't see at all. But you will." She gave her jacket hem a tug. "Now, I gather I'm supposed to travel somewhere and you're to act as my guide. So let me just ask you a question or two and then we can get on with it. You can explain the rest as we go."
He had her attention. Nervous, Alyssa rattled. When she slid into her authoritarian mode, she was afraid. Still, her fear had been too long in coming to be safe for either of them. "How long are you going to talk before you get to your questions?"
She stopped in midsentence to glare at him, then drew in a shuddery breath. "Since I still exist, I assume Heaven and Hell are real. Am I correct?"
He shrugged. "Maybe."
"What kind of answer is that?" She grunted. "Don't you know?"
"What I know isn't relevant. It's what you know that matters."
She rolled her gaze, then asked point-blank. "Am I going to Heaven or Hell?"
Before they were done, he imagined she'd think she'd spent a fair amount of time in both. "Not exactly."
Her frown deepened, and she stiffened her shoulders. "Look, we're discussing my future here. Just talk straight about it, okay? If not to Heaven or Hell, then where am I going?"
"You'll see . . . in good time."
"I don't care for puzzles." A warning in her tone, she laced her hands behind her back. "Actually, I hate them. They irk me."
He well knew that they did. And right now, he was the puzzle irking her most—and thoroughly enjoying it. "Regardless of preference, we must master some puzzles."
"And this is one, mmm?" Caught up in her thoughts, she paced a path on the jagged crystal and nearly walked off its end.
Beautiful. Head to heel. "Exactly." Smiling to himself, Prophet touched the hilt of his sword. The platform began moving with her, staying solidly beneath her feet.
Alyssa groaned.
He hiked a brow. "What is it?"
"Nothing." She flushed and lowered her gaze.
"You must answer me."
"Must?" She shot him a disgusted look. "A little macho, don't you think?"
"Not at all." He slid her a wicked grin. "Well, perhaps a little."
"You're cute." She let her gaze sweep his length. "But not that cute."
If her pupils hadn't dilated and her nostrils flared, he might have believed her. "Cute has nothing to do with it. It comes with clout."
"Whatever." She shrugged, but her cheeks went pink. "I read this book once about a woman who died and was stuck in limbo forever." Alyssa looked up at him, clearly wanting reassurance.
He didn't give it to her. "And?"
"It isn't like that here, is it? I—I don't think—"
"It depends," he waffled, needing to see how she'd react under pressure.
"Tell me it's not like that."
He held her gaze, and said nothing—one of the hardest things he'd ever had to do.
"If it is, I won't stay here." She lifted her chin. "I just . . . won't."
"You can't deny your destiny, Alyssa." For her, limbo would be torture. She was a doer, not an observer. "Remember the rose?"
Blinking furiously, she resumed pacing, stretching her path. "The truth is, I'd rather be in Hell. At least there you know what to expect."
"Fire and brimstone?" he suggested.
She tilted her head. "That's not exactly the way I have it pictured."
Cooking. Alyssa despised it. "Hell's kitchen?"
She went ashen. "Does Hell have a kitchen?"
He couldn't do it. He'd eaten a few of her meals. They hadn't killed him, but they could've. No one in the universe deserved that kind of torture. Especially Alyssa. Cooking would be her hell. "Angel—"
"Since I'm not going there, that's irrelevant. I'm here, for what that's worth, and I don't much like it, either."
She rambled on, asking about getting transfers, dispensations. That tugged at his heartstrings and he tried again to interrupt. "Angel."
Still, she went on. And half-wondering why this woman had to be the woman who tied him in knots, he raised his voice to be heard. "Angel, you aren't going to be stuck in limbo or in any kitchen!"
She stopped suddenly and stared at him; alert, relieved, and hauntingly beautiful. Aching to hold her, he fisted his hands to keep from reaching out to her. It'd been so long. And the odds were stacked against him ever having the chance to hold her again. Maybe just this once.
The amulet at his neck vibrated briefly then stopped. It was time. "You're the product of a failure in the system, Angel."
"Failure?" She narrowed her eyes at him. "I've never failed at anything important in my life."
"That's not true. But it's the system, not you, that's failed."
"The system?" Perplexed, she wrinkled her brow.
He should have known. She'd never accepted anything without proof. "Life, Angel." Noting her confusion, he explained. "From medieval times until the twentieth century, a negative imbalance in the electrical impulses coming from Earth caused many to leave their current level of learning and to proceed on to their next level too soon."
"What?"
"Think of it as a short circuit."
"Uh-huh. And what caused this short circuit?"
He lifted a shoulder. "Some say pollution. Some say greed." He gazed deeply into her eyes. "Many don't say, they just accept."
Alyssa paused to think about this. The hole in the ozone layer near Antarctica? The destruction of the Brazilian rain forest? How could those—or other—things cause this?
No, Prophet was just misguided. Dead was dead and that was that. Still, she'd be stupid not to humor him. She specifically recalled dying and, though she didn't understand it, she was here—wherever here was—and not six feet under in some cemetery. Until she learned the lay of the land, a misguided prophet was better than no prophet. "What do these impulses have to do with me?"
"Like many others, you left your current level too soon—without first discovering all you needed to fulfill your destiny."
"Okay. So . . . ?"
"So," his gaze scorched her soul, "now you must go back."
"Go back?" Innately knowing he didn't mean to her life in New Orleans, she cringed, not liking the sounds of this at all. "To what? Or to where, for that matter."
He sounded sympathetic. "To some of your learning levels."
A shudder zipped up her spine. "To some of my what?"
"To some of—"
"This is a joke," she interrupted, pacing again. "My secretary, right? Margaret is always going on about karma and soulmates and weird—" Alyssa turned to Prophet and planted her hand on her hip. "Did that contrary witch put you up to this?"
"No," he said, giving into the urge to smile. "Your secretary is contrary, but she is not a witch. Nor is she dead. Have you forgotten that you are?"
Her blush told him she had forgotten. She might as well confess. "Transitioning takes time."
"Unfortunately, we've precious little to spare." He lifted a finger.
Their platforms merged, bathing them in a hazy golden light that caressed his skin. A silver speck glittered on his jaw. She brushed at it, then waited for him to explain.
He chose not to. Instead he cupped her face in his big hands, and stroked her cheek with his thumb. His gaze darkened, grew intense and searing. Her cheeks tingled. And she swore she was glowing like his amulet inside. "Prophet? What's happening to me? I—I feel—"
His breath warmed her face. "Shh, Angel." He fanned her temples, her cheeks, with wisps of touch.
Her mind and soul opened, welcoming him. Somehow she knew that resisting would prove futile, but why didn't she want to try? Why didn't she fear him, or resent his invasion?
His effect on her startled her, left her breathless—and believing. "When I go back to these former learning levels, what must I discover?"
He bent low, covered her lips with his. She whimpered. His kiss was staggering, achingly familiar. They'd definitely kissed before, time and again. So sweet. So tender. So . . . long ago.
Rubbing the silky, dark hair covering his chest, she trembled. The scent of his skin, the ripple of muscle ridging his abdomen, every curve and plane of his body that she touched was known to her. Even the jagged scar on his shoulder triggered some forgotten memory just out of reach.
He raised his head. A shadow slanted across his eyes and his voice sounded gruff, emotional. "Angel."
Waves of pleasure rippled through her. "I know you," she whispered. "Prophet, I know you!"
"Yes."
Sensing grief in him, she met his molten gaze. "How?"
He refused to answer. Disappointed, she stroked the ridge of his scar. "What must I discover?"
A slow smile curved his lips, so easy, so sure and devastatingly handsome. "Me."
"You?" She flattened her palms against his broad chest and frowned. "But you'll be with me?"
"Not always." Regret lit in the bottoms of his eyes.
She could ask why, but he wouldn't answer. "Where will you be? How will I know you?"
Certainty replaced the regret. "You'll know me."
That she feared he was right, galled her. "You appeal to me, okay? I admit it. But this goes beyond lust, Prophet, and your ego has no business messing around with my future."
"Your future is important to me. Never doubt it. And if I'm arrogant, well, no one here is perfect." He slid her a killer smile, then shrugged and threaded his fingertips through her hair. "Spun silver." He sighed contentedly. "I remember the feel."
He remembered more than the feel of her hair. She was sure of it. And this tenderness frightened her in a way his arrogance hadn't. It got to her, and it shouldn't. "I know you, yet I don't know you. You say I must discover you, that I'll be in—" she paused to gulp in air, "—one of my former learning levels." She moved her hands to his waist and squeezed his sides. "Don't you understand why I'm confused? I don't feel dead. I feel normal. And you don't look dead to me. Are you?"
"Give it time. You'll—"
"If you'd just explain it to me, I wouldn't need time."
"Patience, Angel." He stroked her jaw, letting his fingertips trail over her parted lips. "You'll find me. You'll make your discoveries, and all of this will become clear to you."
He was about to leave her; she intuited it. Her heart felt bruised. Why did the thought of being separated from him hurt her? Along with everything else, the pain didn't make sense. But her heart didn't seem concerned with logic. It just ached.
Pressing his warm lips against her temple, he whispered. "I'll be with you soon." His grip on her shoulders tightened, then suddenly he let go of her, reared back, and feasted on the sight of her.
The hunger in his eyes worried her. It was as if he somehow knew her intimately. But that was impossible.
He lifted her from the platform, his hands trembling, then released her. "Safe journey, Angel."
Drifting back the way she'd come, she reached for him. "Prophet?"
When he didn't move to draw her back, she shouted. "No! No, Prophet! Where are you sending me? Why are you sending me away?" Tears she didn't understand flooded her eyes. Inside, she felt ravaged. And deep sobs racked her body, tore at her lungs.
She'd gone off the deep end. She must have. She who had never loved, never cried, mourned losing Prophet? How could she mourn the loss of a man she'd just met? A man she knew, yet didn't know? A man, she feared, who wasn't a man?
But mourn him, she did.
Through the increasing darkness. Further and further away from the light. Past the pastel bubbles that burst one by one until fog, then ink black darkness swallowed her.
Fear seized her stomach. She was shrinking, squeezing into a . . . a comfortable jacket.
Then it hit her. Oh God, the learning level was a life! The jacket was her body!
But which body? And in which life?
Two
Prehistory
SHE LAY SPRAWLED in the mud.
Rain, sleet-cold, spit down on her from a sky as dense as slate. Alyssa shivered and hauled herself to her feet.
The terrain, what she could see of it through the blanket of dark clouds, was stark, a vast wasteland of barren ridges and steep, rocky inclines covered with brown mud and scrub brush. Where was she? This was obviously a mountain. But where? And when?
Her muscles knotted and she rubbed her abdomen. Slick, wet fur grazed her palm. She looked down. A pelt, knotted at one shoulder, left her other one bare, and hung down to her upper thighs. She knew furs—mink, sable, fox—but she couldn't identify the animal whose fur she wore. Icy rain stung her goose-pimpled skin, and she hugged herself for warmth.
A harsh whipping sound split the sky. Her instincts warned her to seek cover. Flattening on her stomach under a spiny bush that scratched her back and smelled of sage, she visually searched. An alien bird swooped low in the sky. The whipping noise grew louder, roaring in her ears, and the ground beneath her shook with each flap of the birds long, rust-colored wings. Doubting her own eyes, Alyssa stared at the creature. What kind of bird had a wingspan of twenty feet?
Its long beak fell open, exposing daggered teeth, and it screeched a deafening caw. Alyssa covered her ears with her hands, but kept her gaze glued to the creature until it flew past, then on out of sight.
No mountain she'd read about provided a home to such odd birds. Everything that huge supposedly had been extinct for eons. This place was weird. She had to find shelter. After several steadying breaths, she crawled out from under the bush, shiver upon shiver streaking through her body.
Prophet. She began journeying down the stony mountain. What she had to find was her misguided guide. He could explain—if he would.
The climb was difficult. No trail existed, none that she could find, anyway. And the mud was wet and slick, treacherous. Within minutes, her calf muscles burned and the tendons in her arches ached from the strain of keeping her upright. Climbing the corporate ladder hadn't prepared her for climbing mountains, or for descending them.
By the time she'd hiked to a wedge of flat land, she was sweat-soaked. She paused to rest. Chilly and brisk, the wind bent the sparse grass and tugged at her damp hair. She shoved it back from her face and looked around. "God, talk about barren. And no sign of the misguided maniac." Now why didn't that surprise her? Less frustrated and more irritated, she slung the sweat from her brow. "Some help."
Kicking at a loose stone, she wondered where the Hell she was. Medieval to contemporary times, he'd said, but there was nothing here to give her a clue. God, but it irked her to not know even what century she was in, much less the date. Shielding her eyes with her hand, she scanned in all directions, but saw no signs of life. If anyone was going to find anyone on this godforsaken mountain, it looked like it'd have to be her finding him.
Wait. Hadn't he told her that? Her thigh stung and she slapped at a bug on it. He had. He'd said she had to discover him.
Swallowing a curse, she skirted a scraggly brown, spindly bush that looked like a Plant Hell reject, and continued down the steep slope, regularly checking the sky for signs of the big bird. Dark clouds hovering overhead looked ready to burst any second. Just what she needed. More rain.
Stumbling, she fell into a shallow pit. Muddy water sloshed around her ankles. Under her feet, the earth seemed compressed, dense. How could that be? Elsewhere, the ground had been soft and squishy.
An uneasy tingle crept up her spine. She backed out of the pit and studied its shape. A print? She remembered the size of the bird, and her skin crawled.
By the size of its tracks, the animal would be gigantic. She checked the ground and, a few yards away, found a second print—the mirror image of the first. And twice the yardage beyond it, was another marking. A swipe of smooth dirt looked as though it had been swept by the swish of a huge tail.
"A dinosaur?" Her stomach lurched. "No, it couldn't be." But before she'd seen that bird she would have sworn it couldn't be, either. "Oh God, Prophet!" she cried out. "Get me out of here!"
Blustery wind and the rain pelting against the rocky ground answered her. Prophet did not . . . yet someone was watching her.
The tiny hairs on the back of her neck stood up. She turned in a slow circle and, seeing no one, she tried but couldn't shake the feeling. Someone was watching her every move.
The ground seemed to come to life. A dozen men—bald savages, dripping mud—rushed at her in an ever-narrowing circle, their scowls as fierce as and threatening as the alien bird's daggered teeth. Their eyes blazed, their muddy chests swelled and heaved. Held in their fists were rough, wooden clubs, raised and ready to assault her.
She gauged their distance from her with a sinking heart. Running was futile. One savage grunted at her and pointed up the slope. Suspecting she was to follow him, she did. Her muscles protested the steep climb, cramping, and her mind raced. What would happen to her? Did these barbarians rape? Murder? Enslave?
Fear, unlike any she'd known, assaulted her. Her misguided prophet had sent her straight into Hell.
She tripped over a loose rock and fought to regain her balance. Her captor shoved her toward a black hole in the mountain. At the mouth of the cave, she hesitated, but a sharp smack to her back sent her lurching inside.
Inside the dark tunnels, the air smelled dank. She moved blind until her eyes adjusted and the darkness gave way to a dim, shadowy light. The narrow tunnel opened into a wide cavern that glowed with the eerie glimmers of twilight. Its high walls of rough rock were streaked with thick veins of silver that reflected light from some unseen source high above her head.
A barbarian jabbed her in the ribs and grunted. Her breath swooshed out. She bit back a curse burning her tongue, and glared at him. He pointed a thick beefy finger toward the far cavern wall. Her side throbbing, Alyssa walked toward it.
Two raised steps led up to a platform of smooth, polished stone where a throne had been fashioned from the rock. On it, sat a giant of a man. His feet were bare, his face hidden in the shadows. Shaking inside, Alyssa pulled herself up and looked at the sheen of light grazing the tip of his chin. "Who are you?"
He didn't answer.
Her heart hammered and her pulse throbbed in her head. For the first time in her life, she freely admitted to being more than apprehensive. She was terrified. Faking a boldness she didn't feel, she stepped toward the platform.
The barbarian at her side snaked out a hand and pressed his fingers against the hollow of her throat. She clutched at his fingers, tried to pry them loose from her neck. God, but he was strong. He was blocking her intake of air—she couldn't breathe!
Spots flickered before her eyes. Her knees went weak. The lights dimmed, and she felt herself sliding down to the earthen floor.
When she again opened her eyes, the giant held her in his arms. His face swam before her, a jumble that wouldn't right itself. She blinked to focus. Oh, his eyes. Gray flecks. Wisdom.
"Prophet!" She flung her arms around him and buried her face in the curve of his neck. "Oh God, Prophet."
His chest swelled against her side, and he pressed his warm lips to her forehead. "Hello, Angel."
A long moment later, Prophet set Alyssa to her feet on the cavern floor. "You're safe now."
"Safe? With these barbarians?" She glared up at Prophet. "What am I doing here, anyway?"
He steeled himself for her outrage. "You're discovering fear."
"I know fear." She shot him a glare that would weaken the knees of many a brave man.
"Now, yes, you do."
"God, you're a lousy prophet! I was supposed to discover you, not be mauled by a bunch of bald barbarians wearing tutus!"
"They are not tutus, Angel."
"Whatever!" She deepened her frown. "Where in bloody Hell were you?"
He'd expected her anger. He hadn't expected her to cling to him while she expressed it—not yet. That she did cling, pleased him. She had fulfilled the first of Kevan's images. Pleased at her progress, he smiled down at her. "I've been waiting for you to discover me. And finally you have."
She pinched her lips together. "I swear, Prophet, you'd try the patience of a saint. If I needed to learn fear—which I most certainly didn't—why didn't you just tell me?"
"I can't just tell you." He stepped away from her and sat down on his carved throne. "You have to learn for yourself."
"Something doesn't jive here. You're my guide, but you tell me nothing."
"That's not true, Angel. I've told you many things."
She blew out a long breath. "If you'd just explain the rudiments—"
"You'll figure them out."
"I'm adding difficult to your growing list of vices," she warned, dropping to sit near his feet on the steps.
He curbed the urge to lift her onto his lap, to cuddle and whisper all eternity's secrets into her ear. But he couldn't. She must learn them herself, or she and her love would be lost to him forever.
She gazed up at him over the slope of her delicate shoulder. "Okay, you can't tell me, so I'll tell you my rendition of what's going on." She shifted her backside on the stone, then settled in. "We travel to these former learning levels—you say—of mine. Once there, I must learn something. When I have learned whatever it is, then I discover you. Is that right?"
"More or less." He smiled. "Coming here was sort of a trial run. You've never before been in this time. The other levels will be different."
"Different?"
He couldn't meet her gaze. "We'll meet before you recognize me. It's only after your learning that you'll realize my identity."
"Now we're getting somewhere." She wrapped her knees with her arms. "You aren't so bad, Prophet. It's just that your mind has a strange way of working." She rubbed the mud caking her hands onto the stone step. "I guess it's one of those different drummer things."
He grimaced. "You try to see too much with your eyes, Angel. And not enough with your heart."
"The heart's blind." She laughed. "For God's sake. You're a prophet, you should know that."
Without explaining, how could the Council expect him to succeed? How could the Elder? They knew Kevan's deepest secrets and desires—and Alyssa's, too. They had to know that this would never work. He couldn't lead her to love's light. No one could. She insisted more could be seen with the eyes than with the heart. She required logical reason on insignificant matters, yet accepted matters of consequence with wild abandon. She had no faith in him, or in his abilities. This mission was impossible!
"Prophet, is there a way to bypass these travels and just go straight to wherever it is I'm going?"
"No, there isn't." Refusing to give in to despair despite the odds, he stood up. "Come, Angel."
"Come?" She looked stunned. "Where are we going now?" She curled her fingers around the edge of the stone step. "I just got here."
He frowned down at her. Would she challenge his every word? Resignation had him fighting off a slump. She would. She always had. "We're going to your next level of learning."
"No, we're not. Not yet, anyway. I just got here and I ache like the dead."
"The dead do not ache, Angel."
She opened her mouth to dispute him then, obviously recalling her own death and the lack of aches and pain in the tunnel, muttered instead. "You know what I mean. You can't just jerk me from century to century."
He added a glare to the frown, showing her his displeasure. "I haven't jerked you anywhere, and you will not direct me in my thoughts or actions."
She stood and backed away from him, tripping on the steep steps. He grabbed her shoulders to halt her stumbling. "You're clumsy."
"I am not." She stepped away from him and swept back her mud-clumped hair. "I'm tired."
He grunted his thoughts on that.
Her temper flared. "I am tired! And I'm wet and hungry, and cold, and I smell rank as a sewer. I want a bath. A nice, hot bath." She cast him a hopeful look. "Can you at least guide me to that?"
Far from immune—she rarely had asked him for anything—he supposed that she was exhausted. It'd been centuries since she'd exercised with such vigor. "These are old times, Angel. There is no heat."
"Please, don't tell me that. I need a hot bath, Prophet. I really do. And I want a chocolate bar. The candy can wait. But the bath can't." She brushed at a dry clump of mud clinging to her arm, and swallowed hard. "Look, you guided me into this Hell. The least you can do is guide me to a bath."
Her challenge to prove his worth was open and direct. When the woman set her mind to it, she could rile the temper of a lamb. With a little effort, she could probably get even the Elder wound up. "I can't guide you to something that doesn't yet exist."
"Well, flip."
"Flip?" He narrowed his eyes. "I'm too big to flip, and you're too old to ask me to."
"For pity's sake, I didn't mean to flip in a literal sense." She slapped her thigh. "Yet another affliction? Lord, you're riddled with them!"
"My afflictions are of no consequence. But it's good to know you weren't being literal. Clumsy and whimsical isn't a combination that bodes well for our mission."
She opened her mouth to say something, then without uttering a sound clamped it shut. From the slight movement of her lips, she was either praying for patience, or his damnation. He didn't care to ponder which.
"Can you communicate with those men?" she asked. "The barbarians?"
"Yes." What was the woman thinking of now?
"Great." She smiled. "Have them gather wood for a fire."
"History would be altered," he told her in a tone that would blunt a knife.
"Oh." She blew out a breath that puffed her cheeks. "We're not permitted to alter history, then?"
"Not in that respect, no."
"I mean to have a bath, Prophet. A hot one."
She no doubt would. But she'd have to figure out how for herself.
She spun to face him. "A hot spring! Is there one?"
The hopeful lilt in her tone made him grin. "There is. Follow me."
"Why didn't you just tell me about the hot spring?" She stepped to his side. "You're supposed to guide me."
"Thank you for reminding me of my duty," he said, ignoring her question, and certain he'd be sick of her reminders before they were done.
She must have gotten his point, because she didn't ask again. In silence, they walked into the recesses of the winding tunnel.
"When you aren't guiding a corpse around, what do you do?"
A stab of pain pierced his chest. He reminded himself that she didn't remember him, but the pain didn't ease. Her memory of Kevan Buchannan was buried in the recesses of her mind. And it would stay buried—unless she mastered her discoveries. Without a word, he increased his pace.
She had to fairly sprint to keep up with him. He stepped around a huge boulder and she, unaware that he'd stopped short, plowed into his back. Frowning, he gripped her shoulders.
Alyssa frowned back at him, and added a sigh. Prophet might not have said the words, but his thoughts were clear enough. She resisted the urge to rub the word clumsy from her forehead. "Sorry."
He didn't move. She waited until it became obvious that he wasn't going to move before saying anything. "We can go now."
His frown grew deeper. "I thought you wanted to bathe."
She muttered a curse under her breath. "I do."
He just stood there, looking down at her like she was an idiot and not moving an inch. What was the problem now? "Well?"
"Well, bathe."
Disgruntled, she glared at him. "Where? I don't see—"
A small pool of steamy water appeared. Under a fevered rush of pleasure, her annoyance with Prophet melted. "Is it deep?"
The corner of his mouth twitched. "Cautious now, too, I see."
She'd thought the mountain deserted. She'd not assume again. "A bit."
"This pleases me."
Why his pleasure should warm her heart, she didn't know. What he thought of her shouldn't matter. But it did. He traced the shape of her lips with his blunt-tipped finger. His eyes took on a faraway look that filled her stomach with flutters. "Prophet?"
His expression grew dark. He jerked his hand back and stepped away from her. It seemed that the sound of her voice brought his attention to the fact that he was touching her. But why would touching her upset him?
"The water is shoulder deep. Bathe now, Angel."
His voice had grown gruff. What had she done to upset him? Unable to decipher his mood change, she ignored it and held her smile. "Your shoulder or mine? There's a good foot of difference between the two."
The wariness in his gaze eased. "So there is. And my shoulder would put you underwater." A worried frown creased his forehead. "You do swim, don't you?"
"No, I don't." There had never been anyone to teach her.
Worry flickered in his eyes and his frown deepened, drawing his dark brows together. "The depth is to your shoulder."
His attitude was as much a mystery to her as the attraction that drew her to him. He was a gorgeous man. She couldn't peg it, but the bond between them ran deeper than his appearance. Unfortunately, only he knew what that bond was, and he'd made it clear that he'd no intention of explaining it to her. "You can go now. I'll find my way back."
He crossed his chest with his arms. "I'll wait."
It figured. Not only did her guide not know to bury a corpse, he didn't know squat about women. "Women prefer to bathe in private, Prophet. So if you'll excuse me, I'll get on with it."
He stayed put as if planted. "I can't protect you if I'm not here."
That remark changed her thinking. But it would be a grave tactical error to let him know it. "Mmm, if you insist." She twirled a finger at him.
"You want me to turn my back?"
She stifled a groan. "If it wouldn't be too much trouble."
The Prophet turned his broad back to her. His shoulders shook. She tugged at the fur knotted on her shoulder. The man was a pig—laughing at her for no good reason.
Her clothing fell to the ground. She stepped over it and eased into the heated pool. A pleasured sigh escaped her. "Ah, this is Heaven."
"No, it isn't." The Prophet turned and corrected her. "It's a hot spring."
He was looking at her like she'd lost her mind again. That didn't sit well, but his literal deductions were one of his flaws. She ground her teeth and seethed in silence. He had so many afflictions, she was sure she'd be spending a great deal of her time overlooking them all. Still, the bother of turning a blind eye to them would be easier to stomach if she could find something good about the man.
Aiming her thoughts in that direction, she remembered his kiss. At kissing, he was better than good. And searching further, she was surprised. She trusted him. Regardless of his faults, she knew by their bond that he would keep her safe.
Safe? She'd never in her life depended upon a man to keep her safe. But he would. He had a terrific smile, too. A really terrific smile . . .
She bristled. These good thoughts were coming too easily. "Is there any soap, Prophet?"
He sat down on the ground and leaned back against the big boulder. "You are weak in history, Angel. Soap has not—"
"Never mind." The swirling water stung the cuts on her feet, and she braced her legs. Being warm again felt so good!
Dipping her head back, she scrubbed her scalp, then rubbed the layers of dirt and caked mud from her face and arms. All the while, she watched him from under her lashes.
His gaze never left her, and the look in his eyes was openly carnal. Her heart rate accelerated, and she wished she had a bucket full of cold rain water to splash the heat from her cheeks—and from his eyes. "Could—could you stop staring at me? It's—it's annoying."
His brows shot up. "I annoy you?"
What he did was enrage her senses. Until she'd discovered him, she'd been terrified. But as soon as she'd found him, other, more pleasurable but no less disturbing, emotions had surfaced. He cared for her. How she knew that, she'd no idea. But she was positive that he did. "I don't understand you, or the feelings I have for you. They confuse me."
"It will all—"
"I know," she cut in, giving her shoulders a brisk rub. "Everything will be clear." Sniffing, she caught a whiff of something pungent. "What is that smell? It's bitter."
"Herbs to heal your injuries."
She crossed herself with her arms and looked around. Black mold clung to the cave walls, yet the water she bathed in sparkled through the steam rising from it. "This is an odd, awful place."
The Prophet shrugged a massive shoulder. "If you know another, perhaps."
She balanced on one leg and cleaned her other foot. Rubbing a tender spot, she winced. "I'm glad I discovered you so quickly." The warm water lapped at her shoulder, and she shifted her balance to switch feet. God, the scrape on her leg was awful. It covered her entire shin. Skirting around it, she rubbed her calf. Prophet didn't answer, so she repeated herself. "I said, I'm glad I discovered you so quickly."
His voice held a sharp edge. "I heard you, Angel."
"Well, aren't you pleased that I'm such a fast learner?" Lord, her leg muscles were sore. She glanced up and shot him a smile. "We'll have these travels knocked out in no time."
He raised his knee and rested his arm on it. "No, I'm not pleased."
She stopped rubbing and looked at him. "No?"
"No," he insisted.
"Well, why not, for pity's sake?"
The Prophet stood up. "I don't get to this era often. I had hoped to enjoy its beauty for a while before we moved on."
"Beauty?" She guffawed. "It's hard and barren and ugly."
His gaze bore through her. "Not to me."
A thought she didn't much like flitted through her mind. She'd known him before she'd seen him—as soon as she'd awakened. The rotten scoundrel. She'd learned nothing new here! Wanting nothing more than to scream at him, she forced calm into her voice. "I don't suppose that your liking this era of barbaric brutality had anything to do with my winding up here."
Prophet shrugged. "I might have made a small adjustment in your itinerary to include a brief visit here." He rubbed his jaw. "You needed a measure more fear."
The man was as guilty as sin. Alyssa stomped from the pool to the boulder then glared down at him. "You put me through Hell because you wanted to be here?"
His arm draped over his raised knee, he frowned. "This isn't Hell, Angel."
"Answer my question!"
"I have answered you."
"Prophet," she said from between her teeth.
"I wanted to be here with you. You need fear to survive—later."
"Right." She snapped her jaw shut. "I should wring your neck."
Her chest was heaving, and, after her last remark, so was his.
"Angel, are you threatening me?" He narrowed his eyes to slits and put a hard edge she couldn't miss in his voice.
She stepped closer. "I bloody well am. I could have died in this Hell hole, Prophet. Just because you wanted to drop by."
His gaze slipped from her face to her chest and stayed there. "It's of no consequence."
"My death is of no consequence?" Her blood boiled in her veins. "You insensitive, arrogant, self-centered—"
"Angel."
"—pig-headed man. How dare you—"
"Angel, you're nude."
"—say my death is of no . . ." She stilled, not daring to look down at herself. "Um, nude, did you say?"
He nodded, rocking the back of his head against the boulder. The look in his eyes warmed with mischief and the corners of his mouth twisted into a crooked grin she positively hated.
Looking down, she saw she was naked as a newborn. "For pity's sake."
"Are you upset?"
Damn his innocent tone. "Upset?" she screamed. "Why would I be upset? I always strut around without my clothes!"
His glare wilted her, and she covered her chest with her hands. Where was her bloody fur anyway?
"Not anymore. I don't approve."
She let out a heartfelt groan. The man was driving her crazy. She muttered a few more curses on his head, then opened her eyes. He was walking away. "Where are you going?"
"Come."
"Wait!" She searched the ground for her clothes. "Prophet, wait! I can't find—"
Something whirled around her legs and up over her torso. Her fur. She was dressed. The scratches were absent from her legs. And her feet weren't bruised or even tender! "Did you do that? Prophet, how did you do that?"
His deep voice carried back to her. "It's of no consequence."
Blasted man. She raced to catch up with him. The herbs. He'd said that the herbs were to heal her injuries. So why couldn't he just say he'd done it? Glaring at his back, she mimicked him. "It's of no consequence."
His laughter carried back to her.
"Bloody, blasted man."
THE BARBARIANS had left the cave. Alyssa didn't ask where they'd gone, just as she didn't ask about her food. For the first time since she was a toddler, she ate something she couldn't identify. It looked like paste, had the texture of meal, and tasted bland. It filled her stomach, but it wasn't at all appealing. She couldn't cook worth a flip, but even she could do better than this.
Sitting cross-legged beside her, Prophet rested his hand on her thigh. "Are you curious about your food?"
Her leg jerked, and she saw a twinkle in his eye. "In some things, ignorance is bliss. I vote this is one of them."
Letting out a throaty chuckle, he stood up. "Come."
"Again, come? Where are we going now?" She took another bite. "I'm not ready for another adventure just yet, Prophet."
He held out his hand to her. "We're going to bed."
"To bed?" She jerked back her hand. "Together?"
He looked resigned. "If I'm not with you, I can't protect you."
Every muscle in her body contracted at once. Protect her? In the bath, yes. But in bed? Who would protect her from him? Yet, he was a prophet. And no prophet that she'd ever heard of had romantic inclinations. Maybe she didn't need protection from him.
But this prophet was afflicted. Misguided. And he had the hottest gaze she'd ever seen leveled on her. Sizzling, she lowered her gaze to his chest. "Um, are you suggesting that we make love?"
He shrugged his indifference. "If you like."
If she liked? Talk about an ego death blow. So much for her self-assured sex appeal. "I most certainly do not like."
"Fine." He waved a calm hand at her. "Come."
His nonchalant attitude confused her. He looked like a man who enjoyed women. Hell, what he looked was downright lusty. She'd have to be blind to have missed that. And so bloody virile. So why didn't he like?
She wasn't half-bad looking. She'd even been told she was beautiful once or twice. And the men saying so had been sober. Though beautiful might be stretching the truth, looking at her had never set a man to gagging.
Good grief. What was she doing? She didn't want to sleep with Prophet—not really. Well, okay. Maybe part of her did—the crazy part. True, looking at the man's body melted her bones. But that was his fault. If he wouldn't strut around in that scrap of fur he excused for a loincloth . . .
He was deliberately enticing her. If she wanted him, it was his fault for parading too much tempting skin. How could he expect her to look at him and it not fuel her imagination? Of course her libido kicked in. The man had muscles up the yang-yang. And he flexed them all the time. If he didn't want her to want him, then he shouldn't flex and strut his stuff. She was a normal, healthy woman, not a stone.
She dug her heel into the dirt. The muscled maniac flaunted his body like a beacon, intentionally tempting her. It was definitely his fault that she wanted him. And that was the simple truth.
But if that were true, then why was he indifferent about making love to her? She grimaced. It would've been nice if he'd wanted her—or not wanted her. Lord, his indifference rankled . . . and he knew it. He'd set out to seduce her, knowing he'd reject her. The bloody, blasted man!
"Come, Angel."
His voice was tender, irritating. She tilted her head and looked up at him, letting him see her turmoil in her eyes. "Why is it that when I'm with you, I wind up confused? Until you came along, I knew my own mind." She kicked at the dirt, lifting a little puff of dust. "I think I need some space, Prophet. For perspective—you know? You go on. I'll sleep here."
"It'll grow cold in the night," he warned her, then walked away.
"Prophet?" she called out. When he paused, she added, "Where are those men—the barbarians?"
"They won't return until morning."
"Oh." She watched him resume walking and called out again. "Prophet?"
"Yes, Angel."
She swallowed her pride, determined to ask the question. But if he laughed at her, she'd hit him. Right in his king-sized biceps. "Are there bugs?"
He turned his face from her, and she suspected he hid a smile. But he wasn't laughing. "A few," he confessed. "Most fly, though a few do crawl."
"I knew he was going to say that," she muttered under her breath. "I just knew it."
He disappeared behind his throne. No sooner had he stepped from her sight than she began to imagine creatures crawling all over her. And the temperature instantly seemed to drop twenty degrees. She fought against it as long as she could, but when goose bumps rose on her goose bumps, she slapped at the nonexistent bugs on her legs and arms, and went to him.
Behind the throne in a little alcove, he lay stretched out on the ground, his arms folded and hands tucked behind his head. A furry black animal skin covered him, feet to chest. Asleep, he looked relaxed, even more handsome and . . . warm. "Prophet?" she whispered softly.
He didn't answer. Now what was she supposed to do? She scuffed the ground with her toe and muttered. Well, she sure wasn't going to stand here and freeze while he slept all snug and toasty. "Prophet?"
Still no answer. She nudged him in the side with her toe. "Prophet, are you still awake?"
"Mmm?" He didn't open his eyes.
She couldn't look at his face. She tried, but she just couldn't do it. "I hate bugs."
"I know." He lifted the edge of the fur. "Come to bed, Angel."
THE MAN did have his good points.
Prophet radiated more heat than a two-ton furnace, and his chest made a wonderful pillow. Alyssa closed her eyes and snuggled closer to him. She took in a deep breath. He smelled good, too. Warm and woodsy and male.
She turned and snuggled her backside closer to him. He fitted himself against her and draped her waist with his arm. Even weary-to-the-bone, him being so close heated her blood, but she closed her eyes and willed herself to relax.
Soon the lulling sounds of his steady breathing and the stillness of the cavern soothed her tired mind, if not her tumbling thoughts. Was she dead now? She felt pain here, and desire; she must be alive. The dead didn't ache—according to Prophet. And she had to admit that in the tunnel what she'd felt had been the absence of pain. Here, she ached like Hell. Near sleep, she mumbled. "Prophet, why do I know you?"
He didn't answer. She stacked her hand on his and toyed with his fingers. He had strong hands. Wide, strong, good hands. "Prophet?"
His voice was a husky whisper. "I can't tell you, Angel."
"Why not?" She rubbed his calves with her bare toes.
"A guide must lead, not divulge."
She brushed his arm with her cheek and felt the muscles there swell rock hard. Her heart pounded, and her throat went husky thick. "Did you love me?"
He buried his face in her hair. "Rest now. We leave at dawn."
A knot of fear coiled inside her. She shivered. "When I wake up, I won't be here, will I?"
"Shh, tomorrow is soon enough to worry about the trials ahead." He stroked her hair. "Tonight, sleep. Restore yourself."
The inconsolable ache she'd felt on parting from him in the dark tunnel flared in her again. And, again, she couldn't explain or deny it. Her voice reflected her turmoil. "Prophet, kiss me goodbye."
He shifted his weight and she rolled flat, the back of her head resting on his arm. His gaze told her more than the thousand words he could have spoken. Unbidden, her feelings poured out in words she had never said to another person. "I don't want to be without you."
"Angel." He sipped at her lips as though only she could quench his thirst, telling her with his touch all she needed to hear.
This is what she had missed in life. She arched her neck, granting him access to her throat. This oneness that came with sharing her feelings with him.
He kissed a path down her neck to the soft spot behind her ear, raked her earlobe with his teeth, then returned his mouth to her lips. Her heart pounded against his chest. The feel of his hair against her bare skin had her thoughts fleeing, forbidding any awareness other than the feel of him to exist inside her.
He raised his head and looked deep into her eyes. She felt scorched, branded, soothed.
She felt loved.
"Sleep now, Angel." His breathing ragged, he kissed her eyes closed, pulled her into the circle of his arms and whispered close to her ear. "Sleep."
ALYSSA SLEPT in his arms.
For the first time since he'd last held her, Prophet felt content. She was his love and, before too many more nights passed, she would again be his lover. But not yet. Dear God, not . . . yet.
He studied the full curve of her lips, the gentle sweep of silvery lashes shadowing her cheeks. His angel. His body ached for her, for the sweet pleasure of filling her flesh. But even more than his body, his heart ached for proof that maybe this time their separation would be over for good.
The amulet at his neck vibrated against the hollow of his throat. He cupped the crystal in his palm and sensed its warm glow. The Elder was summoning him.
Sliding his shoulder out from under Alyssa's head, Prophet untangled their legs then waited for her to stop her annoyed grumbling. When she settled back down, he got up.
A short distance away, he met the Elder.
"She lies with you, Prophet?"
"She's my woman, as well as my destiny, your grace."
Looking thoughtful, the Elder stroked his long beard. His eyes, as colorless as the crystal at his neck, reflected no light. "Does she recall Kevan?"
"No." Disappointment shafted through him. "She doesn't."
"I see." The Elder stood statue still for a long moment. "The Council has given your quest much thought. As your trial is a most difficult one, we have decided to grant you a concession."
He didn't like the sound of this. Not at all. "What concession?"
"You may tell your woman of your short-term trial, but not of the changes that must come from her. Those she must learn for herself."
"I'm not sure I understand."
"You may tell her of your next learning level mission. But you are forbidden to reveal the particular tribulations either of you will face long-term, or what she must learn to conquer that level and move on to the next."
Prophet's concern deepened to worry. "Why is the Council offering us this concession?"
The Elder sighed, distinctly imparting that he would rather not say, but realizing he'd only be asked repeatedly until he answered. "The Council is of the opinion your woman will again fail to become universal. But we are not without hope for her, or compassion for you." The Elder frowned. "You have given her your love freely throughout time. The Council feels you deserve the woman you have chosen, and it wishes to give you what assistance it can to assure your mission is successful. That said, I would be remiss in my duty to you if I didn't confess that, even with the Council's efforts, I am personally doubtful that your woman is capable of fulfilling her destiny."
Kevan clamped his jaw. "She won't fail, your grace."
The Elder's expression grew grave. Deep creases formed in his skin and grew deeper. "I hope not, Prophet. For your sake, I sincerely hope not."
Something wasn't right here. The Elder wasn't disclosing everything. Prophet sensed it, though he didn't sense the reason behind it. Regardless, he couldn't allow the Council to make concessions—not without opening his and Alyssa's relationship to intense scrutiny. They would spend eternity trying to overcome the stigma. "Please, express my gratitude to the Council, your grace, but I refuse their offer. Alyssa will succeed—without concession."
"Prophet, don't refuse this offer out of blind loyalty." A warning rode in the Elder's rasp; a warning Prophet couldn't ignore—or agree to accept. "Without help, your destiny will remain an illusion."
Prophet stiffened his spine, clenched his jaw. "My love for her has never been an illusion. And it's not for me to fail or succeed in this quest, and you know it. You yourself so much as said that Alyssa will determine our fates. I believe in her. She'll succeed. She'll become universal and capable of loving. And she'll love me."
The Elder's expression went from grave to grim. "Your confidence in her awareness and abilities is false, Prophet. Your love for her blinds you to the truth. Don't be foolish about this. The treasures of a foolish man are not everlasting."
"Foolish? I love her!"
"Your feelings have never been in doubt. But it's your woman we're discussing, and she does not love you."
The truth stung. "Isn't that the purpose of this mission? For Alyssa to learn the virtues she didn't learn previously, to restructure her character so that she does have the ability to love me?"
"That's your purpose, yes. But your destiny? That, the will of the human spirit shall decree."
Prophet repeated the words he'd heard on beginning this quest. "Have faith in your humble servant, your grace. I'll teach Alyssa to love me. She won't fail."
The Elder sighed deeply. "So you insist on refusing the concession?"
"Respectfully, sir, yes."
"Your faith in one who has let you down so often is commendable, my son. The Council will be most pleased." The pity and worry heard before returned to the Elder's voice. "Personally, I hope you won't regret this misplaced devotion."
Prophet smiled. "Every man must seek his destiny. Loving her is mine. Knowing that, how could my devotion to her be misplaced? How could I regret the choice of my heart?"
"I'll inform the Council of your decision. Though I feel your loyalty to the woman is foolish, I wish you well."
The Prophet inclined his head. The Elder's silvery image faded.
"ANGEL. ANGEL, wake up. It's time to go."
Alyssa opened her eyes. The sleep-soft confusion and unfocused discontent in them stole Prophet's breath.
"Not yet," she mumbled, snuggling deep into the warmth of the fur.
He touched her shoulder, bare beneath her fur wrapper. Her skin was warm, enticing. He forced his voice firm. "Alyssa, we have to go now."
She came fully awake and sat up. "Where are we going?"
"It is time to advance to your first learning level."
She wrapped her arms around his neck and clung to him. "I'm afraid, Prophet. I don't want to leave you."
He held her, smoothed her long, tangled strands of hair. Fear. She had learned blessed fear. His eyes burning, he swallowed a knot of emotion lodged in his throat. "The unknown is often frightening." How could he tell her that her learning would be worse than frightening? She had so much to endure and overcome. He couldn't comfort her. Her fear was necessary to her survival. To in any way ease her mind would put her in further jeopardy.
She reared back and looked up at him. "Will you be with me?"
He nodded. "But you won't know me, not at first."
"Until I learn." His throat muscles constricted. He couldn't speak. He gave her shoulder a little squeeze and again nodded.
"What must I discover?"
"I can't tell you that, Angel."
She nuzzled his neck. "I'll be safe. If you're there, I'll be safe."
His heart lay stone-heavy in his chest. He wanted to scream his outrage that he wouldn't be there. "You must take special care, love."
"Love?" She cast him a quizzical look. "Was I your love? Is that the strong bond I feel between us?"
Prophet hesitated. Should he admit the truth, or not? How much would the Council consider acceptable? What penalty would she suffer if he disclosed too much? Not knowing, he held his silence.
"I was!" She pressed her cheek to his. "I was your love!"
He neither confirmed, nor denied, her suspicions. He couldn't; not without knowing the consequences. Cupping her face in his hands, he lifted her chin and looked deeply into her eyes, letting her see his worry. "Angel, listen. Shh, listen to me. We don't have much time. You must take special care with your safety. That's where you must focus right now. Not on our past."
"Why?"
Trembling, he tightened his fingers on her face. He'd give all he had ever owned to not have to tell her this. Everything he ever would own. "Because not only will you not know me in this next level, I will not know you."
Her fingers dug into his neck. "But if you don't know who I am, how can you guide me?"
Hearing her panic, he wanted to soothe her. But he couldn't. Why did fear have to be her protection? Why couldn't it have been sharing? Opening her heart to feelings? Being vulnerable? "Please, Angel," he whispered pleadingly. "I can't say anything more. We both just have to have faith that you'll make your discoveries and find me."
"Faith?" Now, her eyes too flickered worry. "I don't know . . . This is all so strange. If I don't know you, how will I know to find you?" She squeezed her eyes shut. "No, it can't work. I can't do this without you knowing—"
"You have to." He pulled her into his arms. "You can. We must believe."
"In what?" She reared back and stared at him, panicked. "In my instincts? My abilities?" She clung to him and a strangled cry escaped her. "If those were all I needed, I wouldn't need this mission. I'd have made my discoveries the first time!"
"No, Angel. Not belief in you." His cupped her face in his hands and gazed deeply into her eyes, infusing her with power and strength. "Belief in the ultimate strength of love. With it, weakness becomes strength. Trials, opportunities. Enemies, allies. No adversity, no matter its size or scope, is stronger than love. To succeed, that's what we both have to believe."
Crawling from the fur, she stood up. Her shoulders slumped and fear such as he'd never before seen on anyone's face, etched into hers. "Oh, God."
"Believe it, Angel." She didn't move. "Angel?"
"You don't understand," she said in a faint whisper. "The one thing you say I have to believe in is a mystery to me." Her pale face bleached white. "I've never loved, Prophet. Never."
A dull ache wrapped around his heart. He stood and faced her. "I know. But you have to try—really try. You must not fail." He wrapped her in his arms and pulled her to him until nothing separated them. "Dear God, you must not fail."
Three
Scotland, 1100
LADY ALYSSA pulled the bowstring taut, aimed, and let the arrow fly.
Duncan watched the buck fall and squinted. "You're slipping, my lady. You've missed his heart."
"Check again, Duncan. I've not missed." Alyssa stroked her mare's long, white neck and laughed. "Since I felled dinner, I'll leave getting it to our table in your capable hands—providing you can see it."
Alyssa turned her horse, Streak, toward Cameron holding. The old soldier bit back a smile at her teasing. He thought to protest her returning unescorted, to send a few soldiers with her for protection, but knowing he'd likely get his ears blistered for his trouble, he said not a word.
"You allow her to ride alone?"
Duncan chuckled and turned his mount toward James MacMillian. The fresh-faced youth's misuse of the Gaelic language reminded Duncan that, though he was a native Highlander, James had been born to an English mother. And what he said reminded Duncan that the young warrior was new to Cameron—and to the ways of its lady. "Allow her to ride alone?" Duncan guffawed. "Only three men allow or forbid Lady Cameron anything, James. Best you learn that right away. King Edgar; the Buchannan, her chieftain and allied-laird; and her father, Lord John. She'll heed no other."
"What about Innes?"
Duncan grimaced. "Not yet."
James turned his mount and frowned. "Well, one of them should forbid her to ride alone. 'Tis dangerous."
Duncan shared his soldier's concern, but for all the good it did him, he need not have bothered. Still, he'd done what he could. "She is not exactly defenseless."
James smiled. "Nay, she's not that."
Curious as to what had enraptured James, Duncan followed the young man's gaze to a clearing up ahead. Lady Alyssa had stopped to speak to some of her warriors.
She was a sight to behold. The Cameron plaid, yellow and green and red, draped her delicate shoulder. Sitting astride her white mare, she laughed, and her silver hair, tied at her neck with a length of red ribbon, caught the sunlight.
"She's beautiful, eh, Duncan?" James leaned forward in his saddle and let out a telling sigh.
Lady Alyssa didn't often bother with feminine frippery, but even without it, she was a bonny lass. "Aye," Duncan replied, "she is."
"She looks . . . soft."
Duncan scratched his beard. "She'd plague you with curses if she heard you say that." If she hadn't already, his lady was well on the way to capturing another heart. The feeling that she needed protection rose in the hearts of men as natural as a Highland sunrise took to the sky. And he should know. Hadn't he lost his own heart to her on the very day she was born?
"Still, she looks tender," James insisted.
"She might look tender, but appearances can be deceptive. And in the case of the lady, her appearance is deceptive, indeed."
Duncan had seen to that, spending long hours training her. Since she'd been a wee bairn, he'd pushed her hard. Just as he'd pushed her father in his training years, when Duncan had first come to Cameron from his home in the Southern Uplands.
James sounded breathless, still feasting on the lady. "Aye, deceptive. She rides like the wind, and, though it's inferior, she handles her sword with competence."
"Inferior? Gavin would brand your hide for saying that. He specially made the lady's weapon to accommodate her small frame. But it's a fine piece of work. Perfectly balanced, it is."
"Could be."
"Is, MacMillian," Duncan firmly insisted. "Have you seen her surrender any advantage on the training field?"
"Nay, the lady's lightning quick."
"Damn right," Duncan said, giving his head an emphatic shake. "And agile as a cat."
"But much more beautiful than a cat, eh, Duncan? Much more beautiful."
With another chuckle, Duncan dismounted and studied the arrow in the fallen buck.
"Did she pierce its heart?" James asked from atop his horse.
Duncan looked up at the young soldier. He had much to learn. "She said she did."
"Aye, but—"
"Our lady has not a modest bone in her body, lad. But her word is as solid as God's will."
James's expression grew thoughtful. His horse gave a good snort and James patted its neck to still him. "Duncan, doesn't it seem sacrilege to waste the lady on the likes of Kenrick Innes?"
"'Tis not for us to decide. Your mother being English has made you forget your place, James."
"I know my place," James disagreed. "If Lord Cameron had half the grit of his daughter, he'd break that marriage contract."
Duncan agreed, even if loyalty to his lady kept him from saying so. Lord Cameron didn't match his daughter. He had not the mind of a warrior, nor the heart. And since the death of his wife, Lady Alyssa's fair mother, his lord's heart had been pickled with love for only one thing. His ale.
With a sigh, Duncan pulled out the arrow, wiped it clean on the grass, then slid it between his belt and tunic. "If Lord Cameron did break the marriage contract, Lady Alyssa would abide by it anyway."
"Why?"
"Loyalty to her clan." Duncan mounted his horse and squinted against the strong sunlight, then looked toward the clearing. Seeing his lady ride off, he called out, instructing the men to return the game to the keep.
"I don't see where she'd be disloyal—"
"If you'd stop talking so much, you might see more." Duncan pressed his heels to his horse's flanks and set out in the direction his lady had ridden. James rode at his side.
"Duncan?"
Duncan rolled his eyes back in his head. "What is it now?"
"Don't get sour. I have to ask questions to learn."
The young soldier was right. Annoying, but right. "What's your question, then?"
"How long will you have men to protect her with? To protect Cameron's holding?"
Duncan glared at the brash boy. Even if he was Lord MacMillian's second son and he'd been fostered to Cameron for Duncan's training, the boy was too outspoken by half. That Duncan had worried over the same fears himself just added to his upset.
James shrugged. "With the English raiders growing so bold, war can't be far off. The Buchannan will learn of John Cameron's ineptitude then for sure. And my guess is he won't take kindly to a lady heading one of his allied-vassals."
That learning was Duncan's second greatest fear in life. Being John Cameron's second-in-command, it was Duncan's duty to report his lord's failings to the Buchannan. He hadn't. And that infraction could well cost him his head. But to report the father would be to betray Lady Alyssa, and his head wasn't as valuable to him as her trust.
James swatted at a fly on his cheek. "It's amazing that he hasn't found out before now."
"Aye, it is. It's been five years since her mother's death. Seven since her brother, Paul, passed on. Lady Alyssa's done a fine job, though, woman or no."
"In men's work," James countered. "Now, Lady Megan. She's a fine specimen of womanhood. Mayhap I should marry her."
Picturing Paul's pretty widow with young James had Duncan snorting louder than his horse. "Bah, she's too soft. No gumption."
"Lady Alyssa, then. Mayhap I should marry her."
Duncan laughed from deep in his belly. "Ain't but one man I know could handle my lady, MacMillian. The Buchannan."
"Mmm, didn't he visit here once?"
"Aye."
"How was it he didn't learn the truth then?"
Had James not pledged his loyalty to Cameron, Duncan would have boxed the young soldier's ears. But since he had, MacMillian deserved his answers. His head, too, was on the Buchannan's chopping block. "When the Buchannan came, Lord Cameron and Lady Alyssa weren't at the holding."
"And none betrayed her?" James slid Duncan an astonished look. "Not even Kenrick Innes?"
Hearing that man's name had Duncan's temper heating. "Nay, though that braggart can't claim honor as the reason. With him, it was greed."
"Greed?"
"Aye. When he weds the lady, her power becomes his."
James gave his head a weary shake. "The Buchannan approves the union, then?"
"He does." So far as Duncan knew, it was the only bad decision the Buchannan had ever made. "When Edgar made Buchannan chieftain, he gave his blessing to Lord Cameron. I heard it myself, though bless me for saying that I wish I hadn't."
James MacMillian grew quiet, thinking on all he'd learned. The Buchannan was pleased with Cameron's defense. The stories were legend. The chieftain's praise about the wall enclosing the lower bailey being protected with heated sand instead of boiling water, as was custom, was what had prompted James's father to give him to Cameron in foster care.
Duncan turned south at a copse of pines and headed toward the keep. James followed and let his horse have its head. Would the Buchannan have been as pleased, if he had known that Lady Alyssa had made the change from water to sand? James himself had been stunned by that news. But Kevan Buchannan was a hard man to figure, which James reckoned was why no one had told the laird. It was said that he cherished loyalty mightily.
Drawing his horse to a halt outside the wooden gate, Duncan shouted a greeting to the posted guard, then asked, "Has Lady Cameron returned?"
"Aye, a short time ago. The smith's been injured. She's gone to him."
"I'll tell the cook dinner is on its way," James said.
Duncan nodded and turned his mount toward the cottages inside the lower bailey.
He found her quickly enough, stitching up a nasty slash in the blacksmith's arm.
"Loosen your muscle, Gavin," the lady directed. "Your hide's bending my bloody needle."
Duncan hid a smile. Even in reprimand her voice was soft and husky, pleasant on a man's ears.
"It is loose." Gavin frowned. "Sorry, my lady."
Her throaty chuckle filled the air. "Aye, so it is. Perhaps you need to forge me a needle from your metal, eh? Like you did my sword, only a wee bit smaller."
Gavin looked mortified. "A wee bit?"
"Well," his lady conceded, mischief twinkling in her eyes. "A wee bit more than a wee bit, I suppose."
"Mmm, mayhap I will, my lady." Gavin laughed and looked up at his wife. "Cease your worried frown, Katherine. 'Tis a mere scratch."
"A mere scratch doesn't require threads, Gavin." Katherine's cheeks flushed a bright crimson.
"You think I jest about the needles, Gavin," Alyssa said. "But I am most serious. A metal needle could be heated."
Gavin's brows shot up. "'Tis torture you're suggesting."
Duncan watched Lady Alyssa tie the end of the thread, sprinkle a brown powder from one of her medicine jars into her palm, and splash a few drops of water in it until it made a paste. Then she dabbed the paste on Gavin's cut, chatting the entire time about the smith's work.
Her interest was genuine, Duncan thought. And she was a fine healer. Her mother, too, had possessed the touch.
"That should do it, Gavin." Alyssa gathered her goods and put them in her medicine satchel. "Have a care to keep it clean. 'Tis very important."
"Yes, my lady."
"See to it, Katherine," she told the smith's wife.
Katherine had stood back, so silent Duncan had forgotten her there. Now she smiled. "Yes, my lady."
At the door, Lady Alyssa turned back. "And no ale, Gavin. Not until the threads come out."
The old smith had shown no discord until then. When Lady Cameron pierced him with the needle, he hadn't uttered so much as a grunt. But at the order of no ale, the man was aghast—protesting at the top of his lungs.
"See to it, Katherine!" His lady fairly shouted to be heard above Gavin's complaints, then made quick her exit.
Duncan stifled a chuckle and followed her outside. "Your reminder to Gavin was most timely, my lady."
"Humph! I could sever his arm from his body with less outrage than I can refuse the man his ale." She swung her satchel as she walked, her step lively. "Has Gavin had tragedy, too, Duncan?"
Before he could answer, they'd reached the upper bailey courtyard and a messenger from the guard intercepted them.
"Hello, Sewn."
"Lady Cameron." The messenger paused, trying to steady his frisky mount. "Lord Innes is come. He brings a message from the Buchannan."
"Well, let the man in, for pity's sake." Alyssa stroked the horse's strong neck until he calmed. "Duncan, will you receive him? I'm more dust and horse than woman. It would not please Kenrick to see his betrothed thus."
"Aye, my lady." Duncan tried to bury a frown by stroking his beard. "I'll greet him."
Alyssa smiled her thanks then hurried inside.
In the main hall, Megan was instructing the servants to place new rushes on the floor. Alyssa headed for the wooden stairs. "We have a guest, Meg—Kenrick. See to his comfort, if you please."
Megan took one look at her and burst out of her good humor. "Good heavens, you're a sight!"
Tall and willowy with her pale blond looks, Meg never looked less than perfect. Alyssa gritted her teeth. "I've been on a hunt, for pity's sake. One cannot hunt and not become a sight."
"Up the stairs with you, then. Quickly, before you shame yourself and your clan at being caught in such a ruin."
Alyssa took the stairs in a dead run and didn't slow down until she reached her chamber.
She washed and dressed in the cumbersome chemise and emerald green bliaut that was considered appropriate for a lady, and, wiggling, tugged a roped belt down low on her hips. Lord, she preferred breeches and her plaid. But Innes had gifted her with the god-awful garb. She supposed she should humor him by wearing it. Still, her plaid was more practical, and—she shrugged her shoulders to gain comfort—less restraining.
When she returned to the hall, Kenrick stood near the mantel talking to Duncan. She studied the man she'd been pledged to since birth. Tall as most Scots and as strong-featured, he was far from repulsive, even if his hair was the color of carrots left in the garden overly long. So why didn't her heart quicken at the sight of him? She felt not so much as a flicker.
Megan often spoke of the flutterings she'd felt on catching a mere glimpse of Paul, God rest his soul. True, Megan had loved her husband. But Alyssa was dutiful. She cared for Kenrick. She should feel something good inside.
Soon, she supposed, he would take her to wife. It was unavoidable. She was already twenty-two, long past marriageable age. But he'd yet to mention fulfilling their contract, and she'd just as soon remain a maid as wed him. The man was boastful of his worth. Sinful, that. For now, it seemed that they were both content to leave things as they were. Yet when he demanded she marry him, she would do her duty and become his wife. How she dreaded that day.
He paced impatiently from the table to the hearth. The firelight made his hair look like shiny carrots, and—good God, the man was dressed for battle! How could she not have noticed?
From the steps, she scanned the hall for her father, but he was blatantly absent—again. Megan stood quietly beside a lump draped in cloth on the floor. What had her riled enough to make her wring her hands?
Alyssa entered the great hall, stopped beside one of the long wooden tables in the rear, and waited until she caught Duncan's eye.
When he looked at her, she dipped her head, as was proper, and caught his answering glint of approval. He'd taught her the behavior of a warrior—both on and off of the training field. And one of her first lessons had been to lull others into complacency.
Flaunt not your abilities. Being physically inferior, surprise is your strongest defense. Duncan's creed. How he had drummed those words into her mind!
He addressed her now, his wooden cup clunking against the hilt of the sword strapped to his hip, his expression as rigid as his body. "Lady Cameron."
Her proper title was Lady Alyssa, of course. But when her mother had died, her father had insisted Alyssa be titled Lady Cameron. She hadn't wanted the public recognition; bestowing upon his daughter the title reserved for the lord's wife would surely spur gossip, and the last thing she needed was for the Buchannan to note happenings at Cameron hall too closely. Yet, after losing her mother and her brother, Paul, Alyssa didn't want to lose her father, too. Objecting would have offended him immensely, and her father offended was not something Alyssa or the clan desired or enjoyed.
Chewing a bite from a fat wedge of cheese, Kenrick ambled toward her. "Mayhap you can ferret out your father." He waved the pungent wedge at her. "I've great need to speak with him."
So much for greetings, Alyssa thought. One look at Megan and her sister-in-law's expression said all that needed saying between them. John Cameron was abed. Sotted—again. "My father is indisposed, my lord, but might I be of assistance?"
"Indisposed?" Kenrick's voice thundered through the hall. "Well, un-indispose him, my lady. The Buchannan has called up his allied-vassals. We must leave at once for his castle."
Alyssa's heart skipped, then thudded a wild beat. The Buchannan was mighty. A strong, ruthless chieftain, if legend were believed. He was laird of many clans. Some had no choice. But some, including her own, had pledged him their fealty in return for his protection. Clans Cameron, Innes, Grant, MacMillian, and Lindsay, being the larger of these vassals. And exercising sovereign rights granted him by King Edgar, the Buchannan granted them their own identity as an allied-vassal, a clan, when in fact they were his vassals. Aside from those, his allies were many. Though Scots were brave, not many chose to willingly feud with the Buchannan.
The horrid truth struck her. The Buchannan would have no need to call up his allied-vassals for a feud; alone, his numbers were too great. Which could mean that King Edgar had summoned. And, oh God, that meant war!
She swallowed down a lump of fear. "He has called up Clan Cameron?"
"Aye," Kenrick replied, taking the cup of ale that Megan offered him.
"For what purpose?"
Kenrick slammed the cup down on the long wooden table at Alyssa's side. Ale sloshed over its rim and splattered her bliaut.
"You dare to ask, woman? Summon your father at once. 'Tis not your blood what's called for spilling!"
Anger boiled in Alyssa, but she caught Duncan's warning look and swallowed the sharp reply burning her tongue. "I meant no offense, my lord. I shall—"
"My lord," one of his men interrupted, calling out from the entrance to the hall. "We must ride. A storm blows from the south."
Kenrick gave his man a curt nod, then turned to Duncan. "I leave the task in your hands—and on your head—to deliver the call to Lord Cameron."
Duncan's faded eyes blazed. "Clan Cameron will answer its chieftain's call, Lord Innes."
Kenrick strode from the hall without seeing the anger in Duncan. An anger Alyssa knew well—and avoided at any cost, save truth. She gripped the rough table edge to steady her nerves, but her voice still shook. "It is war, is it not, Duncan?"
"Aye, my lady." He gave her a resigned look. "It is war."
"Why north to the castle?" She dragged her nail over a notch someone had carved into the wood. "Why not south to England?"
"'Tis not a war with England, my lady. Though 'tis the English what attack the Buchannan."
Alyssa grimaced. "Raiders?"
"Aye."
She shook her head. "Fools."
"Aye, fools," Duncan agreed, taking a long draw from his cup. "The Buchannan wants a show of strength to quell any desire the Raider's countrymen might have to follow their lead."
Relieved, Alyssa breathed easier and let go of the table. The splintered grain left pressure dents in her fingertips. Her king had not summoned. Mayhap her secret of leading her clan was safe. "The Buchannan will kill them," she predicted, then called out. "Megan, where is my father?"
"He's on the floor, my lady."
"What?" Alyssa spun to face her sister-in-law. Standing as stiff as a corpse, the woman looked waxy pale. Any second, she'd blink her lashes right off her lids.
Megan bent down and lifted a burlap cloth from the lump on the floor. "I—I knew not what to do, Lady Alyssa. I didn't want to be disrespectful, but there was no time to move him before Lord Innes arrived."
Alyssa's face burned fire hot. She rolled her gaze heavenward, wishing the dirt beneath the rushes would crack open and swallow her.
John Cameron, Lord of Clan Cameron, lay sprawled in a drunken heap on the earthen floor.
Silently, Alyssa cursed her father's weakness. "It's all right, Megan. Your quick thought saved us Innes's scorn. Kindly have your lord put to bed." Duncan's disgust was evident to those who knew him. And, though he tried to hide it, his lady knew him well. "I'm sorry, Duncan."
Duncan cleared his throat. "We must respond to the Buchannan's call." She knew the anger glistening in Duncan's eyes wasn't directed at her, but at her father.
That was worse. Grief made her father like he was. Soul-deep grief. "Aye. Summon the men. Leave only enough to protect the holding. I'll ready quickly."
"Ready?" Duncan's jaw fell slack. "You canna answer the Buchannan's call, my lady! War is men's work!"
In her training, Alyssa had learned the value of suppressing her emotions. She buried her impatience with little effort, and spoke in a deceptively soft voice. "Would you rather have my father guard your back?"
Duncan lifted his gaze to the open stairway. Two guards were carrying a limp John Cameron toward his quarters. Spittle dribbled from the corner of the lord's mouth and his red-streaked eyes rolled back in his head. A shiver crawled up Duncan's spine and anger churned in his belly. "Nay, my lady. But my back is less important than your safety."
"Not to me." She smiled at her faithful second. "I can't ask my soldiers to do battle, if I myself am unwilling. I will not. Surely you see that honor gives me no choice. Not to go would be unjust to my men."
Duncan frowned, deepening the creases in his leathery skin to grooves. "Aye, my lady, I see it. But I don't have to like it."
THE CAMERON soldiers rode due north for two days. Although it was late summer, the wind had a sharp bite to it and the temperature had grown cooler with their climb.
The mountainous terrain gave way to the stark and rugged plateau that marked the border of Buchannan lands. Alyssa had never been this far into the Highlands, and her interest showed. Duncan had long since become exasperated with her many questions. Duncan drew his horse alongside hers. "Well?"
She pulled her plaid closer around her and secured it with a leather strap at her waist before looking at him. "Well, what?"
"What do you think of it?"
"It's a harsh and unforgiving land, I'd say." The air was crisp and sparkling clean. She breathed in deeply. "But a lovelier land I've never seen."
Duncan looked stunned. "Lovely? Bah, you jest, Lady Alyssa. 'Tis barren."
"I do not jest," she insisted. "'Tis lovely. Vast and rugged and strong. God is a most able artist, is He not, Duncan?"
He ignored her question. She gave Streak a pat on the neck and looked up at the late afternoon sky. It was more blue than any she'd looked upon before. "Duncan, mayhap you should not address me as a lady. We are going into battle."
"I still dinna approve—"
"So you've said at least a hundred times in these two days past. Nevertheless, I am going."
"Very well, my la—lord."
Alyssa laughed deep from her throat. "That sounds strange. Well, I can fight as well as a man. Lord will suit, I suppose."
Duncan mumbled the penalty for humility, or, more accurately, for Lady Alyssa's lack of it. "'Tis time we stopped and readied ourselves."
A SHORT TIME later, Alyssa stood at Duncan's side and faced her soldiers. The Cameron plaids were pleated and secured at the waists of her men. Most were bare-chested, but sprinkled through the group were a few warriors who'd added a deep green shirt. And now and then, mainly among the younger warriors, she saw some wearing pairs of black boots.
Her men recognized her, though outsiders would find nothing female in her dress. She'd disguised herself from head to toe. The only color in her garb was her plaid. A black hood concealed her silver hair. Black breeches and soft boots concealed her legs and feet—and, God willing, her sex. Thanks to Duncan's foresight, her disguise would not hinder her ability to fight. He'd insisted—though she'd cursed him mightily for it at the time—that she train in this attire, just in case. Aye, he was a man of vision.
Duncan raised his hand and the soldier's rumblings ceased. "The Lady Alyssa is to be called Lord Cameron until we return to Cameron hold. Any man who defies this order shall die by my hand."
It was the longest speech Alyssa had ever heard Duncan make. When he seated his mount afterward, she knew his patience was on a short tether and she wasted no time in taking to Streak.
They'd been riding a short while, when in the distance, Alyssa saw her scout guard returning to them. His horse's hooves kicked up a cloud of dust that told her he rode at full speed. "Duncan."
"Aye, I see."
Her stomach tensed and Alyssa spurred Streak at the same time Duncan did his horse.
When they drew close enough, the winded guard shouted between gasps. "My lady, they battle!"
Alyssa jerked back on Streak's reins. The horse reared and using her knees Alyssa settled her mare near the guard. "Call me your lord from now on, Sewn. Close your jaw, for pity's sake. It's by Duncan's order. He's threatened the head of any man who doesn't."
Streak tried to take a bite out of Sewn's knee, but Alyssa's sharp reprimand stopped her. "Is the battle far ahead?"
"Nay. In the next clearing." Sewn drank thirstily from his pouch. "But there are many men."
She turned in her saddle and motioned to her soldiers, who were now within shouting distance. "We ride!"
Spurred, Streak thundered across the flat land. The smells of wild leek and heather grew pungent. Alyssa never had been in real battle, and her heart hammered with the force of her mare's hooves. She whispered a prayer to her Maker for the safety of her men, then turned her prayers to preparing herself. She asked for strength, ability, and, please God, courage to do what she must in taking lives.
The battlefield was every bit as horrid as Duncan had sworn they were in his stories of the old days. The ground was littered with bloodied bodies, mostly English, but too many Scottish plaids had fallen for Alyssa's liking.
From her mount, she saw him. A raven-haired giant, dressed only in his red and black plaid. Muscles that were massive and thick bunched in his arms, in his bare chest, and across his broad back. And the hard expression on his face gave truth to every story she had ever heard about his being fierce and ruthless.
Fighting three men at once, he could be no other than the Buchannan.
Skirting the reach of the first man, the laird felled a second one with his sword. The third was not faring well, due to a powerful sword thrust and a sharp kick to his midsection that required a physical strength Alyssa envied.
Two new raiders replaced the ones who'd fallen, approaching the Buchannan from behind. He was still engaged with the third of the initial three raiders, and Alyssa knew he did not see their approach. Her hackles rose, along with her protective instincts. Why was no one guarding the chieftain's back?
Alyssa spurred Streak, then jerked back on her reins. There was no time to waste in getting to him! She readied her bow in a smooth, flowing motion and let the arrow fly. Hitting her mark, she reloaded, and shot again. The Buchannan spun just in time to see the second man's raised sword slip harmlessly from his hand. The man collapsed at his feet, her arrows in his chest. When her laird looked up at her and nodded, she knew he'd seen her bow.
Wave upon wave of raiders assaulted him. And still no one guarded his back. He was an awesome warrior, the most skillful she'd ever seen. But, damn it, he was only human! He was laird, chieftain—vassal to Edgar himself. And someone should protect his back!
Protecting him was her duty. She slid down from her mount and unsheathed her sword . . .
How many souls she sent to their Maker, she didn't know. Nor was there time to ponder on more than staying alive. The battle raged.
Four men attacked at once. The Buchannan felled two. Alyssa engaged the third with her sword. The man was much larger and stronger than she, but he was slower than pine sap. She ended their conflict with a sharp thrust to his heart, then turned.
Her laird now fought two men. She narrowed her gaze on one of them. She had the chance. She should take his back. But even in battle, she considered that dishonorable, so she called out to him. "Come, raider! Fight me—if you're tired of living!"
The raider had no qualms in doing so. "One Scot dies as good as another!"
He was accomplished. Alyssa used every maneuver Duncan had taught her, and a few she'd devised herself, but the man still could not be outwitted. Sure that if her arm suffered one more clash of their swords it would jerk from its socket, she dug deep, called up every ounce of her reserve strength, then feinted left. Her opponent sped past her, and muttered an oath questioning her parentage.
Finally, she'd discovered his weakness. The raider was a hothead, and Duncan had taught her how to disarm a hothead.
She goaded him, teasing and taunting until the man's face was purple and the cords in his neck bulged. Soon, she saw in his eyes the flare she'd been waiting for. His temper had taken over.
Seizing the advantage, she changed tactics, and again fought with aggressive skill. This time, the raider fell.
She turned and saw a dagger raised against her laird. Again, at his back. That he was engaged with another meant nothing to the raider. Had they no honor?
She slid her dagger from her belt. Without pausing to aim, she let it fly. The raider crumpled to the ground. She retrieved her dagger from his neck and closed her eyes to the blood staining it.
Her stomach lurched, threatening to revolt. Blood. The countryside seemed like a river of blood, flowing death.
As quickly as it had begun, the battle ended. The raiders retreated, abandoning their dead—something no Scot, ally or enemy, would do. From King Edgar to the lowliest serf, Scots were loyal to their own. And they buried their own.
On the battlefield, Alyssa bent her head and squeezed her eyes closed. She'd done her duty. She'd killed men, defended her laird, her homeland. Done was done, and she wasn't sorry for her part in it. But she'd be damned to Hell if she had to look upon the blood-soaked ground without losing her stomach. If she had to see the ravages left by war, now that the battling had ended and her laird was safe. She let out a shrill whistle, calling Streak.
"Lord Cameron!"
Stroking her mare, Alyssa heard Duncan's voice and looked around. Seeing him still searching for her, she called out to him. "Here, Duncan. To the east."
She knew the moment he spotted her. His relief was clear and he quit his frowning.
When he stood beside her, she saw an anxious twitch in his cheek. "You are unharmed?" he asked.
"Aye." She smiled at her taciturn second. "I am fine. Weary, but unharmed."
"Return to our camp, my lord. Rest. I will see to burying our dead."
Alyssa swallowed the knot blocking her throat. "How many men did we lose?"
"Seventeen, my lad—my lord." His leathery cheeks flushed at his slip of tongue, and he shot a worried look around to make sure he hadn't been overheard.
Pretending not to notice, Alyssa turned toward a small copse of trees. "Locate the priest. Verify that the ground where my men will rest is consecrated." Her voice sounded strained even to her own ears. When she was certain it wouldn't again crack, she finished. "Call me for the burial. I'll be in the wood."
Duncan's eyes shone bright. "Yes, my lady."
Upset, Alyssa ignored his slip of the tongue.
KEVAN BUCHANNAN sat on the ground and leaned back against the trunk of a huge pine. He tied the leather strap back around his neck and cupped the crystal amulet hanging from it in his palm. Weary, he closed his eyes. The battle had been fierce, but it was over. The raiders, clearly defeated, would not return.
A twig snapped. He opened his eyes.
The Cameron warrior who'd protected his back and saved his life twice—that he knew of—walked within two feet of him without knowing he was there. He sat silent and watched.
The man was slight, small for a Scot. Hell, he was small for a man. His plaid slipped from where it draped his right shoulder, and he pushed it back up with a tiny hand. Stopping in the small clearing, he bent to his knees, then folded his hands and bowed his head.
Kevan had thought to acknowledge him, but realizing that the warrior was at prayer, he did not interrupt. Hadn't he himself retreated to the wood for that same solitude and purpose?
Tugging a pine needle from the soft earth, he chewed on the tender blade, rolled it around his mouth with his tongue, and waited for the warrior to finish. He wanted to meet this man who had fought so ably for him, but not to intrude upon his communing with his Maker.
Intently watching the little warrior, it wasn't until Kevan felt the sting of a blade in his shoulder that he realized there was danger. Brushing against the pine trunk, he struggled to his feet. His right arm was immobile, dangling uselessly at his side. Air rushed past his head, whizzing in his ear. Instinctively, Kevan ducked. Something sped past him, sunlight streaking on its shiny surface. When the raider behind him slid to the ground, Kevan realized the object was the dagger now protruding from the raider's chest.
The little warrior stood beside him, looking up. "You are injured?"
Like his features, his voice was soft for a man's. Kevan pulled the pine needle from his mouth and tossed it to the ground. "Aye, he caught my back." Stepping around him, the warrior untied Kevan's plaid and examined his wound. His shoulder burned like fire. The dagger was buried to the hilt. Kevan grimaced. "Pull it out."
"Aye, Laird. Brace yourself."
The soldier gripped the hilt. The dagger wiggled. Kevan gritted his teeth, stiffened, waiting for the torturous withdrawal.
The soldier whipped the blade out of him with the same urgency it had entered. He heard fabric ripping, then felt pressure against his wound. The man's touch was gentle. Almost too gentle, and his fingertips were smooth on Kevan's bare back. But, in short order, the wound was bandaged.
"That will hold until we get back to camp." The soldier moved to face him. "It's deep, Laird. You need stitching."
The little warrior had torn his Cameron plaid for Kevan's bandage. Knowing that no Scotsman would willingly deface his plaid, Kevan was deeply touched at the warrior's show of respect and loyalty to his laird. But because he was the Cameron's laird, Kevan wasn't free to acknowledge the honor.
"We must hurry," the warrior said. "The bandage is too loose to hold for long."
Such delicate features. Such a soft voice. The little soldier's lashes were silver-tipped. Kevan's scalp tingled. What was wrong with him? He shouldn't notice the color of a man's lashes. And before now, he never had!
"Can you walk?"
He drew himself up. "I am the Buchannan."
The little warrior frowned up at him. "Blast it, man. I know who you are. What I don't know is if you can walk."
No man ever had spoken to him in such an insolent tone. He'd have been dead before the words had passed his lips. But just now, Kevan had to concentrate on the pain, on mastering the fire burning in his back, to stay upright. Colorful spots were dancing before his eyes, he blinked hard.
"Lean on me," the warrior said.
"Nay," Kevan protested. The tree trunks surrounding them swam before his eyes. His stomach lurched. "You're too small. If I fell, I would flatten you."
"I was strong enough to save your hide thrice today. I am strong enough to hold you now."
"Thrice?" Kevan swayed on his feet.
"At least thrice."
Though it took a lot of effort, Kevan raised a brow. "You have a sharp tongue. By what name are you called?"
"Cameron, Laird. Lord Cameron."
Bleary-eyed, Kevan fought to focus and still couldn't. The Cameron was much older than this lad, wasn't he? And John had brown hair, not silver. Perhaps age had changed it. The black hood made it impossible to tell if the silver went beyond the man's temples.
"Come, you are losing much blood." The warrior looped a fragile arm around Kevan's waist. "I must see to your wound."
He heard concern but no panic in the little warrior's voice. "You're a healer, too?"
"I am whatever I have need to be."
Not sure what to make of that statement, Kevan leaned heavily on the soldier, and stumbled his way through the swerving pines.
Alyssa frowned up at her laird. His color didn't at all suit. The lines around the tender skin near his eyes were deep, and the gray cast to his skin worried her. She tried to hurry her steps, but the man was just too large for her to take any more of his weight. God's truth, it was a miracle he was still upright. His blood was soaking his back, and her arm.
At the edge of the wood, she caught sight of one of her men. "Cameron!"
The soldier turned and recognizing him, Alyssa added, "Sewn, come quickly! The Buchannan has been injured!"
Several soldiers wearing Buchannan plaids rushed to her aid. By his limbs, they carried the chieftain back to his camp. For some odd reason, Alyssa couldn't make herself let go. She held the Buchannan's head steady, fearing that if she did release him, he would die before she could see him tended. She looked at the warrior near her side. "Find Duncan, Sewn. Have him bring my medicines from my satchel. Quickly."
Near the campfire, Alyssa swept the stony dirt smooth with her hands, then lifted her torn plaid over her head and stretched it out on the ground. "Put him there. On his stomach."
A warrior with a long scar slashing his cheek objected. "He'll want to die on his own colors."
Praying the laird hadn't heard that awful comment, Alyssa glared up at the man. "Put him down."
Respect lit the warrior's eye, and the four men lowered the laird onto her plaid. "On his stomach," he repeated her words to the others.
The warriors turned Kevan over. Before they had backed away, Alyssa dropped to her knees. As gently as possible, she shoved his plaid down to his trim waist, baring his broad back. She was worried at the amount of blood staining his skin. No wonder the man was as gray as ash.
She scrubbed her hands nearly raw in a bowl of water then took a wet cloth someone passed to her and began cleaning his back to better judge his wound. The man was as hard as rock. Her breath stuck in her throat, and the strangest quivers shook in her stomach. Trying to ignore them, she set about her work.
Duncan came with her medicines and fresh, heated water. With painstaking care, she cleaned her laird's wound. It was worse than she'd first thought. His flesh was torn and jagged. He must have fallen against the pine, elsewise the stab wound would be clean. Pausing, she looked up at her second. "Duncan, I shall have to—"
"Yes, my lord," he interrupted.
She whipped out her dagger. Solemn-faced, he took it and headed to the camp's fire.
"Do we need to build a box, Cameron?"
Alyssa looked up, and squelched her surprise. Hundreds of warriors had gathered around, and more were coming. She frowned at the man. "No, you don't need to build a box." She prayed she was right, that the laird would survive. Surely hearing her say that he would live couldn't hurt.
Pulling bottles of medicines from her satchel, she prepared a sleeping mixture, then forced her laird to drink it, rubbing her fingertips down his throat to urge him to swallow. The stubble of his beard taunted her.
Duncan returned with the blade; it glowed red with heat. Alyssa steeled herself for what she must do. She hated this particular duty of healing more so than any other, for no matter how drugged, the treated always screamed. Hearing such pain come from brave men, and knowing it was she who caused that pain, always tore at her heartstrings. Knowing that she had no choice—that if she didn't do her duty, the patient would die—did not help. The screams that curdled blood would long be remembered by them both. Especially in sleep.
She checked his eyes. Finding them glazed, she took a deep breath and reached for the dagger. Her gaze locked with Duncan's. He knew how much this hurt her; his concern shone in his eyes. She prayed for a steady hand, took the glowing dirk and, prepared to hear her laird's screams till next summer in her sleep, she began her duties.
The Buchannan uttered not a sound.
Had he died? Until she was done, she dared not to look and see. Only when she'd waxed the thread and stitched his wound closed would she know.
The night air was cold, but sweat trickled down between her breasts. He must be dead. Her own shoulders throbbed, ached from being bent over so long, and her knees were stiff from their long contact with the hard ground.
He must be dead. She was done and he had not moved once. Not so much as a single muscle had flinched. She licked the salt from her lips, and bent to look at his face.
Sweat-drenched, the Buchannan looked straight at her, his eyes a clear, cool gray. Shocked, she gasped. Had she taken so long in her repairs that the effects of the sleeping drug wore off? Dear God, how had he borne the pain?
"You are done?" His voice was thready.
"Aye. I'm sorry, Laird. Your pain could not be avoided."
He nodded once, and closed his eyes.
Tears blurred her own. Alyssa blinked, cursing them, and mixed the paste.
She applied it to his wound, taking care to be extra gentle, then bandaged him. "Duncan, I need—"
She looked up to see Duncan holding a warm, wet cloth. Smiling, she took it and began washing the dirt from her laird. "You're always one step ahead of me."
Duncan provided her with a steady stream of the warm, soaked cloths. Her hands trembled over the ridge of muscle at her laird's abdomen, on his powerful thighs, and his thickly muscled arms.
Again, she felt the stirrings low in her belly, the tightness in her chest and throat. He was a magnificent giant—hard and lean and rich with texture. His skin had been tanned golden by the sun and sprinkled with small nicks and scars that didn't diminish his perfection but enhanced it, speaking loudly of his battles and of his bravery.
Long after Duncan proclaimed him clean and sure to catch the fever if she didn't halt the water, Alyssa washed him. He had suffered so much. Her heart bade her to soothe him. When she was certain he was sleeping, she stopped her ministrations and covered him with her plaid.
WHEN KEVAN next opened his eyes, the moon was high overhead. The little warrior slept curled to his side, pinning his chest to the ground by holding his good shoulder flat. Looking past the little bundle, his gaze met Duncan's. "She is asleep?"
"Aye, she is asleep."
The old warrior looked worried. And well he should. Someone had a lot of explaining to do. "Take her to bed, Duncan."
The soldier frowned. "You won't—"
"Take her to bed. And say nothing."
"Aye, Laird. But—"
Kevan pinned Duncan with a warning glare. "And say nothing."
Four
IT HAD BEEN a busy night.
Mindful of Alyssa's womanhood, Duncan had ordered Cameron's campsite set up well away from the other clans. He'd seen to it that the graves were prepared and the burial boxes built. And David, second-in-command to the Buchannan, had verified with the priest, Father Aldwyn, that the Cameron warriors would be buried on consecrated ground.
Had it been winter, Duncan knew his lady would have insisted that her dead return with the living to the Cameron holding for burial. But the ground had not yet frozen, even here in the Upper Highlands, so the dead must be buried quickly.
And he had another worry. He rubbed his hands briskly, but the fire's heat didn't warm the chill from his bones. Nor did the scent of the burning wood hold its usual post-battle, soothing appeal. His teeth were still set on edge. The Buchannan learning that Alyssa was a woman had Duncan damn near shaking in his boots. Not so much for himself, though he was in trouble plenty. But for her. Why had his laird ordered him to say nothing?
The fire crackled and hissed and embers seeped to the bottom of the flames. Glowing ash drifted up on the sharp, chill wind. That question had prompted endless speculation during the long night, but nary a single answer.
Sighing, Duncan scanned the sky. Streaks of pink and gold were quickly giving way to splashes of yellow sunlight. No doubt he would learn soon enough now. Dawn had risen. And Father Aldwyn was ready.
Lowering his gaze, Duncan looked to where his lady slept on the ground wrapped in her plaid. Poor lass. Her face was still streaked with dust and grime from the ride—and from the battle. With her knees curled to her chest, she looked like an innocent child. Unfortunately, the Buchannan wasn't likely to see past his fury to notice that innocence. He'd see a traitor. No more, and no less.
Grimacing, Duncan shook his head. How had he let this happen? He must have been crazed. She shouldn't have been here. Though lacking in humility—and sorely lacking in modesty—she was a lady. Oh, she'd accounted for herself well enough on the battlefield. And, truth be known, he couldn't help but feel a wee bit of pride for his part in that. From all he'd heard, if she had remained safe on Cameron lands, the Buchannan himself, by God, would lay among the dead this morn.
But even if the Buchannan acknowledged that she'd spared his neck, he'd not forgive her for deceiving him.
Shuddering, Duncan jostled her shoulder. "My lady, 'tis time for the funeral."
"Not yet," she mumbled. Forcing one eye open, she snuggled deeper into her plaid. "I ache like the dead."
Duncan's brows shot up. "Do you suppose the dead ache, my lady?"
His words niggled at something in her memory. Smelling the fire, Alyssa twitched her nose. "Nay, Duncan. The dead do not ache."
He straightened. "How do you know?"
How did she know? A strange feeling swirled in her stomach. She frowned up at him. "I'm not sure. But the dead do not ache, and that's the truth of it."
WEARING HER BLACK battledress, Alyssa stood beside Duncan, her hooded head bowed against the sting of the icy wind.
The priest, a short and portly man, walked to the center of the line of Cameron graves. Dressed in the funeral requiem vestments of black with purple trim, he said the words to commit her men's souls to their Maker.
When he was done, Alyssa nodded to thank him, then moved to the first grave and knelt down in the dirt. Burying her clansmen was so hard. A flood of tears burned the backs of her eyes and clogged her throat. She swallowed often to keep them from falling. With trembling fingers, she lifted her dead warrior's hand and pressed it to her chilled lips, then gently lowered it back to the box. Covering her heart with her hand, she whispered a final goodbye to her warrior, a goodbye so poignant and tender and fierce in her heart that only the committed soul could hear it.
Even the wind calmed to a whisper at her demonstration of respect.
Somber and silent, Alyssa moved to the second of her dead and repeated her salute. She did the same at the burial box of the third, then on down the line, until the seventeenth warrior who had died in her service had received her salute of honor, her praise and gratitude for his service, and for his life.
Wounded and raw, she stepped back to Duncan's side and gave him the nod to lower the burial boxes into the ground.
Before he could see to it, the Buchannan stepped forward to the first box. Without so much as a glance in her direction, he heaved the box then lowered it into the waiting grave. His expression grim, he then moved to the next and, one by one, he lowered each of the burial boxes himself.
Misty-eyed, Alyssa worried. Would he rip the threads from his wounded shoulder? His coloring grew more and more gray with each successive box. She wanted to scold him, but the honor he was bestowing on her men, laying them to eternal rest himself, held her speechless.
When he stood at the far end of the line of graves, the Buchannan covered his heart with his hand and, bending to one knee, bowed his head. From the movement of his lips, she knew he was praising her men for their service.
Hot tears burned her eyes. She knew the observing warriors' minds were racing with questions about why the chieftain had bestowed this honor upon her men and none of the others. The Cameron warriors had done their duty to their laird. No more, and no less.
But Alyssa understood his reasoning. This honor to her men was his repayment to her for saving his life. In duty, the men had sacrificed their lives at his call. But she had not been duty-bound to fight. She had battled and spared his life out of devotion and respect for her laird.
He walked around the line of graves and stopped at her side without speaking. She looked up at him, wanting him to see in her eyes how much she treasured the gift he had bestowed upon her men.
The Buchannan frowned. His eyes flashed confusion, then shock.
Dread settled in her stomach like sludge. What happened? What had he seen in her eyes? She licked her lips and tasted—salt? Fearful, she lifted a hand to her face. Her fingers grew wet. Tears? Dear God, she cried!
Fear of his wrath and disgust pumped through her veins. His vassal-lord in tears would mortify the Buchannan! In her years alone with her father, there had been many times she'd wanted to cry, but not since the death of her mother, had Alyssa Cameron wept.
She lowered her head to avoid the anger her laird directed at her. It didn't help. Fury seeped from him like a tangible thing. Her knees grew more and more weak, threatening to buckle under her. She dipped her chin to her chest, and planted her gaze on the ground.
Finally—thank God, finally—the last grave was mounded with dirt. From under her lashes, she risked a sidelong glance at the laird.
Staring straight at her, he withered her with a glare, then walked away. His heavy footsteps lifted dust on the stony ground. Her mouth went dry. Grimacing, she forced herself to look away from his retreating back, away from the bandage she had so gently applied to his shoulder, and settled her gaze at the end of the long line of mounds to where she feared the eighteenth Cameron grave would soon be dug and mounded. Her grave.
WHEN DUNCAN approached her, Alyssa had done no more than return to her clan's campsite and wash her face. A man half again as large as Duncan, yet smaller than the Buchannan, walked at Duncan's side. It was on him that she centered her attention. His gait was purposeful, his expression sour. She didn't have to ask why. She knew. "Well, hell," she mumbled before they drew within hearing distance.
The Buchannan had discovered she was a woman.
And he was not pleased.
Resisting an urge to wring her hands, she tossed the washing cloth onto her satchel. This was all Kenrick Innes's fault. He was her pledge. If he had hauled his arse to her side during the funeral, the Buchannan wouldn't have stood close enough to see her God-awful tears. But, no. Her braggart pledge hadn't bothered to even attend the funeral, much less to stand at her side where he should have been.
Duncan and the stranger drew closer. Despite the chill, her hands went clammy. She wiped them against her hip and swallowed her disgust. She was thoroughly miffed with Innes for not being at the funeral, but the fault for what was coming was her own. If she hadn't cried like a simple-minded fool, there wouldn't have been any tears for her laird to see. God, after fighting so ably, to suffer such humiliation was unjust.
The men stopped before her. She looked at them and nodded.
"Lord Cameron," Duncan's companion said, "I'm David, the Buchannan's second. The laird wishes for you to meet him in the wood."
Alyssa shot Duncan a worried look. His expression was flatter than the blade of her sword. "In the wood?"
"Aye. He said you knew the place."
She supposed she should be grateful. The Buchannan's temper was legend. Fierce and ruthless, it was said. Still, he hadn't humiliated her at the funeral. Nor, it seemed, did he intend to expose her deception to the other clans—at least, not yet. Aye, she should be grateful, and she was. The chieftain's censure would embarrass her men, and they deserved better. "I'll go at once, David."
The man's jaw fell loose. "Sweet Christ, you're a woman!"
"Shh!" Alyssa glanced around to see if they'd been overheard but, busy seeing to their horses, no one was paying any attention to them. She shot David an icy glare. "Of course, I'm a woman—though I'll thank you not to betray me. I would remind you that I saved the life of your laird."
David clamped his jaw and lowered his voice so only she and Duncan could hear. "Who are you that you answer my laird's call? And why does Clan Cameron follow you into battle?"
Alyssa stiffened. That he hadn't shouted didn't fool her. The Buchannan's second was furious . . . and not at all grateful for her service. But he wasn't bellowing his outrage, as most warriors would on finding a woman among them. That was a good sign. "I am Lady Alyssa, daughter of Lord John Cameron, allied-vassal to the Buchannan."
She'd lengthened her introduction and spoken slowly to give him time to adjust.
He didn't. "A lady?" David rounded on Duncan. "You allow your lady in battle?"
Glancing heavenward, Alyssa whispered an urgent prayer, then risked a glance at Duncan. His eyes burned overly bright and his legs were braced. Her stomach seemed stuck in her throat. She'd seen that look before. Her second was bloody furious, a scant step from doing mortal injury. Was the priest still among them? Or had he returned to the Buchannan holding? Tense as strung rope, but much too wise to interfere, she dragged in a shaky breath and held it.
The fury in Duncan's eyes chilled. The danger had passed. He had remembered David's position, remembered that their laird would not look kindly on one of his allied-vassal warriors killing his second-in-command.
A smile that froze Alyssa's blood curled Duncan's lip. "My lady proved herself a skilled warrior capable of saving your laird." He crossed his barrel-chest with thick arms sprinkled with scars and silver hair. "While the Buchannan's back lay open to attack, where were you?"
David grimaced. "Engaged in battle, as you yourself were, Duncan."
"'Tis fortunate for us all then that my lady was here."
A deep flush stained David's neck and face. He shifted his gaze to Alyssa and nodded toward the wood. "Your laird waits, my lady."
"I'm going, David. But first, I order you and Duncan to save your discord for the raiders. You're Scots, valued warriors of your laird. Don't dishonor him—or yourselves—with your tempers."
Duncan bristled, but David accepted her advice with surprising grace. Most warriors considered women chattel—nothing more than the property of the man protecting her. And all warriors, without exception, took offense to taking orders from chattel.
Before David remembered that, Alyssa headed toward the wood.
From behind the trunk of a thick pine, she paused to watch her laird pace the small, sun-dappled clearing. Clearly agitated, he clenched his big hands into fists, time and again. He'd have her neck for deceiving him, all right. She rubbed at her throat, and swallowed. Mayhap her hide, too.
He stopped suddenly beside a spiny green bush and folded his arms across his chest, raising muscles that looked like boulders. "Come."
How had he known she was here? She'd scarcely dared to draw breath. Leaning heavily against the rough bark, she felt her stomach sink to her knees. He not only looked ready to strangle her, God help her, he sounded ready, too.
"Pray, hold me up," she whispered to her wobbly legs and shoved away from the pine. Would he beat her? Or just make her wish he had? Unsure, she stepped out from behind the tree.
Chest to face, he glared down at her, his arms akimbo. A foot or more distance stretched between their shoulders. She stepped back so she could see his face, but his fierce expression made her tremble. She tried and failed to meet his gaze, and let hers drift down to his neck. The cords bulging there were equally daunting, so she dropped her focus lower still and fixed on the crystal amulet hanging around his neck.
Something odd stirred inside her. A warm tingle that shimmied in her breasts and flooded her with a quiet excitement. Why did his amulet set fire to her blood? Whatever it was niggling at her seemed stuck on the frayed edge of her memory. Sure it would come to her later, she concentrated on her laird's words.
"Who are you?"
She took heart. At least he wasn't bellowing—yet. But recalling David's reaction on learning she was a lady, and surmising her laird's would be the same, she braced herself. Mayhap to whisper would soften the blow?
Licking her lips, she forced her expression serene and lifted her chin. Angry silver flecks flashed in his eyes. She lost her courage. "I'm Alyssa, Laird Buchannan."
"Are you speaking to me, or to my neck, woman?"
She stiffened to glare at him for shouting at her, but could only see the underside of his chin. She'd seen weaker-looking rocks. Stifling a groan, she took another step back, and cooled her voice. "I'm speaking to you."
"Then look at me and answer my question. Who are you?"
Now he was yelling, and a muscle was twitching under his left eye. A bad sign, that. When a man's muscles went to twitching, he was typically of a mind to murder.
"Answer me!"
She jerked back, shaking down to her toes. How could the man expect her to think, much less answer? Her ears would ring for a week! "I—I—"
Losing his patience, he scowled. "Quit babbling and talk to me."
"Yes—yes, Laird." Her voice sounded as weak as a weaning sheep's. If the man would just quit snarling at her, she could force some strength into it. "I'm Lady Alyssa. Daughter of your allied-vassal, John Cameron."
Surprise flashed in his eyes. "A lady! It's not enough you're a woman? You have to be a damn lady?"
"I'm sorry." Just then, she truly was. "I had no choice in the matter."
"Still your tongue!" He dragged his fingers through his hair. "A lady. A damn lady."
Not sure if he was speaking to her or to himself, she held her silence and stared at the ground. Not so much as a single bird twittered.
"Your father sent his daughter into battle? My allied-vassal sent a woman—his daughter—to answer my call?"
Alyssa shook like a tree caught in a windstorm. Even in his worst fit of temper, Duncan hadn't matched the Buchannan's fury. Her heart felt sure to pound from her chest. "My father didn't command me to answer your call. And, I would remind you, it was this allied-vassal's daughter who saved your life thrice during battle and treated your wound."
"That is of no consequence. The issue is that you're a woman! A lady!"
Alyssa's temper kicked up. "My actions are of consequence. Woman or no, I saved your life."
His eyes blazed. "You dare to raise your voice to me?"
Had she lost her mind? Railing at the Buchannan? "I didn't mean to, Laird. It just hap—" Why was she apologizing to him? If she hadn't come and fought, the man would be dead! "I don't understand your objection, Laird. You called and Clan Cameron responded."
"My objection, you little hellion," he spat out from between his teeth, "is that a woman under my protection fought at my side in battle!"
Hellion? Oh pity, she'd gone too far. Cringing, she softly corrected him. "Your back, Laird."
"What?" he thundered.
"It was your back." She shrugged. "I fought at your back."
He towered over her. "At my back, then!"
His breath was as scorching as his words. She leaned away from him, bending until she thought her spine would snap. "Being a fair man," she said, hoping he'd see that his behavior toward her was anything but fair, "you must admit that I didn't fail you, Laird. My skill more than compensates for my size and womanhood. And my clan didn't fail you, either. My warriors died with honor for you."
He narrowed his eyes and dropped his voice, lethally quiet. "Your clan? Your warriors?" He palmed the hilt of the silver sword hanging at his side. "Where is my allied-vassal, John, Alyssa? Why do you answer in his stead?"
She couldn't tear her gaze from his sword. The fat rubies and emeralds embedded in its hilt caught the sunlight, and the blade gleamed menacingly. Every warrior knew that touching the hilt of a sword signaled intent to do battle. "I—I ask you to remove your hand from your weapon, Laird Buchannan." She slid him a pleading look. "Please!"
He said nothing, but he lowered his fisted hand to his side. Relief washed through her—until she saw his eyes. He didn't ask again. He didn't have to; she hadn't forgotten his question, or its underlying threat. "Your vassal has not been murdered," she assured him. "But he could not respond."
If she had to admit her father couldn't answer his laird's call because he was sotted to the rafters, she'd die. By her own sword, she'd just die. No warrior should be made to suffer that humiliation. Why even Father Aldwyn would understand and bury her on consecrated ground, though the church forbade that honor to those who took their own lives.
The Buchannan was staring at her, waiting for her to say something more. She twisted her shoulders, and added, "My father was, um, indisposed."
An expression she would have sworn could grow no darker, did. "By whose hand?"
She flashed him her most sincere look. "Not by mine, I swear it." When his hard glare didn't soften, she again slid her gaze to his amulet. "He caused his own damage, I was told. I—I was away from the keep at the time, so I did not witness the—"
He interrupted. "Where were you?"
Alyssa swallowed the lump in her throat. He'd like this answer even less than her last. But at least he'd turned attention from her father. Again, she whispered. "Hunting."
"Hunting." His eyes stretched wide, then the look in them turned as cold as sleet in the dead of winter. "You were hunting?"
Her gaze slid to his scuffed boots. "Aye."
"And did your hunt go well?"
An odd question, but encouraging. He hadn't shouted it. "Aye."
"What did you fell, Lady Alyssa?"
Though he hadn't said it, the insinuation was that she'd felled her father. "A deer, Laird. A six-point buck."
The Buchannan started pacing again. Feeling the fury in his steps, she watched him with a sinking heart. While he wrestled with his temper, she stifled a shiver and whispered an emergency prayer that her laird would win control before he killed her. Then, at least her death would be swift and merciful.
"You hunt. You fight in battle." He jerked at a leaf with such force he nearly uprooted the bush. "You answer my call with your clan, your warriors." Shoving the tip of the leaf into the corner of his mouth, he leveled her with a scathing glare. "Are you a fricatrice?"
Puzzled, Alyssa shrugged. "I might be."
"What?"
"Well, I'm not sure." She blew out an impatient breath of her own. "What exactly is a fricatrice?"
"A woman who is confused about being a woman," he explained.
Alyssa gasped. "You think . . . ? You're asking if I . . . ?" Anger clogged her throat and she stomped toward him. "No!" she bellowed from as close as she could get to his face. "I am not a fricatrice."
A muscle in his cheek jerked, then jerked again. "Mind your tone, woman. I am your laird."
In her anger, Alyssa had forgotten who she was yelling at. Dear God, when she'd wept, had she lost her sense with her tears?
She bowed her head and stared at the ground, grappling for control of her emotions. Why did this man upset her so? "I suppose you will have me flogged for deceiving you." She peeked up at him. "I know I must repay to allay your anger, but I also must be truthful. I would do the same again."
He heaved a sigh that could fell a pine. "I take exception to your insult, Alyssa. Scots protect their women. They don't flog them." He wagged a warning finger in her direction. "But could I prove you a man, I would strip the hide from you, bit by bit."
Alyssa squeezed her eyes closed and thanked her Maker. Her laird wanted to, but his honor forbade him to beat her. "'Tis fortunate I'm not a man, then."
"I've seen nothing womanly about you. Tell me, my lady, do you also possess the skills of the female, or only those of men?"
It was a backhanded compliment by her reckoning, but under the circumstances, it was more than she'd expected. She'd dared the wrath of her laird, and that had to be a tree-sized splinter under his skin. "Nay, I'm afraid I do not do so well at women's skills."
He grunted his displeasure at that disclosure. "Why not?"
When she didn't answer, he persisted. "You will not ignore your laird."
Well, if this just didn't take the bark off the tree. Male warriors weren't expected to excel at women's skills. Nor women in men's. So why did he expect her to excel in both?
She gave him a good frown, showing her own displeasure. "I can't cook or run a house, and that's the truth of it. The only sewing I've mastered is in stitching up wounds. But, as you yourself know," her chin came up, "I am not without value."
"Your mother has been remiss in her duty to you."
"My mother is dead."
"Your father, however, is not dead—if your word is truth."
"You've no right to question my honor."
"You deliberately deceive me, vow you'd do so again, and you dare to say I've no right to question your honor? What honor?"
She started to explain, but he lifted a hand to halt her. "No, woman. Don't open your mouth. Don't whisper a single word." He snarled. "If you so much as groan, you'll be in serious jeopardy."
If his black expression was any gauge, she was already in serious jeopardy. She snapped her jaw shut. Clearly, now wasn't the time to push her laird further. The ungrateful lout didn't deserve an explanation, anyway. She pursed her lips and crossed her arms, certain that while he had the strength to draw breath, he'd not stop bellowing at her.
He proved her right. "Your father has failed his daughter and his laird." The Buchannan frowned, paused pacing and stared at her. "His laird is angry."
He certainly was. Alyssa squared her shoulders. "Clan Cameron hasn't failed you. My father has served you well."
"I am not appeased, Alyssa. In fact, my anger with your parent—and with you—is too great at present to be just. Leave me now. When I decide your fate, I'll summon you."
Dear God, she couldn't leave him in this state. Though he denied beating women, his anger would fester until he ended up having her beaten, anyway. And then he'd strangle her. "But—"
"Leave me now."
Shaking, she turned away with one consolation. At least she could be buried with her clansmen. She'd best warn Duncan to dig another grave.
"UNGRATEFUL," Alyssa muttered, snatching up a cake of soap and clean clothes from her satchel.
By the time she'd gotten back to her campsite, she wasn't worried about getting flogged, or about the Buchannan strangling her. She was too bloody angry to care what he did.
The lout could be merciful. He could be grateful. But, no, not him. He had to dismiss her—without as much as a whisper of praise for her efforts. She snorted her feelings on that. The man was a lout. A very large, very loud, very ungrateful, lout.
She stomped down to the small stream tumbling through the glen. The smell of the fragrant pines, though robust and sweet, didn't soothe her frayed nerves or her temper. What had the man expected her to do? If her clan hadn't answered his call, he'd have declared war on their heads. It wasn't bloody likely he wouldn't have noticed their absence. And a moron would know war with the Buchannan would annihilate Clan Cameron. He couldn't have expected she'd permit her clan to be annihilated.
Confident that Duncan would see to her privacy, she stripped off her clothes, stepped around a mossy stone, then edged down the sloping shore and waded into the water. It was frigid. Before she'd wet more than her ankles, her teeth started chattering. The sun was warm, but the wind had a nip as cold as ice on her bare skin.
Gritting her teeth, she ventured thigh deep but, unable to swim, she didn't dare go any further. The ground didn't appear to sink.She couldn't be certain of it, or of her footing against the current. Currents could be wickedly swift and unforgiving.
Washing quickly, she scrubbed her scalp with her fingers. Lord, but it was tender. Having her hair cramped up under her hood for so long had smashed it flat. Cupping her hands, she drizzled cold water over her head, rinsing the dirt from her hair. Long before she finished, the tips of her ears felt frozen. Her temper, too, had cooled.
Fluffing the long wet strands clinging to her shoulders, she shivered against chills. Whatever her laird did to her, she deserved it. She'd deceived the man for five years, after all. And that kind of loyalty, he couldn't afford to approve. He'd have to kill her—or lose face with the clans.
Resigned, she completed her bath and left the water. Since he knew her identity, there was nothing to be gained by wearing her disguise. But dressing as a woman might affect the way he killed her. She truly doubted it, though. He was terribly angry.
Still, looking soft and feminine couldn't hurt. Duncan had always advised using any weapon one could muster in times of distress. And if her laird's anger with her didn't qualify as distress, nothing did.
IN HER ABSENCE, the clans had all gathered near the Buchannan's camp. Paying their respects before departing for their own holdings, Alyssa supposed.
Dressed in a flowing green gown, she couldn't escape their notice unless she walked miles out of her way, and there wasn't any sense in bothering with that. The clans would learn of her duplicity anyway. She might just as well face their scorn now and have the matter done.
Stiffening her shoulders, she walked down the trodden path to the huge clearing, looking neither left nor right. She didn't have to see the men's faces to know that she'd been noticed; not with the sudden silence following in her wake proving it.
Giving herself a serious lecture on courage, she kept walking toward the cluster of sage, where her clan stood gathered. She couldn't avoid their glances, and with each step, her feet felt heavier. By the time she could clearly see their faces, more than nine hundred men stood watching.
Before she could get to her own clan, Kenrick Innes caught her eye. His face was the same shade of red as his plaid, and his jaw was clenched tighter than Streak's when she was set on refusing her bit. But Lord Innes didn't look like he could be soothed.
Well, wasn't just everyone fired up at her today? Alyssa held her back straight as a blade, resisted the urge to smooth her skirt, and kept walking.
To a man, silence fell. Kenrick braced his fists on his hips and blocked her path. "Good day, Lord Innes," she said, smiling brightly and trying to skirt around him.
He grabbed her upper arm and jerked her to a stop. "What are you doing here?"
Somehow she held onto her smile. Why didn't someone start talking? Brawling? Anything to shift the attention away from her. Out of the corner of her eye, she saw the Buchannan. The ungrateful lout looked amused—and like he'd no intention of intervening. In more ways than one, he'd have his pound of flesh. "Clan Cameron was called, Lord Innes. You yourself delivered the message."
He raised his hand as if to strike her. She glared up at him. Her men circled her but, without her express order, none moved to stop him. She caught a glimpse of the Buchannan—none blocked his view—yet she didn't know what to make of his expression. He no longer looked amused. He looked bloody bored.
Kenrick's shout reclaimed her gaze. "I'll not bear your insolence, woman. You've no business here."
Alyssa bit her tongue till it bled, but it didn't soothe her temper. She'd had enough, by God. She'd been asked if she was a fricatrice, been belittled for her lack of women's skills, been dressed down in private—and now publicly, in the presence of all the clans. Well, someone else could just have the pleasure. She'd been gifted with a belly full of other people's anger already this day. "Are you suggesting, Innes, that I ignore my laird's call?"
"Lord Innes, Alyssa." Kenrick stepped toward her. "And you received no call. It's your father who should be here."
The crowd's mumbles and mutters of agreement evidenced their opinion, and did nothing to cool her temper. It escalated from a steady simmer to a full boil. "My father couldn't respond. You well know that a Cameron must lead Cameron warriors into battle, just as you know I'm the only other Cameron to accept this duty. I'm loyal to my laird, Lord Innes. And I couldn't send my soldiers and stay behind like a coward. Could you have done that? Would you send your warriors off to fight without you?"
"I am not a woman."
"And I am. By God's choice, my lord, I am a woman. Say you God erred?" She heard many shocked gasps. Before Innes could answer, she rushed on. "Nay, I thought not. Woman or no, I am first a Cameron. An allied-vassal to Laird Buchannan. True, as a woman, I could hide in the safety of Cameron hold. But as a Cameron, I could ask no warrior to risk his life while I protect my own."
"I rue the day I must wed you, Alyssa Cameron." Kenrick bellowed. "A real woman, you are not."
The watching warriors fell silent. The insult was clear, and Alyssa supposed their reactions to it were mixed. Scanning their expressions, she saw everything from pity to outrage, and sent them a look to remind them that, had Kenrick made such a remark to the lord of any other clan, that man would have declared war on Innes before he had blinked. A few expressions turned sheepish.
Duncan stepped forward, reaching for his sword. Alyssa stretched out her arm and stayed him. "No, Duncan. He is my pledge."
She narrowed her gaze, leveled her betrothed with a warning glare. "Be grateful we are to wed, Lord Innes. If we were not, I would take your life for your insult. I am a woman, yes. And all I have done, I have done with honor and in loyalty to my laird."
Her implication that Innes had not been honorable in his attack on her was clear. Because they were to wed, she was being merciful, granting him quarter.
Kenrick slapped her.
She fell to the ground. Before she felt the sting on her cheek, she cried out, "No, Duncan!"
She'd seen Innes's strike coming. Yet she made no move to stop him or to deflect the blow.
And every warrior present knew she could have.
"My lady. You permit him to strike you?" Duncan reached down to help her to her feet.
"Don't touch me." From where she lay, she glared up at her pledge. Her voice shook with rage. "Strike me again, Innes. I've shamed you and dishonored my clan by fighting at its side. I've shamed my laird—hell, even my king. Well, go on. Beat me. Make me pay for my treachery."
The veins on Kenrick's neck bulged. He yanked her to her feet and raised his hand. She steeled herself for the blow that would knock her senseless.
"Release her." The Buchannan shouted, striding forward. "Release her, Innes."
Kenrick blinked. Alyssa held her breath. The battle in Kenrick's eyes was fierce. He would kill her, but he feared his laird's wrath.
The Buchannan shouted. "I said, release her, Innes—now!"
Kenrick growled from deep in his throat and flung her from him. While she caught her balance, Duncan stepped between them, rage and disgust warring in his eyes.
She looked at the crowd, afraid to move. To a man, their expressions were grim, their eyes ablaze. The sharp wind had their hair slicked back against their skulls, their clothes rustling. And far too many of them had lowered a hand to their sword's hilt. Good God, what had she done? They were standing in line for a turn at her.
Shivers raced between her shoulders and up her neck. She darted a worried look at Duncan. He didn't speak, but he looked . . . pleased?
Afraid to believe her eyes, she checked again. He did look pleased. The other warriors would feel little different than Duncan. Their anger wasn't directed at her, it was directed at Innes.
"You forget you are a Scot, Innes." The Buchannan folded his arms over his chest. His bandage looked stark against his bronzed skin. "We do not beat our women."
No man flinched as much as a muscle—or doubted the Buchannan's resolve.
"She's my betrothed," Innes reminded his laird. "I have the right to do as I wish with my chattel."
"Aye, you do. But she is not your chattel, Innes. She is mine." Though he hadn't raised his voice, his tone cut to the quick. "Betrothed is not wed, and I, not you, am her laird."
Though his gaze never left Innes, the Buchannan's next words were spoken to Alyssa. "My lady. You saved my life at least thrice in battle. As repayment, I offer you three requests."
The warriors gasped. One said, "She's Lord Cameron what fought at the Buchannan's back."
Murmurs and comments rippled through the crowd.
When quiet fell among the men, the Buchannan spared her a glance. "Being a woman, you had no duty to fight. Yet you did, and I am pleased with you. State your requests, Lady Alyssa. But be warned. I'll deny any request to declare war on Innes—unless he raises his hand to you again. Should he do that, I'll declare war on him myself. You are not a warlord, but you are under the protection of one. Mine."
As astounded as the warriors, Alyssa swallowed her pride and faced her laird. "I request release from my marriage contract with Innes."
Whispers filtered through the throng of men. While none appeared surprised by the request, the air crackled with tension during the wait for the Buchannan's response.
"Done. But, while your betrothal to Innes is severed, another will be formed—imminently."
Disappointing, but expected. And he couldn't do worse for her than her father and she already had. Her heart thundered. "Second, I ask that you permit me to head Clan Cameron," she paused and looked to Duncan for approval and, seeing it, continued, "as I have done these five years past."
The crowd's whispers grew to mumbles and outcries of shock.
Again, the Buchannan held his response until silence fell. "I'll return with you to the Cameron holding and then determine your suit. But know this, my lady. If I grant your request, the current laird must die."
Alyssa shook down to her toes. "Then I withdraw that request, Laird. My goal was to protect my people, not to bring death to my father."
"I'll consider this withdrawal." The Buchannan stepped closer to her and softened his expression. "And your third request?"
My but he was handsome when he wasn't growling or snarling. "Mmm, with all due respect, a question, please?" Those odd quivers were dancing in her stomach again. Why did looking at the Buchannan affect her so strongly?
"Aye, you may ask."
"Must I marry?"
"'Tis your duty."
She knew her duty, yet she'd hoped . . . Her spirits sank. Well, pity. There was no escaping it . . . unless—of course! The Buchannan would refuse. And because he had, his honor would forbid him to deny the withdrawal. He wouldn't kill her father!
Her spirit soaring, she looked up at her laird. Sunlight streaked his black hair glossy. Appealing, that. He still looked bored, but she knew he wasn't. He was intent—and interested. "May I choose my husband?"
Duncan groaned and mumbled a warning not to push her laird too far.
"You may state your desire," her laird said. "But choosing your husband will remain my decision."
She frowned as though puzzled. "Forgive me, Laird, but I wish to understand. Is your reasoning that you must approve my choice to be sure he is worthy of me?"
The Buchannan's chest swelled. "Aye. 'Tis my duty to see that you'll be protected." He slid Innes a glare. "And well-treated."
Alyssa bit back a threatening smile and feigned demure innocence. "I trust your judgment, Laird."
The Buchannan's expression softened. "Of course, you do. I'm your laird, Alyssa."
Dear God, he'd no idea what he'd done. He had taken her bait! Her knees knocked together and she prayed for courage. "If I must marry—"
"You must."
"Then, my third request, Laird Buchannan, is to marry . . . you."
His brows shot up. "What?"
He looked shocked. Certainly he was shocked; how could he not be? No woman would dare ask her laird to take her to wife. At least none had—until now. But she was desperate to save her father. "If I must marry, I request—"
"I heard your request, woman."
Hoping she looked innocent, she glanced up at him. "You would treat me well—'tis your nature—and surely you approve yourself suitable." She paused to pretend to weigh a matter, then went on. "And, well, I think you are able to protect me. Don't you agree?"
Duncan groaned, deep as the tortured.
James MacMillian wailed. "Aw, hell."
David gasped "Sweet Christ," and his jaw fell slack.
With each negative reaction, Alyssa felt more droplets of sweat pop out on her skin. Even the wind stilled, waiting. She had issued a challenge no man, least of all a chieftain, could deny answering.
Just when Alyssa was sure he'd murder her, she saw the white line circling his mouth fade. He reared back and roared laughter. The clans, save Innes's, joined him.
Alyssa frowned. This wasn't the reaction she'd planned on getting. She slid the men a withering glare to silence them, then looked back at the giant. "I didn't mean to amuse you, Laird. I was serious."
"By God, you are an insolent lass."
"Insolent?" Alyssa fairly shouted to be heard above the laughter. "Nay, I'm not. I don't jest in matters that affect the future of my clansmen."
The truth in that comment restored quiet. Tension mounted. Alyssa's nerves strung tighter than a stretched rope. When he didn't respond and she couldn't stand the wait another minute, she prodded him. "Well, do you grant or deny my request?"
The Buchannan sobered. "You do not jest?"
"About the security of my clan?" She thrust out her chin. "Nay, Laird, I do not jest. You offer more security to my clan than any other man known to me."
His gaze grew solemn, measuring. He brazenly scanned her length, his expression as masked as if carved in stone. She stiffened, swearing if he'd been any other man, he would regret that look. But he was her laird. In the eyes of Scotland, it was his right to do with her what he wished. So in silence, she weathered his perusal, promising herself that later he'd somehow pay for her embarrassment.
"David." The laird abruptly turned to his second.
"Yes, Kevan."
"Summon the priest." The Buchannan smiled and, while there was certainly humor in it, there wasn't a speck of warmth. "Saddling another with the tortures of controlling the hellion is an unfair test to any man's loyalty, eh?"
Silence fell. Seeing spots, Alyssa blinked and reminded herself to breathe. But even sucking in deep gulps of air didn't seem to help her starved lungs. Her chest fairly throbbed. "You—you accept? You mean to marry me?"
The Buchannan's voice thundered. "I wed!"
It was a short speech, but long enough to state his intent. Shouts and raucous roars rolled through the hills.
Near to fainting, Alyssa pressed her hands to her middle. She wouldn't lose her stomach. No matter what, she wouldn't. What in pity's sake had she done? The man wasn't supposed to agree. He was supposed to feel guilty because he refused. He was supposed to not kill her father.
Sensing someone's gaze boring into her, she looked and clashed gazes with Kenrick Innes. Hatred burned in his eyes, a dark and evil hatred that threatened her a hundred fold more than his striking her had. Her heart turned stone cold. He gave her no choice. She glared back at her former betrothed and solemnly nodded.
The message sent had been received and answered.
They were enemies.
Until death.
Five
SOME PREDICTED the Buchannan would kill her within a month.
Some predicted Lady Alyssa would have him crazed within a week.
And some predicted King Edgar would kill them both long before any of the other forecasts came to pass.
On hearing of the prophecies circulating among the warriors, Lady Alyssa took to her horse without disclosing her thoughts on the matter. But Duncan knew from the way she shot out of the camp, riding hell-bent-for-leather, she was none too pleased.
And when David reported the predictions to his laird, Kevan's deep rumbling laughter echoed through the Highlands.
Sitting beside the campfire, David slapped the dust from his boot and frowned over at his laird. "'Tis no time for laughter, Kevan. The men admire her prowess, but I've heard more than one question her—"
"Her what? Her loyalty?" Sharpening his sword blade on a whetstone, Kevan scoffed, not missing a stroke. "Only a fool would question her loyalty to me now. The woman fought. She saved my life."
The steady scraping grated at David's raw nerves. That his laird wouldn't like what was being said about his betrothed was about as clear as the waning sun hanging in the western sky. "Nay, 'tis not her loyalty what's in doubt. The men agree she's a fine warrior."
"Her ability speaks for itself," Kevan agreed, still rhythmically scraping the blade. "So what do they doubt, then?"
Firelight gleamed off the length of the blade. David preferred looking at it to meeting the hard look Kevan had levied on his head. He rubbed his neck and again considered not telling his laird of the gossip. But likening that action to treason had him flushed and reconsidering. Besides, he'd been Kevan's second too long to take serious offense at the man's glares. Still a bit of space between them was wise—in case the laird reacted first, then thought.
As David stood, his knees cracked. He grunted and pulled a log from the pile of gathered wood, then dropped it on the fire. A shower of sparks lifted and floated on the wind. It was unwise, dangerous, to provoke the laird, but he must be told.
Kevan tested the edge of the blade with his thumb, then returned it to the stone. "Well?"
"Her womanhood," David fairly whispered.
The scraping ceased. Kevan looked up at his second, his expression masked. "Her womanhood?"
"Aye."
Narrowing his eyes to slits, Kevan shifted his hand to the hilt of the sword. His voice went soft. "You forget the woman is to be my wife."
"Nay, I haven't forgotten, Kevan." David's words tumbled over themselves getting out of his mouth. "'Tis not me who doubts Lady Alyssa is a woman. 'Tis mainly Innes's warriors."
"Ah . . ." Kevan's manner eased. He moved his hand and returned to his sharpening. "Innes has changed his mind. He wants the lass, after all."
"Mayhap." Never so glad to hear the infernal scraping in his life, David stared into the fire and shoved at a fallen log with the toe of his boot. "Will you be giving her back to him?"
"Nay. The woman is mine."
David's sigh escaped before he could stop it. "So you're really going to wed her?"
Kevan's brows shot up. "I said I was."
"Aye, but I thought mayhap you were goading the girl for being so, er, forward and asking you to wed."
"Nay, though forward she was, I mean to make her my wife." Kevan ran his thumbnail over a plump ruby embedded in the hilt of his sword. Scratching at a bit of dried blood smeared on the stone, he grinned. "She requested me."
A smile curved David's mouth, too. Clearly the laird didn't oppose his wife being forward, at least not with him. "That took courage."
"I don't think the woman lacks courage." Kevan chuckled and scratched his head. "But God-given sense is another matter."
David smiled down at the ground. It was hard to believe, but Kevan was in a good humor over the issue. And, though David feared his curiosity would spoil his laird's fine mood, he risked asking the question uppermost in everyone's mind. "Why did you give her three requests? The clansmen—no doubt, even the lady herself—expected you'd kill her for her deceit."
"I might have, if I'd known marriage to me would be one of her requests." Kevan laid his sword aside and cocked his head. "The truth of it is, though a woman and not duty-bound, she risked her life for her clansmen and her laird. For that, she deserves to live." He held out a hand. "Give me your blade."
David unsheathed his sword. "I should be stoning your sword, Kevan, not you mine."
"The grinding soothes me." He took David's sword, tested it, frowned at the dullness, and put it to the stone.
Stretching behind him, David retrieved his flask and two cups. He filled one with ale, and passed it over. "You've explained why you spared her life, but why are you wedding her?"
Kevan took the drink. "What say you? Would you have left the hellion to Innes?"
Swallowing a long draw from his cup, David frowned. "Nay, the bastard doesn't deserve her."
"I didn't think so, either."
Understanding lit, and David quit his frowning. "That's why you allowed him to strike her." His ale sloshed in his cup. "I wondered about that. You wanted just cause to break the betrothal."
Kevan didn't answer.
He didn't have to. David smiled. "And all the clans witnessed his abuse themselves." The fire popped and David watched sparks fly into the air. "She could have stopped him."
"Aye, she could have," Kevan agreed. "But she didn't."
"She's clever, isn't she?"
Before answering, Kevan took a long swig of ale. "She is. Too clever for her own good, I fear. But I'll take her in hand."
Two guards came to warm themselves at the fire. David lowered his voice so just his laird could hear. "Her first request was simple to figure. Only a fool would want to wed Innes. Though, I think if you'd denied it, she would have done her duty."
"She would," Kevan said without hesitating.
"It's her request to marry you that has me puzzled."
Kevan shrugged. "I didn't agree to withdraw her second request. Her father's life—and the future of her clan—was in jeopardy. The woman knew that if I permitted the withdrawal, her father would no longer be lord of the clan. 'Tis simple, David. Honor is what prompted her request to marry me."
"Honor?" David sprawled out on the ground and folded an arm behind his head. Soon it would be twilight, his favorite time of day.
"Aye. If we are wed, her clan is safe and—"
"And so is her father's life. You wouldn't kill the father of your wife." Grinning, David slapped at his thigh. "The woman is more than clever. She is cunning."
"Damned cunning, though I expect she thought I'd refuse," Kevan agreed. "But marrying her won't stop my beating a little sense into her father. His daughter fighting in battle." Kevan grunted lustily. "The man should die."
"She won't like that." David's smile turned to a grimace. "There'll be trouble with Innes, too. He wanted her lands, I fear, more than he wanted the lady."
"Her father's lands belong to me."
"Then mayhap Innes does want the woman." David shrugged. She was a bonny lass, to be sure. But she was a better warrior than Innes, and David didn't think the man's pride would let him forget that.
Kevan's expression grew deadly. "The woman, too, is mine."
The lethal edge in Kevan's voice had the hairs standing up on David's neck. "And what is yours, you keep."
His laird didn't answer, just stared at David with eyes hard as iron and as frigid as the stream in high winter. David blinked and looked away. "Innes will never give her his loyalty."
"She shamed him. But he shamed himself more. Still, he'll think the wounds she inflicted deepest," Kevan predicted. He sighed and rubbed his sore shoulder. The bandage would need changing soon. It was gray with dust from the winds. "I'll give him time to see to his wounds. Then, she'll have his loyalty . . . or I'll have his head."
His laird's mind was an intricate maze that David had difficulty understanding. "If you're willing to kill him, why didn't you let Lady Alyssa declare war on Innes?"
"She isn't a lord. She has no right to declare war. She's a woman under my protection."
"And your women do not fight in wars." David grew thoughtful, then added in a lighter tone, "But as her husband, you will fight."
"If there is need, of course. 'Tis my duty to protect what is mine."
"I think, Lady Alyssa is not the only one who's cunning. Still, she won't appreciate your relieving her of her sword."
"What she'll be is bloody furious," Kevan speculated, giving David's blade a long swipe from hilt to tip. "But I'll not leave her empty-handed."
Perplexed, David asked, "What weapon will you give her?"
The devil danced in the laird's eyes. "A broom."
"Sweet Christ." David sat straight up. "Mayhap you shouldn't wed her, Kevan. If you do what you say, she's sure to be a shrew. The woman will make you crazed." And every Buchannan warrior and allied-vassal would be mighty miserable. An unhappy laird sure as certain meant everyone would be unhappy.
Kevan paused, as if considering it. "Mayhap I shouldn't. Who shall we wed the hellion to, then?" Testing the blade edge, he grunted. "Mayhap you?"
"Nay—Nay, not me." David stammered. "She'll be a handful, without a doubt. She's skilled, and never have I seen one more beautiful to the eye, but there's not a drop of humility in her body, nor modesty in her soul. I'm not of a mind to take my wife and my sword to bed at night for the rest of my days."
Humility.
Modesty.
Feeling as if he'd been struck by a lightning bolt, Kevan went statue still. The amulet at his neck vibrated, then glowed. He turned from David and cupped the crystal in his palm. Memories of other places, other times, flooded his mind. The Elder . . . The Elder was summoning.
Kevan hauled himself to his feet. "Send word to the lady, David. We wed now."
"But the priest hasn't returned—"
Kevan glared down at his second. "Go get him." He knew his voice was cold-to-the-bone, but he couldn't melt the ice from it. "Get him, David. Now."
Leaving David gape-jawed, Kevan turned from the fire and headed toward the wood. His second no doubt thought his lady had already made him crazed.
When he reached the small clearing, Kevan again cupped the crystal. "Your grace?"
"Here, Prophet."
The wisp of sound came from behind him. Kevan turned. From among vapors of silver mist, the Elder of the Council of Perfection stepped out into the sun-dappled clearing, then walked to meet him.
"You have seen your woman," he said, more than asked.
Was their mission here over? What had been accomplished? Had Alyssa failed because she'd fought? "I have."
"And your findings?"
Kevan swallowed the bitter taste in his mouth and spoke the words that had put it there. "Alyssa is brave, loyal, and skilled in this level, your grace, but she is not yet humble or modest."
The Elder frowned. "This is not a good sign, Prophet."
"Nay, but she has shown promise—at least in humility."
"Promise?" The Elder dipped his chin. "In what regard?"
"When she buried her men, she knelt to each of them and recited something. From her expression, I'm certain the words came from her heart. It was . . . tender and very emotional, your grace."
A weak glimmer flickered in the Elder's left eye. The right one remained flat, void of light. "What did she say?"
Prophet had grown accustomed to seeing no light reflected in the Elder's eyes. It seemed odd to see a gleam present and, though he knew he shouldn't, he stared. "I couldn't hear her words; no one could—I've asked those who stood closest. But after I lowered the boxes into the graves, I went to her." A knot of emotion lodged in his throat. Kevan cleared it. "She was in tears, your grace. Alyssa was in tears."
The flicker in the Elder's left eye grew to a weak glimmer. "She cried?"
"Aye, I saw the evidence of it myself. Her face was smudged with dirt from the battle." He lifted his fingers to his own cheek and let them drift downward. The tears streaked a path straight to her chin."
"I am encouraged by this news. Most encouraged." The Elder rubbed his frail fingers over the crystal at his own neck. "It is but a small step in her journey, yet it is definitely a step toward the light."
Kevan reveled in the Elder's pleasure. "Given time, she will make her discoveries, your grace. I have every faith in her."
"You always have." The Elder sighed. "I shall inform the Council. You know I shall have to remove your memory—and your powers of vision."
"Aye, but not without regret, I would guess."
The Elder smiled. "You would guess right. I still have my doubts about your woman's worth, Prophet. But I have none about yours, and you want her. So, I wish her every success."
"Thank you." A respectful smile tugged at his lip. "I have it on the best authority that one should not doubt, but have faith, in one's humble servant."
"Indeed?"
"Aye." So the Elder wouldn't admit that it had been his voice Prophet had heard when beginning the quest. Had it been? "Alyssa will succeed, because she must."
"For both your sakes, I hope you're right." The Elder stepped back into the silver mist, then faded.
Kevan found himself standing alone in the small clearing. Hearing hoofbeats, he turned toward the sound, but saw no one. Who had been watching him? Why? And how in bloody Hell had he gotten to the wood without knowing he'd left the fire?
RETURNING TO Cameron campsite, Alyssa felt closer to fainting dead away than she ever had in her life. Clammy and dizzy, she crawled down from Streak's back and walked toward the fire. She spread her hands over her stomach and took in deep breaths to calm herself, then stared without seeing into the flames.
Avoiding the rumors racing through the camps, she'd ridden hard to unleash. But the turmoil she'd felt then was nothing to compare with what she felt now. It was on the way back to camp, near the small wood, that she'd been . . .
Her head swam, and she closed her eyes, told herself to settle down. What she'd seen didn't bear thinking on. Stifling shiver upon shiver rattling up her spine, she forced her mind to focus on something else. The weather. She'd think about the weather. "Pity, these Highlands are cold," she mumbled to herself. Even in the light of day, she'd not gotten hot. But now that the sun was sinking low over the mountain, her toes were near on to numb.
"My lady?"
She jerked, then seeing her second relaxed. "Yes, Duncan?" She moved closer to the fire.
"The priest has arrived." He moved to her side. "You're white as snow, lass. Be you ill?"
Alyssa pulled her plaid tighter around her. "Nay, Duncan. Truth is, I'm scared out of my wits."
The old soldier guffawed. "I don't believe it.
"Well, 'tis truth."
"You faced the raiders without losing your wits. Yet your hand trembles at wedding your laird?"
Wedding her laird. She swallowed hard. Was he an angel from Heaven, or a warlord from hell?
She shot her second a solid frown. "Damn it, Duncan. He was supposed to refuse. "With a heartfelt groan, she kicked a stone into the fire. A spray of sparks flew into the air. "He was supposed to let Father live. He was supposed to let the clan go on as it has in the past. Why can't bloody men just do what they're supposed to do?"
The brown warrior's leathery skin crinkled near his eyes. "He'll make you a good husband, lass. The Buchannan's hard, but fair." Duncan's voice grew chill as the wind. "And he'll never strike you in anger."
"Are you still festering over that? For pity's sake, Duncan. I wanted Innes to strike me. 'Twas the only way to turn the other warriors support from him to me."
"You've done that." Duncan gave his beard a rustling swipe. "Though you're fighting for your laird rankles them some."
Alyssa bristled. "A man's loyalty is proven when he fights. Mine is suspect because I fought. Where is the justice in that, I ask you?"
"There isn't any," Duncan said with a shrug. "You're a woman. You shouldn't be in battle, and that's the truth of it."
"Well, that ought not to be the truth of it."
"I don't see why you're so fired up, my lady. A woman could have no better husband than the Buchannan."
"Better? Humph! I don't want any husband. Especially that foul-tempered, ungrateful—"
"Hush, lass." Duncan spoke softly to take the sting from his words. "You have to marry. You can give me all the frowns you want, but if I was you, I'd be smiling."
"Smiling." she screeched. "This is the worst day of my life, and you want me to smile?"
"Aye. In fact, you ought to be bloody happy."
"Happy? For pity's sake, Duncan. Did you get hit on the head in battle? What I am, is bloody miserable."
Duncan pursed his lips and stroked his beard. "You could be dead—or worse."
"Worse?" She reached for him. "Oh, God. You did hit your head!"
He brushed her hands from his forehead. "Nay, woman. But you might have. Quit your railing and think. You could be marrying that braggart Innes. And if that isn't worse than death, I don't know what is."
Her proper second was gone. Her friend and trusted family member, the tower from which she drew strength, had come. Duncan knew instinctively what she needed. He always had. And now, she suspected he hid a snarl under that iron gray tuft growing on his chin. "Duncan? I've never heard you speak ill of Innes."
The old soldier shrugged. "Until today he was betrothed to my lady."
"He is a horrid braggart." Alyssa whispered her agreement.
"Aye. You're well rid of him." A twinkle lit in Duncan's eye. "Now, the Buchannan. There's a man worthy of you."
Alyssa worried her lip with her teeth. Had she seen and heard what she thought she had in the wood? "Do you really think he's worthy, Duncan?"
He tweaked her chin in a rare display of affection. "Aye, lass, I do."
She looked up into the face of the man she trusted above all others. "You don't find him . . . odd?"
"Odd?"
"Never mind." Alyssa lowered her gaze. Duncan would think her crazed. She couldn't tell him that she'd seen the Buchannan talking to a white-haired man with no eyes in his sockets.
Mayhap she was crazed. For when she'd looked to where his eyes should've been, she'd seen clean through to the land behind the stranger. Oh, if only she could have heard all their words.
She stifled a surge of shivers. Was it any wonder she was scared out of her wits? What she'd seen would scare the skin off the Apostles, for pity's sake. She was an excellent warrior, but a mere mortal.
"Lady Alyssa."
Recognizing young MacMillian's voice, she turned to face him. "Yes, James."
"The Buchannan says you're to come now. It is time to wed."
Panic seized her. "Duncan, I can't do it," she whispered.
Duncan nodded at James to leave them. When the boy had gone, he turned back to Alyssa. "You must."
"No," she insisted. "You don't understand. He's—he's different. He's not like you and me. He talks to men with—"
Duncan wrapped her shoulder with his arm. "Now, lass. You've made a bargain. He's wedding you at your request. If you refuse, he'll take revenge on your people. Do you want their blood on your hands?"
"No, but—"
"No buts, my lady." He gave her a squeeze. "You're just a bit jittery. All brides go through that."
"They do?"
"They do."
THE PRIEST STILL wore his funeral vestments.
David took one look at Father Aldwyn and said, "Father, you should change clothes. No lady wants the priest at her wedding dressed for a funeral. She's bound to take it as an omen."
"I have no others. When we were ordered to come back, I'd not yet returned to the keep." Alden grimaced. "Mayhap the lady will take offense, Kevan."
"Offense or no, she'll not complain," Kevan replied.
"Complain, nay, I imagine not. But my dress will offend, Kevan. Mayhap the lass will even suffer hurt feelings. I'd not want—"
"We wed now, Aldwyn," Kevan interrupted. "She requested we marry, you forget. The woman won't care if you're stark naked."
"We'll soon see how she takes it," David said, then groaned. "Sweet Christ! Nay, I don't expect she will complain."
Kevan turned and saw Alyssa. Dressed as she had been for battle, Alyssa wore her black breeches and boots, her hood, and her Cameron plaid. Kevan laughed at her deliberate attempt to goad him. She wasn't fainthearted, he'd give her that. But she had much to learn about his ways. She couldn't have done anything that would have pleased him more.
Her face was pale, her chin quivered, and, when she saw Aldwyn's black and purple vestments, surprise flickered in her eyes but, without uttering a sound, she took her place at Kevan's side.
Aldwyn cleared his throat.
"Laird," she whispered up at him. "Before we wed, may I speak with you?"
Kevan started to refuse, but her hand on his forearm was trembling, so he granted her request. "Wait," he said in Aldwyn's direction, then led Alyssa away from the campfire.
Facing him, she looked up. Her emerald eyes clouded. He didn't like it. "What is it, Alyssa?"
"Are you very devout, Laird?"
Her question was too forward, not at all modest, but the worry in her face told him his answer was important to her. He didn't want the shrew in her to emerge before she'd even said the vows. Later would be soon enough to take her in hand. "Aye, I suppose I am."
She gave him a little smile that sped his heart from its steady thump to a wild thunder. He frowned. "Come."
When they again stood before Father Aldwyn, Kevan nodded. "Begin."
The observing warriors fell quiet and Father Aldwyn started the ceremony. When he asked Kevan if he took the woman to wife, the laird answered in a shout. "Aye, I agreed, didn't I?"
Alyssa prayed he was the angel she thought, and not the warlord from Hell he resembled, but the roar of his voice made her wonder. Yet, angel or warlord, the Buchannan was not a liar. And after telling herself so twice, she was convinced. He'd said he was devout, and she believed him. The shout obviously had been meant for Innes and his men.
Father Aldwyn, too, had grown wary at his laird's bellow, and backed away. Reflex had Alyssa tugging him toward her.
Kevan frowned. "Unhand the priest, woman."
Alyssa glared up at her laird. "Your roar sent him too near the fire. The tail of his cassock was in the bloody flame."
The stunned priest smiled his gratitude.
Her laird merely lifted a brow. "Get on with it, Aldwyn."
"Don't bother asking, Father," Alyssa groused. "Since I must marry, aye, I'll take him."
Damn if she didn't sound disgruntled! Kevan wanted to laugh. He wanted to throttle her. He did neither, but squeezed her shoulder and hauled her to his side. "She must marry. So, I guess, that's that."
The priest's forehead furrowed. Kevan nearly chuckled. "Quit your frown, Aldwyn. She took me."
"We are wed?" Alyssa asked the priest.
Looking like he was praying for patience, Aldwyn let out a resigned sigh. "Aye, you are wed."
The Buchannan turned and kissed his wife.
Alyssa vowed her stomach had fallen to her toes. She felt the stirrings in their tips—and up through her body to the crown of her head. But Megan couldn't have been talking about this. No man's lips could steal a woman's breath. It had to be the air. Of course, it did. Even so, lord, but this Highland air was thin.
Kevan grunted softly and deepened the kiss, rubbing his lips against hers in the most pleasant way. Her heart skipped, then thudded, pounding against her ribs. Dear God, maybe a man could steal a woman's breath. Could he kill a woman with his kiss?
Kevan raised his head. Bemused, Alyssa looked up at him. Instead of the tender look she expected, he roared laughter.
Heat swept up her neck to her face. "What has amused you, laird?"
"None who look at you now would dare doubt that you are a woman."
She gasped and shot him a fierce glare.
He ignored it. "My name is Kevan. We are wed now."
Alyssa swallowed hard. The man in the wood had not called him Kevan. He had called him Prophet. That, she had heard. Was he a seer, then? And more importantly, seer or no, was he good or evil? "Aye, blessing or curse, we are wed."
His hand tightened on her shoulder. "You will not speak so to me, Alyssa. You are my wife, and I forbid it."
"I am not free to speak my mind?"
"Nay, nor are you free to speak my mind. Learn that now."
Alyssa's hands flew to her hips. "Are you trying to provoke my temper?"
He laughed at her. "Nay, you little hellion. I was trying to soothe it."
Alyssa opened her mouth to let him know what she thought of that statement, but his lips came down on hers, and his tongue darted into her mouth. Stunned by the intimacy, she tried to pull away, but he tugged her closer, and the feel of him hard against her belly sent the fight flying right out of her.
When he raised his head, she found herself fitted against his chest. Her feet dangled far above the ground, and her hands were wound around his strong neck. When had he lifted her? When had she returned his embrace?
Dazed, she looked into his eyes. The color of heated metal, they shone with amusement. God help her, it wasn't the air, after all. It was him.
With her still in his arms, he turned toward his clans. "My wife."
Cheers rumbled through the hills, and Alyssa forced a calm expression to her face. It was most difficult. Her anger with him was gone, but her body shook with bloody stirrings.
Then she saw Innes in the crowd. The hatred in his glare joined the hot stirrings in her blood, and she shivered.
The Buchannan looked down at her. "What is it, wife?"
Now she saw his tender expression, his concern. And, suddenly, she was very happy for the security of her husband's arms. In them, she felt safe. She smiled up at him. "'Tis nothing, Kevan. Nothing at all."
AFTER THE WEDDING, Kevan questioned each Cameron warrior in private. And from each warrior, he received positive responses regarding the status of his allied-vassal.
"You seem pleased, Kevan," David said.
"Aye, I am. Alyssa has lorded Cameron well."
"She has the loyalty of her men. That's evident," David replied.
Kevan's mood grew black. "She was neglectful only of her own safety."
"So they said." David drank from a pouch and held it out to Kevan. "But that was told to you in confidence—for her own good."
"That was told to me in confidence to spare the teller from suffering her wrath." Kevan took the pouch and chuckled. "She has their loyalty, aye. But they've a healthy fear of provoking her, too. Admirable combination, that. Call Duncan to me, David. Let's see what he's about."
When the old soldier stood before his laird, Kevan leveled him with a hard glare. "You are more loyal to your lady than to your laird, Duncan. This does not please me."
Duncan stiffened. "The lady is loyal to you, so my loyalty was never tested by conflict."
"And if it had been?"
Duncan held his laird's gaze. "Praise God, I did not have to choose. I've been with my lady since she was a bairn."
"Answer my question, Duncan." Kevan drummed his fingers against the tree stump—their makeshift table. "I lose patience."
"If my loyalty to you would have been at risk, I wouldn't have pledged to my lady. She's a competent leader, Laird. Her skills are many, and she's always been devoted to you."
Though not unmoved by Duncan's impassioned speech, Kevan forced his voice to remain firm. The warrior had willingly deceived him, after all. He couldn't afford to look lightly upon that. "You need not defend the lady to me. I am her husband. But your own defense is another matter. You deliberately failed to report the incompetence of your lord, John."
"Aye, it was deliberate," Duncan confessed. "I have no defense."
"None?" A sliver of surprise slipped through to Kevan's tone.
"Nay, Laird. None."
Lady Alyssa joined her husband and Duncan by the fire.
Kevan spared her a glance. "What do you want, wife?"
"As these matters affect—"
Her head was bowed and she spoke to the ground. Kevan groaned. "Cease your mumbling and speak up."
When she looked up at him, her cheeks were rosy red. "As these matters affect Clan Cameron, I wish to offer my opinion—should you care to hear it."
She wanted, to hear what happened. And because she'd twisted the truth about that, Kevan was half-tempted to refuse her. But this was the first request she'd made of him since becoming his wife, and he didn't want to start their marriage with her thinking him unreasonable. With her skills, she'd likely avoid requesting anything further from him, and then he'd be spending the next fifty years running after her and insisting she should. "You may attend, but you will not interrupt."
"Of course not, Laird."
"Husband, Alyssa," the Buchannan growled. "I am your husband. Call me that, or by my name. Hearing my wife call me laird grates at my ear."
"Yes, husband."
The old soldier's faded eyes lit up with warmth. Kevan wondered why. "You stand before your laird, Duncan, and offer no defense for your actions. What punishment do you consider just repayment for your offense?"
Duncan stiffened. "Any my laird demands."
"Even your life?" Kevan asked.
Alyssa whimpered and Kevan glanced at her. She'd grown pale, white as her mare. "Well, Duncan?"
"Aye, even my life."
Alyssa clenched her hands into fists and her chin quivered, but she said not a word. Fear for her second's life shone in her eyes. Kevan steeled himself against sympathy for her. "My anger is great, Duncan. In fairness, I will hear your lady before I decide your fate. You may leave me."
Without a word, Duncan crossed his heart with his hand, dipped his head in salute, then took his leave.
"Alyssa, come."
She walked the distance between them with her head down and her shoulders slumped. That surprised him. She was a proud woman. But it was also a telling sign of how deeply she was affected by the uncertainty of Duncan's fate. When she stood before him, Kevan lifted her chin with his hand. "I will hear you now."
"Do not kill Duncan." Her voice was a strained whimper of sound, and her eyes openly pled.
"You may not direct me, Alyssa." Kevan softened his voice. Though he wasn't a man given to explaining himself—especially to a woman—he didn't want her to cry. "Duncan failed in his responsibility to me. That cannot go unpunished."
"But he did it to protect me. Please, Kevan. Duncan has cared for me my entire life. He's guarded and taught me to defend myself—and you. It was he I fashioned myself after, his qualities I sought to make my own."
Kevan glowered at her. "Do you love him, wife?"
"He's been both father and mother to me. I trust him."
Family. She cared for Duncan as a father. Kevan's anger eased. "But do you love him?"
An uncertain frown wrinkled her brow. The wind tossed her hair forward, she brushed it back over her shoulder. "I know not what love is. But I do care for Duncan. More so, God forgive me, than for my blood father."
She dropped to her knees, and put her hand on his thigh. "Please, husband. Please, do not kill him."
The pain in his wife's voice hit Kevan like a stallion's kick to his stomach. "You beg on your knees for his life?"
Her eyes were bright and glossy, and tears clung to her lashes. "I beg on whatever I have that will allay your anger."
Her answer infuriated him. When she bowed her head to her chest, he glared down at her crown. If she gave her life for any man, it should be for him, not Duncan. He was her husband. The wind carried her fresh, soapy scent to him, and his throat muscles seemed to thicken. "On your own life, Alyssa? Will you give your life for his?"
She didn't look up at him, as he'd hoped she would. Her expression often spoke more than her words. But her hand squeezing his thigh, fell slack. She probably didn't realize that she'd given him his answer.
"Aye," she whispered, her voice cracking. "He's more valuable to you."
She spoke to his knees. He cupped her chin and lifted so he could see her face. His heart slammed into his throat. "Tears? Do you cry for yourself, wife, or for your warrior?"
"Kevan, I give you my word. Duncan has served you well. If one of us must die to appease you, take my life. Not his."
"You are no longer Lady Alyssa, nor a Cameron," Kevan said softly. "You are Lady Buchannan. My wife."
"Aye," she sobbed. "But even as Lady Buchannan I'm worth less to you than a trusted soldier such as Duncan. Please, Kevan. I—I beg you."
Hearing broken sobs from his proud little warrior wrenched Kevan's heart. She'd sacrificed her pride, and he knew that had cost her mightily. He hugged her to him and lifted her into his arms. "Hush your tears."
She clung to him and cried. He tightened his hold. She fitted in his arms like she was born to them, and a protective tenderness he didn't understand surged up from deep inside him. "Shh, enough. Enough. Duncan is safe."
She looked up at him and sniffled. "You will not kill him?"
"Nay." Kevan brushed at a tear clinging to her cheek with his thumb.
"Or me?"
The joy on her face stole his breath and set his heart to pounding wildly. That irritated him and he snarled at her. "Nay—not just yet."
"Oh, Kevan." She buried her face in his neck and showered him with tiny kisses. "Thank you."
Her affection stunned him, but it pleased him, too. It was a wife's duty to cling to her husband, to show she cared for him. "Alyssa. Alyssa." He reared back. "Quit your kisses, woman. I wish to speak to you."
She stilled in his arms, and he smiled to soften his reprimand. "First, never underestimate your value to me. You are my wife. Second in my heart only to my God and my King. And next, never kiss me like that—"
"I'm sorry. I didn't mean to kiss you at all. It just—"
She meant never to kiss him? Not bloody likely. "Hush, damn it."
Her eyes grew wide and worried. She was nervous, he realized. He frowned at her. "You're supposed to want to kiss your husband, Alyssa."
"Oh."
He couldn't tell if that pleased her or not, and decided it did. She'd take years of instruction. And surprisingly, he was quivering with anticipation at the thought of teaching her. "Never kiss me like you did." He brushed her lips with his words, teased her lips with the tip of his tongue. "Kiss me like this . . ."
Her every thought fled her mind. The sounds of the crackling fire, of the men readying to leave and the steady whistle of the wind all disappeared. She heard only her husband's assurance of her value to him, and the soft murmurs of pleasure vibrating deep in his chest.
"A man can only clear his throat so many times without choking to death, Laird."
Without setting Alyssa from him, Kevan turned to David and growled. "You'd best have good reason for—"
David grinned. "The clans are waiting to pay their respects before they leave. If you've time for them, that is."
David's goading hit its mark. Kevan laughed deeply, his chest rumbling against hers. Heat surged to her cheeks.
He set her down and pulled her to his side. "Aye. We have time, don't we wife?"
"Yes," she whispered. "We have time."
Outside, Kevan accepted the clan's respects and the well wishes on his marriage with Alyssa standing at his side. Grant and Lindsay pledged their loyalty to his wife of their own accord, greatly pleasing him. But Clan MacMillian was less enthusiastic. Its lord was still smarting over his second son, young James, being fostered for training to a clan being led by a woman.
At the first stirrings of conflict, James planted himself at Lady Buchannan's side. His father glared at him, but James refused to move.
The barrel-chested lord grunted his displeasure. "You don't regret giving your pledge to a woman, James?"
"Nay, I don't. You've seen her skill and courage. Would you regret your pledge to her?"
"She's a woman." The MacMillian's shout threatened to topple James from his feet.
"Aye," James responded, grinning appreciatively. "She is that."
The gathered men chuckled.
"And you are a fool!" James's father shot back.
"A fool?" James guffawed. "I'm no fool, my lord. Lady Buchannan's training has served me well. I have learned much about defense under her direction." He looked at his father's injured arm pointedly. "Enough to survive at least this battle without injury."
Kevan stifled a groan. With aid like young James was giving, he'd be at war with the MacMillians before the moon rose full.
The wounded lord leveled his son with a hard glare. Kevan waited, feeling tension build between his men and the MacMillians. The lord would either kill his son--in which case, Kevan would have to kill the lord—or he'd praise him. And from his expression, James's father could go either way.
"So you have escaped injury. 'Tis your duty to stay fit to serve your laird." MacMillian turned to Lady Buchannan and dropped to one knee on the ground. "And to serve his wife."
The tension drained from Kevan's body. The MacMillian warriors followed their lord's lead, dropping down on one knee and crossing their hearts with their right hands. In unison, they paid homage, pledging their loyalty to his wife.
Lord MacMillian stood up, took to his horse, then shouted in a gruff voice from his stallion's back. "Duncan, train him hard. My son has much to learn about risking the wrath of his lord."
"As best I am able, Lord MacMillian," Duncan shouted back.
Alyssa whispered to Kevan. "You've not yet told Duncan his fate?"
"Nay."
"But—"
"Hush, wife. I will tell him soon. Him fearing his punishment a little longer is not so costly a repayment, now is it?"
Alyssa's expression soured and she muttered. "Nay, husband. It is not." She put her hand on his forearm. "But, please, not overly long."
That she'd touched him pleased Kevan. And she wasn't trembling. He smiled down at her. "Nay, wife. Not overly long."
Six
"WHY DON'T you sit down, Lady Buchannan?"
"I can't, David." Alyssa worried a path near the fire. What was taking so long? She looked down at David, working near the fire at softening a stiff, new saddle. "Might you call me Alyssa?"
"All right, Alyssa. But your pacing a trench in the soil isn't going to bring Kevan out of the wood any sooner."
"Poor Duncan. Kevan won't hurt him will he? I mean, really hurt him. It's true his shouts could fell trees, but if Kevan struck him—well, Duncan would never raise his hand to his laird. Not even in defense." That worrisome thought had her pacing double-time. "He's a good man."
"Aye, he is. Kevan has—"
"Kevan?" She frowned. "Not Kevan, David. 'Twas Duncan I meant."
"Oh."
"Don't you see? This is all my fault." She swept her hair back from her face and rubbed at her temple. "Oh, why did I let Kevan talk to Duncan alone?"
"Let him?" David asked. Didn't the woman know that an entire clan couldn't stop Kevan Buchannan once his mind was set?
Alyssa sighed. "You might not have noticed, David, but Kevan is a wee bit upset with Duncan right now."
"Sweet Christ, a wee bit upset?"
Alyssa's frown changed to an incredulous look. "You hadn't noticed? Well, trust me on this, David. He is. Poor Duncan."
"Poor Duncan? Lady Alyssa, a stone would know the laird is angry enough to murder the man. He deceived his laird. Sweet Christ, it's a miracle the man's still breathing."
Alyssa's lower lip started quivering. "But Kevan gave me his word."
David's expression softened. His lady was truly worried. "Rest easy then, my lady. If Kevan gave his word, Duncan will not die by the laird's hand."
"When he's angry, is it just prattling?" Her voice trembled. "I—I mean, does he execute his threats?"
"I've never known him to make a threat he wouldn't carry out, my lady. But if Kevan gave his word, Duncan is safe."
"He did. He promised." She flashed David a weak smile. "Besides, he's only a wee bit upset."
Resigned to easing her fears, David agreed. "Aye, only a wee bit."
"Kevan's a man of honor. Of course, he will be reasonable—won't he?"
David scratched his neck. The Buchannan reasonable? Deciding he'd best not answer that, David compromised. "Aye, he's a man of honor."
"Oh God, I wish I could be sure." She turned and nervously jabbed at the fire's embers with a crooked stick. "Not that I doubt your word, but, well, to be honest, David, Kevan was a wee bit more than a just a wee bit upset."
"Aye," David agreed. He'd listened to his laird rave for hours. "A wee bit more, to be sure."
"You doubt my word?"
Alyssa spun around. Kevan stood alone, his legs braced, thunder in his expression. She tried to look past him, but her giant husband planted himself so all she could see was his chest. "Where is Duncan, Kevan?"
"You doubt my word?" He repeated his question in a shout.
She glared up at him. "I was just worried. Where is Duncan?"
Kevan's nostrils flared. "Gone."
"Gone?" She sent him a blank look.
"Gone."
Alyssa's heart stopped. Duncan was gone. Kevan had killed him, anyway! He'd lied to her, and killed him, anyway. Her voice grew lethally soft. "Gone, Kevan?"
"I left him in the clearing."
"You what?" She squeezed her hands into fists. "You left Duncan. I expected that of the raiders, but not from you." She turned and let out an ear-piercing whistle. "And David said you were a man of honor."
David watched her stomp away. "Where is she going?"
"To find truth." Kevan pursed his lips, his mind clearly far away.
"There's no saddle," David warned, seeing his lady mount her mare. "She'll break her neck."
"Nay, curse or blessing, she won't." Kevan sat down and called for food.
"But—"
Kevan lifted a quelling hand. "She's capable."
David tossed the saddle soap aside. "She thinks you've killed him."
"I know."
"But you didn't." David hated to admit it, but he wasn't at all sure.
"I gave my word."
"Then why—"
"She doubted me. The hellion must learn my value herself. Telling her would do no good."
David shook his head. "It seems a cruel way to treat a new bride. But, no doubt, you have your reasons."
"No doubt."
ALYSSA SCOURED the wood and found no trace of Duncan. Had the Cameron warriors already retrieved his body?
Hot tears, anger and fear, warred in her. Squeezing her knees, she turned Streak and headed for the Cameron campsite.
Thundering past the Buchannan camp, she refused to spare her husband a glance, though from the corner of her eye, she saw him eating a fair dinner. How could the lout eat? He'd just killed the finest man who'd walked this earth!
Near the Cameron campsite, Sewn was preparing the horses to leave. Alyssa called out to him. "Sewn, wait! Where is Duncan?"
"Resting peaceful, my lady," he shouted, then pointed, stabbing the air. "Up ahead."
It was true, then. Kevan had killed him. Oh God, Duncan was dead!
Alyssa felt numb. She nudged Streak forward. Slowly feeling returned, and with it came cold fury. Her husband or no, Kevan Buchannan would rue this day. He was not a man of honor. He was arrogant. A liar. And, as God was her judge, he would pay for taking Duncan's life.
She saw her faithful second, resting peacefully on the ground as Sewn had said. She slid down from Streak's back, unable to look away. Her heart wrenched, ached deeper than any pain she'd ever suffered.
At his side, she fell to her knees and buried her face in his chest. "Oh, Duncan. I'm so sorry. I'll never forgive myself for trusting him. Never."
A strong arm closed around her back. A shiver crept up her spine. "Duncan?" She reared back, and saw his eyes. "Duncan!"
Her tears began in earnest. So did her rambling.
The old warrior frowned. "Slow down, my lady. I can't make sense of your prattle."
"He said you were gone," she cried in broken sobs. "He said he'd left you in the wood. Oh, Duncan. I thought he'd killed you."
"Killed me? Nay, I gave my pledge—"
"But you'd already given him your pledge."
"Not as a lord."
Alyssa gasped. "A lord?" She clutched great handfuls of his plaid. "Kevan made you lord of Cameron?"
"Aye." A smile peeked out of a crack his wiry gray beard.
"That blasted man." She thunked a fist against Duncan's chest.
His breath swooshed out, and Duncan's smile faded. "You don't want me to lord Cameron?"
"Oh, yes, Duncan." She firmed her jaw. "I do. No better man exists." She swiped at the tears on her cheeks with an angry hand. "'Tis Kevan I curse, not you. I should ram my sword through his heartless gut."
Duncan's voice grew hard. "I will not permit that, my lady."
"He let me think he'd killed you."
"You must be mistaken, lass." Duncan patted her arm on his shoulder. "Our laird is not cruel."
"He is cruel. A vile specimen, I tell you."
Duncan let her pace and rant for a full half-hour before he interrupted. "Sit down, my lady. And shut up."
Alyssa's jaw fell slack. "What?"
"Do it."
Alyssa dropped where she stood. Duncan lowered himself beside her on the ground, then took her tiny hand in his. In all her twenty-two years, he'd never told her to shut up.
His expression was grave. "Did your husband say he'd killed me?"
Alyssa thought back to Kevan's exact words, then shifted uncomfortably. "Well, no. Not exactly."
"Well, what exactly did he say?"
Heat scorched her cheeks. "He said you were gone. That he'd left you in the wood." She frowned. "What was I supposed to think?"
"He spoke the truth. He did leave me in the wood. And I expect he meant I'd gone home, my lady."
"Gone means gone, Duncan. He knew what he was doing. He wanted me to think you dead."
"Now why would he want you think that, do you suppose?"
Alyssa lowered her gaze to the dirt. "He was angry with me."
"Mmm, and would you be knowing why?"
Her face pinched in a proper pout, she looked up. "It was his fault. He—he . . ." Was it his fault? Well, pity. She lowered her gaze to the dirt. "I doubted his honor."
"You what?" Duncan groaned. "Dear God, what are you about, Alyssa Buchannan? When it comes to men, have you no sense? You should trust your husband."
Alyssa stiffened. "He hasn't earned my trust."
"You married him. You gave him your vow, my lady."
She had given him her vow. "But—"
Duncan pressed his fingertips over her lips, halting her words. "He's your husband, lass. Trust him."
Ashamed of herself, Alyssa swallowed hard, then nodded.
Duncan lowered his hand. "I must go. Cameron lies vulnerable in my absence."
"Aye." Alyssa stood up. "Duncan, I'm happy Cameron will be in your care. It soothes me knowing my people will be safe."
Duncan gave her a reassuring look. "Your father is safe, too, my lady. As is Lady Megan. Father Aldwyn goes with me to Cameron. When he returns to you, I'll send news of them."
Alyssa blinked to keep threatening tears from falling. She wrapped her arms around Duncan's waist and pressed her lips to his shoulder. "Thank you, my lord."
Duncan raised her head and again pressed his fingers to her lips. "Go to your husband, my lady. Be open with your heart. He deserves your trust."
Though terrified of his response, Alyssa must tell Duncan what she'd seen. He was a lord now. He must be prepared. "Duncan, you do not know what I saw before Kevan and I wed."
Duncan smiled. "Aye, I do. In the wood, you saw your husband talking with the white-haired man."
"Aye!"
Duncan nodded. "I was there, too."
"You were? Then you saw—" She gripped his forearm and squeezed. "The man had no eyes, Duncan! Did you see that?"
"No eyes? Nay, my lady. He had eyes brighter than the noon sun."
"He didn't! I saw through his sockets, Duncan. Clean through!"
"To me, they were bright, my lady." Duncan shrugged. "An angel by my reckoning."
"Good God, you sound so—"
"Calm?" Duncan suggested. "Mayhap. You don't live as long as I have without realizing there's more in this world you don't understand than there is that you do."
"An angel?" Alyssa considered it, then worried her lip with her teeth. "I don't know, Duncan."
"Listen to me," Duncan said, growing firm. "Your husband is special, Alyssa. Follow him. Think with your heart and your head but, in the end, follow him. There, you'll find contentment."
"Duncan, you sound so strange." She cocked her head and slid him a perplexed look. "Not at all like you, but you, nonetheless."
She looked at his neck. A crystal amulet like Kevan's hung in the soft hollow of his throat from a leather strip coiling around his neck. She touched the stone, looked up into his eyes, and saw wisdom. "Duncan," she whispered, stroking the creased skin near his eyes. "I'll follow him. I give you my vow."
The old warrior smiled. "You have pleased me greatly, lass."
Her voice choked. "I'll miss you."
"We'll meet again, my lady. That, I vow."
"Kevan once asked me if I loved you. I told him I didn't know what love was." She looked up from the ground into his eyes. "But if I did know, I would love you, Duncan. I really would."
"Aye, I ken your meaning, lass." He dragged a rough thumb along her jaw. "Have faith in your humble servant. You will know love."
His words confused her, but before she could ask him to explain, Duncan looked past her shoulder. "He waits, my lady."
"Who?"
"Your husband."
Alyssa turned and saw Kevan astride his stallion. The beast was hands taller than any other she'd seen, and on him, Kevan looked every bit the warlord from Hell she'd feared him.
"Come," he said.
Alyssa gave Duncan a loving hug. "God speed."
"My lady." Duncan crossed his chest with his hand.
Again she noticed his amulet. He'd not worn it before. Was it a symbol of Kevan's lords? Nay, not her father, Innes, nor the MacMillian wore such amulets. Only Kevan and Duncan. Why was that?
Alyssa stopped beside Kevan's horse and let the powerful beast sniff her hand.
"Careful," Kevan warned her. "He doesn't take well to strangers."
Alyssa smiled up at him and stroked the horse's nose. "We are not strangers, are we? What's his name, Kevan?"
"He's a horse, wife. He has no name."
That comment had her giving him a good glare. "Every living thing deserves a name of its own." She stroked the horse and her expression softened. "He's beautiful. Mayhap you should call him that."
"Beautiful?" Kevan guffawed. "I'll not ride an animal named Beautiful, Alyssa Buchannan."
"Well, you can't call him horse." She rubbed the beast's neck. "So what will you call him?"
"Mine. Just as I call you." Kevan reached for her. "Now get up here."
"I'm not sure I like being compared to a horse you won't even name."
"Alyssa," he warned.
"Oh, all right." She walked over to where he could lift her, and grabbed hold of his muscular arms. "Have a care not to rip your stitches."
When he'd settled her in front of him, she stiffened her spine, refusing to touch him any more than she had to. "There, I'm here. Are you happy?"
"Aye, I am." The awful man grinned at her. "And my stitches are fine."
He spurred the horse, and they rode out of the camp. On the other side of the copse of trees, she turned to look at him. "Where is Streak?"
"What streak?"
She let out an exasperated little sigh. "My mare, Kevan."
He looked serious, but there was a strange glint in his eye. "Gone."
Oh God, not again with his gone. Alyssa bristled. Another test. He was forcing her to ask, which, she supposed, she should have done about Duncan, too. That had been a mistake she wouldn't repeat. "Where has she gone, Kevan?"
"To my holding. David will care for her."
She refused to turn to look at him, but by his tone she knew he was pleased that she hadn't railed at him again. "And are we going to your holding, too?"
"Aye."
"Is it far?"
"Nay." He slid his hand around her waist and splayed his fingers across her stomach. "We're on Buchannan lands now."
Those stirrings in her belly were driving her mad. "Why does Father Aldwyn return with Duncan? Don't you trust your new lord-vassal?"
"Aye, I trust him. Elsewise he'd not lord at Cameron. 'Tis you I wanted Aldwyn away from."
"Me?" She frowned at the saddle horn and gripped it hard. "The man's a priest. I've done nothing to him."
Kevan grunted. "He's too soft. When I teach you your place, he would take pity on you."
Alyssa glared back at him. "I need no man's pity."
"Not yet," Kevan agreed on a resigned sigh. "But if you're half the hellion you've been, you will." Kevan grinned, and added, "But don't worry overly, wife. Margar will give you all the sympathy you need."
"Is she your mother?"
"Nay, but she is a mother to all. A sweet, gentle soul."
THREE HOURS INTO the night, Alyssa gave up her stiff back and relaxed against her husband. Her spine tingled, protesting. The moon was but a shadow, and Alyssa could see little by its light. But Kevan seemed at ease, and his beast, surefooted.
Lord, it had been a long day. Kevan learning her identity, the trouble with Innes, her wedding, then Duncan.
Well, it was past now. Done was done and things would settle down soon. At least by returning to her husband's home now, she wouldn't be confronted with his wanting to bed her this night.
A wife should know her husband first, shouldn't she? For all she'd learned about him, Kevan was still a stranger. Oh, she knew well enough that he expected she'd fight against his bedding her. And for that reason alone, she'd not do it. No matter how awful it was, she'd submit to her husband. To really get the better of him, what she should do was attack him, just like in battle. Do the unexpected. And mayhap she just would . . .
Pity's sake, this day had been too full.
Lulled by the steady movement of Kevan's mount, by the feel of her husband's arms wrapped tight around her waist, Alyssa felt her eyes drift shut. She turned her cheek until it rested against the warmth of his chest, not minding the cool night air at all . . .
Kevan knew the moment she fell asleep. She'd fought against it a good hour, but the quiet of the night pulled too strong. He should have waited till morning to return home. She was weary, he knew, but damn it, she was his wife. He couldn't sleep with her at his side and not take her. She was a beautiful woman, tempting. Her silver hair, soft and shiny, begged for his touch. He stroked the flesh at her ribs, just below her breasts. She was firm from strenuous exercise, but her curves remained soft and womanly. He wanted her, aye, but the first time he took her, he wanted it to be in his home. Was that so wrong?
He grinned and tugged her backside flush between his thighs. She'd be glad they'd ridden now, come morn. She'd not feel much like sitting astride a horse then.
A jolt of desire surged heat to his loins. His little warrior was passionate in her fury. And when she'd tended his shoulder, she'd concentrated on nothing else. Would she devote herself with that single-minded passion in his bed? Oh, she'd fight him like the hellion she was—at first. But then the passion would flare in her, and she'd fight even harder to quench it. Anticipating the battle, Kevan grew hard. And more anxious than ever to get home, he spurred his horse.
The powerful beast responded immediately. Beautiful? A laird, a chieftain vassal to Edgar himself, riding a horse named Beautiful? The woman was crazed. Kevan guffawed, then sobered. But a laird riding his beautiful woman, ah, now that was another matter. Eager, he dug his heels into Beautiful's flanks.
Seven
"WE'RE HOME, wife."
Alyssa opened her eyes. Kevan was holding her in his arms. She'd drooled on his shoulder in her sleep. She brushed at the spot and saw that they were standing inside a great hall with ceilings higher than any she'd seen—and more people than she'd expected, given the late hour of their arrival.
A wiry little woman dressed in black, with a face too lined to merely be called wrinkled, studied her through watchful eyes. Uncomfortable, Alyssa whispered, "Put me down, husband."
"You wed, Kevan?" the little woman asked.
"Aye, Margar."
"What is she called?"
He set Alyssa to the floor then slowly perused the room. Alyssa forced her expression serene, and prayed he wouldn't call her what he did more often than not—hellion.
"My wife."
His wife? She wasn't his horse, for pity's sake. She had a name. "I'm called Alyssa," she told Margar, then looked at her surroundings.
A huge fireplace in one end of the great hall filled the air between the smooth brown stone walls with warmth. Rushes on the floor led to three long wooden tables surrounded by stools. Directly across from the entrance was a hallway. "What does that lead to?"
"The kitchen, my lady," Margar said.
Alyssa dismissed that, and continued her sweep of the hall. To the left of the entrance was a screened buttery and an additional two tables that each could seat forty men. "So many tables! Are there that many that we feed, husband?"
He grinned. "Aye."
"The Buchannans are good hunters, I pray."
"None starve," he said in a curt tone.
"What's in that room?" She pointed to the left of the front entry, then further down the same wall. "And there?"
"That is a bathing room, and the other is the chapel."
"A bathing room? Indoors?"
Kevan chuckled. "Aye. Indoors."
"A bathing room indoors," she muttered, turning her attention to the right of the front entry. "Imagine that." She stepped closer to see inside a turret that led to a balcony which circled the hall on the upper floor. "Spiral stairs? I've never seen spiral stairs."
"They are safe, my lady."
It was David who answered her. Alyssa turned, and smiled. "They are wonderful, are they not?"
David shrugged. "They're useful."
She turned and walked back to Kevan. "Your home is unusual, Kevan."
"Our home, Alyssa. You are my wife."
"Yes. I think I shall be happy here."
"You shall."
His arrogance amused her. "Are you certain?"
"I am."
She plucked a leaf from his hair and closed it inside her palm. "How do you know?"
"I'm your husband. I insist you be happy."
Alyssa frowned. "You can't insist someone be happy. They either are, or they aren't."
He gave her a glare that set her knees to shaking. She probably shouldn't correct him in front of his men. "But mayhap you can," she amended. "If you say it's so, then I believe you. You are a man of your word."
His eyes twinkled. He knew she talked not about happiness, but about Duncan. "Do you think I could have a bath?"
"Aye. Margar—"
"The water waits. James told us of your arrival."
Alyssa felt a flash of surprise. "James MacMillian is here?"
"Aye." Kevan acted as if it was of no import.
"Why?"
"Duncan requested I train James."
Duncan had vowed to the MacMillian to see to James's training as best he was able. Kevan was a superior warrior; James could have no better teacher. "And you agreed?"
"I did. Do you challenge my right?"
"Nay," she said, smiling up at him. She stepped closer, and too short to reach his mouth, she pressed her lips to his shoulder. "I don't challenge you, husband. Your kindness is most touching."
"Kindness? You insult me, wife."
He did look insulted. That blasted muscle was twitching in his cheek again. Alyssa frowned up at him. "I was praising you. James is from Cameron. He will ease my homesickness. That's why you brought him here."
Kevan flushed and shouted at her. "I brought him here to train, and that's that. Go. Have your bath, then go to bed."
Ignoring his fit of temper, she crooked a finger at him, motioning for him to bend down. When he did, she kissed him solid on the lips.
Raising her head, she went to step away from him and found she didn't touch the floor. She smiled into the most furious face she'd ever seen. "You can put me down now, husband."
Kevan plopped her to the floor and slid her a withering glare. Her laughter echoed through the hall. "Thank you, Kevan. You are most thoughtful."
"Alyssa," he warned her in a threatening tone.
"I'm going." She called back over her shoulder. "You need a bath too, Kevan. Come."
David gasped and his face turned red as blood.
Margar stifled a cackling chuckle.
Young James muttered, "Aw, hell."
Kevan silenced them all with one scowl. "David," he bellowed. "Clear this hall."
"Aye." He scrambled to do his laird's bidding.
Within minutes, the hall stood empty, save Kevan and David.
"Don't kill her, Kevan," David said. "She's new to you. She doesn't yet know your ways."
Kevan's thick brows knit tight above his eyes. "I won't kill her. But if I have to shave her tongue, the woman will learn to behave."
"Kevan," Alyssa called from her bath. "Come before the water cools."
David swallowed a groan. "She's had no mother, Laird. She doesn't realize her behavior is too . . . too . . ."
"Forward?" Kevan suggested.
David lowered his gaze, relieved. "Aye. Forward."
"She will," Kevan vowed. "And she'll start learning now."
"I'll, um, see that no one enters the hall." David's mumble fell on Kevan's back. "Sweet Christ," he muttered. Kevan wouldn't beat her, would he?
Nay, David assured himself. The laird disapproved of beating women. But then he'd never before been confronted with a woman like Alyssa . . .
Letting out a whistling sigh, David leaned back against the door. "Not a modest bone in her body. Sweet Christ."
KEVAN STOPPED just inside the bathing room door. Alyssa smiled at him from inside the great wooden tub. His stomach muscles clenched. Her skin was wet and her cheeks flushed. A more beautiful woman he'd never seen.
"This is wonderful, Kevan." She splashed her bare shoulders. "Come."
He swallowed a knot in his throat. His chest tight, he stripped off his plaid. He had been angry with her, but just now, the reason why escaped him. She wet her lips with her tongue and his heart thudded in his chest.
He eased into the tub beside her.
"This is clever, to have benches to sit on." The torchlight sparkled glimmers in her hair. "Was it your idea?"
"Nay, Margar suggested it for bathing bairns."
Alyssa blinked. He was looking at her so strangely. His eyes were still hot, but no longer with anger. She knew she'd goaded him horribly, but his people must learn that she was not merely chattel. And Kevan must learn that she didn't intend to be treated as such. Duncan said to follow him, and she would. But in her own way. And with her pride intact.
She lifted a cake of soap from its holder. "Shall I wash you, Laird?"
He swallowed and clenched his jaw. "Husband, Alyssa."
"Aye, I'm sorry, husband. Mayhap I won't forget so quickly once you've bedded me."
His eyes stretched wide. "Being without modesty 'tis a horrible flaw for a woman."
"Only because you expected me to fight you. No, don't deny it. I know you think I'm a hellion, but I'm not. Truly, I'm quite easy to get along with."
He grunted his thoughts on that.
"I am," Alyssa insisted. She soaped a cloth, then rubbed it against his chest. "I know you've not seen much of that side of me, but I can be soft and . . . and affectionate. I've not had much practice at it, but I know I can be."
"Do you always rattle on when you're afraid?"
She stilled and looked up at him. He was amused. She poured out her feelings to him, and the blasted man was amused.
He was also right. Sighed, she looked down. His body shone clearly through the water and he was stiff there.
"Alyssa? Alyssa, would you look at my face?"
On fire, she looked up at him.
"You've never seen a man nude before."
"I have," she said, "in treating wounds. But—but not one so, so . . ."
"Ready?" he suggested.
She splashed her cheeks with water to cool them. "Big was my thought, husband. That's the truth of it."
He laughed, leaned back against the edge of the tub, and closed his eyes. "Wash me, wife."
"Does it hurt?" Her voice sounded pitiful.
He cranked open one eyelid. "What?"
"Such swelling. Does it hurt?"
He gave her a woeful look, but his eyes twinkled mischief. "Aye, 'tis almost unbearable. Come. Ease my pain."
"I—I don't know how," she confessed in a tiny whisper. "There was no one to tell me."
"I will."
"I'll wash you first." She swallowed hard, prolonging the inevitable. Good God, and she'd thought going into battle had been frightening. "Then you can tell me."
She soaped the cloth and set about her task, her thoughts running wild. "Turn, and I will wash your back."
"Save some skin."
"Sorry," she mumbled. "I guess I am a wee bit nervous." She rubbed his strong shoulders, careful of the threads in his wound. Her stomach filled with flutters. Startled, she dropped the cloth. She didn't reach down for it, but smoothed his skin with her hands. Wet and slick, the feel of him had her fighting for breath. Her fingertips tingled, her heart thudded, and she grew mesmerized by the feeling of her hands stroking his back.
With handfuls of water, she rinsed the soap from him. Tiny droplets clung to his skin and the urge to lick them from his flesh overwhelmed her. She bent closer. "Kevan? Is it wrong to—"
His voice was as ragged as his wound. "Nay, wife."
She swept his slick skin with long, lush brushes of her tongue. He let out a groan that sent streaks of heat racing through her. "You taste good," she whispered, then drifted a lazy path across the width of his shoulders and up to the juncture of his neck. His hair, moist with water lay in soft curls and she brushed at them with her hand to reach the sensitive skin underneath.
He trembled, and she eased her way to the soft spot behind his ear and nuzzled. He shuddered. "Is this permitted? For a wife to do this?" she asked in a throaty whisper.
"It is, aye." he murmured, arching his neck to grant her access. "And most pleasant."
He eased his hand around to the small of her back and pushed. Her breasts, so sensitive and full, flattened against his bare back and her nipples crested. She let out a little moan and flicked at his ear with the tip of her tongue.
He groaned her name, tugged, and she found she was facing him, seated on his lap, straddling his thighs. He swirled his tongue around her nipple. It looked distended, and its color had deepened to a dark rose. A tiny pulsing that started in her breast streaked down her middle. Going liquid inside, she vowed she would die if he didn't take her breast in his mouth. When she was sure of it, finally—sweet Heaven, finally—he covered the peaked nub with his lips, and exhaled. His hot breath sent shivers streaming through her; shivers that shattered heat low in her belly. "Kevan, please."
"Please what?" he whispered raggedly against her skin, his hands roaming her back, shoulders to waist. "Tell me what you please."
She dragged her fingers against his scalp and pulled his head down to her breast. "Taste me, Kevan. I—I hurt."
He laved her nipple with his tongue. Her muscles contracted, and she whimpered, tightened her hold on him. With her mouth, she sought his skin, kissing his shoulders, the nape of his neck, his ears—any and everywhere she touched. He suckled hard, tugging her nipple deep into his mouth with a taunting pressure that fairly had her lifting off of his lap.
"So sweet," he whispered against her wet skin, then moved to stand up.
"No." She pressed her body more fully into his. Warm water swished out from between them. "No, don't stop."
"Your first time should be in bed." He gentled the rough rasp from his voice and rubbed her side from her tiny waist, past the flare of her hip, to her silky thigh. "I'm not easy to accommodate, lass." He tugged her down, proving his point.
His hard shaft pushed against her bottom. Still, Alyssa protested. "The fire's too hot. Without the water to cool me, I'll surely die."
He worked his strong fingers gently over her buttocks. "Nay, you won't."
"I will, Kevan," she insisted. "I know I will."
"I don't want to hurt you."
"You won't," she whispered, covering his lips with her own. "You won't."
Her tongue found his and mated. The fire burning inside her grew to a raging blaze that scorched her with heat. Kevan rubbed her flat belly, her tender thighs, and finally . . . Oh, pity.
She spread her legs, welcoming him, and he stretched his fingers up deep inside her. The sensation of fullness made her muscles tense, rebel against the invasion, but the warmth felt so good. Instinctively, she arched against his hand, and he withdrew. About to protest, she felt him lift her hips. She clutched at his shoulders and let him guide her down onto his swollen shaft.
With a guttural groan, he worked his magic. His lips enticed, invited, entranced, at once soothing and fanning the flame burning hotly inside her. He entered her slowly, and catching his rhythm she lowered herself onto him a bit more quickly than he would have done.
"Patience, Angel," he grated out from between his teeth. It will hurt, but only for a time."
Alyssa tensed in his arms, and Kevan soothed her, rubbing her tender opening with his fingers. The skin burned, first to accommodate him, then eager for more of him, and soon, it was she who bucked against him, wanting all of him inside her to squeeze and hold tight.
His muscles bunched under her hands, quivering against the tight control he held on his needs. Alyssa reveled in the knowing. He wanted her to enjoy his body as much as he enjoyed hers. He wanted to bury himself in her flesh, to let her feel the fury of his passion—she sensed it. But he was holding back for fear of hurting, or frightening her. She wished he wouldn't. She yearned to see the mighty warrior lose his control in her arms, to feel the wrath of his passion and the full-brunt of his desire.
She eased until she could stand the waiting no more, then thrust herself down on him. Pain, expected but shocking nonetheless, riveted to her core. She went stiff as a board and cried out.
"I tried to tell you," Kevan whispered calmly.
"This is no time for lectures, Kevan Buchannan. It hurts like hell."
He chuckled. "In a moment or two you won't think so. Don't move, angel. Not yet."
If he thought time would ease this pain, he was crazed. Fighting the tears stinging her eyes, the urge to move off of him, she bit down into the soft flesh at his shoulder.
He cupped her head in his hands and covered her lips in a searing kiss. A kiss that breathed new life into the embers of her desire. As the fever caught her, the pain changed, and an irresistible urge to thrust against him assaulted her. She fought the feelings, but her hips refused to stay still. They demanded she move, becoming more and more insistent, until she gave in to the impulse. Kevan whispered soft words of encouragement and took over, setting the rhythm for the communion of flesh that began with time.
The feel of him stroking her inner flesh sent her spiraling headlong into a world she had never known. The pleasure of their joining had his eyes glazed, his chest heaving with sharp breaths, and his expression hard and intent. The friction of him coming flush against her, of the water lapping at her breasts, coupled with the feel of his powerful shoulders lifting, his muscles bunching and flexing under her hands, driving her deeper and deeper into desire's clutches. She went willingly. Gladly. Gloriously.
The candlelight kissed his sunned skin gold. Her hands trembled, grazing his body. She wanted to touch him everywhere, to mark his body as hers for all time. Giving her wishes free rein, she delved deeper still into desire, so deep she feared she'd never return, and she didn't care.
Too soon, the intense pleasure sent her tumbling. Her heart thundered, her body tensed. The tremors quaking her insides grew to blinding spasms and burst. At the same time, Kevan shuddered, nearly crushing her in his embrace, and deep inside her, she felt him pulse. He, too, had come to this magical place.
Content and as weak as a kitten, Alyssa collapsed against him. He slid his hands from her bottom up her back and wrapped her to him. Nuzzling his way to her mouth, he gave her a long, lingering kiss.
"Angel?" Caressing her name, he sounded pleased.
"Aye, husband." She buried her nose against his neck, closed her eyes, and inhaled his masculine scent.
"You learn quickly."
He was pleased. Tingles of pleasure rippled through her and she smiled into his neck before rearing back. "Aye. But I think we should perfect your teachings, husband. As with any skill, ardent practice is required."
Kevan cuddled her to him and let out a satisfied sigh. "Aye, wife. Ardent practice."
Eight
"I MIGHT HAVE known," Kevan muttered to himself. Where else would he find his wife but on the training field?
He watched her instruct James in the use of a bow. A line of warriors stood nearby, and they seemed to be listening intently. Kevan didn't interrupt, but monitored both her actions and those of his men from where he stood.
A sweat-soaked David joined him. "Morning, Kevan. Sleep well?"
"Aye." Kevan answered, ignoring David's attempt at sarcastic wit. He hadn't slept much at all—not that he'd minded. And David knew it. Kevan nodded toward Alyssa. "How long has she been here?"
David frowned. "Long enough."
"Let me hear it."
"You aren't going to like it," David warned.
"No doubt. But tell me anyway."
"She's instructed Iain that the use of water to secure the wall is archaic and directed him to use heated sand."
Kevan grunted. "I've seen this method at Cameron. It's effective."
David propped his dusty boot on a rotten tree stump. "She told the smith his iron hammerhead is too small—overworking his wrist—and to fashion one half-again as large, but to lengthen the handle only by one quarter."
"Why one quarter?" The woman's ideas, thus far, had merit, though he couldn't tolerate her interfering with his men.
"Too long a swing makes for inaccuracy," David informed him.
Kevan grunted again, and added a sigh. "What else?"
"She's given the men instruction on the use of clubs. Tam laughed at her. Said it'd be a sorry day when he'd be felled by a woman."
"And?"
"And she damned near beat him to death." David swiped his forehead with his fingertip, then flicked sweat onto the ground.
"Tam?"
"Aye."
Kevan grimaced. "But he's good with a club."
David sighed. "She's better. He fell mighty hard, Kevan."
Kevan rubbed his neck. "Is there more?"
"You really want to hear the rest?"
"Nay, but I guess I'd better. The complaints will brush the rafters before nightfall."
"She's nicked a letter on Colin's chest—a B—with her sword. And—"
"And? She brands one of my best warriors, and there's yet more? Christ, the sun isn't even fully overhead."
"There's more," David said, then winced. "But not much. She's told Margar all the women must carry daggers. She'll teach those who don't know, how to use them."
"What?" Kevan rounded on David.
His second shrugged and slid Kevan a look meant to remind him that David was merely the messenger. "She says that should the men be absent and the need arise, it's their duty to defend the Buchannan keep."
"Oh God." Kevan squeezed his eyes shut. His days of peace at his holding were over. And it was his wife's fault. He should have followed his first instincts where the woman was concerned and that was that. She'd have his home stuffed to the rafters with complaints for the rest of his days. Women with daggers? Good God, she'd have his men deserting.
"Aye, she says, too, that women shouldn't be depending on their men to handle matters the women can handle themselves."
His jaw so tight it pained his teeth, Kevan asked, "What matters?"
David turned red from the neck up, and his voice dropped, weak as a bairn's. "Hunting."
"I'll kill her with my bare hands." Kevan started across the field.
"Laird, wait," David said. "Her idea has merit."
Kevan spun back to his second. "Have you lost your mind?"
"Maybe," David confessed, his look saying that siding against his laird when he was of a mind to murder surely had him considering the possibility. "Nay, nay," he amended his position. "I've not. Innes isn't crazy enough to attack your warriors, but he will attack. In some way he'll seek revenge."
"Against our women? Only a coward would attack women." Innes had physically attacked Alyssa already, in the presence of men. Still angry that he'd been forced to let that happen, Kevan prodded. "So?"
"So the women should be able to protect themselves—at least with daggers. Your wife's an able teacher. What will it hurt?"
David had a point about Innes, and the raiders were growing more and more bold. "I'll allow this." Kevan wagged a finger at his second. "But when the first woman raises a dagger against her husband, you'll see what it can hurt, and you'll be duly reminded that training the women was your idea."
Kevan frowned in the direction of his worrisome wife. Standing down-field from James, she shifted her balance from foot to foot. Her concentration on the MacMillian's son seemed intense. She spread her legs and the fabric covering them pulled taut across her thighs, exposing the sweet curve of her hip. She might not be a modest woman, but her immodesty certainly had its benefits. Mayhap he should take her back to bed and remind her who she belonged to.
Kevan shifted his gaze just as James raised his bow and took aim against Alyssa. "MacMillian! No!"
The arrow flew.
Running, Kevan let out a war cry that thundered through the lower bailey and had all heads turning. He saw his wife standing stock still, the arrow in her hand, confusion on her face.
He came to a bellowing halt. "MacMillian!"
James ran to his laird's side. "Aye."
Kevan grabbed James by the shoulders and shook him, doing his damnedest to rattle some sense into the boy. Tiny pelts worried Kevan's back—Alyssa's fists? "Stop it, woman!"
"What are you doing? Have you gone daft, for pity's sake?" Hands on her hips, she glared at him. "Put that boy down." She stamped her foot. "Damn it, Kevan, put him down."
Kevan glowered at James. "You will never, never again take aim against my wife."
Still dangling a good foot off the ground with Kevan's hands clamped around his throat, James gasped, his face blood red from lack of air.
"Kevan Buchannan, you have lost your mind. James didn't take aim against me. I was teaching a lesson. Couldn't you see that?"
"Teaching my men to catch arrows?" Kevan tossed the boy into the grass and planted his hands at his hips. "It's you who's lost her mind, wife."
"Mayhap I have. I married you." Alyssa glared up at him. "You insisted I be happy here. Look at this face. This is not the face of a happy wife." Alyssa stormed from the training field.
With a resigned sigh, Kevan watched her go. "David, tell the men I'll hear them now."
"Don't you want to go—"
"Nay." The woman fairly stomped her way to the upper bailey. "Her collar's a bit warm. It'll take a while to cool."
"Aye, it will," David agreed. "A good, long while."
"Mayhap by the time our first son is born, eh?"
"Mayhap." David grunted. "But I wouldn't count on it."
THE SOLDIERS stood in line. Kevan sat at a makeshift table at the northern foot of the training field. The hall would be a more comfortable place to hear the complaints against his wife—there would be many—but angry as she was, he thought the hall too small for both of them.
Iain was first.
"Your complaint?" Kevan asked.
"I have no complaint, Kevan."
Surprised, Kevan said, "I was told Lady Buchannan gave you instruction."
"Aye, she did," the baldheaded Iain responded. "She has a firm grasp of strategic defense. Her suggestions were—"
"Suggestions?" Kevan interrupted.
"Aye."
"She did not direct you to alter your methods?"
"Nay. But she suggested sand to replace the water. I'm of a mind to agree it's wise. As is her idea of guarding the back wall—"
Kevan rolled his gaze. "The back wall is a mountain, Iain."
"True, but mountains can be scaled, Laird. She told me how it could be done with metal spikes pounded into the rock."
"So you will guard the back wall and use the sand."
"Aye, I will."
Kevan nodded and laced his fingers together atop the makeshift table. "And you've no complaints."
"Nay, nary a one."
"Very well, Iain. You may leave me."
"Laird?" Iain lifted his bushy brows. "May I consult Lady Buchannan on the matter of the lower bailey tower?"
Kevan propped his elbow on the table, slumped over, and rested his chin on his hand. He should have known. "Aye, you have my permission, Iain. Though the lady will be busy for the next few weeks."
"No hurry. I'll wait."
Kevan gave Iain a brisk nod. "Next."
The smith stepped forward.
"Your complaint, Angus?" Kevan asked.
"I have none."
"Then why are you in line?"
"To defend my lady."
"Against her husband?"
"God's truth, Laird, you look more than a mite upset with the lass."
"You aren't displeased with her instructions, either."
"Nay. Don't know why I didn't think of her suggestions myself." Angus shook his head and grunted. "Too used to the old ways, I suspect. And my lady is most concerned about my wrist, you know."
The wrists Angus flexed upward were as thick as Alyssa's neck. But the man seemed pleased to hold Alyssa's concern. Kevan sighed. "If you've no complaint, take your wrist back to the shop and do as your lady bids."
"I just wished to offer my defense," the smith said, walking away. He stopped suddenly and turned back. "Er, Laird? When it's done, may I consult my lady on the hammer?" Looking sheepish, Angus added, "She is most—"
"I know," Kevan muttered, fearing it would always be this way. The worrisome woman had captured more than one heart here already. And why that pleased him, when he ought to be mad as Hell at her for her interference, he couldn't say. "She's concerned about your wrist," he told Angus. "Aye, you may show her the hammer—but not for a few weeks."
The next man hobbled forward. Kevan didn't recognize him, but that came no surprise. Half of the man's face was bruised purple, his bare knee was an ungodly shade of green, and a knot on his upper arm stood raised a full two inches. Still, the man smiled. David had said Alyssa'd beat Tam half to death. Could it be? "Tam?"
"Aye, Laird. 'Tis me." Tam gave him a gap-toothed grin.
Surprise spiked down Kevan's backbone. "You lost two teeth in the battle with your lady?"
"Aye, I did. And more's loose. She done me up proper, now didn't she?"
"I would agree." Baffling. The man didn't seem to resent being beaten to a pulp by a woman. "Do you wish to file a complaint against your lady?"
"Nay." Tam guffawed. "I can't afford to. She'd beat me to death."
The warriors laughed with Tam, but, Kevan noticed, none denied his claim. He groaned deeper. "You, too, wish to defend her?"
"I do." Tam stiffened. "'Tis my own fault, she beat me senseless. I sort of," he paused and rubbed a knot on his head, "made her do it."
"Mmm, 'tis a sorry day, I hear. One fit to be felled by a woman."
Tam chuckled. "It is that. I meant no offense to your wife, Laird. I just didn't think anyone that little could do much damage to a full-grown man. She is a soft-looking little thing, ain't she now?"
Kevan's mouth twisted into a wry grin. "Aye, she looks soft. But she isn't. What say you to that?"
"I won't make the mistake of riling her up again, is what I say. It'll be summer afore my teeth don't rattle and my jaw quits its ache."
Kevan nodded, dismissing Tam.
"Laird?"
"Aye, Tam."
"I granted her no quarter. She bested me, pure and simple. Done things I ain't never seen. Reckon you would let her teach the men some of them?"
This was not what Kevan expected from his wife. "Aye, Tam. I reckon I would. You may ask her. But—"
"I know. She will be busy for the next few weeks."
"Next."
Colin stepped forward.
"Do you defend or complain?"
"Defend," the young warrior said.
"I'm surprised, Colin. I understood she carved a letter on your chest with her sword."
"She did."
"Yet you defend her?"
"Aye."
"Why?
Colin shrugged. "I deserved it. We were sparring, and I got cocky. Careless, I believe she said." He looked awed. "It's like Tam said, Laird. She's so little that I didn't think her any challenge." His expression said he didn't feel that way anymore. "Before I could blink, she nicked a B on my chest. Said it would remind me I was a Buchannan warrior and my laird wouldn't be pleased if my sauciness got my carcass carved."
"Sauciness?" The odd term caught Kevan's ear.
"Aye." Colin frowned. "I don't know the word, but I sure enough got her meaning."
"What say you to that?" Kevan asked.
"She's right. I mean, you'd not be pleased to see me gouged, would you?"
"Nay, Colin. I would not."
"And don't worry about me getting the fever," he hastened to assure his laird. "My lady pasted my wound. Smells rank as the stable, but she says it's gotta be done." Colin took two steps, then stopped and turned. "Laird?"
Kevan let out a massive sigh. "Aye, Colin, you may ask her for instruction in use of the sword."
Colin grinned and stepped aside.
Weary, Kevan dipped his forehead into his hands and closed his eyes for a long minute.
"Get out of me way, boy. I got no time for standing in no line."
Surprised, Kevan looked up. "Margar?"
"Aye. I want me say, if you've time to listen to an ordinary woman."
"You have a complaint against your lady?"
"Aye, I do."
"Speak your piece."
"Lady Buchannan may be a wonder on the training field, but she ain't worth spit in no women's work. I've lived sixty-three summers without carryin' a dagger and I ain't wantin' to carry one now."
"Ah, I see," Kevan said.
Margar shrugged. "Course, that ain't to say the other women shouldn't. If you boys ain't around, I guess we women ought to be able to hold the keep together. But I ain't interested in carryin' myself, Kevan, and that's that."
"Have you spoken of this to your lady?" Kevan asked.
"No, and it ain't likely I will. I'm too damned old to be runnin' around without my hide."
"If you don't want to carry a dagger, I'm sure your lady will understand. Explain your objections to her."
Margar huffed and snapped her jaw shut.
"As to her not knowing about women's work, I'm of a mind that she should learn. What say you to that?"
"Aye, she surely should." Margar nodded. "It ain't right that a woman can't cook. We got no need for a skinny laird. Mountains ain't puny. It ain't right, and that's all I got to say."
"I'm not skinny, Margar," Kevan said in a gentle tone.
The old woman's chin came up. "You ain't been eatin' her cookin' either, now have you?"
"No." He rubbed his cheek to hide a smile. "I'll leave teaching her in your capable hands, then."
"But—"
"Now, Margar. You agreed she needed to learn. She is your lady. She should learn from the most skilled. And you are the most skilled, aren't you?"
"Aye, and you know it," Margar said, thrusting her chin up. She sighed and shifted uncomfortably. "But she ain't likely to wanna learn."
"Oh, she will, Margar," Kevan promised. "She will."
KNEADING A HUGE bowl of bread dough, Alyssa blew back a strand of hair falling forward into her face. That awful man. Making her ache for him, then refusing to ease her pain until she "attempted" to learn women's skills. She'd show him, by God. Anyone could do these mindless tasks.
She squeezed the mixture with her fingers, pretending it was Kevan's vile neck. So he thought she had no value, did he? Well, he'd best think again.
"God, it's hot in this kitchen." Alyssa looked back over her shoulder. "Margar, does this look right?"
The old woman ambled over and dipped her head to look into the bowl. "You've overworked it again. It looks like leather."
"Well, hell. Now what do I do?"
"Start over."
Alyssa groaned. "Again?"
"Again. All I can say, child, is the animals never had it so good afore you started learnin' to cook."
"I'm trying. I just can't seem to get it right." Alyssa dumped the contents from the bowl into a bin. Her first two lumpy attempts already sat there, mocking her. So mayhap cooking wasn't a mindless task. Mayhap it was just trivial.
"Quit your bellyaching and try again." Margar shuffled to the other end of the kitchen, muttering under her breath and shaking her head. "Sooner or later you'll get it right."
It had been the most miserable two weeks of Alyssa's life. Cooking, sewing, washing clothes, cleaning floors. She was sick of it. "Well, it'd better be sooner. I told Kevan I'd cook his meal tonight."
"Oh God."
"Margar! It's your fault I'm stuck doing these idiotic chores. I should be on the training field. I'm getting soft."
"If you think feeding your man is idiotic, you be soft all right. In the head."
Margar dumped flour in Alyssa's bowl. A fine dust settled down the front of her dress. She swiped at it, and the flour from her hands smeared on the garment as well. She didn't bother to complain. Margar was as sympathetic as a stone. "Why do I let you talk to me like that?"
"Because I tell the truth. Ain't no quicker way to soothe or rile a man than to mess with his stomach. And that's that."
"Well, get ready for black thunder, then. I promised Kevan roasted mutton, and if making this bread is any sign, he'll be riled for a week."
"Maybe longer," Margar predicted. "Add some flour. Your dough looks like soup."
Alyssa groaned.
"PSST."
Kevan heard the noise and turned.
"Psst. Over here."
"Margar?"
"Shh!" Margar bent double, her black dress wrinkling in folds over her lean stomach. She looked half-a-beat from stomping her booted foot. "You want she should hear you?"
"Who?"
"Alyssa."
"Why should—"
"Shh! It's you I'm thinkin' about, boy." She motioned with a gnarled hand. "Get over here."
Kevan stepped into the shadowy alcove under the stairs. "What the devil's gotten into you?"
"Here," she said, shoving a cloth wrapped bundle into his hands. "Take this and go outside."
"What is it?"
"Food. Alyssa told me she's cookin' for you tonight."
Kevan frowned and pushed the bundle back toward her. "If she's cooking, the least I can do is eat what she prepares."
Margar arched a brow. "You ever eat anything she's cooked?"
"Nay, but I will tonight."
"Best you hold onto that, then." Margar gave the clothwrapped bundle a pat. "I'll not stand by and watch my laird starve."
"Her cooking can't be that bad," Kevan protested, forcing her to take back the food.
Margar snickered. "It's worse. I ain't never seen such a spittin' mess as that woman makes in the kitchen. The animals are happy, but truth is, some of it even they won't eat."
"You jest." Kevan leaned back against the wall.
"I'm sorry to have to say, I ain't. 'Tis the pitiful truth I'm telling ye."
"Even the animals won't eat it?"
"Not all of it." Margar sighed. "Can't say I blame them, though. Her bread dough could choke a horse—if his teeth be strong enough to get the mess to his throat. And when it's elsewise, the stuff could stick a soul to chewing for a full week."
"A full week?" Kevan swallowed hard and reached for the bundle. "You'd best give that back to me. Like you say, my clan's got no use for a skinny laird."
She passed him the bundle with a weary nod. "Aye. Nor a puny one, to my way of thinkin'." She started to walk away, stopped, and looked at him over her slumped shoulder. "You still gonna try what she cooks?"
"Aye. I suppose I'll have to."
Margar gave him a sympathetic nod. "You're a brave man, Kevan. A mighty brave man."
ALYSSA HAD the mutton on a spit, the bread baked, and a jug of ale full and ready.
"Lord, Margar, I'm more nervous than I was fighting the raiders. My stomach's in knots."
"Nervous about cooking a meal at your age. Pitiful, pure and simple. I guess you can't help it though, with no mama to teach you. But we ain't got time for your bellyaching. Our boys is hungry."
"Those boys are full-grown men. Giants, every one of them."
Margar leveled her with a mutinous look. "I've raised more than half of them from bairns. Be they tall as mountains, they is still my boys."
Alyssa clutched at her stomach. The lass was scared out of her wits. It'd do her good, Margar decided. In the end, she'd be fine. Soon as she learned the value of women's work. But that could take a while. Her lady was a mite stubborn.
Kevan's health was another matter. Well, now, if he ate what his wife cooked . . . Oh, it wouldn't kill him. But he might not feel too perky for a spell.
Wiping a flour film from the table, Margar cackled softly to herself and studied her lady, dusting the flour off of her chemise. She was a bonny lass. Did her laird realize he'd fallen in love with his little wife?
Twasn't likely. His wife didn't realize it. She didn't realize she loved him, either—yet.
Margar smiled to herself. It'd be a sight to behold. Them learnin' what she'd known since the night Kevan had brought his bride home. And it'd be a joy to see her boy tame the lass. Or get tamed. Either way, it'd sure enough be a sight to behold.
"Ready, Margar?"
"Aye. Ready as I'll be gettin'."
Alyssa grabbed the jug of ale and nodded toward the pit. "The mutton is done."
Margar looked at what was once a fine leg of lamb, and winced. "Aye, it is that. Well done."
"Do I look all right?"
"You got flour on your nose. Bring the mutton. I'll go on with the ale."
"All right."
Margar made her way down the corridor between the kitchen and the hall. She stopped at the buttery and filled a second jug. Her boys needed ale—more than she could carry—to get through the coming meal. If they got sotted, mayhap they wouldn't notice what they were eatin'.
Nay, she decided. No one could get that sotted.
When she entered the hall, Kevan and some of her boys were already seated at the table. A grimmer group of faces, she'd never seen.
"Margar," Kevan whispered. "How is it?"
She filled his cup, sighed, then stepped back. "Well, the mutton's charred a beautiful shade of black, and the bread'd make good rocks—if you're of a mind to stone anyone. 'Asides that, everything's just fine."
Kevan swallowed hard, feeling like a condemned man. "What else are we having?"
Margar slid him a pointed look. "Nothin'."
"Oh."
"The ale's all right." Margar pinched her lips. "If I was you, I'd be drinkin' a lot of it."
Silent, Kevan nodded.
When Margar bent to fill the other goblets, Kevan saw a shiny dagger hanging from her belt. He smiled at that. Seemed his wife had a way of making people do what she wanted, whether they wanted it or not. Swaying Margar wouldn't be easy; it never had been. How had Alyssa done it?
Standing at the end of the table, Margar pulled herself up to her full height and stared at the men as if they were still bairns. "I got somethin' to say to you boys, and I mean for you to hear me. If you're of a mind to eat a decent meal around here again, you'd best not hurt my lady's feelings." Margar grimaced, pitting the deep wrinkles in her face. "She's worked hard. She's failed worse than any I've ever seen, but it ain't got spit to do with her effort. So eat hardy, boys. And, later, if you should happen by the kitchen window—and you're still able and willin' to swallow—you might just find a fruit pie or two on the window ledge." She gave them a wink. "Repayment for your bravery."
Seeing Alyssa entering the hall, Kevan coughed and Margar turned around. His lady was struggling under the burden of bringing the heavy platter to the table.
Young James MacMillian took one look at her burnt offering and muttered what every man at Kevan's table was thinking: "Aw, hell."
A table full of glares aimed in his direction had the young warrior's face and neck turning blood red.
Alyssa dropped the platter onto the table with a healthy thunk that jarred many a tooth. She stepped back, gave Kevan a nervous smile, then took her place at his side and anxiously watched the men.
When no one reached for the food, Kevan issued the order, "Eat."
Forks clanged and stools scraped. The men filled their plates. Kevan withheld a grimace at the meager portions. He considered sliding James a reprimanding look for not taking more meat—he was the youngest of the warriors—but the boy sent him such a pleading look, Kevan didn't have the heart to order him to suffer.
Midway through the meal, Alyssa turned to him. "Kevan," she whispered, "have you noticed how quiet everyone is tonight?"
Their stomachs were in revolt and she expected them to talk? He started to tell her the truth, but her hand on his forearm was trembling, and she looked so worried. "Aye." He covered her hand with his and gave her a reassuring pat. "They're enjoying the food." He lied with a good heart and a clean conscience, hoping to Hell she wasn't going to ramble on like she usually did when she was nervous. His thoughts were occupied.
How could he bury his bread in the earthen floor—and not get caught?
The problem was getting it down there without his wife knowing it. He considered dropping it—nothing that heavy could bounce—but it could leave a hole in the floor. He rubbed at his temple, considering it. Nay, that wouldn't work. She'd surely notice a hole in the floor.
He should eat. If he didn't, she'd probably get upset—and Margar would never cook another meal. That thought had him raising his fork. Besides, he really didn't want to get Alyssa riled up again so soon. When he'd started touching her again, it'd taken a week to calm the woman down. She'd damned near killed him. Every time he happened upon her she gave him that look and whispered all soft and sleep-soft sexy, "Kevan, I'm in pain."
His blood stirred at just the memory. Most pleasant, that. No man could ask for a sweeter death, but he wasn't ready to leave her forever. Not just yet.
"How's the mutton, David?" Alyssa asked, then took a sip of water from her goblet.
As he rolled the food around in his mouth, his face contorted and his eyes became glassy. "It's, um, fine, my lady."
His look turned sour and, when he swallowed, he eased his hand to his neck to help shove the stuff down his throat.
"Are you having trouble swallowing?" Alyssa asked, looking worried.
David's eyes bulged. "Um, no, my lady. No trouble at all."
She frowned her concern. "Then why are you rubbing your throat?"
Before answering, David took a large gulp of ale. The spirits, or her unwavering gaze, had his face as red as his plaid. "My throat's fine." He grabbed the pitcher and refilled his glass, then drank like a man half-dead from thirst.
"Are you sure, David?" she persisted. "You look a bit flushed."
Kevan caught David's pleading look. "He's fine, wife. Quit badgering the man."
"Well, he looks flushed to me." Ignoring Kevan's order, she stood up and walked around the table to David, then tested his forehead with the back of her hand. "You've got no fever."
David groaned and reached for his ale. "I'm fine, my lady. Just fine."
"You'd best slow down on that, just in case," Alyssa said, staying his hand.
"Aye."
As Alyssa walked back around the table, Kevan saw her look down and knew she'd noticed Tam worrying something on the floor with his foot. He stifled a groan.
"Is your foot troubling you, Tam?"
Looking guilty as sin, the soldier shook his head. "Nay, my lady."
"Oh," Alyssa said. "You're out of bread. Here, let me get you some."
Kevan knew the thunk he'd heard a moment earlier had been in vain. He hid a smile behind his hand and watched Alyssa serve Tam a large hunk of bread. His look of sympathy joined the others aimed in Tam's direction. After all, the man was short on teeth.
Everyone departed the table as soon as possible, leaving Kevan and Alyssa alone. She bowed her head and folded her hands in her lap. From the movement of her lips, Kevan suspected she was praying. When she raised her head and kept her eyes closed, he was sure of it.
"Well," she said. "Aren't you going to pray?"
"Now? The table isn't my place of prayer."
She turned a baleful look on him. "Mayhap it should be. I've not cooked for your men before. They could use the extra protection."
A fat tear rolled down her cheek. "Oh, Kevan. It was . . . awful."
A hard knot lodged in his chest. He opened his arms to her. "Come."
Alyssa fairly flew to him. She crawled onto his lap and snuggled close. Kevan cradled her to him. The poor lass wept her heart out.
"I tried, Kevan," she sputtered between muffled sobs. "I really did. But women's work is so hard for me. Nothing is precise or the exact same twice in a row, and every time I add flour, it should've been water. I wound up with enough dough to make shoes for half your clan!"
"Shoes?"
With a hefty sniff, she nodded, her eyes woeful. "My dough is tougher than any leather, husband, and that's the awful truth."
She sobbed harder than ever. Her whole body shook against his. Kevan rubbed her back with tender strokes. "'Tis all right, lass."
"And the men were so kind. Not one complaint. They're surely half-starved—those who haven't lost their stomachs. And poor Tam." She let out a wail. "He probably lost another tooth!"
She shuddered and snuggled closer, burrowing into his chest. "Why can't I do it, Kevan? Even Tam's daughter, Maven, can cook—and she's only seven summers."
Kevan lifted his wife's face with a finger under her chin. "But can she use a sword? Has she the mind and heart of a warrior?"
"Nay, I think not. But she can roast mutton without burning it beyond recognition. And she can sew, too." Alyssa sniffed, then sniffed again. "I confess, husband. I can't do that, either."
"Have you tried?"
"Aye, Cellina and Celwyn have tried to teach me." She brushed at her eyes and crawled from his lap.
Moments later she returned with what he supposed was a garment, though he couldn't be sure. Not wanting to make her feel worse, he sat silent until she identified the article.
Her lower lip quivered. "It's a shirt, Kevan. For you. Except I put the sleeve where the neck is supposed to be, and the opening at the bottom somehow—I'm not sure what happened—but it got too small."
"So it did. But 'tis a good color," he offered.
That brought about a fresh stream of tears. "I didn't choose the color."
She threw the misshapen shirt into the fire and watched it catch flame. "Cellina said it was Tam's favorite. And Celwyn said Angus liked it." Her slumped shoulders still shook. "They thought mayhap you would like it, too."
Poor lass. More than likely this was the first time she'd tried and not succeeded. Her spirit was bruised. Deciding he'd take her to bed and soothe her, Kevan walked up behind her and lifted her into his arms.
"Kevan, I'm a failure."
"Nay, love, you've not failed."
She wrapped her arms around his neck. "I wanted you to think me of value."
"I know your value. 'Tis you who's forgotten." He mounted the stairs. "But I'll remind you."
In their chamber, Kevan set her on the floor beside their bed. He cupped her face in his big hands. "Alyssa, listen to me, love. Hush your tears." She lifted her gaze and met his eyes. "Of all your work, one task is most important. Being my wife. And in that, I swear, you have no equal."
THE AMULET at Kevan's neck vibrated against his throat. He motioned to the other mounted warriors, then broke away and crossed the heathered moor. At a distance, he assured himself he was alone, then responded to the summons from the Elder of the Council.
"It is good to see you, Prophet."
"You, too, your grace."
"Is your woman with you?"
"She's my wife." His satisfaction in finally having the right to say those words had his throat husky. His wife. Finally—dear God, finally—Alyssa was his wife.
The Elder nodded. "What progress has she made?"
Again Prophet noticed the weak gleam in the Elder's left eye. Odd, that the right remained flat and colorless. "May I ask a question?"
Elder nodded.
"Your eyes—the left has changed. Why?"
"At this time, that is of no consequence. About your woman—"
Prophet accepted the topic change with a pang of disappointment. The Elder often refused to answer his questions, or answered with a cryptic message that required a lot of thought to decipher.
"She's made remarkable progress in humility, your grace. Just last night, she prepared a meal that has half the warriors suffering stomachaches." Kevan smiled. "She prayed for their protection against her cooking. And tears are common to her now."
"This is good news. Positive progress, Prophet. I am most pleased." The Elder paused and gave Prophet a shrewd look. "But what you are telling me is that she still hasn't learned that all deeds, all things, have value."
Prophet rubbed at the back of his neck. "Unfortunately, that's true. She still considers women's work trivial. But she has learned that it's not easy to master." He recalled how she'd wept at her failure, and how he comforted her. "That is progress, isn't it?"
"Of a fashion." The Elder stroked his beard. "You know, Prophet, a wise man never tries to change the color of the leaves. He accepts them as they are. Yet in their own time, according to season, the leaves do change."
Prophet frowned. "I shouldn't attempt to change Alyssa?"
"Your woman must change, or you'll lose her."
"Then what wisdom is in the message? I don't understand."
"Perhaps the season will guide you. Perhaps." The Elder turned and cupped his crystal. "Seek your message in your destiny, Prophet. Your answer waits there." The Elder faded.
"Kevan?"
Confused, disoriented, Kevan spun around and looked up at David on his horse. Where was his own horse? How had he gotten to the ground? And where were his men?
"Kevan, be you ill? You're pale as a ghost."
"Nay, I think not."
"Young James found evidence someone's scaled the back wall. No one was seen, but 'tis clear someone has passed into the lower bailey. Your wife is already there."
ALYSSA CAREFULLY studied the stones. Faint marks streaked the wall from top to bottom on both sides. She moved on to the nearest tree. Just above her head, the bark was gouged, the new wood not yet weathered. And close by, a slash scarred a little fork. She touched her fingertips to the cut. They grew sticky. Oozing sap, the cut was fresh. A flash of yellow caught her eye. Snagged on a limb was a piece of torn fabric. She retrieved it.
Blue and yellow. Her scalp tingled and she squeezed the fabric into the palm of her hand. "Innes."
Looking for Kevan, Alyssa saw many warriors searching the spiky grass, the length of the wall—the entire area of the breach. She felt a burst of pride for young James. He had a sharp eye to notice the scrapes on the stone wall. Duncan had trained him well.
When she found Kevan, he was in a barren clearing, talking with David. Alyssa stepped to his side and listened.
"I'm sure of it, Laird," David said. "Only raiders would slide the wall."
"It wasn't just raiders, David," Alyssa contradicted him, hoping Kevan wouldn't lose his patience before he listened to what she had to say. The man did take exception to being told even the tiniest things. "It pains me to say it, but it the intruders were Scots."
Silence fell around them, and the men nearby moved closer.
"Alyssa, watch your tongue." Kevan sent her a dark look to match his tone. "What Scot would attack my hold?"
This answer would put him in a rage that'd last a week. "Innes."
Surprisingly, the man's expression softened. "I know you've reason to hate the man, wife. But remember that when you name him, you name my allied-vassal."
"I hate the man, and that's the truth. But he would breach your holding—dishonorably through your back wall, and not through your gates, I might add—and that, too, is truth."
That telling muscle near his eye was twitching something awful, warning her to tread with care. "You're speaking in anger."
She ignored it. "Aye, I am angry, husband. If a dishonorable vassal to my husband isn't worthy of anger, I sure as certain don't know what is. But I'm not being unfair to the man. I have proof."
Skepticism riddled his face. "What proof?"
"This." She held up the torn fabric she'd been clenching. "It's part of a plaid, and the colors are known to me."
"Who wears those colors?" David asked.
Another bloody test. This holding was brimming with them. Alyssa looked up, but not at David. She settled a frigid gaze on Kevan. "Innes."
"Are you sure, wife?"
"Aye, I am sure." So was Kevan. What mighty laird wouldn't know his vassal's colors? He was still testing her, and she was growing tired of it.
"Innes' colors they are, Laird. I've seen them often," Young James joined them, then glanced at Alyssa. "But no Scot would slide the wall, my lady. These men wore boots that left marks for all to see. Only raiders would make such a blunder."
Feeling violated, Alyssa stepped closer to Kevan. "That's true."
"You agree, my lady?" James asked, sounding confused. "But—"
"I agree that raiders scaled the wall. But—though it sickens my stomach to say it—it was Scots what dropped from the trees." She looked up at her husband. "I found the fabric caught on a limb, Kevan. There were fresh gouges in the bark still oozing sap."
David tugged at his lower lip. "So which is it—Scots or raiders?"
Alyssa pressed a hand to Kevan's forearm, surprised at how tense and hard his muscle was when he appeared so relaxed. "They work together," she said. "Their breachings are too near one another. One must know the other's moves."
"Exactly." Grimacing, Kevan turned to David. "Send two warriors to King Edgar. Have them ride swift and on separate paths. Tell Edgar I have declared war on Innes."
"Do you request his aid?"
"Nay, I want to kill the bastard myself."
The black look on Kevan's face had the hairs standing up on Alyssa's neck. "Kevan, you're going to kill your vassal?"
"He breached my holding and my trust. Aye, I'll kill him."
She wondered which transgression Kevan found most offensive.
"But first, I must find him."
"I'll help you."
He gave her hand on his arm a gentle pat. "Nay, you'll stay home."
"But I'm a good warrior. Who'll guard your back?"
"You'll stay home, I said. You're my wife, woman, not one of my men."
"But, Kevan—"
"Damn it, Alyssa, you must stop challenging me. I grow weary of it." He stepped away from her, clearly grappling to control his temper. "Go back to the hall. Return to your women's work and leave us to ours."
Without a word, she turned and mounted Streak. Her plaid draped her shoulder, askew—the knot had loosened—and hot tears burned eyes. Knowing she risked feeling the brunt of his temper, she glared down at him.
An odd feeling slammed into Kevan's chest. A powerful certainty that he'd seen her strike this same pose before—somewhere, at some time, a long time ago. But he couldn't have; he hadn't known her a long time ago.
Mute, she turned her horse toward the keep, dug in her heels, and rode like the wind.
Censure laced David's voice. "She was worried for your safety, Kevan."
"She's my wife. It's her duty to worry about me." Kevan looked from Alyssa back to his men. Their disapproval was evident in their grim expressions. "You want her dead?" he asked them. "It's for her that Innes dares my wrath."
Tam raised his club. "He'll have my lady over my dead body!" The gap from his missing teeth had his words whistling.
"And mine," the burly smith added, flexing his wrist.
Soon all the men were shouting their vows. Their affection for his wife touched Kevan deeply. He well knew she wasn't an easy woman to love.
Though she was usually right, she was the most worrisome little warrior he'd ever seen. She kept him half-crazed, challenging his authority at every turn. Since she'd been here, he'd spent more time pulling her off of the training field than he did training his men. Hell, between that and soothing her pain, what the woman had him was completely crazed.
Thinking he could use a little soothing himself, he frowned and rubbed at the knotted muscles lining his neck. The woman set fire to his blood in every way, and that was the sorry truth. He thought he'd get over this gripping need for her—God knows, he'd tried—but no matter how often he took her, or welcomed her, he wanted her still more. Aye, it was a gripping need—an affliction. But why hadn't the damn thing eased?
He couldn't answer that question now any more than he'd been able to answer it the thousand other times he'd asked it. When the sun set over the mountain and done was done, the affliction burned stronger than ever.
He was getting soft, he decided. Soft and crazed. Nay, she wasn't an easy woman to love. Challenging, opinionated, always telling everyone what to do . . . But, by God, she was his woman. And he . . . he—loved her?
Shocked, Kevan stood stock still. The truth hit him with the force of a sledge. He did love the worrisome woman. How had she made that happen?
What did it matter? Though it proved he was crazed, he loved her. And if Innes wanted to try to take her, let him. The braggart would die.
Kevan saw his horse. "Beautiful," he groaned. Only that worrisome damn woman would name such a beast Beautiful. He guffawed. What laird ever rode a horse named Beautiful?
His answer had him shaking his head. The same crazed laird who loved that worrisome damn woman. And was wanting to know if she loved him back. Frowning at that thought, Kevan rode to the keep.
THE HALL was empty.
Kevan dragged a bench out from under the table, sat down, then propped his head in his hands. What if she didn't love him? The woman was wild in his bed, but that was lust and making love was new to her. Bah, of course she loved him. It was her duty. And, God help him, he knew Alyssa took her duties to heart. He didn't care for the feeling that she loved him out of duty, though. The woman ought to be loving him of her own free will.
Footsteps sounded off to his left. Hoping they weren't his wife's, Kevan looked up and saw Margar coming through the corridor from the kitchen. He let out a relieved sigh.
The old woman looked surprised to see him. "Kevan, why be you here this time of day?"
"I'm thinking." He straightened up and propped his elbow on the table. "Have you seen Alyssa?"
Margar filled a goblet with ale and set it on the table in front of him. "Oh, I seen her all right. She's madder than—"
"I know she's upset," Kevan interrupted. The last thing he needed right now was more trouble.
"Upset?" Margar guffawed. "She lifted the rafters two feet with her curses on your head. If you be thinkin' you can calm her down in a piddling week this time, boy, you'd best be thinkin' again." She pulled out a bench and sat down across from him. "What did you do to her?"
"She didn't tell you?"
"The things she was yellin' ain't fit to repeat. Didn't make a spit of sense, either."
"I declared war on Innes. She wants to fight—"
"And you ain't lettin' her," Margar finished for him. "Why? She ain't worth spit here, but she's a fine warrior."
"Have you gone daft? She's my wife."
"Mmm, and mayhap you love her?"
Kevan stared at her, stunned. "You knew? I only realized it myself."
"If you'd look with your hearts and not your eyes, you'd both be seein' a lot more." Margar stretched out a gnarled hand and tapped his forearm. "If it's consolin' to you, know the lass loves you, too."
"Nay, she doesn't." That truth had him frowning. "She thinks I'm impatient and stubborn."
"You are. But she loves you, anyway. She just don't know it yet."
Seeing Margar was serious, and knowing she was much wiser than he in these matters, Kevan pursed his lips to hold off a smile. "Mayhap I should tell her." Of course the woman loved him. She came to him for comforting, didn't she? Aye, she loved him, all right. She'd damn well better.
"Mayhap you shouldn't." Margar slid him a warning look. "She's too riled, Kevan. If I was you, I'd keep my distance for a spell."
"Mmm, mayhap you're right." He scooted back on the bench, straightening. The rushes under his feet crackled. "Where is she?"
"Out." Margar looked away.
Worry flitted through his stomach. "Out where?"
Margar's look soured. "Training the women with their daggers—and with the bow."
Kevan let out a weary sigh and rolled his eyes back in his head. "She's added the bow. I gave no permission, of course—she didn't ask for it. Why in blazes must that woman always challenge me?"
Looking sympathetic indeed, Margar stood up. "Like I said, she's riled. I'd be lettin' her mull the matter for a while. Your carcass wouldn't look good on a spit."
Kevan bristled. "She wouldn't kill me, Margar. I'm her husband."
"Nay, she'd not kill you. The woman loves you. But she might take pleasure in woundin' you a wee bit. Angry women have their ways of gettin' even, Laird. And that's worth rememberin'."
Nine
FROM UNDER her lashes, Alyssa watched Kevan strip off his plaid and toss it onto a chest. His expression wary, he eased into bed beside her and settled down. He thought she was sleeping, but the man should know better. She was angry. And it was past time he knew it.
"Well, husband. I take it you're through avoiding me."
"I wasn't avoiding you, wife." On his back, he folded his arms behind his head. "I was protecting you."
"Protecting me?" She turned over and looked at him, rustling the quilts. Moonlight streaked his strong features. He wore a lazy expression now, the one that crooked up the left side of his mouth just enough to set her heart to thumping. "You supped with Celwyn and Angus hoping your absence would sweeten my temper—and you know it. I wish she'd turned her bees loose on you."
Kevan looked like he'd been kicked and hadn't seen it coming. But his eyes glinted mischief. "Angus's wife wouldn't harm me. Neither would you. You're much too gentle, unless . . . Alyssa, are you saying you have a temper?"
She glared at him. "Nay, I'm just as gentle as your crusty Margar."
Kevan slid her a wicked grin. "Crusty? She's a fine woman."
"She's a crusty, contrary witch." Alyssa narrowed her eyes at him. "And don't change the subject. I'm angry with you, Kevan."
"Come." He stroked her side, ribs to hip. "Forget your anger. Let's be loving, instead."
She jerked away from him, taking the covers with her. Let the lout freeze. "You ordered me to the hall. I'm more of a mind to take a club to you than to be loving."
"First bees and now the club." He squeezed her thigh. "You know I don't approve of threats, Alyssa. Especially ones made by my wife."
Her skin prickled, and she swatted at his hand. "It's no threat. You'll not touch me, Kevan, and I mean it." A shudder shook her stomach, and she vented the worry uppermost in her mind. "You leave to kill Innes. Without me guarding your back, some raider—mayhap Innes himself—will run a sword through you." Her voice trembled and hot tears blurred her eyes. "So what does your approval matter? You'll be dead, and I'll—I'll be without you."
Kevan brushed at her cheek with his fingertip. "You'll miss me, then?"
Vexed at herself for showing him her weakness, Alyssa snatched the rest of the covers. "Nay, you're a fool to refuse my offer of help. I'll be glad to see your back."
"Mayhap I am a fool," he said softly. "I'll miss you."
She looked to see if he was mocking her, but saw only tenderness. Her heart sank. How could he do this to her? Make her care for him, and then put himself in danger senselessly. "You won't miss me. You'll be dead."
"Even dead, I'll miss you." He held his arms open to her. "Come, be loving. I've a need to hold you."
"I don't want to be held," she lied. She wanted it more than she'd wanted anything in her life. "I want to—"
"Alyssa."
"Nay!"
"You fear my death and yet you refuse to let me hold you?"
Sensing a change in him, she searched his face. His eyes were hot, but they'd gone hard as metal. What right did he have to be angry? "If you die, 'tis your own fault for being stubborn."
"Stubborn?" His shout echoed off the walls.
"Aye, stubborn," she yelled back, matching his fury.
"You're trying my patience again, wife." His voice shook. "I grow weary of your insults."
He grew weary? The man was crazed. Arrogant, annoying, demanding—crazed. She leaned toward him and, nose to nose, asked, "How could I try your patience, husband? You have none."
She plopped back on the bed and turned her back to him.
"I've been very patient with you. But you can only push a man so far."
"You order me around like a serf. Refuse me everything—even a simple ride on the moor."
"I gave you permission to ride."
"With a guard." She punched her pillow.
"To protect you."
"Damn it, husband. If there were trouble, I'd have to protect my guard, and well you know it."
"You're challenging my authority yet again?"
"I'm a woman, not a bairn, Kevan Buchannan. I don't need—"
"You're my wife. Don't condemn me for doing my duty to you."
"I will ride alone. I always have and I always will."
"So in this, too, you'll deliberately disobey me."
The lethal edge in his voice set her spine to tingling, but her pride wouldn't let her back down. "I will ride alone."
"You will not," he said from between his teeth. "What you will do, is follow my lead. My arms wait. Come!"
She didn't move.
"Are you daft, woman? Don't understand your jeopardy?"
"I'm in no jeopardy."
"Aye, you are in great jeopardy," he contradicted her. "Still your tongue and be loving. My anger grows stronger with your every word."
"I'll not do it, Kevan." She plucked at the threads in the quilt.
"Then you leave me no choice but to punish you."
Finally the stubborn lout was getting the message that he couldn't order her around. Alyssa shrugged and nearly smiled. "I've suffered your punishment before, husband. You don't beat women, and not touching me hurts you just as much me—this time, it'll hurt you more. You're the one who wants to be loving, not me. So what will I suffer? I won't, I'd say."
"You'd be wrong, you little hellion. I don't beat women, but I warn you, I've been known to put an insolent lass over my knee. Now this is the last time I ask. Do you come?"
She snapped her jaw shut. "When Hell turns to ice, husband."
Kevan sat up and lowered his legs from the bed to the floor. "You leave me no choice." He looked back at her, his expression black as night. "The fault for what comes is yours, not mine."
Pity, what had she done? Alyssa scrambled up and rushed toward the door.
"Don't do it. Don't even think it."
She stopped in her tracks, looked back, and realized running would only make it worse. She leaned back against the smooth stone wall. Why had she goaded him? She knew his temper! "Kevan, you wouldn't."
"I will." He walked toward her, his jaw set.
"I'm no bairn!"
"Nay, you're not. Your insults were deliberate. And you will suffer just punishment for giving them."
"Kevan, don't do this." Frantic, she licked her lips. "For pity's sake."
He kept coming.
"I—I'll never forgive you. Never."
He spanned her ribs with his big hands. "Aye, wife, you will."
"I'll not." She pushed at him, but he didn't budge. Trembling, she looked up and saw his fierce scowl. Her fear deepened.
"I asked only that you be loving. In anger, you refused. You've earned your troubles, now you must learn their value. I won't beat you, Alyssa, but your backside will well remember this night."
He carried her back to the bed. Sitting on its edge, he stood her before him. "You've challenged my authority, my worth, and my value to you as your husband. You've levied curses on my head, wished me ill, and tried my patience more often than you've blinked. I've tried explaining this through my treatment of you, but it's clear that you must learn it for yourself. There are two kinds of pain. Both are meant to punish, but only one is inflicted for good reason, with honor and respect. The other is inflicted to embrace anger. You refuse me the pleasures of loving to torment the need in me for you. It's just that you suffer both pains. Then you'll see how they differ, and I pray you will not soon forget the lesson." He grimaced. "I take little pleasure in this, but it, too, is my duty. I won't neglect my duties to you."
With a gentle hand, he loosened the ribbons and her nightgown slid down, puddling at her feet. He tugged at her hips. She struggled, but within seconds, she was draped across his thighs, her face brushing his calf. "Kevan, no."
"I wanted only for you to follow my lead. Only to protect you and be loving with you. That's all I wanted."
The emotion in his voice struck her deep. She thought back, and everything he had done, he had done for just those reasons. She suddenly felt overwhelmed with shame. He'd acted honorably from the start. He'd tested her to learn her ways. She'd tested him, she'd thought, to prove her worth. But she hadn't. She'd meant to best him. "I was wrong. Punish me, Kevan. Give me back my honor."
Kevan stared at the back of her head, admiring her more in that moment than ever before. Even now, she remained a warrior at heart. Though the task turned his stomach, he lifted his hand, and did his duty.
When it was over, he stood her up, turned his back, and stared out the window.
Alyssa cried in earnest, but she had begged no mercy. Her backside still stung, yet she knew he had held back. Not once had anger crossed his palm. Most importantly, she'd regained her honor, without costing him his.
His shoulders were slumped. "Kevan?"
He turned and she saw the pain in his eyes. "I never want to do that again. You're my wife, Alyssa."
She eased her arms around his waist and leaned against his chest. "I know. You lead me to protect me. I know the difference now. And no anger has the power of pleasure."
He pulled her closer, tighter, and shuddered, his warm breath fanning her neck. "Nay, love. No anger has that power."
He kissed her tenderly, then released her and returned to their bed and stretched out. God, he was a beautiful man. Virile and strong, and the look in his eyes was so . . . possessive.
"Come." He lifted a hand.
Wasn't he finished? Her heart slammed against her ribs. Her knees grew weak. But she did as her husband bid, and prayed her backside wouldn't regret it. She lay down beside him on her stomach, braced herself—and waited. Trust. He was testing her trust.
The hands that touched her now were gentle, soothing. And the lips that followed them gave loving kisses to tend the flesh he'd made sore.
His voice was thick, husky. "Turn over, wife."
Desire burned in his eyes, but she saw pain there, too. What he had done to her, he'd done in duty, but it had brought him no joy.
He rolled onto his back and opened his arms. "Come. Be loving."
She met his embrace. He caressed her body with kisses until she thought she would die if he didn't give her more. When it finally came, his entry was powerful, their mating, wild and abandoned. She strained to satisfy a need for him that burned beyond desire, its pressure building stronger and stronger in her center. More and more dense. She cried out to him. "Kevan."
His steady thrusts grew rampant, frantic. She couldn't hold back. The tremors racking her body stormed to shudders. His body tensed. She heard his primal cry. Felt the full, round swells of his buttocks grow hollow with his last explosive thrust. And deep in her womanhood, she felt him pulse, filling her with his seed.
"Husband," she breathed against his lips, then settled into a loving kiss.
Kevan let her have her way, but when she released him, he reclaimed her sweet lips. He demanded this kiss be different than any he'd given her before. This kiss was meant to touch her mouth, aye. But he also meant to touch her heart.
He must now repay his debt to her. With grace, she had accepted her destiny. And in loving him from her heart afterward, without anger, without resentment, she had eternally captured her husband's soul.
DURING THE NIGHT, Alyssa grew chilled and reached for her husband to steal some of his warmth. "Kevan," she mumbled.
When she found her bed empty, she came fully awake. "Kevan?"
"Here, love. By the window."
"What is it? Are you ill?"
"Nay, 'tis nothing, love. Go back to sleep."
He didn't sound like it was nothing. Alyssa crawled out of bed and went to him. The floor under her feet was cold, and she shivered. "Kevan?"
He wrapped her in his arms. "You should be in bed. In no time you'll be chilled to ice."
"You'll keep me warm." She snuggled to him. "What's troubling you?"
"We leave in the morning for Innes's holding. I'll be taking young James with me."
"Young James, but not me." She failed to keep disappointment from her voice.
"You must stay home." His hand brushed her bottom, and she winced. "Does it hurt overly much?"
"Not overly much." She looked up at him and asked the question she should have asked him before. "Why can't I go with you?"
He pressed his lips against her forehead. "You must defend our home."
Alyssa blinked. "That's why you want me here?"
"I want you safe. But you are a skilled warrior and, if the need arises, who better than you to defend my people?"
He did think her of value. A knot swelled in her throat. "I'll miss you."
"You're not going to challenge me?" There was pleasure in his voice.
"I think not. You're a most convincing husband."
Kevan frowned. "I hope that means I'll never have to discipline you again. I want—"
"Only to lead me, to be protective, and loving." She nodded. "I remember. And I, too, prefer pleasure to pain."
Kevan smiled down at her. "You're not angry with me."
"Nay, you didn't do it to be cruel. 'Twas your duty." She stroked his jaw. "And I think that this punishment, too, hurt you more than it did me—though you'll not have my trouble sitting down for the next few days."
His eyes twinkled. "You are in pain, love?"
She gave him a woeful look. "Aye, husband." Raking his bare thigh with her fingertips, she let her hand drift up under his plaid and captured him. "Unbearable pain."
THOUGH ALYSSA prayed it wouldn't, dawn came.
She had hoped to see tinges of pink blend with lavender and gold, but when she looked out of her bedroom window, it was an angry sky she saw. A blanket of slate, swirling amid thick patches of dense fog and forbidding masses of burgeoning clouds.
Resisting the urge to bury her head beneath the covers, she swallowed a knot of apprehension and looked across the room. Kevan was preparing to leave. God, but he was big. And powerful. That he could inflict pain didn't surprise her. But how could such a massive man be so tender and gentle?
His scent clung to her skin. She inhaled deeply and watched him belt his plaid and slide his dagger into place. His hands were strong and able, agile and quick. They were hands she depended on, hands the Buchannan clan depended on, and she trusted them. Completely.
He reached for his sword and a thick shock of dark curls danced on his neck. She remembered the silky feel of them in her hands. "Kevan?"
He settled his sword and looked up at her. "Aye?"
"Something has worried me overly long. May I ask you about it?"
He stopped and waited, granting her his full attention.
"The day we wed, who was the white-haired man in the wood?"
He looked puzzled, his brows arched in question. "What white-haired man?"
"I wasn't spying, but I was there. I saw you talking with him."
"I spoke with no white-haired man there, Alyssa. I know no white-haired man. But I did find myself in the wood, and—"
"And?"
He looked wary. "I don't know how I got there. I remember hearing hoofbeats, but—"
"They were Streak's," Alyssa said. "I'd ridden her hard and stopped there for her to rest. If you don't want to tell me who he was—"
"I don't know who he was. Or if he was. One minute, I was talking to David near the fire, the next, I was standing alone in the wood. I vow that's the truth, wife. I spoke with no white-haired man."
Alyssa measured him with a level look, never doubting his honesty. Kevan Buchannan would never swear on a matter he knew was false. "Where did you get your amulet?"
Kevan palmed the crystal. "I don't know. I've always worn it."
"Duncan has one like it," Alyssa said. "He began wearing it the day you made him lord of Cameron."
"Where did he get his?"
"I thought you'd given it to him."
"Nay. I've never seen another like mine."
She crossed the room and rested her head against his chest. The chill night air smelled fresh and crisp. "Duncan said you were special. He believes in angels, you know." She looked up at Kevan. "I do, too."
"You think I'm an angel?" He smiled down at her.
"Nay, love, you're too wicked in bed to be an angel. You're most definitely a man. But I do think you might keep company with an angel." When he didn't accuse her of being crazed, she went on. "I think the white-haired man is an angel. You seemed to know him well, except—"
He stilled at rubbing tiny circles on her back. "Except what, love?"
Alyssa frowned. "I couldn't hear everything, but he called you by another name."
Kevan tensed. "What did he call me?"
Alyssa reared back and watched his eyes for any flicker of recognition. "Prophet."
Kevan was silent for a long moment, then shook his head. "It means nothing to me." He shot her a worried look. "If this happened, then why don't I remember it?"
"I don't know. But I do know what I saw and didn't see."
"Didn't see? That's an odd choice of words."
"Not really. What I didn't see was truly odd, though." She licked her lips, then whispered to lessen the shock. "Kevan, the man had no eyes."
"No eyes?" Kevan squeezed her. "Have you been tipping the jug, wife?"
"For pity's sake, you know I never touch spirits. My father—"
"Mayhap you should. If you see angels with no eyes without ale, mayhap with it you'd—"
"Stop it," she interrupted. "I'm telling you the truth. Doesn't it concern you that you've spoken to a man you don't recall? To a man who's clearly not a man?"
"I don't remember it. To me, it didn't happen."
"But it did happen, Kevan. I saw it happen."
He let her words settle between then, then cupped her face in his hands. "I don't know what it means, love. But if the man is an angel, then we must have faith that he means us no harm." He touched his lips to her forehead. "Now, I must go. My men wait."
Alyssa released him and stepped away.
"Walk down with me?" He held out his hand.
Her heart in her throat, Alyssa took it, laced their fingers together, then they started down the stairs. "At Cameron we have a tradition. We toast our men going to war. May I do that here?"
"If it pleases you." Kevan left the steps and started toward the door.
She smiled up at him. "It does."
He lifted her hand, pressed it to his lips, then opened the door.
Outside, a messenger covered with dirt and grime met Alyssa and Kevan on the keep's landing. A spark of recognition niggled at her. Dark circles under his eyes and the slump of his shoulders told her that the man was tired. He must have ridden hard. She didn't know him—that she was sure of. Yet she had seen him before . . . somewhere. The battle, mayhap?
The guard fidgeted under her gaze and addressed Kevan. "Laird, Innes and the raiders have joined forces—just as Lady Alyssa said. They've attacked the MacMillians. Word is they've killed the lord."
Alyssa gasped, caught Kevan's arm in a death grip. "Oh, God, James."
"He knows about his father," the messenger told Alyssa, then turned to Kevan. "He's saddling your stallion now."
Minutes later, Alyssa handed the mounted warriors bundles of food and goblets filled with ale, then climbed the steps to the front door of the hall. She turned and smiled at the men, but her lower lip quivered. "You're precious to your people. I charge you to take care and return home safely."
The men drank their ale, and Margar swiftly gathered their cups. When she returned to Alyssa's side, Alyssa again addressed the warriors. "And don't worry about your food. I didn't cook it."
Laughter filled her ears, and she sought Kevan. He was smiling down at her from astride his beautiful stallion. He looked magnificent; strong, virile, and loving. It was a picture of him that burned into her memory, and claimed its own corner of her heart.
She gave Beautiful's silky neck a gentle pat, then stepped to her husband's side. "God speed."
Kevan bent down and kissed his wife. Her lips were soft, open, and giving, drawing him, and he surrendered to her kiss.
Hearing whistles and cheers, he raised his head. Alyssa sat full in his lap, smiling up at him. He stroked her cheek with his thumb. "I've need to say something to you, wife. I wanted to wait until we were alone, but I must say the words now—before I go." He looked deeply into her eyes, his own full of conviction. "I love you, my lady. I always will."
"Oh, Kevan," she cried, her eyes filling with tears. She wanted to tell him that she loved him, too. But she'd never felt love and, though she felt much for him, she couldn't be sure it was love. She'd not sin against her husband by lying to him—even unintentionally. "Come home safe to me."
He nodded and set her to the ground.
As the men rode off, she walked among them. "Tam!" she called out. "Don't mix your food with anyone else's. Yours is soft, to not annoy your loose teeth."
"Aye, my lady." Tam chuckled. "'Tis truth they still rattle."
"A reminder to use both ends of your club."
Alyssa turned and saw James. She flagged him down. Her heart ached at the pain etching his face. "Try not to worry, James. Rumors of death are often not true. Until you settle your doubt, have hope. Elsewise you could grow careless." She took his hand and pressed it to her face, tears slipped to her cheeks. "I can't lose you, too. I've buried too many of mine already."
James blinked hard. "I'll take extra care, my lady, to spare you distress."
"When you see your father, give him my wishes for his good health. I don't believe him dead, James. I don't know how I know this, but I do. Your father is safe."
"If you believe it, then so will I. I'll give him your message."
Alyssa nodded and watched young James ride away. Seeing the smith cross her path, she brushed at her wet cheeks and yelled out. "Angus, have a care with your wrist! Bind it before battle!"
He grinned at her and waved the strip of cloth she'd given him the night before. "I will, my lady."
"David!" she shouted as he passed. "David! For pity's sake, guard your laird's back—and your front! You're a demon like your laird, but I've grown used to you. If I lose what's mine, you'll suffer my wrath!"
"You're a true Buchannan, my lady. As selfish as the laird himself."
"I'll have your word." she shouted. "And if you fail—your hide."
"You have my vow," David yelled back over his shoulder and gave her a silly grin. "I know, we're precious to our people—and to our lady!"
Tears clogged her throat. "Aye," she whispered. "Aye."
A horse whinnied and Alyssa turned. Kevan looked down at her from astride Beautiful's strong back. "And what are your instructions to me?"
"Come home, Kevan." She looked up into the most tender face she'd ever seen. Her heart shattered. The danger he faced was for her. "Just . . . come home."
"You have my vow—and my love." He brushed a tear from her cheek. "Protect my people and my home, wife. And, if you've time to spare, pray, use my absence to practice your cooking."
Alyssa laughed through her tears, silently vowing to put her heart to the task. "Aye, you wicked man. I will. Hurry home to me."
Ten
"ALL RIGHT, ALYSSA. Enough is enough." Margar thrust a wooden bucket filled with soapy water into her lady's hands. "You've been bawling like a sick sheep for two days. 'Tis time to get to work."
"I have not," Alyssa protested, then flushed with guilt and took the bucket. Water sloshed onto the hem of her skirt and splattered on the floor. "Just two nights."
"Finding your bed empty ain't pleasant, I know. But you're the laird's lady, and you ain't setting what I call no fine example."
"I've done my work."
"Aye, you have. With not a wink of a smile for no one, nor a kind word neither." Margar muttered and swiped at the air between them with her hand. "I thought you had courage. But you ain't got spit."
"My husband's off fighting a war—my clansmen—and you want I should laugh and be happy? Kevan could be dead as we speak."
"So you miss your man. You think the rest of the women ain't missin' their men, too? What about Cellina? Her Tam's with Kevan. So's Celwyn's Angus. But they ain't borrowin' trouble, child. And you shouldn't either. Enough'll find you without your lookin' for it."
Alyssa worried her lower lip with her teeth. Kevan had left his people in her care, but she'd been so lost in her own worries, she hadn't considered the worries of his clan. She'd insulted his people. Her people. Would she never learn? Looking down at the bucket near her feet, she said, "What should I clean?"
Margar sent her a shrewd look. "Your heart still ain't in women's work, is it?"
"Nay, I confess, it's not. But I have learned it's not easy work."
"Still, you think it ain't important."
Alyssa shrugged and looked down at the floor.
"I be talkin' to you, my lady. The least you can do is look at my face."
Alyssa snapped her head up. "Don't scream at me. I feel what I feel."
"Aye, there is your feelin's to consider. You can't help it if they make you stupid."
"Stupid?" Alyssa glared down at the old woman. "I'm not stupid."
"You can't cook, leastwise not without making my boys sick for days. And you can't sew, except for wounds. You can't even clean worth a spit." Margar's hands settled on her hips. "I say you be stupid."
"Margar, I'm getting angry with you," Alyssa warned. "All right. So I can't do those things. But even Kevan agrees I have value. I can do other things."
"Beddin' your man and doing a fine job of that don't take sense, Alyssa Buchannan. That you do with your heart." The woman thrust out her pointed chin. "You be stupid."
"What do you want from me, you old witch? You know I've tried. It isn't that I won't do women's work, I—I can't do it!"
"Aha!" Margar slapped her thigh. "Now we're getting somewheres. Sit down, child. Now, this old witch is gonna help you."
Alyssa dropped to a stool and propped her elbows on the table. "You've been helping me, Margar. I just can't do those things. I hear you, but somewhere between my mind and my hands your instructions get warped." Alyssa groaned. "Mayhap I am stupid."
"You are." Alyssa shot her a surprised look, and Margar nodded. "I told you, you was. Would I lie to my lady?"
"Well, you don't have to sound so bloody happy about it."
"Oh, but I am happy, child."
"Why? Do you hate me? Is that it?"
Margar sat on the stool across from her and bent over the table. "No, child. I couldn't help you until you'd help yourself. Think for a minute. What would happen if no one did women's work? Tell me."
"There'd be nothing fit to eat."
"Aye, what else?"
"Everything would be filthy. The keep wouldn't be fit to live in."
"Aye, go on."
"We'd all be without clothes. No one would sew."
"Some of my boys might enjoy that for a while," Margar cackled, "but come winter, they'd get a mite chilly. What else would happen?"
Alyssa considered, but could think of no other consequences. "I don't know."
"You've forgotten the most important thing we women do in our work."
Alyssa frowned. "What?"
The old woman's eyes grew misty. "We give our care, child. A bit of our hearts goes into fixin' meals what fills the stomachs of ours. Into the stitches we make with the needle and thread for them." The old woman smiled. "Now you tell me. Ain't that important?"
Alyssa lowered her head. "I—I guess I never thought of women's work quite that way. But it's true, isn't it?"
"Every word, child."
The old woman rested her hand on the table. Alyssa really looked at it for the first time. Margar's fingers were crooked and bent, her knuckles, raw. Her skin was angry and red, irritated from too many hours in water and from exposure to the harsh, Highland winds. The tips of her fingers were nicked with cuts and her nails were jagged. Yet with all their flaws, Margar's frail-looking hands were as strong and able as Kevan's.
Both gave love.
Alyssa lifted the hand she'd studied and pressed it to her cheek. Tears burned her eyes, and she slid from the stool and buried her face in the old woman's lap. Margar stroked her hair with a gentle touch.
"I'm sorry. You knew your value all along. Yet, fool that I am, I had to be told."
"'Tis all right, child. My heart's got a good home in you."
Margar patted the tears from Alyssa's cheek with the edge of her sleeve and smiled—then she slapped Alyssa.
Stunned, Alyssa cupped her stinging cheek. "Why did you hit me?"
"You called me an old witch, you little hellion. Even my boys know better than that."
Alyssa's laughter echoed through the hall.
"Them tables is filthy," Margar said sliding from the stool and disappearing down the corridor to the kitchen. Her voice carried back to Alyssa. "Best get 'em scrubbed."
"Aye, Margar, I will."
LATER THAT DAY, Alyssa turned her full attention to Margar's instructions, determined to confront the enemy kitchen like she'd confronted the enemy raiders on the battlefield. She'd succeed in preparing something edible or die trying, and that was that.
"Well," Alyssa looked at Margar, dancing with excitement. "Is it fit to eat?"
Margar broke the bread and sniffed it.
"What are you smelling it for?" Alyssa asked impatiently. "What I want to know is if you can swallow it."
"In any work, you gotta use all your senses, child. Would you ride into a stable smellin' of smoke?"
"Are you daft? Of course I wouldn't."
"Well, you don't go eatin' without sniffin' first either. 'Afore it gets to the mouth, it's gotta pass the nose. If it don't smell good—"
"It'll not get to the mouth," Alyssa finished with a smile. "You know, Margar, I think if I thought about women's work like I do men's, I would do better. What think you of that?"
"Mayhap you ain't stupid after all."
"So how does it smell?"
Margar grinned. "Good enough to eat."
She took a bite and swallowed. "A wee bit tough. But it ain't bad. I've served worse myself—in my younger days, of course."
"Of course," Alyssa agreed. "And the mutton?"
"Well," Margar said, looking down at the roasted meat. "It ain't black. That's a good sign."
"Sight before smell, eh?"
Margar's blue eyes gleamed. "You be learnin', child." She sniffed the meat, popped a bite into her mouth, then chewed slowly.
Alyssa held her breath, and when she couldn't bear to wait another second, groaned. "Well?"
"In a minute," Margar said, shushing her with a slap to her forearm.
"The waiting is making me crazed. Is it so tough you can't swallow?"
"Nay." The old woman grinned. "'Tis so good I don't want to."
Alyssa beamed.
WEARY, ALYSSA went to bed with a bittersweet heart. Her progress in women's work had made her proud, but her worry about her men overshadowed her pleasure. Where were they? Was Kevan safe?
She whispered a prayer to her Maker, pleading that all would return home upright in their saddles. Pleading that Kevan's angel, the white-haired man from the wood, would keep watch over those close to her heart. And pleading that David would keep his vow, guarding Kevan's back and his own life, as well.
In the middle of her lengthy plea, Alyssa gave a great yawn, and her lashes fluttered to her cheeks.
Late in the night, Alyssa tossed and turned, hovering somewhere between wakefulness and sleep. Again and again, she saw the face of the guard who had informed Kevan of the attack on MacMillian. His sharp features, the dark circles under his eyes, haunted her. Where had she seen him? Where?
And then she knew.
"Oh God!" Screaming, she jerked awake and bolted froth her bed. "The guard! Dear God, the guard!"
Eleven
ALYSSA SHOOK Margar's shoulder.
Margar slung the bedcovers back. A dagger flashed.
Gasping, Alyssa jumped back. "Margar!"
The old woman groaned. "What the Hell be you doin', child? Tryin' to get yourself killed?"
"Margar, listen! It's a trap! The men, the MacMillian's attack. 'Tis here. Innes will attack here!"
"What?" Margar sat straight up.
"The guard who sounded the call. I remember him. He was Innes's man. When Kevan called up his allied-vassals, I saw him at Cameron. He came into the hall to warn Innes of a storm."
"They'll not attack till morn," Margar predicted, her blue eyes gleaming. "But you be the warrior. What do we do?"
"You mean to help me defend the keep?"
"Ain't no man gonna run me outta my home without me takin' a bit of his hide with me." Margar got out of bed and reached for her plaid. "I been practicin' with my dagger. And with the bow."
Alyssa wanted to laugh. Margar's insistence that'd she'd touch no weapon had been fierce. But Kevan was right. The contrary witch had a soul of gold.
"Well," Margar asked her. "Ain't you gonna rub my nose in it?"
"Later," Alyssa promised. "Right now there's too much work to do."
TOGETHER ALYSSA and Margar woke the keep and ordered everyone—men, women, and children—to the hall.
When they'd gathered, Alyssa studied them. There were few men in the group. After praying for divine intervention, she told the clan of her suspicions.
"Silas," she addressed the warrior she knew to be the most able horseman. "Ride tonight. Find your laird and inform him. Have another man go on to the MacMillian. Tell him Lady Buchannan requests his aid. Make sure you tell him it is me and not Kevan who calls. If I'm wrong—which is possible—I'll not make my husband look a fool, save for marrying me."
Silas crossed his heart with his hand. "I'll leave at once, my lady."
"Tell your laird I expect they will test the back wall. But have a care leaving, Silas. They no doubt have guards elsewhere."
"I know." Silas grinned. "My hide is precious to you."
That he didn't challenge the orders of a woman pleased Alyssa, and she smiled. "Aye, Silas. It is that."
Silas left the hall. Many of the women were sniffing, crying into their plaids.
"Cease your weeping!" Alyssa bellowed. "You are Buchannans. Do not shame your laird with weakness. Honor him with your courage."
"But we don't know what to do."
"I know you're afraid, Celwyn," Alyssa told Angus's pretty wife. "But fear has its value. It will keep you cautious. You all have been taught to use the dagger and the bow. In battle, anything can be a weapon. Don't stop to think. Let instinct guide you."
"But, my lady," Celwyn interrupted. "We're women."
"Aye, we are." Alyssa smiled. Scanning, she made eye contact with every woman in the hall. "An advantage, I would say. We have the skills of men—and the cunning of women."
Margar cackled. "Innes will rue this day."
"Aye," Alyssa agreed. "The bastard will that."
"I'll get food ready. Women, too, will need strength for battle."
It was Tam's daughter, Maven, who spoke. Alyssa smiled down at her. Only seven summers, and the lass was thinking clearly. She'd grow to a fine woman in the Buchannan clan. "That's a good idea, Maven. And, if you would, boil some water. As much as you can."
"I will," Maven promised. She called to three other lasses, and they left for the kitchen.
"There aren't enough of us to guard the holding, Lady Alyssa," Angus's son Patrick said. "What say you to that?"
"You're right. But we can protect the upper bailey wall, defend the keep."
"What about the people in the lower bailey?" one woman asked.
"Bring them inside the upper wall. The animals, too. I want no provisions left for Innes and the raiders in the lower bailey. But, pray, we must be quick to prepare. If not the comin' morn, Innes will surely attack the next."
"I'll rouse the lower bailey," Celwyn said. She turned to Patrick. "You see to the animals—and don't forget my bees."
Alyssa listened as the women began making plans. It surprised her that before executing them the women and the warriors sought her permission. She whispered a prayer to her Maker that the women and children would be more cunning than Innes was skilled, that their desire to keep their homes safe would outweigh the advantages of Innes's warriors. And most of all, she prayed that Kevan would not be long in returning—for Alyssa Buchannan, his warrior wife, was terrified.
That day, spent busy in preparation, passed without incident. By moonlight, Alyssa rode Streak around the inner perimeter of the upper bailey wall. Women were posted every six feet.
Having abandoned their dresses, they had donned shirts and their plaids. Sand was hot and ready. So was water—just in case. Arrows were lined up and waiting, as were the odd household items the women had chosen to have at hand.
At first Alyssa couldn't fathom what use vats of honey would be, nor the vats of dye that had been brought into the hall earlier that morning. But the most strange of the household items she saw collected were brooms. Almost every woman had brought hers. What use were brooms against swords?
What use, indeed. She shook her head and kept riding, paying close attention to the back upper bailey wall. Every third guard was a warrior, fully armed. Some of the older children were there, too, aiding the women and warriors. The rest were minding the younger children in the upper rooms of the keep.
She rode through the lower bailey, then slid down from Streak's back and took her position behind a tree. Her defense strategy was bold. But if her plan failed, the empty cottages would be razed, and the animal pens and the stables destroyed.
Fear churned in her stomach. She prayed that Silas had reached Kevan. It would take another day before Silas would reach the MacMillian, and then two days for Kevan to return.
If these women were warriors, they would stand a chance of defending his home until Kevan returned. But they were not warriors. They were mothers and wives—at best, poorly trained to defend. How many of them would have the heart to kill a man? How many of them would die . . . ?
The alarm sounded.
The back wall of the hold had been scaled. Thank God, near the copse of trees.
Alyssa gave thanks to Duncan for training James so well, for warning her that dishonorable men would attack at night. And thanks to her Maker for blessing them with the light from a full moon that made slipping silently from tree to tree much easier.
Even in the semidarkness, the raiders were easy to see. They dressed like the English and were more noisy than a pack of hungry wolves just starting to feast. Innes's men wore plaids—though the scum wore not their own, but the colors of the MacMillian. Wondering where they'd gotten them worried her spine with shivers.
An owl's call caught her attention. All of the men coming over the wall were now inside. The women must move quickly, before the attackers spread out. Alyssa gave the responding signal and moved.
"Innes," one of the raiders called out in an elevated whisper. "The ground is sticky!"
Alyssa let out a war cry. Honey rained from the trees onto the men. Instantly, there was confusion. The men twisted and jerked about, their shouted curses filling the brisk night air.
The women dropped from the trees and ran for the gate to the upper bailey.
Alyssa waited the agreed time, then screamed at the top of her lungs. "Celwyn! Margar!" Then she called out to Tam's wife. "Cellina! Now!"
Hearing the swarm of bees, Alyssa turned and whistled. Goose bumps prickled her flesh. God, she hated bugs, but for the bees, she must feel grateful. She glanced at the men fighting Celwyn's bees, swatting and swinging wildly. Celwyn had said that bee stings could be painful, and, considering the screaming going on, Celwyn was right. But Alyssa denied the men even a pang of pity. They were attackers and deserved their due.
Streak nudged Alyssa's side, and, mounting, she shouted, "Patrick?"
"We've got them on the run to the loch, my lady. Kathleen will return Margar to the keep."
Margar wasn't too happy with the idea of mounting a horse, but she didn't complain overly much. Alyssa was grateful for that.
At her side, Alyssa warned, "You know this is just the beginning."
"Aye," Margar agreed, cackling. "But 'tis a fine one. Bee stings can be very painful, child."
"Especially so many of them," Kathleen added.
Alyssa nodded and rode hell-bent-for-leather toward the loch.
Duncan's creed crossed her mind. "Flaunt not your abilities. Being physically inferior, surprise is your strongest defense."
Well, Celwyn's bees had indeed been a surprise. When she'd suggested the idea, Alyssa and the male warriors had thought Angus's wife crazed. But the idea had more merit than any other—and less risk of injury—so Alyssa agreed. And once their wives gave them a good talking-to, the men weren't overly opposed. The bees had been effective in immobilizing the attackers—and in sending them running for the cold numbing waters of the loch.
Alyssa smiled and bent low against Streak's neck. No doubt what waited for them at the loch would come as a surprise, too.
As Alyssa dismounted, she heard the first splashes—and the first order to fire. Strategically positioned, the women let loose on the raiders and Innes's men with a barrage of arrows.
In no time the men were crying retreat.
BACK INSIDE the upper bailey, Alyssa gave Streak her head and turned her own thoughts to the uncertain future. How many attacks would there be before Kevan returned? Against how many attacks could the women defend? And at what cost?
Nearing the stables, Alyssa felt a stone clip her shoulder. She cried out and unintentionally jerked back on the reins. Streak reared, and, unprepared, Alyssa found herself fighting to keep her seat. She looked in the direction the stone had come. "Innes."
His expression was ink black. "Aye, my lady. 'Tis your betrothed."
Betrothed? Had he gone mad? "Leave my husband's land, Innes. Else suffer his wrath."
"The Buchannan is gone."
Alyssa heart almost stopped. "Gone?"
"Gone."
The last time she'd been told that, she'd assumed gone meant dead. She'd not assume again.
"Where, Innes? Where is my husband?"
"He is dead."
"Nay!" Kevan couldn't be dead. She would know it. She would feel it in her heart. "You lie."
"I killed him."
Sword in hand, Alyssa dismounted and let out a war cry that echoed through the upper bailey and bounced off the stable walls.
Innes drew his sword, stood ready for her assault.
From the first clash of metal, the fight was fierce. Innes might be crazed, but that had not affected his skill with the sword. She used all of her abilities, concentrated on nothing other than the battle. Still, though she could match, she could not exceed his skill.
"Enough!" Innes yelled, backing away from her.
Confused, wary, Alyssa let him retreat. Easing her dagger from her belt, she concealed it in her palm.
"Your husband is dead, Lady Alyssa. Do you wed me, or do you die?"
Alyssa pushed aside the pain wrenching her heart and gave her fury free reign. "I die."
"So be it."
Before he could advance, Alyssa charged. Knocked off balance, he lost his footing and the dagger aimed at his heart sliced an angry streak across his cheek. He screamed, his eyes growing wild.
Alyssa whistled and Streak came running. She was on her mare before Innes stood and raised his own dagger. "Oh God!" she cried, digging in her heels and flattening herself against Streak's neck.
But the dagger didn't come. Alyssa looked back to see Innes straddling the upper bailey wall.
"We are not done, my lady." he shouted. "You will die."
Twelve
"I DON'T KNOW how Innes got inside the upper bailey, Margar." Alyssa paced back and forth before the fireplace in the hall. "I only know that he did."
"That wall was heavily guarded, child. He couldn't have just—just appeared outta thin air."
"Patrick," Alyssa said, looking at the young man sitting at the table closest to her. "Don't get sotted on that ale. We've got to find the breach."
"'Tis still dark. They'll not be attacking again till morn."
Alyssa glared at him. "And did they attack in the light of day this time?"
"Nay," Patrick said, red creeping up his neck. He pushed the goblet of ale away from him.
"My lady?"
Alyssa turned to see the pretty little blonde who'd returned with Margar to the keep. She looked scared out of her wits. Not knowing the young woman well, Alyssa raised a questioning brow to Margar.
"Kathleen," Margar whispered so only she could hear. "She's to wed Collin come summer."
Kathleen dipped her head, and Alyssa asked, "What is it, Kathleen?"
"I know how Innes might have gotten into the upper bailey."
"Well, speak up, child," Margar snapped.
Alyssa silenced Margar by placing her hand on the old woman's forearm. In a soft voice, she said, "Go on, Kathleen."
"In the back of the stable there's a small door. It leads through the wall."
Margar cackled and her blue eyes gleamed. "Aye, Alyssa. She speaks the truth. 'Tis where all the lovers go to be alone—'afore the vows, so to speak."
"Patrick, round up the men," Alyssa said. "Celwyn, Cellina, come."
When the women were gathered, Alyssa smiled. "Remember what you were telling me earlier about the brooms?"
"Aye," both answered in unison.
"Well, I think we've a need for just such a weapon."
AT THE STABLE, Alyssa turned to Celwyn and Cellina, and whispered, "Are you ready?"
The women nodded. Forcing a grin, Alyssa started a gossipy round of chatter and entered the stable. "Aye, Kathleen will wed Collin come summer."
"She'll have his bairn in her belly long before then, is my guess," Cellina said. "Not that I blame her. That Collin's a charmer, and fine-looking, too."
"He is that," Celwyn said a little breathlessly. "Eyes as blue as a summer sky." She paused to shake the dust from her broom. "Course, he's no better-looking than my Angus. A finer man ain't been born." She gave the stable floor a swipe, raising a cloud of dirt.
Working her way to the back of the stable, Alyssa spotted the little door Kathleen said tunneled through the bailey wall. Sure enough, it was slightly ajar, its leather hinges cut. And large footprints were clear in the dust, their toes pointing into the stable. Her eyes narrowed and she gave the floor a good sweep, forcing dirt into the tunnel. "This floor is pitiful. I'll have the stablemaster's head for this." She turned, but kept one eye on the little door. "Come look at this mess back here. A whole corner of wet straw, stinking to high heaven!"
The other two women ambled over.
"A mess, it surely is," Celwyn said, slipping Alyssa her dagger.
Alyssa nodded and eased the weapon into her belt.
"Oh, aye," Cellina agreed. "We'll help you here, then do the rest, my lady."
Soon the women had the entire back stalls filled with a cloud of choking dust. Their plaids had been raised to cover their noses and mouths. Alyssa whispered, "Do you—"
Through the little door, sounds of coughing and sputtering erupted. Then Alyssa heard the first clash of metal. "They fight!" she told the women. "Quick, help me get this log in front of the door!"
The door blocked, the women ran outside and grabbed their bows. Engaged with their swords, the warriors fought the raiders. A few had already been subdued, and were being tied with lengths of rope and ordered to sit along the inner, upper bailey wall. Climbing to the top of the wall, Alyssa warned the women. "Get a clear aim, and keep your head down!"
Cellina and Celwyn positioned themselves and raised their bows.
Just as she was drawing her bow, Alyssa heard Innes's voice coming from around the corner of the stable. He sounded out of breath, and his voice came from inside the upper bailey!
Turning, she climbed down the wall and crept toward the sound. When she could make out his words, she stopped.
"Were you asleep?" Innes asked.
"No," someone sounding like an Englishman said. "I saw them. But they was women, and they wasn't armed. Carryin' brooms, is all. I can't kill no woman bent on sweepin'."
"Fool! Who do you think shoots those arrows now? Some of the Buchannan's black-faced sheep?"
Alyssa readied her bow and stepped away from the corner of the stable. A fist to her jaw sent her sprawling.
She scrambled, but her plaid was caught. She looked and saw a foot clamping it to the ground. Following that leg upward, she saw Innes's scowling face.
"Aye, 'tis my lady. Kill the rest, but not this one. I want to kill her myself—later."
The look on his face was openly carnal. She was terrified, but she glared up at him and thrust out her chin. If he would just step a wee bit closer—
A war cry that set her heart to singing ripped through the upper bailey.
She screamed, "Kevan!"
Innes moved.
Alyssa aimed a strong kick to his groin. She missed, catching his abdomen, but he doubled over long enough for her to draw Celwyn's dagger. When he jerked upright, she let the weapon fly.
Innes crumpled to the ground.
Not daring to stop to make sure he was dead, Alyssa ran toward the sound of Kevan's voice, screaming his name. She heard the thunder of Beautiful's hooves, and heard him call her. "Alyssa!"
And then she saw him. Her heart skipped, then pounded in her chest, and tears washed down her face. Running, she mumbled over and over again. "Thank God. He's alive. He's . . . alive!"
He scooped her onto Beautiful's back and clutched her to him. "Alyssa! Are you all right, love?"
His arms trembled and she collapsed against his chest. "Kevan," she sobbed. "He said you were dead!"
"Angus!" he shouted back at the smith just passing the gate into the upper bailey. "Take my woman to the keep."
"Nay," Alyssa whispered. "Cellina and Celwyn are at the stable."
"Oh, God," he mumbled, then turned back to his men. "Come!"
When they arrived back at the stable, Kevan was prepared for a grim scene. He was not prepared for what he found.
Lined along the inner, upper bailey wall, tied with rope and gagged, sat the raiders and Innes's men. Stripped bare, their faces, hands, and feet were branded with dye.
"They look injured. Damned if they don't look bee stung, too," Tam said, grinning.
"They are," Alyssa told him.
"Celwyn's bees?"
"Aye," Alyssa said, watching Patrick come closer to Kevan.
"Innes?" Kevan asked Patrick.
"He's dead." Patrick looked up at Kevan, his expression worried. "I know you wanted to kill him yourself, but somebody put a dagger in his heart. I wish I could say it was me. He touched my lady, laird. I wanted to kill him."
"Alyssa?" Kevan asked softly. "Did he hurt you, love?"
"Nay. He touched my plaid's all. I kicked him, Kevan. The only skin the man met with was the underside of my foot." She looked down at Patrick. "'Twas Celwyn's dagger what killed Innes, though I threw it. Fear not, your laird is pleased with you. As is your lady."
Smiling, Patrick looked up at her. "What should we do with them?"
Kevan looked to the prisoners. "I say we beat a little sense into them, then see where their loyalty stands."
"Cellina?" Tam spurred his horse forward. "What are you doing here?"
Cellina slung her bow to her back. "Defending the keep, Tam—with Celwyn."
"Celwyn?" Angus said, wide-eyed. "Fighting like a man?"
Angus's wife stepped from the stable out into the open, her bow in her hand. "Hello, love," she said to Angus. "'Tis a fine night, is it not?"
Alyssa, Cellina, and Celwyn, exchanged an understanding look and burst into laughter. Tam and Angus slid worried glances at Kevan.
"Don't look at me. They're your wives." He nodded toward Alyssa. "I've got my own troubles to deal with."
"Kevan." Alyssa admonished him. "We did protect your keep. You'd think a body would be grateful."
"Aye, Alyssa," Celwyn agreed. "You'd think a body would be grateful."
Tam frowned at Cellina. "Well, aren't you going to agree?"
"Do I need to?" Cellina asked softly. "This is our home, Tam. Yours and mine."
Kevan turned his horse toward the keep. "Well, my lady, it looks like the days of men riding lord over their women are numbered."
"Aye," Alyssa said, her eyes sparkling in the moonlight. "It does at that."
IN THEIR BED later that night, a satiated Alyssa cuddled to her husband's side. "How did you get back to the keep so soon?"
"The white-haired man. I saw him in my mind and he warned me to turn around. On the way back, we met Silas."
She worried her lip with her teeth, her insides rattling. "I've a need to say something to you."
He brushed her hair back from her face. "What is it, love?"
"When Innes told me you were dead, I thought I'd died, too. I—I—don't know how to say it, Kevan."
He cupped her face with his hands. His expression so tender, so loving, tears welled in her eyes.
"Say, I love you, Kevan," he instructed her.
She smiled up at him. "Is that what this is I feel?"
"I hope so." He smiled back at her. "'Tis only right. I am your husband."
"You are arrogant."
"That, too."
"So?"
"So?"
"So don't you have a need to say something to me?"
"Nay, I think not." His eyes twinkled mischief.
"Kevan," she warned.
"I love you. There, is that what you wanted?"
"Aye."
"You're frowning. Don't you want me to love you?"
"Aye, I do," she assured him. "It's just that I'm confused. How do I know if this is love I feel? I mean, I care for you. If that is love, then, aye, I love you."
Kevan held his smile. She had progressed. She cared, but she had not yet learned the true meaning of love. She felt it. That was evident in her actions. But she didn't recognize what she was feeling. Her pride. Her pride had not yet fallen to free her.
"Is this caring of yours different for me than what you feel for Duncan?" he asked.
"In ways, aye."
"Then mayhap it is love," he said softly.
His lips covered hers and Alyssa felt her insides glow. Memories flashed through her mind of another place, another time. A dark tunnel. Light. A crystal platform. A magnificent giant. An alien bird and barbarians. A silver-veined cave. Sleeping in this man's arms. Dazed, she broke their kiss. "Prophe . . .
The Prophet smiled through the tears sliding down his cheeks. "Angel."
Thirteen
ALYSSA SCOOTED to her side of the bed. "Damn you, Prophet!" Alyssa swore at him. "If you weren't dead already, I'd kill you."
Prophet frowned at her. "It is of no consequence."
"Spanking me like a child. Do you know what would happen to you if you pulled a stunt like that in the twentieth century?"
The Prophet shrugged a massive shoulder. "It is of no consequence," he repeated.
"Is that all you can say? It is of no consequence? Why you—you—" she stammered, seeking just the right word.
"I am whatever I need be, Angel. I did much less to you than any other man would have done to a disrespectful wife in this time. Besides, you asked me to. Remember—your honor?"
"You sorry, low down, rotten—"
"Husband?" he suggested, lifting one brow. "Was your marriage to me that horrible?"
"It was worse than horrible. You made me cook."
"And sew," he reminded her, pausing to pat his stomach. His lips curled ever so slightly. "According to Margar, you did well at both—eventually."
She clamped her jaw shut and glared at him. "Do I still know how to use a sword?"
"We are still in this time, Angel."
She whipped around, but Prophet caught her and lifted her into his arms.
"You are still my wife, too. Do you require another lesson in humility?"
"You wouldn't dare," she said from between her teeth.
He smiled and nuzzled her neck. "I would."
"Put me down, you overgrown pain in the—"
"Don't say it, love." Laughing, he set her on her feet and stretched out on the bed. "Come, be loving to your husband. Soon, we must leave."
Alyssa's heartstrings gave an unexpected jerk. "Leave? Oh God, you mean we've got to go to another place?" She grabbed up a bunch of the nubby quilt and squeezed it. "I won't do it. Do you hear me? I won't do it."
"You will. Now, cease your nervous chatter and come love me. My arms wait."
"After the way you've treated me?" She rolled her eyes back. "You've got to be kidding. I do have a little pride left—no thanks to you, I might add."
"Alyssa." His eyes held a warning. "Remember pleasure. Remember your words to me. No anger has the value of loving. Do you remember?"
"Yes," she said, scooting toward him on the bed, her anger leaving as quickly as it had come. "I remember."
"Do you no longer care for me, because you know I am Prophet?"
The look in his eyes scorched her soul. "I don't know what I feel. I'm confused. And that's the truth. I think—"
"What?" he prodded.
"I care for Kevan. And I think I might just care a little for you, too. Though only heaven knows why."
He smiled and held open his arms. "Then come, Angel. Love both of us, for we are one and the same."
LYING IN THE prophet's arms, Alyssa snuggled to him and let out a satisfied sigh. Kevan Buchannan might hold her heart, but Prophet had claimed her soul.
He brushed her eyelids with his lips. "Have you decided?"
"Decided what?" His scent filled her nostrils and she played with the hair on his chest, curling it around her fingertip.
"Do you care for me as much as you care for Kevan?"
Toying with the amulet at his neck, Alyssa felt it vibrate and looked up. "Prophet, it glows!"
"Aye," he said, untangling himself from her and standing. "Come."
"You have a thing about saying that, you know." She sat up, watched him rise and reach for his plaid. "Where are we going? I'm not going to leave here yet." She slid off the mattress and tugged on her chemise, then followed him. "I mean it."
He stopped and turned around. She plowed into his back and almost fell down. When he had her steady, he smiled down at her.
"Don't you dare call me clumsy, or I may get that sword anyway."
"You followed before you asked where we were going?"
"Yes," she answered, not understanding the importance. "So?"
"So, this pleases me." He bent down and gave her a quick kiss. "Come, there is someone I want you to meet."
"Your grace," Prophet called out.
The old man from the wood appeared before her. Alyssa gasped. He did have eyes! Both were flat and colorless, but she couldn't see clean through them. Her knees shook and she clung to Prophet's arm.
"Angel, this is his grace, the Elder of the Council of Perfection."
Not sure what to do, Alyssa bowed her head.
"You are the Prophet's Lady?"
Alyssa looked at Prophet. "I—"
"She is," Prophet said.
"I asked your woman, Prophet," the Elder said not unkindly.
Alyssa swallowed hard. "I am. You're Kevan's angel."
The Elder smiled. "Not quite, but angel will suffice." He rubbed his long white beard. "The Council is most pleased with your progress. You have learned much in this level."
"You mean it's all true. Everything Prophet said about the negative impulse imbalance, and—and—going back?"
"You doubt my word?" Kevan asked her.
That her remark hadn't pleased him was an understatement. She looped their arms and stroked the back of his forearm with her thumb. "No, darling," she said, looking up at him. "I don't doubt you. Not really. It's just—"
"Hard to accept?" the Elder suggested.
Alyssa nodded.
"It is of no consequence," the Elder said.
Alyssa shot Prophet a murderous look. "Now I know where you got that."
Prophet smiled down at her.
"Child," the Elder said. "Tell me what you've learned in this level."
Alyssa let go of Prophet's arm and paced a short path before the window, organizing her thoughts. Neither the Elder nor Prophet rushed her. Sensing the importance of her answers, she was grateful for that. "Well, back in the twelfth century, when a woman didn't follow her husband's rule, she got her socks knocked off."
The Elder gave her a puzzled look.
"Discipline," Kevan interpreted.
"Ah." The Elder cleared his throat and asked, "And was the punishment just?"
Heat seared her face and Alyssa looked down at the floor. "It was, your grace."
"Fine," he said, sounding pleased. "Is there anything else you learned?"
"Oh, yes," Alyssa assured him. "I learned to cook and to sew, and . . . Never mind. The rest isn't important."
"What is it, child?"
Prophet stepped into her path, took her hand, and gave it a reassuring squeeze. "Speak your heart."
The look in his eyes confirmed her feeling that this conversation with the Elder was extremely important. Trembling, Alyssa held on to Prophet's hand for support. "During the battle everyone worked together. We defended the keep by blending the ways of men and women. The broom was as valuable as the sword. Without both, I think we would have failed."
"So, what does this mean to you?" the Elder asked.
"Both deeds—no," she paused and looked deep into Prophet's eyes. "No. All deeds hold value. One depends on the other. Kevan, God love his heart and protect his stomach, depended on me to feed and clothe him. I depended on him for strength and for protection." She wrinkled her brow. "Yet, when threatened, he depended on me to protect his people." She turned to look at the Elder. "See what I mean?"
"I do," the Elder said, then studied her through those odd eyes of his. "And did you come to care for Kevan?"
"Yes, I did," she confessed. "Marriage to him wasn't always pleasant. At times, Kevan could be, er, difficult. But there was something very special about being in his care. Something almost, I don't know . . . magical."
"And so it should be," the Elder said. "Tell me, child. Do you feel this same magic for Prophet?"
Prophet's hand grew rigid on hers. She didn't dare risk a glance at him. He'd said to speak her heart, and she intended to. "Prophet is Kevan. How could I not care for him?" She gave the Elder a shaky smile. "But my feelings for Prophet are different, too."
"How do they differ?" the Elder asked.
"I'd rather not explain, your grace." She looked up at him and felt heat flood her face. "A woman must be allowed to keep a little of her pride."
"Pride," the Elder repeated, casting a pointed look at Prophet.
Prophet groaned. "Not—"
The Elder silenced Prophet with a stare, then spoke to Alyssa. "Yes, my dear, you do have an abundance of that."
Alyssa looked at Prophet and, when she looked back, the Elder was gone. Her heartbeat tripped, then sped. "Did I say something wrong?"
Prophet cupped her face in his hands. "No, love."
He had that look in his eye. He was about to leave her. Her heart wrenched and she shook. "Prophet?"
"Yes, Angel." He drew her hand to his mouth and pressed her fingers firmly to his lips, pain etching his face. "It is time."
"No!" she cried, slumping against him. "I don't want to go. Can't we just stay here?"
He stroked her face, his voice gruff with emotion. "Kiss me goodbye, love, for when we next meet, you'll not know me."
Her heart slammed against her ribs. "And you? Will you know me?"
"No, Angel, I will not."
It was inevitable, they had no choice. Tears burned her eyes. "Kiss me now, then," she said raggedly, feeling as though everything good in her life was being snatched away from her. "I don't think I can bear this parting. I'll surely die."
He dipped forward and took her mouth in a kiss rife with desperation, rife with hunger and sorrow and fear. Kevan and Prophet melded, became one in her mind, and Alyssa told him all she felt for him with her kiss.
He breathed against her lips, "I love you, Angel."
Fourteen
England, 1800s
"MILADY?"
The fire in the bedchamber grate crackled and hissed. Lady Alyssa Cameron looked up from her needlework. "Good morning, Meg."
As she passed Alyssa a cup of chocolate, her abigail's expression wrinkled into a frown. "You still look a bit undone."
After three and a half weeks abed with the fever, Alyssa still felt a bit undone. "You worry about me far too much. I'm better. Really."
Sniffing, Meg moved to the bed and fluffed the pillows none too gently. "I still think that cork-brain doctor should have bled you. Everyone knows you have to let the fever out."
"I wouldn't let him," Alyssa reminded her, though when she'd refused the doctor, Meg had been in attendance. Dear Meg was always in attendance.
Meg pulled a shawl from the closet and draped it over Alyssa's shoulders. "Then the doctor should have sent you to Bath."
"I refused that, too. Maybe I should have taken the waters, but—"
"But the truth is you didn't feel well enough to make the journey, and you know it, milady," Meg chided her. "Now ain't it?"
The trip to Bath from London wasn't an arduous one. But in mid-January, when a person was already indisposed, the journey could be as lethal as the fever. "I'm fine now," Alyssa said, ignoring her question. "Besides, no doctor or waters anywhere could match the care you gave me right here at home. And that's the truth of it."
"You ain't fine," Meg contradicted her. "You're weak as a kitten."
"Meg, for pity's sake. I'm not that fragile."
Muttering, Meg tidied the room, and Alyssa let her gaze drift to her bedroom window. The weather was gray, overcast, and dreary. Much like her mood. Meg was right. She was weak as a kitten. Her inactivity had left her too much time to think, and if that wasn't enough to gloom a body nothing was.
A loud clash sent her gaze darting toward the fireplace.
Still muttering under her breath, Meg lifted the poker and stabbed at the logs. Sparks spewed like a fireworks display at Vauxhall Gardens.
Alyssa flinched. The fire required no attention. She eyed her abigail warily and discovered she was in a full-fledged twitter. "All right, Meg. What's wrong?"
"When you've finished your chocolate, his lordship is wanting you down in the library."
A knot of unease formed in Alyssa's stomach. Meg, who always spoke with the frank and direct honesty of a child, hadn't glanced her way once. Something was most definitely amiss. Something most serious. The knot in Alyssa's stomach grew larger, tighter, but she forced herself to remain calm, to delicately investigate. "How is my father?"
"I haven't actually seen his lordship, Milady."
Meg still didn't look her way, but color flooded her profiled cheek. That was all the answer Alyssa needed. Her father, John Cameron, earl of Bradbury, was either in his altitudes or cup-shot.
Her thoughts reverted to that October morning. Had it been just months ago? It seemed lifetimes had passed since her father had come home dazed, his clothes splattered with blood.
Shivers crept up her backbone. No, she refused to dwell on that nightmarish morning, or on the endless night preceding it. And especially not on what had come afterward. Quickly, she stood up. "I'll go at once."
Wearing a worried look, Meg left the chamber.
Alyssa frowned. She and Meg were very near the same age, and, with conditions being what they were at Cameron House, she'd never bothered to demand Meg hold her tongue. Partly because only God could enforce such a demand, but more so because she depended on Meg's forthright manner. Her silence indicated how deeply she was troubled, and that caused Alyssa grave worry.
Setting her needlework aside, Alyssa smoothed the folds of her lavender muslin skirt. If her father had been foxed and now suffered the after effects, the rest of the inhabitants in his establishment were suffering as well.
She shut her eyes for a scant second, refrained from asking God yet again why He'd taken her dear mother, and instead prayed her father would develop an affection for some suitable lady of the ton. Then she stiffened her spine and quit her chamber.
From the grand staircase, she saw Burns leaving the library. One look at her father's butler had shivers streaking up her spine and racing across her shoulders. Usually placid-faced and imperturbable, that worthy frowned until his black brows slashed an angry bar across his forehead.
Her father was cup-shot, she predicted, feeling more than a little resentment. Why must he be in this condition now? Why must he call her now, when she felt far from well and unable to hold her own in a confrontation with him?
She tapped on the library door, and heard him bid her to enter. Her knees weakened and her stomach fluttered. "Please, God," she whispered, "let him know what he's about." She walked in and shut the door behind her.
Seated at his big desk, he attempted a smile. It seemed more like a grimace. "Ah, Alyssa."
"Good morning, Father." He still wore last night's evening clothes and the stench of soured port reeked from him, making her knees grow weaker still.
"Sit down, my dear."
She eased onto a burgundy leather, wing-back chair and studied him. What she saw did nothing to dispel her growing concern. Though he squinted, his quizzing glass did not mask his red-streaked eye. It mirrored its dull, exposed mate. His cravat, limp and smudged with dirt, sagged. With a sinking feeling, she considered the whole of his appearance. Disheveled. Disreputable. She homed in on his expression. Disturbed?
Alyssa trembled. She couldn't forget the last time he'd wandered around throughout the night. The sight of the clothes he'd worn home then; crumpled, bloodied. His ordering Burns to set fire to them in the library grate. Nor could she forget the Lord Chancellor's discreet inquiries that had come afterward, her father's black rage and the express orders he'd issued forbidding that the subject be mentioned again.
"I hope you are feeling well."
His voice sounded relaxed, but tension lined his face, crackled in the crisp air between them.
"Much better, thank you."
"Good. Good."
His expression eased, yet he fidgeted with his timepiece. Something more than the after effect of over-imbibing was amiss, and, God, how she feared learning what. Her temples began to throb. "Meg said you wished to speak with me."
His fair skin flushed. "Because of your illness, I didn't bother you with this matter. However, I can wait no longer."
"Father, how intriguing you sound."
"Intrigue is not my intention," he assured her, not quite meeting her eyes. "I was waiting for the proper moment. Now that you've recovered, well . . . Well, I must inform you posthaste." He cleared his throat. "You've received an offer of marriage from a most suitable young man—and I have accepted it."
Her ears had failed her. They must have! "You accepted?"
Her father raised his hand. "Now, before you lie low in a swoon—"
"I do not swoon, Father."
"Nevertheless, I'll hear no objections. Your betrothed is a wealthy member of the ton, his looks are all the crack to members of your sex, and, most importantly, I have accepted him."
"But—But you gave me your word. You promised I could choose my own husband." She held herself rigid to stave off despair. "How could you do this, Father?"
He sent her a hard, flat look that warned her his temper was held on short ribbons. "You are twenty-two, long past marriageable age. I've permitted you to reject suitor after suitor for frivolous reasons, but the time has come to see to your future. And the time has long since passed for you to take your place in society as a married woman."
"Who is this man?" She feared she knew. And she also knew she must be prepared to play her part in the coming charade. God grant her strength.
"Lord Innes."
She smothered a small gasp. Though she expected it, hearing the name shocked her dizzy. But, in His mercy, her Creator answered her prayer, and she burst into laughter. It almost rang true to her own ears. "Oh, Father. You had me going with this Banbury tale. But your ruse is up. You'd never approve a match with a high-flyer." She paused to dab at her eyes with a lacy hanky, then still smiling, asked, "Shall I tell you where you erred?" Quickly, before he could interrupt, she continued. "Lord Innes visits White's nightly. Why, I'd be more a widow than a wife. Any other man would have been far more believable, I would say."
While her merry laughter again filled the room, she gauged her father's response. Finding it lacking, she added, "How very clever of you, Father, to amuse me out of my tiresome ennui."
"I am not relieving you of boredom." John Cameron stood up behind his desk, his hands curled into fists. "Nor will I permit you to speak of your betrothed in such a disrespectful manner."
Alyssa's smile faded and her heart lay stone heavy in her chest. Her ploy had failed. He would not relent. Stricken, she whispered. "You are serious?"
"Most serious."
"Father, no!"
He glared down at her. "Cease your impertinence at once. It is a good match, Alyssa Kathleen. The banns have been called, and—"
"What?" Alyssa jumped to her feet. "That is not possible."
"It is fact," Lord Cameron insisted, returning to his seat. "You wed Lord Innes tonight."
The banns had been called. His words reverberated in her mind. The room spun around her, and she crumpled to the floor.
For the first time in her life, Alyssa Kathleen Cameron swooned.
ALYSSA OPENED her eyes. Daylight slivered into her chamber around the edges of the draperies drawn closed over the window. She was still abed! Talking to her father had been a dream.
Relief came, and she let it wash through and soothe her. She had been ill for such a long time. Of course, that was the reason for her nightmare. Her father would never insist she marry Innes. Of all men, not Innes.
She remembered her father's bloodstained clothes. His insistence that he remembered nothing of where he'd been after he'd left White's with Innes that night. Tremors raced between her shoulders, through her chest, pitting her stomach. Wed Innes. That had been a dream, hadn't it?
She saw her needlework in the chair beside the fire. The peonies on the border. She'd not yet started them.
Scrambling from her bed, she checked. Two peonies boasted threads. Her memory flashed, and she recalled sitting by the window that morning, working the Spanish blue petals. "Meg! Oh, God, Meg!"
Meg burst into her chamber, her cap askew, her blond curls tumbling. "What is it? Are you worse again?"
Alyssa's heart lodged in her throat. "My father. Did I speak with him this morning?"
Meg worried her lower lip with her teeth. "Yes, you did. And swooned, pretty as you please."
"Oh, God," Alyssa mumbled.
"Please," Meg said, taking Alyssa by the arm. "Sit down—here by the window. It is an awful shock, to be sure."
Numb, Alyssa collapsed onto the seat. "It's true, then?"
"If you're meaning about you marrying that Lord Innes, it is. His lordship says you're to be dressed and ready to leave for the church at six o'clock." Meg's jaw looked corset-cinched. "Disgraceful, it is. Making a lady wed at night."
Through startled eyes, Alyssa looked up at Meg. "At night?"
"Yes, Milady."
"I won't do it. I won't marry him at all, but—at night? Oh, Meg. You must be mistaken. My father would never insist—"
"I tried to explain to his lordship. Proper ladies marry only in the morning, I said to him. But he heard none of it."
Tears clogged Alyssa's throat. She swallowed them. "Why is he doing this to me?" She slung her needlework against the wall. "I'll not do it. I'll not marry that scapegrace. I'll—I'll leave."
"Considering the fate of the first Lady Innes, and things being what they have around here, I figured those would be your feelings." Meg settled sympathetic blue eyes on her. "Unfortunately, so did his lordship."
"What do you mean?"
"As soon as I heard the awful news, I took the liberty of borrowing a few shillings from your reticule and bribing James into hiring a carriage." Meg's eyes burned bright with anger. "I knew you wouldn't leg-shackle yourself to the likes of that Innes."
"Oh, Meg, you're an angel." Alyssa hugged her, then reared back. "When do we leave?"
"We don't." Meg frowned. "James got caught. Burns heard tell of a strange carriage in the neighborhood and investigated. There was nothing James could do but fess up." Meg's lower lip quivered and her eyes filled with tears. "Oh, his lordship is in an awful rage. James was beaten and his lordship ordered Burns to flog him first thing in the morning."
"He can't do that. It's—barbaric. Oh God, Meg, surely that's against the law?"
"I don't know, Milady, but he's ordered it done either way. And—and he's locked you in your chamber, too. Anyone letting you out before the wedding will be given the same as James."
Alyssa's stomach gave a great heave. She pressed her hands over it, willed it to settle down. "Is James hurt?"
"Not really," Meg reported between sniffles. "The stablemaster's heart wasn't in the beating. He's grown fond of James, to be sure. But—but the flogging—"
"Blast him!" Alyssa strode over and tugged at the door. When it didn't give, she muttered an oath that put fire in Meg's face and fresh tears in her eyes. "He means to make me do it, then."
"He does, milady," Meg sobbed. "He truly does."
Alyssa reached into her reticule and pulled out three gold coins. "When you can, give these to James. It must be tonight, Meg. Before—before morning. Tell him to see a doctor tonight, and that I'm sorry." She gave Meg a pointed look. "He must not be flogged."
Meg nodded and tapped on the door. It opened, and she looked back. "Try not to give into the blue devils. Burns ain't flogged James yet, and you ain't married. Not yet. Something will happen to lighten your heart. The entire household—except that feckless Burns—is praying hard."
Knowing Meg was trying to comfort her, Alyssa forced a smile to her mouth. "Thank you."
Meg nodded, and, clutching her skirt, went out. The door closed behind her. The lock clicked. The mantel clock struck like a death knell.
Alyssa refused herself the luxury of tears. In four hours she'd be forced to wed Innes. Feeling as she did, fearing him as she did, how could she bear marriage to him?
Her stomach clenched into knots. How could her father do this? True, since October he'd grown more and more strange, but could being a widower for so long do that to a man?
No, she decided. It was the drink. His fondness for liquor had dulled his wits. And, too, might he be suffering a relapse of gaming fever? Meg had relayed James's concern about her father's again frequenting White's. After that awful, unexplained night, he had stopped going—at least for a short time.
"Think. You're not addlepated," she told herself. "There must be something you can do to get out of this."
Digging through her reticule, she found she had less than a pound. Unless she could get out of her chamber and into the library undetected, she couldn't get to any of her jewelry either.
Her mother's jewelry. Had her father located her mother's missing diamonds? Until she married, she could wear only her pearls. Still, she must remember to ask him about the diamonds.
For pity's sake, she chided herself. At the moment, her mother's diamonds were the least of her worries.
The gravity of her situation settled on her, wiping all thoughts save one from her mind: leaving was an impossibility. Even if she managed to slip from her window, three floors above ground, she'd surely break her neck. And if by some miracle she did get to the ground uninjured, she still had nowhere to go—and no way to get there.
At four-thirty, she faced defeat. She was trapped.
Sitting near the window, she stared out at the carriages proceeding down tree-lined Whitehall en route to Hyde Park. Tears brimmed in her eyes and fell unchecked to her cheeks. She let herself cry, let her soul pour out its anger. God, how she despised futility.
When she felt empty, she brushed at her face with the back of her hand, closed her eyes, and lifted her face toward Heaven. "I know that in these modern days there are no armored knights rescuing ladies in distress. They've gone with the dragons." Her voice trembled and shook. "But, dear God, I'm so frightened. If you could spare just one . . . He needn't be perfect. Please! I—I don't know what to do."
She opened her eyes and hugged herself. Memories of how things had been when her mother was alive came to her. She'd been happy then. Secure and loved and protected.
But her mother was gone now. And her father was . . . different. She could depend only on herself for guidance. And she knew in her heart she could not marry Innes. She could not, would not, make a mockery of the sacred vows.
Her stomach churned. How much would she forfeit to protect those vows? Everything?
Her father had removed every other alternative. Resolved to what she must do, she stood up. At the bowl and pitcher, she poured a measure of water and splashed her cheeks. Looking into the cheval glass, she saw that the skin around her eyes had become puffy and swollen, her nose, an unsightly red slope in her blotched face. "You look like the bride of Innes," she told her reflection. "But he'll not have you. Not tonight. Not ever."
The decision had been made.
Fifteen
MEG PULLED her stone-drab cloak closer around her slender body and slipped out of the Cameron establishment's servant's door.
The cold air fogged her breath and stabbed at her lungs. Overhead, an angry sky thick with fat heavy clouds threatened to burst. She hurried her step.
When she left fashionable Whitehall and turned left onto Piccadilly, she looked back and sighed her relief. No one had followed her. By the time she passed Piccadilly Circus, the sharp bite of the cold wind had her bones near frozen, and the rain had begun. She skirted south of Hyde Park and finally turned onto Knightsbridge.
It was an impressive street. A good address for the elite members of the ton. She saw the number she sought—329—printed on a discreet brass plate on the fence wall, then looked up at the house. Long, arched windows stretched deep into the four high steeples, and a recessed entry led to angled mahogany doors. She hurried up the walk and lifted the great brass knocker.
Soon, a tall familiar man, standing very erect and sporting the tiniest flecks of grey at his temples, answered. He frowned. She'd known before she'd come that he wouldn't be pleased. Before he could turn her away, she sputtered. "I've come to see his lordship."
"His lordship is occupied at present," the butler replied in a tone sharp with reprimand. "May I tell him who called?"
"Meg," she said, her eyes narrowing. She was tired, cold, and near soaked to the skin. "You'd best be telling his lordship I'm here. He told me I should come if it was important, and 'tis—'tis—" The gravity of her lady's situation hit her and she burst into tears.
"Parks?" A deep-timbered voice came from inside the great hallway. "What woman has been reduced to tears on the doorstep of my establishment?"
Before Parks could respond, Meg cried out. "'Tis me, milord. Meg!"
The great giant suddenly appeared, all dark and handsome as she remembered him.
He took her by the arm and led her inside. "What is it, Meg? You're pale as a ghost."
"And frozen, too, milord." This was no time to stand on manners.
"Come." He urged her into the library and down into a chair by the blissfully warm fire. "Parks, bring Meg a hot cup of tea."
"There's no time for that." Meg slid Parks an uneasy glance that she knew he'd noticed, though he pretended he hadn't.
"Speak freely. Parks holds my confidence in the matter of your lady."
Meg nodded and offered Parks a smile. He smiled back. "You said I should come in a dire emergency. And, oh, milord, my lady has landed in trouble aplenty."
His lordship's expression grew anxious. "The fever?"
"No." Meg frowned. "Her father's forcing her to wed that Lord Innes—tonight!"
"I see."
"I tried to hire a carriage, but James—you recollect young James MacMillian, milord. Well, he was caught in the act, and now Lord Cameron's ordered him flogged."
"Flogged? That's barbaric."
"So says milady," Meg said with a nod. Her lordship's cheek muscle twitched, then twitched again. He was far from pleased by any of this news. "She gave me blunt to send James packing before tomorrow."
"She told you this?" Parks asked.
Meg turned toward the older man. "She said to tell him to see the doctor tonight, that he mustn't be flogged. She wants him to leave before her father can see the deed done, to be sure."
The earl and Parks exchanged a glance, and Meg could have sworn she'd seen a twinkle in his lordship's eyes.
"Don't worry, Meg. Matters are well in hand. Go back to your lady and help her dress for her wedding." He turned to his butler. "Parks, have Major take Meg back in the carriage. But not too close to the house." He looked again at Meg. "We don't want anyone to suspect anything's amiss."
A twinkle was definitely in his lordship's eyes. And, Meg realized, he hadn't been in the least surprised by her news. Oh, the man would have made a fine gamester if he'd been inclined in that direction. Thankfully, he was not like Lord Cameron. Her lord had no use for games of chance. Hadn't he proven that by installing her as Lady Alyssa's abigail?
"Can you get to James?" the earl asked.
"Yes, they've got him bound down below 'til morning."
His lordship frowned. "Daniel will be waiting with the carriage for you both at the corner of Oxford and Bond at midnight."
"But, milady? I can't just leave—"
"You must. The risk has grown too great for you to remain at Cameron House any longer."
"And you're sending Daniel for us?" Meg asked. "Oh, begging your pardon, milord, but Major won't take kindly to a footman handling the ribbons of one of your fine carriages."
"Major will be otherwise occupied this evening, Meg." Again his lordship exchanged a knowing look with Parks. "Daniel will bring you and James here. Then tomorrow we'll send you to the house in Chatsworth."
Meg hid her disappointment. Chatsworth wasn't Brighton, but at least she'd be back under one of her lord's roofs.
The earl patted her shoulder. "When a certain matter of consequence has been resolved, I'll see to it you're returned to Woodwind Manor."
"Yes, milord." Meg smiled up at him. Surely no finer noble had ever graced this earth. "It'll be grand to be home again."
"It'll be good to have you home again. A year is a long time."
Meg left his lordship's establishment with a light heart. What the earl had in mind, only the good Lord knew for sure. But she'd be willing to wager her ivories that Lady Alyssa would not be marrying Innes this night!
Sixteen
ALYSSA SAT STIFF in a straight-back chair, her arms folded across her chest, a mutinous expression on her face.
She looked up to where her grandmother's wedding gown hung waiting. Her heartstrings suffered a hard tug. Though simple, the silk gown was beautiful. Its high-waisted bodice and flowing white skirt were separated by a narrow width of silvery ribbon, and fine Belgium lace rose high onto the throat. The accompanying trailing scarf of delicate gauze lay on her bed, waiting to be pinned in her hair so its long ends draped her bare arms and fell down her back to the hem of her gown. A wreathed headdress of delicate pink baby roses lay beside the scarf. So pretty, so pale, and, now, so threatening.
She shuddered. For so long she'd dreamed of the day she would wear these clothes. But in her dreams she had never suffered this dread, or faced a future as bleak as the one before her now. In her dreams, the man she wedded was one she'd developed a partiality for—not Innes. Her flesh crawled. Never Innes.
"Milady, you must get ready, now. It's gone five-thirty." Meg reached for the gown.
"I'll not," Alyssa said in a quiet voice. She meant her words. And she would not alter them.
"But his lordship—"
"You may tell his lordship that if he wishes a Cameron to wed Lord Innes, he may do so himself. I'll not do it."
Meg stood gaping at her. "But—"
"I mean it, Meg." Meg swayed on her feet, and Alyssa added, "Don't you dare swoon on me. Someone must tell my father that I refuse to go through with this farce, and I'm not free to leave my chamber."
"He'll be spitting mad," Meg said, casting her a worried look.
Alyssa refused the plea in Meg's voice. "I'm sorry you have to bear the bad news, but I've no other choice. I'd rather be dead than Innes's wife."
"Yes, I'm sure you would. May I tell Burns, instead? I shouldn't mind so much, if I can tell him. Let him feel the brunt of his lordship's wrath."
Alyssa resisted the urge to smile. The feud between Burns and Meg had begun before their introduction had been completed. "So long as my message remains unaltered, you may tell whomever you wish."
With a bob, Meg turned and left. Alyssa was unsuccessful in stopping a smile from forming on her lips. Her own circumstances were dire at best, but Meg would relish the ear-blistering his lordship was about to bestow on the stuffy Burns.
Scant minutes passed. Then she heard her father's bellows, his furious footfalls on the grand stairs, and his harsh order to "Open that door at once!"
She vowed she'd remain calm, that she'd injure her pride no further by losing control of her emotions. It still amazed her. She had swooned. Her illness, she decided. She'd no doubt grown weak during her illness.
He stormed into her room. His face fiery-red, his neck veins bulging, he scowled at her through his quizzing glass. God, how she despised that quizzing glass.
"I demand you explain yourself," he said. "What do you mean, you refuse to marry Innes?"
She swallowed the fear that had her throat muscles quivering. "You gave me your word that I could choose my own husband. I'm holding you to your promise."
"I've given you to Innes."
Alyssa curled her fingers deep into her chair arms. The scrolled wood cut into her flesh. She looked up at her father. He was afraid, she realized. Why did he fear her refusal? "You gave me to myself first, Father. I was no longer yours to give to Innes."
"You are a woman. You belong to me until I've given you to a husband—which I have done."
He jerked the wedding gown from its hanger and thrust it toward her. She didn't accept it, and the gown crumpled to the floor.
He raised his hand and jabbed a pointed finger in her direction. "I'll not tolerate disobedience from my daughter, Alyssa Kathleen. You will marry Innes, I swear it. Now dress, or I'll drag you to the church nude."
"Father, you—"
"It is your pride at stake," he bellowed. "Not mine."
Alyssa gasped. "You wouldn't."
He stood, his legs planted on the floor, his arms folded across his chest. "I would."
The stubborn set of his jaw, the angry look in his eyes, boasted convincing evidence that flooded her with pain. "Knowing I am against this marriage, you would force me to wed him? Of all men—him? What has Innes done to you, Father? Has he threatened you? Me? Please, tell me."
"He's done nothing, save offer you a means of getting off the shelf. Twenty-two and not yet wed." He dragged his hand through his thinning hair. "Save me, you are the sole Cameron, Alyssa. The line must continue. I must have a male heir, and it's your duty to provide—"
"I know my duties, Father," Alyssa began, "but—"
"You have ten minutes. In five, Burns will come to assist you in dressing." Her father turned and stormed from the room.
Meg stepped out of the corner and closed the door. "Burns to assist you! Oh, milady, please let me dress you. No lady should suffer the indignity of having a butler dress her. Please."
Unable to speak, Alyssa nodded. She'd been hopeful that when her father realized the depth of her resistance, he would relent. But he hadn't withdrawn his demand. And she feared she knew the reason.
Numb, leaden, she stood up and allowed Meg to do what she would. This wedding would not occur, regardless of the cost. But she could only escape her locked chambers in Cameron House by going to the church. To the church, but never down the aisle.
By the time they arrived at the church, Alyssa was no longer numb. She was furious. Her father stepped out of the carriage and offered her his hand. She ignored it. Alone, she walked inside.
Meg hurried to her side and pointed to an antechamber. "In there, milady."
Alyssa went into the small waiting room. She paced and prayed for intervention. Something—anything—that would spare her being leg-shackled to a man she feared.
"You're wearing out the bishop's carpet," Meg said. "And you're so flushed. Won't you sit down and rest for a minute?"
"Oh, Meg, I have so little time left. I cannot believe that my father is doing this." Alyssa continued pacing, growing more and more loud in her complaints until she was fairly shouting.
Grim-faced, her father entered the room. "The entire populace inhabiting this church—including Mrs. Drummond Burrell, I might add—is well aware of your discord. I demand that you hold your tongue."
"I won't. I will not marry him, Father, and that is the truth of it. Why are you—"
Her father grabbed her arm. "You will marry him." He clenched his teeth. "Meg, leave us."
He squeezed, and Alyssa's arm throbbed. She nodded, and Meg stepped into the hallway. The hem of her gown got caught between the closing door and its frame, and knowing she was nearby gave Alyssa comfort. "Just tell me why."
Her father's eyes filled with pain. "I'm bankrupt, Alyssa. If you marry Lord Innes, he'll clear my debts."
Alyssa's eyes rolled back in her head. "Father, this is no time for a Banbury tale—"
"Still your tongue, daughter. Don't you realize your jeopardy? If you refuse to wed Innes, you'll be reduced to hiring yourself out as some woman's companion. There is no blunt."
Alyssa gasped. "None? Not a pound, a shilling? Father, how could that be?"
Sweat dotted his forehead, but he didn't answer. Nor did she expect him to. She knew the reason for their dire circumstance: White's. Her father had lost his considerable fortune gaming. And, she was now sure, her mother's diamonds, as well. "Do you realize my jeopardy in being married to him? Remember Hedwig, Father."
The look in his eyes changed from discomfort to fury. "I warned you to never mention her name to me. You must marry Innes. I'm—I'm done up."
Done up? Icy dread crept up her spine. She'd heard those words before. And, if only in her heart, she knew the result of them. "We'll go away," she said. "Disappear, like Beau Brummell did last year."
He held her hands tightly. "If you don't marry Innes, I will be forced to flee my creditors like Beau fled his. But I'm not the darling of the ton that he was, Alyssa. I doubt I'd be lucky enough to end my days obscure on the Continent—or even in debtor's prison, for that matter. My fate would be more immediate. Is that your wish for your father? Can you be that selfish, that ungrateful?"
Alyssa swallowed her bitterness. He had created his own difficulties and hers. Yet she was the one given the responsibility of resolving them. His expectation that she do her duty was clear. She could resent the situation—and him. She could detest both, but it would have no effect. God help her; unless she wished her father dead, she had no choice but to marry Innes. "All—all right, Father," she relented. "I'll do it."
Her father whimpered. "Thank you, my dear. I knew your pride would serve me well."
Alyssa wanted to snap at him, wanted to slap his quizzing glass from his hand. But she didn't. It would serve no purpose. It didn't matter now. Nothing mattered now. Not anymore.
A knock on the door claimed their attention.
"Yes," her father responded.
"It's time," Meg said.
Alyssa walked to the door and turned to her father. "I do this because I have no choice. But I will never forgive you, Father. You sold me to a man I fear enough to take my own life. If I could but find a way, I would leave the two of you to your fates without a backward glance."
"You must not speak of suicide. It's a sin."
"What you have done to me is the sin."
"Alyssa." he gasped. "I love you."
"Don't you dare speak those words to me. You hate me. You have since the day my mother died."
"That's not—"
"How dare you deny it? It is true," she insisted, glaring at him. Her tone chilled to ice. "Come, Father. Give me to Innes. Walk down the aisle with your only daughter. Touch her arm for the last time before you give her in marriage to a murderer."
He looked stricken, but he did not respond. Alyssa turned and left the room. She heard his following footsteps.
At the nave, she took his arm and felt it tremble, then wondered if she were the one who trembled. Again, she besought her Maker. Please, before we reach the front of this church, please make Father come to his senses and take me out of here.
Straight ahead at the altar, she saw Innes, his hair the color of fresh-boiled carrots, his clothing impeccably cut. Her stomach revolted, lurched, and she swallowed hard, drew in three deep breaths to calm herself.
They were halfway down the aisle now. Each step, taking her closer to hell. And for the first time, she knew how a man felt on his last walk to the gallows. Hopeless. Resigned. Her father was going to go through with it. He was going to complete his sale of her to man who'd killed his first wife. God, she silently cried. Help me!
But God didn't answer.
Innes watched her approach. His gaze devoured her. Alyssa cringed and turned to look at those assembled. She swallowed hard. Was she the only person in all of England who had not known about this wedding?
The patronesses of Almack's were in attendance. Lady Jersey, who had recommended Meg, sat grim-faced. Lady Sefton, the kindhearted woman who had launched Alyssa's coming out and assisted in her introduction to court, sent her a sympathetic look. And Mrs. Drummond Burrell, the most arrogant dictator of the wishes of the patronesses, the woman who most terrified young women entering the marriage mart, sat looking down her disdainful nose. Alyssa immediately lifted her chin and stiffened her spine.
Near the altar now, she saw the Duke and Duchess of York, both of whom she'd developed an affection for on her childhood visits to Oatlands. They, too, looked uncomfortable, but, like the others, they would not intercede.
She looked from face to face. Did none of them know about Innes? Did they not care? Had the members of the ton she had considered her friends, her extended family, turned out en masse only to witness the fall of her pride, her destruction?
Then she saw the truth in their eyes; their pity, and their disgrace. They did know what Innes was—and what would happen to her. Yet, none would break the bonds of regimented society to aid her.
Never before had she felt so alone, so utterly isolated. Her observations should have prepared her for the reaction of the ton. Why did she entertain a certainty that she was different than any other member falling from grace? She wasn't different. Her reluctant behavior, her marrying a wastrel at night, would be the latest on dit, the scrap of gossip that would be wagged on every tongue.
Until tomorrow.
Then their condemnation of her would turn even more grim.
But she would no longer hear it.
How would her father, Innes, her friends in the ton feel then? Cheated? Gulled? Would her father or Innes feel so much as a pang of remorse?
She was there now, beside Innes at the altar. Sickly sweet, the scent of his cologne hung in the still, damp air, curdling her churning stomach. She broke out in a clammy cold sweat.
Her father released her and stepped away. She smothered a whimper and looked at him. He seemed relieved, and her heart shattered all over again. "Goodbye, Father," she said, then turned her back, knowing her message had been understood.
In the church that had grown silent as a tomb, she heard his footsteps recede, the wooden pew creak under his weight. And those sounds gave her the answer she had to accept. To protect himself, John Cameron would allow his daughter to sacrifice her life, to commit the most shameful, the most unpardonable of all sins. The sin for which no man or woman could atone: suicide.
She tried to absorb the shock, to summon the bravery to do what she must. Of both their sins, surely his was the greater. He could have prevented her sin, and he chose not to.
Innes held out his hand. She refused it. He slid her a murderous look, and without the slightest hesitation, she answered it with one of her own. He would know of her disdain, both before and after this ceremony. And come morn, all of London would know of it, too.
To eliminate any family debt to her father, she would marry Innes, become leg-shackled to him for life. That much she owed to the memory of her dear mother. But her life was a matter of hours now, not years.
When Innes came to her bed, he would not find a terrified virgin waiting. He would find a corpse.
And, in her heart, she believed God would understand and forgive her.
Resigned, Alyssa looked at the bishop. Short and portly, he had a distinctive bump in the center of his nose. His eyes held sympathy and his round cheeks were stained red. Everyone had indeed heard her complaints. There would be no doubt what had precipitated her suicide. Her heart slammed against her ribs. Her suicide. Somehow, she must find the courage. She must go to her grave with her honor, her pride intact.
Lingering remnants of hope ordered her to cling to precious life, to silently beg God for just one rescuing knight. But the time for hope, for faith in intervention, had passed.
She held the bishop's uneasy gaze, nodded, and mentally detached herself from the ceremony. Clutching the bouquet of baby roses in her hand, she looked down. A bright red drop of blood was soaking into the white silk. Again she saw her father's blood-stained clothes. A whimper crawled up her throat and died.
The bishop droned on. With each of his words, she receded deeper and deeper inside herself. Then he stated the vows. Honor. Obey. Cherish. Calling her back.
Looking at her expectantly, he instructed her for the second time to repeat them. She prayed for forgiveness. To lie in God's house: surely no sin, not even suicide, could be more offensive. She'd be in Hell until the end of time.
"Lady Alyssa?" the bishop prodded.
She opened her mouth to do his bidding. No sound escaped her throat. She could not speak. She swallowed, and tried again. Her lips moved—she felt them moving under her fingertips—but no sound came forth.
Panic welled. Her stomach pitched and quivered. Whispers from the guests reached her ears. Then a commotion in the back of the church had all heads turning—including hers.
A rakehell demon, masked and huge and swathed in black, moved toward her up the center aisle.
"She'll not wed him!" his deep voice thundered. "This woman is mine."
His words roared through the church and echoed in her ears. Innes stepped between them. The demon smiled. A cold, hard smile, the likes of which she'd never seen.
Alyssa shut her eyes to close out the image that had shivers of fear scattering along her spine. This wasn't happening. It was a trick of her mind. God's punishment for her intent to take her own life. He'd not deigned to provide her with a rescuing knight, and, when she'd taken her destiny into her own hands, in His anger, He'd sent her a bare-necked demon from hell!
Fists clashed with flesh. The splintering sound of crushing bone grated at her ears. She snapped her eyes open. Innes lay prone on the floor, his jaw hanging at an odd angle. Gasps, shocked outcries filled the church. Her father stood up.
"Sit down, Cameron," the demon ordered.
Her father slid back into his seat. Ladies swooned until the pews held more women prone than upright; more escorts and husbands waving fans and attending them than those keeping cautious watch on the demon.
He raised his hand toward her, palm up to the heavens. His voice was soft now, gentle. "Come."
One word. With one word a stranger had done more for her than her own father, more than acquaintances she'd known for years. She didn't know the giant, yet something in his voice, in his tone, bade her to follow him.
A flash of impressions filled her mind. Coat, waistcoat, cut of the finest fabrics. Inexpressibles, a fine leg. Hessians, good quality. Bare throat.
The images stopped.
Her gaze locked onto a crystal amulet hanging from a strip of leather coiling around the demon's neck. Crystal. Her heart throbbed a familiar feeling. Yet it was a feeling she couldn't define or describe. Crystal. Her future with him could be no worse than with Innes. Not that she had any choice. The demon's jaw was clamped closed. He would take her, should she refuse to go to him.
But she would not refuse. To stay meant certain death; to go, a second chance for precious life. She lifted her gaze to meet his and an unearthly sense of rightness, of well-being and contentment, suffused her. She stepped over Innes's supine body and into the demon's arms.
Smiling, he lifted her and turned toward the back of the church. Alyssa's heart thumped against her ribs, against his chest. He was strong and hard, smelling of horse and leather and man.
Lady Jersey sat serene, her hands folded in her lap, a twinkle in her eye. Could nothing unnerve that woman? Alyssa wondered. Mrs. Drummond Burrell wore her habitual look of disdain. Mimicking it, Alyssa sent it back to her. And near the back of the church lay poor Meg, sprawled on the floor, holding a vinaigrette close to her nose.
The demon touched Alyssa's hand. "Let go of the flowers," he said softly. "They are his. I want you to have nothing of his."
Her eyes met those of the man holding her. Warm. Gray and wise. He knew her. He knew her and he'd come for her. She released the bouquet, and watched him toss it. It thumped against Innes's chest, then slid to the floor.
She looked up at the man holding her. They shared a poignant smile. His expression changed, and she read his intent in his eyes. She could turn away. But she didn't. Instead she lifted her face to meet his, and accepted his kiss—his gentle, tentative kiss that so quickly deepened. And, God help her, be he demon or knight, she kissed him back.
He held her firmly, kissed her thoroughly, kissed her senseless, then raised his head and faced the guests.
"Hear my warning," he roared. "Any man who tries to take my woman from me shall die by my hand. This I vow before God and man."
His chest still vibrating against her side, he turned and strode from the church.
His woman. Alyssa sighed, content to relax her head against his shoulder and just hold on.
Seventeen
THE HORSE'S hooves thundered along the road north.
Perched in front of the demon, Alyssa tried to collect her scattered thoughts.
He wouldn't tell her his name, where or why he had taken her, but he had been attentive. Before he'd positioned her in front of him on his powerful black stallion, he had wrapped her in a warm, sable-lined pelisse.
It was then that she'd seen his family ring. And then that she'd known she'd seen it before—somewhere.
Strong moonlight lit the road and the crisp air made fog of her breath. She held herself stiff, distancing her back from his chest, certain that her spine would snap from the jarring ride.
"Lean on me, Alyssa," he told her.
"I'd rather not."
"Do it."
His voice was as hard as his chest. Deciding it unwise to rile him, she lifted her chin and leaned back. "I am not afraid of you, sir."
He tightened his arm around her waist and pulled her flush between his thighs. "That is good to know."
The blasted man sounded amused. Her stomach fluttered, but she didn't object. His warmth felt too good. And this time, his strong hold and daunting size didn't frighten her. Both assured she would retain her seat--even at the breakneck speed they traveled.
Should she be grateful, or afraid of him? For what seemed forever, she vacillated between those two emotions. Fate had delivered her to him. She was not to die yet, and for that she must be grateful. Still . . .
Screwing up her courage, she asked the question she wasn't certain she wanted answered. "Do you intend me harm?"
"You need not fear me." He spoke next to her ear, his warm breath rippling down her neck.
"I don't fear you." Scrunching her shoulder, she turned her face toward his. "But I insist you tell me why you abducted me."
"Not now, Alyssa." He slid his hand up her ribs and halted just beneath the hollow of her breast. "I would remind you, dear lady, that you're in no position to insist on anything."
"I'm not your dear lady." Her voice failed to carry the vehemence she desired. It sounded husky. That was his fault. If his saying her name didn't make her feel like she'd been caressed, she could have railed at him properly.
"We'll discuss this under more comfortable circumstances. Hush now."
His thighs bunched astride her hips. The horse snorted and sped up, making further conversation impossible. What manner of man was he? Affluent and educated—his dress and speech told her that. And for now she supposed she must be content knowing no more. Still, until she knew his intentions, she couldn't help but to alternately thank and curse him. Silently, of course.
She'd seen him angry at the church. Though directed at Innes, his anger had made her knees weak—an affliction she'd suffered entirely too much today. She didn't like it. But she'd like having his anger fall on her head even less. And, certain her temper would only goad his, she prudently held her tongue.
Outside London, near a small copse of trees, he reined in and let out a shrill whistle. Her heart thundering, she turned to look at him. "What are we doing? Why have you stopped?"
"It's all right. You're safe."
"Of course, I'm safe. I'm not a fainthearted miss, sir."
"That, too, is good to know." An infuriatingly amused curl swerved his lip.
"I fear, you are knowing far too much—" Pursing her lips to go on, she saw his gaze hold on the trees and looked there herself. A carriage pulled by four matching grays appeared. Two men up top, sat dressed to the nines in ornate livery. The hair on her neck prickled. "Who are they?"
"Friends, my dear."
Before she could remind him again that she was not his dear, the carriage joined them on the road.
"Milord." The coachman addressed her captor.
Nodding acknowledgement, he dismounted then held his arms out to her.
Milord? Confused, Alyssa slid down. He was a noble? A lord?
"My dear," he said, "may I introduce Major, my coachman."
"Milady." Major inclined his iron-gray head.
Estimating his age near fifty, she met his lively eyes and nodded. Being introduced eased her fear. If her abductor felt free to identify his coachman, to call her his dear, he must not mean her harm. Had he intended those reassurances?
After settling her inside the carriage, he sat down opposite her and rapped against the ceiling, signaling Major to proceed.
"Who are you?" she asked, feeling anger fill the place in her fear had deserted. "And, pray, do answer me, milord. I've grown weary of surprises this day."
His mask rode up on his cheekbones, giving her a glimpse of his straight, white teeth. "I will soon be your husband, Alyssa."
Shock careened through her. "My what?"
He chuckled, deep and throaty, and draped her legs with a blanket that had been beside her on the seat. "Your husband, milady." Brushing the cover smooth across her skirt, he tucked the ends under her kid slippers. His hand grazed her silk-hosed ankle. "You feel nearly frozen. Shall I hold you?"
"No." Her husband? "Are you daft?"
He shrugged. "I've been called daft once or twice—and worse. But don't concern yourself, my dear. My mind is as fit as my body."
She frowned. "From what I've seen thus far, milord, I would say your wits are lost inside your body."
He looked puzzled. "Was there a compliment hidden in that statement?"
She sent him a chilling smile. "And I thought my insult quite clear."
"Had you meant it, it would have been. But you lied."
"I did not."
"You did," he countered. "Don't you want to know where we're going?"
"You won't guide me so easily, milord. I did not lie," she insisted, knowing she'd lied through her teeth. "Where are we going?"
"You lied." He smiled.
Alyssa vowed she'd not explode. "Milord, I've had just about enough—"
He yawned.
She scowled at him. "You're rude, too."
"I'm bored. If you insist on telling falsehoods, my dear, you must learn to become poker-faced."
"You're annoying me."
"Good. Perhaps if you grow sufficiently annoyed, you'll ask where we're going."
"You are the most arrogant man, I've ever had the misfortune to meet. Now where are you taking me?"
"I am arrogant," he confessed, not sounding at all repentant. "We are en route to Scotland. Gretna Green, to be precise. You will marry me there. Then we'll retire to my country estate for our 'going away.'"
Alyssa stared open-mouthed at him. "I'll not marry you."
"We'll stop in Carlisle for fresh horses," he continued as though she'd voiced no objection. "I expect you to pay for them—the parson, too—though, of course, I'll provide the necessary funds." He smiled. "Brides are not prone to carrying their reticules on their walks down the aisle. Why is that, do you suppose?"
"You're mad," Alyssa said, finding only enough of her voice to whisper. How could the daft man smile at her?
"Quite the contrary, I assure you. If the validity of our marriage is challenged for reasons of duress—I would remind you that I did kidnap you, my dear—we must have a witness able to testify that you paid for the horses. Any charge of duress will then be nullified."
He looked so pleased with himself. "I'm not likely to forget that you abducted me, milord. And, since you did, pray tell me, why should I do what you ask? I would think you'd be concerned with the imminent dangling of your feet from the cinching of a noose around your neck."
He flashed her a wicked grin that lifted his mask and crooked up the left side of his mouth just enough to set her heart to thumping. "I'll not hang, my dear. I wouldn't think of making you a grieving widow. No," he leaned back against the seat and gave his legs a lazy stretch. "I prefer that our marriage be a long one."
She scowled at him. "You've not answered my question. Why should I do as you ask?"
Like a sleek, dark cat, he leaned forward. Their faces very close, his breath warmed her cheeks. "Because you're mine."
She opened her mouth to rail at him, then closed it without uttering a word. When she thought she could speak without screaming, she uncurled her fists. "I belong to myself, milord."
His voice lost its light banter and he resumed his lazy sprawl. "You were nearly Innes's. I sensed you weren't wedding him of your own free will. Was I mistaken?"
"No." She confessed to what everyone present in the church had known. "You were not."
"You might as well wed me, you know. Even if I returned you to London—which, of course, I shall not do—none would believe your virtue intact. Especially those who witnessed the abandoned kiss you gave me in the church. Thank you, incidentally, for that kiss. It was most pleasant, dear lady."
Hearing amusement in his voice, she shot him a haughty look. "I've reminded you several times, sir, I am not your dear lady. And no gentleman would mention that kiss."
"You've already said I'm no gentleman," he reminded her.
"An assessment you've proven correct."
"And never disclaimed."
"You're a lord," she challenged. Didn't the dull-wit realize he'd been insulted?
"Indeed I am. But then so is Innes." He stroked his jaw, looking every inch a rakehell. "Tell me, my dear. Do you consider him a gentleman?"
She wanted to slap him. He knew she hated Innes. Why did the cad persist in taunting her? As stubborn as he was offensive, she refused to answer him.
He laughed. "He won't marry you now, you know."
In that, he was right—thank God. Still, her pride insisted she contradict him. "Lord Innes is my betrothed."
"Was."
"The man isn't dead, milord." She remembered the odd angle of Innes's jaw. "Is he?"
"No. But he is no longer your betrothed."
"I can't say that displeases me," she admitted, not sure quite what to make of her captor. "It's a relief to be free."
"You are not free." His hard look lent sharp emphasis to his contradiction. "You're mine."
She lifted her chin. "And how did you arrive at this conclusion?"
The horses slowed to a stop. "Major?" her captor called out.
"No worry," the coachman called back.
The stop remained unexplained, but her captor didn't appear uneasy. The blasted man seemed relaxed. He turned on the seat and his knee brushed against her thigh. She jerked away and glared at him. Though he held her glare, she couldn't help but notice that he didn't glare back, and, feeling petty, she looked away.
They sat in silence for long minutes. Battling the urge to tap her fingers on the carriage wall, she heard the coachman climb back atop the box. Soon they were again on their way.
The quiet night and rhythmic motion of the carriage conspired against her. Her eyelids grew more and more heavy. Weary, still recovering from the fever, she fought the affects of the day's excitements. But the needs of her body claimed victory, and soon her eyes drifted closed.
"ALYSSA? ALYSSA, wake up."
She was so warm, so comfortable. "Just a few more minutes, Meg," she mumbled, snuggling deeper. Slowly, she became aware of a pleasant scent. A man's scent! Wrapped in a man's arms! Gasping, she bolted upright.
"Careful." Chuckling, he steadied her, his hands at her waist. "I'm sorry to disturb your rest, but we are in Carlisle. You must pay for the horses."
She sat on his lap? Mortified, she tried to free herself, but he refused to release her. "I won't do it." Fighting him was futile—he was twice her size—and unwilling to expend wasteful energy, she stilled.
"You will do as I've asked," he insisted. "I want only to protect you, Alyssa. And I will protect you. Please do not force me to implement harsh methods against you to do so."
Only to protect you. His words niggled at some long forgotten memory. But, like his signet ring, recalling where or when she'd encountered them escaped her. His threat was clear. She'd have to be a fool not to know that he'd meant it. "Are you always so forward, milord?"
"Yes." He pressed the funds into her hand and closed her fingers around them. "Give all of this to the stablemaster. There's a hundred-guinea fee included for the witness. I want him to recall you."
She had to remind herself not to shout. The man was slow-witted. He must be. Nothing else could explain his behavior. "Shouldn't a witness know more than my face? Must you stand at my side masked like a highwayman?"
"A valid point. I knew you'd be quick-minded as well as beautiful." His smile wobbled his mask. "Be still now. I don't wish to drop you on your elegant—"
"That's quite enough, milord," she said in her most haughty voice. But, taking his advice to heart, she dared only shallow breaths for fear her backside would leave his hard thighs and meet with the harder carriage floor.
He reached up and untied his mask. Alyssa found she was trembling. Though honesty forced her to admit she trembled not in fear, but in anticipation.
His raven hair curled long on his neck, a bit too long to be fashionable, but oh so attractive. His clean jaw shaped a strong and arrogant face, the perfect foil for his eyes. They were his most remarkable feature, the clearest gray she'd ever seen. Striking. Haunting.
"You're staring, my dear lady. Could it be that you're bemused? By God, I believe you are."
Bemused fit her feelings precisely, but she'd die before admitting it to him. He was the most handsome man she'd ever seen, stirring something deep inside her. Shifting on his lap, she gave him a good frown. "Not hardly, milord. Actually, you're quite ordinary," she lied. "And arrogant."
"Ah, it's too late for falsehoods, milady." His eyes danced mischief. "You were caught with the truth in your eyes."
She lifted her chin a fraction, then stared down her nose at him. "You are no gentleman."
He laughed. "So you've said. Permit me, however, to introduce my disreputable self." He nodded and deposited her on the seat. "Kevan Buchannan, seventh earl of Sussex, milady."
Before she could respond, he alighted from the carriage and assisted her down.
With him beside her, she paid the stablemaster for the horses, smiled at his delighted look on taking the funds, and returned to the carriage, knowing all the while that now she must do something to forestall this marriage. Yet she'd didn't feel the urgency to take the drastic measures that she had with Innes. And she didn't understand why she didn't. Both men were criminals. One a murderer, the other a kidnapper.
She would have died on marrying Innes, but was the rakehell who'd kidnapped her any better? In these modern days, what kind of lord would kidnap a wife?
When they were again underway, she looked at the handsome man sitting opposite her. "Are you truly Lord Buchannan? I admit I'm fatigued, milord. My perception might be askew. I believe you wealthy and educated, but I am not so weary that I accept your identity without question. What you've told me appears a Banbury tale."
His chest swelled. "My dear lady, I am not accustomed to having my identity—or my word—questioned."
"You abducted me," she argued. "That is not the behavior one would expect from a man of noble birth."
"One must follow the dictates of one's conscience. I am who I profess to be."
Unimpressed by his lofty manner, Alyssa stared at him.
"I see you require proof." He sighed. "Very well."
He raised his walking stick. Alyssa flattened herself against the seat. "Don't you dare strike—" She fell silent under his scalding glare.
Without a word, he tapped the head of his stick against the inner roof. Heat burned her face, and she felt certain she'd die from embarrassment.
The carriage drew to a halt, and he turned toward the window. "Major, kindly inform the lady of my identity."
The coachman's voice rang out from atop the box. "Kevan Buchannan, seventh earl of Sussex."
"Thank you, Major." Lord Buchannan grinned at her, softening his inflexible features. "You may proceed."
Far from soothing, Major's affirmation upset Alyssa more. Why would a noble commit such a heinous crime as kidnapping?
Blunt, she decided. He must be penniless. "Milord," she said in a soft voice, wishing to give him no offense. He had saved her from Innes and sure death, after all. She supposed he deserved civility, if not kindness. "I expect your reasons for wanting to marry me have to do with straitened circumstances—"
"You said you believed me wealthy," he interrupted. "You were correct. I have no need of your funds, nor do I desire your dowry. You may keep it for pin money."
Alyssa swallowed hard. She had no dowry. She had nothing. Her father and Innes had seen to that. "Then why—"
"I am twenty-seven," he interrupted. "It's time I marry. You are twenty-two, outspoken, opinionated, and in dire need of a husband. Regardless of your father's poor influence, you are of good stock and gentle birth. Simply put, my dear, we suit."
Alyssa shot him a look of pure disgust. This Lord Buchannan knew a bit about her and her father. But how much? Did he know her father was done up? She couldn't bear him, or anyone, knowing that. Bankrupt. Debtor's prison. Death.
She swallowed a knot of fear. Dear God, in leaving as she had, what had she done? Though her father had condemned her, she could not condemn him. "I can't marry you."
He took her hand in his, entwining their fingers. "You have no choice, my dear." His voice wasn't unkindly.
A warm tingle coursed up her arm to her shoulder. She jerked her hand free. "Why must you steal a wife? A woman betrothed to another man?"
"I thought I'd made that clear." He frowned, "You were betrothed to another. You aren't anymore."
"I hate to appear bold, milord, but more often than not your explanations leave a great deal to be desired."
"Perhaps." He shrugged. "I'd hoped to spare your tender feelings."
He leaned forward and clasped her hands in his. Was the regret in his eyes genuine? Her wariness doubled.
"You are no longer betrothed to Innes," he said softly. "You are betrothed to me."
"I don't understand why you insist—"
"Innes wagered you, my dear," he interrupted. "And he lost."
Spots flooded her vision. She fought to keep from swooning. She wasn't fainthearted, but the fever, the shocks, threatened to have her becoming so. "You are deceiving me, milord." She forced her voice strong. "How dare you utter such untruths?"
He reached into his pocket and withdrew five cards. "I won you with this hand."
He passed her the cards. Their fingers brushed and a little tingle scattered up her arm. Two twos and two fours. The fifth card was the ace of hearts. "This proves nothing," she insisted.
"Look at the back of the ace."
He held the lantern so that she could see. She read Innes's familiar scrawl acknowledging his loss to Lord Buchannan. "Dear God," she mumbled. "Twos and fours?"
Lord Buchannan nodded, his look triumphant, not at all sympathetic. Blasted man. "You won me with this paltry hand, and you will hold me to the wager?"
"I will. Paltry or no, that hand was enough. You are mine."
Her temper flared. "Milord, I am convinced that you are who you say. And I am convinced that you did in fact wager and best Lord Innes. But I am a woman, not a bit of horseflesh that can be wagered and lost. I do not see why—"
"Because," he cut in, "if you don't fulfill your obligation to me by becoming my wife, you shall do so by becoming my lightskirt. Less dignity and prestige, but either alliance is fine with me. I'll leave the choice in your able hands, my dear."
"But—"
He folded his arms across his chest, his expression dark and demanding. "Which do you prefer?"
Dear God, he was serious! She gripped the edge of the seat and squeezed hard. "You cannot force a woman of gentle birth—"
"I can," he insisted in a tone that sent her heart to thumping and her ears to ringing. "You forget my position—and your own. Now choose."
Alyssa hesitated only a moment. Her father was already undone. She would rather be dead than any man's lightskirt. It seemed fate had taken her father's dilemma and her own future from her hands. "Very well, milord. I have no choice." She lifted her chin. "Though I believe you a rakehell, I will marry you." She worried her lower lip with her teeth. "But—but you must give me your vow of secrecy regarding this wager." She paused to ponder, then added, "And it's only fair that you know of my own vow, though it isn't one I'll state publicly with the others."
"I'm listening."
She attempted to level him with a haughty glare. "You, milord, will never know a moment of contentment in your marriage to me."
He smiled. The left side of his mouth crooked up, and her heart lurched. Blasted man. How did he do that to her?
"I accept your terms. On my honor as a . . . rakehell, was it? Yes. On my honor as a rakehell, I vow I shall never tell a soul that I won you in a game of cards. And, somehow, my dear lady, I will stumble through life without the benefit of being content with you."
How dare he laugh at her? Had the man no sense? "I am most serious regarding this matter," she warned him.
"I'm certain you are. Might I suggest we rest for a while, my dear? There will be ample time to discuss our future later."
Wordlessly, she sat back on the seat and closed her eyes.
Alyssa drifted between hours of hazy sleep and hours of wakefulness, hours of cursing his temerity and hours of being grateful, even flattered that he wanted to marry her.
During one such nap, she heard Kevan calling her and opened her eyes.
"Put on your gloves."
Looking pleased, he glanced out of the window. She snatched up her gloves and tugged them on, her gaze following his. "Where are we?"
Passing over a narrow bridge, the carriage lurched. Alyssa lost her seat.
He caught her in his arms, his pleasant scent teasing her nostrils. When he didn't release her, she looked up and met his gaze.
"Come."
Hot and dark, his eyes held her captive. She wanted to look away, but lacked the strength. His hands at her waist, he lifted her onto his lap. Her heart skipped, then thudded wildly. Her gown crinkled against his hard thighs. His lips hovered mere inches above hers. "Milord?" she whispered.
He dipped his head until his lips brushed against her mouth. "Yes, my dear. We have arrived. Welcome to Scotland's Gretna Green."
Eighteen
"I WON'T DO IT, milord." Alyssa clenched her hands into fists at her sides. "I will not be married by a man in his altitudes."
"Alyssa," Kevan insisted, "be reasonable. He is authorized to perform marriages by the Church of England. If you refuse, then we must be married by the blacksmith. Do you want an 'over the anvil' marriage?"
Alyssa glared at him. "I'd prefer to be married by a metal anvil than by a cup-shot parson, and that's the truth of it."
Kevan let out a sigh and resisted the desire to pace the innkeeper's private salon. She was stubborn, and the three day journey had done little to improve her disposition. But he'd wanted her for over a year, and he'd gone to great lengths to get her. If a blacksmith suited her better than a cup-shot parson, so be it. He turned to his coachman. "Major, get the smith."
Minutes later, Alyssa said the vows that made her his wife. A coil of tension slowly unwound inside him. Until she'd actually said them, he hadn't been at all certain that she would go through with it. His heart pounded then lurched in his chest. His wife. He rubbed his cheek to hide a smile. By God, life looked good.
In a covert glimpse, he saw her jaw snap shut. His smile faded. Though elation soared in him, Alyssa looked far less pleased with her circumstance. But then, he reminded himself, she didn't understand her circumstance. Once they settled in at Woodwind, she would realize that marrying him had been a wise decision.
And he would take great delight in her learning—once he got past her temper. Though, if the glare she had leveled on him provided any indication, that could take a while. He stifled the urge to rub his neck. His wife was a spirited woman. But he would tame her. A thrill of anticipation shot through him. She wouldn't like it, but he would tame her.
The smith spoke the final words, and Kevan bent to do what he'd waited fourteen long months to do. He kissed his bride.
This kiss bore no resemblance to the one she'd given him at the London church. Alyssa was neither soft, nor yielding. But he'd surprised her then, and gratitude had ridden companion to her turmoil. Expecting this kiss, she was skittish, defiant, her inexperience more discernible.
Gently coaxing her, he was not disappointed. He knew the very instant she forgot her displeasure and opened herself to him. A little whimper escaped her throat, whispering her delight. Beautiful. He sighed against her soft lips. From the crown of her silver-haired head to the toes of her white kid slippers, she was the most beautiful woman he'd ever seen. And now she was his.
He forced himself to release her. Flushed a becoming pink, she looked bemused. Warm and protective urges he'd known before, surged from even deeper inside him—an effect he'd deemed quite impossible.
Her eyes were smoky soft, intoxicating. "Milord?"
He heard confusion in her tone. She didn't understand the feelings his kiss had awakened in her. But he understood them. Breathing in her scent, warm and sweet, he smiled his contentment, and corrected her. "Kevan, love. You're my wife now."
"Yes." That thought seemed to jolt her, and the softness in her expression disappeared. "Yes," she agreed in a tight little voice. "Curse or blessing, I am your wife."
He didn't take insult. Nor did he smile, though he wanted to. It seemed his wife, too, at times preferred wearing a mask. But her righteous indignation proved a poor substitute for cloth. She feared him. Placing himself in her position, he understood her fear. He didn't like it, but, considering his actions, he understood it. Unfortunately, she was not likely to believe his explanations. But soon he would put her fears to rest. "Have you paid the parson?"
"Smith," she informed him in a voice that pinched more than a new pair of boots. "The man is a smith."
He resisted a chuckle. "The smith, then."
"Not yet."
Her annoyance amused him. Did she expect her anger to cool his ardor? The idea was laughable. He'd pursued her relentlessly. And, being as territorial as men have been about their women since the beginning of time, he conceded that as surely as he breathed, his obsession would continue until time's end. He forced his voice stern. "Please do so, milady. The hour grows late."
She slid him a mutinous glare, then thrust the blunt into the smith's hand. Her scowl threatened to lay the poor man low. With a swish of her skirt, she bent over the table and signed the parchment.
Kevan risked smiling at her back. And, not for the first time, he suffered a twinge of doubt. Would the delectable Lady Buchannan like what she learned about him? Her gown pulled taut across her hips. A jolt of desire surged to Kevan's loins. She'd better, he decided, catching a glimpse of her ankle—the same ankle he'd touched in the carriage.
This marriage was for life, and the thought of her nagging him into his grave years before his time was not a pleasant one.
What was he doing? he chided himself. Worrying over a woman? And a tiny woman, at that. A strong wind would surely blow her over. He crossed his arms over his chest. She would grow fond of him. He would demand it. She was his wife. It was her duty to not only like him, but to love him. And, by God, he'd see she did her duty.
She straightened and held the quill out to him. "Milord?"
She'd avoided using his name again just to be contrary, he was sure, and her tone held a distinct challenge. A mere slip of a woman dared to challenge him? Arching an amused brow, he accepted the quill. Bringing her to heel promised to be a most enjoyable challenge. "Thank you, my dear."
He affixed his signature to the document, feeling her gaze heat his back. She could be difficult. But he'd already learned the value of varying his actions. Of all of them, she seemed to dislike his feigning boredom the most.
Yet she was not an easy woman to unbalance. An admirable trait, that. Not many of her gender found the combination of his size and dark looks easy to address. But Alyssa clearly had no qualms with letting him feel her temper. When he'd told her to choose between becoming his lightskirt or his wife, she'd looked ready to lay him low. He'd liked that, too.
He shuddered at the risk he'd taken in letting her make that choice. What would he have done had she chosen to bed him, but not to wed him?
His answer required no thought. He would have done the same as any man set on marrying: dragged her here, kissed her senseless, and kept her senseless until after they were wed. Though that endeavor held an enticing appeal, his use of force hadn't been necessary. Why had she conceded?
He slid his wife a thoughtful look. She stood glaring at him. Her reason was of no consequence, he supposed. What did bear consequence was his mission. And, thus far, it had been a smashing success.
Responding to inane comments and well-wishes from Major, the smith, and the innkeeper, he pondered the matter of intensifying his relationship with his wife. Devotion, he decided, accepting a glass of brandy from the innkeeper's wife. Yes, that strategy appealed. Since her mother's death, Alyssa'd had no one she could depend on. He'd be the man she could lean on for support, the man she could come to with her concerns. That suited. As her husband, those rights were his due, as was her affection. His chest swelled and he lifted his glass to toast his wife. By God, life looked good.
Soon Kevan tucked the marriage document inside his coat, and returned with his wife to the carriage. When Alyssa settled, he wrapped her legs with the blanket. "I know you've been ill, love, and I'll do my best to see to your comfort, but we must return to my home in Brighton at once."
"I am not your love, Kevan." She swatted at his hand resting on her knee. "And kindly refrain from taking that liberty with my person. You wanted me as your wife, and you've won. But, as I have promised, it'll be no pleasure."
"Very well, my dear. But remember this: you are my wife. For now, I will permit your virgin sensibilities to repel my touch. But you will accept my endearments without complaint, and you will play the part of my devoted wife in the presence of others."
"And if I don't?"
"Do not push me, Alyssa." His eyes narrowed. "I want to be loving with you. To lead you, and to protect you. A wise woman accepts her destiny—without force."
THE JOURNEY to Brighton took three days, and, more fatigued than she realized, Alyssa slept through a great portion of it. Several times during the trip, she had awakened in Kevan's arms, her head resting against his shoulder. Now it was he who slept, and she wondered if he had studied her sleeping countenance.
Though massive, without the black clothes and mask, Kevan seemed less formidable. His dark head rested against the carriage wall and rocked gently with the rhythm of the ride. His features, softened in repose, made him more appealing, more like the rescuing knight she fancied had abducted her because he had a partiality for her.
He was her husband. Her husband. Being married to this intriguing stranger, this lord who behaved as anything but a lord, amazed her. Had she somehow conjured him up?
She let her gaze slide his length, from the tip of his dark head, down to the toes of his black boots. She pinched her forearm purple, assuring herself that he was no dream. But, still unconvinced, she gave in to temptation and touched the arch of his lip that crooked up when he gave her that special smile. Her fingertip trembled. His jaw, slightly roughened by a day's growth of beard, provided undeniable proof. This man was flesh and blood. And, pity, but there was a lot of flesh.
Sitting back, she felt him graze her finger with his teeth. Her gaze darted to his.
"You may touch me whenever you like, Alyssa."
Her face flooded heat. "I don't wish—"
"Do not lie, my dear. Buchannans are people of their word." He licked the tip of her finger with his tongue. "You want me."
"I do not."
"You do," he insisted.
"Kevan. I don't even know you. How, pray tell me, could I want you?"
"You do."
She glared at him. "I'll admit I like knowing you're a man of your word," she said, thinking to appease him and turn the subject in one swoop. It salved her conscience, too. She hadn't lied. Not once had he attempted to take liberties with her person, though she did wish—in between her engaging pastime of flinging silent curses on his head—that he would kiss her again. It was sinful, the things his kiss and its memory brought to her mind.
He cast her a wicked smile. "You want me. No, don't bother to glare at me, Alyssa. I'll not wither. Just tell me what draws you to me."
Why did she feel drawn to him? He was devastatingly handsome. But his appeal ran deeper than his good looks. "I'm not," she lied.
"Perhaps my attentions to your comfort," he suggested. "I would remind you, my dear, few men realize the attachment between physical and emotional comfort. Is that what makes you want me?"
A wise man, this one, and arrogant, too. "I don't want you."
He ignored her. "My thoughtfulness?" He lifted one shoulder and a brow. "I have provided you with appropriate clothing and warm blankets. Or maybe what makes you want me is my romantic nature."
She guffawed. "You're arrogant, milord. And about as romantic as a stone."
"Alyssa, you wound me. I present you with a wall flower every morning." His eyes lit with mischief. "Or was that another of my women?"
Alyssa clamped her jaw shut. The maid at the inn had gushed, saying each flower held a special message. She'd given Alyssa a list of them. The wall flower meant patience and affection. Had Kevan known that? More than likely he hadn't. "No, milord. It's not one of your other women. I receive your flowers. I see you require your Creator's protection against your faulty memory. I shall request His indulgence on your behalf."
"You believe it necessary?"
The vile man knew his goading had hit its mark. "I do. Because I'll tell you now, I'll not tolerate you giving flowers to another woman."
"I knew you were drawn to me," he roared, smacking his thigh. "You're jealous. By God, you are. You're jealous."
"What I am, milord, is sorely tempted to slap that smirk from your cheeks. While I am not a violent woman, I assure you that neither am I a meek one. I realize that although I am your wife, I am a stranger to you. So I suppose it only fair to warn you. Do not push me too far, or you'll find our marriage intolerable."
"You've already vowed I'll know no contentment with you. What more can I lose? No, I think I will love pushing you too far, my dear. You're exceptionally attractive when your temper is up. And it flares quite often, doesn't it?"
"When you must attempt to soothe my temper and fail, I daresay, you won't appreciate it quite so much."
He looked at her, the devil in his eye. "That is the part I look most forward to, my dear."
"Failing?"
He slid her a slow, sure smile. "No, love. The soothing. I'm told, I'm rather good at it."
Blushing to the tips of her toes, Alyssa swallowed her reply and stared out the window. When had the weather turned so unseasonably hot?
FINALLY, THE SUSSEX coast scenery was soothing her frayed nerves. So much worry and concern for the future had occupied her during the journey. Her father had in effect sold her to Innes. The hurt and anger that came with the knowing wounded her heart. In turn, Innes had lost her to Kevan. But for that, she could feel only gratitude. And she'd married Kevan. Done her duty, fulfilled a commitment she hadn't made, but one that should insure her father's safety. Any man of honor would agree.
But Innes had no honor. He'd proven that by attempting to wed her after he'd lost her to Kevan. And what about Kevan?
He was an enigma. What had he wagered? Why had he done all this? He'd said he wanted a wife. But an earl—especially one so powerful, so appealing in person, and so able to provide security—didn't have to resort to abduction to get a wife. Any unmarried woman in England would be happy to wed him. Which meant he wanted her specifically. But why?
Stealing a look at him from under her lashes, she watched him gaze out on the scenery. Could he be as relaxed and rested as he appeared? She felt as tense as a stretched rope, and tired to the bone.
"Are you comfortable, my dear?" he asked.
She kept her frown inside. "I'm weary of traveling, milord."
"But you are not unwell?" He sounded anxious.
She hastened to reassure him, though she didn't understand why she felt the need. "I'm fine, just tired."
"We'll arrive soon. Shall I tell you of an interesting journey?"
She nodded and sat back to listen. Kevan embarked on a recollection of his experience ballooning. While he talked, she studied him.
As long as she remained civil, Kevan had proven himself a most interesting companion. Though she still found his massive size daunting, he was quite gentle with her. At least he had been—so far. And he had a keen mind, a warm wit that she found more than a little appealing.
His coachman, Major, was pleasant and a crack with the ribbons. He seemed happy in Kevan's employ. His horses were well-treated, too. A woman could learn a great deal about a man by the way he treated his servants and his horseflesh. If his house was well-run, she'd know for certain her rescuer was a knight, and not a demon. But either way, she had to accept him, and her lot.
If she found him a demon, she had her work cut out. She'd not be bedded by a demon and, from the way he looked at her, Kevan Buchannan would not honor her virgin sensibilities very long.
He kneaded his muscular thigh with the palm of his big hand. Her own thigh tingled. She'd become his wife. Blessing or curse. And she couldn't help but pray that their marriage would prove a blessing. Since her mother's death, Alyssa had been plagued with curses.
The settling tone of Kevan's voice countermanded her worries and lulled her to sleep.
"WE'RE HOME, love," Kevan said, rousing her.
Alyssa awakened bristling against his endearment, but she held her silence. Straightening up, she admitted—if only to herself—a certain anticipation. She looked out of the carriage window. The property, rich in thick green foliage and sun-dappled by huge firs, appealed. Along the road to the manor house, she caught glimpses of distant outbuildings, stables, cattle pens, and ploughed fields that were dormant this time of year. Well-tended, his home provided a serene and welcoming view. "It's lovely, Kevan."
"I hope you will be content here. I enjoy Woodwind."
"And if I'm not?" Her heart pounded, waiting for his answer.
"Then we will leave. I have others."
That concession surprised her into smiling. It seemed ungracious to vow misery on a man willing to give up his home to see her content. And, considering that the man was her husband, it seemed positively foolish.
She had wedded him of her own accord—more or less. Well, she bowed to honesty, she'd wedded him, anyway. Still, she'd no intention of wasting this second chance for a full life. He had abducted her, yes—and even now he wouldn't tell her why—but if he hadn't, she'd be dead. That truth set her back on her heels. Wasn't gratitude a good reason to try to make their marriage a success? A just cause to treat him fairly? She decided. "I know we will be content here, milord."
"You have accepted me, then?"
He returned her smile, and her pulse sped. Her meaning was not lost to him. He knew her vow to make him miserable had been rescinded. Her future, though uncertain, would not be hampered by angry, passionate vows made in fear. "You are my husband, Kevan."
Looking pleased with her, he agreed. "I am."
The carriage rounded a curve and the gray stone manor house came into sight. A grand two-story Tudor structure, with arched, mullioned windows and a tower that stretched past a huge rose window above the front door presented a stately facade of timeless elegance and strength.
The carriage drew to a halt in the front drive. Kevan got out, then assisted Alyssa. She swallowed hard to assuage a fist of fear that formed in her throat and threatened her disgrace.
On the ground, she looked down an impressive line of servants, all spotlessly clean and dressed in crisp uniforms that depicted their positions. All with curious eyes. And all breathlessly waiting to see if she would be a tolerable mistress, or one who would make their lives a living hell.
Having lived with fear herself, she recognized theirs, and, anxious to relieve them, she smiled. "Kevan, I wish to meet everyone."
Her lord raised his brows, but she thought she saw a glint of approval in his eyes. Standing at her side, he began the introductions.
Try though she might, Alyssa simply could not keep everyone's name and face aligned. When the last of the introductions had been made and she and Kevan neared the doorstep, she felt grateful for the smiles coming her way. This would be her home, these people, her people, and she wanted their acceptance and regard.
Kevan lifted her in his arms and carried her into the great hall. When he set her onto her feet, he settled his hands on her shoulders and urged her to him. She went willingly, and his eyes grew warm with affection.
"Welcome home, milady."
His soft emphasis on the words claiming her as his own captured her breath and fed her fantasy that he'd married her because he held a secret admiration for her. She could no more resist his kiss than she could swim. "Thank you, milord."
When he bent down, she raised up to meet him, to welcome the magic that flowed between them. His gentle lips wiped her mind as clean as a freshly washed slate. And not because she wanted to, but because she had to, she raised her hands to cup his face.
The texture of his skin had her fingertips tingling, gliding the length of his jaw, stroking his cheekbones. The angles that had looked so hard, softened, welcoming her touch.
She was a woman feeling strange things. Dark and compelling things that must be sinful. A woman suffering the need to press her body against his, to feel the warm strength of his body against hers. Utterly sinful things. Utterly glorious things.
His tongue pressed between her lips, forcing them open. Gasping at the intimate contact, she jerked away. But he held her to him, and her own arms . . . When had she lifted her arms to circle his neck? Her heart threatening to bound from her chest, she met his gaze. His eyes were hot, filled with purpose, and his gaze held her enthralled.
The sound of footsteps preceded a male voice. "Milord?"
The spell holding her captive broke, and Alyssa looked at the butler, Parks. Though tall and erect, he bore no resemblance to the stuffy Burns. There was even the hint of a smile curving his lips. The heat scorching her cheeks cooled, and Alyssa decided she liked him.
Kevan refused her attempts to step away from him. Applying firm pressure to her waist, he hauled her flush to his side.
His smile carried through to his voice. "Yes, Parks?"
"The staff would like for me to convey their best wishes on your marriage."
"Thank you."
It was a customary response, but in it Alyssa heard true gratitude.
"We would welcome your lady with a celebration this evening, milord—with your approval."
Kevan smiled and pressed Alyssa to him. "By all means. But allow us a short respite, if you please. Milady has been ill, and I want her to rest."
"Yes, milord."
Kevan lifted Alyssa's chin. "Will six be acceptable, love?"
Alyssa nodded. Kevan was setting the tone for the servant gossip that would filter from this house to the houses of Brighton. His endearments were not meant for her. Still, his kisses made her hungry to hear the terms of affection he had insisted she accept. He'd spoken them often enough for her to become accustomed to hearing them, but in six short days, how had he instilled in her the desire to hear them? Or her wanting to believe them?
"Six o'clock, Parks." Kevan turned with her toward the grand stairs. "Milady and I will retire until then."
Flooded with heat, Alyssa opened her mouth to protest, but Kevan's warning look kept her silent.
Bristling and stiff-spined, she walked with him up the sweeping staircase where generations of Buchannan portraits hung. Every male had the same dark looks, the same wise eyes, and, oddly, each wore a shirt open at the throat. Each also wore a crystal amulet like Kevan's. Her chest tingled. Was the amulet a family tradition, then?
When she screwed up the courage, she intended to ask Kevan about the amulet's significance. Then perhaps she could learn why seeing the crystal had such a profound effect on her. His signet ring tugged at her memory. But the amulet tugged at her heart.
Above stairs, near the end of a long hallway, Kevan stopped and opened a heavy carved door. "This is your chamber, my dear. You can view the rest of our home at your leisure."
The room was large and tastefully decorated in a deep mahogany wood that boasted intricate rose carvings. Delicate and exquisite. Satin, brocade, and velvet—all in white—draped the bed, the windows, and a small lounge near the far wall. Though untouched by color, the room was made rich by the many textures in the luxurious fabrics, bespeaking a quiet gentle elegance that greatly appealed to her.
"Will it suit?" Kevan closed the door.
Alyssa turned and glared at him. "The room is perfect. Your behavior, however, does not suit, milord."
"Excuse me?" he said, his puzzlement clear in his eyes.
"Why did you intimate that we would be resting together? Parks will think—"
Kevan assumed a bored stance. "Parks will think that I'm making love to my wife. Which is precisely what I want him, and everyone else, to think."
"Kevan, your servants are not fools. Nor am I. Too soon you'll call a lightskirt to your bed, and the truth will spread like a brushfire."
Kevan smiled, but there was no humor in his eyes. "My dear, Lady Buchannan. If you fear another woman occupying my bed, you may halt any intrusion by appearing there yourself."
Alyssa narrowed her eyes and sent him a solid frown. "Is that an ultimatum, milord?"
His eyes glinted like hard metal. "Every man has baser needs. If his wife refuses to satisfy them, then what alternative does a husband have but to take a lightskirt?"
She stomped toward him, anger heaving her chest. "You agreed to honor my virgin sensibilities until we feel less like strangers, but you will do this? In the house I am to make my home, you will brazenly take another woman into your bed? Dear God, Kevan. You could sire a bastard—in our home!
He shrugged an unconcerned shoulder. "Would it bother you, love?"
"Bother me?" she shouted. "Bother me?" She drew in a sharp breath and choked on her blistering retort.
"I asked you a question," he persisted.
"Would it bother you if I took another man to my bed?"
He looked down at her, the force of his gaze weakening her knees. "I have not refused to make love to you, Alyssa. And I do enjoy having a woman in my bed." He walked to the mantel and fingered a shiny candlestick. "Never is a woman more lovely to her lord than when she's in his bed and he's filling her body."
Alyssa gasped. "Do not speak of such things to me."
"Why not? Husbands often confide these matters to their wives, and I am no exception. I intend to confide my darkest desires to you."
She jerked off her gloves and slung them onto the vanity. "You may keep your desires, milord. But you'd be wise to confide your intentions."
"What intentions?"
"For pity's sake, Kevan." She gave him an accusing review. "Just look at you. Your taking a lightskirt won't be long in coming."
"You think me virile." He smiled, looking very pleased with himself. "By God, you do. You think me virile."
"Don't look so elated, milord. What I think you, is daft."
"You don't," he countered. "You've no need to be embarrassed, love. It's more than permissible for a wife to find her husband appealing."
She found him arrogant—and lusty. But admit that? Never. He'd taunt her forever. "Appealing?" She thrust out her chin. "It is you who finds your countenance virile and appealing. I said daft."
"You lied."
"I didn't."
"You did."
"Kevan, I'm growing hostile," she warned him.
"You did lie, darling." He gave her that grin. "But I forgive you. Still, you might be right about my impatience. But I promise not to neglect my responsibility to pleasure you, too."
"Responsibility." Exasperated and totally vexed, Alyssa stamped her foot. "Would you turn your mind from matters of the flesh long enough to consider the damage you'll do? Think of the scandal, blast it. Your taking a lightskirt so soon after we've wed—even without your siring a bastard—would have our names being wagged on the tongue of every member of society. They'll say such awful things. Can't you just see that wicked Mrs. Drummond Burrell looking down her disdainful nose?"
"Most men keep a lightskirt, Alyssa. You know that."
"But not so soon."
Kevan's expression grew dark as a thundercloud. "Then your objection isn't that another woman will share my passion. Only that she will share it so soon after we wed. You fear what others will think? What they'll say?"
"Of course, I care. We live in society, Kevan. And they will hear of your untimely infidelity. No matter how cautious you are, word will filter from the servants into Brighton, and from there it will fly to London like a swarm of bees carrying it on their buzzing wings. Our marriage will be a laughingstock." She paced and gave him a firm negative nod. Other men might, but her husband would not keep a lightskirt. "No, it just won't do. I won't have it."
Kevan stepped into her path. She stopped in front of him and looked up. "I won't have it, Kevan."
"Fine." He spoke so softly she had to strain to hear him.
"Fine?" Her heart pounded. "You agree, then? You'll not take a lightskirt?"
"Will you come to my bed?" he countered.
She turned away from him, felt his hands slide to her shoulders, his chest press against her back, and then, dear God, those magical lips of his lingering on her neck.
"I'd prefer you in my bed, darling," he whispered in a husky voice. "You're my wife. I want to love you, to awaken your body, to see your loveliness in my—"
"Kevan," she whispered on a moan. "Please, stop. Please." Fighting her attraction to him was growing more difficult by the moment. Why were her emotions so involved? Her fantasies were just that—fantasies. Kevan did not hold a tendre for her. He'd told her why he'd wed. Forcing her logic through her muddled emotions, she turned in his arms. "You want an heir."
He smiled down at her and squeezed her shoulders. "That, too."
Her mouth went dry. "Too?"
His eyes turned molten, scorching hot. "I want you."
Tremors jolted her body. "Blast and damn," she shouted, jerking away from him. "I knew you were no gentleman, but I didn't think you an incorrigible rake. It's most unkind of you to toy with my tender feelings."
"I agree."
She spun to face him. "You agree?"
"I do."
"Why you arrogant—"
"Alyssa, before you rant, shouldn't you listen?"
"I do believe I've heard quite enough for one day, milord. Of all the—"
He caught her shoulders and kissed her quiet.
She felt the fight seeping from her and doubled her efforts to hold onto it. Still, he proved stronger-willed, and the battle of their tongues, tangling, warring inside her mouth, made her somehow forget her exact objection.
He raised his head and sought her eyes. "If I had been toying with your tender feelings, then I would have thought myself cruel. But I was not, Alyssa. I am not."
She let out a small gasp. "You are."
He laughed at her. "I know my thoughts, dear lady. You may not direct them. And the thought of you in my bed is distinctly clear."
She squeezed her eyes shut. "You're a wicked man, aren't you, milord?"
"Perhaps," he whispered in a rakish tone. "You would consider my thoughts at this moment most definitely wicked."
Her eyes snapped open. "Have you no shame?"
"None at all. I have every right—no, every duty—to bed my wife, and . . . By God, you're blushing. Has no one ever told you how beautiful you are? How desirable?"
Well, pity. The scapegrace had her feeling bemused again. Certain her demon-knight would see it and torment her for it, she gave him a good glare to express her displeasure. "Of course not."
He smiled and stroked her cheek. "I'll not either, then. I'll show you how beautiful you are to me." His voice dropped even lower. "Will you come to my bed willingly?"
Temptation scorched her. She sank her teeth into her lower lip, demanding that her heart stop trying to rule her head. "Not yet, Kevan. I can't . . ."
"To prove myself honorable, I'll give you a little time, then," he promised, whispering close to her ear. "Until you're willing—provided you don't take overly long. But you must not refuse my touch, Alyssa."
She looked up at him, knowing fear shone in her eyes. "I won't refuse your touch, or even your embrace, but—but you must not take a lightskirt in my home, Kevan. No woman is to share your bed. I—I—"
"Your pride could not bear it."
Her heart was what couldn't bear it, but her pride proved easier to admit to, so she didn't correct him. His eyes promised understanding, and, unable to speak, she nodded.
"I'll bring no lightskirt into your home. In return, you must welcome my kiss and my touch whenever and wherever I desire. I'll not be denied that pleasure, too, by my wife."
He had not agreed that there would be no lightskirt, only that he would not bring her here. Few nobles abstained from indulging in dalliances, and she supposed she should consider herself lucky that he'd conceded insofar as he had. But she didn't feel lucky. She felt angry. The thought of Kevan showering another woman with his affections, smiling at another as he smiled at her, made her livid, her thoughts wicked. Still, Alyssa was not ready to share his bed, and until she was, she had no choice but to agree.
Her head downcast, she nodded, accepting the terms of his compromise.
Kevan raised her chin. "Look at me."
She met his gaze and stifled a shudder. Desire burned deep in his eyes. His hands slid down the lengths of her arms and up her sides to her ribs, branding her skin through her clothes. Her knees grew weak, and she tried to look away.
"No," he demanded in a harsh whisper. "Look at me."
Alyssa forced herself to hold his gaze. His fingertips brushed the upper swell of her breasts and a shiver of excitement raced through her. Could he hear her heart pounding? Feel the tremors storming through her body?
"You will come to me, Alyssa. I want my wife in my bed. I've a need to feel her hands on my body, a need to bring her pleasure."
He captured her lips in a gentle kiss that deepened until it seared her soul. A kiss that left her breathless and melting against him.
Too soon, he released her, and, before she fully regained her senses, he disappeared through the door that she assumed connected their chambers. Her blood coursed through her body, her heart pounded in her head. And a deliciously sweet ache throbbed in her center, a throb she'd suspected in the carriage and now knew for certain linked itself to Kevan's touch.
Dragging in breath, she wondered. Could a woman die from her husband's kiss? No. She clasped her hands at her chest to slow her heart. If a kiss could be lethal, she'd be stone dead. Lord, could Kevan kiss!
"AH, MILADY, you're awake. My name is Lacy. I've come to help you dress."
Alyssa turned from the window and smiled at the young woman addressing her. A shock of thick red curls peeked out from under her cap.
"What gown do you fancy?" Lacy turned and opened the closet.
With a pang of longing, Alyssa thought of the beautiful clothes she'd left at her father's house. "I—I'm not sure." Kevan had provided her with traveling clothes—excellent ones, but did she own one appropriate for a celebration?
"Haven't you looked at them?" Lacy's eyes stretched wide. "His lordship sent to France for them special."
"He did?" A ripple of delight spread inside Alyssa. A man wouldn't bother attending a woman's wardrobe unless he held her in affection. Would he?
"Yes, ma'am." Lacy's nod set her curls to bouncing. "Each collection that arrived was prettier than the last."
Collection? Alyssa's heart tumbled. "When did his lordship do this?"
"Let me see," she said, disappearing inside the closet. Her head jutted out. "It was after Brighton—before the new year, a year past. But don't you be worrying none. They're of fashion. Timeless. Every one of them."
A shiver crept up Alyssa's backbone and prickled her skin. She'd been through Brighton that summer. Accompanied her father to Bath to take the waters for his gout. And they'd come to Brighton afterward to sea bathe, too. But she was certain she'd not seen Kevan then. A woman with eyes and her wits about her wouldn't forget him. Such an imposing presence. If she could just place where she'd seen his ring. It should be easy. The ring bore such a distinct design. A jewel-studded sword . . .
Lacy stepped out of the closet holding a deep blue silk gown. "Will this suit?"
Alyssa fingered the rich fabric, and her breath caught. Fragile, diaphanous, it had no equal. "Yes."
She looked through the closet. Gowns of all kinds were arranged in a neat row: carriage, court, dinner; evening, full-evening, garden; morning, riding, walking, and on and on. Her head was spinning. Each one was more beautiful than the last. Exquisite fabrics, simple designs, delicate, intricate trims. Some with ribbons, some with braid or fur, and all perfectly matched to her taste.
She moved to the dresser and opened each drawer. Then went on to a second chest of sorts and did the same. Her every need, from perfume to parasols, including ornaments for her hair, had been provided. And of all the bonnets, not one boasted a plume. She smiled at that. Plumes were not to her liking—nor, it seemed, to Kevan's.
In discovering her treasures, she'd acquired a bit of knowledge about her husband, too. He had a partiality to blue. Many of the gowns were in various shades of Bishop's, Clarence and Spanish. He bent toward simple designs, understated and elegant, and he purchased only items of excellent quality.
While his choice of outer garments told her of his restraint, the undergarments and nightwear he'd selected spoke of a very different man. A rogue.
They were sinful! Mere scraps of the most beautiful lace she'd ever seen, and sheer gauzy fabrics that were silky to the touch and near translucent to the eye.
How in the world did he expect her to wear such things? Just looking at them set her aflame with embarrassment. Did married women actually appear before their husbands in such a state of near nudity?
She lifted a fan and cooled her cheeks. Walking past her bed, she saw that both pillows were indented. Had Kevan rested there beside her?
Her glance went to his bedside table. On it, she saw a green shamrock. She left it there to flutter in the breeze from the open window and resisted the urge to pull the little flower list from her reticule. "Lacy." She turned toward the bright-eyed abigail. "We must hurry."
Lacy did hurry, and in no time Alyssa was standing before the cheval glass examining herself. The gown, square-necked and scooped low, flattered. And the deep blue color had a startling effect on her eyes. "You've worked a veritable wonder, Lacy. I like my hair swept back like this, too, though the ringlets tickle my nape."
"It's the newest rage, milady. You've got good hair. Fine as silver silk."
Lacy left the chamber, and Alyssa rushed to retrieve her list. "Shamrock. Shamrock." She slid her fingertip down the list. "Shamrock." A broad smile creased her lips. "Faithfulness."
Kevan understood the symbols of the flowers.
Nineteen
FROM HIS BEDROOM window, Kevan saw Alyssa strolling through the garden, her bonnet in her hand. Sunlight sparkled on her hair, loose and spilling over her shoulders. His heart leapt mightily, and he had to reassure himself that she was truly his wife.
The breeze flowing in through the window held a slight chill, and he realized that she wore no shawl. How he longed to warm her but his decision to first earn her trust had been a wise one. For him, an aching one that his body protested more each night, but for his wife, the right one.
He turned for the door. "Hold breakfast, Parks. I'm joining my wife in the garden."
"Yes, milord."
He stopped by her room, then made his way to the garden. If he had bedded her right away, perhaps her reassurance would have come at once. But, considering her past, her ill-treatment at the hands of her father and Innes, the risk was too great. Their marriage must be a good one, an exceptional one—for both of them. Earning trust took time. Oh, Alyssa would be worth the wait; his heart knew that, but his body needed convincing that the torture it endured in waiting was justified. What could he do to speed up the trust-building process? He rubbed his neck, and a slow smile curved his lips. Yes, a little friendly torture might be just the thing . . .
Seeing her ahead on the stoned path, he called out. "Alyssa?"
She turned and smiled, her eyes trusting, pleased to see him. He melted. In six short weeks everything had changed. She'd grown accustomed to him and his home, to sharing his life. She stopped on the path and waited for him. "I brought your shawl. It is March, love, not June. You'll catch a chill."
He draped the garment over her shoulders and lifted her hair. Its silken strands taunted his fingertips. Longing to give in to passion, to tangle her hair with his hands, to fill her body with his, he pressed his lips to her cheek and settled for the satisfaction he felt at their progress. She no longer stiffened at his touch, but seemed to welcome it.
"Thank you."
The brisk air had her cheeks flushed. Her scent mingled with the fresh, crisp, earthy ones of the park.
"May I walk with you?"
"Of course, milord. I thought to view the lake." She smiled up at him. "It's quite possibly the most beautiful place on earth."
Kevan took her arm and covered her hand with his. Of all his properties, Woodwind was his favorite. He'd grown from boy to man here, and that Alyssa found beauty in it pleased him.
They walked in comfortable silence through the park; past the rose garden his mother had designed two decades earlier; past the long, sweeping beds where seven varieties of irises lay dormant until summer. Under a huge fir, near the bank of the lake, Kevan stopped. Surrounded by the sense of home that had given him such security as a child, he faced his wife—and his uppermost concern. "Alyssa, are you content in your marriage to me?"
A faint blush darkened her cheeks. "These past weeks have been pleasant, milord."
Pleasant. A ripple of contentment suffused him. According to Meg, Alyssa had known little pleasure since her mother's death. That she found it in their marriage pleased him greatly. "Do you miss the bustle of London? The season will begin in a matter of weeks."
"No, not really." Squinting against the morning sun, she looked out onto the water. "I like the quiet here. And the solitude."
Though he had observed her appreciation for the country, he suspected that she was afraid to return to London. Her welcome there was uncertain. She'd eloped, after all, with a man who had stolen her from the arms of her betrothed. That blemish on her reputation, and on his own, combined with the abduction had caused quite a scandal among the ton. So much so that Lady Jersey had written, insisting that something must be done about "those certain events" before he and Alyssa returned to London.
"I prefer the country, too," he told her. "I'm not much for the social whirl, or for the machinations of the elite."
"Mmm."
The lake captured Alyssa's attention, and he followed her gaze. Massive trees draped long, graceful limbs over the banks.
"It's lovely, isn't it? The way the water sparkles, like thousands of diamonds bobbing on its surface refusing to sink?" She let out a sigh of contentment. "I must confess, milord. I have developed a tendre for this spot."
Kevan lifted her hand and pressed it to his lips. "It's you who sparkles, my dear. My own diamond of the first water."
Smiling, Alyssa met his gaze, saw the moment affection became desire in his eyes. The cool air seemed to warm between them, then to heat, scorching her through her clothes. Her throat tightened and she whispered. "Kevan, please."
"Yes, love," he whispered. "I please to touch you. Come."
She protested, remaining firm on the path at the lake's edge. "It is the light of day. There are people about."
He stood facing her, his arms at his sides, his gaze burrowing into her soul. "Kiss me. Please, Alyssa. I've a need to touch you. Don't make me take from you. Just once, give to me."
The longing in his eyes, the need in his voice, wrenched at her heart. He'd been so good, so thoughtful in seeing to her needs, her whims. Honorable. Loving. Gentle. And she'd known so little of all three qualities.
How could she explain her feelings to him? She wanted his touch, his kisses, even more. She had wanted them for weeks. But to admit that, she must forfeit her pride. And without her pride, she had nothing to hold him.
He knew her to be a lady. He did not know her to be an impoverished one. She'd come to their marriage with nothing except her grandmother's wedding gown. No dowry, no holdings, no jewels. Her worthlessness alone made it humiliating for her to reach out to him. But the other—her father's situation—made reaching out impossible.
No, no matter how she longed to, she could not give herself completely to this marriage. Or to Kevan. When he learned the truth, he would surely set her aside. She must hold onto her pride. When Kevan left her, her pride would be all she would have.
She remembered the water lily she'd found on his pillow that morning. It meant, her list said, purity of heart. Though she could not give herself totally, she could not refuse him. Not when he had given so much. "Please, milord. Kiss me."
His kiss was warm, tender, and, when she demanded more than his gentle exploration, he gave her shocking proof of his desire. His tongue pressed between her lips. She tried to pull back, but he refused to allow it, pulling her closer to him instead. Their mouths merged, his lips rubbed against hers, encouraging her to grow more bold in her timid participation. She parted her lips. When his tongue touched hers, a burning flared to life deep inside her that made her certain she would catch flame and disappear in a puff of smoke.
His lips slid across her cheek and trailed down her throat, nibbling, teasing her flesh. Warm and sweet, his uneven breath set her to trembling, to tingling.
Kevan murmured into her neck. "Let me love you, Alyssa. I need you so much."
She couldn't answer. Again his lips taunted her throat, the underside of her chin, the hollow behind her ear, setting fires that burned far beneath the skin he touched. He raked her earlobe with his teeth. A warm pleasure spread through her and settled in her breasts, hardening their centers that pressed firmly against his coat. She wanted him, too; and silently she cried out all he longed to hear, all she could not speak.
She raised his face for her kiss, and let out a telling moan. So much emotion etched his features: his desire to please her, his need to belong, to feel welcome in her arms. And, for the first time, Alyssa sensed in Kevan a vulnerability, a certainty that she could hurt him. With that startling realization, she also sensed his trust, his faith that she would tread lightly and not abuse this humbling power she held.
In that dawning moment, Alyssa knew that—this once—she could refuse Kevan nothing. He deserved all she could give him. And, later, if she found herself stripped bare to the bone, she would look back on this day without regret. She whispered. "Oh, Kevan. Please, hold me."
His hands splaying the width of her back, he spread and cupped his fingertips, then pulled her tight against his hard length, curving their bodies into a perfect-fitting form. His hands drifted down, low on her spine, and their mouths fused. His kiss was long and languid, lush, weakening her knees, and her resolve. She cursed the obstruction of their clothes—her muslin skirt, his buckskin breeches—and conjured again her fantasy of them in the lake together. Their bodies nude and as slick as the seal she'd touched at the shore, skimming each other in a sensuous, seductive dance. Oh, her thoughts grew more and more wicked. How did he do this to her?
Then his tongue tangled with hers, and she decided she didn't care how. She just forfeited herself to the magic of his touch.
Too soon, he groaned against her mouth and lifted his head. She looked up at him, her arms wrapped about his neck, and told him with her eyes all that she felt, willing him to see the words he could not hear because she could not speak them.
"You're too tempting, love." His hand on her face trembled, his fingertips touched her as though they were committing her every nuance to his memory. His voice grew husky, thick. "We'd best go back. Parks is holding breakfast."
Crestfallen, Alyssa nodded. He had not understood. This moment, like so many before it, was lost.
On the walk back, Kevan carried the conversation. When a reply seemed necessary, Alyssa responded, but her mind was on more important matters. How could she get her message to him?
"Love?" Kevan stopped on the path and gently clasped her arm. "Do you realize your insult?"
"Insult? Excuse me, milord?" Her cheeks warmed, and she confessed. "I was wool-gathering."
"Indeed you were. You've agreed to paint the manor house purple with lavender dots, to accompany me on my morning rides wearing nothing but a cloak, and to swim naked with me in the lake."
Alyssa gasped and felt her warm cheeks blaze.
Kevan chuckled. "No, don't think to protest, love. You are a Buchannan. Your word is your bond."
His twinkling eyes held a gleam of mischief. Responding to that banter, Alyssa managed a deep sigh, her own mood growing light. If they swam naked together, surely . . . "Well, milord. I am Buchannan. And we are women of our word. But this agreement does create a pucker to be resolved."
"How so, my dear?" Facing her, he feigned a frown and a serious tone.
"I cannot abide the color purple." She bit her lips to keep from smiling. It was nearly impossible. Oh, he looked gorgeous.
"I see." He pretended serious consideration. "I care not for the color myself. And I care even less for lavender dots. I'll permit a change of heart on that matter."
"My lord is most gracious." She dipped her chin.
He sent her a stern look. "The other two agreements, however, I shall hold you to. Repayment for neglecting your husband, milady."
Alyssa's teeth worried her lower lip. Her heart was sure to leap from her chest. "Oh, dear. I fear that concession alone doesn't resolve my dilemma. While I'd be delighted to accompany you on your morning ride—securely wrapped in my cloak, of course—"
"Of course," he heartily agreed. "We must have a care not to malign your character."
"Indeed." She nodded, a delighted participant in his whimsical fancy. "However, I'm afraid the other item in our agreement is not within my grasp." She stepped closer, touched her hand to his forearm, and lowered her voice to a confidential whisper. "The horrid truth, milord, is that I cannot swim."
"Mmm, a most troublesome inconvenience." He rubbed his chin, worried his neck, then covered her hand on his arm with his free one. "I suppose then, milady, 'tis your good fortune that you married a humble, but gallant, gentleman who would delight in removing that obstacle from your path."
A thrill of sheer joy raced through her. "You'll teach me to swim?"
"I will."
She beamed a genuine smile and pecked his cheek with a kiss. "Your chivalry is unsurpassed, milord."
"Ah," he said on a sigh, trying to appear disgruntled, and failing miserably. "The trials we men endure to preserve the honor of our ladies."
Her voice twinkled merriment. "Your undying devotion, milord?"
"Always, my dear lady. Always."
Though his tone sounded light, his words held the ring of truth. Sure she was floating, her feet dangling above the stone path that had been under her feet, she smiled up at him.
"The second portion of that particular agreement, however, does not require that you swim. Only that you join me in the water."
"Nude." Her smile turned to a frown. "The penalty of wool-gathering in your presence, milord, is steep."
He gave her a wicked grin. "But pleasurable, milady. I give you my vow."
"Brazen is more apt, I would say." She had only not to refuse him. But did she dare? The expression on his face, so open, so loving, enchanted her. She must accept him, she decided. Later, when he learned the truth, if he did set her aside then at least she'd have these memories of him, of his loving, to fill her days and warm her nights.
Excitement danced through her veins. "I believe you, milord. You, too, are a Buchannan. Your word is your bond." Would he understand this time? Would he realize that she was not opposed to him coming to her chamber in the night? That she welcomed his presence in all areas of her life?
He held her in a gentle caress, then stepped away. Her heart waited. But as Kevan bent down, picked up a stone, then tossed it out into the lake, her spirit plummeted with the rock. He had not understood.
"Soon it will be two months since we wed, love. Have you notified your father?"
She trapped her disappointment in a small sigh. The man was not dull-witted. Why then had he turned the subject? Did he truly want her, or only the chase?
"Alyssa?" He turned to face her. "Have you had contact with your father?"
"I've told him that I am well and that I've wed. But I've not told him where we reside."
"Why not?"
"If he has need, he knows how to contact me. But I won't have him here, Kevan. I—I can't."
"Because he drinks?"
"No." Hot with embarrassment, Alyssa looked up at her husband through eyes that pled he ask no more. How could she tell him the truth? About her father selling her to Innes. About Innes's poor wife, Hedwig. About her own fear of her father's part in that tragedy. That he was ruined, and, according to Lady Jersey's last letter, vowing to challenge Kevan to a duel?
No, it was too much to expect a husband to tolerate, or to accept. She must keep the two men apart. For different reasons, both had grown too important to her. One because he was bloodrelated. Though her love for him died the day he thrust her into the arms of a murderer, her loyalty to her mother remained. For her, Alyssa would maintain contact with him. The other man, her darling demon-knight, had rescued and married her. And with six weeks of endearments and loving touches and unexpected conversation, she'd grown accustomed to him, and indebted. He'd given her a treasure she had sorely missed since her mother's death: happiness and peace.
"You need not explain, love." His quiet voice blended with the calm chirping of a pair of wrens. "I trust your reasons warrant your actions."
"They do, milord."
"Then we'll speak of it only at your desire." He hooked her arm in his, patted her hand, and started walking.
Near the edge of the park, Alyssa stopped. The time had come to take in hand the matter of her marriage. "May I ask you a personal question?"
He smiled. "You are my wife, my dear. Concerns expressed between us require no permission."
She held her breath. "Have you ever been in love?"
Kevan chuckled. "At least a hundred times."
"Oh." She lowered her head to shield her disappointment.
"Before I left the schoolroom."
She looked up. His eyes twinkled, and his mouth curved into that crooked smile that lifted his lip on the left side just enough to set her heart to thumping. "And after you left the schoolroom, milord?"
He reached up and stroked her cheek between his finger and thumb. "Only once since then."
She shouldn't have asked. Why had she? It was foolish, destructive, to delve into his affections for another woman. What demon had possessed her to do such a thing?
The reason was simple and suddenly clear. At some time during these past weeks, Kevan Buchannan had stolen her heart. She'd developed a true affection for the man.
"Alyssa?"
Her attention reverted to the subject of her thoughts. A wicked grin curved his lips, making him look every bit like the rakehell demon she'd once thought him. "Dear, God. What did I agree to this time?"
He looked smug, satisfied. "To swim with me now."
"But—but it's cold, Kevan."
"You gave your word."
She looked into his eyes. The warmth there could set snow to blazing. "I—I'd rather—"
"I'd rather," he interrupted, "you kept your word, love. You are—"
"A Buchannan," she finished for him. Secretly thrilled and pretending discord, she took his hand and turned back toward the lake.
ALYSSA PEEKED out from behind a huge fir. Kevan stood chest deep in the water. Just looking at his bare chest, and feeling the cool nip of the air on her own bare skin, set her to shivering.
"Come, Alyssa."
"Turn your back," she yelled out, whirling a finger she doubted he could see.
Like a dutiful husband, he turned, and, keeping her gaze on him the entire time, she sprinted the short distance to the lake. "Don't you dare turn around, Kevan Buchannan."
She tested the water with her big toe. "It's warm!" Her exclamation sounded like the accusation she'd meant. "Why didn't you tell me the lake was fed by a hot spring?"
Kevan grinned and turned. "You didn't ask. Are you pleased?"
"You turned!"
"Of course, I did. It isn't proper to address a person's back, love. Of all people, I do not wish to insult my wife."
Kevan kept his gaze on her face, though the temptation to devour her slender form with his eyes burned almost irresistible. She must learn to trust him though, and that incentive kept his gaze locked above her shoulders. Without her trust, he would never win her heart. And his own heart could accept no less.
As she waded deeper into the water, she glared at him, her cheeks bright with spots of color. Her breasts dipped beneath the surface, and she looked up at him.
"I'm ready to swim. I do hope you're an able teacher, Kevan. Are you? I've always wanted to learn to swim, but in London there was no opportunity, and, well, to be quite frank, the water intimidates me some, though—"
"Must you always chatter when you're nervous, love?"
Her eyes stretched wide and her cheeks colored from pink to rose. "Evidently, milord. When one doesn't float, it's quite frightening to be surrounded by water. Will you teach me that first—to float, I mean?"
He smiled. Not because of her vitality, though he loved that about her, but because she had admitted her weakness. She trusted him. Had her revelation been intentional? "I will. Come."
She walked into his outstretched arms. He turned her, his big hands spanning her ribs. The feel of her bare skin under his palms sent waves of pleasure pounding through him.
Alyssa, too, trembled, and looked at him over the slope of her shoulder. "Kevan, I've a need to ask you something."
She looked nervous enough to start chattering again. "What is it, love?"
Licking her lips, she looked up at him. "It is a serious matter," she warned him. "I want your frank opinion."
"Very well."
"The truth is, I've a dilemma, Kevan. I've no wish to jeopardize my mortal soul or to displease my Creator—He's given me a true treasure, you see."
When it became evident that she wasn't going to say anything more, Kevan prodded her. "Yes?"
Her face colored to cherry red, and she lowered her gaze to his chest. "Is it . . . sinful to enjoy your husband's touch?"
Kevan's heart slammed against his ribs. So innocent, so unsure of propriety. Had no one explained the ways of a man and woman to her? Sensing her deep embarrassment, he knew to handle the topic not with the gentleness he desired, but with clinical detachment. "Anything that feels natural between husband and wife is normal. Anything that doesn't, that makes either party uneasy, is degrading and should be avoided."
She nodded, seemingly pleased. "Thank you."
He wanted to hold her, to show her all of the natural, loving things he felt for her. But he couldn't. Not yet. Alyssa needed time to assimilate, time to heal from the lifetime of wounds her father had inflicted upon her. Thank God, Innes hadn't added to her injuries. It was rumored that the man had a black heart and a cruel hand.
Kevan turned her body until her shoulder brushed his chest. "You must trust me, or we will not succeed."
Alyssa nodded. "I do trust you, Kevan."
Smiling his pleasure at that disclosure, he guided her backward and placed one hand under her shoulders, the other under her lower back. The tips of her breasts peeked from under the water's surface and crested. Her gaze shot to his, but he pretended not to notice, and she relaxed.
"Good. Now I'm going to let go of you. Arch your back just a bit. When you feel your legs begin to sink, kick ever so gently." He slid his hand down her silky thigh to her calf and demonstrated. "Do the same with your head."
"I—I can't kick my head, Kevan."
"Sorry, touching you has my mind a bit fogged. I meant your arms, of course. You can swish your arms. Like this."
She licked her lips with the tip of her tongue. "I understand."
His gaze held hers. "I'm going to let go now. I won't let you go under."
"I'm not at all sure I really want to learn to swim, Kevan. In fact, I've decided that . . ."
Her nervous chatter returned with a vengeance. Kevan listened to her ramble for a full minute before he tried to interrupt. "Alyssa."
She didn't even pause for breath. It was amazing that such a tiny—he let his gaze rove her naked form—though perfect body could talk so long without drawing breath. "Alyssa."
"So you see, Kevan. It's really foolish for a married woman of twenty-two—"
"Alyssa!" he shouted. "You're floating."
As soon as his words sank into her mind, Alyssa's body sank into the water. Laughing, Kevan pulled her up just before her head dipped beneath the surface. He drew her into his embrace.
Wide-eyed, delighted, Alyssa looked up at him. "I did it, Kevan. I did! I floated!"
"Indeed you did." He raised her high in the air, spun, and let her slide down his length until his lips found hers for a victory kiss.
Bare flesh grazed bare flesh. Breathing grew rapid, shallow. The feel of her slick, wet skin meshing with his had his body tense, longing, aroused. Still, fear rode alongside passion in her kiss. Regret washed through him, and, fighting to hold his emotions in check, he raised his head. It was not yet time.
Clinging to him, she looked up at him through somber eyes. "Kevan, I—I—"
"I know, love. You're not ready." His body shuddered as he hugged her to him for a long moment just to relish the feel of her naked body pressing against his. "But soon, mmm? I need you, milady."
"Soon."
"ALYSSA?"
"In the library, Kevan." Alyssa called out. She stuffed her needlework into a basket and set it on the floor. Lord, her manners were becoming atrocious. "Ladies do not yell." She recalled the soft rebuke Lady Jersey had first issued to her at the young age of ten—or had she been nine on that visit to the Jersey's country house?
Still, she smiled like an imp, the country permitted ladies all sorts of liberties that were refused them in the city: walking the grounds without an escort, swimming with her husband and without her clothes.
Her heart quickened. Such scandalous behavior! But Kevan had sworn that anything feeling natural between man and wife was not sinful. And she was more than happy to believe him. His chest had the most wonderful feel to it. And his thighs. Hair-roughened, strong. Powerful.
Heat clearly associated with Kevan infused her with longing. Did all men feel like him? She pondered and decided they couldn't. Kevan was special, different, the last rescuing knight. And if he didn't forget his manners and take her to bed soon, she was going to throw a full-fledged fit.
The subject of her thoughts strode into the library holding a dark green wine bottle. With a slight pause in his step, he brushed her temple with a kiss and retrieved two glasses from the sideboard.
"What is that?" Alyssa asked, pointing to the bottle.
"This, my dear, is mead."
"Are we celebrating?" Alyssa patted the seat beside her on the divan. She certainly felt ample cause to celebrate these days. How accustomed she'd become to Kevan's open affection and thoughtfulness. How many wives in all of England, she wondered, were presented with a fresh flower and a shamrock each day of their married lives? A kiss, when their husband came or left? A secret smile that spoke of genuine pleasure merely to look upon them? His care more than eased the pain inflicted by her father, more than—
"We are indeed celebrating." He sat down beside her. "My clever wife learned to float today."
"Kevan." All she could speak was his name, but her heart felt so much more, and suddenly tears were threateningly close.
"Don't you want to know about the mead?" he asked, as if sensing her mood. "Margaret makes it herself from an old family recipe."
Margaret, Kevan's crusty cook, was herself a Buchannan tradition. "A veritable wonder in your kitchen, milord."
"Do you know that mead is nearly extinct?"
He sounded disgruntled. As though the world would stop its revolutions should the drink face such a fate. "Mead wouldn't dare," she said.
"I should certainly hope not."
"You've told me much about mead, milord, but you've yet to tell me what mead is."
He gave her that grin that set her heart to thumping. "A honeyed wine, love." He filled their glasses and passed one to Alyssa. "It's quite mild. Very pleasant to the palate."
"Mmm." Alyssa accepted the glass. "Shall we toast?"
"Of course." He raised his glass. "To your amphibious victory, and, of course, to our marriage."
Alyssa raised her glass to his. "In the hope that I do not awaken with gills and fins, I attribute my victory to the skills of my excellent teacher. And I drink, of course, to our marriage." Their glasses tapped with a delicate tinkle. Alyssa tilted the crystal against her lips. The smooth drink slid down her throat. Amber and sweet, though not too sweet, nor too strong.
"Hand me your glass, love."
His throaty voice held an odd quiver she'd not heard before, and Alyssa studied him. Somber, serious-expressioned, he sat motionless, waiting. Her body tensed. Though his intent was unknown, his manner proved the import of his request. She extended her goblet toward him.
Their fingers brushing, Kevan took the glass from her hand, turned it to where her lips had been, and drank.
Her heart thudded a wild beat till it felt full to bursting. This gesture, like the flowers, was symbolic. Her darling lord had just bestowed upon her an esteemed honor too few wives had ever been granted: he saluted his lady.
Unshed tears blurred her vision, and her throat tightened. "Thank you, milord." She moved closer to him on the divan until their thighs met, then pressed her lips to his warm cheek. Remembering Meg's warning that husbands detest demonstrative wives, she quickly looked into the fire.
He draped his arm around her shoulder. "Do you like the mead?"
"I do. It's very good." She looked from the hissing fire to him and nipped at her inner cheek. "Are you certain this is a mild drink?"
Kevan watched her raise her glass to her rosy lips and envied the wine that would soon flow past them. When she swallowed, so did he. "Mead comes with its own legend."
"Really? I'm partial to legends."
Her slender fingers curled around the stem of the glass. He swallowed his envy of the crystal, too. She took another sip, and Kevan raised the bottle. She nodded, and he refilled her glass. "It's called the wine of the bee."
Her laughter floated through the room. It was a pleasant sound he'd never tire of hearing. "It's quite old, you know. You should show a bit more respect."
"It doesn't taste old," she countered.
Kevan arched a brow and watched his lovely wife grow more and more loose-limbed. At her request, he refilled her glass. "This bottle isn't old, love. The recipe is old. It's said that mead dates back to 2000 B.C."
"Oh my, that is old." She raised her glass and took a healthy swig. "Is that the legend, then?"
"No. The legend is much more interesting." Why was she studying his hand? She seemed almost mesmerized by it. "In ancient times, it was abundantly supplied to the groom for a month following the wedding."
"It is a wedding drink, then?"
He nodded. "It is sometimes called that."
"Oh, dear."
Her hand settled on his thigh. Startled by her touch, he jerked, but she didn't seem to notice.
"I've been remiss in my duty to you, milord." She worried her lip with her teeth and stroked the length of his thigh. "Pray, forgive my neglect."
His muscles knotting, Kevan knew he'd forgive her anything. He covered her hand with his and resisted the urge to clear his throat, though a tightness there robbed him of breath. "Neglecting to give a man the mead is a serious offense."
She stretched across his thigh to set her empty glass on a small table, stood up and kept his hand clasped in hers. "You might find mercy in my ignorance, milord. Until tonight, I didn't know the delicious elixir existed."
"Mercy is a noble virtue," he agreed.
Her gaze grew more warm, but she no longer smiled. "Indeed, it is."
The air between them seemed charged, causing a subtle shift in their relationship. Seeing her lips form a soft pout, her pulse throb at the base of her throat, he knew he was undone. For six weeks, he'd concentrated on helping her grow accustomed to him in a gradual, natural way. Six weeks that had almost cost him his mind. God, how he wanted her. He couldn't think, couldn't concentrate on anything other than the desire she stirred in his blood. But feeling the changes in her responses to his advances—accepting, expecting, and lately, even anticipating—had been worth his discomfort. "A man kissed is more apt to be merciful," he murmured, looking into her eyes. "Would my wife care to induce me?"
"She would, milord. She truly would."
Bending forward, she cupped his face in her hands. Her sweet scent hung between them, and his heart thudded. Her lips covered his, and he guided her down to sit on his lap. Her arms curled around his neck, her fingers toyed in the hair at his nape as if she enjoyed the feel of him. With a little shudder, he settled into their kiss.
She tasted of mead and Alyssa, and he knew he'd been right in waiting for her to come to him of her own will. A whimper rushed from her throat, and her mouth opened on his, her tongue brushed past his lips and teeth to find his tongue and mate. His breathing grew ragged, his body hard, aching to know more of her.
Her parted lips slid across the blade of his cheek, her warm breath blazing a path along the line of his jaw and down onto his neck. Then she whispered, "Kevan?"
He opened his eyes to find her studying him intently, her emerald eyes smoky with desire. "Yes, love."
"I want your child."
His thudding heart stopped. "My child?"
"Yes."
Kevan swallowed the boulder that seemed lodged in his throat. She wanted him, but too timid to admit that vulnerability, she transferred her feelings into words she found easier to speak. Still, she must come to terms with them. Before he made love with her, she must know that her needing him made her no weaker than his needing her made him. "Are you saying that you want me?"
She didn't answer.
"Alyssa, answer me."
Her eyes grew darker, pulling him into their depths. But she uttered no sound. "Please, say the words, love. I've a need to hear them."
Though he felt her body tremble against his, she did not lower her gaze. "God forgive me, I do want you, Kevan."
With a silent prayer of thanksgiving, Kevan hugged her to him, felt the rapid beat of her heart against his own thundering chest. For a long time, he sat there, cradling her to him, trying to puzzle out why wanting her husband should require God's forgiveness. Arriving at no answer, he decided that later, after he'd bedded her, become her husband in every sense of husbandry, then she would be more open to explaining. And, God's truth, then he'd be more able to concentrate on her worries.
Nestling her in his arms, he stood and mounted the stairs to her chamber.
He kicked the door closed behind them. Beside her bed, Kevan set her to the floor and stepped back.
"You've had a great deal to drink, Alyssa. I want no regrets."
Alyssa glared at him. Couldn't he see? Didn't he feel that she wanted him? Afraid he would change his mind, her words tumbled from her mouth unchecked. "Are you implying that I don't know my own mind, Kevan Buchannan? Because if you are, I assure you that I am not addlepated, nor am I foxed. If you weren't such a dull-wit yourself, you would have known that the time had come to con . . . con . . . Blast and damn!" She stamped her foot in a fit of frustration. "Time to do this long ago. If you don't want me, just say so. You don't have—"
Kevan kissed her quiet.
She was nervous—and at least half-foxed. When he felt her surrender her fear, he teased her warm neck with his lips and whispered against her skin. "I want you, love. I've always wanted you. But never more than at this moment."
Her fingers curled into his waist. "Why now?"
"Because I know you aren't doing this to appease me," he replied. "You aren't, are you?"
Alyssa felt the last remnants of rebellion drain from her, and passion flare. "No, Kevan. I want you."
She watched his emotions race across his face. Searching, sobering, solemn, then searing. "Alyssa," he whispered, then began removing her clothes.
His hand trembled on her gown. She seemed so sensitive, intimately aware of the first nip of air touching her skin. The first brush of his hand on her spine, brushed her heart as well. Dear God, his eyes. Would she ever tire of looking into his eyes?
His voice, deep and husky, beckoned. "Come, wife. Be loving."
Beside her in bed, Kevan turned on his side. The fire flickered golden light on his bare skin, and she wondered: were all naked men so beautiful? His body differed so greatly from hers. Even more so than she'd realized during their swim. Dry, his chest felt different, too. Warm and silky, hard and soft—all at once—tempting her fingertips. She remembered him telling her he wanted to feel her touching his body. Her hand drifted down to the soft hollow between his ribs. His muscles quivered, and she looked down a trail of dark hair that led to . . . to . . . "Dear God, Kevan."
"It's all right," he whispered, a smile in his voice. "I'll be gentle, Alyssa."
"But you're so—"
"I'll be gentle, love," he interjected, claiming her lips. "Trust me."
Timidly, she stroked his shoulder from the soft spot at his throat to the rounding of his upper arm, then back again. No silk, no velvet, ever felt so fine. She followed the hair-roughened trail to his abdomen. He inhaled sharply, sucked in air, and she felt his muscles clench under her hand. At her waist, his fingers squeezed her flesh, then glided upward until his thumb swept tiny circles in the hollow under her breast.
At his neck, the crystal amulet absorbed the brilliant colors from the flame. She touched it and found it warm from his skin. A feeling of familiarity suffused her, a sense of rightness, of content. "Kevan?"
"Shh, not now, Alyssa," he whispered, removing the last of her hairpins. Her hair fell loose, tumbling to her shoulders. His hands tangled in its length. "Later, we'll talk," he promised. "Till dawn, if it pleases you. But right now, love me, darling. I've waited so long to love you."
He gave so much, asked so little. She longed to please him, and she wanted—just this once—the freedom to show him all she felt for him. She adored him with her eyes, with her hands that were quickly losing their timidity, with her soft words whispered in a husky voice she hardly recognized.
Following his subtle lead, she soon learned what brought him sensual delight, and then reveled in his throaty murmurs telling her of his pleasure. "Oh, Kevan, you are so good at this," she breathed against his heated skin. "I knew you would be so good at this."
She tilted her head. His lips sipped at the skin at her throat, awakening in her body a desire that until now had lain dormant. He took her breast in his mouth, and she shuddered. He was a rake. A glorious, magnificent rake. Surely, no gentleman held the power to reduce his woman to this mindless state of bliss, to inflame her body with such exquisite sensation. Only a rake could incite this wantonness in his woman—and make his woman rejoice because he had.
He shifted his weight and, remembering his size, a flicker of panic shot through her. "Kevan, wait."
Hovering over her, he looked down, his hot eyes reassuring. "Trust me. You are my wife. I want only to be loving with you."
Her heartstrings felt a mighty tug. She raised her hands to circle his back, her hips, to meet his hard flesh. "Come, Kevan."
Pain, sharp and rending, blurred her pleasure, and she cried out into Kevan's mouth. He stilled and soothed her with his hands. The stabbing pain eased, but the sensation of fullness seemed strange, foreign. Slowly, she grew accustomed to the feel of him inside her.
"Does it still hurt?"
"Only a little," she whispered. "Will it be like this every time?"
"No, darling." His muscles bunched, and he swept her temple with his lips. "Just this once."
"Good," she replied, glad that the pain would not come again. Yet she felt strangely deflated, too. "Is that it, then?"
Kevan smiled down on her and waited until she met his gaze. "No, love. We've just begun."
Then he began the timeless rhythm as wondrous as a snowflake, as indescribable, irrepressible, as love itself.
Their coupling flooded her with feelings, created a need in her that commanded fulfillment. A strong and steady growth toward something unknown. With a mind of its own, her body bucked against his, demanding that he increase the pace of his thrusts, that he take her to the something her body sought.
"Easy, love. Not yet," he whispered, torturing her crested nipples with hot lashes of his wet tongue. "You feel so good. Too good to rush. I must love you . . . longer."
She panted, feeling raw desire, hot and fluid, rushing through her veins, smothering all but the need to quench itself. "Please, I—I—"
Melding, their hips ground together. He stoked the fire in her until its flame burned wild, scorching her every pore. A strange sensation of pressure built to pain in her center and her hips thrust hard. She tried to still them, but couldn't. Her body was no longer hers to command. "Kevan," she cried, tasting the salt on his neck. She must ease this pressure. She must, or she'd surely die.
"Let go, love," Kevan grated out in a harsh whisper. "Let go, and come to me."
His words heightened her sensitivity, and, two rapid-fire strokes of his body later, a shattering burst deep in her core. Brilliant spots flashed before her eyes, and her body racked with uncontrollable tremors. Was this pleasure-pain normal? Natural? Frightened, she cried out. "Kevan!"
He moaned, baring his teeth. "Oh, God, Alyssa. You feel so good."
He groaned her name again and again. The spasms inside her rippled to delightful shudders, and atop her she felt Kevan tense, his chest heave, his hollow buttocks grow round under her hands. Then with a savage thrust, he drove her up on the bed, and spilled his seed. Throbbing, his great frame shuddering, he collapsed against her.
A long moment later, he raised his head and sought her lips for a lush, languid kiss. He breathed against her mouth, winded, sweat glistening on his slick body. "You have accepted my body and my seed, milady. Now you are truly my wife."
Twenty
ALYSSA AWAKENED, her head pounding. She forced her left eye open. Bright sunlight flooded the room, and, wincing, she groaned. Dear God, she was cup-shot. She, who had silently condemned her father's lack of self-respect in allowing himself to enter this god-awful state.
Had she known then of the pain and suffering involved, she would have been showing the man more sympathy.
The door to her chamber opened, but she couldn't make herself look to see who had entered. "Go away," she muttered, then pulled the covers up over her head.
"Good morning, love."
The sound of Kevan's voice brought her memories of last night into sharp focus. Her churning stomach knotted, then lay quivering. Had she really told him she wanted his child? Had she really done all of those things to him? Had she really . . . Oh God, she had. She squeezed her eyes closed and groaned again, deeper.
Kevan pulled back the coverlet and sat on the edge of her bed.
"Don't rock the room," she moaned. Swaying toward him, she gripped the bed to still herself. Maybe he wouldn't notice that things weren't normal. And even if he did, she assured herself, Kevan would be sympathetic. He'd consider her tender feelings and pretend ignorance. He was a darling man.
He chuckled.
"Lout," she muttered, then crossed her lips with her finger and hissed a heartfelt "Shh!"
"Drink this, love. It'll make you feel better."
"Dead people feel better than I do, Kevan," she mumbled into her pillow. "I must get well enough to die. Bury me in my blue satin." She peeked at him through one eye. "It is your favorite, isn't it?"
"Come on," he said, sitting her up. "You aren't going to get off so easily as to die. You'll have to stay with me and suffer."
"You'd end the misery of your horse, but your wife you force to suffer?"
"I don't make love with my horse, my dear."
"Selfish lout," she muttered, finding his amused tone annoying. "You're no gentleman, Kevan."
Her body felt limp as a doll made of rags. Her mouth was cottony, her tongue, thick. She leaned heavily on Kevan and felt the rim of a glass press against her lips.
"I know. Just swallow, darling," he coaxed her. "A little more."
"Enough," she pled. "That concoction tastes vile."
"True," he agreed. "But it is effective." He set the glass on the bedside table and urged her back to her pillow. "Rest now, and in a few minutes you'll feel like a different woman."
Alyssa sank back into her pillows and mumbled that she'd never be well again. The last thing she recalled before sleep claimed her was the feel of Kevan's cool hands soothing her forehead.
ALYSSA OPENED her eyes slowly. The room had stopped spinning, and she felt no pain. Gingerly, she got out of bed. At the pitcher and bowl, she splashed her face and throat with cool water. Much better, she decreed. Near normal.
She looked up into the cheval glass and regret hit her full force. Dear God, what must Kevan think of her? She'd been sotted—and wanton! And, again in her mind, she heard every warning Meg and Lady Jersey had issued about a wife's proper conduct. There wasn't one rule, not one warning, that she'd not violated.
"Ah, I see you're awake."
Alyssa spun around to see Kevan near their connecting door, inside her chamber. She couldn't face him. She couldn't! Good lord, why didn't the floor open up and swallow her? "What are you doing here?"
The smile on his face faded, his expression became unreadable. "I came to see if you were feeling better."
The drink. That's why she'd behaved so . . . "What was in that mead?"
He seemed baffled. "Mead is mead."
"Kevan," she warned him.
He shrugged a massive shoulder. "Long ago, some professed it had medicinal properties. Others said it was an intoxicant—which, after seeing its effect on you, I would agree—and others claim it, er, heightens sensitivity, makes one impatient for lovemaking. That, however, is merely a tale."
Alyssa gasped. "You drugged me, Kevan Buchannan! You rake. You scoundrel. You—you—"
"Husband, Alyssa," Kevan said in a deceptively soft tone. "I am your husband. I did not drug you. You overindulged of your own will. A fact I pointed out to you before we made love last night. I would remind you, my dear, that you agreed there would be no regrets."
She ground her teeth. He had said that. She clearly remembered hearing him say those words. And her own that followed them. "But you knew—"
"I knew I'd die if I didn't make love with you soon. I knew my patience had grown as thin as your gossamer nightgowns. I knew I wanted nothing more than to do all that we did last night."
Her heart shattered. Physical. He wanted her body only because he'd been denied it. Her refusal had increased his ardor. He felt no love, no emotional affection. What he described was not making love, it was slaking lust!
Pain knotted her chest. She knew pain, and she knew how to bury it, using her pride as a shield. Last night she had given everything she possessed: herself, body and soul. And this morning, Kevan had mocked her offering, equated what they'd shared to satisfying lust.
But no more. If she admitted her weakness for him, if he learned what her father had done, or of his financial condition, Kevan would leave her. He'd probably, God help her, request the Prince Regent's permission to seek a divorce!
Oh, no. No. He might leave her. That she could not prevent. But he would never know that if he did, her heart would leave with him. If refusing him her body would keep him married to her, then that was what she must do.
"What's wrong with you, love?" He stepped toward her. "I know I hurt you last night."
Her hands trembled to touch him. She clasped them in the folds of her gown and turned her back on him. "Just—just leave me alone, Kevan. Please. Just go away."
His footsteps heavy, Kevan walked to the door joining their rooms. "I'll give you a few minutes to come to terms with yourself, but we can't go back, Alyssa. You're my wife in every sense now. You will sleep in my arms every night and awaken in my bed to my touch each morning. I won't let you take us back to what we were before."
He walked through and closed the door. Her heart shattered and hot tears burned Alyssa's eyes. Threat or promise, his words expressed that which she most wanted. But if she surrendered, his conquest would be complete. She wanted more from her husband than his lust. She wanted his heart. And, because of her father, she was not free to seek it.
She turned toward her bed. On the pillow where Kevan had rested his head lay a single budding stem. She looked at the list and groaned. "The passion flower."
ALYSSA READ the letter delivered that morning from Lady Jersey. Then she reread it. The scandal regarding her, Kevan, her father, and Innes had started to fade. The Prince Regent had usurped the interest of the ton. When he'd gone to open Parliament in January, he'd been hissed, and the latest on dit was that his daughter, Princess Charlotte, was heavy with child. She freely admitted that the babe was expected in early November. And she'd announced, too, her desire to bear fourteen children! Her goal: to outbirth her grandmother, the Prince Regent's mother, who, together with the virile and faithful King George III, had graced the earth with thirteen children.
The ton was appalled.
Alyssa wished she could seek the old queen's advice. Obviously, that woman knew how to hold on to her husband. Of course, Alyssa reminded herself, during his marriage, the king had gone quite mad, which was why Prinny had become Prince Regent. Tapping her chin with her fingertip, she decided that perhaps she'd best rely on her own instincts after all.
Lacy burst into Alyssa's chamber. Alyssa eased the letter into a drawer in her vanity.
"Sorry, milady. His lordship says you're to come to the library right away. I'm to begin packing your things."
Alyssa's heart almost stopped. Kevan had been angry, yes. But angry enough to send her away? Had he already tired of his conquest? "Packing?" she said quietly. "Am I leaving, Lacy?"
The young maid pulled a trunk from the closet and blew back a red wisp of hair that had slipped out from under her cap. "Yes, milady." She ducked back into the closet and brought out valises and boxes for Alyssa's bonnets. "His lordship says to have everything ready in an hour."
Numb, Alyssa made her way down to the library. Her knees threatened to collapse with every step she took. Kevan was banishing her! With a heavy heart, she knocked on the library door.
"Come."
She entered and closed the door behind her. "Kevan, where am I going?"
"London," he said, sitting back in the heavy chair behind his big desk."
"Why?"
"Sit down, Alyssa."
His expression was benign, just as her father's had been the morning he'd told her she was to wed Innes. "No, thank you," she said in a voice sounding more firm than she felt.
Every God-awful event in her life, she'd learned sitting in a library: her mother's death, her father's drinking and gaming habits, her forced marriage to Innes, and now Kevan's banishing her. Until now, she'd been forced to accept whatever horror had befallen her—or she'd swooned. Regrettable, that. But, this time, she vowed she would do neither. This time she would fight. "Why are you sending me away?"
He leaned forward and made a steeple of his hands. "I brought you to Woodwind to give you the chance to accept me as your husband. I've been patient. I've done all I know to do to make our marriage comfortable for you. Last night, I thought I'd succeeded. This morning, however, I realized I'd failed."
Her wanton behavior had disgusted him. Heat seared her cheeks. She'd been warned repeatedly by both Meg and Lady Jersey. She knew that as her husband he expected her to restrain her drinking, her passion. Yet, she'd overindulged in both. "I've displeased you, so you're removing me from your presence." She walked around the corner of his desk, and, at his side, glared down at him. "You knew I was inexperienced. You knew, and still you punish me for it?"
"Going to London has nothing to do with last night, Alyssa. This trip is a direct result of your actions this morning."
She didn't believe him. This "trip" was a result of last night as sure as she breathed—and his denial infuriated her. She settled her hands on her hips and thrust out her chin. If she'd failed him in the marriage bed, it was his fault. God knows, she'd been willing. And she'd surely been welcoming. What more did he expect of a virgin? "I won't go, Kevan."
He looked up at her, his voice flat. "You will."
"No, Kevan. I'm your wife. I am not some little dasher that you can sleep with and then cast aside. We wives have more grit. You've only to look at Caroline to see that. Our Regent no doubt has contemplated every alternative save murder to rid himself of her. Yet she remains his wife." So far the Prince hadn't attempted divorce either. But considering Kevan's black mood and the deep frown that made a formidable bar of his brows across his forehead, she thought it prudent not to mention that.
"Be ready to leave for London in one hour."
Alyssa stamped her foot. "Kevan, no!"
He jumped up. "One hour."
Tears stung her eyes. "So you will send me back to face the gossip-mongers alone."
"Alone?" Kevan sighed. "No, Alyssa. Though I've felt alone many times in your presence—and never more so than in your chamber this very morning—I shall not send you alone. Since the day you first strolled into my life, you have never been alone."
Before she could absorb the full meaning of this disclosure, his glare grew hard, accusing, and he fired a barrage of questions at her.
"Why did you refuse to acknowledge any change in our relationship this morning? Why do you not trust me? Have I given you cause?"
"No. From the moment I first saw you in the church, I felt some trust in you. And it's grown, Kevan. I swear it." Unable to hold his angry gaze, she lowered hers to his boots. She wasn't to go to London alone. Would he send Lacy with her, then? God, how she wished Meg were here! She forced her gaze up to his chest. "Who is going to London with me?"
"I am."
Her head snapped up. "You? But I thought—"
"Your thoughts were quite clear." He lifted her chin and forced her to look into his eyes. His whispered words sounded strangled. "Alyssa, can't you see? Our marriage would suit if only you and I were involved."
"What do you mean? You sound as though you're accusing me of having a lover."
"No, nothing so simple as another man, wife. What stands between us is worse than a lover. I could fight another man for your heart. I can't fight your damned pride. Not here." He raked his hand through his dark hair. "God knows, I've tried."
Without another word, Kevan stormed from the room. Alyssa watched him go, confusion whirling through her. Kevan wanted her, but only if he couldn't have her? Was that it? She wanted him, but she couldn't admit that she did, or she'd lose him. He was banishing her to London as punishment for . . . for . . . what? The answer to that remained a mystery to her. Yet in this banishment, he was going with her.
All of this nonsensical mess, and he says her pride is in the way? She let out a joyless laugh. Her pride lay tattered in her bed, lost somewhere between the mead and Kevan's thieving her affection. And what did he mean about her strolling into his life? Exactly when had that happened? He'd kidnapped her, for pity's sake.
ALYSSA THOUGHT the six-hour trip to London the longest journey of her life. The dreary weather didn't help. A steady drizzle pelted against the carriage, making the heavy silence between her and Kevan even more oppressive. She sat in one corner; he, opposite her, in another. They avoided looking at each other—and, when caught sneaking a covert glimpse, he looked and she felt guilty as sin.
Unable to coax herself out of it, she succumbed to what Meg would call a severe case of the blue devils. God, how she missed Meg.
She risked a glance at Kevan. He looked so solemn. That familiar and beloved twinkle was absent from his eyes. Even without it, he looked gorgeous. Unapproachable, but utterly gorgeous. His massive shoulders were well-defined in a blue coat of superfine, and his waistcoat was cut deep. A snowy white, frilled shirt protruded from underneath, and his cravat was still crisp and perfectly tied, despite the long day's journey.
As she studied him from beneath her lashes, Kevan stretched his legs and crossed his ankles. Fawn colored inexpressibles hugged his muscular thighs, and, gazing down the length of his legs, she saw that, in spite of the rain and mud, his black boots still sported a fine polish.
Her gaze returned to his broad chest. She could almost feel the texture of him hidden beneath his clothes. His bare skin, smooth and rough, hard and soft, all at once; his muscles, rippling, quivering under her hands, dancing to her touch; the silky, fine curls on his chest that tickled her cheeks and taunted her breasts he'd made sensitive. Her heart thudded and that heat Kevan created in her streaked to her center. If she just closed her eyes . . . Yes, she could imagine the taste of his lips, the salty tang of his skin on her tongue . . .
"Alyssa, you're flushed," Kevan said. "Are you ill?"
Her thoughts and her body conspired to betray her. Her eyelids snapped open, and knowing her face had flooded with guilt, she met his cool, detached gaze. The encounter left her bereft, and she dropped her gaze to the diamond stick pin in his cravat. "No—no, milord. I am fine."
She risked a glance and saw him nod, then turn back to look out of the carriage window. With effort, she stifled a sigh and bit back the desire to involve him in conversation. She missed his subtle—and not so subtle—flirting, the camaraderie they'd shared these past months. She missed—him. And, God help her, she didn't know how to bring him back. Worse, she wasn't at all certain why he'd left.
Much later, the sound of his voice, rich and deep-timbered, tinged with laughter and desire, penetrated her sleep-fogged mind.
"Alyssa, we're home. Alyssa?"
She heard him, but she refused to open her eyes. If she did, she knew his voice would again become void of emotion, else angry. She felt too vulnerable to face either of those and London, too.
As she hoped he would, Kevan lifted her. The haven of his strong arms was a lure she couldn't resist. She snuggled to his chest and laid still until he climbed the stairs inside the house. Then curiosity bested her, and she peeked out.
Down below, surrounded by house, a breath-taking courtyard boasted vivid color and a profusion of blossoms.
He left the viewing-glassed hallway and entered a chamber. The scents of lavender, oil, and leather blended with Kevan's own, and filled her. He stopped walking. Her arms around his neck, she kneaded his nape and rubbed a curl clinging at his collar between her fingertips. Silently, she willed him to keep holding her.
His chest rumbled against her cheek. "You can stop feigning sleep now."
Alyssa's eyes flew open. Her gaze locked with his. "Put me down."
He ignored her, and sat down in a deep leather chair near the fireplace. Alyssa tried to wiggle from his lap, but with a firm hand he held her on his thighs.
"You might as well sit still, love. Until I permit you to, you won't move; and until you tell me why you pretended sleep, I won't permit you anything."
Alyssa smoothed the deep folds of her velvet traveling gown, certain that her cheeks now matched its deep claret color, for heat surely scorched them. "I don't know what you—"
He stroked her chin. "Don't lie to me, Alyssa. You are a Buchannan."
She lowered her gaze to the white frills on his shirt and debated telling him the truth. She decided she might as well. They were in London now. He'd learn her shameful story anyway. If their marriage was to have a prayer for success, she had to be honest with him—starting now. Her voice shook. "I—I needed to be held."
"You had only to tell me, love. Feigning sleep is not necessary."
Blast his gentle voice anyway. And the tenderness in his eyes, too. Why couldn't he roar, set her blasted ears to ringing? Blasted man.
Her chin quivered, and she bit her lip. Tears slipped to her cheeks. For pity's sake, why did she insist on humiliating herself by bawling like a babe all over the man? He probably thought he'd married a pump, not a woman. "You were so angry with me." She paused and gave in to an indelicate sniff. "I didn't know how to—to—"
"I wasn't angry, darling," he said softly. "I was livid."
Her surprised gaze collided with his and her jaw fell open.
With a fingertip under her chin, Kevan closed her mouth, then dabbed at her eyes with a square of white cambric cloth he'd pulled from his pocket. "The night I spent with you in my arms meant everything to me. And you denied it meant anything to you."
She'd hurt him, and, retaliating, he'd brought her here to punish her. "I was embarrassed, Kevan," she whispered. "And I was timid."
"Of me?"
Now he sounded shocked. And, horror of horrors, her blasted eyes were hot and burning again. Cursing her lack of control, she wedged them shut. She dipped her head and studied her hands, gripped together in her lap. "Yes, of you. But I was more timid of me. When my mother died and my father began drinking, I learned not to need anyone. Last night, I needed you. It frightened me." She looked up at him, knowing pain and confusion were evident in her eyes. "Needing you made me weak. And, this morning, when you talked of what you'd wanted from me being only physical—"
"Your pride," he interrupted with a sigh. "Just as I said." Kevan stroked her cheek with a gentle hand. "Be careful, love. Pride has destroyed many a soul. Don't let yours become its victim."
"Don't you understand, Kevan? The pride you curse is all I have. And I've not much of it left—speaking with you as I am, so freely."
"You are my wife," he disputed. "You should feel free to tell me anything."
"Anything? Even matters which might disgust you? Matters that a wife is schooled to constrain?" She cast him a doubtful look. "Is this true, Kevan?"
"I swear it."
Her teeth worrying her lower lip, she searched his eyes and saw truth. In a shaky voice, she began her sorry tale. "I shall tell you, then. But if I appall you, it is your own fault."
"You cannot appall me, Alyssa. I'm your husband. Your concerns are mine. Your fears, your troubles, both mine. As is all else of importance to you."
"I—I was foxed," she confessed, staring at her hands again. "But—but only a little bit. I knew what I was doing." The God-awful truth gurgling in her throat spewed forth. "Oh, God, Kevan. You've married a . . . a . . . a wanton!"
He pried her hands from her face where they covered her eyes. His voice softened, his gaze grew tender. "I've married a passionate woman, for which I am most grateful."
"You can't mean that," she said, choking on a sob. "You're just being kind, trying to spare my tender—"
"At present, I'm concerned with truth, not your tender feelings." He narrowed his eyes and his lips hardened in a grim line. "And I don't appreciate your directing my opinions, milady. Haven't I told you that before? By God, I know I have."
"You mean you aren't displeased by my—my—" Her cheeks grew hot.
"Your passion?" he finished for her, seeming to have no difficulty saying the words that she'd found impossible to utter.
She nodded.
He looked deeply into her eyes. "I am most pleased with you."
"Really?" Her heart flipped over in her chest.
"I said I was." He frowned. "Must I repeat myself? And take that off," he motioned toward her bonnet, "I'm tired of dodging those damned posies."
She untied the ribbon. He lifted her bonnet and set it on the floor beside the chair. Biting a smile from her lips, she rested her head against his shoulder, and felt his sigh meld with her own. "You do care for me, then, don't you, Kevan? It is a true affection?"
His lips brushed a tender kiss to her brow, and his arms closed around her. His hand rubbed small emphatic circles of reassurance along her spine. "I do, dear lady."
"Will you always?" Her heart threatening to leap from her chest, Alyssa opened one eye and held her breath, dreading, yearning for, his answer. "Regardless of what you learn?"
His hand stilled. "I will."
She raised her head and studied his eyes. They didn't waiver. "I'll have your vow, milord."
He pursed his lips and rubbed a strand of her hair between his fingertips. "When we married, I gave you my vows, milady."
Alyssa screwed up her courage and took in a deep breath. The time for honesty had come. "I must tell you some rather unpleasant things. You must listen, and you must not forget your vows to me. I am your wife, and you must not forget all you have pledged."
"You're directing again, Alyssa."
"No, milord," she disagreed. "Only reminding."
"As I recall, you've already protected me against a faulty memory. Now, tell me your worries, my dear."
She licked her lips and took in another quivery breath. "I was sold to Innes, Kevan. My father is—is done up. Gaming at White's, I suspect, though I was not told so specifically."
Kevan didn't utter a sound, just began again rubbing the tiny circles on her back. Why didn't he react? She'd just admitted that she was impoverished. "Did—did you hear me?"
He replied. "I did."
"Well?"
"Well, what?"
Laughter had his shoulder rumbling against her ear, and she reared back. He looked truly baffled. Didn't he understand what she'd revealed to him? "Blast it all, Kevan. I've just told you I'm penniless."
"Your father is penniless," he corrected her. "You are not. You are my lady, Alyssa. Did I not salute you with the mead at Woodwind?"
"You did, but—"
"Have I not married you?" he interrupted. "Made vows to you?"
"You have, Kevan, but—"
He continued on. "I'm one of the wealthiest men in England, Alyssa Buchannan. Which means that you are far from penniless. In fact, my dear, you are one of England's wealthiest ladies."
Alyssa closed her eyes, prayed for patience, then again looked at her husband. "Are you addlepated, Kevan Buchannan? I've just told you that my father sold me for enough blunt to avoid debtor's prison. Did you understand me?"
"I am not addlepated, love, and, of course, I understood you. Your disclosure required no interpretation on my part. You, however, have not yet understood. Your father's finances are of no consequence."
"Of no consequence?" She whispered to soften the God-awful blow. "I have no property, no holdings, no dowry. I—I have nothing of value, Kevan."
"Nothing of value?" He sounded shocked, but he looked angry. "I didn't marry you for money, Alyssa. And, though you were sold, I won you from Innes. I knew how he'd acquired you. Everyone did."
Alyssa's scalp tingled, her body shuddered with icy shivers. "Everyone?"
"Everyone."
Alyssa groaned and buried her face in his neck. "Oh God, Kevan. I'll never be able to show my face in London again."
"I don't see why not."
His throat vibrated against her cheek and she raised up. "For pity's sake, Kevan Buchannan. I swear, I think you're daft at times. I was sold. I have nothing. And all of London knows it.
"Darling, you know members of the ton often marry for money. I don't see why—"
"But I didn't. I was sold to one man and eloped with another—a rakehell demon who kidnapped me from a church, for pity's sake."
"Ah, I see." Kevan cast her a wicked smile. "But you must admit, love. The intrigue proved very romantic. Even to the ton."
"You want to see me humiliated," she accused him. "That's why you brought me here."
"I would never wish to humiliate my wife," he countered in a hard voice. "Your damnable pride stripped from you—by God, I would. But humiliated? Never."
She gave him a good frown. "Do you know, milord, that my father intends to challenge you to a duel?"
"I do. Innes is said to be contemplating a challenge as well."
Her fingertips dug into his shoulders and she drew in a sharp breath. "Why?"
"He wants you."
"No." Her flesh crawled. "He—he can't."
"He does," Kevan insisted.
Her hands clenched into fists against his shoulders. "I cannot abide him."
"That is good to know. I'd hate to have to kill him."
His eyes glinted with a cold fury she'd never seen in them before, chilling her to the bone. She shivered. "You would kill him?"
Kevan didn't answer.
The hair on her nape prickled. "I heard your vow at the church, but—but I thought you just said that so no one would follow."
His voice grew hard as his eyes. "You are mine."
The truth dawned on her then. "You meant it? You would truly kill any man who tried to take me from you?"
He didn't answer. Just looked at her with those hard, steady eyes. He'd meant it, all right. And she didn't know whether to hug him or hit him. A spurt of joy took hold in her heart. He really did care for her. But—but to kill a man . . . ?
She cupped his cheek; she'd held softer rocks. Still, she forced herself to smile, and, when his jaw softened under her hand, she felt a bit better. "Unless provoked, you won't duel either of them, of course."
He didn't comment.
"Kevan," she insisted. "Will you?"
"We'll see."
"Kevan Buchannan, we will not see." She couldn't withhold her panic. "You must not duel my father. He's an excellent fence."
"Thank you for reminding me," he said in a stiff voice that made her wish she hadn't yelled at him. Lord, the man did take exception to her raising her voice.
He gave her a lazy grin. "Your concern for my safety pleases me."
How did the man switch emotions like that? She narrowed her eyes at him, letting him see her feelings about that. "Of course, I'm concerned. You're my husband, for pity's sake."
Kevan kissed her temple. "I am. Blessing or curse."
She gave his shoulder a smart whack, then snuggled against him. "It is a blessing and you know it."
His arms around her grew tight, and she heard his satisfied sigh. "Yes, my dear lady, it is."
A knot rose in her throat. Against his shoulder, she whispered. "I'm afraid, Kevan."
"We'll settle, love. Though my personal opinion is that your father deserves a sound thrashing, I won't give it to him—unless provoked. I know it would distress you." His breath was hot on her neck. "You've suffered enough distress at that man's hands already."
She kissed his shoulder. "Thank you, milord." That issue resolved, Alyssa turned the subject to another of her fears. "Can we go back to Woodwind?"
"No."
"No?"
"No," he firmly insisted. "You can't run, Alyssa. You must face society."
That he knew why she wanted to leave didn't surprise her. "You know that the ton will shun me, Kevan."
"None would dare," he scoffed. A muscle in his cheek twitched, then twitched again. "You are the wife of a powerful lord, Alyssa. Remember that."
"I would remind you that you kidnapped me from my wedding to another man. And also that we wed at Gretna Green. The ton will feel we're beneath polite society."
"Thank you again, dear lady, for your protection against my faulty memory. I do hope our Creator isn't growing weary from all the indulgences you've requested of Him. Perhaps you'd best request one more though—for yourself."
Puzzled, she stiffened. "Whatever for, milord?"
"It seems you've forgotten a most important point."
"Oh?"
He nodded. "We are polite society, darling. And together we're much too clever to waste such valuable gossip."
"Waste it?" She eyed him warily. "Kevan, have you gone daft?"
"Indulge me by listening, love. The ton is intrigued with romance, is it not?"
"I suppose," she said uncertainly.
"Its dubbing Prinny as the prince of pleasure is adequate proof, don't you agree?"
Thoughtful, Alyssa pursed her lips. "They do call the Prince Regent that, don't they?"
"They do," Kevan said. "Now, having proven that the ton is intrigued with romance, I ask you: What could be more romantic than a man stealing his lady from the arms of another?" Kevan smiled and leaned back. "Nothing, by God. Absolutely nothing."
"What does this have to—"
He gave her a weary nod. "Alyssa, for a clever woman, you're decidedly slow on matters of the heart."
"I think I take that as an insult, milord. Use caution, else you'll do irreparable damage to my tender feelings. And remember, if you please, that I haven't had the benefit of your experience."
"No, you haven't." He laughed at her.
She frowned. "Now I'm certain I'm insulted. You find me lacking."
"Only in the nicest way."
She lifted her chin. "Smirking at your wife is most rude, milord."
"But, darling. I'm no gentleman."
"No, you're not. But you are mine, Kevan." She let out a resigned sigh. "And I suppose that makes it my duty to make you into one."
"Never, my dear lady," he said in a voice of stone. "Though before we return to Woodwind, I've no doubt you'll have even the most arrogant of Almack's patronesses eating out of your beautiful hand."
"That would be impossible."
"It wouldn't. Stop disputing me, darling. It is not only possible, but sinfully simple. All we must do is show our devotion, publicly flaunt the fact that we're besotted with each other." He smiled. "The ton will be enchanted."
He pressed his lips to her palm. She smiled into his chest. He didn't realize he'd done it. Surely he didn't. But did his slip indicate the feelings in his heart? He'd called her his love, his dear lady, again and again, but to show, to flaunt, devotion and affection, one must feel devotion and affection. And, wonder of wonders, his cherished disclosures had come after she'd told him all that stood between them.
Well, almost all. She still hadn't spoken of Hedwig, or of her father's blood-stained clothes. But Kevan had heard—and accepted—enough for one night. "I think I like this speaking freely with you, Kevan."
He crushed her to him. "Of course, you do, love. I'm your husband." He pressed a quick kiss to her temple. "Now. I think, first thing tomorrow, you must visit Bond Street, mmm? A new gown for court. Maybe something in green. I've developed a fondness for green. The particular shade of your eyes when you're loving me." His own eyes took on a dreamy look. "Yes."
"You're no gentleman, milord," she reprimanded him. But her heart wasn't in it, and, from the caressing smile on his sweet lips, her demon-knight knew it. "Besides, I do have gowns I've yet to wear."
"Nonsense," he argued. "Every woman being presented to court needs a gown of her own choosing."
Alyssa smiled. "But I've been presented at court."
"Not as my wife."
Her reluctance refused to go unspoken, and she wondered if he had a secret power that forced her to reveal her thoughts. She lifted the amulet at his neck and rubbed it between her fingers. "Wasn't once enough? It was awful, Kevan. Must I go through that crush of swooning women again?" She nuzzled his neck. "I'd rather return to Woodwind with you. We could swim."
"Don't tempt me, love. You must be presented. It's even more important because of our circumstance. I abducted you from a church, I would remind you. The bishop could demand reparation. And, I do believe, my dear lady, you've forgotten the first rule of defense."
Alyssa trapped her disappointment in a small sigh. "I know little of military matters, milord. What is the first rule of defense?"
Kevan nipped at her neck. "Attack."
Twenty-one
THE CRYSTAL AMULET at his throat vibrated.
Pain seared Kevan's chest. Memories flooded his mind. Alyssa. Angel!
He cupped the crystal in his palm, untangled himself from his wife's limbs, and eased from her bed.
Next door, in his own chamber, he answered the summons of the Elder of the Council of Perfection. "Yes, your grace."
The Elder appeared, a thick, silvery mist swirling around him. "Prophet," he said in his familiar, husky rasp. "It is good to see you, my son."
Prophet nodded. "It's good to see you, too."
The Elder inclined his head and slowly blinked. "Your woman is with you," he said more than asked.
Kevan nodded. "As in Scotland, she is my wife."
"How does she progress in overcoming the fault of pride?"
Prophet rubbed his neck. "She's begun, but not yet mastered this level. Her confusion is great. Here, too, her father has made her tender years painful. But she is learning to trust and to risk embarrassment."
"Still, she has not yet become universal."
The Elder's left eye reflected a glimmering light, though the right one remained flat. His movements were slow, measured, as though each motor skill utilized required Herculean strength. Prophet frowned. "Are you ill, your grace?"
"It is of no consequence." The Elder repeated his observation, a strange sadness in his voice. "She has failed to become universal."
Prophet contradicted him. "She has succeeded in revealing her discomforts to me. At cost to her self-respect, she revealed truths that embarrassed her greatly. It was difficult for her, your grace. Her distress—"
"Has an event occurred wherein she has felt compelled to sacrifice her pride for the benefit of another?"
"She nearly married Innes to protect her father."
"But she didn't?"
Prophet felt heat crawl up his neck. "She would have."
"Then why—"
"I abducted her."
The Elder stroked his beard. "I see."
"The man is a scoundrel, your grace. I couldn't let her fall victim to him. She's but an infant at restructuring. She needs time to learn the value of sacrifice with specific regard to pride. Just as she learned the value of all deeds in Scotland."
"She was quite a firebrand in those days." The Elder stroked his beard and smiled. "Quite a firebrand."
"She still is," Kevan said. "But she is different, too. Much more gentle and aware of her emotions. She cries easily here, and seeks comfort in me."
The Elder's lips twitched as though this news pleased him. "I see that once again your woman has captured your heart."
Prophet nodded. "She is my woman, my lady, and my—"
"Destiny?"
"Yes, your grace." Prophet smiled. "My beloved destiny."
The Elder turned to go. "The Council will be appeased with her progress for now." He looked back over his shoulder, his glimmering eye a mirror of his inner pain. "But you must move more quickly. Time waits for no man. Pursue your destiny, Prophet. Master time. And remember the leaves."
"They change without urging. In their own time," Prophet said, repeating a message the Elder had given him long ago. "I remember, and I've not forced her—other than to wed me. But even then I gave her a choice."
The Elder frowned. Prophet had seen that rare display of emotion only twice. And both times serious consequences had followed.
When he was seven, just after his father's funeral, he had encountered the Elder for the first time—and been gifted with the visions that were natural to him, but frightened others.
Twenty years later, the Elder frowned again. The day Kevan had envisioned Alyssa's funeral in New Orleans. And that frown had signaled the onset of their travels, their mission to alter history, to teach Alyssa to love, and the risking of his eternal peace, for without her his soul would surely die.
What would happen this time?
"The ton of this time is a superficial breed, Prophet. To them, appearance is everything. Proceed with caution, else all could be lost."
"I'll do my best, your grace. Losing Alyssa now, after so many trials . . ." Fear choked him. "We've come so far."
"The leaves, Prophet. Remember the leaves." The Elder's silvery image faded.
Kevan found he was standing alone in his bedchamber. The room was dark and cold, no fire burned in the grate. Puzzled, he rubbed his neck. He'd been asleep in Alyssa's bed, his wife nestled in his arms. When had he risen? And why in bloody Hell didn't he recall rising?
AT THE SIDEBOARD, Parks pressed the spigot on the coffee urn and filled a cup. "Good morning, milord."
"Good morning." Kevan sat down at the head of the long mahogany table. "Has Meg arrived?"
"Yes, milord. She's taking her ladyship a cup of chocolate at present. It should be a most interesting reunion."
Kevan narrowed his eyes. "Was Meg briefed on what to tell my wife?"
"Of course, milord." Parks placed the cup on the table. "Breakfast?"
Kevan grunted and unfolded his newspaper. He'd read no more than the front page when squeals of delight pealed out above stairs. Chuckling softly, he glanced up at the ceiling. Alyssa was pleased. Content, he returned to his paper.
Minutes later, he heard her hurried footfalls on the grand stairs. He dipped the paper and looked over the top. His heart swelled and damned near burst. She looked like a joyful sprite. Fresh and soft from sleep, her silver curls tangled about her face. Her nightgown clinging to her ankles, exposing her bare feet.
"Oh, Kevan!" She rushed to him and covered his face with tiny kisses.
"Madam, you've—" Parks fell silent, having intercepted Kevan's meaningful nod.
Kevan cleared his throat and glared at the ogling footmen. They promptly turned to face the wall. That they were smiling did not please him.
"Not now, Parks," Alyssa told his man between rapid-fire kisses. "I'm thanking my husband for being the most wonderful man in all of England—no, the whole world!"
"Alyssa," Kevan protested between chuckles. "Alyssa, please! You'll have poor Parks swooning." He lowered his voice to a whisper. "You've forgotten your robe, my love."
Alyssa gasped. "Parks, tu—turn around at once."
Kevan watched that worthy struggle to bury his smile and do as his lady bid. It pleased him, too, that Parks had kept a sharp eye on the backs of the footmen.
Alyssa lowered her voice, but far from mortified as she would have been a mere month ago, her eyes twinkled merry mischief. "I apologize, milord, but a wife's gratitude cannot wait. Your coat, if you please." She reached toward him and wiggled her fingers for him to hurry.
He arched a brow and gave her his best rakehell look. "I rather like your—"
"Kevan." She stamped her foot. "Your coat."
Grumbling false annoyance, Kevan stood, removed his coat, then held it open for his wife. When she slipped it on, the sleeves covered her hands and the tails brushed the back of her calves. She looked enchanting, like a child playing dress up. But she was no child. No. His spirited wife was all woman. He sat back down, certain that no man could be more content.
"I'm very pleased with you, milord." Alyssa bent over and pecked his cheek. "That's for rescuing young James. No, don't deny it. And don't badger Meg, either. I'm not slow-witted." She kissed him more fully. "And that, you wonderful man, is for Meg. I can't believe she's really home! And this," she kissed him breathless, "is because of all the women in England, you had the good sense to choose me." She smiled down at him, then added, "You may turn back now, Parks."
He did, and, Alyssa hesitated, then kissed Kevan again. Surprised, he looked up at her. "And what was that for?"
She slid him a wicked grin. "That was for me."
With the grace and bearing of a queen, she turned and strode from the room.
Parks attempted to muffle his soft laughter with his hand. Kevan glared him into sobering.
The worthy cleared his throat. "I apologize, milord. It's just that milady's, er, lack of restraint is a delight to these old eyes."
Kevan arched one brow. "I noticed your delight." He watched his wife climb the stairs. The hem of her nightgown hiked up, exposing a healthy length of luscious-looking leg. His heart thundered a wild beat, and his stern tone grew husky. "And I agree. She is a most delightful woman."
"Yes, milord, she is."
TO KEVAN'S bitter disappointment, it was a very different Alyssa Buchannan who returned to their Knightsbridge establishment that afternoon. From the library, where he was knee-deep in account ledgers, Kevan heard Parks greet Alyssa in the main hall.
"Should the footmen retrieve your purchases from the carriage, milady?"
"There are no purchases, Parks."
The strain in her tone drew Kevan's full attention.
"Begging your ladyship's pardon, but I understood you were returning from Bond Street."
"Blast and damn, Parks." Alyssa shouted. "There are no purchases."
Silence filled the hall. Kevan frowned and sat back in his chair. For Alyssa to raise her voice, to curse Parks, something serious must trouble her. Her fondness for his man had been evident from their first encounter. Should he go to her? No, he decided. Would she seek him out? Did she value their relationship enough to share her little troubles with him as a wife should?
"Oh, Parks," Alyssa cried. "You didn't deserve that. Forgive me, please."
"Of course, milady."
Dejection, not anger, filled her tone now. "I'm going to my chambers. I—I promise to remain there until my temperament improves. With any luck, I may be out by the turn of the century."
"But, milady," Parks gasped. "'Tis but eighteen seventeen!"
"True." She held her skirt and lighted on the first step. "I may need more time."
A distinct sob preceded her flight up the stairs. Kevan rose to go to her, but Meg's words to Parks stopped him.
"She didn't mean to snap, you know." Meg paused, as though to remove her cloak. "Poor love, I ain't never seen the likes of it."
"What happened to her?" Parks asked, clearly concerned. "She was in such high spirits this morning. Delightful spirits."
"Those nags from the ton is what happened. They devoured her, pretty-as-you-please at the modiste's."
Parks voice elevated an indignant level. "But she's his lordship's wife—a countess. They wouldn't dare."
"They did," Meg assured him. "And you could've set a dish of chocolate on that Mrs. Drummond Burrell's chin, she held it so high. Damn her uppity nose. She led the pack of them, to be sure, and her not fit to wipe my lady's boots."
"Her ladyship must have been mortified," Parks said.
"Oh, she handled herself like the lady she is, but they crushed her tender feelings, to be sure. None went so far as to cut her—they ain't that brave—but God's truth that might've been kindlier than what they done."
"Kindlier to cut her?" Parks sounded torn between outrage and disbelief. "Good Lord, what did they do?"
"Fired nasty questions at her about his lordship and that rubbish Innes. Too many spiteful things to recollect precisely. They pecked at her like a flock of vultures."
Still talking, Meg and Parks left the hall. Kevan sat back in his chair, making a steeple with his fingers. The time had come to take matters in a firm hand. Those self-righteous gossipmongers would welcome his wife with open arms or, by God, they'd suffer the consequences. And the consequences would be dire, indeed. For years, he'd had the ability to open enough closet doors to bury them all under the skeletons they had hidden. And shunning his wife was a surefire way to have him opening every one of them. One by blasted one.
A short while later, Kevan summoned Parks. "Please see that these are delivered at once."
Parks took the small stack of sealed envelopes and left the library. Kevan laced his fingers behind his head and smiled. Tomorrow at two, Almack's patronesses: Ladies Jersey, Sefton, Castlereagh, Cowper, Princess Esterhazy, Countess Lieven, and Mrs. Drummond Burrell would gather. And, with luck, they'd be charmed right out of a voucher for his own sweet Countess. Without luck, they'd be blackmailed.
His gaze shifted to the ceiling. Above stairs, his wife still paced her chamber. Before he attempted to charm the other women, he must soothe his wife into a sweet temperament. He frowned. Charming the patronesses'—reputed for the most part to be arrogant and disdainful—would be a far easier task.
THE SKIN AROUND her eyes puffed out and the tip of her nose looked ripe as a cherry. Frowning, Kevan passed her his handkerchief and sat down beside her on the lounge.
"You said we were too clever," she reminded him in a shaky voice. "You said that they wouldn't dare shun me. That the ton would think our circumstance an enchanting, romantic intrigue." Her voice cracked and she sobbed. "You said, I wouldn't be—be—be humiliated."
"I said, that before we retired to Woodwind you would have them eating out of your beautiful hand, love. I did not say that there wouldn't be a few rough encounters between now and then."
"Rough encounters?" She dropped the twisted handkerchief into her lap. "My God, Kevan. Those women did all but lay me low."
"A few gossipy women making snide remarks cannot harm you. If you'll trust me, we can turn this incident to your advantage."
"How?" She gave him an indelicate snort. "I swear, Kevan. I think you spent too much time under the water at the lake." She pursed her lips and narrowed her eyes. "I warned you that your brain would get damp doing that."
The afternoon she referred to was one Kevan remembered well. It was the first time she'd expressed concern for his wellbeing. Her concern had been outlandish, of course—whoever had heard of a damp brain?—but she'd given him precious concern nonetheless. A poignant smile touched his lips. "My brain is fine, darling."
A fat tear rolled down her cheek. "Oh, Kevan. It was bloody awful. I never want to leave this room again."
He wrapped his arms around her, felt her body shudder. His heart wrenched in his chest. "Come to bed with me, love," he whispered close to her ear. "I've a need to soothe you now. Tomorrow things will look brighter. I give you my vow."
Kevan stood up, and Alyssa stepped back into his embrace. His arms closed around her, protective as an enveloping cocoon. He, too, would care for his charge until, like the butterfly, she felt ready again to emerge on her own.
ALYSSA LOOKED UP from her needlework and watched her husband pace the library floor. "Kevan, do sit down. You've been in a twitter since you returned this afternoon." What's troubling you?"
Heaving a sigh, Kevan dropped down beside her on the divan. His gaze continued roving the shelves of books behind his desk. "It's nothing of import, love. Did you have a good afternoon?"
He was lying. "I weeded the flower garden." She stitched a blue peony on the border of what would soon be a footstool cover. "What is the flower for trust, Kevan? Is there one?"
He didn't answer.
Alyssa looked up and frowned. The man wasn't attending. His gaze held fixed on the mantel clock. What was bothering him? He'd left in good humor and returned just after four highly agitated. Still, she couldn't resist the urge to give him his comeuppance. He'd penalized her for wool-gathering often enough.
Alyssa bent to her stitchery and watched him through her lashes. "I've learned that I'm going to give birth to twin buffoons in a year's time. Much like an elephant, don't you agree?"
His fingers tapped his impatience on the arm of the divan. "Yes, dear."
She rolled her eyes back in her head. For pity's sake, had her conversation grown that boring to him? "I had an interesting visit with the Duke of York," she ventured. "He called this afternoon."
"That's nice."
"Mmm. He said you were a sorry lout and that a woman would have to be foxed or a beetle-head to force her person to withstand your presence." She shrugged. "I agreed, of course."
"Of course."
She narrowed her eyes at him, but he didn't notice. "I told him that you have the cutest mole on your bottom, and that if one didn't speak to you overly long, but lingered in a prone position, your appearance was quite pleasant."
"I'm sure he is well-versed in such matters."
Alyssa's frown deepened. "I'm certain he is. He also said that a woman who was unfortunate enough to develop a tendre for such a lout as yourself had to be either a high-flying gamester or a chucklehead. I agreed with this, too, and added that she must also be daft."
"Mmm . . ."
"Kevan," she bellowed, elbowing him in the ribs. "What is the matter with you?"
"Ouch!" Kevan looked stunned.
"Kevan Buchannan, you haven't heard a word I've said."
The brass knocker sounded, and she heard Parks answer the door.
"Are we expecting guests?" Kevan asked.
"Not that I know of," she replied. "We are not finished with this discussion, milord. Your insults must be atoned."
"My what?"
Alyssa gave him a proper glare. "You've called me a highflying gamester, a chucklehead, agreed that I'm birthing twins next year—like a bloody elephant, I might add—agreed that I must be foxed because I care about you—and, though that is more than enough—you called me daft."
Kevan's jaw fell slack. "You care about me?"
He looked stunned. Bemused. Certain that in all her ramblings, he'd heard no more than that, her ire cooled. She nodded to let him know she meant what she'd said. "I care very much, milord."
A slow smile spread across his face. "Alyssa."
"I'll see it gets to Lady Buchannan," Parks voice carried through from the hallway and then he entered the library. "Begging your pardon, milady."
"Yes, Parks," she replied, her gaze remaining locked with that of her speechless husband.
"This just arrived. I said I'd see to it at once."
Alyssa shifted, took the envelope Parks offered, and saw a merry twinkle in his eye. "Thank you."
Kevan leaned back and yawned. The faker was a bit too disinterested for her liking. When he didn't ask about the envelope, she knew the truth. Her demon-knight already knew its contents. His agitation had been anticipation—uncertain anticipation.
Afflicted with a slight shake, Alyssa opened the envelope and read its contents. Her heart threatened to bound from her chest.
Now Kevan asked the perfunctory, "What is it, love?"
She smiled at her deceitful, delightful rogue. "It's a voucher, dear. To Almack's."
His lofty expression portrayed bored acceptance of his due. But his eyes gleamed satisfaction. "Ah . . ."
"Ah, indeed, you fake." Fairly bubbling inside, Alyssa wound her arms around his neck, settled herself squarely on his lap, then hugged him hard. "Oh, I don't know how you managed it, milord. But your lady is most grateful."
His lips parted for her kiss. And when she'd done the pleasurable deed properly, she raised her head.
His breathing as erratic as after a long swim, her husband slid her a lazy smile. "I do love seeing my lady grateful."
"Oh, she is, milord." Stroking his cheek, she screwed up her courage and watched him study her through her lashes. Her blood rushed through her veins, her pulse pounded in her ears. "Come above stairs with your lady, Kevan."
He looked surprised. "In the light of day."
Alyssa swallowed hard. "Your lady has a need to express her tender feelings, milord. Do you suppose tender feelings know it's not night?"
Parks again summoned them from the doorway. "Excuse me, milord."
Kevan shut his eyes for a scant second. "Yes, Parks."
"Lord Cameron and a member of the king's guard, Sir Duncan, have requested a moment with you and milady."
Alyssa groaned at this interruption of her first sexual invitation. She would never know Kevan's reaction now. Kevan turned and glared at Parks—until he saw that worthy's gloomy expression.
"Show them in, please," he said.
Alyssa scooted from his lap and smoothed her silk skirt. She turned and put her hand on her husband's arm. "Please, milord," she whispered. "No duels."
Kevan gave her hand a reassuring pat, but he did not give her his word. Her pounding heart raced.
The guard and Lord Cameron faced Kevan and Alyssa. Her father's eyes were red-rimmed behind his quizzing glass, and he dabbed at the corner of his mouth with a square of white cambric. She shifted her gaze to the guard. His leathery-skinned face held a stern expression, but his eyes were steady, and she judged him a fair man.
Kevan did not offer them a seat, nor did they look as though they would accept one.
"Milady. Milord." The guard said, shifting his weight on his feet. At his side, Alyssa's father stood silent.
Kevan stood, towering over the two men. "What is your purpose here?"
Alyssa cringed, but the guard's stern expression held.
"You have been accused by Lord Cameron of kidnapping the Lady Alyssa and forcing her to wed you against her will."
Alyssa jumped to her feet and rushed to Kevan's side, cursing herself for not expecting her father's intrusion. "Father! How could you?" She turned to the guard. "This is not true."
Her father's glare was cold, detached. "Do not protect this criminal because you were forced to share his bed, daughter. He must suffer just punishment for his crimes against us."
"Cameron," Kevan said in a tone so soft that Alyssa had once mistaken it for boredom. "You are a guest in my wife's home. I warn you to watch your tongue in her presence. Your days of insulting her are over."
Alyssa interrupted before her father could respond and start a duel in their own library. She addressed the guard, who seemed acutely aware of Kevan's anger. "My husband has committed no crimes against me."
"The church held witnesses," her father countered. "They will testify to the contrary."
Alyssa swallowed her anger. After all her father had done to her, he had the gall to accuse Kevan of abuse. But she must remain calm, appear collected—no. No, she decided. To protect Kevan, she must appear amused. She let out a little laugh that even to her sounded convincing and again directed her comments to the guard. "I assure you, sir, my husband did not force me to marry him. Actually, quite the opposite occurred. I insisted on becoming his wife." She had chosen wife over mistress, so in a way, she supposed her choice could be construed as insistence. "I paid for the horses at Carlisle, too. You may check with the stable master there—and the parson, too. No, I do believe it was a smith who wedded us." She turned to Kevan. "Wasn't it, darling?"
"Alyssa," Kevan said, draping her shoulders with his arm and pulling her close to his side. "Be still, love."
"Was the man a smith, dear?" she insisted.
"Yes, love. Now be still."
Seeing the affection between them, her clinging to Kevan's waist, him sheltering her, seemed to confuse the guard. She'd no doubt her father had been most persuasive in his arguments against Kevan. He had a gift of being most persuasive—when it suited him.
"Charges have been made, milord," the guard said. "I must investigate."
"By all means," Kevan replied. "Do your duty to your king."
"I deny the charges," Alyssa blurted out. "I am supposedly the victim, but I tell you, sir, I am no victim. There's been no crime."
Vacillating emotions crossed the guard's face. Her father snorted.
"Lies," he drawled, crossing his chest with his arms. "All lies. It is plain the criminal has threatened her."
Kevan's expression grew dark as a thunder cloud. She pressed against his waist in a silent plea, begging him to let her father's insult pass.
"Refrain from insulting my wife, Cameron, else suffer the consequences."
Alyssa intervened, again addressing the guard. "Kevan is the one person in my life who has not threatened me." She glanced at her husband and caught a peek of the crystal amulet at his neck. Her heartstrings suffered a vicious tug, and a compelling need to speak the truth overwhelmed her. She turned to Kevan. "Milord, forgive me. I must confess."
"No, Alyssa," Kevan insisted. "I forbid it."
He would suffer the indignity of false charges to protect her tender feelings. Tears threatened her eyes, and she blinked them back. She gave her husband a loving look and stroked his cheek with her hand. "I must, my dear."
"Now we shall hear the truth," her father said, thrusting out his chin.
Alyssa glared at him then looked at the guard, her stance reeking defiance, daring challenge. "My father sold me to Lord Innes, sir, who then wagered and—thank God—lost me in a game of whist to my husband. Though Kevan had every right to claim his ownership of me under the betrothal contract he won, at no time did he ever demand that I wed him. Lawfully, I was the man's chattel. But, gentleman that my husband is, he left the choice of wedding him to me." She smiled at her husband, who no doubt recalled the incident quite clearly. Mistress or wife, he had said. Choose. "And I am most pleased with my decision."
"You lie," her father shouted. "You were forcibly removed, kidnapped—from the church. There were witnesses."
Kevan stepped toward her father. Oh lord, he looked ready to cause serious injury. "That is the second time tonight you've called my wife a liar, Cameron. If there is a third, regardless of the fact that I'd hate to ruin my wife's carpets, I will spill your blood."
Incensed herself, Alyssa stepped between the two men. Patting Kevan's chest, she glowered at her father. "Do not continue this farce. I was not kidnapped, and you bloody well know that's the truth of it."
Before he could answer, she turned to look at Kevan. "Now, love, my father is no match for your strength. Buchannans do not kill the weak and afflicted."
She turned again toward her father, calling up an indignant scowl. "Did Kevan snatch me from Innes's side? Did he drag me? Well, did he? Or did he hold out his hand to welcome me, if I chose to come to him? Well? Will you admit the truth or continue to lie?"
He said nothing, but his face flushed an angry red. Alyssa deliberately softened her tone. "I went willingly, Father. And it was the best thing I've ever done."
She prayed for forgiveness for the Banbury tale she was about to use to embellish the truth, then turned to the guard. "Before I entered the church, I knew Innes, the disreputable cur, had wagered me. Fortunately for me, Kevan won. I should die before wedding Innes, and to that my father can testify," she paused to spare her father a glance, "should he choose to speak the truth once this night."
"You knew this before entering the church?"
Alyssa avoided a direct response to the guard's question. "Kevan informed me of the wager and offered to marry me. We staged the abduction together. I'm sure you understand now, sir. My husband did not abduct me. He rescued me from Innes and from the ton."
The guard gave her a puzzled look. "The ton, milady?"
Alyssa smiled. "Being sold and wagered is not socially polite, sir. The earl thought that creating a romantic intrigue would whet the interest of the ton. And he was right. He knew that it is every woman's secret desire to be whisked away by a handsome rake. The ton's condemnation turned to envy. Surely you can see the value of such an intrigue now, sir."
The old guard scratched his head. "I suppose so."
"No. No, no, no." Lord Cameron insisted. "He kidnapped her and forced her to wed."
"Sir, if you would please observe," Kevan said to the guard. He turned to Alyssa. She saw his intent in his eyes and stepped into his embrace. He kissed her breathless, then turned to the guard. "Is the affection you just witnessed the type a woman kidnapped and forced to wed would give to a husband she did not want?"
The guard's eyes were glazed. "No, milord. I can't say that it—"
"Don't you dare believe that trickery." Lord Cameron interrupted. "She was a virgin. Of course, she's suscept—"
"Lord Cameron, I insist you use more discretion in your comments, and refrain from raising your voice in the presence of a lady," the guard coldly insisted. "It appears to me that this is a love match."
"Utterly ridiculous," Cameron muttered. "This is a sham, I'm telling you."
The truth struck Alyssa like a blow. He wanted her marriage set aside. Her father still harbored hopes of forcing her to wed Innes. Even now, knowing her wed and bedded, her father intended to use her to settle his debts! She chilled to ice. She half-expected her voice to frost the air. "You are mistaken."
He shot her a look of pure hatred. Kevan's arm at her waist tightened around her, and she leaned heavily against him. She'd been right all along. Her father did hate her.
"Sir," she addressed the guard, her voice a ragged whisper. "You must forgive my father's false accusations. I'm sure they were not intentional, but, you see, the day I was to wed Innes, my father was cup-shot. He'd been out all night the evening before and, that morning, when he informed me that I was to wed, he was still in his altitudes."
She swallowed back tears, ignored the pain constricting her chest. "I'd been ill with the fever for nearly a month. While I was abed, he posted the banns. He did everything that needed doing to see me wed to Innes. When I protested the match, he commanded me to it. Even after—" she bowed her head, swallowed, then looked up, "—even after I vowed suicide."
"Alyssa."
It was Kevan who protested now. She turned her face up to look at him. "I'm—I'm sorry to shock you, milord, but I must speak the truth. I'll not have your character maligned and his go untainted. He has caused this muddle with his manipulations. He has committed the crimes." She fought the upheaval in her stomach, threatening her disgrace. "I mean no disrespect, milord, but my father's condition that day did alter his perception of the events that occurred. The truth must be told."
"Darling, I'm so sorry," Kevan whispered so only she could hear.
"You officially deny the charges then, milady?" The guard spoke softly.
Alyssa knew he already had her answer, but he needed this particular question answered specifically for his report to the Prince Regent. "Most emphatically, sir." Alyssa swallowed hard and set out to destroy the last remnants of doubt—should any exist—in the guard's mind. "I will neither permit nor assist in this unjust persecution, sir. I love my husband, and, if this travesty is pursued, I will not hesitate to seek the aid of the Prince Regent. Being a romantic man by nature, I am sure that, once given the circumstances, he would support my cause."
The guard stammered. "I—I'm sure that won't be necessary, milady."
"You refuse to arrest him, then?" Cameron asked.
"Without the lady's testimony, Lord Buchannan cannot be convicted of any wrong done against his wife. And she denies that a crime has been committed."
"I will never testify against my husband."
The guard nodded. "I apologize for the intrusion. Good night, milady. Milord."
The guard left the room and stood waiting in the hall for Lord Cameron to join him.
Her father glared at her. "You are an ungrateful and selfish child, Alyssa Kathleen. I'm glad your sainted mother cannot see how disreputable you've become. I will never forgive you for your lack of loyalty—nor will Innes. This is not over."
"Do not threaten my wife, Cameron." Kevan's tone held a lethal warning. "I've granted you liberties tonight that I will not allow you in future. I should hate to kill the father of my wife, but if you inflict yourself upon her again, I will. Have I made myself clear?"
Her father turned and strode to the door. "It is well she is someone's wife. For this night she's become no man's daughter."
Twenty-two
RUBBING HIS NECK, Kevan paced Alyssa's chamber. She sat perched on the edge of her little vanity stool, stiff-spined and fingering her hairpins scattered on a gold tray. Forcing his hand to his side, he paused behind her. "Why did you tell them about the wager?"
She lifted her brush and avoided his eyes. Her fingers tightened around the handle until her knuckles bleached white, but her voice sounded whisper-soft. "Because you refused to tell them."
That much he'd assumed. What he wanted to know was why she'd told them. "Alyssa, will you look at me?"
Her gaze met his in the looking glass; clouded, shielding. "We agreed not to disclose that information," he reminded her.
"I know, and given a choice I wouldn't have. But the guard was not convinced, Kevan, and I—I—"
He forced his tone gentle. "You what, love?"
"Blast and damn." She stiffened, ground her teeth. "Why must you grow tender when I am most weak? Why can't you scream at me, or shout, or do something angry—oh . . . oh, for pity's sake," she finished on a groan.
Tears brimmed in her eyes. Pretending not to notice them, he took the brush from her hand and worked it through the long silver strands spilling down her back. The scent of roses, clinging to her hair, filled the air between them. "Should I feel anger?" He rested the back of his hand against her warm nape. "I don't know what to feel, or what to think, for that matter. Why did you confess our circumstance?"
She looked at him in the glass. Resigned. Accepting. "I had no choice. The guard had to be told," she said, muffling a tiny sniffle. "You—you don't know my father. He doesn't issue idle threats."
A tight knot formed in his chest. Her father had, by God, disowned her. Yet she accepted her loss, and feared for her husband's safety. Kevan stepped to her side and set her brush back on the gold tray. Squatting down beside her, he cupped her face. Her delicate chin quivered in his hands, tightening the knot in his chest. Tears clung to her silver-tipped lashes, and he swept her soft cheeks with gentle strokes of his thumbs, secretly wishing he had killed the man who had caused her tears, knowing that if he had, he would cause her to shed yet more tears. "Are you afraid of him, darling?"
She worried her lower lip with her teeth and again avoided his eyes.
"Answer me, love." He forced his voice calm and coaxing. "What has he done to you?"
She stiffened, shuddered. "Nothin—"
He slid his hands down her throat to her shoulders. "Do not lie to your husband, love."
She met his gaze, her eyes pleading, and Kevan felt his heart twist, the knot in his chest grow to the size of his fist. "Alyssa, please. Talk to me."
"He wasn't always like this," she stammered. "Before my mother died, he was all anyone could want in a father." She paused to swallow and her trembling grew to shudders. "Then he began drinking. Not much at first. But, in time he grew worse. The episodes became more and more frequent."
An unholy fear clawed at Kevan's stomach, but he knew not to interrupt. This disclosure embarrassed and hurt his wife. If he so much as breathed too harshly, he knew she'd reveal no more. He felt her emotional struggle; the war between her loyalty to her dead mother, to her family's name, and her desire to be honest, to not break her vow to honor her husband. And, forcing himself to wait, to not coerce her into a decision to trust him, he silently cursed the father for the harm he'd caused the daughter.
She turned toward him on the little stool. "Last October thirteenth, my father didn't come home. He'd—he'd stayed out before, but, somehow, I knew this time was different." She took in a sharp breath. "I sent Burns to look for him, but he could not be found."
She tried to veil her despair, but Kevan saw it in her eyes, heard it in her quivering voice. Whatever she had suffered then, she suffered again now in reliving the incident.
Her head bowed, her shoulders slumped, Alyssa let out a shuddering breath. "It was late the following afternoon before he returned to the house. His clothes were . . . bloodied, and he was cup-shot. He—he swore he couldn't recall where he'd been, or what he'd done."
"He'd no idea?" Kevan asked, before he caught himself.
"None." She twisted away from him. "Please, milord. I—I must stand."
Kevan rose, and Alyssa stood up. She walked to the window and stared out into the moonless night. He lifted her needlework from a chair near the fireplace and sat down, his gaze settling on her back.
"Did you know that Innes was once married, milord?"
A cold shiver slithered down Kevan's spine. Seeing where this conversation was leading, he began praying he was wrong. "No, love I didn't."
"I'm not surprised." She tapped the glass pane with her spread fingertips. "You spend so little time in London." She stiffened. Her fingers slid down the glass to the window sill, then curled around the ledge. "She was a German duchess. Hedwig was her name. She was very wealthy, very beautiful . . ." A strangled noise gurgled in Alyssa's throat, and she sucked in a great breath that heaved her shoulders. "She is dead now."
Kevan's blood chilled to ice. "How—" His voice failed. He cleared his throat, then tried again. "How did she die?"
Alyssa turned toward him, her expression wooden, her eyes dull and empty. "She was murdered, milord. Stabbed repeatedly in the chest."
"Dear God." Kevan stifled a gasp. "And you think your father had something—"
"He was with Innes that night," she interrupted. "They were seen together at White's."
"But that doesn't mean—"
"He was also seen leaving White's with Innes."
Kevan's scalp tingled, his muscles grew taut. "And he returned home in bloodied clothes." She nodded.
A muscle in his jaw twitched. "Were their activities that night investigated?"
"Yes. This is not easy for me to admit, Kevan, but I believe they lied to protect each other."
"Then why in the name of God were you going to marry Innes?"
"I had no choice. My father told me he was done up." She scrunched the folds of her skirt in her hands. "I knew that he meant not only bankrupt. You see, I'd heard those words before."
"When?" Kevan's lungs clamored for air. Alyssa, usually warm and passionate, appeared so detached and remote.
Her gaze slid to the floor. "A scant week before Hedwig's murder, Innes spoke them to my father." She looked up at Kevan, her words tumbling, rushing out. "If I had refused to wed Innes, my father would have been charged with murder—or killed."
Kevan's head reeled. He gripped the chair arms. "Did he murder the woman?"
"I—I don't know. Sober, he would never do such a thing. But foxed? I just . . . don't know." She rubbed her forehead and sighed. "In my heart, I believe Innes responsible. I overheard him tell my father that his wife's wealth was in some sort of trust. I'm ill-read in such matters. But Innes did say Hedwig had refused to grant him control of her blunt. Unless she died, he said, he would be done up."
"Dear God."
Alyssa's eyes stretched wide, terror invaded their emerald depths. "This is not over, Kevan. I left the church with you believing my prayers had been answered. I'd prayed so hard for intervention. I—I didn't think—" Her voice broke and she sobbed. "But now, Oh God, now I fear my not telling you of this first has put you at risk, too." Tears coursed her cheeks. "I am so sorry."
Kevan felt her pain, her fear. "Don't, Alyssa. Please. Never regret coming to me. The risk doesn't matter. What does matter to me is that you trusted me enough to tell me this now. I need not be reminded that you had little cause to trust me earlier, my lady. I kidnapped you and forced you to choose between becoming my wife or my mistress." His eyes grew tender. "And still you lied to protect me. You mourn not your own loss; fear not for your own safety, but for mine." He grunted. "By God, you're a true treasure."
"I'm not, milord. But I thank you for saying so. In truth, I mourned losing my father long ago." She dipped her chin, entwined her hands. "Do not forgive me too easily. I vowed to honor, then deceived you. You are my husband now. But before I wedded you, I should have told you the truth." Her teeth raked her lower lip and she looked up at him. "I pray my insult hasn't altered your perception of our marriage from our blessing to your curse."
His heart shattered. Losing her mother during her tender years and in a very real way, her father, too, Alyssa had little reason to trust anyone. Yet she'd come to trust the stranger she'd wed, and he knew—perhaps better than she did herself—the value of the risk she had taken willingly. "You've told me now, love." He opened his arms to her. "Come."
With a whimper that tore at his heart, Alyssa flew to him and crawled into his lap. He cuddled her to his chest, stroked her warm scalp, and massaged the tension knotting her neck, her shoulders. His head lolled back against the chair and he closed his eyes, offered her comfort until her deep sobs ebbed.
"Enough, milady," he whispered, his throat thick, his own eyes misty. "I can't bear to see you shed another tear. We will resolve these difficulties."
Alyssa looked up at him, biting her lip to halt her chin's quivering. "How? Oh, God, Kevan, please don't set me aside."
"Set you aside?" How could she consider such an absurdity?
She nodded. A glistening tear fell from her lash, rolled down her cheek, and dripped onto his fingertip. A surge of tenderness suffused him. She cried—for him. His arms cinched around her, drew her closer, and his voice choked. "No, love. Nothing will part us. You have my vow."
Her arms curled around his neck, and she buried her face at his neck. "I was so afraid that once you knew, you'd hate me for deceiving you. I feared you'd seek a . . . a . . . a divorce."
"Never," he vowed in a harsh whisper. "You are mine."
"Yes," she whispered back. "And you are mine."
Contentment washed through him. He let her hold him, relished being held by her, then separated their chests so he could see her eyes. "The difficulties I mean to resolve aren't between us, love. I mean to see that you're protected. And, considering all you've told me, I think we'd be wise to do a bit of investigating ourselves."
"No, Kevan, please." Her voice shook, her fingers dug into his shoulders. "I should die if my father is a—a—"
She couldn't say the word. Nor would he force her to hear it. Not yet. Not unless it proved true. He pressed his fingertip against her lips. "Shh, listen to me, love. It's ignorance we must fear. We must know our enemy. Trust me in this."
She nodded. "All right. I will follow your lead."
He gave her a tender smile. "Thank you, love."
THREE TORTUROUSLY long days passed without incident, and Alyssa began to relax. She convinced herself that her father had spoken in anger, that he had descended from his altitudes and realized that Kevan wouldn't sit idly and watch his marriage destroyed or his wife harmed.
She looked down the long length of the breakfast table to where Kevan sat reading the newspaper. He'd been livid with her father for insulting her. And had her husband not wanted to protect her tender feelings, she strongly suspected her father would have suffered Kevan's wrath that very night. Her heart wrenched in her chest. Her husband was huge, a massive man, yet beyond doubt her gentle knight. She cocked her head. Had his size truly once frightened her? Had she truly once doubted his goodness, feared him, and thought him a demon? How outrageous those thoughts seemed now. How utterly ridiculous.
He smiled at her over the top of his newspaper. Caught staring, she felt her heart flutter embarrassment, but her lips curved upward. "What has amused you, milord?"
"This article in the Register. It's a retelling of an incident that occurred in Grimsby a year and a half ago."
"Share it with me, then," she invited.
"It seems a widow encumbered with the debts of her departed husband wanted to remarry. To exempt the new husband from acquiring the old husband's debts as well as his wife, she jumped into her intended's arms from a window before witnesses."
Kevan laughed from deep in his chest. Perplexed, Alyssa frowned and lifted her cup to her lips. "Why would jumping rid him from debt?"
"Because when she jumped, my dear lady, she was naked."
Sputtering on the hot tea, Alyssa felt heat surge to her face. "Dear God, naked?"
"Naked," he repeated, a chuckle lingering in his voice. "The woman interpreted the law to be such that if she had nothing, her intended would inherit nothing. These debts, stood between them, you see."
"So she removed the obstacles between them by coming to him bare?" she asked, setting her cup to its saucer.
"That was her intent. The article quotes her as saying, she'd not so much as a pin in her hair."
Parks strode into the breakfast room. "Milord, excuse me. James MacMillian has returned."
Tucking the newspaper under his arm, Kevan stood and dropped his napkin onto the table. "Forgive me, my dear. This is an urgent matter."
"Of course." Alyssa tilted her head to receive his kiss. "Meg and I shall likely be gone before you are done."
He paused. "Where are you off to?"
"Bond Street. A gown for Almack's next week."
Kevan smiled. "Something green, I hope. Emerald, like your eyes."
She felt her insides go soft. "If it would please you."
"It would." He bent and brushed her cheek again.
"Very well." Her heart nearly careened out of her chest.
"Take Parks with you," he instructed, "and be cautious."
PARKS ACCEPTED the outing with grace and a stiff jaw, as he did everything else. Unlike her father's Burns, Parks was decidedly human, and for that, Alyssa was grateful.
Directly, Alyssa, Meg, and Parks arrived at the dressmaker's shop. Just outside the door, Alyssa paused and turned to Parks. "I won't subject you to entering. We'll be half an hour. No more."
"I think his lordship would rather I—"
"Nonsense," Alyssa protested, trying to dispel his obvious unease-- "Meg is with me, and we'll venture nowhere else. We'll be safe as babes in our cribs."
"But, milady—"
"I insist, Parks." She smiled to soften the sting of her orders. "I know how much you men detest escorting a shopping woman." She turned for the entrance. "Half an hour."
Meg turned to Parks and frowned. "You might as well accept it. She's a mite stubborn, to be sure."
Parks blinked twice, the only outward sign of his displeasure, and relented. "I'll wait here at the door."
Alyssa thought the modiste gracious, her greeting pleasant, considering the last disastrous visit she'd made to the tiny woman's shop. She explained the occasion requiring a special gown.
"I know just the thing," the woman said to Alyssa. "We must first select a pattern." She waved a hand toward the pattern room. "If you please."
Alyssa turned to Meg, following behind. "Choose a fabric you like."
Meg began to protest, but Alyssa would hear none of it. "I insist. You need a new gown. Something bright and as cheerful as your disposition. You're too young to wear those drab colors you're so fond of."
"Pink," the modiste suggested. "With your pale coloring, pink would be just the thing."
Meg's cheeks flushed. "No, milady. I have—"
"Claret," Alyssa said. "Select three, Meg. One pink, one claret, and one in any color you choose—so long as it isn't dreary."
"But—"
"For pity's sake quit your frowning. You know how determined I can be."
Meg flashed an excited smile. "To be sure, I do. Thank you, milady."
"Well, go on," Alyssa urged her. "And don't forget pretty trims. Ribbons and braids, whatever strikes your fancy. And bonnets. You must have bonnets to match each gown."
"Yes, milady." Smiling, Meg turned toward the fabrics, a youthful spring in her step.
The modiste whispered, "You are very gracious to your abigail, madame."
"She is also my friend."
"I see. You are both blessed with fortune, then."
Those words forged Kevan's image in her mind, and a thrill rushed through her. "Oh, yes. I am most blessed."
The tiny woman smiled. "Then come, step in here and we will select a pattern that will make you shine like the first water diamond you are. All of Almack's will envy you."
Almack's could keep their envy if only Kevan would lose his restraint. Since her revelation about Hedwig, he'd been loving, but he'd not bedded her. She didn't understand his behavior. His desire was as evident as always, but her attempts to let him know that his attentions were welcome had been met with staunch reserve.
Then she recalled the words he'd spoken at Woodwind. You will come to me, Alyssa, he'd said. Certainty flooded her. That must be it. Before her father's intrusion that night, she'd invited Kevan to make love with her. She'd sought his affection. After hearing her confession that she found suicide preferable to wedding Innes, Kevan doubted his welcome. He needed her reassurance.
For pity's sake. While she waited for him to come to her, he waited for her to come to him! Oh, that blasted man. That darling, blasted man. How could he think himself anything like Innes?
Anxious to return home, Alyssa stepped behind the curtain into the pattern room. This would be the quickest dress order in history.
A man's thick arm snaked around her neck and squeezed, slamming her back against a hard chest.
Alyssa gasped. Twisting, she tried to break away, to scream. A pungent cloth bore down on her nose and mouth. She couldn't utter a sound! Acrid fumes stole her breath. Spots flooded her eyes. Fear clawed at her stomach.
"At last we meet again."
That voice. The hair on her neck stood on end. Icy dread suffused her limbs. Dear God, Innes . . .
She strained to see him, but instead saw the modiste laying prone on the floor. Panicking, she fought harder.
The cloth! What drug sodded the cloth? Holding her breath, she caught his coat sleeve, jerked hard. Innes trapped her arm at her side, smothered her face with the foul-smelling cloth. Opening her mouth, she thrust her tongue into the fabric, trying to create a gap between the cloth and her face, searching for untainted air. Her tongue, her nostrils, tingled and grew numb. She had to breathe. The tingling sensation seeped into her chest. Then into her arms and legs. Terrified, she felt her strength drain away and darkness swallowed her.
Twenty-three
"GONE?" KEVAN gaped at Parks. "What do you mean, gone? She couldn't just disappear!"
Parks dabbed his damp brow with a square of cambric cloth. "I saw no one enter or leave, milord."
"I was in the shop with her and heard nothing," Meg added, wringing a lacy handkerchief in her hands. "Until the modiste starting groaning, not a peep came from that room."
Kevan forced his fears aside. For his wife's safety, he had to remain calm, lucid. "Get James MacMillian—and that guard who was here with Lord Cameron. Blast and damn! I don't know the man's name."
"Sir Duncan," Parks supplied. "He left his card for her ladyship. In case she changed her mind."
"Send Major, Parks. I want those men here right away. And have someone see if the Lord Chancellor is available. Tell him the matter is most urgent. Request, do not demand, his presence."
"Yes, milord."
"And Parks. Tell the footmen that if Lord Cameron should call, admit him at once and bring him to me."
"But you forbade him the house," Meg reminded his lordship. Her hand clamped over her mouth. She'd spoken before she'd stopped to think. His lordship would surely take offense.
Preoccupied, he didn't. "Things have changed now, Meg. Everything . . . has changed now."
JAMES ARRIVED first and was ushered into the library.
"What have you learned?" Kevan asked.
The young man's cheeks were ruddy from the cold. He moved toward the fire, talking as he walked. "Cook at Cameron House says her lord ain't been home since yesterday morn. If she hears anything, she'll send word straight-away. And she said to tell you special that she'll be keepin' her ear to the doors. Has a fondness for Lady Alyssa, she says."
"And at Innes's?" Kevan asked.
"His house is closed up tighter than a corked bottle, milord. Stable's empty, too. Everything. The neighbor's groom, Jerome, says Innes was in residence and things were normal—like four days ago. Then, quicker than you can spit, the house was shut down and everyone gone. Left day afore yesterday."
"Day before yesterday?" Kevan frowned. "And Alyssa wasn't abducted until this morning. Check the inns within two hours ride of here—all directions. I know Innes is responsible. When we find him, we'll find Alyssa."
"Milord?" Parks tapped on the library door.
"Come."
"Sir Duncan is here."
"Show him in, Parks."
"I'll get right on that other, milord," James said.
Kevan nodded and James made his exit. Kevan stood to greet the guard, who on entering the library made no effort to hide his outrage. His clothes looked like he'd slept in them and his cravat was clutched in his hand.
"Lord Buchannan, I do not appreciate being dragged from my bed, handed my clothes, and thrust into your carriage with the most mundane of explanations. That you wish to see me is an inadequate excuse."
Major had taken his orders to heart. "Innes took my wife."
The old man's eyes narrowed. "When?"
"This morning. He abducted her from her modiste's shop on Bond Street. My men are searching all of the main roads and I'm gathering as much information as possible. Lord Cameron hasn't been seen since yesterday morning, and Innes, not since he closed down his house two days ago."
Duncan plopped down in a heavy chair that groaned under his weight. He was a big man, only slightly smaller than Kevan. And when his body tensed and his eyes clouded as they were now, he appeared formidable. Kevan held his gaze.
"Why do you think Innes took her? Regretting his loss?"
"Exactly."
"And her father?" Duncan asked. "Is he involved?"
"I don't know. But he has motivation for wanting his daughter wed to Innes. Strong motivation."
Kevan poured two glasses of port at the sideboard, then passed one to the guard. "I need your help, Duncan."
Duncan nodded. "You have it. But I'll tolerate no lies, Lord Buchannan."
"Kevan."
"Kevan," Duncan repeated. "I believe you won the lady as she said. Has a ring of truth to it, that. But I do not believe you staged the abduction."
"Why not?"
"Your lady doesn't lie well. Her skin gives her away."
"I love my wife, Duncan. I vow it."
"I believe you. I also believe she is content with you. And that is one reason why I will help you find her."
"One reason?" Kevan asked. "Are there others?"
Duncan drained his glass and set in to the table with a thunk. "Innes killed his first wife. I know it as well as I sit here and breathe. But I can't prove it."
What both men feared passed in a glance between them. Would Innes make Alyssa his next victim?
Footsteps at the doorway had both men turning.
"Excuse me, milord," Parks said. "This just arrived. I thought it might be important."
Kevan took a buff colored envelope from Parks's outstretched hand. "Who sent this? The envelope bears no seal."
"I heard a knock. It was on the steps, but I saw no one."
Kevan nodded. Sweat dotted his skin. With a trembling hand, he opened the envelope and read:
Weep not for treasures lost.
Sob when they are found.
Emeralds once gleaming fiery bright
Sparkle not beneath the mound.
-13-
Kevan's skin grew clammy. Trembling, he passed the note to Duncan. "Here's our proof. It's from Innes."
Duncan read the note, the creases in his leathery skin deepening. "Innes."
"If we seek my wife, he'll kill her." Kevan swallowed his anguish.
"He will regardless," the older man predicted. "Unless we find her first. How did you know it was Innes?"
"I won my wife with a pair of twos, a pair of fours, and an ace. The cards total thirteen."
"I see."
"And you?"
Duncan grimaced. "Innes's wife was stabbed thirteen times."
Twenty-four
THE LORD CHANCELLOR, tall, gaunt, and somber-eyed, presented himself at Kevan's Knightsbridge establishment just before dusk.
Escorted into the library, he folded his long body into the chair Duncan had occupied earlier that day.
"I apologize for my delay, Kevan. The matter was unavoidable."
"Thank you for coming," Kevan said, wanting to rush through the amenities. "Port?"
"Yes, please."
Kevan filled and passed him a glass. Without further delay, he informed the lord chancellor of his complaints against Innes. He presented the note and the cards as evidence, and conveyed his concern for Alyssa's safety.
"These are most serious accusations."
"They are, John," Kevan agreed. "But they are founded."
"In circumstance, yes." Doubt riddled the man's brow. "What is it you wish from me?"
Seizing that uncertainty, Kevan met the old man's gaze and held it. "Alone this evidence seems paltry. But combined with known facts regarding the murder of Innes's wife, Hedwig, the evidence becomes more than substantial."
"How so?"
Kevan spoke slowly, distinctly. "Hedwig was stabbed thirteen times."
"An unlucky number, thirteen." John refilled his glass at the sideboard. "I am privy to the particulars of that case. And I, too, confess to suspecting Innes. How may I assist you?"
"I want the locations of all of Innes's properties, and any known to be frequented by him. Can you provide them?"
John nodded and stood. "We'll begin tonight."
"John, please don't delay. I must find Alyssa quickly." An icy shudder gripped his body. "I believe Innes intends to kill her."
The lord chancellor's Adam's apple bobbed and a knowing look settled in his eyes. "I'm sorry to have to say that I agree with you, Kevan."
"But you do."
Regret flashed in John's eyes. "Yes, I do."
ALYSSA AWAKENED in a dark room. She couldn't quite remember where she was. She lay still, giving her head time to clear, her eyes time to focus.
A dim light filtered in through the partially drawn drapes at the window, and she made out the shadowy silhouettes of the bed, a desk, and several chests.
Relieved to find she was alone, she eased from the bed and opened the drapes wide. Moonlight flooded the room. Decorated in Chinese red, the room was opulent, the furniture fine and well-cared for.
Memories flooded back. Innes. The abduction. The vile cloth covering her face, her strength draining. Then awakening in a carriage, a bitter elixir being poured down her throat. Innes's fingers on her neck, forcing her to swallow . . .
Dear God. She had to get out of here. But where was she?
Looking out of the window, she saw three stories of windows stacked between her and the ground. Not a tree, a trellis, nor any portion of the house jutted nearby. Nothing that would assist her in a downward climb.
She went to the first of three doors inside the room and turned the knob. Seeing only a closet filled with a woman's clothes, a pang of disappointment shafted through her, then apprehension. Were they Hedwig's?
A shiver raced between her shoulders. She shut the door quickly, then tried the second. It was locked. Did it connect to the hallway, or to Innes's chambers?
The third and final door creaked open. She peeked out into the hallway. A grizzle-faced man sat slumped against the wall in a chair beside her door, his light snore ruffling the silence.
Her heart thudding, she inched past him, and on down the hallway. The thick carpets under her feet muted the sounds of her footsteps. The staircase was dark and narrow. Easing down it, a stair creaked under her weight. She bit her lip and fought the instinct to freeze. Her blood pounding in her ears, she forced herself to keep moving, to keep her moist palm firmly gripping the slick banister, feeling her way to the ground floor.
Finally, she reached the last step. She looked from left to right in the dim darkness and saw nothing move. Quickly, she crossed the expanse to the front entry. As her hand curled around the doorknob, her heart lurched. Was it locked? Oh God, please don't let it be locked. Swallowing hard, she twisted the knob. It turned.
"Good evening, my Ladybird."
Gasping, she jerked the door open and tried to rush through. Innes caught her arm, yanked her back. "No," he shouted. "You may not leave me again. You've only just arrived." He slammed the door shut.
Alyssa glared at him, cursing her fear, her inferior size. "Let go of me. You have no right—"
"I have every right," he bellowed, jerking her against his chest.
She struggled against his embrace. His foul breath, rank as sour port, had her stomach churning. "Let go of me."
"Never."
Like a vulture swooping down to attack its prey, his head lowered, his wet lips crushed down, assaulted her mouth. Dear God, she silently cried. "Oh, God. Noooo!"
She twisted her head. He grabbed it in his hands. "Don't make me angry," he warned her, his tone rough, threatening, frightening. "You won't like me angry. I could . . . hurt you."
Remembering Hedwig, Alyssa stilled. His lips again covered hers and she stood passively in his embrace. Tears burned the back of her eyes, but she vowed not to let them fall. Kevan. She must think of Kevan. Where was he? Did he know where she was? When—dear God, please!—would he come?
Innes raised his head, triumph burning in his eyes. His arm swathed her like a shroud and he buried her at his side. "You have much to learn about pleasing a man. But don't worry, I will instruct you."
Certain she would be sick, she closed her eyes to fight the waves of nausea rolling through her. Once, she'd decided to end her life rather than suffer this man's touch. But then she'd been alone and without hope.
She wasn't alone anymore.
Kevan. She would think only of Kevan, see only his image in her mind. She'd picture herself escaping, gaining her freedom from Innes and finding her way back to Kevan. She'd picture him coming, finding her. And the two of them killing Innes—before he killed her.
He forced her into a lamplit salon, shoved her down on a wide divan, then sat down beside her. He pressed his thigh against hers. Her flesh crawled, and she moved away.
Sliding across the damask cushion, he followed her. "You can't escape me, Alyssa. Haven't you learned that yet?"
Her anger rising, she bit the inside of her cheek, clenched her hands on her lap into fists to keep from striking him. "Why have you done this?"
Innes smiled, but there was no tenderness in it. Only lust burned in his eyes. Lust and hatred. "I want you."
When Kevan said those same words, she felt warmed by them, cherished and loved. From Innes they sounded wicked, ugly and evil. "You had me and you wagered me to Kevan." To herself, she added a silent prayer of gratitude that he had. "My value meant little to you. My husband—"
"You will not speak of him to me!" Innes's skin flushed and he fell silent until his color was almost back to normal. "You refused to become my wife, Alyssa."
"That was later," she reminded him. "You'd already lost—"
"I had not," he interrupted. "While you were abed with the fever, I visited your chambers. I'd arranged the match with your father long before. When I told you we were to wed, you laughed in my face." His eyes grew cold, hard. "You shouldn't have done that."
"I was fevered," she countered. "I remember seeing no one."
"You saw me." He scowled his insistence and squeezed her arm. She bit her lip to keep from crying out. "But you aren't laughing now, are you? Nor will you ever laugh at me again."
Being physically inferior, surprise is your strongest defense. Unbidden, the instructions filled her mind. Lull your enemy into complacency.
Taking in a steadying breath, she heeded the directives. "If I offended you, I apologize. But I would remind you, I was ill. Much of the time, I knew not what I said or did." Watching him closely, she saw his expression soften. "Please, let us forget this unfortunate incident, Lord Innes. Send me home."
"This is your home. At least for now," he informed her. "We are going to America." His eyes grew cold as sleet. "You will live with me openly there—as my mistress."
Alyssa gasped. "I'll not."
"You will," he contradicted her. "I wanted to make you my wife, but you scorned me. My honor demands satisfaction, and I shall have it. You suffering the indignity of Phryne should suffice admirably." He shrugged. "Though you don't share the physical features of the Athenian courtesan, you shall share her reputation as a woman of easy virtue. And you shall earn that reputation."
He lifted his chin, his expression amused. "I've always been possessed of a most generous nature. When I tire of you, I shall invite any man expressing interest to share your charms."
She wanted to kill him. Keeping her expression passive was almost beyond her ability. Still, she gave the task her full effort. "Kevan—"
Innes slapped her.
Her cheek stung, and tears sprung to her eyes, but she blinked them back and glared at him.
"You will obey me, woman. Never speak that man's name in my presence again. This time, I will forgive your insult. But should it happen again, I'll take a stick to you."
Alyssa believed him. Furious, she forced herself to sit mute until the anger eased from his expression. Dear God, he'd gone mad. Fear prickled her skin, raising it to gooseflesh. And, worse, he intended to make her the victim of his madness.
"Until I tire of you, I will treat you well," he assured her. "But only so long as you please me. You must do what you're told, when you are told to do it; heed even my tiniest wish without question. You needn't bother glaring, Ladybird. One way or another, you will satisfy my desires. Suppress your rebellious nature and accept that, then you'll have no cause for complaint."
"And if I refuse?" Her voice was but a whisper of sound. She hated it. Hated her fear of him, her weakness, her lack of ability to fight back. She hated him.
His lips spread back, baring his teeth in a grim smile. She couldn't stifle a shudder.
"Should you dare to refuse my slightest whim, you will find your circumstance extremely unpleasant. To cause me annoyance, will cause you pain." His paw-like hand gripped her face, pinched her cheeks until her teeth cut into the soft flesh of her inner cheek and the taste of blood filled her mouth. "But let's not talk of unpleasantness, mmm? You are not a foolish woman, merely an ignorant one who has now been enlightened." He lessened the pressure and stroked her aching jaw. "I am a wealthy man, Ladybird." His fingertip grazed her skin, down her throat to the valley between her breasts. "I can make your life paradise or hell, and I assure you, paradise will be much more to your liking. All you must do to get there is whatever I demand of you—both in and out of my bed."
She was going to lose her stomach. She swatted at his hand. "I'd prefer to reside in Hell than to suffer your slightest touch, and that's the truth of it."
Before her eyes, he altered. The veins in his neck bulged, his jaw compressed, and an angry white line circled his mouth. "Very well." He stood and jerked her to her feet. "Then, first, you shall have your hell."
He dragged her up the stairs and shoved her into a small tower room. Cobwebs tangled in her hair. Dank and musty, the air reeked of disuse. A naked cot pressed against one wall, a chamber pot against another. A tiny window caked with dirt and the grime of neglect let through no more than a dim sheen of light from the coming dawn.
Alyssa closed her eyes, refusing to utter a sound.
Without warning, Innes ripped the clothes from her back. She snapped her eyes open and fought his hands. Too strong for her, he accomplished his task. In moments that seemed lifetimes long, she stood before him: naked, embarrassed, and terrified.
Praying for strength, she resisted the futile urge to hide behind her hands, stiffened her spine, and forced her voice strong. "So, now you will add rape to your list of crimes."
He smiled his cynicism. "No. Though you deserve a sound thrashing with the stick for your insult, I shall spare myself the bother. Soon enough, you'll beg me to give you my seed."
She thrust out her chin and stared into his eyes, silently praying that he would leave before her knees gave out and she collapsed. "Before begging anything from you, I will die."
He laughed, a high-pitched maniacal shriek that grated at her ears, mocked her defiance. "You will beg me," he predicted. "Hell grows most tiresome. You'll soon thirst for the passions of paradise. And I'll be delighted to give them to you, my dear. As soon as you request them—on your knees."
"You intend to keep me here until then?"
"But of course." He waved a hand. "What better Hell could there be? Look around. One window, much too small for escape. One door, which I assure you will be bolted and guarded at all times. Yes, I agree, the conditions are most primitive." He pursed his lips and cocked his head. "But you did say that you preferred hell."
He turned and walked toward the door. "Shall you kneel to me now? Spare yourself the hardships that you will suffer for naught?"
Alyssa thrust out her chin, glowered at him. "If I fail to, Kevan will kill you for this, Innes. And when he does, God forgive me, I will rejoice."
He laughed. "Kevan is dead. Bend to my will, Alyssa. Please me, and you will not suffer."
She swallowed her panic. If Kevan were dead, she would know it. She would feel it. "I'll never kneel to you. Never. I swear it."
He strode back toward her. She drew in a sharp breath and held it. He bent to gather her clothes, and she let her breath out slowly.
A scowl as dark as night made a grotesque mask of his face. "As you wish. But know this: as long as you live, you shall be mine. Please me, or suffer the tortures of hell."
Innes turned and stepped into the hallway.
The door slammed shut.
The bolt slid home.
The lock clicked.
Alyssa stilled her thundering heart with a hand to her chest, and looked around. One door, heavy and locked. One window, too high, too small, to aid her escape. A bare cot. A chamber pot. And nothing that could serve as a weapon against Innes. Nothing.
Dear God, she was trapped.
Twenty-five
"YOU MUST eat, milord."
Kevan looked up at Meg, his eyes haunted. "I've no appetite."
Meg frowned down at him. Unshaven and weary from investigating leads on his wife's whereabouts, he'd grown gaunt. There was a desperate look about him now.
Two long weeks had passed. And no further word had come from Innes. Meg gave her lord a sympathetic look and left the library.
In the hall, she saw Parks, a slump in his normally erect posture. He, too, wore the signs of strain.
She pulled an envelope from her pocket and passed it to him. "Something must be done, Parks. Have someone take this to Lady Jersey. She'll know what to do."
Parks took the envelope and nodded to a footman lingering in the hall. "See this delivered at once."
A scant hour later, swathed in plumes and a bright green poke bonnet, the esteemed Lady Jersey strolled into Kevan's Knightsbridge library.
"Parks, tea, if you please." She smiled at Kevan. "Good morning, milord."
"Sally?" Kevan narrowed his eyes, watched the lady remove her gloves. "What are you doing here?"
"I've come to straighten out this inexcusable mess."
She sat down in a chair across his desk—the one Alyssa favored. Pain twisted in his chest.
Lady Jersey frowned. "Why haven't you spread the word about Alyssa's abduction?"
With great effort, Kevan stifled a groan. If nothing else could be said for the Jersey, she was persistent. "My wife is a proud woman. You know that. I wanted—"
She interrupted with a shrewd glance and an impatient wave of her hand. "To protect her from gossip-mongers who are sure to speculate that she either left willingly with Innes, or that she was raped by him during her incarceration."
Kevan flinched and nodded. "You are—"
"Blunt." Again she finished his statement.
Parks set the tea tray on a table near her chair.
"Thank you, Parks." The forward woman smiled up at his man. "Please bring his lordship something more substantial than scones to eat. He looks—dreadful."
"Yes, milady," Parks replied, a decided twinkle in his eye, his back as straight as the jewel-studded sword hanging above the mantel.
"I'm not hungry."
"Go, Parks. Bring the food." Lady Jersey turned her frown on Kevan. "I'm most annoyed with you already, milord. Do not test my patience. I agreed to assist in your little deception with Alyssa because I've a fond memory or two of your father—Lord, you do remind me of him in his salad days—and, of course, I agreed because I myself married at Gretna Green. A most romantic encounter that I hope you made as memorable for Alyssa as my dear husband did for me." She cleared her throat, and her voice grew stern. "However, I doubt you did. You've botched this entire romance with your wife, and I am far from pleased with your performance."
Kevan couldn't keep the groan from passing his lips. "You neglected to tell me that Innes had been married."
"You neglected to ask," she countered. "Poor Hedwig. She was a lovely woman. Impeccable lineage, you know."
She paused to pour two cups of tea, then passed one to Kevan and watched him raise the cup to his mouth. "You are aware that Innes murdered her."
Kevan sputtered hot tea down the front of his coat of superfine.
Lady Jersey smiled and thrust a linen napkin in his direction. "Close your jaw, Kevan."
Dabbing his chin, then his coat, Kevan frowned at the lady. "How do you know Innes murdered her?"
"You men are such foolish creatures, my dear. You've not yet learned to seek the counsel of women in matters of importance."
"Sally," he warned.
Sally Jersey shrugged. "I hired her maid."
"She saw—"
"Of course not. Innes would have killed her, too, in that case."
"Then how do you know?"
"Because her maid knew of the discord. Innes is quite a gamester. You did know that, of course. After all, you exploited that shortcoming." She sipped her tea, then went on. "The simple truth is that Innes wanted control of Hedwig's wealth, and she refused him."
"But he was her husband. Alyssa said something about a trust—"
"No, not a trust. Hedwig's wealth was settled on her. Innes did receive a huge dowry to compensate though."
"And when Innes wanted more, Hedwig refused."
"Exactly." Sally leaned forward in her chair. "Hedwig's maid overheard the argument. Innes told Hedwig she was more valuable to him dead."
"I suspected as much." Kevan passed his cup to Sally to refill.
She poured and passed the delicate piece of china back to him. "Do you know where Alyssa is?"
"No, I don't," Kevan admitted, dragging a frustrated hand through his hair. "We've tried all of Innes's properties, those of his friends, inns. There's no sign of them."
Lady Jersey let out an impatient sigh and her gaze rolled heavenward. "In twenty-four hours, I'll have your answers."
"How?"
"Men," she said in a tone ripe with disgust. "Will you never learn? I intend to use the most reliable source of communication—the best source of information—in all of England." Lady Jersey gave Kevan an enigmatic little smile. "Servants, my dear."
His hopes dashed, Kevan frowned. "We've spoken to servants—though none of Innes's could be located."
Lady Jersey thrust out her chin. "And how many women have you spoken to, Kevan Buchannan?"
"I'm not sure," he admitted.
"Humph!" She let out an indelicate snort. "None, I'll wager. A pity. Had you come to me sooner, this incident could have been resolved within days."
The lady stood. Kevan rose to his feet. "Thank you for your concern."
Sally Jersey smiled and drew on her gloves. "I know my reputation denounces my kind heart, Kevan, but you love the chit. She is a delightful woman, if a bit too proud. A most suitable match for you, my dear. Your father would have been pleased."
Kevan bowed, realizing that the fondness Lady Jersey confessed to holding for his father was in truth much more. She'd clearly held him in deep regard.
From the door, the lady directed. "Eat. And get yourself up to crack, my dear. You look dreadful."
Kevan grinned. "My apologies, milady."
"Keep them. You remind me so of your father. He, too, wore that amulet, you know. He confided to me once that it had special powers." She smiled wistfully. "Such a wit, your father. Such a dear, dear wit."
The lady moved from sight and Kevan cupped the crystal in his palm. A jolt rocked his body and settled in his feet. Yes, he remembered. He'd been young, only seven when his father died. But he recalled something . . . Elder. That was it! Elder.
He concentrated, trying to remember more.
THE OLD HOUSEKEEPER hobbled into the tower room. Dragging her right leg, she bent beside the cot and set a tray of food on the floor. "It ain't right," she muttered. "A body ought to have a table to eat at proper."
The food she'd brought in last night hadn't been touched, and grumbling her worries about that, she lifted the untouched tray and took a gander at the naked woman huddled on the bare mattress. She lay still as a corpse. "Pitiful. A body ought to have a blanket, too. Old, drafty tower. Chill a body to the bone. It just ain't right."
She turned toward the door, damning the devil for seizing her lord. Refusing the poor lass even a blanket. "A little food twice a day," he'd said, measuring out a portion too sparse to feed a sparrow, to her way of thinking. "And a little water for drinking, but not too much. Let her lips crack and split. The chit will learn to obey her master."
It was sinful. That spawn of the devil would surely roast in hell. Treatin' a lady like he was. A lady! She nodded wearily. But him roasting later wouldn't spare the lady suffering his Hell now. Oh, there wasn't no fire, but his tower was sure enough Hell for the lady. Him torturing her like he was. Damned able-bodied, weak-spined men, too scared to help her, too. It just wasn't right.
She hobbled back over to the still woman and whispered. "I would kill the he-devil myself, if I could. He's got no pistols, else I'd shoot the devil dead, I would. Treating you what has a soul worse than an animal what has none. I done what I could fer you, though. Tried to kill every spider in the house, and anything else able to crawl. God'll have His due," she predicted. "And that's all I got to say. God'll have his due."
The lady didn't open her eyes, but the old woman nodded anyway. Her eyes misted and she cursed her old age, her crippled body, and her weak spirit. Even if she had been able-bodied, she wasn't sure she had the pluck or the cunning to face the devil's spawn alone.
He wanted to break the lady's spirit. But what he'd soon have was a dead lady. Poor lass wasn't a grumbler though. In all her days in this god-awful room, no matter how much he tormented her, she'd said but one word: Kevan.
The old woman backed out of the rank-smelling room, dragging her crippled leg and relocking the door behind her. She thought about leaving it unlocked, but there was no sense in the risk. The lady was too far gone to escape by herself, and wasn't no one left now to help her.
Carrying the tray made the stairs a trial. Especially with that he-devil standing, as he was, down at the foot of them. Lord, he looked mean enough to spew brimstone. She took her own words to comfort. God'll have His due.
"Has she eaten?"
"No, milord. Not a morsel in three days, nor no water neither."
He stormed past her up the steps. "By damn, the chit goes too far."
The old woman stayed flattened against the wall. She held her breath, prayed for the woman upstairs, and while she had her Maker's ear, she spared a word for herself, too. When Lord Innes got angry, everyone in his path suffered mightily.
IN THE BED he'd shared with Alyssa, Kevan cupped the crystal in his palm. Inwardly, he expected nothing to happen. But a flicker of hope that something might burned in his soul. He closed his eyes and whispered. "Elder. Elder. Elder."
He opened his eyes and kept his voice steady. A silvery mist appeared beside his bed. A shiver raced up Kevan's spine. He fought his fear. He had no other option, Alyssa had no other hope, he had to pursue this queer phenomenon. He chanted. "Elder . . . Elder . . . Elder . . ."
The Elder of the Council of Perfection appeared. Memories flooded Kevan's mind. Alyssa. Visions.
Angel!
"Hello, Prophet."
A shudder of relief filled him. "Your grace."
"She is in Scotland, son. Just across the border, not two miles from where you wed in Gretna Green."
"Is she—" A knot in his throat prevented Prophet from continuing.
"She's alive."
Prophet shuddered and squeezed his eyes closed. "Thank God."
"Prophet, look at me."
The Elder's right eye remained flat. His left one glimmered and flickered light. He seemed even more weak than he had been when they'd last met. "Your grace, I've asked before and you refused to answer. I ask that you answer now. Are you ill? What does the change in your eye signify?"
"It is of no consequence at this time, Prophet. Alyssa is where you must center your concern. Her jeopardy is great. You must not delay. Write down what I have told you and hurry, son. If she dies now, your trials will end here. Your mission will have failed."
The Elder's urgency mingled with Prophet's own surprise. "We will not fail. Not now." Prophet insisted. "Why won't I recall your words?"
"Your woman's discoveries in this level are not yet complete."
"I don't understand. She has forsaken her pride."
"Only to you," the Elder countered. "And that is not exposing herself to ridicule. Though she's yet to realize it, in her heart, she knows you love her. She's risked nothing." The Elder raised his hand. It seemed a difficult task, requiring great effort. "Her pride must fall publicly, before those unsympathetic to her feelings. Only then will she successfully complete this level."
Kevan wrote down the information the Elder had given him, then looked up. He wanted to say so much, but the words seemed to tangle in his throat. "Thank you, your grace."
The Elder nodded, then in a grave voice warned. "The wind blows change among the leaves, Prophet. The season draws near. In it, seek your destiny and your woman."
The Elder's image faded.
Kevan found he was sitting in bed, a note in his hands. He read it aloud. "Alyssa. Two miles from Gretna Green." It was his writing, but when had he penned it?
Then he recalled what he'd been doing just before. "Elder."
His heart thundering, he got up, looked into the cheval glass, and fingered the crystal at his neck. Something had happened. What remained a mystery, but something had happened. The amulet did have a special power!
A sharp rap on his door had Kevan spinning around.
"Milord?"
Wiping sweat from his palms and tugging on his breeches, Kevan responded. "Enter, Parks."
"You must come at once. The library is full. Lady Jersey has returned—Sir Duncan and James Macmillian, as well. They—they all arrived at once."
Kevan smiled at a very agitated Parks. After twenty years of service, that trusted worthy had lost his calm and become quite emotional. "Make them comfortable. I'll be down directly."
"Milord."
The fear in Parks's voice raised gooseflesh on Kevan's arms. Bracing himself, he turned around.
"I found this parcel on the doorstep." He passed a small box to Kevan.
His stomach muscles clenched like he'd suffered a great kick. "Go on now," Kevan whispered, unable to lift his gaze from the box. "Alyssa is alive, I know it."
"I'll wait—"
"No, go on." Kevan insisted. "See to our guests."
Parks left his chamber, but Kevan heard his man's footsteps halt just outside the door. He, too, feared the contents of the box.
Sweat trickling down his neck, Kevan opened the box and reached inside. He lifted and recognized a fat wad of delicate fabric. Holding the chemise he'd bought for Alyssa in Paris, his hand began to shake violently. He caught his breath, strangled a wounded cry in his throat. Forcing himself to shutter the images her clothing invoked, he separated the folds. The fabric had been torn—in places shredded. His heart slammed against his ribs, then lay like a stone in his chest. Long clumps of silver tresses spilled across his palms. Tears of rage blurred his vision, clogged his throat. And among her severed locks lay a folded page, mocking him.
He set the parcel down gently on his bed, then swiped at his eyes with an angry hand and jerked up the piece of paper.
The silver filly struts no more.
Broken by a crack-whip's skill.Ah, the ribbons handle well.The docile mare, lays winded—And tarnished.-13-
Anger, agony deeper than any Kevan had known, seeped into his pores and smothered him.
The bastard had raped his wife.
Twenty-six
WILD-EYED, KEVAN rushed into the library. "She's in Scotland."
"We know."
It was Lady Jersey who spoke. Kevan grabbed his silver sword from above the mantel, its rubies and emeralds embedded in the hilt catching the light from the fire.
"I learned from the servants," Lady Jersey said.
"An innkeeper," James disclosed. Kevan's gaze drifted to Duncan.
"Cameron."
"Cameron?" Kevan paused.
Duncan nodded. "Found him trussed like a bird set for the table in his own attics not an hour ago."
"Innes?" Kevan asked.
"Innes trussed him up," the Lord Chancellor said, walking into the library. "And Cameron's confessed that he knew of the plot to kill Hedwig. But he insists he did not aid in her murder."
"Parks!" Kevan called out.
"Yes, milord," Parks said on entering the room. "The carriage is out front. Major is on the box. And the footmen and grooms are ready and waiting for your instructions."
Kevan nodded. "My stallion, too, no doubt."
Parks gave Kevan a rare smile. "No doubt, milord."
Kevan started toward the door. James stood up. "I'm going with you."
"Let me hear from you, Kevan," Lady Jersey called out to his retreating back. "He reminds me so of his dear father."
DISGUISED AS a beggar, Kevan knocked on the rear door of the isolated castle. Knowing that Alyssa was somewhere inside had him calling up every sliver of control he possessed to keep from setting his shoulder to the damned thing.
An old woman with a malformed leg answered, wiping her hands on her dirty, black gown.
"Good day, ma'am," Kevan said, dipping his head.
Her eyes narrowed. "What are you about?"
"I've come for—"
Her gaze settled on his signet ring, and her face, too lined to be considered merely wrinkled, lit up. Her voice dropped to a whisper. "Praise God, you've come for the lady. Tell me, boy. Be you Kevan?"
The woman was shrewd. He nodded once and prepared himself to stifle her, should she cry out a warning.
The old woman smiled. "She's in the tower, she is. Half-starved. I—I—tried to feed her—"
"Innes?" Kevan cut in.
"Still abed," she told him.
Kevan pulled his sword from its sheath. Its silver blade glinted menacingly.
The old woman didn't flinch. "I hope yer good with that. Innes is a bastardly devil, but he's a fine fence."
"How many guards?" Kevan asked, ignoring her remarks.
"There ain't any. He went wild in one of his rages and run 'em off."
"Which room is his?"
"Top of the stairs. Second door." The old woman looked worried. "I done what I could for your lady, Kevan. He's given her a hard time, he has, and me too weak to stop him. The lass never gave up hope that you was coming, though."
Swallowing the pain that statement caused, Kevan gave her a curt nod. "You must leave this house. Have you a place to go?"
"Don't worry about me. Just kill that devil's spawn afore he kills you. And get yer lady out of here while there's still life in her."
Kevan crept up the stairs, easing his feet between the banister spindles to avoid warning creaks. In the hallway, he stopped and put his ear to the second door. Innes's muffled snores penetrated the wood.
Lightning quick, Kevan stormed into the room. Before Innes opened his eyes, Kevan had his sword point pressed against Innes's throat. "Wake up, bastard!" Kevan shouted. "You will see the man who kills you."
Innes eyes snapped open. Fear burned deep in them. "Buch—"
"You abducted and raped my wife. For this you will die. Could I kill you a second time, I would. For Hedwig's murder. Make your peace with God, Innes. You have ten seconds."
Innes's arms fell lax at his sides. His fear changed to resignation, then to cold hatred. "I found my peace, Buchannan," Innes sneered. "In bed with your—"
Kevan pressed the point, and Kenrick Innes spoke no more.
Wiping the blood from his sword, Kevan sought the tower room. Back in the hall, he saw the old woman.
"Is he dead?" she asked.
"He is."
She nodded, then motioned with her hand. "This way."
Kevan followed her. At the tower door, she fumbled with the keys. Impatient, he rammed the door with his shoulder.
The door swung back and slammed into the wall behind it. The foul stench in the room had his stomach heaving. Then he saw her. Laying curled into herself on a filthy, bare mattress. "Alyssa?"
She didn't move.
On his knees beside her, Kevan gently stroked her face. Seeing the bruise on her cheek, those peppering her arms, her legs and shoulders, had him wishing Innes could die again, could suffer more. "Alyssa? Answer me, love."
Shadowing her cheeks, her silver-tipped lashes fluttered open, and he saw her eyes. They were dull, withdrawn, and not so much as a flicker of recognition greeted him. Fear constricted his chest. Did she not know him? "Alyssa, it's me, love, Kevan."
Blinking, she whimpered, her voice a raw croaking whisper of sound. "Kevan?"
He brushed at the tears on his face, and gruffly ordered the old woman. "Get her some water."
The old woman returned with a glass. Kevan lifted Alyssa, pressed the glass to her lips.
"Milord?"
Kevan recognized Major's voice, coming from the hallway. Seeking to protect his wife, to prevent anyone else knowing the conditions she'd been forced to endure, he shouted. "Do not come in here! She is alive."
He turned to the old woman, sensed and felt the fear in her. "Where are my wife's clothes?"
Tears wet the old woman's face. "He tore them, milord. But Lady Hedwig's—"
"No!" He closed his eyes, clenched his jaw. Alyssa would not wear another of Innes's victim's clothing. Nothing of his—not even the dust from this house would touch her again. He looked at the frightened woman. "Leave this house now."
Alone with his wife, Kevan pressed his lips to her temple. He raised her onto his lap and rocked her in his arms as one would a child, comforting her, comforting himself. "You're safe now, love." Tears trickled down his face and dripped onto his wife's head. "I'm sorry, darling. I'm so sorry. When you most needed my protection, most needed me, I failed you. Oh, God," he cried. "I failed you."
Pressing his cheek to her crown, Kevan cried.
She had suffered, but she had survived. His deep sobs grew weaker. In spite of him, she had survived.
He removed his coat, and gently put it on his silent wife, recalling another time, a more pleasant time, when she'd wiggled her fingers and demanded his coat. She'd enchanted him that morning; pecking his face with rapid-fire kisses, stealing his breath with long languid ones. He heard himself ask: "And what was that kiss for?" And he heard her spirited reply, "That was for me." But now, except for her pitiful whisper of his name, she uttered no sound. And he prayed that all she had suffered at Innes's hands had not broken her spirit.
He spoke to her in soft, crooning tones, not sure if his attempt to comfort was for her benefit, or his own. "We're going home now, darling. To Woodwind. You love Woodwind. We'll swim in the lake—you can practice floating. You'll be fine, you'll see. Once we get home, you'll be fine." He said the words, praying they were true. Then he stood, and carried his wife out of hell.
His men waited at the foot of the front entry steps. Major stood in front. Beside him was young James MacMillian, tears streaking down his pinched face. Major stepped forward, and Kevan watched his sweet-tempered coachman lift his gaze from Alyssa to meet Kevan's eyes. In that instant, Major seemed to age twenty years. And never, in all their years together, had Kevan seen the look of cold fury Major wore now.
"Innes?" Major asked, his voice hard as metal.
Somber-eyed, Kevan replied. "Dead."
The old man nodded once. "Burn it?"
Kevan's own fury found vent. "To the ground."
Twenty-seven
KEVAN SAT DOWN under the huge fir, looked down the sloping bank of the lake to the water, and watched Alyssa float on her back. A smile curled his lips.
"Is this right, milord?" she shouted. "To cup the hand this way?"
"Perfect!" he shouted back.
It had been a long four months since he'd found her in the tower. But her progress confirmed his decision that Woodwind would aid her in recuperating. Not that there hadn't been tense moments. Beginning just minutes after their return when Meg had refused to allow the doctor to bleed Alyssa. She insisted that Alyssa felt only cork-brains held with the practice. He'd deferred, and Alyssa's injuries had mended quickly. In less than a month, the doctor pronounced her fit—physically.
"Kevan, watch this." Alyssa turned over onto her stomach and executed a perfect breast stroke. "I shall soon challenge you to a race, milord."
Because she expected him to, Kevan guffawed. "If that's your intent, you'd best double your practice laps."
The water carried her laughter to him. "I've tripled them, milord. I'm taking no chances."
He held his smile, but it proved difficult. His guilt at failing her swelled inside him. Her emotions were still jumbled. It'd taken two months of humoring her before she began talking about the time she'd spent abducted. Innes had not raped her, thank God, but he had threatened to, and Alyssa had fought him. She'd suffered bruises, aching limbs . . .
Tormenting images of her trying to defend herself against Innes had acid churning in Kevan's stomach. She was so tiny. He pushed his heart down out of his throat.
A honey bee buzzed by and lit on a white iris near his shoulder. Alyssa turned at the lake edge and began swimming back toward him. Kevan sighed. The experience had, of course, changed her. How could it not? It had changed him, too. Rage against Innes had long since become a constant companion, but the helpless feeling that came with it still created new pain, heaped more guilt on the old. Innes had died for his crimes. Why didn't it seem like enough?
Alyssa stood in the water and waved to him, her hair falling in soft, wet curls around her face. The muscles in his chest clenched. Beautiful, and finally—dear God, finally—happy again.
"I've only to practice my other strokes, Kevan. Then I'll come out."
He returned her wave. "All right, love."
She'd often talked of how vulnerable, how angry, she'd felt at not being able to defend herself against Innes. And she'd insisted she be taught.
With each new skill, she grew more vibrant, more like the spirited woman she had been before. Yet she was different, too. Bolder, more confident, stronger. She made a diligent student; studied hard, learned well. He tore a sprig of grass from the earth and flung it down. But then, she would. She had the strongest possible motivation.
Smoothing her hair back from her face, Alyssa stepped from the water onto the bank. Sunlight made sparkles of the tiny droplets of water clinging to her bare skin.
Catching his breath, Kevan felt his body grow hard and prayed that another four months wouldn't pass before he made love with her again. Though her nightmares had long since ended and she still slept in his arms each night, she had not once turned to him.
He watched her climb the bank, admired the sleek way she moved. Why couldn't he just ask her to make love with him?
No, he decided. He had forced her into marriage, into his life. He could not force himself into her body, as well. He had no right. He'd failed her. She needed time to heal. Then, perhaps, she could forgive him and come to him again.
She stopped beside him under the fir. "The water feels wonderful, milord. You should have joined me."
He smiled up at her. "I can't keep up with you anymore. You improve each day." He passed her a towel, knowing that she would think he meant her swimming, not her mastering her fears.
Two weeks ago, before she would step from the water, she'd still been twirling her finger at him to turn his back. When she first neglected to do so, he'd kept his eyes on her face. But for the last week, he'd grown more bold, feasting on the sight of her. And she had not complained. Would she soon be ready for him again?
She smiled and dried herself with the thick white sheet, then slipped into her cloak, leaving her dress draped over the bush just behind him.
Kevan stifled a grimace. The doctor's insistence that these memory lapses were shock-related wore thin. Alyssa grew more and more content, yet the lapses did not diminish, but grew more frequent.
Rubbing her hair and face, her skin flushed a healthy pink. "I've come to enjoy bathing in the lake a great deal, milord."
"Seeing you happy pleases me." Kevan stood up and spoke gently. "You've forgotten your dress, love."
"I did not forget—this time," she said, stepping toward him.
A mischievous gleam lit her eye, and she pressed her palm against his chest. His heart tripped, then pounded, and his muscles all contracted at once. In their seven-month marriage, he'd slept with his wife most nights, but he'd made love to her only twice. She'd come to him the night of the mead and once in London. But he recalled every blissful second of both times—and he yearned for another.
She tilted her face up to his. "I recall a promise made to my husband at this very site. He caught me wool-gathering one morning, and it seems I agreed to ride with him, wearing naught but my cloak."
Kevan could barely speak. "I remember."
"Well, milord. We Buchannans honor our word."
His delicate little wife graced him with the sweetest smile known to man, then let out an ear-splitting whistle. Her white mare and his bay stallion answered by coming to her side.
Her eyes dancing, she looked up at him and burst into laughter. "Do close your mouth, Kevan. You'll catch flies. And you know I can't abide bugs."
He remembered her hysteria on seeing a wood spider on her chamber wall, her telling him that Innes had tortured her with spiders, forced her to lay on that filthy cotton and suffer spiders crawling on her bare body.
Anger surged through Kevan. But Alyssa's throaty laughter acted as a soothing balm, and again he managed to leash it.
"Are you impressed, milord?" she asked, her fingers sliding down her mare's reins.
"I am." He chuckled. "Where, dear lady, did you learn that?"
"Major taught me," she replied. "If a person is unable to get to her horse, then her horse should know to come to her. Don't you agree?"
"I dare not disagree," he countered. She'd become a crack shot. And the Chinese cook she'd employed had shown her how to toss an attacking man like a stick. Secretly, Kevan thought the cook's fighting skills, and not his culinary ones, had prompted Alyssa to hire him. But that, too, Kevan understood. "I don't know what other skills you've acquired of late and chosen not to disclose."
Her eyes clouded. He thought her recalling the incident, as they'd come to call the time she'd spent abducted, but she held her smile and her tone sounded pleasant enough. Mounting their horses, Kevan sensed change rife between them, daring him to hope that his prayers for her recovery had been answered.
Alyssa spurred her mare. She rode through the break in the hedgerow behind Kevan, and on into a wide meadow sprinkled with wild daffodils. Sun-warmed, the bright flowers filled the meadow with their sweet scent. She inhaled deeply.
It seemed especially hot for July, and after a time, she saw Kevan rein in under the shade of a craggy oak. Anxious to get into the cool shade, she followed and stopped beside him.
He caught her at the waist and helped her dismount. Her flesh tingled. She sucked in a sharp breath, her gaze darting to his. Tension creased the corners of his mouth, not welcoming or shunning, and his eyes grew solemn. Uncertain of his feelings, she stepped away.
He spread his riding coat between two gnarled roots jutting out of the ground near the trunk of the oak. "Come," he said. "I've a need to talk with you."
A quiver raced through her and shook her stomach. The night they'd made love he'd said he'd a need to hold her. Why had he bedded with her, but not bedded her? Had the incident made her repulsive to him?
A man has needs, he'd told her. Needs that, she believed, any man must satisfy. Had he taken someone else? He'd been with her at Woodwind the entire time, but—but he could be satisfying those needs with someone in her home. He'd agreed not to do that once. But circumstances were different now. Much different.
Alyssa sat down and watched Kevan pace before her. Serious and intent, he frightened her. And fearing Kevan was a foreign emotion. One she did not like. Her tension mounted until her stomach threatened to revolt. Beads of sweat popped out on her skin, then trickled down between her breasts.
"I've wanted to tell you this since the beginning, Alyssa," he said at last. "I didn't then because I doubted you would believe me. Somehow, the time never seemed right. I feared your reaction. Then the incident happened, and I worried that I'd waited too long. I vowed then that on the day I felt you had sufficiently recovered, I would delay no longer."
He glanced at her, then looked away and continued his pacing. "This confession is difficult, my lady. I pray it does not cost me your affection."
"This hesitation is most unlike you." Had he taken someone? Did he mean to set his wife aside?
"The behavior requiring this confession is unlike me, too," he said. "But I want no secrets between us."
She screwed up her courage, certain that on hearing of his infidelity her heart would shatter and she would die. "Is it another woman? Is that it?"
He laughed. Not a nervous, guilty laugh, but a deep, lusty one that told her he found the thought of taking someone else outrageous.
"My heart belongs to you, love. How could another woman replace you in my bed?"
His heart? His heart—hers? She cocked her head and studied him. He sounded convincing, but a remnant of doubt remained in her heart. "Many men—"
"I am not many men," he interrupted. "I am your man, darling. There is no other woman, nor will there ever be."
She believed him. Relief washed through her and cleansed her of fear. His heart. Hers! "What is it, then?"
His hands clenched into fists, his sharp words sounded clipped, and guilty. "I knew you before I entered that church, Alyssa. Before I challenged Innes for you at the gaming table."
She waited, but he said no more, so she prodded him. "And—"
"And?"
He looked as puzzled as she felt. Alyssa shrugged. "I assumed that you knew me, milord. You called me and my father by name. A dullard wouldn't kidnap a stranger to marry her. Nor would he wager to win her." She smiled. "And you, milord, are far from dull."
He sat down beside her and waited until she looked up at him. "Why have you never asked why I took you, or what I'd wagered?"
Alyssa worried her lower lip with her teeth. Could he feel her heart pounding? She supposed she should be honest with him. The time for secrets, for lies between them, had passed. Hadn't Kevan proven that by confessing his deception now? "I never asked because your true reasons weren't apt to be as flattering as the ones in my fantasy."
He took her hand in his. His eyes, so somber, pierced her soul. "Tell me your fantasy."
"No, Kevan. I'll not say." Her gaze dropped to the grassy earth. His thumb rubbed tiny circles on her wrist, thrilling and soothing her at once. "You'll think me whimsical."
He raised her face, and cupped her chin in his big hands. "I think you beautiful. Please, I must know."
The plea in his voice touched something deep inside her. She met his gaze, saw his need reflected as clearly as a looking glass would reflect her own. "I pretended that you took me with you because you loved me."
He didn't smile as she feared he would. His hands trembled on her face. "I do love you, Alyssa," he said.
She covered his hands with her own. "You don't have to lie to me, Kevan."
"I've not lied. I love you, darling."
Truth shone in his eyes, and her heart took flight. The urge to laugh and cry hit her at once. "Kevan?"
He lowered his hands and clasped hers. "I saw you in Hyde Park, taking the air with your father. You were beautiful—the most beautiful woman I had ever seen. Pale blue muslin, ribbons, a little lacy parasol protecting you from the sun."
He had a faraway look in his eyes, and Alyssa knew he was not seeing her as she was today, but as he'd seen her on that day so long ago. "You are serious?"
"I am. You'll think me daft, but I recognized you, Alyssa. I can't explain it, but I knew you." He nodded for emphasis. "I sought your father the next day and asked for your hand rather than for permission to call on you."
She gasped. "Kevan, that's it! That's where I saw your insignia. I thought I'd seen your ring, but I hadn't. That's why I couldn't recall who I'd seen wearing it. It was your card I'd seen. It was your card."
"I did leave my card with your father," he said. "I couldn't wait to make you my wife." His tone deepened, etched with a hardness she'd not often heard. "That's when I learned you were betrothed."
Alyssa felt stunned. Special and cherished, but stunned. "But that's impossible, milord. That was a year ago."
"Twenty months," Kevan corrected her. He lifted a twig from the ground and squeezed it in his hand. "Your father refused me. He told me of your betrothal to Innes. I resolved to move Heaven and earth to take you from him. A few discreet inquiries in town, and I learned that gaming was his weakness." Kevan's eyes clouded. "But no one, damn it, mentioned his wife."
Alyssa's thoughts whirled. She grasped Kevan's bent knee. "But—if my father refused your suit because I was betrothed back then—"
"I know." Kevan covered her hand. "Innes's wife was still alive."
"Oh God." Tremors racked her body. "My father knew. He knew Innes planned to kill Hedwig."
"Yes, love, he knew. Your father had lost his fortune and was deeply in debt to Innes by then. Though your father was stained in blood, it was not Hedwig's. He did not kill her. Innes did."
"But, Kevan—"
"No, listen love. The blood was Innes's way of forcing your father to cooperate, to provide an alibi. Your father was sotted and gulled into swearing that he and Innes were together at the time Hedwig was murdered."
"But my father could have prevented it," Alyssa cried.
"Perhaps." Kevan sighed. "But I think Innes would have found another way to see the deed done. Take solace in knowing your father did not hold the knife."
"I can't. My father sold me to a man he knew was a murderer. I suspected—but, damn him, he knew. Even after you and I wed, he tried to separate us, to force me to wed Innes. I cannot forget that, milord. I—I won't."
"I understand, love. But don't let your anger fester and poison you. Let yourself heal. Neither of them can hurt you anymore." He pushed that topic aside, saying, "We're drifting from my confession. My apologies, my lady." He pressed his lips to her fingertips.
Tingles of pleasure rippled up her arm and settled in her heart. "Please, tell me everything. Then we can forget this matter once and for all."
He nodded. "After I learned of Innes's weakness, I turned my efforts to breaking your betrothal to him. Had I known of Hedwig, it would have been a simple matter. But I did not. So, I tricked Innes into wagering you."
"Tricked him?" She smiled. "You tricked Innes?"
"I did." Kevan looked extremely embarrassed. "I'm sorry, Alyssa. I've ruined your reputation—but I had no alternative." He let out a deep sigh. "While I'm confessing, I suppose I should confess this, too." He paused and reached for her, raised her onto his lap, and leaned back against the rough trunk of the oak. "With all that has happened, if I could go back and start again, to have you at my side, I would repeat my actions with but one exception."
Her face pressed to his chest, she heard the steady thump of his heart. "What would that be, milord?"
"I would accompany you to the modiste's and prevent the incident."
Alyssa's heart sang. It was most difficult to feign calm. But she knew she must. For Kevan, she must. "Your love has come at the cost of my self-respect. Between your trickery and the manipulations between Innes and my father, you've all done me a horrid injustice."
"I would agree, my dear," he said. "But I wanted only to protect you, to be loving with you. That's why I placed Meg in your home. I had to know that you were safe until I could find a way to make you my wife. When you wed, I feared Innes would be the man at your side. And, you must admit, he came damnably close."
She nuzzled his neck. Even then, he had sought to protect her. "So Meg, too, was your device."
Kevan's arms tightened around her. "She was."
She longed to thank him for his care, but knew she could not. Not yet. Kevan felt responsible for what Innes had done to her. She had to find a way to remove his guilt. "And Lady Jersey, of course, knew all of this."
"Yes." Kevan took her hand from his shoulder and drew it to his lips. "I'm sorry. The deceit, the embarrassment, that you felt compelled to lie—"
"Lie?" She reared back. "I have not lied to you, Kevan." Oh, how she adored this man. His soft smile, his wise eyes, his patience, his loving nature.
"Not to me. For me," he said. "You told the king's guard that you loved me."
"I did," she said, cagily avoiding confirmation or denial. Her heart threatened to fly from her chest. Kevan loved her. He wanted her love. All he had done, he had done because he loved her, because he wanted her as his wife.
Once he had told her they would suit, if she forgot her pride. Well, she would forget it—after he'd suffered long enough to deter him from deceiving her again. Inside, she smiled, but it did not cross her lips. Lady Jersey would heartily approve.
Now. How exactly should she go about revealing that she'd rid herself of the annoying vice he'd sworn stood between them? She could simply tell him that she loved him.
No, too much had transpired; he would think she acted in gratitude, not love. She had to do something more. Something that would remove all doubt from Kevan's mind and heart forever. He'd given her a romantic intrigue that most women only dreamed of. How could she reciprocate?
Then she recalled the incident in Grimsby.
Perfect! A shiver of delight tripped up her spine. Absolutely perfect. "Kevan, I wish to go to London. Please, love. Will you take me?"
Kevan's heart stopped. He looked at her. Flushed with excitement, her eyes dancing, she captured his heart all over again. He couldn't have refused her request if he'd wanted to—but he didn't want to. He wanted to give her the world, the stars—any and every other thing she desired. The cause of his pleasure with her was simple.
For the first time, his wife had called him her love. "We'll leave today."
Twenty-eight
ALYSSA SEALED the envelopes. Looking at the names she'd written on them, she verified her choices, one last time.
Monk Lewis. Fashionable author. Close friend and confidant of the royals. She envisioned him telling the Duchess of York what he would soon witness. As a child, Alyssa had grown fond of both the Duke and the Duchess. But only a paper skull would believe they'd approve her actions.
She squeezed her eyes closed. Please, God, just let Kevan approve. She swallowed and looked down at the second buff-colored envelope.
George Cruikshank. Popular caricaturist. As her witness, he no doubt would find plenty to whet his imagination.
Alyssa swallowed again—hard. To assuage Kevan's misplaced guilt by forsaking her pride, she must endure a total sacrifice. One that left Kevan no plausible doubt of her affection or of her intention.
She lifted the third envelope. William Cobbett. Publisher of the Weekly Political Register. Her cheeks burned hot. He, too, would denounce her actions—in print. Everyone in London would know what she'd done within a day—if not sooner. Juicy gossip travels much faster than news from a printer's press.
The Lord Chancellor. Even the House of Commons would not be spared from hearing of her exploit—nor would they be denied the opportunity to condemn that exploit.
And Sir Duncan. By all means, Sir Duncan. The guard who had come with her father to the Knightsbridge house to arrest Kevan—and hadn't. Why he hadn't still mystified her. He knew she'd lied—she'd seen it in his eyes. It was no small comfort to her that in seeing what she was about to do, Sir Duncan would know his decision back then had been the right one.
Selecting these witnesses had been a painstaking affair to which she had devoted considerable thought. Kevan must understand the significance, the sacrifice she was making. He must understand that with this spectacle, she offered him her heart.
He might think her a fool. She bit her lip and tapped the envelopes into a neat stack. Then again, he might not. Lord, what a risk!
Feeling her confidence waiver, she called out before she could change her mind. "Meg?"
"Yes?"
Lifting her chin, she passed the neat stack of envelopes. "Ask Parks to please see these delivered."
Her abigail frowned. "You're going to do it, then?"
Only a dullard could miss hearing Meg's disapproval. Alyssa's chin lifted a fraction higher. "I am."
Meg sighed and took the envelopes. "I hope you know what you're doing."
Still muttering, Meg left the chamber. At her vanity, Alyssa read the invitation from Almack's that had arrived that morning. "Wednesday," she whispered to herself, "will be a most extraordinary day."
She lifted the water lily she'd found on Kevan's pillow that morning and inhaled its sweet fragrance. Its meaning was not on her little list, but she knew that anything that smelled so heavenly couldn't be bad. It just couldn't.
WEDNESDAY MORNING Alyssa met Kevan below stairs for breakfast. As he was already seated at the head of the long mahogany table, she walked to his side, placed a chaste kiss to his cheek, and handed him the written invitation.
One of his brows arched up. "What's this?"
"Read it, milord," she instructed, taking her seat at the opposite end of the table. "Tea, please, Parks."
"Yes, milady."
"I'm invited to witness a startling metamorphosis—outside your window tonight at precisely six o'clock?"
"Yes, milord." She nodded. "And, pray, do not forget we go to Almack's tonight, as well."
"Alyssa?"
She ignored his puzzled look. "I'll say no more, Kevan. You must appear beneath my window at the appointed time to learn anything else."
Tapping the invitation against the tabletop, Kevan gave her a wary look. "Very well, my dear."
MEG ARRANGED Alyssa's hair in soft loose curls.
"Are you sure you don't want it up? It's grown quite a bit."
"Not so much as one hair pin, Meg," Alyssa insisted, remembering Kevan's specific remark about the woman at Grimsby. Meeting Meg's worried look in the cheval glass, Alyssa smiled.
"Maybe the doctor wasn't cork-brained," Meg said. "When you had the fever, Oh God, maybe he should have bled you."
"Don't be ridiculous. Would you calm yourself? I know exactly what I'm doing." Alyssa's stomach fluttered. The doubt that had nibbled at her insides since two minutes after the invitations left her hands progressed to a full-fledge chewing. "I think."
Meg groaned. "Does his lordship know what you're about?"
Alyssa worried her lower lip with her teeth. Clenching muscles joined the chewing doubt rattling around inside her. "Not yet."
"Oh God." Meg groaned again—deeper.
Alyssa turned a hard look on her. "Would you stop beseeching your Maker? Interrupting Him is practically all you've done for the past three days. I don't want God annoyed, Meg. I've enough to contend with here."
"I can't help it, milady," Meg cried. "This scheme will destroy what's left of your reputation, to be sure."
Alyssa slumped. "God, I hope so."
Meg's eyes stretched wide as saucers. "What?"
Alyssa thought to explain, but Meg already looked sure to swoon. "Never mind. Did you get the flower?"
"James did."
Alyssa glanced at the mantel clock. "It's time. Get the flower and check with Parks to make sure he's ready."
"Milady, please don't do—"
"Scoot, Meg!"
"KEVAN?" Standing on Kevan's lawn, the Lord Chancellor's brows raised high on his face. "What purpose has this intrigue?"
"I've no idea." He looked at the men present. Sir Duncan, Lewis, Cruikshank, Cobbett—and standing to one side, Parks. "What's that you're holding?"
Whist-faced, Parks glanced at Kevan. "'Tis a cloak, milord."
"Whatever for? It's July, man."
"Yes, milord," the unperturbed Parks replied, looking up at Alyssa's window.
"Kevan?"
Hearing Alyssa's voice, Kevan looked up, too. Smiling, she tossed a flower down to him. He caught it. His heart slammed against his ribs. She couldn't possibly understand this flower's symbol. Her calling had him craning his neck to look up at her.
"It's a narcissus, Kevan," she said in a solemn little voice. "It means pride, if you aren't knowing."
His heart swelled till he feared it would burst. She'd cast her pride aside—for him. For him. He smiled up at her. "I know."
Worrying her lower lip with her teeth, she nodded. Her gaze shifted to the men assembled. "Gentlemen, thank you for attending. I've asked you here to act as witnesses to a startling metamorphosis: Mine."
She stepped back from sight. Mumbled whispers broke out among the men.
"What is she doing?"
"Kevan, has she recovered?" the Lord Chancellor asked.
Naked as a newborn, Alyssa stepped out onto the window ledge. Shocked gasps escaped the men assembled, and a slow smile spread Kevan's mouth. "She's recovered," he said, his voice thick with poignant emotion. "Thank God."
"Milord," she said in a solemn little voice. "I come to you with nothing—not so much as a single pin for my hair. I have no material holdings or possessions, no dowry—and no pride. My only gifts to you this day are these: a reputation stained by impropriety, a spirit sorely tested and weary, and a body exposed to reveal its every imperfection. I cannot offer you my heart, milord, nor my soul. Neither do I possess. Both were given to you long ago." Her chest heaved, as though all she had said measured naught to what she yet faced. "Do you bid me come?"
Kevan couldn't speak. Of all she could have done, of the many ways she could have told him of her love, none other could have conveyed her devotion to him with more eloquence. Feeling humble, proud, he held his arms, open to his wife. "Come."
She graced him with a smile that dimmed the sun, and jumped.
Cradled in his arms, Alyssa clung to him. "I love you, Kevan."
Beside them, Parks unfolded her cloak, and Kevan draped it around her, unwilling to part with her long enough to properly wrap her in it. Parks stepped back, and Kevan pretended not to see his man's chin quiver or to hear his sniffle.
"A delight to these old eyes," Parks whispered the very words he'd said once before. Kevan felt Alyssa smile against his neck and wondered if any man before him had felt so much love for any woman. The words burned his throat, insisting he speak them. "By God, Alyssa." He waited until she looked up at him. "I do love you so."
Looking into each other's eyes, they shared a smile, then Kevan carried his wife across the lawn and into their home.
The Lord Chancellor watched them go. He heard their laughter carry back to him on the warm summer breeze. His vision blurred and a tightness in his throat had to be swallowed down.
"Imagine. A countess jumping like that—bare to the skin!"
It was Monk's voice, the chancellor heard. "Yes, imagine indeed. We should all be so fortunate."
"This entire display makes no sense," Cobbett said, clearly perplexed. "She's already married to him. Why did she do it?"
"Her father's debts?" Cruikshank suggested.
"No, they've been paid." Sir Duncan contradicted that conjecture, looking to the Lord Chancellor like he was incredibly satisfied with himself. "What a woman she is."
Persistent as a hound on a hunt, Lewis crossed his arms over his chest. "Who paid the debts?"
"Lord Buchannan," Duncan disclosed, his leathery cheeks splitting in a wide grin.
Cobbett scratched his balding head. "Then why did the countess jump?"
A deep sense of rightness, of well-being, suffused the Lord Chancellor. And, he honestly admitted, a healthy touch of envy, too. Duncan was right. Lady Buchannan was a most unusual woman. "This had nothing to do with money," he told the others. "Come, gentlemen. Allow me to tell you a remarkable story of romantic intrigue. It will answer your questions—outrage you. And it will enchant you."
"I DO NOT regret my actions, milord," Alyssa said to Kevan. "But I do not wish to attend Almack's while news of them is fresh on the tongues of the ton."
Kevan sent her a stern look that did nothing to settle her quivering stomach. "We're going."
"For pity's sake, Kevan. Why must we?" She clenched her hands into fists. "I—I guess I should not have publicized my metamorphosis after all. Perhaps I should regret—"
"Don't, Alyssa." His voice was firm. "You removed the last obstacle between us. Don't grow weak-spined on me now."
"Weak-spined?" She glared at him. "It's not for me that I am concerned."
"Isn't it?"
"No." She frowned and twisted her dainty hanky around her fingers. "Everyone will say you've married a chucklehead. My reputation is already smeared beyond reparation. It's your reputation that concerns me now."
He wrapped his arms around her, pinning hers between them. "Every man at Almack's—hell, in all of England—will envy me."
Alyssa swallowed hard and risked the question that could send her spiraling into the worst case of the blue devils known to woman. "You aren't ashamed of me?"
"You professed your love for me in a way no man has the right to expect. But any man would gladly die for what you've given me." He paused to touch her face, to let his hands grow tender and drift down her neck to her shoulders. His eyes warmed to molten silver. "I feel many things for you, but shame has no place among them. Your courage has humbled me, dear lady."
She lifted her gaze to his. "I'll go with you to Almack's, Kevan."
He slid her a wicked grin. "Of course, you will."
She opened her mouth to complain, certain he'd manipulated her, but he refused her even the hint of an utterance by kissing her quiet. And long before he raised his head, she couldn't recall just what objection she'd been going to voice.
Alyssa stepped into Almack's. Her arm linked with Kevan's, she felt grateful for his unwavering support. Her knees threatened to buckle any moment, and her heart thundered so loudly she was sure that everyone in the crushed assembly rooms could hear it.
At least if they shunned her, she looked her best for it. According to Kevan, the flowing white gown threaded with silver gave her an ethereal look that he found hauntingly beautiful. Between that comment and the warm desire in his eyes, she'd nearly swooned.
That truth brought a smile to her lips. She, Alyssa Cameron Buchannan, who had swooned but once in her life, had merely to receive that look from her husband to become faint.
Lord, how the man affected her. He looked magnificent in black knee breeches and a dress coat with long tails that defined his broad shoulders. Strong, dark, and powerful. Breathtaking. His white neck cloth sported a brilliant diamond pin, but it was no more beautiful than the sparkling emeralds he'd gifted her with earlier this evening. She resisted the urge to touch the stones at her neck, on her earlobes, and at her wrist.
"Ready?" Kevan asked, his voice a sweet caress.
The urge to remind him of her affection just once more—before the fall—overwhelmed her. She touched his arm with her free hand. "Kevan, darling, I do love you."
"I love you, too, Lady Buchannan." He squeezed her hand, and she felt her confidence soar. His voice dropped to a whisper between them. "You are a countess, milady. You are polite society. Remember that." He smiled, and the left side of his mouth crooked up. Her heart skipped, then thudded.
Guarding the staircase, Mr. Willis stepped toward them, then ushered them forward to the landing of the grand stairs.
"My Lord Earl and Countess Buchannan," he announced in a clear, strong voice.
The ballroom fell silent. Alyssa stifled a groan. Kevan took her arm and, stiffening her spine, she began the long descent.
At the foot of the stairs stood the Prince Regent, looking up at them. Her heart stopped, her stomach sank to her knees. He would order her to leave. Remove her from polite society. Perhaps—perhaps he'd even banish her from England. "Kevan . . ."
"Smile, love," he whispered. "Everything is fine."
Stepping from the stairs, Alyssa curtsied. When she rose up, the Prince took her hand.
"My dear Lady Buchannan, I did so hope you'd attend this evening."
Casting a worried glance at Kevan, Alyssa responded. "Thank you, Your Royal Highness."
"May I call you Alyssa?"
"If it pleases you."
"I have heard of your metamorphosis, Alyssa. I am touched by your beauty and equally by your devotion to your lord."
Sure her cheeks would ignite and flame at any moment, Alyssa fought to find her voice. "You are most kind, Your Highness."
"Prinny," he said. "It would please me. I find I am quite awed by you, dear lady. Though ever appreciative of members of your gender, being awestruck is not a position I find myself in often." He turned to Kevan and lowered his voice so only the three of them could hear. "And I openly admit my envy of you, sir. To be held in such deep regard by one's wife is a treasure far more precious than any other." His voice dropped even lower. "And who better than I would know?"
Alyssa smiled. The prince's discord with his wife was legend. They not only didn't suit, they despised each other.
Kevan responded with his usual diplomacy. "My wife is my treasure, sir, though I share your dilemma. At times, I, too, am awed by her."
The Prince Regent and Kevan exchanged a knowing look, then the prince said, "But it is a discomfort you are more than grateful to endure."
"Privileged to endure," Kevan amended. "And humbled."
"Tell me, dear lady," the prince said. "Loving your husband as you do, have you any love left for your country?"
"Why, of course, sir." Alyssa couldn't suppress a mischievous streak that chose this awful time to present itself. "Looking through eyes that love, one cannot not help but see beauty in all things."
Certain that he'd been insulted, the prince's jaw gaped open. Alyssa let out a little laugh. "Though I have always loved England, my regard for her is even greater now."
"Do you know what I think?" the prince asked her.
"I wouldn't presume—"
"I think you've deliberately teased your prince."
"Though I spoke the truth, I confess I did."
"I also think, Kevan, that we should be glad this dear lady of yours is not opposed to our crown. She'd either love or tease us out of it."
"Now it is you who tease," she told him.
He cast her a shrewd look. "Only a little, my dear." He brushed Alyssa's hand against his lips. "Do enjoy your evening."
"I believe I shall now, sir."
The prince took two steps and stopped. Looking back over his shoulder, he asked, "Does it subside, Kevan?"
Kevan shook his head. "I'm afraid not, Your Highness. It is a lifelong affliction, I fear."
The prince let out a wistful sigh, then walked on.
"Kevan?" Alyssa asked. "What did he mean?"
"Your charm, my dear. I fear I'd better watch my step. Our prince is quite taken with you."
Alyssa smiled up at him. "You have no cause for concern, milord. My heart is yours for all time."
ALYSSA TURNED on her side and brushed back the crop of silver curls that had fallen to her eyes. "Kevan, it was amazing, was it not?"
Kevan scrunched his pillow and turned toward her, his hand draping her bare stomach. Her eyes still danced with excitement. "What, love?"
"Tonight. The reaction of the ton. I was certain that even your being an earl wouldn't stop them from cutting me direct."
Kevan let his hand drift up over her breasts to her creamy throat, then on to her cheek. She scooted across the bed and snuggled closer to him. Did she know how much that telling action pleased him? "I told you they would be envious. And they are."
"But even the women were gracious."
"How could they resist such romance?"
Alyssa smiled. His heart flipped in his chest.
"Kevan?"
"Mmm?"
"There's still something I've yet to do to make our love complete."
"What, my dear?" More complete? Could life get any better than this?
Alyssa took a deep breath and spoke her heart. "I want to make love to you. I've a need to share with you all I feel in my heart." She held his somber gaze, though it was the most difficult thing she'd done in her life. "You've not bedded me since the incident. Is it that you don't want to?"
"Oh, God, Alyssa, no." He held his arms open. "Come."
Alyssa met his embrace with an abandon that flared her desire to fever-pitch in an instant. All of the pent-up longing, the need for him she'd borne for months, the fear that he no longer wanted her physically, melted and drained away. With little whimpering cries, she adored his body, telling him of her love.
He drank from her lips, feasted on her body, then buried her head against his thundering chest. His fingers caught in her hair, immersed themselves, and massaged her scalp. "I need you. So much that the ache to hold you has nearly driven me mad. I didn't think you were ready to forgive me. You've been through so much—no small part of which was my own doing. Do you hear my heart, love? It speaks clearly of my wants."
"I hear it." She looked up at him, her eyes misty. "I am so happy. It's almost a dream. You've given me so much, and I—I—"
Fingering his crystal amulet, she fell silent. "Dear God. Your—your eyes . . ."
She looked deep into them, captured, mesmerized by all that she saw. Flecks of gray. Wisdom. Purpose. Authority.
Memories of another place, another time, washed through her in a great flood. In a hospital bed—alone and dying. A dark tunnel. Light. A crystal platform. A huge bird and barbaric savages. A silver-streaked cave and a bed of fur. Scotland. Her beloved Scotland and a battle of wills—then loving. Elder. "Oh, God . . . Oh, God . . ." Tears streamed down her face. "Prophet!"
He captured her in his embrace, buried his face in her hair, and squeezed her to his length. "Angel."
Twenty-nine
"PROPHET," Alyssa muttered against his neck, "let go of me!"
"No," he refused, keeping her pressed to his chest. "I've a need to hold you."
"And I've a need to wring your blasted neck."
He reared back, his voice boomed. "You dare to threaten me?"
She glared at him until he loosened his grip, then scooted to the edge of the bed. "Where's that damn gun?"
"Teaching you to shoot might have been a mistake." Smiling, Prophet grabbed her arm and tugged her back. With a swoosh of breath, she fell against him. "But wringing my neck doesn't require a gun, Angel. Unless . . ." He gave her an inquisitive look. "Have you decided to shoot me instead?"
She glared harder. "Don't you dare start with those literal deductions of yours. I'll not have it."
"You were about to make love to me," he reminded her. "To share with me all you feel in your heart."
The blasted man. Taunting her. At a time like this. "You kidnapped me," she accused. "I should do both. Wring your neck and shoot you."
"Ah, but I rescued you too," he said. "Did you forget that?"
Grudgingly, she admitted that he had. His fingertips swirled on her bare back. She stifled a groan. Why did he have to touch her now? His fingertips inched around her sides and up her arms, and she silently begged him not to touch her breasts. They were already anticipating his attention, tingling, growing full. She squeezed her eyes closed, trying to hold onto her anger. "You had Meg spy on me. Did you forget that?"
"To protect you," he whispered, his warm breath fanning her temple. "Angel, look at me."
"No," she said, keeping her eyes shut. His fingers cupped her tingling flesh, his thumb swirled around her nipple, his nail softly scraping. Her breath caught. "Well, flip," she complained, losing the battle to her body.
"You are not being whimsical, are you?"
Alyssa opened one eye to peek at him, and frowned. His eyes were hot, molten silver. "No, I'm not being whimsical. If I wanted you to flip, I'd flip you. Chow Ling taught me how."
He laughed at her. She grunted her displeasure at that. Concentrating was becoming so difficult. "Did you have to make my father a murderer?"
Kneading her flesh, he traced the hollow beneath her breast with his fingertips. His voice grew husky. "I did not make your father anything. He is not a murderer, Angel. He is an accomplice because he did not attempt to prevent Hedwig's murder, though I doubt he could have. But for his crime he's been transported, not executed. The Prince Regent saw to that."
Alyssa smiled, her brows rising and falling in a telling way. "A charming rogue, our prince of pleasure."
Prophet frowned. "A scapegrace who'd sell his royal soul for a woman like you."
"His soul?" Alyssa guffawed. "Oh, Prophet, you are afflicted."
He slid his big hand around her ribs to span her back, then let it drift down her spine to her buttocks. Was he jealous of the prince? She stroked Prophet's bare chest, rested her cheek against his shoulder. "Maybe I won't shoot you after all."
He reared and slid her a look that melted her bones. "Thank you for your consideration. Perhaps I am afflicted. I know exactly how the prince feels."
Something in Prophet's tone frightened her. Alyssa sat up, her hip at his side. "You mean about selling his soul, don't you?" She didn't wait for an answer; she didn't need one. "What have you done, Prophet? Have you sold your soul for me?"
"No," he whispered, rolling onto his side. His fingers laced with hers and rested on her thigh.
"But you've risked it," she suggested, innately certain he had done exactly that. She sensed it. Just as she'd sensed his signet ring, his crystal amulet, held significance. Fear tasted bitter on her tongue. "Kevan—"
"Prophet, love," he corrected her. "Cease your frowning."
He'd not answer her questions. She looked at his amulet, then at the sweet curve of his lips. "Should I kiss you, or shoot you?" Oh, she wanted to kiss him so much. A memory tugging at her had her adding, "And don't you dare say it's of no consequence. God, I hate it when you say that."
He smiled. "I prefer the kiss. And I've been patient long enough. Come love me, Angel. I've a need to hold you."
She leaned over him, half-draping his chest. "Do you love me? I know Kevan loves me but, when you're Prophet, do you?"
"I do," he said softly.
Pleasure rippled to waves inside her. She stacked her hands on his chest and looked up at him. "Why?"
He cupped her face in his hands, rubbed circles in the little hollows of her cheeks with his thumbs. "You are my destiny, Angel."
The heat in his eyes had the muscles contracting low in her belly. "And are you my destiny?"
His chest rumbled against her ribs. "I cannot answer that."
"Can't or won't?" she asked, stiffening against him. "I know how you are about that 'a guide must lead, not divulge' business."
"I'm pleased you recall my words," he said, not answering her question.
She worried her lip with her teeth. "Do you, um . . ." She couldn't do it, she decided. She could not ask the man his opinion.
"Angel, there are no barriers between us here. You must be honest with your husband."
"Well pity, Prophet. I guess I'm a wee bit confused. All the levels are mixing together on me. I married Kevan—twice, actually—but I've not married you."
"We are one in the same man. You are my wife."
"I am?" She gave him a wary look. "Are you sure?"
"Positive," he answered in a tone that had her hackles rearing.
"Fine," she said, letting him see her annoyance.
"Fine," he repeated, looking mildly amused.
"Well?" She thrust up her chin.
He arched a brow. "Well?"
The blasted man. He was going to make her ask. She drew in a deep breath and blew it out slowly. The urge to shoot him had returned with force. "Well, do you want my love or not?"
He laughed at her. "Want it? Nay, wife. I don't want your love. I demand it."
"Afflicted." She rolled her gaze heavenward. "You can't demand love, Prophet." As she nodded negatively, her chin rubbed back and forth on his chest. Then she lowered her forehead, and muttered into his skin. "I tried to tell you not to swim underwater so long. I warned you that your brain would get damp. That was wrong, of course, but—"
"Of course," he agreed. "A damp brain is—"
"Don't get too cocky. You certainly sound oxygen-deprived. Demanding love. How utterly ridiculous."
"It is not ridiculous. I'm your husband. It's my right to demand your love, and I do. You know that it's a wife's duty to love her husband, Angel. And you did boast to me that you always do your duty."
He was teasing her! Alyssa felt stunned. Prophet never teased. Kevan, yes. But not Prophet. She sought his eyes for confirmation and found it. Her heart soared. "I did say that, didn't I?"
"You did."
Alyssa smiled down at him. "I do believe that love is what I feel for you, Prophet. In Scotland, too, I suspected as much." Feeling mischievous, she nursed her lips with her tongue. "But how does one know for certain? What are the symptoms of this affliction?"
"Were you a man," he warned her, "I would take that remark as an insult and demand repayment."
"You once thought me a man," she said, her voice husky. "Remember?"
He nodded and nipped her shoulder with his teeth. "I remember. My little warrior in Scotland. What a hellion you were. You fought well."
He didn't sound displeased with thinking her a hellion, he sounded amused. "I did fight ably. Duncan trained me well."
"I'm glad you asked me to marry you then."
Her pleasure faded and heat scorched her face. "I didn't."
"You did," he insisted. "But I forgive your faulty memory."
"Oh, all right. So I did. I must have been out of mind."
"On occasion," he said, agreeing with her.
"Prophet," she warned.
He slid her a wicked smile.
"It's most unkind of you to remind me that I had to ask you to marry me. You're no gentleman, milord."
He shrugged. "I know."
She gave him a good frown. "Actually, you're a pain in—"
"Actually," he interrupted, his eyes hot, heavy-lidded with desire, "I'm in pain. Unbearable pain." With his tongue, he trailed a path up her neck to the tiny soft shell of her ear and lifted her on top of him. "Come, Angel. Be loving to your husband. My arms wait."
Far from disgruntled by his arrogance, Alyssa melted into Prophet's embrace, gave herself totally to his kiss. Kevan she cared for as much as she cared for herself. But Prophet, oh, there was something irresistible about Prophet that drove her beyond caring about herself. He riled her temper, robbed her of the ability to think, and twisted her into an emotional being that tossed logic out with the trash and focused only on feeling. He nibbled at her lips, sent her spiraling off to that magical place only he could take her, and she imagined his smile. Dear God, his smile made her boneless, made her feel as though the sun had burst its warmth inside her and melted her into a hot, steaming pool of liquid love.
"I can't wait, Angel," he whispered, harsh and grating, from between his teeth. "It's been too long."
"I don't want you to."
He took her swiftly, thoroughly, completely. Their passion raged, wild and abandoned, and quickly fired. And lying replete, deeply satisfied and content in her husband's arms, Alyssa drifted to sleep.
Prophet remained awake, waiting, unwillingly to forfeit a scant moment of his time with Angel. When she recognized him in this level, he knew that two of the original three glimpses of the future seen in his contemporary level vision had come to pass. In Scotland, when the back wall had been scaled by the Raiders and Innes's men had dropped into the lower bailey from the trees, Alyssa had accused Innes. Kevan had ordered her to return to her women's work. She'd gone, but not before she'd glared down at him from the back of her white mare, the Buchannan plaid draping on her shoulder. Here in England, Kevan had kidnapped her from the church he'd seen in his vision. She'd worn the eighteenth century wedding gown and had been about to marry the English lord she did not love.
Only one vision remained unfulfilled. Alyssa, sitting in her sterile office, absorbed by her computer and refusing to marry him. And if she'd failed, it too would come to pass. If she'd succeeded in her discoveries, that history would be altered. Their love, and his soul, would be safe.
Prophet shuddered at the uncertainty of their future and looked at his wife, sleeping curled to his side. Her silver-tipped lashes shadowed her cheeks, and a tide of tenderness flowed through him. Had she learned, made all of her discoveries? Had she become universal, capable of loving? Or would she again refuse to marry him?
The Elder summoned.
PROPHET UNTANGLED his limbs from Alyssa's, eased from the bed, then stepped into his adjoining chamber. His right hand crossing his chest, his head inclined, he greeted the Elder.
"Prophet."
The Elder's left eye was fully lit, but his shoulders sagged. He looked weary, worn, and bent. Prophet frowned. "Your grace, what troubles you? Each time I see you, your health seems to have further deteriorated."
"It is of no consequence," the Elder said in his gravelly voice. "Your woman has succeeded in this level."
"She has." Prophet smiled.
"The Council is pleased with her progression."
"And surprised, I imagine."
The Elder nodded. "Pleasantly, though." His expression grew grave, etching deep lines in his forehead. "You must proceed to the last level without delay. Time grows short, Prophet. Very short."
Warning signals fired like shots in Prophet's mind, setting off tiny explosions of fear that rocked his body. Stiffening against them, he lifted his chin, squared his shoulders. "My woman has conquered pride. What must she discover in this final level?"
The Elder looked weaker, more weary. "I am instructed by the Council not to disclose what will next follow. But know this: your courage and strength and that of your woman—even your love for her—will be sorely tested. Of all the learning levels, the coming one is most critical."
Gooseflesh raised up on Prophet's arms. "Why?"
"It is the consummation, the culmination of your efforts. Your woman must prove that she's become universal, that she has acquired the ability to love. Your soul is in danger, Prophet. Extreme danger."
Fear knotted in Kevan's stomach. He met the Elder's gaze.
"Have faith in your humble servants, your grace. My woman has met every challenge, succeeded in every test. She will not fail me now. Our—"
His voice weak, a thready reflection of sound, the Elder interrupted. "Seek strength in your destiny, Prophet. Remember the leaves. They must change." Before Prophet's eyes, the Elder grew weaker still. "The season . . . is come."
The Elder faded, and the silvery mist vaporized.
Prophet returned to Angel. His heart lay like a stone in his chest. Beside her in bed, he pulled her warm, sleep-soft body into his arms. She smelled of roses, and he inhaled greedily. She sniffled, and his heart wrenched. Squeezing his eyes closed, he held her tighter. "Love?"
"We—we're leaving again, aren't we?" She whispered into his neck.
The pain in her voice formed a lump in his throat. "Yes, darling. It's time."
She looked up at him, tears clinging to her lashes. "Why can't we stay here? I want to go to the theater with you. Garrick is dead, but Kean lives. He's supposed to shine as Richard the Third. Please, darling. Give me two more weeks."
She sat up and pressed her hands against his chest. Moonlight set her tear-streaked cheeks to glistening. "I want us to see Vauxhall Gardens, to share the "dark walk" that lovers stroll. We'll feast on a supper-box, and watch the fireworks from under the stars. And afterward, I'll feed you plump cherries, and . . . and . . ." She strangled a sob. "And I'll hold you." Her body shuddered hard. "Oh, God, Prophet. Don't leave me again."
Tears burned his eyes and he clutched her to him. He needed these things as much as she did, if not more. She didn't know of the coming danger, of the risks they would soon face. His voice grew ragged. "If we could, where else would we go?"
Her cheek against his chest, she lay quiet for a long minute. "Astley's. We'd watch the ponies race."
"Ours would win, of course," he said.
"Of course." He felt her smile, her lips brush against his throat. "And you'd give me a victory kiss like you did at the lake when I learned to float."
"I would." His own lips curved at that. "Where else?"
"We would go home," she said, her voice cracking, "to Woodwind—just once more. We'd swim in the lake, and make love under the big fir where you sat to watch me practice my strokes."
"I've often imagined making love with you there," he said, pressing his lips to her temple.
"So have I," she confessed. "Oh, Prophet, I—I—"
Her voice broke, and his heart shattered. She asked him for so little. Two weeks! But time was the one thing he could not give her. The Elder had been explicit. The season had come.
He softened his tone and rubbed reassuring circles on her back. "You felt this same reluctance to leave Scotland, Angel. But you found happiness here."
"I know, but—"
"We must go, love. We have no choice."
She looked up at him, her anguish in her eyes. "I love you, Prophet. Damn it, I don't want to be separated from you again."
Didn't she understand that he didn't want to leave her? That leaving her brought more pain to his chest than he had suffered in dying?
She didn't, he realized. She couldn't. She had no memory of Kevan Buchannan in the contemporary level. She had become his mistress then, but not his wife. She'd been incapable of loving, therefore, incapable of knowing love's pain.
And if she hadn't mastered her trials, she would never again be his to love. She'd be lost to him forever. He tightened his arms around her, not a whimper of protest crawling up his throat. She could not fail. She could not fail!
"Kevan, can't you talk to the Elder? Can't you make him—"
"No, my love," he said firmly. "I can't."
"But—"
He pressed his lips to her temple in a kiss rife with tenderness. "I can't."
"Something feels . . . different this time. It frightens me."
His heart thudded, then stopped. He dared not to ask what. He dared not. "I'll be with you."
"But I won't know you." She buried her face in his neck, her fingertips in his sides. "Dear God, I can't stand it. I can't."
He kissed her forehead. "You must. And so must I."
"But you won't know me!" she cried.
He closed his eyes, summoned a courage he didn't feel. "Not at first."
Words seemed to rush from her. Angry and bitter. "How many more times, Prophet? How many more times must I find you only to lose you again?"
Fear churned in his stomach. If she failed to prove her success, they would never be together again. He couldn't speak.
"Prophet?"
He heard her worry, but his own had grown too great to conceal. Through anguished eyes, he looked at her. "This will be your last level, Angel."
"And then?"
He watched her swallow, saw her emerald eyes cloud. "I don't know," he confessed.
"You don't know? What do you mean, you don't know? What kind of answer is that, for pity's sake? You're a prophet—my guide. You love me, damn it. You're supposed to know—"
A lone tear sliding down his cheek stunned her silent. She touched it, and whimpered. "Dear God. This next level is of consequence."
"Yes."
His fear stole into Alyssa like a living, breathing thing. She drew in a ragged breath. "I'm frightened."
He met her gaze and held it. "I'm frightened, too." He rolled until she lay beneath him, chest to chest, thigh to thigh. "Love me, Angel. Love me like this is the only time in your life you'll have the chance to love me."
The despondency in his voice, the grim lines of dread creasing his face, the stark and desolate panic in his eyes, startled her. Alyssa went numb. "Is that possible?" she whispered. "Could this be our last time together?"
Prophet flinched and looked away.
"You can't shatter my dreams," she told him. "I won't let you. We're going to grow old together, to have children, and a home." She touched his cheek. "Look at me. Damn you, look into my eyes. See the truth there."
He pivoted his neck and met her gaze. She looked like his little warrior. Serious. Determined.
"You once told me that to succeed in these trials, I must believe in love. That in it weakness becomes strength."
He studied her face, the shape of her nose, her eyes, her chin. "And you told me that love was a mystery to you."
"I've found my faith now," she assured him. "I believe in you, and in your abilities. I trust you." She paused rubbing his arm, and squeezed. "Don't let your belief in me waver. Not now. We've come so far. We'll do what we must. We have to. I—I need you now."
He hugged her to him and rocked. "I won't abuse your need. I swear it. Oh, God, Angel, I love you so much."
"I know." She gave him a smile that seemed to sear him. "Until we next meet, I will miss you, darling."
"You won't remember me," he reminded her.
She sensed the hurt that knowledge brought him. "I love you. My heart will remember that." She kissed him, lovingly, longingly. "I promise you, my heart will never forget that."
Thirty
Contemporary New Orleans
"THIS COULD be it, Margaret." Alyssa swiveled in her office chair and banged her knee on an open desk drawer. She hissed in air, cupped her injured anatomy, and groaned. "God, that hurts."
Sympathetic as a stone, Margaret lifted the phone receiver and, holding it by the cord, let it dangle near Alyssa. "If you keep the boy waiting all day, this'll be it, all right."
Alyssa reprimanded her secretary with a grunted harumph. "Duncan Foster is hardly a boy."
The old woman pursed her lips, pitting wrinkles at the sides of her mouth. "If he's younger than God, to me, he's a boy. Besides, you've never seen him. You don't know squat about him."
"Not true," Alyssa disagreed. "I've talked to him, and I know that anyone who's accomplished all he has with Paragon Oil in the past three years, couldn't be a boy. He's probably older than God with a gray beard and horns to match his God-awful disposition."
Margaret wiggled the receiver. "You gonna talk to him, or daydream about the boy's assets? Without that contract, we got spit."
"Since when is an awful disposition an asset?"
Margaret shrugged. "You're doing fine, aren't you?"
Alyssa narrowed her eyes at the wispy woman with more wrinkles than face. "Why do I tolerate you?"
"Because I'm good." Margaret headed to the office door. "And because I keep your butt out of slings."
"True, but you should be less obnoxious. I am your boss, you know."
Margaret's bony shoulder raised up. "It's your aura. You need a man to sweeten your soul. Nothing like a good roll in the hay with a hot-blooded man to—"
"Margaret," Alyssa warned.
"I know. I know. You're not shopping." Margaret shot her a disgusted look. "Maybe in your next life you'll have more sense."
"Would you stop with that stuff. I've heard all about karma and soulmates and me finding a man to—to . . ." Heat flooded her face. Annoyed by it and at Margaret for putting it there, Alyssa blurted, "More than I care to hear."
"Window-shopping is free." Margaret pointed to the phone in Alyssa's hand. "Don't forget that's in your hand for a reason. Without that contract, we got spit."
Muttering under her breath, Alyssa turned back to her desk and banged her knee on the same open drawer. She gritted her teeth, slammed the blasted thing and, punching the button on her phone, forced a smile into her voice. Nodding her approval, Margaret stepped into her outer office, leaving the door cracked open so she wouldn't miss a thing. Alyssa's smile became genuine. "Good morning, Mr. Foster."
"I've reviewed your proposal, Cameron," he said in clipped, terse tones. "Paragon's interested."
Alyssa's heart started pounding. "Good. I'm sure the computer system and programming we've outlined will save Paragon—"
"I've seen your savings projections," he interrupted. "The system is good, but the programming lacks finesse. On-line's is better."
The man was as offensive as a line-tapping hacker. Her heart plummeted. Was he giving her the contract or not?
"Paragon wants the two of you to team up."
Work with her chief rival? Was the man out of his mind? Oh, how she'd love to hang up on him. To tell him what to do with his rude manner and his blasted Paragon Oil. But she couldn't. She was a newcomer in the field, and, though she'd done well in the past year, she didn't have the luxury of alienating anyone. Not that she ever would. Old offenses never die. They lurk in the shadows until the worse possible moment, then pounce out to bite you. "What exactly do you have in mind?"
"I've set up time on the island for you and Buchannan to brainstorm. You leave Friday. Monday afternoon, we'll meet and see what you've got."
Kevan Buchannan. Again. Programming genius. The man who set the industry standards. Her chief rival. Alyssa swallowed her frustration. She couldn't afford it. Half a contract was better than no contract. Besides, she brightened, one never knew what one could learn from a genius. "Has Mr. Buchannan agreed?"
"Monday. My office at three o'clock. And, Cameron, I expect results. Paragon has high standards. If you want this contract with Buchannan, exceed 'em."
Alyssa bit back a sharp retort. Foster's position was clear. Buchannan's contract was secure. Her own was not. "I intend to, Mr. Foster."
"Hold on."
Before she could blink, the line went dead. Then an equally abrasive female introduced herself as Mrs. Stone and began doling out instructions. Jotting them down, Alyssa bet Foster's secretary didn't give him the flack that Margaret gave her. But then Mrs. Stone probably didn't have Margaret's assets, either.
The woman finished, and Alyssa repeated: "Biloxi Marina, slip twenty-seven, Friday at six." She tapped her pen against her desk blotter. "Why Mississippi?"
"I'm sure I don't know, Ms. Cameron. Perhaps Mr. Foster can answer your inquiry. Shall I connect you?"
Set firmly in her place, Alyssa frowned. "No, it's not important. Just curious."
"Mr. Foster does not promote curiosity."
Nor, obviously, did he promote freedom of thought. Alyssa rolled her eyes back in her head. "Thanks."
She hung up and slumped in her chair. So much for her long-awaited R and R weekend. Being stuck in Paragon's luxurious island condo with a wimpy genius, she was more apt to have two plus days of tension and stress.
She chided herself for her unkind thoughts about Buchannan. She'd never even met the man, for pity's sake. Still, geniuses were notoriously weird—and wimpy.
ALYSSA STRUGGLED down the wooden-slatted boat dock. Squeezing the handle of her leather suitcase, she hiked it up so it'd stop banging her calf. Now it banged her thigh. "I don't need this," she muttered, spitting wind-whipped hair away from her mouth. "I really don't need this."
Leaving New Orleans during peak traffic in the middle of a hellacious storm, finding a place to park away from the beach and the salt spray that'd rust her new Volvo in a heartbeat, hobbling down an endless dock in high heels, lugging two tons of suitcases and trying to dodge the cracks between the wooden boards was not a good way to start the weekend. Tension and stress. Already twinges of pain in her temples signaled an imminent, whopper headache.
She looked down at the white numbers painted on the weathered dock. Forty-three. She grimaced. Nine hundred miles to go. Overhead, dense gray clouds churned in an angry sky and the blustery wind smelled of rain and sea. Foster sure had picked a lousy day for a boat ride.
"Miss Cameron?"
She turned to see who had called her. Wearing sun-washed jeans and a white shirt, the man approached. He couldn't be Buchannan. Far from a wimpy genius, this man was magnificent—firm, muscular, a heavy-boned giant. His black hair curled low on his neck, his wide mouth set in a tentative smile.
He drew closer. She met his eyes and heard whispered secrets of purpose, wisdom. In her mind, images snapped like a camera shutter. A signet ring on his left hand. A strip of leather coiling his neck, holding some glowing object. Him astride a powerful black stallion, then walking through a winding tunnel, wearing a minuscule fur loincloth. And flowers. Why did she see flowers?
Her heart thundered. The flowers he held were for her! How she knew this, she'd no idea, but she was certain. Emotional sensations bombarded her: wary disbelief, then fear; annoyance, then tolerance; acceptance, then respect; trust, and then love.
Love? The case slipped from her hand and thudded on the dock. Dear God—love!
Standing beside her, his smile faded. Worry etched the tender skin around his eyes. "Miss Cameron?"
A light rain misted her face. He seemed to want reassurance. Thinking to give it to him, she stepped to retrieve her case. Her heel dropped into the space between two smooth slats. Her ankle turned, and she lost her balance. "Oh—Oh my—"
He caught her in his strong arms. They tightened around her like heated bands, just under her ribs. She looked up at his face. For some reason, she couldn't hold his gaze. She looked at his throat. Bare. No glowing object. Her pounding heart eased.
"Are you all right?" he asked.
All right? No, she wasn't all right. Who was this man? Why had she just run an emotional gauntlet for him? "I'm—I'm fine." She straightened up. Pain sliced through her ankle, and she winced.
"You're hurt." He squatted down, his fingertips testing her ankle.
She looked down at the crown of his head, not at all certain he hadn't brushed his hand across her heart. She lifted her hand to touch the masculine curls at his nape, dampened by a sheen of misty rain.
He rotated her foot. "Does that hurt?"
Pain shot up her leg. She jerked her hand back. "I—I think I've sprained it."
"You did." He looked up at her, his eyes sober, his tone resigned. "It's swelling already."
"Wearing heels wasn't one of my brighter ideas. I'm a bit of a klutz," she confided. God, he had soul-searing eyes. They invited her confidence. "Go ahead. Say it."
"Why?" He shot her a puzzled look. "You just did."
His confusion tugged at her heartstrings, made her more nervous. Why? "Who are you?"
"Kevan Buchannan," he said, standing up. "I'd better carry you. The boat's still a bit further."
She should refuse. But the rain was progressing from a fine mist to a heavy sprinkle and the lure of his arms tempted her beyond good sense. She superimposed cool logic, too, forcing it past the maelstrom of emotion she was experiencing. If he held her, she might see more images, might understand her intense reaction to him. She nodded her agreement.
He lifted her. The feel of his arms under her thighs and wrapping her shoulders sent her heart racing. He'd held her before—and she'd liked it.
"Hold on," he instructed.
She chided herself to gain control of her emotions, then curled her arms around his neck and forced her voice calm. "I've heard a lot of good things about you, Mr. Buchannan, but not of your chivalry."
He grinned and lifted her higher. "Remiss in your homework, Ms. Cameron?"
"Mmm. Evidently." She looked down and saw his ring—the ring she'd envisioned in such vivid detail. Her heart slammed against her ribs. The gold mounting, the silver sword, and the emerald insignia—all exactly the same!
The tiny hairs at the back of her neck stood up. No. No, she told herself. She'd no doubt seen the insignia while researching him and On-line.
"Loosen up a bit, Ms. Cameron. You can trust me. I won't drop you."
Realizing she had his neck in a death grip, she eased her hold. Heat surged to her face. "I'm sorry, Mr. Buchannan. I—I didn't . . ."
He smiled. "This is going to be a long weekend if we Mister and Ms. our way through it. Please, call me Kevan."
"All right." She couldn't help but notice that carrying her and her two tons of luggage didn't seem much of a task for him. Lord, he had sexy shoulders. And a long stride.
"I probably should dump you. You're becoming stiff competition."
His grin belied his words, and a smile curled Alyssa's lip. "Thank you, I think."
"I intended a compliment," he said. "You've earned it. Paragon's insisting on a joint venture is proof."
He wasn't a man prone to flattery, or false praise. Hearing respect in his voice, she felt a rush of pleasure. "I'm satisfied with my progress." Moist from the rain, a dark curl clung to his ear. Her fingertips itched to feel its texture. Could it be as soft as it looked? She inched her fingertips closer. "It's an uphill struggle."
"Always. How did your cat react to being deserted for the weekend?"
"I see you've done your homework. But your bio on me is outdated. Tabby died."
"I'm sorry." He looked as though he meant it. "What else important has changed?"
How perceptive he was to know that Tabby wasn't just a cat. "Not much."
"Have you married?"
What an odd question for him to ask. Ah, she decided. The condo. "No, there's no jealous husband to come pounding on the door tonight." He grew more loose-limbed, as though he were relieved. "Is there a jealous wife?"
"No. Too busy to spend much time socializing."
"Me, too." His easy admission surprised her, but not as much as her own. "Dating is hard work." Silky slick. She rubbed the curl between her thumb and forefinger. Her heart beat faster. Soft, and silky slick.
He stopped walking. Her gaze darted to his and her breath caught. He didn't speak, just looked at her, his expression odd and unsettling. Thunderstruck. A raindrop glistened on his upper lip. The urge to lick it off, to taste him, swelled in her like rippling water disturbed by a plunked stone.
What was she doing, for pity's sake? This man was her rival. Her business rival. Had the rain soaking her skin soaked her brain as well? "Why have you stopped?"
Kevan stood stock still. It took a moment for her words to sink in, and another longer one for him to get the vision of her in his bed, naked, making love with him, out of his mind. He cleared his throat. "We're here."
"Oh." Her cheeks tinted a warm pink.
Still feeling dazed, he boarded the boat and dropped Alyssa's case on the deck. "Will you be all right there?" He nodded toward the passenger seat.
"Yes."
Could she feel his heart hammering against her side? Reluctant to let go of her and not understanding why, he lowered her into the passenger's seat, then stepped away. The woman was beautiful, but he'd met beautiful women and he'd never fantasized any of them so vividly. He'd never seen himself making love—or felt himself making love—as he had when he'd looked at Alyssa. In his mind, she had accepted him into her body. And he had accepted her into his heart.
"The storm's getting closer," she whispered.
Kevan looked up. Thunderheads billowed in the southern skyline. "Yes, it is. The harbor master says it'll blow over in no time, though."
"I don't know, Kevan. I've got this feeling—"
"The boat's safe," he assured her, hoping to ease her frowning. "I checked the log. It's weathered more storms than you'd care to hear about."
"Is the boat yours?" she asked, stowing her purse in a compartment beside the seat.
"Foster's. But I am experienced."
Alyssa rubbed her temples. The twinges in her head were growing worse. Stress, Doctor Samuels had said. Working too hard. Enjoying too little. She was tense. Who in the field could find a way around Kevan Buchannan's shadow without getting tense? Or without working their socks off?
Well, flip. Maybe she was stressed. She began the relaxation exercises Dr. Samuels had given her. Why didn't they seem to help? He'd know more, once the results of the CAT scan came back and she proved him wrong. A brain tumor. At her age? What a ridiculous diagnosis.
"If you'd feel more comfortable, we can wait out the storm," Kevan said, looking concerned again.
"No, let's go for it. I need a hot bath and a bed to feel more comfortable," she confessed. "It's been one of those weeks."
WATER SPLASHED over the side of the boat. Alyssa dipped her head to shield her eyes from the salty spray. She clutched the dashboard in a death grip and peeked at Kevan.
"Check your life jacket." He yelled over the roar of the boat's engine and a loud clap of thunder. "Cinch it down!"
Hard, squally rain pelting her, Alyssa nodded. Rough seas had her stomach queasy, her head throbbing. The pleasant hour's ride had digressed to a treacherous nightmare. "What about you?" she shouted back.
"Too small." His voice carried on the roaring wind.
The sky grew darker. Night quickly approached. Could Kevan see? Could bigger boats in the Gulf of Mexico see their running lights?
She turned to ask him, but his expression stopped her. Intense concentration etched his face. Gripping the steering wheel had the muscles cording in his forearms. The churning seas grew more violent by the second, and Kevan looked as though every ounce of energy in his massive body was engaged in keeping them afloat.
The heavy rain continued to beat down on them. Darkness fell. How long had they been out here? She couldn't see her watch. Three hours? she guessed. Four? It seemed like forever. Where the Hell was Paragon's island anyway? An hour, his secretary had said. One bloody hour.
Lightning streaked the black sky for a brief second, illuminating vicious white caps on the choppy swells. Her head bowed, her gaze fixed at a point off her right shoulder, she caught a flashing glimpse of trees. "Buchannan!" she screamed, pointing to them. "Go there!"
He nodded and began turning the boat. The waves pounded the hull, jarring her teeth, her spine. God, just get us to land. Just don't let us drown.
A second flash of lightning lit. Over the sea of foam, she glimpsed the trees bending to the whipping wind. They looked so far away. So small . . .
Waves crashed steadily over the bow of the boat. Then a new sound caught Alyssa's attention. A train howled in her ears. The urge to cover them, to stop the shrill, painful noise, warred with her knowledge that she had to hold on. The sound grew louder, louder, louder.
Trains . . . Oh, God. Oh, God. A water spout! She whipped around in her seat. "Buchannan!"
A shadowy flying object clipped the side of his head. He slumped forward over the steering wheel. The boat sped up, turned parallel to the waves. More and more water swamped the hull. And Buchannan did not move.
Fighting the gravitational pull that pinned her against the seat, Alyssa struggled to get to him. She slung her sodden shoes from her feet and grabbed the windshield with both hands, pitting herself against the wind, the salty spray stinging her eyes, the flood of water filling the boat. She dodged flying debris, inched her way closer, closer. "Buchannan. Buchannan, answer me."
He still didn't move.
The howling train sound, shrill and piercing, threatened to shatter her eardrums. Fear, gripping her, intensified.
The engine sputtered and died. Kevan rolled back, his head lolling against the side of the boat. Blood streamed down his face.
Flinging wet clumps of hair back from her eyes, Alyssa braced her legs, forced herself to wait until the boat rolled. When it did, she lunged for him. But the boat didn't dip as it had been doing—it raised high, spun, then slammed down with a powerful splat on the churning water's surface. Her ankle smacked against the seat support. Pain shot up her leg. Before she could think, both she and Kevan were in the water.
Choking, she spit the saltwater from her mouth and screamed. "Buchannan! Buchannan, where are you?" Treading water, she twisted in a circle, searching the darkness. "Buchannan!"
Then she saw a dim shape—his white shirt. Dear God, he was face down—and—and sinking!
Her instincts told her to dive. She ripped off her life jacket and followed him, slicing through the choppy surface and spreading her arms wide.
Her lungs clamored for air, her chest drew tight, painfully tight, but she couldn't go up. Somehow, she knew this was her only chance to find him. Blinded by the darkness, she felt for him, widened her search, praying he was near. Her chest throbbed, screamed for oxygen. She felt disoriented, and gave herself a good mental shake. Something hard rammed into her back. Stifling a gasp, she whipped around. His shoulder!
Relief washed through her. She felt her way to his head, twisted him, and started kicking her way to the surface, her ankle protesting the pressure. Seconds later, she realized that, unconscious, Kevan would breathe—and drown.
Sliding her fingers across his cheek to his lips, she pinched them together. Then, wrapping her free arm around his neck, she clipped his nostrils closed.
Her lungs screaming for air, her leg muscles cramping, her ankle throbbing, she broke the surface. Gasping in great gulps of air, she raised Kevan's head.
Battling the waves, trying to tread water and keep both their heads above water, she felt his throat until she reached his pulse point. It was faint, but steady. A wave splashed her face, burned her eyes. She cursed Duncan Foster, his lousy boat, his inadequate equipment—and Buchannan, for not coming to. Her hand on his chest, she felt him draw in a shallow breath, then rolled him onto his back.
Looking around, she stopped dead in the water. Where was the boat? She moved slowly, waiting for lightning. Which way were the trees? Turning in a circle in the water, she dragged Kevan with her, and saw an ominous, dim shadow.
Straining to see, combating the angry waves, trying to roll with the swells, to keep Kevan's head above water, she worked her way toward the dim lump, convinced that it had to be the boat. What else could it be?
Her muscles burned like fire, protesting her every stroke. "Just a little further, Buchannan. Just three more feet."
A wave crashed into her face. She sputtered. Lightning flashed. Dead ahead, a fin protruded from the water. Her heart lurched. Terrified, stunned, she couldn't move, couldn't tear her gaze from that fin. Something bumped against her back. She screamed and jerked. The boat! Her hand slipped and she lost her grip on Buchannan. Grabbing at him, she caught his sleeve and pulled him back.
Quickly, she slid down the hull and worked her way to the back ladder, dragging Kevan, watching for the fin, cursing the darkness. Every tidbit she'd ever heard about sharks tormented her. Noise attracts them. They circle their prey. They feed at night. Blood increases their appetite. She thought of Buchannan's injury, knowing that his blood was seeping into the water, calling the shark.
She felt her way past the outboard motor and grabbed the ladder, twisting until she hooked her leg over the rung. How in the name of God was she supposed to get Kevan into the boat? Twice her size. Twice her weight. And where in bloody Hell was that shark?
"Damn this darkness! Damn it!" she cursed, struggling with Buchannan's limp weight, turning him in the water to catch him under his arms. Though aided by the buoyancy of the water, the first two rungs were difficult. "One more," she told him. "Please, God. Just one more."
Again and again, she tried, but she couldn't lift Buchannan high enough to drag him over the edge of the hull. The blasted motor was in the way. Motion, she decided. Motion would give her momentum.
Forward and back, she rocked, faster and faster, until Kevan's legs arced close to his chest. She grabbed his pant leg and jerked. Oh God, she was falling forward—into the water! Screaming her frustration and fear, she flung her body backward.
Her body slammed onto the boat-deck with a bone jarring thunk. A scant second later, Kevan fell across her, his shoulder smashing into her chest. Her breath swooshed out.
Sprawling on the deck, winded, she instructed herself to breathe, and reached for his shoulder. Panting, she called out to him. "Buchannan."
Gasping, she inched around until she freed her chest, then felt her way to his face. "Damn the night. Damn the dark, damn night." She stopped her fingers on the side of his face where she'd seen the blood. They grew warm and sticky. "Buchannan?"
He didn't answer.
She scooted out from under him and turned him over onto his back. "Buchannan?" Hovering over him, she dipped her forehead to his chest, tears burning her eyes. "Buchannan, for God's sake, please."
But Kevan uttered not a sound.
Thirty-one
THE SUN BEAT down on her back. Before fully aware or awake, Alyssa felt the throb at her temples, the grit of wet sand under her cheek. She cracked open one eye. The glaring white boat deck blinded her, and she quickly squeezed her eyes shut. Boat deck? Buchannan!
She sat up, searched the shambled deck, but found no Buchannan. Above the top of the hull she saw trees. Relief and fear mingled inside her. She rose to her feet, sore all over, and called out. "Buchannan?"
How had they gotten to land? Was he all right? The boat had bottomed out on the sandy shore. Where were the hotels? The cottages? And where in bloody Hell was Kevan Buchannan?
Squinting against the strong sun, she looked up then down the stretch of sandy white beach. Desolate. Isolated. No sign of life. A sinking feeling seized her. Had he come to, stumbled around, and fallen overboard? "Buchannan!" she screamed.
She fought panic. He couldn't have fallen overboard. He couldn't have. He'd been unconscious.
She'd ridden out the storm before falling asleep. If he'd come to, he'd more than likely been groggy, disoriented. He could have stumbled . . .
"Shut up," she told herself. "He—he didn't."
Tears came anyway. At first just a steady flow coursed down her cheeks. But anger at him leaving her, at her fear of being left, warred with an inconsolable sense of loss, and her silent tears grew to deep, racking sobs. "Damn you, Duncan Foster. Damn you and Paragon Oil. Damn your blasted contract, and your bloody boat, and . . . and . . ." She hugged herself with her arms. "Oh God, Buchannan. I knew you. I—I knew you!"
She bowed her head and cried.
Water splashed. Alyssa looked up.
"A bit lazy this morning, aren't you?"
"Buchannan," she whispered breathlessly. "Buchannan." She half-jumped, half-fell, out of the boat. Pain shot through her ankle. Wincing, she hobbled through the shallow water to him, flung herself against his chest, and locked her arms around his waist. "Oh, Buchannan. Oh, God. You're okay." She smiled up at him. "You're okay."
Kevan's heart contracted, and he circled his arms around her. "I'm fine, Alyssa."
A fresh stream of tears washed her cheeks. "I—I thought—"
She couldn't say the words, but she didn't have to say them. He gently brushed her cheeks with his thumbs. "I explored the island," he said in a soft voice. "Don't you remember me telling you?"
She squeezed him closer. "No."
He held her head to his chest and stroked her hair. "Come to think of it, you did just grunt."
Lifting her in his arms, he held her for a long moment, then met her gaze. "Your ankle," he said. "You shouldn't be walking on it."
"If you think my ankle's bad, you should be inside my head."
He frowned. "Pain?"
"Major pain."
"Happen often?" he asked, walking toward the shade of the palm trees.
Resting her head against his shoulder, she closed her eyes and murmured. "Mmm-hmm. Dr. Samuels says it's stress."
"Well," Kevan stepped ashore, "this time you've got cause. I hope that harbor master's life insurance is paid up."
"I hope Foster's is, the jerk."
Kevan sat down under a palm tree and held her on his lap. "Lie down and I'll massage your head."
She scooted until her neck rested on his thigh, then closed her eyes. "Where are we?"
"Later. Right now, relax."
Looking down at her face, at the sweep of silver-tipped lashes shadowing her cheeks, Kevan had to remind himself to breathe. Slightly parted, her lips looked soft and kissable. He drew tiny circles with his thumbs, starting in the center of her forehead and rippling wider until he reached her temples. Then he added his fingertips at the base of her skull, working up, then down, her neck.
"Mmm, that feels so good."
He agreed. Her throaty murmur had his heart thudding. What would kissing her be like? Would she be anything like he'd experienced in his fantasy? Aggressive? Gentle? Intoxicating? He studied the shape of her jaw, the slope of her neck, the curve of her shoulder exposed through the gap in her blue silk blouse. Creamy smooth, soft-looking, touchable. The kind of skin that once touched, a man would feel forever.
"There aren't any hotels here, are there?"
He sighed. "Afraid not."
"No phones, or anything else?"
"Afraid not."
She opened her left eye and squinted up at him. "This island is little and deserted, isn't it?"
"Afraid so."
"Will the boat start?"
He swallowed hard, stalling to gauge her reaction.
"Well," she asked. "Aren't you going to say 'afraid not'?"
"The gas line is hacked."
"Hacked?"
"Can't this wait?" he asked. Her forehead had wrinkled with worry or pain. He didn't know which, but either wouldn't help her headache easing.
"I want to know."
"The line looks hacked," he said. "The prop looks chewed."
She scooted so that his hands worked her shoulders. "Probably the shark."
"The shark?" His hands stilled. "What shark?"
"Rub, Buchannan. I ache like the dead. The shark that almost had us for a snack."
"What?" he roared.
She jumped. "Shh!"
"What the Hell are you talking about?" he shouted in a whisper.
She whispered back. "During the water spout, we were thrown overboard. Jaws came calling."
"Water spout? Overboard? Jaws?" His blood drained to his feet. "How'd we get back into the boat?"
"I fell us back in and bailed out what water I could until you came around. Well, groaned, anyway."
He cast her a wary look. "How do you fell someone anywhere?"
"Calm down, Buchannan. We made it, didn't we?" She grimaced and put his hand on her forehead. "I couldn't lift you." She squinted up at him. "You're a big man. In case you haven't noticed, I'm petite."
"Tiny," he corrected her.
"Whatever." She stifled the urge to yell at him. She hated being called tiny. Hated it. Next to him, King Kong would look tiny. But she was not. She was petite.
"What about the shark?"
"I'm getting to that," she snapped, not bothering to hide her annoyance. "I saw it. But I couldn't lift you over the hull. I decided if I could get your body moving, maybe momentum would carry us. It did. We were falling back into the water. So—"
"So you fell backward into the boat and pulled me with you," he finished. "Good God, Alyssa. I could've crushed you."
"You did."
"Is anything broken?"
"My spirit's a little bruised and my disposition is shot to hell, but other than that, I'm fine. Move a little to the left, would you? God, my head's splitting. Oh, yes. Right there."
Kevan moved his thumb to her temple. The woman was incredible. She risked her life to save him. Fought rough seas in a storm, a water spout, outran a shark, and fell him into a boat. "Good God."
His stomach knotted. Hers growled. "Hungry?" he asked.
"Famished. I could use some dry clothes, too."
"There aren't any," he advised her. "The restraining straps broke. Both of our cases are gone."
She let out a resigned sigh. "Why doesn't that surprise me?"
"We've got food, though. And fresh water. We'll be fine. There's a little lagoon—"
"For pity's sake, Buchannan. How can you sound so calm? We're stranded. We've got no engine, no oars, no radio—"
"You're going to make your head start up again," he warned.
She frowned up at him. "Shut up and rub, Buchannan. Would you just rub?"
He ran his fingertips along her scalp and smiled down at her. "Things could be worse, you know."
She flashed him a glare. "Rub."
HE WAS ENOUGH to vex a saint. Alyssa glared down at Kevan. Sitting in the sand, his back braced against the tall palm, the blasted man looked completely content. "Look, Buchannan, I'm fed up with your attitude. I should've let you drown."
He cocked his head and looked up at her. "So why didn't you?"
Why couldn't he get irrational—just once? He wasn't bloody human. "I couldn't afford to. After we kill Duncan Foster—"
"Slowly, of course," he interjected.
"Of course," she agreed. "And after we demolish Paragon Oil, I need you to get that bloody contract with them. Joint venture, remember?"
"I'm not apt to forget. That's all I've heard out of you for the past three weeks. But tell me, if we kill Foster and demolish his company, why do we want the contract?"
"We don't," she said. "We just want to be the ones to tell him to stuff it."
"Tell who?"
"Are you paying attention, Buchannan? Foster. We want to tell Foster to stick his contract in his ear."
He shook his head. "You're driving me crazy, woman. If Foster's dead, how are we going to tell him to shove his contract?"
"Oh, for pity's sake, Buchannan. I don't mean to really kill him. I just want to blister the man's ears for a week or two."
"Oh. And you want me to blister him, too."
"Don't you want to blister him?"
"Not exactly." He popped the tab on one of their last two cans of Coke. "I didn't set the rules, Alyssa. Working with my chief rival wasn't my idea of a good time, either."
"I know that." Sunlight glinted on his signet ring. Alyssa felt the same odd tug on her heartstrings she experienced every time she saw it—which, considering their circumstance, had been darned near every waking moment.
He held out the can. She took it, sipped, then passed it back. "Don't you ever get annoyed? Frustrated?"
"Sure. I'm human."
Buchannan, human? Alyssa measured him head to toe. She supposed so. He certainly looked human. The sun had tanned his skin golden to his waist, and the dark springy hair on his chest definitely incited human temptation. What he looked, she amended, was gorgeous. She lowered her gaze to the sand-caked cuffs of his jeans. "I'd be a lot more comfortable with you if you'd throw a fit once in awhile. It's not natural to take being stranded for three weeks in stride."
He smiled. She wanted to rip it off his face.
"Being upset isn't going to start the engine. Only a gas line will do that."
"Shut up."
He grinned up at her. "That's the way to win friends and influence people."
She glared down at him, her hands on her hips. "Aren't you miserable?"
"Actually, I'm quite comfortable," he said, his fingertip circling the top of the Coke can. "The sun feels good, the weather's warm, and the sounds of the surf are soothing."
"You've baked your brain. The sun is hot. Not warm; hot. The weather is sultry—sultry, Buchannan. Maybe even sweltering. And the surf brings sand to my mind. In my ears, between my teeth, and up my—"
"Enough, Alyssa," he said firmly. "I won't let you spoil this for me."
"Spoil—what?" She swatted at a sand fly that had the poor judgment to light on her calf.
He frowned. "If you weren't stranded here with me, where would you be?"
"Bombing Paragon Oil—and Duncan Foster."
His frown deepened and he added a sigh.
"Working," she confessed.
"Right. So would I. We'd both be stuck in our offices."
He had a point. She'd needed a vacation for a long time. Weren't her headaches proof of that? They'd started out as an occasional nuisance and worked their way up to a daily hindrance. But a trip that included a Hilton, a shower—body lotion—was more what she'd had in mind.
She sat down beside Kevan and nudged him with her shoulder. "Share the tree."
"Why? There's a whole island of them."
She grinned at him. "I want this one."
"You want me to kill any bugs that happen to creep along."
He didn't sound condemning, just cocky. "True," she admitted, patting his thigh. "See, I do think you have value."
He propped the can of soda in the sand and shifted over. "I could be even more valuable to you."
The suggestive tone in his voice set her heart to thumping. "Oh?"
"If we agreed to merge."
"Merge?" She swallowed hard. As propositions went, his was definitely weak. Was he out of practice? She took a sideward glance at him. Not bloody likely. That he'd been on the receiving end of propositions until now was more apt the truth.
"We'd both have more time."
What was he talking about? "More time?"
"Sure." He swiped at his chin with his bare shoulder, then looked at her. "And less stress. You might even ditch the headaches."
Well, sex was supposed to be a stress-reliever, but surely he felt more . . . Lord, the man was gorgeous. His dark lashes, penetrating eyes. And he had great hands. Wonderful hands.
"We'd also merge our talents." He lifted the can, took a long draw, then swallowed.
Her heart crashed into her stomach. "Our talents?"
"Yeah."
He looked awfully pleased with himself. "Um, I can only speak for myself in this, but, well, I'm not . . . the thing of it is . . ." The knot in her throat continued to grow till she couldn't speak.
"Alyssa, can't you see the benefits of merging our businesses?"
She gave him a sickly smile. "Our businesses."
He frowned. "You're beginning to sound like a mimicking parrot. Are you too hot? Been in the sun too long?"
"Yeah," she muttered. Why did she feel so deflated? "Entirely too long."
"You're no slouch, Alyssa. You've come a long way in a year."
"In your shadow," she said, adjusting to the topic shift. "What's it like being a genius? Does everything just come to you?"
He laughed, but there was no humor in it. "No, nothing just comes to me."
Their shoulders brushed, and she looked from the sun-spangled surf to him. He stared intently at her, and a honeyed warmth stole through her limbs.
Come on, Buchannan, she silently urged him. Do it. Would you just do it?
Kevan looked away. Alyssa swallowed a groan, deciding the blasted man was never going to kiss her.
"I see benefits in a merger, Alyssa."
The honeyed warmth flowed through her veins. She curled her toes in the sand. "Why?"
He pursed his lips. "It's cost-effective. Half the overhead, half the staff. One office instead of two."
"One less rival," she suggested, blaming the sun for her prickly temper when she knew darned good and well the sun had nothing to do with the heat torturing her. Kevan caused it.
"For you, too," he countered. "Are you afraid to work with me, one-on-one?"
She guffawed. "Not bloody likely."
"Well," he said. "Think about it."
"All right. I will." She looked out on the horizon. Water, water, and more water. "Do you think they're looking for us?"
"Who knows?" He shrugged. "Even if they are, where are they looking?"
"Damned storm." Alyssa jumped up, began pacing in the sand.
Kevan shot her a lazy warning. "Don't get yourself worked up. Your head—"
She rounded on him. "Don't you get it, Buchannan? We don't know where we are. They don't know where to search for us. And we don't know—"
"Who's getting the Paragon contract," he finished. "I know. You've mentioned it all, okay?"
The niggling headache she'd been fighting all afternoon burst into a full-fledge throb at her left temple. Groaning, she sank down beside him and closed her eyes.
"You've done it again, haven't you?"
She didn't bother denying it. "Yes."
"Alyssa, you can't let things get to you like this," he said. "Come here."
He patted his lap and Alyssa lowered her head onto his thigh. His method of massaging had become almost routine. He cupped her head with his hands, his fingers at the base of her skull and his strong thumbs at the center of her forehead, rubbing tiny circles that fanned out until he reached her temples.
Soon, the pressure eased and he began massaging her skull. He rested her head in his palm and worked his way down her neck.
"Better?"
Totally relaxed, Alyssa murmured, "Mmm."
"I never thanked you for saving my life." His voice, always soothing, sounded deeper, huskier than usual.
"No, you didn't." She wet her lips with her tongue. "Have I thanked you for the massages?"
"No, you haven't."
The pain in her head had stopped. God, he was good at this. She looked up at him. "Guess that makes us even."
He dipped his head closer until the tips of their noses rubbed. "Guess so."
Her heart thundered. She'd waited weeks for him to kiss her. He slept beside her. They ate the provisions that hadn't washed overboard from the same fork. He'd even shared his toothbrush. But not once had he tried to kiss her. Oh, he'd watched her. Lord, had he watched her. The heat in his eyes could melt snow, and make her sizzle. The sexual tension was as thick as fog between them. So why in bloody Hell didn't he kiss her? Maybe she should just kiss him.
She probably looked like a dreg. No brush, no makeup, his shirt that fit her like it was made by Omar the tent maker. "Kevan?"
"Yes?" He reared back.
She looked past his shoulder and saw her clothes draping a spiny bush further down the beach. Were they dry yet?
His fingertips brushed across her lips. "Sand," he explained. "You look worried."
"It's nothing." She closed her eyes. Saw the spots the sun made on her lids. Was there a name for that? Kevan's hands worked their magic. His thighs, too, brought snatches of Heaven to her on this God-awful island. Strong and hard under her neck, they had her imagination running rampant. Sweat trickled down between her breasts. Had June always been so sweltering hot? Stupid question, she told herself. It was him. God, he smelled good. She bit back an unsatisfied groan.
His hand cupped her head and lifted. His thigh muscles flexed. Alyssa's eyes sprang open just as his foot stomped the sand.
"Bug?" Her heart started pounding.
"I got it."
"Are you sure?"
His look was tender. "I'm sure."
If she didn't do something, she would surely attack the man right here. Or worse, ask him to attack her. Batting her lashes, she let out a fluttering breath and mimicked Perilous Pearle just after her rescue from Dastardly Dan and his buzzing saw blade. "My hero."
He smiled, but his eyes burned with more than mischief. "When a hero performs a chivalrous act, his lady usually rewards him."
Her heart took off like a rocket "Is that a fact?"
"It is."
"But I'm not your lady," she reminded him.
"I think you are, Alyssa."
She swallowed hard. "So what are you suggesting?"
Crinkling at their corners, his eyes teased. "Whatever."
"Whatever?" she repeated. He nodded, and her own mischievous streak flared. She'd rattle his cage, or bust. "Okay, Buchannan. I'll marry you. That's your reward." She made herself sound and look disgruntled. "I guess after all this, I owe it to you."
"Marry me?" He was back to looking thunderstruck. And to looking at her like she'd slipped over the edge.
"Sure." Somehow she managed to keep her expression bland. Meryl Streep couldn't have given a better performance.
"You don't think that's kind of permanent?"
She shrugged. "You said whatever."
"I did, but I had something a little less—"
"Restrictive?" she suggested. Lord, he had tensed up. She thought she just might be insulted. She'd make any man a fine wife. Not that she wanted to marry him, she hastily assured herself.
"No." He rubbed his neck. "Not exactly."
The man looked pale enough to faint. Keeping her expression bland proved almost impossible. She didn't know whether to fan him or to knock the stuffing out of him with her fist. "Well?"
"More immediate," he said, finally. "I had something more immediate in mind."
He smiled that smile and her heart melted. "Like what?" Oh, he was adorable. A king-size hunk of confusion.
"Like—" Kevan looked down the beach and smiled. "Like, I think you'd better retrieve your clothes."
Alyssa looked at the spiny bush. Barren? Her gaze darted and she saw her clothes tumble down the beach to the water. "Well, flip."
She scrambled to her feet and chased her clothes into the surf. Muttering curses, she retrieved her wayward laundry and tromped back ashore. Kevan's laughter floated to her on the warm breeze. "Blasted man," she muttered.
"I'm going to the lagoon," she called out to him, then turned for the path.
He lumbered to his feet and followed her down to the sparkling pool. "Sun's going down. You'd better let my shirt dry, or you'll catch cold."
Bent at the water's edge, she rinsed her blouse and gritted her teeth. "I don't have anything else to wear."
"I know."
Seething, she frowned at him over her shoulder. "If you were half a gentleman, you'd give me your pants."
"I would?"
The man had pure devilment in his eyes. "You would. And you'd take yourself off somewhere until my clothes dried, too."
"I gave you my shirt, woman. I'd say that makes me half a gentleman. I'm spending my days bare-chested for you. I can't say I'm anxious to spend them bare-assed, as well. Rays can be wicked on delicate anatomy."
"As thick-skinned as you are? I doubt it." Alyssa fought a smile lurking just behind her lips. "You should be thanking me for taking your shirt, Buchannan."
"Why?"
"You're getting a great tan."
"Forget it, woman," he insisted, folding his arms across his chest. "You're not sweet-talking me out of my pants."
She shot him a solid frown. "Selfish lout."
"True," he agreed, walking toward the path to the beach. "I'm taking myself off, Alyssa," he called back to her. "But it's a small island. If you want privacy, stay put. And you'd better get that saltwater off your skin before you shrivel up like a raisin."
She stood up, her hands at her hips. "Anything else, majesty?"
"Yes." He stopped and looked back at her, his gaze slowly roving her wet length. A slow grin spread over his face. "In stomping bugs, use the ball of your foot."
Alyssa wanted to smack him. Instead she gave him a haughty look.
"I'd do it now, if I were you."
"Do what?" She prayed for patience. The man's brain was definitely sun-baked, scrambled.
His expression remained bland. "Lift your left foot and stomp."
Realizing what he was telling her, Alyssa looked down. The biggest spider she'd ever seen crawled over her toes. Seemingly frozen, she let out a blood-curdling scream.
Seconds after Alyssa's face bleached white, Kevan stomped the spider. She shuddered, but seemed unable to move. He wrapped his arms around her. She stood stiff-spined, trembling. "Alyssa, honey, it's all right."
"Damn you." she bellowed, pounding her fists against his chest. "Damn you. You knew. You knew, and still you—" A deep sob escaped her and she slumped against his chest. "Oh God, Kevan. It crawled on me!"
Why hadn't he realized? Why hadn't he known that her fear of spiders was so strong? Why had he assumed she had the usual distaste for them that most women had? "It's over" he crooned, holding her hard against his chest. He brushed her hair back from her face, lifted her chin to look down into her eyes.
He'd seen terror before. Men being lowered into the rat pit in the desert. Those tortured men had worn the same look then that Alyssa wore now. His heart shattered, his stomach soured. He thought he might be sick.
"Oh God, I'm sorry." He buried her face in his chest, held her while she cried. His own eyes grew moist, his throat tight. Tenderness welled inside him. He wanted to pull her inside him, wanted to protect her from hurt and fear and pain. He wanted to be loving.
But he couldn't. Not completely. He had no right. They were competitors, not lovers. Yet, she had proposed . . .
Thirty-two
FOUR WEEKS. Kevan tossed a log on the fire. Could their situation grow more grim?
The barren island provided water, but no food. Soon their dwindling supply would be depleted. He'd augmented their diet with fish from the gulf, but a piece of string and a rusty hook found on the boat, did not a decent fishing rod make.
During their stint on the island, one thing had been proven. He now knew for certain what he'd suspected on the boat dock in Biloxi: he was in love with Alyssa Cameron. But whether he should thank his lucky stars, or curse the devil for it, he didn't know.
Flames licked at the logs, and sure the fire would burn through the night, he crossed the sandy beach to the palm-rush bed he and Alyssa had made.
Lying there, she smiled up at him. His heart skipped a full beat. Firelight dancing on her silver hair enhanced her features that required no enhancing. His shirt hiked up high on her thigh, revealing a long, healthy length of sun-kissed leg. Beautiful. Gutsy. Desirable.
The physical attraction between them had escalated to fever pitch. Rife with desire, he'd tried not noticing her. But he couldn't seem to help himself. She was a complex woman. Courageous in saving his life, yet terrified by a spider. He saw everything. And he loved everything he saw. The way she moved, the low and husky sound of her voice, the way she snuggled to him at night, always touching.
His emotional responses to her were unbidden, unprecedented, and unwanted. He hadn't intended to, but he'd fallen in love with Alyssa Cameron. And somehow he had to teach her to love him back. She desired him. A blind man would know that. And desire was a start. But it wasn't enough. Turning her desire into love couldn't be that difficult, could it? Of course, it couldn't. Not for him. He was a genius. If a way could be figured, by God, he'd figure it. And if one couldn't be figured, he'd figure it anyway.
He lowered himself at her side and rolled to face her. The rushes crunched under his weight.
"Kevan?" She moved closer, rested her head on his upper arm.
He circled her shoulder and drew her to him. "Yes."
"Tell me about this merger idea of yours."
He looked down at her upturned face. God, her eyes were beautiful. Emeralds. Sparkling emeralds that haunted and winked at him at the same time. Mesmerized, he said, "Marriage," then quickly added, "of our businesses. Equal control and responsibility."
Trapped between them, her hand flattened against his chest, making his muscles quiver. "Why?" she asked. "I mean, I'm up and coming, but you're established. What benefit is there for you?"
Being close to you, he thought. Having time to figure out how to make you love me. He swirled circles on her back and inhaled the balmy night breeze. "You're good, Alyssa. So am I. Together we'll be great."
She arched a dubious brow at him. "Equal. In every way?"
His chin grazed his collarbone. "With one stipulation."
She frowned and tried to move away. "I knew it."
He held her to him. "You haven't heard me out, and already you're complaining?"
"You forget I know you, Kevan Buchannan. A woman can't spend four weeks with a man and not know how his mind works. You're a shrewd businessman, a sharp analyst, and a bloody genius. With all of that going for you, you don't need me, and, unless you did, you wouldn't merge."
He did need her. He didn't want to, but he did need her. "I want you."
"Why? What good—"
Kevan's lips twitched. "The truth is I'm backed against the wall."
Alyssa laughed. "The Kevan Buchannan—up against the wall. Who do you think you're kidding?"
He turned until he hovered over her, one arm on either side of her head. "This is no joke."
She met his eyes. "No, I can see it's not."
"Well?" His gaze settled on her lips and held.
"I think," she said in a husky voice, "I'd better study on this awhile."
"Okay." He didn't move. He wanted to turn back, to look away from the sweet arch of her lips, the tiny lines creasing her skin at the point her lip and cheek met. But he couldn't.
"Tell me your stipulation."
Her arms were pinned to her sides. He heard her grab a handful of leaves, heard them crunch. He lifted his hand slowly, fearing she'd bolt, and feathered her cheek with his fingertip. "I'd rather kiss you."
She drew in a sharp breath. "You would?"
"I would."
"Why haven't you?"
"We're rivals." She wasn't opposed then. He slid his hand to her temple, through her damp silky hair, and cupped the back of her skull.
"Not here," she countered, leveling him with the eyes of an angel, the voice of a temptress. "What harm can come from one little kiss?"
What harm, indeed? She had no idea what she did to him. Or she had every idea. She was quick, he decided. She knew. And she approved. Somber, he locked gazes with her. "I'm going to kiss you, Alyssa Cameron. And when I'm through, I'm going to kiss you again."
Her fingers inched up his chest, stroked the width of his shoulder, and settled on his bare throat. "When you do, Kevan Buchannan, I'm going to make love to you. And the way your body taunts mine, I'm not sure once will be enough."
His heart pounded like a jackhammer. "You're sure about this? We won't always be on this island, you know."
"God, I hope not." She smiled.
His heart melted, but he forced himself to think. He couldn't have regrets. Desire didn't grow to love under the weight of regrets. "What happens later, when we get back to the real world?"
"That depends. If we take this personal relationship any further, we can see what we think about that. But, Kevan, if we do, then there can be no merger. It's got to be either personal or strictly business between us."
"No."
"Yes," she countered. "We have to keep our business and private lives separate."
"No way."
Alyssa fought the flutters in her stomach. "Think about it. If we have a hot and torrid affair, and something happens, how well could we work together, then?"
He gripped her shoulders and squeezed. "Nothing will happen. I won't let it."
"Kevan," she whispered, cupping his jaw with her hands. "You might not be able to help it. Things happen."
"I want you."
Alyssa felt her resistance melting. He did want her. Evidence of that was blatant: the tension in his body, the determined look in his eyes, the stubborn set of his jaw. "Right now, you want me. But tell me. If we weren't stuck here together, would you give me a second glance on the street?"
"Yes, a second. And a third and fourth." On his side, he propped up on his elbow and cupped his head in his hand. "You don't understand. I'm not some stud that decides he wants a woman and just takes her."
She reared back. "You're picky about who you sleep with, mmm?"
"Yes, I am." He frowned and thunked his hand against his chest. "This body is my home. My soul lives here. My thoughts and dreams, my hopes and needs, live here. You're damned right, I'm picky about who I share it with."
She took his hand, placed it on her chest. "And my soul lives here. All that I am, all I want to be, is right here. I know me, Kevan. If I share all of me with you, and then lose you, I—I can't work beside you every day. We'd both be miserable."
He understood. And he loved her for it. What she didn't realize, it seemed, was that she'd just admitted how much she cared for him. But did she love him? Lust was fine on occasion. But not on this occasion. It was time to shake her up a bit. "I'm sorry, Alyssa, but I refuse to accept the marriage proposal of a woman I've never kissed."
"What?" Her mouth gaped.
"You proposed to me," he said. "Did you forget?" He rolled flat and pulled her on top of him, then brushed her hair swinging into his face back over her shoulder. "Don't bother trying to renege. I won't let you. Buchannans stick to their word, and if I marry you, I have to know you'll uphold the tradition."
With a groan, she pressed her forehead to his chest. "Why are you tormenting me?"
Her breath tickled his skin. He tilted her head back. Tears? Tears clung to her silver-tipped lashes, making spikes of them. "I don't mean to torment you. Marrying you was my stipulation to the business merger."
"It was?" She sounded incredulous.
He nodded, and for a long moment, she just looked at him, her emotions racing across her face.
"Never would I marry a man," she paused and grabbed a breath, "I haven't kissed."
He smiled. "We can remedy that, if it's your only objection."
Her eyes were slightly somber. "For now, it is."
His arms hung loosely around her neck, he lifted his hands to her head and brought her down to him.
"Kevan?" she whispered, her lips brushing his.
"I know, love. Personal relationship only—for now." Their lips met, gentle and tentative, exploring. He rubbed her cheek with his fingertips. Sweet. She tasted so sweet. Warm as the sun, soothing as the sea. She drank from him as if parched, as if he were a vessel that quenched, satisfied. He splayed his fingertips on her back, let them drift down her backbone to the sweet curve of her hips.
Her hands caught in his hair, her fingers sliding against his skull. He licked the slick white of her teeth, explored her mouth and found her tongue. And when they rubbed together, the sexiest whimper ever vibrated against his mouth.
She backed away to look down at him, fondling a bit of his hair between her fingers. "It's so soft, Kevan. I love your hair. It curls around my fingers and clings to me."
He sipped at her lips. Had she felt the explosion in her heart that he'd felt in his? "I want my second kiss." She wouldn't refuse. She looked as bemused as he felt.
Alyssa drew her knee up between his thighs. He hissed in a ragged breath, cursed the rough fabric of his jeans between them. Her eyes were serious, so serious his heart constricted. He'd known it would be like this between them. And, looking into her eyes, he realized she had known, too.
"Marry me, Kevan."
A jolt started in his stomach, shot up to his head, and streaked down to his toes. "Marry you?"
"Yes."
"You're serious about this. You're really proposing?"
"I am. Again—though I wasn't serious before. But I am now." She worried her lower lip with her teeth. "Look. You want me. I want you. You want my company." She flattened her hands on his chest, slid them to his shoulders and squeezed. "And I want your company."
She didn't want his business. She wanted him. And, God knew, he wanted her. But an odd glimmer in her eye kept him from accepting outright. She seemed nervous. "What aren't you telling me?"
Alyssa sucked in a deep breath. Grazing his hair-roughened chest, her breasts tingled. Would he shy away from her? The others had. Everyone who'd meant anything to her had run. She didn't, dear God, want to lose him. But she had to risk it. In fairness to him, she had no choice. She forced herself to look into his eyes. "When I saw you on that boat dock in Biloxi, I wasn't looking at a stranger."
"You weren't?"
"No." She bit her lip. How much should she confess? No more? A little more? God help her, all of it? "I knew you, Kevan."
He started to speak and she covered his lips with her fingertips. "Please. I know it sounds crazy. But let me finish." He nodded, and she continued. "When I saw you, I got these visions in my head—"
"Visions? What kind of visions?"
"Images of you," she replied, her head rocking on his arm. "You were you, but . . . different."
"You're not making sense."
"I know."
"You look sad. I didn't mean to offend you."
"You didn't. It's just—well, it's difficult to explain."
"Let's try again," he suggested. "What did you see?"
"Your signet ring. And I saw you riding a huge, black stallion."
"You saw my ring?"
She nodded. "That's not all. You were somewhere, I don't know, kind of dark and eerie. And you had on a fur loincloth."
"Alyssa, are you trying to tell me that you see images like this often? I sense you're afraid. Are you?"
"Oh God, Kevan. I'm more than afraid. I'm terrified."
"Why?"
She lowered her gaze to his chest. His voice sounded so soft, tempting her to confide in him. But she'd lost people before. People she'd thought cared about her. Would he be any different? "I see things, but not like this time," she said, hedging, yet staying within the bonds of truth. "I wasn't looking for you, for any man."
She watched his pulse hammer in his throat. "I don't understand what you're telling me."
Awfully close to tears, she looked up. He'd leave her, too. Just like all the others. But it was better if it happened now—before she'd grown too accustomed to him being in her life. That was a lie. She was already attached, addicted to him, and she knew it. But right now, she needed that lie. "I'm telling you that when I saw you on the dock, I felt love for a man who wasn't known to me but wasn't a stranger. I'm telling you that since then, I've found you annoying, aggravating, and a too-calm pain in the ass, but—"
"Thank God there's a but," he interjected.
"But," her voice grew tender, "I've also found that your afflictions make me love you more, Buchannan. Not less."
"You love me?"
He looked spectacularly stunned. Alyssa figured she looked just like she felt: scared to death. "Yes, I do. I love you, Kevan. And I want you to marry me."
Thirty-three
A KNOT THE SIZE of Texas lodged in Kevan's chest. He looked down at Alyssa, sprawled on her back in the prickly sharp palm rushes. Protected only by the thin fabric of his shirt, she looked content, comfortable. Firelight bathed her with a warm glow, flickered shadows in her eyes. And never had he seen a woman more beautiful, more serious, yet serene.
"Kevan?" she whispered.
Her husky voice flowed through him like warm red wine. He met her eyes, saw her desire and her trust. He saw her uncertainty, too. But soon that glimmer would fade. He would show Alyssa that while she'd fallen in love with a vision of a man, a real one had fallen in love with her.
Her fingers brushed against his bare throat. He swallowed and caught her fingertips in this mouth, gently raked them with his teeth.
She turned, half-draping his chest, her thighs tangling with his. "Are you going to marry me?"
Her wayward hand cupped his jaw, stroked down the center of his neck to his chest, then slid the blade of his collarbone to his shoulder. "I want you forever. Not just for tonight." She paused and drew in breath. Her heaving breasts had a button on her shirt poking into his ribs. The expression in her eyes went from serious to solemn. "If that's not what you want, don't take me, Kevan. Please."
"You say you love me, but I think you love the man in your visions—or you think you love him." He took her hand from his shoulder and placed it over his heart. "Do you feel that?"
She nodded, and he released her hand. She kept it there, pleasing him. He clasped her arms and drew her fully atop him, letting her feel the effect of his desire; his physical and emotional reaction to her. "I'm no vision, honey. I'm flesh and blood, body and soul. I don't want a woman in love with a vision in my arms. I want my woman—one who's in love with me—in them."
A tender smile hovered on her lips. "You're arrogant, Buchannan."
"I'm arrogant." He shrugged, and the fear of her rejecting him drained away.
"You are." She nibbled at the tip of his chin, then reared back. Her smile returned. "I know my own mind."
"You think you do," he countered, not doubting her sincerity, but her perception.
"I do," she insisted, tapping her fingers on his chest. "Are you afraid of me?"
Alyssa could hurt him. Devastate him. Damned right he was afraid of her. He laughed. "You're too little to incite fear."
"I'm just right and you know it." She slanted him a wicked smile. "Which is precisely why you're terrified."
She expected him to deny it. He could see that she did in her eyes. He returned her smile with a devilish one of his own and 'fessed up. "Terrified."
"I knew it."
He sighed and felt her rise with his expanding chest. His hands at her waist threaded around her back and tightened. "At least, terrified."
She looked at him with that solemn, trusting look that turned his mind to mush and made his heart as soft as peanut butter. "I'll protect you," she promised, nodding to emphasize that she meant what she said.
Love for her spread like warm fingers through his every pore. "I don't need your protection, honey. I do need your assurance that love is what you feel for me."
"I want you," she said.
"That's lust."
"I know you."
He slid his finger through her hair. "That's illusion."
"It's not. Blast, Kevan, I'm not an idiot. I know my own heart."
"You think you do."
"You're being difficult."
"I'm being cautious."
"Of me?" She sounded stunned.
"Of you—and of me."
A twinkle of understanding lit in her eyes. "It isn't me you're unsure of. It's yourself."
"No," he denied it, and it was true. It was her feelings he didn't trust. Not yet. Of his own, he was certain. He loved her.
"I don't believe you." She thrust out her chin.
"I know." He'd been going about this all wrong. The woman had muddled his mind. He'd tie their lives so close together, she'd never be able to loosen all the knots. And in the doing, he'd teach her not to think she loved him, but to really love him.
She rested her head on his shoulder. "Maybe I shouldn't marry you." When he didn't answer, she went on. "You're a lousy fisherman. Admittedly arrogant, irritating, and the most aggravatingly calm man I've ever known." She raised her head, propped her chin on her hands atop his chest. "Margaret would consider those traits assets, but I'm sure marriage to you would only double my stress."
"Probably." He turned his head to her neck and rubbed his lips against her skin. Warm and creamy, and her pulse stormed just beneath her skin. "Who's Margaret?"
"My secretary. A witch with a heart of gold." She dipped her chin, denying him access. "You aren't going to disagree with me about the stress?"
"No." He nuzzled and nipped at the hollow of her throat. "Marriage to me probably would double your stress. God knows, marriage to you would double mine."
"You're an awful man. I withdraw my proposal."
She looked and sounded totally vexed. He wanted to smile, to laugh, to hug her so hard he absorbed her. "You can't," he forced his tone serious. "I gave you my shirt."
"And refused me your pants."
"True, but I killed your spider."
"After it crawled on me."
Feeling her little shiver, he held her tighter. "I massage your head."
She glared at him. "You cause my headaches."
"I don't. You had them before."
"You cause them now," she insisted. "And why in bloody Hell do you flaunt your body all the time?"
He could sooner tame a tornado than follow her thoughts. "You've got my clothes. How can I not flaunt my body? You want me to wear leaves?"
"I've got your shirt. Not your clothes."
"I'm wearing my pants. What more do you want?"
She sounded confused, annoyed. "I want—I want—" She scrambled off him, stood up, and jerked at the buttons of his shirt. They popped off and sprinkled the sand.
"Alyssa, what's wrong with you?"
"You're what's wrong. You want your shirt. Here," she slung the offending article at him, "take it. And keep the bloody thing on."
The shirt landed on his chest then slid into the sand. Kevan looked up. Her breasts heaved with anger. She looked gorgeous—and ready to kill him. He wanted to laugh. Sexual frustration was stamped all over her. "Alyssa, come here."
"What for?" She looked down at him like he was a bug that'd crawled out from under a stone. An ugly bug.
"I'll give you what you want."
She arched a brow. "Oh, and what's that?"
"Me."
Her hands settled on her hips. "I don't want you." Naked as an infant, she strode down the beach.
What had he done? Feeling his own temper rise with his confusion, he went after her. "Alyssa."
She marched on, past the scraggly bush and onto the path to the lagoon. He jogged to catch up with her. She broke into a sprint.
"Alyssa, what just happened?" The woman's logic was a maze.
"Some genius. Just go away, Buchannan."
He caught her by the arm. She twisted and he backed off. She started running again. Damn it, what had gotten into her? "I didn't want my shirt back," he called out.
She paused and turned. "Stuff your shirt."
"Are you ticked because I wouldn't give you my pants?" He stopped, jerked the metal button from the fabric, the metal zipper down, stomped out of the jeans, and grabbed them up.
On the wide path to the lagoon, he caught her and pulled her to the grassy ground. Panting, he pinned her legs between his thighs. "I said, here are my pants."
She glared at him. "Stuff your pants, too. I don't know what in God's name I saw in you—"
Kevan kissed her quiet.
She writhed, trying to free herself from him, pounded her fists on his shoulders. He grabbed her arms and raised them above her head, then shifted until he covered her length. He used his body to persuade her, to entice her to give up her anger. "Welcome me," he breathed against her lips. "Please, Alyssa. I want you."
Her hands stilled and he released them. Before he could blink, her furious blows again pounded his shoulders.
"Do you know how hard it was to propose to you? Do you know how hard it was to say I love you? And look what you do," she cried, raining blows on his chest. "You're despicable."
He didn't stop her. He licked her lips with his tongue, stroked her arms with his hands.
She whimpered and murmured against his mouth. "I hate you, Buchannan."
He rubbed his lips to the corner of her mouth. "Welcome me, honey. You love me." He cupped her heavy breast in his hand, whispered all of the things he wanted to share with her.
A little gasp rushed from her throat. "Oh, I hate you." Her voice a mere thread, she lifted her body to mold to his.
Open-mouthed he kissed his way to the opposite corner of her mouth, her warm breath tingling his cheek. "You love me."
He caught her hard nipple between his finger and thumb and rolled it gently. A tortured moan crawled up her throat. She turned her head, offered him her creamy neck. "Oh, Kevan. Oh God, I hate you."
He taunted, teased, and tasted. Tracing the shell-curve of her ear with the tip of his tongue, the soft hollow behind her ear with the tip of his nose, then, raking her lobe with his teeth, he whispered, "You love me."
Inside, Alyssa cried. Spasms ripping through her, she flattened her fisted hands against his shoulders. What did he want? He wanted her. He didn't want her. Couldn't he decide? She loved him. By damn, she knew her heart.
"I want you, Alyssa," he murmured into the curve of her neck. "I really want you."
Oh, why did his skin have to feel so good? Why did her hands insist on smoothing a path over the muscles bunching in his upper arm? Why did he make her forget everything—everything except how wonderful it felt to be held by him? He stroked a lingering, languorous path down her center. She caught his hair in her hands, and whispered the lie. "I hate you."
"You love me." His lips covered hers, caressing, teasing, torturing and pleasing. His persuasive tongue forced her mouth open and invaded, sweeping her teeth, the soft ridges of the roof of her mouth, and finally—dear God, finally—her tongue. Tiny explosions rocked her body. Moaning her pleasure, she whimpered a protest.
She knew him. She knew the feel, the taste, the scent of him. His touch, the honeyed warmth surging from her center and spreading through her limbs, the powerful emotions filling her heart till it threatened to burst. All of these things, she knew. "Oh, Kevan." She circled his back with her arms and pulled him to her.
He kissed her deeply, lovingly, then raised his head and breathed against her temple. "By God, you do love me."
Rearing back, he looked down at her. She met his eyes, fearing he'd again belittle the value of her love by throwing it back to her. She lifted her chin. "Yes."
She watched him swallow, then again sought his eyes. Tenderness. Purpose. A gentle pleading shone in them. "I'm sorry I hurt you. Marry me, Alyssa."
She gave him a siren's smile. "Of course."
"Of course?" A warning shot went off inside his head. "That's why you withdrew your proposal."
"It is."
"I think," Kevan said with a mock frown, "I've been had."
Alyssa smiled up at him. "Not yet, darling. But soon."
Kevan laughed from deep in his chest. "You're a wicked woman, Alyssa Cameron."
"I'm a lady, Buchannan." She wiggled until his arousal fitted between her thighs.
His eyes darkened with possessive desire. He arched his back and entered her body. "You're my lady."
Warm and wanting, her yielding body accepted him. "Always," she promised. "And you're mine, Buchannan. Only mine."
"Always." He began the rhythmic ritual of man joining woman, the act of loving that comforts, commits, and communes bodies and souls. "Always."
"KEVAN?"
Kevan opened his eyes. His limbs felt lethargically heavy. Alyssa's smiling face greeted him, which made the leaves pricking into his back worth every stab.
"We'll get married as soon as we get home," she said, the pink tinges of dawn melting around her. "Then we'll merge our businesses, and you'll spend your days and nights with me. Agreed?"
She looked like a content kitten. Like with one more stroke, she'd purr. "Good morning," he said, just to annoy her. God she was beautiful, especially when her fire was up.
"And you needn't bother trying to hassle me today. You can't."
He feigned a frown, not at all surprised that she had him figured. "Why not?"
"Because you wonderful man," she paused to peck a chaste kiss to his chin, "I know the truth."
"Aha. And what truth is that?"
Cupping his face in her hands, she grew serious. "You love me, Buchannan. God help you, me—both of us—you love me every bit as much as I love you."
"You don't seem happy about it," he said, seeing no sense in denying what they both knew to be true.
"It's scary." She licked the lips he longed to taste. "What if—"
He pressed his fingertips against her mouth. She fell silent. "No what ifs, honey. Life's full of them. What matters is that I love you. I've never said that to another woman, Alyssa. I'll never say it to another woman."
"Don't make promises you might not be able to keep. Things happen. Nobody knows what the future holds."
"I promise." He looked her straight in the eye. "No matter what happens, I'll always love you."
She shuddered, and he had the feeling that somebody'd walked over his grave. "Alyssa? Look at me." She lifted her head, her eyes filled with worry. "What is it?" he asked.
"I never thought I'd love anyone. Not like this."
He gave her a tender smile. "Love's a reason to celebrate, honey, not to mourn."
She smiled. It didn't reach her eyes, but worry did.
"You're right." Her fingers slid down his bare throat. "Did you ever wear a strip of leather around your neck? One with something shiny—no, not shiny. With something glowing—hanging from it?"
He opened his eyes. "What?"
"A strip—"
"I heard you, love. I just don't—" Sensing the question was important to her, he answered. "No, I haven't."
"Oh."
That disclosure either worried her more, or disappointed her. "Why?"
She shrugged and stood up. "Just wondered."
Dressed in her skirt and torn blue blouse, she turned and looked out on the water. The light breeze had her white skirt tight against her legs and ruffled the kick pleat in back so it flapped in the wind. She was a beautiful woman. Tiny but strong, lissome—and tense. "Seeing more images?" he asked.
Her shoulders lifted. "A few."
He heard pain in her voice, and something that warned him not to push her. "Do you want to talk about them?"
"No." She paused a long moment, her back still to him. "No, I don't. But I know we have to."
She seemed panicky. He clenched his fists at his sides, fighting off a sense of dread stealing through him. "When did these visions start?"
She turned to face him. Her skin had paled, and her voice had become hesitant. "When I was seven and my father died. They happen often, Kevan, and they've frightened more people away from me than I care to remember."
He wanted to hold her, but he had the distinct feeling that she didn't need holding. She needed words. "I'm not most people. I love you."
She seemed to relax just a bit, not holding her back quite so straight. "I see things," she warned him.
"I know."
"No, Kevan. I mean, I see things. They appear. I—I—"
"People? Events? What?" he asked, forcing his voice bland though his inquisitive nature was titillated.
"One person—appears. The rest I just glimpse. Kind of like looking at a photo."
She wasn't crazy. She was dead serious—and scared. "Who appears?"
Alyssa grew rigid, scarcely daring to draw breath. So far, Kevan's reaction had been mild, curious. But, she reminded herself, the worst had not yet come. "He's called the Elder."
"Un huh. And what does this Elder do?"
She frowned at him. "Don't patronize me, Kevan." She rubbed her forehead, then lowered her hand to her side. "Sit down and let me explain. It's simple really, but you've got to keep an open mind, okay?"
Kevan lowered himself to the sand and leaned back against a palm trunk.
Alyssa sat in front of him, her legs bent at the knee. "When I was seven, my father drank himself to death. The night of his funeral, I went to bed, but I couldn't sleep. I couldn't understand why he'd had to die." She paused to check Kevan's expression, and finding it conveyed nothing of his thoughts, she continued. "I was crying, muffling the sound with my pillow so my mother wouldn't hear me. She detested any display of emotion. Considered it a weakness, especially in me."
His lips twitched like he wanted to say something, then decided against it. "She was a good mother, Kevan. My father's drinking hurt her and she believed that not feeling was the only way to survive. But she was wrong."
Alyssa took a deep breath. "I know she was wrong because the Elder told me she was."
"When he appeared to you?" Kevan asked.
"Yes." She flicked a strand of hair behind her shoulder. "Lying there, I saw a silvery vapor fill my room like a big cloud. This old man stepped out of it. He said he was the Elder of the Council of Perfection." Recalling the incident, she smiled. "I asked him if he was an angel."
"Are you sure you weren't dreaming, honey?"
"I'm sure," she said. "The Elder smiled at me and said that calling him an angel would suffice. I didn't know what suffice meant. But he didn't look angry, so I supposed he'd meant he was an angel. I asked him about my father; why he died."
"What did he tell you?"
"He said," she hesitated and looked deep into Kevan's eyes. "He said that my father's trials had ended in this level. That he had other discoveries to make in a different level."
"What did he mean?"
"That it was time," she said simply.
"Very interesting, but time for what?" Kevan rested his hand on her thigh. "Honey, maybe you were dreaming, or maybe it was shock. Stress can do strange things to an adult, and you were just a child."
"No, Kevan." She might as well tell him the rest. "As recompense for losing my father, the Elder gave me the gift of sight. He said that the Council had made the concession, given me the gift, because of my mother's denying her emotions. They felt that fulfilling my destiny in this level would be impossible if I didn't have the faith of their service."
"I don't understand."
"Think with your heart, Kevan, not with your brain. Since that first time, I've seen the Elder many, many times. Hundreds of times. Every time I do, and sometimes when I don't, I have a vision."
"Have any of them come true?"
Somber, she met his gaze. Now came the time when he would emotionally run. "All of them."
Thirty-four
"KEVAN, WAKE UP." Alyssa shook his shoulder. "Blast it, Kevan, would you wake up?"
He rolled over and opened one eye. "Just five more minutes, honey."
"There's a boat coming just after dawn."
Groaning, Kevan shut his eye. "Right."
She shook him again. "I saw it, Kevan. Come on, wake up."
Grumbling, Kevan hauled himself to his feet. "If you woke me up for no reason, you, dear lady, are going to pay."
She smiled at him. "Are you always this grouchy in the morning?"
He glared at her. "I'm usually worse."
"Oh, pity, we're in trouble. I hate to break this to you, lover, but I'm a morning kind of person."
He rubbed his neck and let out a deep yawn. "You'll learn better." Stretching his shoulders, he worked out a kink just under his left shoulder blade. "If the boat's not coming 'til dawn, why do I have to get up now?"
"You believe me—about the boat?"
"Are you lying to me?" he asked.
"No."
"Then why shouldn't I believe you?"
"You should," she said. "It's just that—never mind. There are two reasons to get up now, genius. First, so you can do your half of the cleaning up around here, and two—"
"Wait a second. Back up. This is a deserted island."
"It is. And all we're leaving on it is footprints. The world's trashed out enough as it is."
He rubbed his chin, wishing for the zillionth time he had a decent razor. She had a valid point. "All right, we'll clean up. Do I have time to wash my face?"
She smiled. "Only if you wash the sand out of your beard."
He slid her a reprimanding look. "You know I hate cheerful in the morning, Alyssa."
"I know."
Grunting at her for seeming so pleased with herself, he turned for the path to the lagoon.
"But you'll learn better."
He stopped, and, looking back over the slope of his shoulder, he leveled her with a frosty glare. "The Hell I will."
Alyssa shrugged off his anger like it was a pesky fly. "Fine. If you'd rather have Hell in the morning, I'll do my best to accommodate you."
He turned and crossed his arms over his chest. "That sounds a lot like a threat."
She grinned. "It sure did, didn't it?"
He walked back to where she stood. Without a word, he scooped her up and slung her over his shoulder. Placing a hand firmly on her rump, he took off toward the lagoon.
"Oh, Kevan," she cooed at him. "I just love your caveman tactics." Then she burst into laughter.
He sidestepped a sticker bush that oozed a clear, gummy-looking substance, and sought his memory to classify it. Her hand slid to his buttock. Seconds later he felt it sting. "Ouch, damn it."
Alyssa pinched him again. "I don't appreciate being ignored. When a person says, 'I love you, darling,' you're supposed to say, 'I love you, too.'"
"Pinch me again, and I'll make you think love."
She laughed at him. "I'm not afraid of you, caveman. Bullying me won't work."
"Oh, really?"
"Really," she said, nipping his back with her teeth.
"Woman, you're getting under my skin."
"God, I hope so."
He stopped at the edge of the lagoon and slid her down his length until her chest met his. Her laughter rang out. He captured her lips and kissed her until she clung to him, until her laughter ceased bubbling in her throat.
Feeling wicked, wonderfully wicked, at what he was about to do, he raised his head.
"No, Kevan," she ordered him. "Don't you dare."
"Dare what?" he asked, knowing full well they both knew his exact intentions.
"You've got that look. The same one you had when you deliberately snared my blouse with the fish hook and ripped it right off my back." She worried her lip with her teeth and tried to wiggle out of his arms. "Kevan, honey," she said, tapping a long finger to his chest. "You wouldn't throw me in, would you? It's barely dawn. The water is—"
"Wet," Kevan finished, throwing his weight. They both tumbled and plunged into the water with a great splash.
Alyssa came up sputtering. "Kevan Buchannan, you are a maniac. A misguided, annoying pain in the—"
He dunked her.
She bounced up from the shallow bottom gasping. He backed away.
"That's it, buddy," she vowed, slapping the water from her cheeks. "You're going down."
Smiling, Kevan planted his feet in the soft lagoon floor and crossed his chest with his arms. Staring down his nose at her, he tried not to laugh. She was so angry she wouldn't be able to spit for a week. "Going down? Me? Is that so?"
She splashed him. A water fight ensued, and when the sunlight crept higher to flood the tree-shadowed lagoon, they were laughing like children.
"Enough, Kevan. It's full dawn."
"Can't take it?"
She paddled over to him, arcing ripples in the water by trailing her hands. She stopped in front of him, standing so close that when he drew breath, her soaked blouse grazed his chest.
Crooking a finger up at him, Alyssa smiled. "Come here."
He cast her a wary look. "I don't trust you."
"I want to kiss you," she said.
He bent down. Her arms loosely draped his neck and her lips met his. Deciding all she really wanted was a kiss, he settled into it, relaxed his guard. Her hand drifted the width of his chest. "Mmm, that's nice," he said against her mouth.
She smiled, and lowered her hand to his waist. "Isn't this a much nicer way to start the morning?" She curled her leg around his thigh. "I like your kissing more than your grumping. Don't you?"
"I do."
"You're a very good kisser." She curled a fingertip at his chin. "I'm not sure I approve. It must have taken a lot of women for you to become this accomplished."
"A few," he confessed. "Think of it as a fringe benefit."
"Would you care to explain that?"
"No, I don't think I would. Now you've got that look."
"What look is that, darling?"
"The one you had when I tried to shave and found out you'd used my razor on your legs. The very one that tells me if I open my mouth you're going to rip my tongue out."
"Such violence. And I thought you a peaceable man." She tut-tutted. "Still, I think you'd better explain."
He arched a brow at her implied threat. "And if I don't?"
Smiling sweetly, she let her hand drift across his ribs, then quickly swept down and captured him. "Go down, Kevan."
"Alyssa," he said, letting out a nervous laugh. "Come on, honey. You wouldn't—"
"I would. Go down, Kevan."
"You realize you'll pay for this."
"God, I hope so."
Smiling, Kevan dutifully dunked himself—and took Alyssa with him.
ON THE BEACH, Alyssa curled her toes in the sand. Sitting back to back with Kevan, she looked out over the sun-sparkling water and saw no sign of the boat that would rescue them. "Kevan?"
"Yes."
"You are going to marry me." The sea breeze whipped a strand of her hair across her face. She brushed at it and looked back at him. "I mean, you haven't decided against it, have you?"
A muscle in his cheek twitched. "I'm going to marry you."
Relief eased the tension in her. His hand draped his steepled knees and sunlight glinted on his signet ring. She frowned. "The visions don't frighten you?"
He pivoted on his rump until their knees met. "They don't frighten me."
"Good." She tried a tentative smile.
Kevan didn't smile back. "You're going to marry me, aren't you?"
She worried her lower lip with her teeth. "Do you love me?"
"Forever," he vowed.
"I'm going to marry you."
He closed his eyes for a scant second and his expression eased. "My being a genius doesn't frighten you?"
He hadn't run. She'd risked telling him the truth—down-playing the extent of her visions—but the truth. And Kevan hadn't run. "No, you don't frighten me. I love you."
"You will," he promised, sealing their bond with a heart-melding kiss.
When he released her, Alyssa stood up and scanned the open water. Rigging rose high above the water line and the outline of a squatty shrimp boat broke the pencil thin line of the horizon. She extended a hand down to him. "Our ride's here."
Looking out on the water, Kevan squinted. Alyssa watched him and not the boat, fearing, anticipating, his reaction. Would he run now? Would he?
Wary, Kevan turned to face her. For a long moment, he studied her eyes, then a brilliant smile spread on his face.
Thirty-five
ALYSSA HUNG UP her office phone and cleared a spot on her cluttered desk to rest her head. The pain at her left temple had grown almost unbearable. In seven hours she would marry Kevan. Getting married in itself incited stress. Marrying Kevan, the man in her visions, pushed her beyond stress and headlong into anxiety. Especially after last night.
She groaned and rubbed her left temple. The pain throbbed stronger, gripping her like a pulsing fist. Last night's vision had shattered her. Kevan had been with her, but, of course, he'd seen nothing. Should she marry him? Knowing what she knew now, was it wrong to grab what happiness she could in this life?
Pain streaked through her chest. The Elder was summoning. Alyssa forced her head up, her eyes open. A silvery mist swirled in thin bands beside her desk, growing thick as fog. From within it appeared the Elder of the Council of Perfection.
"Child?"
Alyssa bowed her head, crossed her heart with her hand. "It's good to see you again, your grace."
"You are in pain."
He waved a bony hand knobby with blue vessels. It seemed a great strain for him, and, immediately, the throbbing in her head stopped. "Thank you. Are you ill, your grace?"
"It is of no consequence," he replied, his right eye flat and colorless, his left flooded with light. "Have you found him?"
"Yes, I have. And you were right, of course. I saw Kevan's ring, before I saw him."
"And the other visions? Of Scotland and England?"
"I saw those, too. And one of a dim and eerie place with odd glimmering light. He wore a loincloth there."
"Yes, I know." The Elder stroked his long white beard.
Alyssa wasn't surprised by his disclosure. It had happened often through the years. "You also know about the vision last night."
"The one regarding your death?" he asked, his voice deceptively calm.
Her heart plummeted and she fought the urge to cry. "Yes."
"The season has come, child. The leaves are changing."
Tears clogged her throat. "I'm to marry him today. How can I do that, knowing I'm going to die?"
The Elder graced her with a tender smile. "All mortals must die, child."
"But they don't know when," she countered. "I do. I—I can't do it, your grace. I love him. It'll hurt him more to lose a wife than to lose a lover."
The Elder nodded. "If your heart knows, you shall not know."
Alyssa pondered then voiced her interpretation. "The heart can't discern the difference. Love is love, and either way Kevan will suffer, is that your message to me?"
"You have learned well, child. The Council is most pleased with you."
"Thank you." Alyssa inclined her head. "I'm concerned about you. Why do you seem so ill? What is the significance of your eyes?" She smiled at him. "And please don't say, 'it's of no consequence' because I shall then be forced to disagree with you."
"It is of consequence," he said in a matter-of-fact tone. "The season is come, not passed. Marry your heart's desire, Alyssa—you must to fulfill your destiny. And take joy in your time together."
"Yes, your grace." The tears threatening her, spilled down her cheeks. "He loves me."
"Yes, he does."
"And I love him, too." She resisted the urge to wring her hands in her skirt, keeping them tightly fisted at her sides. "With all my heart."
"Yes, I know."
"I don't want to leave him. It took so long to find him. What else must we do?"
"Have faith in your humble servant." The Elder's image, the vaporous mist, faded.
Alyssa plopped down at her desk. She served the Elder, the Council. Who served her?
The intercom buzzed. Alyssa started, then lifted the phone. "Yes, Margaret."
"'Bout time you answered. I've got work to do, you know."
"Margar—"
"I thought you'd want to know," Margaret interrupted. "We haven't got spit."
Alyssa stiffened. "What are you talking about?"
"We sent a messenger over to Paragon Oil to drop off those papers to Duncan Foster."
"Yes, so?"
"So," Margaret said sharply, "Paragon Oil isn't there."
"How can Paragon not be there? Honestly, Margaret, have you dipped your head in one too many weird books?"
"I said, Paragon isn't there. The office is rented to an oil company, all right. But it isn't Paragon."
"Well, what is it?"
"Horizon Oil," Margaret informed her. "They've been there three years."
"I don't believe it."
"James MacMillian didn't either. But he learned different. On his way back to the office, he did some checking. Horizon's been in that same office three years, just like the man said."
"What man?" Alyssa asked, wondering what exactly was going on.
"Kenrick Innes."
An ill feeling overcame Alyssa. One she didn't understand, but couldn't deny. "Have James come to my office."
"Yes, ma'am."
"And Margaret. You'd better get Kevan on the phone for me. Something's rotten in the woodpile."
"And you can bet your bippie it isn't a log."
Alyssa rolled her gaze heavenward, hung up, and re-dialed Paragon's number. Her hand, holding the receiver, felt clammy. Less than twenty-four hours had passed since she and Kevan had returned to New Orleans. And with each one of them, this Paragon Oil thing had become more baffling.
A high-pitched signal pierced her ear. A recording followed.
"Your call cannot be completed as dialed. Please check the number and dial again."
Alyssa followed that advice twice, then called the phone company. Eventually, she was connected with customer service, and finally with a supervisor named Mrs. Serge.
"That number hasn't been active for years, Ms. Cameron."
"That's impossible," Alyssa countered. "A month ago, Paragon Oil—"
"I'm sorry. Hold please and I'll verify."
Kevan strode into Alyssa's office, bent over her desk and kissed her. "Hi. Busy?"
"On hold," Alyssa whispered.
He walked around, helped her to her feet, sat in her chair and pulled her onto his lap. His satisfied sigh made Alyssa laugh. "Kevan Buchannan, you are incorrigible."
"I know." He smiled and nibbled at her earlobe, not at all bothered by his shortcomings. "What's this about Paragon?"
"James went to deliver the proposal. Paragon's address turns out to be Horizon Oil's headquarters. And Paragon's number is dormant, Kevan. I've got a woman verifying that now."
"A subsidiary, maybe?" he suggested, moving down to taste her neck.
"Ms. Cameron," Mrs. Serge said, coming back on the line.
"Yes."
"That number's been inactive for three years. It belonged to a skating rink before then. We assigned it twice afterward, but the clients complained about receiving too many calls from kids, so we pulled it."
"Is that uncommon?"
"Oh, no," she assured Alyssa. "Quite common, in fact. I also ran a check on Paragon Oil."
Alyssa knew what was coming. Not why, but what. "There isn't a listing," she said.
"No," the representative confirmed, "there isn't."
"Thank you, Mrs. Serge."
Alyssa dropped the receiver onto its cradle, then looked at Kevan. "We've been had."
KEVAN STOOD beside Alyssa in Kenrick Innes's sleek executive office. Innes lounged back against his desktop. His flaming red hair glinted in the sun streaking in through vertical blinds at the window. Why had Alyssa refused his offer to sit down? Had she hated the man on sight, too?
Kevan stifled a shiver. He hadn't experienced that feeling before: hating a total stranger. But he hated Innes.
"You're sure about this," Alyssa asked. "You've never heard of Paragon Oil?"
Innes's laugh was as crafty as his eyes. "Oil's my business, Ms. Cameron. If Paragon existed, I'd know it."
Kevan caught Alyssa's arm. "Thank you for your time." He extended his hand to end the brief meeting.
Alyssa stood woodenly at his side. She said nothing, and she didn't accept Innes's hand.
They exited the chrome and glass office, rode down to the street level floor in a wide, paneled elevator, then crossed the lobby filled with lush, green foliage. Alyssa still hadn't said a word. But when they stepped outside, she stopped, took in a deep breath, and turned to him.
"Kevan, I hated that man."
He felt relieved. Upset, Alyssa ranted, she didn't clam up. "I did, too."
She frowned. "Do you know why?"
"No," he replied. "Just a feeling. You?"
She wrapped her body with her arms. "Every time I looked at him, I saw spiders and . . ." She gave Kevan a negative nod.
"And what? What else did you see?"
He saw fear in her wide eyes. "Blood," she whispered, looking shaken. "I saw blood."
"Have you done that with anyone before?"
"No, I haven't." She reached out and clasped his hand. "Do you think he lied?"
"I think we'd better find out." Kevan glanced down at his watch. "But it'll have to wait. Right now, we've got something more important to do."
"What?"
Kevan smiled. "We're getting married."
Alyssa's jaw fell slack. "It's that late?"
"Ten till five."
She grimaced. "Well, flip."
"That enthused, huh?" He forced the grin from his face.
"Blast it. I wanted to get dressed up, to look gorgeous for you." She arched him a warning look. "I only intend to do this once."
"Damn right," he agreed. "And you're already gorgeous."
He bent and kissed her there on the street.
THE JUDGE'S chambers smelled of old money, lemon oil, and cherry tobacco. Files and opened books littered every inch of the wide desk. Feeling bittersweet, Alyssa stood beside Kevan. He took her hand, and she felt his slight tremble. How she loved this man. And, God forgive her, how she would hurt him.
The judge adjusted his thick black-framed glasses, and began the ceremony. His rich melodious voice soothed her, brought the Elder's rasped words of comfort to her mind: "Have faith in your humble servant."
She responded at the appropriate times. So did Kevan. Then he was saying he loved her, kissing her, and the ceremony officially ended.
They were married. Kevan Buchannan was now her husband. And, soon, he would be her widower.
God help them both.
KEVAN WANTED to shake her. Two months they'd been married. Alyssa'd been amiable on everything: merging their businesses, their homes, their lives. Two months, and not once had she raised her voice or vented her hellish temper. It wasn't natural, or normal. Not for Alyssa.
Lying in bed, he looked at her. Rigid as a board, she sat at her vanity, brushing her hair. It shone like spun silver. He scrunched his pillow and folded his arms behind his head. "We need to talk about this."
Her brushing hand hesitated for a brief second. "About what, darling?"
"About your not showing up for work until noon today. And, when that mystery's resolved, we can discuss your seeing a doctor instead of a quack."
"I went for a walk, Kevan, and Dr. Samuels is not a quack."
"You walked for four hours?" He felt his temper rising and squelched it. "Were you off trying to resolve the Paragon thing again? Never mind. Don't answer that." He raked a hand through his hair. "We agreed to drop it. To let the whole Paragon issue remain unsolved."
"We did."
Kevan felt his gut knot. His suspicion had been growing for weeks. Did Alyssa think that he wasn't measuring up to his visionary counterpart? Was she in love with the vision and not the man, after all? By God, he needed an answer. Feeling more vulnerable than he ever had in his life, he asked her. "Is there another man? Is that it?"
She dropped the brush. "No!"
"For God's sake, Alyssa, would you look at me?"
Her shoulders lifted and she slowly swiveled toward him on her stool. "There is no other man, darling. I swear it. I love you."
The sadness in her voice cut him like a knife. "Where were you, then?"
Alyssa paused. She'd love to tell Kevan where she'd been. But she couldn't. She didn't know herself. She'd racked her brain all afternoon, but she recalled nothing between leaving home at 7:30 and arriving at their office at 11:30. And she couldn't tell Kevan the truth about why she couldn't remember. She had promised herself to protect him as long as she could.
Unable to meet his eyes and lie, she studied her hands folded in her lap. "I was investigating Paragon." She looked up at him. "Did you know that no articles of incorporation were filed? No Louisiana business license was issued. No charter, no—no nothing."
Kevan's voice softened. "I know, love. We found that out six weeks ago."
"Yes," she agreed, having no memory of that at all. "That's right."
Pain seared her left temple. She pressed her fingertips to it.
"Hurting again?" he asked.
She walked over and lay beside him on the bed. Her silk gown tangled with their thighs.
Kevan drew her close, began massaging her forehead. "Sweetheart, I want your promise to forget about Paragon. I don't know who set us up, or why, but it's not important anymore. You've got to accept that we'll probably never know."
"But—"
"I want your promise," he said firmly. "You're driving yourself crazy with this, honey."
"I know you're right, but it doesn't make sense. No one goes through that kind of trouble without a reason. Somebody, somewhere, wanted us on that boat—and on that island. I want to know who and why."
"What's the difference now?" His thumbs slanted above her eyes. "We found each other. It's over, honey. Let it be over."
"Aren't you curious?" she asked. "Right there . . . Oh, God, you've got wonderful hands."
He smiled. She didn't see it, but she felt it, and smiled back.
"I saw a cat today," Kevan whispered. "One like Tabby. He was at the pet shop over on St. Croix. Would you like him?"
Alyssa's chest constricted. "No," she whispered in hushed tones. "I don't want to share you, Kevan. Not yet."
Kevan let out a deep sigh. "You've got me worried, love. That meeting with Greyson this morning was important."
"I'm sorry. I—I just had to walk for a while."
"Did you think about seeing Dr. Chandler?"
"Yes."
"And?"
"I know you don't like Dr. Samuels, Kevan. But I'm really comfortable with him."
"He's not helping you, babe. There's got to be more he could be doing. What about the headache clinics I've read about? Has he recommended one?"
"He's treating me. Stress is stress. Relaxation exercises, rest, quiet, calm time—"
"Pain killers," Kevan said, a trace of bitterness in his voice.
"I don't take them, darling. You know how I feel about drugs."
He buried his face at the curve of her neck. "I'm scared, Alyssa. I don't want to be without you."
Oh God, had he guessed the truth? She reared back and looked down at him. "Kevan?"
"I've got this feeling that something's wrong. Please," his voice cracked. "See Dr. Chandler for me."
Alyssa swallowed the tears clogging her throat. "All right, darling. I will."
He smiled and kissed the tip of her chin. "Thank you."
When he started to move away, Alyssa held him to her, hot tears burning her eyes. "I'm sorry about this morning."
"I handled it."
"Kevan," she whispered. "Love me."
"Always," he said, his breath warming her cheek.
His lips settled on hers, and Kevan made slow, sweet love to her, showing her all he felt in his heart and proving his words true.
Thirty-six
"YOU BETRAYED ME." Alyssa accused her body, reflected in the bathroom mirror. "You recognized him on sight. You made me love him, and now you're dying. You're making me leave him." She covered her mouth with her hand. Oh God, how can you do this to me now?
"Don't, child."
Alyssa spun around and saw the Elder. He looked weaker than before, as though he himself stood at death's door. "Your grace, what's wrong?" She stepped toward him.
"No." He raised his hand to stay her. "You must not touch me. Not yet."
"Why?" She stepped back, and the truth hit her. Feeling stunned, she confronted him. "You're dying, too."
"It is of no consequence."
"It is of consequence," she argued. "You must be here for Kevan. He will need you . . . after . . ." Her voice trailed. She couldn't make herself say the words.
"You're tormenting yourself, child. And you're tormenting Kevan. He fears you love your visionary man and not him. Why have you not told him how serious your illness—"
"He'll know soon enough." She lifted her chin. Her voice quivered. "The blackouts have started."
The Elder nodded. "It is time."
Finality suffused her. "You've come for me, then?"
"Yes." Sympathy softened his expression.
"Please, your grace. Don't make me leave him like this. Let me—" Her voice broke and she swallowed hard. "Let me tell him goodbye. I—I can't just . . . just leave him without saying goodbye. He needs time to say things, time to prepare himself. He—He—Oh, God—he can't just find my body here on the floor!"
The Elder looked torn.
"Your grace," Alyssa sniffed. "I'm begging you. Please! Kevan would feel responsible. He'd never know peace. Please, don't make me do that to him." Tears spilled down her cheeks and her body shuddered deep sobs. "Please, don't make me hurt him like that."
"Very well, child. The Council shall grant you three days in which to prepare him. But, know that you will aid him little in his grief. It cannot be otherwise."
Alyssa squeezed her eyes closed, blotting out the images of Kevan finding her lifeless body on the bathroom floor. "Thank you, your grace."
The Elder stepped toward her. "You shall not suffer, child."
"I shall," she whispered. "How can I not suffer, when I know that Kevan will?"
"Painless love would be joyless love," the Elder said. "For the two are inseparable." His left eye blazed like fire, his right one remained flat and colorless. Lifeless.
"But you'll take care of him. You'll protect Kevan, as you have me."
"As best I am able. The leaves rustle in the wind, yet they do not fall. Autumn is upon us. Too soon all will perish under winter's bitter ice."
"Have faith in your humble servant, your grace. I have not forgotten. Nor have I forsaken."
The Elder nodded once and lifted his hand. Alyssa felt a whimper threaten her throat and prayed for courage. His hand came toward her, its blue veins raised. He flexed his wrist, and she saw his palm. A silver sword like the one in Kevan's signet ring marked his skin. "You're Kevan's angel!" she gasped. "Elder, you're Kevan's angel!"
The Elder smiled and cupped her cheek.
Crying, Alyssa smiled back.
FRANTIC, KEVAN stormed into the apartment. Her Volvo was downstairs. She really was here. "Alyssa!"
Room to room, he searched. The kitchen, living room, bedroom—all empty. He turned, stumbled over her vanity stool, and saw a glimpse of peach fabric. The gown she'd worn to bed last night. His blood drained to his feet. "Alyssa?"
Kneeling beside her on the bathroom floor, he bent over her, his heart hammering hard enough to ring his ears. She had a pulse.
Scrambling for the bedroom phone, he dialed 911, gave the dispatcher the data, then rushed back to his wife. "Alyssa, look at me, honey. Talk to me. Please, do something. Anything!"
But Alyssa lay still. Deathly still.
Just as he'd envisioned her.
Thirty-seven
"SHE HAS A brain tumor, Kevan," Dr. Samuels told him.
Feeling as if he'd been kicked in the gut, Kevan slumped against the wall outside Alyssa's hospital room door. He looked up at the grim doctor. "What can you do?"
Dr. Samuels's bushy brows knitted. He avoided Kevan's eyes and spoke softly. "We're trying to keep her comfortable."
Pain sliced through Kevan's heart. "She's dying?"
"I'm sorry."
"Sorry?" Kevan roared. "You're sorry? You said the headaches were stress. You said rest, relaxation exercises, taking it easy—"
"She refused to let me tell you. I couldn't breach her confidence."
"She knew?" Kevan went numb.
"I told her months ago."
"Months?" His head whirled. "How many months?"
The doctor ignored his question. "She wanted to spare you as long as possible, Kevan. She didn't want your last months together to be sad ones."
"Last months? I've only had her three months. Damn her," Kevan swore. Pain, rage, and fear warred inside him. "Damn her for—"
Dr. Samuels grabbed his arm. "For carrying the burden of knowing she was dying alone? For wanting to protect you, to shorten your grief?"
Kevan drew in a breath, held it until he thought his lungs would explode, wishing that they would. "On the island. She told me then she would protect me. I—I never dreamed . . ."
"Being angry with her is a normal reaction," Dr. Samuels said in a compassionate voice. "But save it, Kevan. Alyssa has so little time left. Just days, maybe. I can't be sure. Her tumor has grown rapidly—unusually fast."
"Oh God." Kevan hunched against the wall. Numb, leaden, a fist-sized knot of tears damming his throat.
The doctor put his glasses back on and patted Kevan's arm. "I'm sorry. She's a special woman."
Kevan looked up at the doctor. Tears he couldn't stop trickled down his cheeks. His voice sounded like the grated whisper of a very old, very tired man. "Is she suffering?"
"No, she isn't."
"Will she?"
"My experience says yes. But we'll do all we can to make it easier on her, I promise you. Morphine helps."
"Alyssa hates drugs."
"I'll be honest, Kevan. By the time the patient is in Alyssa's current state, we're usually administering the maximum dosage we can without risking a drug-induced coma. Your wife is an incredibly strong woman."
Kevan swallowed hard. "Yes, she is."
"Stay here as long as you like," Dr. Samuels said. "I'll check on Alyssa."
"Doctor?"
At the door, he looked back. "Yes?"
"The tubes and the IV," Kevan said. "Get rid of them."
"Kevan—"
"She's dying, doctor. They won't save her. The one through her nose to her stomach—it hurts her throat. I can feel it. And the IV has her arm red and swollen. Just—Just get rid of them, or I will."
"All right, Kevan."
DEATH was calling.
For three days, Kevan had stayed at Alyssa's side. Had watched her strength dwindle, her pain mushroom. He sensed death lurking, smelled it, tasted its bitterness on his tongue.
"Kevan?"
She called him in a ragged whisper that shred his heart. She looked so fragile, so damned weak and fragile. "I'm here, love."
"Come." She patted the bed with her hand.
"Darling, I can't," he whispered. "I could hurt you."
In the dim, pre-dawn light, he saw her lick her lips. "I'm dying, Kevan. This will be our last dawn."
His heart shattered. "Not yet. Please, darling, not yet. I—I need you."
"Come," she insisted. "I've a need to hold you."
Tears glistening on her silver-tipped lashes broke the straggling bits of his control. He stretched out beside her and gently cradled her in his arms.
"I want you to listen to me, Kevan. There isn't much time left."
"Oh, God, Alyssa." He pressed his cheek to her crown.
"Shh, you must be strong now. I know you've loved me. I have since I saw you at the marina in Biloxi. I recognized you from before."
"Before?"
"The images I'd seen. We lived them, Kevan. We had children. Whole lifetimes together. Listen, darling. It's important. You must live, Kevan. Be happy. You've been the best thing that ever happened to me. You didn't run. I told you the truth, and you didn't run. If I die believing you're miserable, I'll never rest. I won't, Kevan."
"Alyssa. Darling, please." Oh, God, she was slipping away from him. Slipping away—and he couldn't hold on to her. He couldn't make her not die. Why couldn't he make her not die?
Her voice grew thready. "I don't want to leave you. I love you, Kevan. But it hurts so much to stay. So much . . ." Her gaze found his. "Tell me I can go. Tell me you'll be all right."
"Alyssa. Alyssa. Oh, God, Alyssa. Don't die. Damn it, don't leave me."
"Kiss me, Kevan. It'll be so long till I feel you again. Kiss me goodbye and tell me you love me."
Swallowing back sobs, Kevan pressed his lips to her cool ones. So still. Oh, so still. "I love you, darling. All my world. Forever." He swallowed the pain constricting his throat. "Go, my love. Stop . . . stop hurting."
She opened her eyes and smiled, wearing the first serene look he'd seen on her face in months. "I love you." She touched his cheek ever so gently and whispered. "Prophet."
"Alyssa! Alyssa, no!" Kevan cried. "No, not yet. Please, just a little more time. Just one more minute. Oh, God, Alyssa. Not yet. Please!"
Kevan held her, rocking back and forth on the bed, knowing his wife was dead, praying he was wrong, wishing he were dead, too. He nestled his face into the curve of her neck and whispered. "I'm frightened, Alyssa. Oh, God, I don't know what to do. You weren't supposed to die. Women live longer than men. We were supposed to have children. Damn it, we were supposed to grow old together!" He sobbed. "Oh God, Alyssa. I can't stand this. Nothing can hurt this bad. Nothing can hurt this bad . . ."
Thirty-eight
THE FUNERAL was over.
Kevan stood alone beside Alyssa's grave, the sun beating down on his back. The mourners had gone, but their flowers lay bunched and sprawled, littering the ground at his feet. She'd been well-loved.
He dragged in a breath, forcing his lungs to expand whether they chose to or not. Live. Be happy, she'd said. But she hadn't told him how. How to go on. Without her, nothing seemed important, connected, or relevant. Nothing seemed alive. She hadn't wanted to leave him. God, how that hurt—and helped. He, too, had been well-loved.
The dirt now formed a mound over her casket. Feeling hollow and empty, Kevan stepped closer and knelt, putting his hand on the warm ground. "I love you, Alyssa. As God is my witness, I'll keep my promise. I will love you forever."
Again he heard her final "I love you" and felt her hand on his face. Again he heard the last mystifying word she'd whispered: Prophet.
"I don't know what you meant, darling. I don't understand. Was I supposed to understand?"
A long shadow crossed her grave. "Hello."
Kevan looked back. Brilliant sunshine melted the features of a large man's face. Kevan stood. The man's iron-gray beard wiggled, and the yellow tabby cat resting against his barrel chest purred with each of the man's strokes to its back.
"I'm sorry to intrude," he said.
"Then why are you?" Kevan asked, sensing something familiar about the man.
"You look like you need a friend."
"A friend?" Kevan laughed, but there was no humor in it. "No. My friend is dead and buried."
The old man's leathery skin crinkled at the corners of his eyes. His empathy was blatant. "Losing someone you love is difficult."
Kevan didn't answer.
"Your wife?" the man prodded.
"Yes." An odd sensation crept over Kevan. The man seemed more than familiar. The cat purred, claiming Kevan's attention. "My wife had a cat once, a tabby."
"I know."
Kevan lifted startled eyes. "You knew my wife?"
"Aye, I did. 'Twas many years ago, but I knew her."
An amulet catching the sunlight winked at Kevan from the gap in the old man's shirt. The crystal hung suspended from a strip of leather wound around the man's neck. Kevan's heart thundered. Alyssa had asked him if he'd worn such an amulet. "You're Duncan Foster."
"Aye, I am."
"Are you Alyssa's Elder?"
The old man gave him a negative nod. "Nay, I'm not the Elder, but his emissary."
"Before she died, Alyssa said some things that I didn't understand."
"Mayhap I can help. What did she say?"
"That we'd lived other lives together."
"Aye, 'tis true, that."
Kevan swallowed his surprise. "She also said—Prophet."
Duncan smiled. "Ah, yes. And what did you reply?"
Not expecting that reaction, Kevan frowned. "I didn't. Do you know what she meant? What—who is Prophet?"
Duncan's eyes clouded, his smile faded, and his hand stroking the cat stilled. "You do not know."
"Should I?"
"I'd hoped—never mind. I must go now."
"Wait, Duncan," Kevan called out to the old man's retreating back. "Wait!"
But Duncan Foster didn't wait. He vanished into a silvery mist.
ALONE IN his office, Kevan turned off his computer and stared at its blank screen. "Prophet," he said aloud, feeling the syllables roll off his tongue. "What were you telling me, Alyssa? What?"
He dragged his hand through his hair. She knew him. She had visions, glimpses of the future that had frightened others away from her. She'd protected him, said the images she'd seen of him were from lives they'd shared before. Logically, he thought it improbable, not impossible, but in his heart, he believed her.
He believed her about the Elder, too. After seeing Duncan Foster disappear into the silver fog—just as she'd said the Elder disappeared—how could he not believe her?
A pain seared his chest. The ticking of his office clock grew to a steady thump inside his head. Weary, he cleared his mind, concentrated on the sound, hoping to forget for just one second that this morning he'd buried the only woman he would ever love.
The ticking sound faded.
Images filled his mind.
A cemetery, Alyssa's cemetery, grew focused, clear. He saw himself as an apparition, standing beside Alyssa's rain-swept grave. A crystal amulet hung from his neck, a silver sword from his side. He bent down, touched the cold mound of wet dirt covering her casket. She rose from beneath the ground and followed him.
A second, sharper pain seared his chest. He put his fist over his heart. A silver vapor grew from a thin, swirling band to a thick, still cloud opposite his desk. From its midst appeared an old man, who looked a scant step from death. Bent and crippled, the white haired man hobbled forward.
"Elder?" Kevan's mind flooded with memories. Panic set in. "Angel. Where is she?"
The Elder's raspy voice was a wisp of sound. "Your quest is ended, Prophet."
"Oh God, we failed."
"If you failed, you have not failed. You sought your destiny—and won."
"Won? How have I won? Alyssa is gone. She died! I—I'll never have her with me again."
"Your lady is of no consequence."
"No consequence? She's everything to me. Why did we fail? She loved me. She made her discoveries—all of them. How did we fail?"
The Elder's left eye sparkled. The right remained flat. "She exceeded the Council's expectations, I agree. Still, the love you shared lacked perfection."
"It didn't," Kevan argued. "Her last word proves it. She said Prophet, your grace. She recognized me!"
The Elder said nothing, merely looked at Prophet.
"She put me first in her life—before everything. She even protected me from her illness, to spare me while she suffered."
"A most admirable woman, I would say."
Kevan's stance grew defiant. "I demand proof. I want evidence supporting the Council's decision."
"Because you forfeit your soul?"
"Because I love my wife. Because loving her is my destiny. Because without her, I have no destiny."
"There is no proof to give you, Prophet. Do you lack faith in the decision of the Council?"
"No. Yes. I don't know." Prophet shut his eyes, regained control, then reopened them. "I lack acceptance, your grace. Not faith."
"Seek acceptance in your heart. Remember the leaves, Prophet. The season has come. Alyssa changed—in her own time—just as the leaves change. Seek your destiny in the season. It is there you will find your answers. And your acceptance."
The Elder's silvery image faded. The sounds of the ticking clock grew more and more loud.
Drained, Prophet sat back and propped his feet on his desk. His memory of Prophet, his quest, his lives and trials with Alyssa, remained.
"Seek your destiny in the season," the Elder had said. Alyssa had changed. In her own time—like the leaves. She'd learned the value of fear in prehistoric times. To honor his decisions, modesty and humility—that every deed, good or bad, had value—in Scotland. In England, she'd grown more gentle. She'd learned the prejudice of pride—and the value of forfeiting it for what she believed an honorable cause. In this life, Alyssa had proven herself. She'd lived the discoveries she'd made. He knew she had.
Before their travels to her learning levels, she'd been absorbed by her work, incapable of loving. She'd been his mistress, his lover, but not his wife. That, she'd refused. After her discoveries, in her altered history, she'd worked, yes. But he'd come first with her. She'd not excluded him from any facet—any facet—of her life. She'd protected him, and loved him. Above and beyond all else, she'd loved him.
Then how had she failed? Why had she been given the gift of visions, and he'd been denied it?
A tingle started in Kevan's skull and spread down through him until the tips of his toes felt like they were waking from sleep.
"If you fail, you shall not fail. Seek your destiny—and win."
The Elder had said that when offering the challenge at the very beginning. And when he'd accepted, he'd been told: "May wisdom realized through your gift lead you now in following your heart."
The tingling grew stronger. More messages from the Elder came back, replayed themselves from Kevan's memory. "Your confidence in her awareness, in her ability is false . . . Your love blinds you to the truth . . . the treasures of a foolish man are not everlasting."
"Oh, God," Kevan mumbled. "A wise man never tries to change the color of the leaves. He accepts them as they are. Yet according to season, the leaves do change . . . the season will guide you . . . Time waits for no man. Pursue your destiny . . . Seek your message . . . Seek your acceptance . . . Seek your destiny!"
What if it wasn't her awareness or abilities that required his confidence? What if it was his? What if the wisdom realized through his gift, wasn't his gift of visions, but his gift of loving Alyssa? Loving her, he would accept her as she was, not attempt to change her. He would have adapted. He would have changed. He would have sought!
When Innes held Alyssa hostage in England, the Elder had said: "If she dies now, your trials will end here. Your mission will have failed." Not Alyssa's trials. His trials!
His. And each time the Elder appeared, he'd grown more weak, his eyes more . . . Kevan sat straight up. He grabbed his chair's arms and squeezed. "Eyes are the mirror of the soul. The Elder's eyes!"
Groaning, Kevan slumped forward, his forehead resting in his hands. Dear God, he'd been blind. Both eyes flat. The left growing stronger with each of Alyssa's discoveries, and the right—Oh, God—the right represented his own learnings!
While he'd led Alyssa to love's light, the Elder—the Council—had been leading him! He'd learned. Yes, he'd learned, too.
But what had he learned? And why hadn't the Elder's eyes reflected those learnings?
Kevan sat back, concentrated hard. He'd detoured to prehistoric times to restructure Alyssa's character, to teach her fear. He'd saddled her with his choices. And he'd learned that she should make her own decisions.
Growing excited, he recalled Scotland and the events occurring there. Then again he asked himself what he'd learned. The answer came easily. To accept Alyssa's limitations, to applaud her abilities. A woman warrior loved no less, nor any more, than a woman cook. And in England?
In England, he'd grown determined to humble Alyssa because she denied him what he wanted: her acknowledgment that their relationship had altered to what he, not they, desired from it. He'd taken her to London to force her pride from her. And she'd protected, humbled him, by sacrificing all she possessed for him. And in this life?
He'd meant to teach her love. How laughable that sounded now. She'd proven her love by risking her own life to save his in the water. Then again by shielding him from love's pain, by keeping her illness from him as long as she could. He'd taught her nothing.
But she'd taught him a great deal. In not realizing the true value of her love, he was unworthy to receive it. But Alyssa loved him anyway. He couldn't teach her love, because love could not be taught. It was a gift. The most precious of all gifts.
Kevan let his head loll against the back of his office chair. Resignation filled him. The Elder was right. Their love was not perfect. But it wasn't Alyssa who had failed. She had become universal, capable of loving. It was he who had failed. His love was the imperfect love. Throughout time, he failed to accept her as she was. He, who boasted at the beginning that she'd yet to learn that love is pure, people are not, had failed.
Something vibrated against his throat. Kevan reached up, cupped something warm in his hand. In the window behind his desk, he saw his reflection. His amulet!
"Have faith in your humble servant."
Swiveling, Kevan saw the Elder standing straight, looking strong. Relief washed some of his bitterness away. "Your grace, you've recovered."
The Elder's eyes were both flooded with brilliant light. His body, though aged, appeared healthy, vibrant. His soul had recovered. "It is of no consequence."
Kevan smiled. "No, your grace. I suppose it's not."
Elder treated him to a rare smile. "None master time or destiny, Prophet. We only serve them."
"I know—now."
"The Council is pleased with you."
"Thank you. But my discoveries have come too late. Alyssa . . ."
"If you fail, you shall not fail. Remember? You sought your destiny—and won."
Their gazes locked and held. The Elder stepped forward and cupped Prophet's jaw in his hands. Pain seared Prophet's chest. With Alyssa not there to share it, his victory was as hollow as his heart. He smiled his regret, slumped forward, and died.
THE LONG DARK tunnel gave way to light; bright, compelling, and warm. Kevan floated closer, wanting yet fearing the warm brilliance enshrouding him.
A looming shadow blocked his path. "Move," he called out. "You must move."
He drew closer, and the shadow took form, became a woman. Hovering nearby, Kevan studied the vision of naked splendor. She stood on a crystal platform, a crystal amulet at her neck, a silver sword at her side. Her long, silver hair flowed down past her shoulders and her perfect body held him enthralled. Was she a goddess?
Then she opened her eyes.
"Dear God," Kevan gasped. "Angel . . ."
She smiled at him through her tears and held out her hand. "I've been waiting for you. Come."
He eyed the distance between them and recalled that when Alyssa had come to him in the tunnel and she'd tried to touch him, the distance between them had grown greater.
"Have faith in your humble servant." Unbidden the words filled his mind.
"Angel, I love you."
"I love you, too."
He stepped forward. Their platforms merged. As they embraced, a cry of relief escaped them both.
"Kevan. Prophet," she cried, wrapping her arms around him. "I love you." She raised her lips for his kiss.
He held her for long moments. Letting the pleasure of holding her flow through him, soothe him. He kissed her again, poured out his deepest feelings in a way that only she would understand. And she kissed him back. Lovingly, longingly, laughingly.
"I thought I'd never see you again," he said, his voice husky.
"You knew you would."
"I feared."
She smiled. "Fear has its value, Prophet."
He returned her smile. "Yes."
"Are you ready to go?"
"Where are we going?" he asked. "Is there another level?"
Her laughter, warm and lusty, filled his ears. "No, darling. We may go where we wish. Our love has ended the need for trials."
"Really?"
She nodded. "Where shall we go?"
Kevan thought for a second. "Prehistory. Back to the barbarians."
"No," she disagreed. "I don't think so."
"But they treat me so well—"
"For pity's sake, Prophet. They treat you like a bloody king."
"What's wrong with that?"
She glared at him. "You're too authoritative already, is what's wrong with that."
"Alyssa."
"No."
"Well, flip." He heaved a sigh that could fell a tree. "What do you suggest then?"
She hid her pleasure that her literal husband had coined her very non-literal phrase, backed out of his arms, and entwined their fingers. "To the future, I think."
"Come on, Angel. Life's too complicated in the future. You know what Dr. Samuels said about you and stress."
"That's all over now." She gave him a sly smile. "Besides, when hasn't life with me been complicated?"
Kevan pressed her fingertips to his lips for a quick kiss. "How about the fifteen hundreds. We skipped that era."
Alyssa looked skeptical. "I don't know, Prophet. Wasn't that crazy Henry's turf? The man approved divorce, for pity's sake." She gave Kevan a thoughtful look. "No, definitely the future."
"Angel."
"Yes, Kevan."
"Prophet, love," he reminded her.
Alyssa shrugged. "One and the same." He squeezed her hand, and her heart lurched. God, it felt good to have him to hold onto again. How much she'd missed him, how empty she'd felt.
His eyes warmed with possessive desire. "Let's decide where to go later."
"All right. What do you want to do now?"
"I want to love you." He smiled that smile, and her heart thumped that thump. "Come."
Alyssa followed him. Where they went was of no consequence. They'd be together.
"I liked Scotland," Kevan said. "Why don't we go back there?"
"You were too chauvinistic in Scotland, darling."
"You loved me there," he countered.
"I've always loved you, Prophet."
"No, not always," he said. "Not always."
And hand in hand, they walked into the light.
(Please continue reading for more information about Vicki Hinze)
About Vicki Hinze
Vicki Hinze is the award-winning author of 30 novels, 4 nonfiction books and hundreds of articles, published in as many as sixty-three countries. She is recognized by Who's Who in the World as an author and as an educator. For more information, please visit her website at www.vickihinze.com.
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{"url":"https:\/\/www.zbmath.org\/?q=an%3A1184.34056","text":"# zbMATH \u2014 the first resource for mathematics\n\nGlobal dynamics of a class of SEIRS epidemic models in a periodic environment. (English) Zbl\u00a01184.34056\nSummary: We study a class of periodic SEIRS epidemic models and it is shown that the global dynamics is determined by the basic reproduction number $$R_{0}$$ which is defined through the spectral radius of a linear integral operator. If $$R_{0}<1$$, then the disease free periodic solution is globally asymptotically stable and if $$R_{0}>1$$, then the disease persists. Our results improve the results in [T. Zhang and Z. Teng, Bull. Math. Biol. 69, No.\u00a08, 2537\u20132559 (2007; Zbl 1245.34040)] for the periodic case. Moreover, from our results, we see that the eradication policy on the basis of the basic reproduction number of the time-averaged system may overestimate the infectious risk of the periodic disease. Numerical simulations which support our theoretical analysis are also given.\n\n##### MSC:\n 34C60 Qualitative investigation and simulation of ordinary differential equation models 92D30 Epidemiology 34D05 Asymptotic properties of solutions to ordinary differential equations 34D20 Stability of solutions to ordinary differential equations\nFull Text:\n##### References:\n [1] Baca\u00ebr, Nicolas, Approximation of the basic reproduction number $$R^0$$ for vector-borne diseases with a periodic vector population, Bull. math. biol., 69, 3, 1067-1091, (2007) \u00b7 Zbl\u00a01298.92093 [2] Baca\u00ebr, Nicolas; Guernaoui, Souad, The epidemic threshold of vector-borne diseases with seasonality. the case of cutaneous leishmaniasis in chichaoua, morocco, J. math. biol., 53, 3, 421-436, (2006) \u00b7 Zbl\u00a01098.92056 [3] Baca\u00ebr, Nicolas; Ouifki, Rachid, Growth rate and basic reproduction number for population models with a simple periodic factor, Math. biosci., 210, 2, 647-658, (2007) \u00b7 Zbl\u00a01133.92023 [4] Hirsch, Morris W.; Smith, Hal L.; Zhao, Xiao-Qiang, Chain transitivity, attractivity, and strong repellors for semidynamical systems, J. dynam. differential equations, 13, 1, 107-131, (2001) \u00b7 Zbl\u00a01129.37306 [5] Li, Michael Y.; Graef, John R.; Wang, Liancheng; Karsai, J\u00e1nos, Global dynamics of a SEIR model with varying total population size, Math. biosci., 160, 2, 191-213, (1999) \u00b7 Zbl\u00a00974.92029 [6] Li, Michael Y.; Muldowney, James S., Global stability for the SEIR model in epidemiology, Math. biosci., 125, 2, 155-164, (1995) \u00b7 Zbl\u00a00821.92022 [7] Liu, Wei Min; Hethcote, Herbert W.; Levin, Simon A., Dynamical behavior of epidemiological models with nonlinear incidence rates, J. math. biol., 25, 4, 359-380, (1987) \u00b7 Zbl\u00a00621.92014 [8] Ma, Junling; Ma, Zhien, Epidemic threshold conditions for seasonally forced SEIR models, Math. biosci. eng., 3, 1, 161-172, (2006), (electronic) \u00b7 Zbl\u00a01089.92048 [9] Song, Mei; Ma, Wanbiao; Takeuchi, Yasuhiro, Permanence of a delayed SIR epidemic model with density dependent birth rate, J. comput. appl. math., 201, 2, 389-394, (2007) \u00b7 Zbl\u00a01117.34310 [10] Sun, Chengjun; Lin, Yiping; Tang, Shoupeng, Global stability for an special SEIR epidemic model with nonlinear incidence rates, Chaos solitons fractals, 33, 1, 290-297, (2007) \u00b7 Zbl\u00a01152.34357 [11] Thieme, Horst R., Uniform weak implies uniform strong persistence for non-autonomous semiflows, Proc. amer. math. soc., 127, 8, 2395-2403, (1999) \u00b7 Zbl\u00a00918.34053 [12] Thieme, Horst R., Uniform persistence and permanence for non-autonomous semiflows in population biology, Math. biosci., 166, 2, 173-201, (2000) \u00b7 Zbl\u00a00970.37061 [13] van den Driessche, P.; Watmough, James, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. biosci., 180, 29-48, (2002), John A. Jacquez memorial volume \u00b7 Zbl\u00a01015.92036 [14] Wang, Wendi; Zhao, Xiao-Qiang, An epidemic model in a patchy environment, Math. biosci., 190, 1, 97-112, (2004) \u00b7 Zbl\u00a01048.92030 [15] Wang, Wendi; Zhao, Xiao-Qiang, Threshold dynamics for compartmental epidemic models in periodic environments, J. dynam. differential equations, 20, 3, 699-717, (2008) \u00b7 Zbl\u00a01157.34041 [16] Zhang, Fang; Zhao, Xiao-Qiang, A periodic epidemic model in a patchy environment, J. math. anal. appl., 325, 1, 496-516, (2007) \u00b7 Zbl\u00a01101.92046 [17] Zhang, Tailei; Teng, Zhidong, On a nonautonomous SEIRS model in epidemiology, Bull. math. biol., 69, 8, 2537-2559, (2007) \u00b7 Zbl\u00a01245.34040 [18] Zhang, Tailei; Teng, Zhidong; Gao, Shujing, Threshold conditions for a non-autonomous epidemic model with vaccination, Appl. anal., 87, 2, 181-199, (2008) \u00b7 Zbl\u00a01144.34032 [19] Zhao, Xiao-Qiang, Dynamical systems in population biology, CMS books math.\/ouvrages math. SMC, vol. 16, (2003), Springer-Verlag New York \u00b7 Zbl\u00a01023.37047\nThis reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.","date":"2021-08-01 17:40:20","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 1, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.7572033405303955, \"perplexity\": 7354.166473489951}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2021-31\/segments\/1627046154214.63\/warc\/CC-MAIN-20210801154943-20210801184943-00683.warc.gz\"}"}
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Kultur im Gugg is a venue for contemporary art and culture in Braunau am Inn in Austria. The building was originally a fire-fighting equipment factory.
Theatres in Austria
Buildings and structures in Upper Austria
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\section{Introduction}
The effect of gravitational lensing constitutes a unique research tool
in many astrophysical fields, since it allows one to investigate the
structures of both the lenses (e.g., galaxies and galaxy clusters) and
the lensed background sources, as well as to probe the three-dimensional mass distribution of the Universe. In particular, one of the most spectacular phenomena associated with
the gravitational deflection of light are the giant arcs observed in galaxy
clusters, which are caused by extended background sources lying in
the regions where the lensing magnification produced by the cluster is
strongest. The effective source magnification can easily reach $\sim 30$ in
these cases, providing the opportunity to detect and spatially resolve
the morphologies and internal dynamics of high redshift background
sources at a level of detail far greater than otherwise possible. An
illustration of this powerful technique was presented in
\cite{SW07.1}, where a magnification factor of $16$ by the cluster
RCS~0224-002 allowed them to study the star formation activity, mass and
feedback processes of a Lyman break galaxy at $z\sim5$, something that
(without the help of lensing) would not be possible beyond $z\sim2$
with current instruments.
A particularly interesting application of gravitational lensing is the
so-called arc statistics, i.e. the study of the abundance of large
tangential arcs in galaxy clusters. Among other things, this abundance
is sensitive to the cluster mass function, the cluster dynamical
activity (e.g., infall of matter, mergers, etc.) and internal
structure of host dark-matter halos (e.g., triaxiality and the
concentration of the density profile), which makes arc statistics a
unique tool to study the cluster population. Arc statistics
studies at optical and near-infrared wavelengths have been numerous in
the past decade on both the observational \citep{LU99.1,GL03.1,ZA03.1}
and theoretical sides \citep{BA94.1,WA98.1,BA03.2,ME03.1,WA05.1,FE08.1}.
All the currently known giant arcs come from detections in the
optical. However, the fraction of lensed sources observed in the
mm/submm wavebands is expected to be much larger than in the optical
\citep{BL96.1,BL97.1}: Due to the spectral shape of the thermal dust
emission, the observed submm flux density of dusty galaxies with a
given luminosity remains approximately constant in the redshift range
$1 \lesssim z \lesssim 8$ instead of declining with increasing
distance (usually referred to as "negative K-correction", see
\citealt{BL93.1,BL96.2,BL02.1}). This effect, together with the steep
slope of the observed submm number counts, produces a strong
magnification bias that makes submm galaxies (hereafter SMGs) an ideal
source population for the production of lensed arcs.
The SMGs were first detected about a decade ago with
SCUBA\footnote{Submillimeter Common User Bolometer Array
\citep{HO99.1}, which used to be mounted at the James Clerk Maxwell
Telescope (JCMT) located in Hawaii}
\citep{SM97.1,HU98.1,BA98.2,EA99.1}. The current observational
evidence indicates that these objects are high-redshift dust obscured
galaxies, in which the rest frame FIR peak of emission is observed in
the submm band. Their FIR luminosities, in the range $10^{11}-10^{13}
L_\odot$, are $\sim 100$ times higher than what is observed in local
spirals. Their energy output seems to be dominated by star formation
processes induced by galaxy interactions/mergers, although a good
fraction ($\sim 30-50 \%$) of SMGs also seems to host an Active
Galactic Nucleus \citep[AGN, e.g.][]{AL05.2, MI09.1}. The
available evidence also suggests that SMGs might be the progenitors of
massive local ellipticals \citep{LI99.1, SM02.1, SM04.1, WE03.1,
GE03.1, AL03.1, AL05.2, SW06.1,SW08.1, MI09.1}.
In the $\sim 30$ clusters observed with SCUBA
\citep{SM02.1,CH02.2,CO02.1,KN08.2}, only 4 multiply imaged SMGs have
been reported to date \citep{BO04.1,KN04.1,KN08.2}. This extremely low
detection rate is due to three major limitations of current
$850~\mu$m surveys: (i) very small sky coverage ($\sim 3$ square
degrees, including all cluster and blank field surveys), (ii)
confusion limited maps at $\sim 2$~mJy (which means that only the
brightest members are detected) and (iii) insufficient resolution
($\sim 15\arcsec$) to resolve extended lensed structures. Current
efforts to increase the surveyed area at 850~$\mu$m include the
SASS\footnote{SCUBA-2 All Sky Survey, a $\sim 2 \times 10^4$ square
degree survey with a $5 \sigma$ depth of 150 mJy and $~15\arcsec$
resolution}, the SCLS\footnote{SCUBA-2 Cosmology Legacy Survey, a
$\sim 35$ square degree survey with a $5 \sigma$ depth of 3.5 mJy and
$~15\arcsec$ resolution} and the all sky survey that will be carried
out with the HFI bolometer on board of the \emph{Planck}
satellite\footnote{$5 \sigma$ depth of $\sim 350$ mJy and
$\sim50\arcsec$ resolution}, but their resolutions will still be
insufficient to identify lensed arcs. The only instrument that can
currently provide sub-arcsecond resolution in submm (at $890~\mu$m) is
the SMA\footnote{The Submillimeter Array in Hawaii}.
However, the tight correlation between radio synchrotron and FIR
emission observed in star-forming galaxies \citep{VA73.1,HE85.1},
provides an alternative way to obtain high resolution images of SMGs.
Commonly referred to as "the FIR/radio correlation", it covers about
five orders of magnitude in luminosity \citep{CO92.1,GA02.1} out to
$z\sim 3$ \citep{KO06.1,VL07.1,IB08.1,MI09.1}. The standard model
about its nature considers that both emissions are caused by massive
star formation: While young massive stars produce UV radiation that is
re-emitted in the FIR by the surrounding dust, old massive stars
explode as supernovae, producing electrons that are accelerated by the
galactic magnetic field and generate the observed radio synchrotron
emission \citep{HA75.1,HE85.1}. Therefore, given the possible common
physical origin of both emissions, radio interferometric observations
can be used as a high-resolution proxy for the rest-frame FIR emission
of high-$z$ galaxies observed in the submm.
The advent of ALMA\footnote{The Atacama Large Millimeter Array in
Chile} will open a new window into mm/submm astronomy at sub-arcsecond
resolution and sub-mJy sensitivity, allowing the detection of resolved
gravitational arcs produced by SMGs. Although its small instantaneous
field of view (FOV) severely limits ALMA's survey capability, a 25
meter submm telescope (CCAT\footnote{Cornell Caltech Atacama
Telescope}) is going to be built on a high peak in the Atacama
region to provide wide field images ($\sim 400$ arcmin$^2$)
with a resolution of $\sim 3.5\arcsec$ at $350~\mu$m. With the
combined capabilities of both instruments, arc statistics studies in
the submm might be possible.
At the same time, radio interferometry is also experiencing
major technological improvements. In particular, the
VLA\footnote{The Very Large Array in New Mexico} and
MERLIN\footnote{The UK Multi-Element Radio Linked Interferometer
Network} are currently undergoing major upgrades which will boost
their sensitivities by factors of $10-30$ and dramatically improve their
mapping capabilities. The new versions of these arrays
(\emph{e}-MERLIN and EVLA) will be fully operational in 2010 and 2012
respectively. In order to assess the prospects for the study of
gravitationally lensed arcs at submm and radio wavelengths, in this
work we report detailed theoretical predictions about the abundance of
arcs produced by the SMG population at $850~\mu$m and 1.4~GHz.
The paper is organized as follows. In Section
\ref{sct:statistics}, we introduce all the relevant quantities that
are necessary to derive the total number of arcs detectable on the
sky. In Section \ref{sct:general} we present and discuss all the
observational information about SMGs that is required for the
subsequent strong lensing analysis: morphology, redshift distribution
and number counts. A description of our cluster population model and
the way in which the abundance of large arcs is computed is given in
Section \ref{sct:model}. The derived arc redshift distributions and
number of arcs are presented in Section \ref{sct:results}, while in
Section \ref{sct:relations} we discuss how these relate to previous
findings in the literature. A summary and conclusions are presented in
Section \ref{sct:conclusions}.
The adopted cosmology corresponds to the standard $\Lambda$CDM model with cosmological parameters inferred from the WMAP-$5$ data release in conjunction with type Ia supernovae and baryon acoustic oscillation datasets \citep{DU09.1,KO09.1}, namely $\Omega_{\mathrm{m},0} = 0.279$, $\Omega_{\Lambda,0} = 0.721$, $\sigma_8 = 0.817$ and $H_0 = h 100$ km s$^{-1}$ Mpc$^{-1}$,
with $h = 0.701$.
\section{Strong lensing statistics}\label{sct:statistics}
The choice of the best parameters to be used in order to characterize
the morphological properties of long and thin gravitational arcs is
still a matter of debate. In this work, we adopted the quite popular
choice of the length-to-width radio $d$, which has to be
larger than a certain threshold $d_{0}$ (usually $7.5$ or $10$) in
order to consider an object as a giant arc.
Given a set of background sources placed at redshift $z_\mathrm{s}$,
the efficiency of the galaxy cluster population to produce arcs with
length-to-width ratio $d \ge d_0$, is parametrized by the optical
depth
\begin{equation}\label{eqn:tau}
\tau_{d_0}(z_\mathrm{s}) = \frac{1}{4\pi D_\mathrm{s}^2} \int_0^{z_\mathrm{s}}\int_0^{+\infty} n(M,z)\sigma_{d_0}(M,z)dM dz,
\end{equation}
where $D_\mathrm{s}$ is the angular diameter distance to the source
redshift and $n(M,z)$ is the total number of clusters present in the
unit redshift around $z$ with mass in the unit interval around
$M$. The cross section $\sigma_{d_0}(M,z)$ is the area of the region
on the source plane where a source has to lie in order to produce (at
least) one gravitational arc with $d \ge d_0$, for a single cluster
with mass $M$ at redshift $z$. This depends in general on the cluster
structure, the source properties, and the redshifts of both the
cluster and the source. Since in realistic situations sources are
distributed at different redshifts, we can calculate the average
optical depth by integrating $\tau_{d_0}(z_\mathrm{s})$ over the
source redshift distribution $p(z_\mathrm{s})$,
\begin{equation}\label{eqn:av}
\bar{\tau}_{d_0}(z_\mathrm{s}) = \int_0^{z_\mathrm{s}}p(\xi)\tau_{d_0}(\xi)d\xi.
\end{equation}
In this way, the total number of arcs with length-to-width
ratio $d \ge d_0$ can be calculated as \citep{BA98.1}
\begin{equation}
\mathcal{N}_{d_{0}} = 4\pi N~\bar{\tau}_{d_0},
\end{equation}
where $N$ is the observed surface density of sources, and
$\bar{\tau}_{d_0} = \bar{\tau}_{d_0}(+\infty)$ is the total average
optical depth (i.e., the average optical depth with the integral extending to
all possible source redshifts). Therefore, the number of arcs produced by a given population of
background sources can be calculated by providing the following
observational constraints: (i) the characteristic source shape and
size, which is necessary to compute the cluster cross sections
$\sigma_{d_0}(M,z)$, (ii) the source redshift distribution $p(z_{s})$,
which is necessary to evaluate the optical depth $\bar{\tau}_{d_0}$,
and (iii) the cumulative source number counts $N$.
\section{Characteristics of the SMG population}\label{sct:general}
\subsection{Source shape and size}\label{sct:shape}
In strong lensing statistics studies, it is customary to characterize
the size of elliptical background sources using the equivalent
effective radius $R_\mathrm{e} \equiv \sqrt{ab}$, which is the radius
of a circle that has the same area of the elliptical source with
semi-major axis $a$ and semi-minor axis $b$. In addition, the
orientation of sources is randomly chosen, and to account for the
different source shapes the value of the axis ratio $b/a$ is
considered to vary within a certain interval. The typical values of
these parameters used in optical ray-tracing simulations are
$R_\mathrm{e} = 0.5\arcsec$ and $b/a$ randomly varying in the interval
$[0.5,1]$ \citep{ME00.1,ME03.1,ME05.1,FE06.1}.
Due to the low resolution of submm single-dish observations (e.g.,
FWHM $\sim 15\arcsec$ for SCUBA at $850\mu$m), current estimates of
the typical size of SMGs are based on continuum radio
\citep{CH04.1,BI08.1} and millimeter \citep[e.g.][]{TA06.1}
interferometric observations of small source samples. In particular,
Biggs \& Ivison (BI08 hereafter) combined $1.4$~GHz data from the VLA
and MERLIN to produce high resolution radio maps of $12$ SMGs detected
in the Lockman Hole. The deconvolved sizes derived from these radio
maps (obtained by fitting each map with an elliptical Gaussian) are
consistent with \cite{CH04.1} (see also \citealt{MU05.1}) and
\cite{TA06.1}.
\begin{figure}[t]
\includegraphics[width=\hsize]{Figures/axisDistribution}\hfill
\caption{Effective radii and axis ratios derived for the $1.4$~GHz
radio counterparts of the $12$ SMGs presented in \cite{BI08.1}. The red
points correspond to the $890~\mu$m counterpart of GN20 detected with
the SMA, whose size was derived by fitting a Gaussian (triangle) and
an elliptical disk (square) to the data \citep{YO08.1}. Error bars
are computed through standard error propagation.}
\label{fig:ad}
\end{figure}
\begin{figure*}[ht!]
\includegraphics[width=0.5\hsize]{Figures/widthDistribution}\hfill
\includegraphics[width=0.5\hsize]{Figures/widthDistribution_10}
\caption{Arc width probability distributions derived from a set of
sources at $z_\mathrm{s}=1$ that were lensed by (the three projections of)
the most massive cluster of the \emph{MareNostrum} simulation
at $z=0.3$. The two panels illustrate the difference between selecting
arcs with a length-to-width ratio $d \ge d_0 = 7.5$ (left) and $d \ge
d_0 = 10$ (right). The black histograms were produced using the
typical source size of SMGs at 1.4~GHz and $850~\mu$m assumed in this
work ($R_\mathrm{e} = 0.25\arcsec$ and $b/a$ randomly varying in the
interval $[0.3,1]$). The blue histograms correspond to optical sources
as usually described in lensing simulations ($R_\mathrm{e} =
0.5\arcsec$ and $b/a \in [0.5,1]$). The red dashed region shows the
$150$ mas resolution limit of the $e$-MERLIN radio interferometer at
$1.4$~GHz.}
\label{fig:wd}
\end{figure*}
Figure \ref{fig:ad} shows the effective radius and axis ratio for each
of the $12$ radio sources reported in BI08 (black circles). Note that,
although the $b/a$ interval $[0.5,1]$ used in optical lensing
simulations contains 11 out of the 12 radio sources, there are several
error bars that extend below its lower limit. In addition, the optical
effective radius of $0.5\arcsec$ is not suitable to describe
them. Since the source sample is too small (and the error bars rather
large) to derive a reliable size distribution , we decided to use an
effective radius close to the median of the sample. As a result, the
size of the 1.4~GHz radio emission produced by the SMG population has
been characterized in the following by $b/a$ randomly varying within
$[0.3,1]$ and $R_\mathrm{e} = 0.25\arcsec$.
Since SMGs seem to follow the FIR-radio correlation
\citep[e.g.][]{KO06.1}, their emission at both 1.4~GHz and $850~\mu$m
is expected to be associated with massive star formation. This means
that, as a first approximation, the same morphological parameters can
be used to characterize the sizes and shapes of SMGs at radio and
submm wavelengths. This choice of parameters for the submm emission is
also consistent with the recent SMA observations presented by
\cite{YO08.1}, which have partially resolved the $890~\mu$m emission
of a SMG (GN20) for the first time (see Figure \ref{fig:ad}).
If we wish to characterize gravitational arcs via their
length-to-width ratio and make comparisons between observations and
theoretical predictions in an unbiased way, it is crucial to resolve
their width. To address if the resolution provided by radio and submm
instruments could be an issue for arc statistics studies, we investigated the width distribution of arcs produced by a population
of sources that is being lensed by a galaxy cluster. In particular, we
used the most massive lensing cluster at $z=0.3$ from the
\emph{MareNostrum} cosmological simulation \citep{GO07.1}, a large
$n$-body and gas-dynamical run, whose lensing properties recently have been studied by Fedeli et al. (2009, in preparation). The mass
distribution of this cluster was projected along three orthogonal
directions, for which we derived deflection angle maps by standard
ray-tracing techniques \citep{BA94.1}. Then, a set of sources at
$z_\mathrm{s} = 1$ (source redshift at which the lensing efficiency
peaks for lenses at $z \sim 0.3$) with $R_\mathrm{e} = 0.25\arcsec$
and axis ratios randomly varying in the interval $[0.3,1]$ was lensed
through the three projections. As usual in this procedure, the sources
are preferentially placed near the lensing caustics following an
iterative procedure to enhance the probability of the production of
large arcs. The bias introduced by this artificial increase of sources
is corrected for by assigning a weight $\le 1$ to each source, which is
reduced at each new iteration step (see \citealt{MI93.1,BA94.1,BA98.1}
for further details).
The black histogram shown in Figure \ref{fig:wd} corresponds to the
width distribution of arcs derived from this simulation. For
comparison, we have also included the corresponding distribution
derived from the parameters used in optical lensing simulations (blue
histogram). The two panels illustrate the difference between selecting
arcs characterized by $d \ge d_0$ with $d_0 = 7.5$ (left) and $d_0 =
10$ (right). As expected, reducing the source equivalent size produces
a decrease in the width of lensed images. Note also that the behavior
of the distributions is practically independent of the minimum
length-to-width ratio used to select the arcs. The most important
feature, however, is that both distributions drop to zero for widths
below $\sim 0.2\arcsec$, meaning that virtually no radio/submm (or
optical) arcs have widths smaller than that value. At 1.4~GHz, $\sim
0.2\arcsec$ resolution is already accessible with
MERLIN/\emph{e}-MERLIN ($\sim0.15\arcsec$). Therefore, resolving the
width of long and thin images for arc statistics studies is in
principle already possible at radio wavelengths. However, until the
advent of ALMA, the $\sim 0.75\arcsec$ resolution of the SMA at
$950~\mu$m will only be able to resolve a very small fraction of
arcs produced by the most extended SMGs.
\begin{figure*}[ht!]
\includegraphics[width=0.5\hsize]{Figures/zDistribution}\hfill
\includegraphics[width=0.5\hsize]{Figures/cumulative}
\caption{\emph{Left panel}. Redshift distribution of SMGs derived
from the spectroscopic sample of \cite{CH05.1} (cyan histogram) and
the photometric sample of \cite{AR07.1} (dark-grey histogram). The curves
SPZ and PHZ correspond to the best fits provided by Eq. (\ref{eqn:zd})
to the spectroscopic and photometric data, respectively. The curve CHM
corresponds to the best Gaussian fit to the simple evolutionary model
for SMGs used in CH05 (as quoted in CH05), normalized to the redshift
interval $[0,+\infty]$. Note that the binning adopted here is
different from the one used in CH05, so the "redshift
desert" in the redshift interval $z=1.2-1.8$ is not evident. However, changing
the binning of the histogram changes little of the subsequent
fit. \emph{Right panel}. The cumulative distributions corresponding
to the fits reported on the left panel, calculated by using
Eq. (\ref{eqn:pz_cum}).}
\label{fig:zd}
\end{figure*}
Finally, we would like to stress two points related to the choice of
source morphological parameters presented in this section. First, the
most luminous SMGs seem to be the result of merger processes (e.g.,
\citealt{GR05.1,TA06.1}), hence it is unlikely that their true shape
is elliptical, as we assumed. However, if a merging source is lensed
as an arc at a particular wavelength, irregularities in its shape and
internal structure will not significantly change the global
morphological properties of the arc, like the length-to-width
ratio. What can happen is that the length-to-width ratio of an arc
changes with wavelength because the emitting region of the source at
those wavelengths have different sizes. For some of the wavelengths
the source might even look like a group of small isolated emitting
regions instead of a continuous one, which means that in the image
plane it will be observed as a group of disconnected multiple images
instead of a full arc. A very illustrative example of this scenario is
SMM J04542-0301, an elongated region of submm emission which seems to
be associated with a merger at $z=2.9$ that is being lensed by the
cluster MS0451.6-0305 (\citealt{BO03.1,BE07.1}; Berciano Alba et
al. 2009, in press). Until more complete information about
the average structure of SMGs becomes available, we believe our
approach to be the best that can be done.
Second, since the radio sources studied by BI08 are brighter than
$50~\mu$Jy, the typical size derived from this sample might be
different from the one that could be derived from fainter SMGs. Note,
however, that the change of the cluster cross section with source size
has a very small slope for $R_\mathrm{e}$ between 0.2$\arcsec$ and 1.5$\arcsec$
\citep{FE06.1}. Therefore, deviations from $R_\mathrm{e}=0.25\arcsec$ within this
interval (which is two times larger than the interval that contains
the sizes measured by BI08 and \cite{TA06.1}, see Figure 6 of BI08) will
have a negligible effect on the derived number of arcs.
\subsection{Source redshift distribution}\label{sct:redshift}
A key point in trying to estimate the abundance of strong lensing
features that are produced by the galaxy cluster population is the
redshift distribution of background sources. Distributions peaked at
higher redshift, or with a substantial high-$z$ tail, will have in
general more potential lenses at their disposal, and hence will produce
larger arc abundances as compared to low-$z$-dominated
distributions. In addition, the lensing efficiency for individual
deflectors is also an increasing function of the source redshift.
The most robust estimate of the redshift distribution of SMGs to date
is based on the $\sim$ 15~arcmin$^2$ SCUBA survey carried out by
\cite{CH05.1} (CH05 hereafter). Radio observations were used to
pinpoint the precise location of the submm detections, allowing the
identification of optical counterparts that could provide precise
spectroscopic redshifts. The final sample is composed of $73$ SMGs
with $850~\mu$m flux densities $>3$~mJy and radio counterparts with
flux densities at $1.4$~GHz $>30~\mu$Jy.
On the other hand, the SCUBA Half-Degree Extragalactic Survey (SHADES,
\citealt{MO05.1,VA05.1}) is the largest ($720$ arcmin$^2$) $850~\mu$m
survey to date\footnote{The largest SMG survey to date (0.7
deg$^{2}$) has being carried out at $1.1$ mm with the AzTEC continuum
camera mounted on the JCMT \citep{AU09.1}}. From their catalog of 120
SMGs, 69 have robust radio counterparts with $S_{850~\mu m} \geq$
3~mJy and $S_{1.4~\mathrm{GHz}} \geq$ 20~$\mu$Jy. Photometric
redshifts for this sub-sample were calculated by \cite{AR07.1} (AR07
hereafter) by fitting Spectral Energy Distribution (SED) templates to
the available photometry at $850~\mu$m and $1.4$~GHz, including upper
limits at $450~\mu$m (additional photometry at millimeter wavelengths
was also used for $13$ out of the $69$ sources). The histogram of the
resulting photometric redshift distribution, together with the
spectroscopic one reported by CH05, are shown in Figure
\ref{fig:zd}. The accuracy on the photometric
redshifts derived by AR07 is $\Delta z \sim 0.65$. Note
that the requirement for a radio counterpart biases these two redshift
distributions against SMGs with $z > 3$, due to the less favorable
K-correction in the radio compared with submm. Using a simple
evolutionary model, CH05 estimated that the fraction of SMGs
($S_{850~\mu m} >$ 5~mJy) that is missing between $z \sim 2.5$ and $z
\sim 5$ in their spectroscopic redshift distribution is $\sim 35\%$, a
number that is in agreement with the fraction of radio-unidentified
SMGs reported in \cite{IV02.1,CH03.1} and the SHADES survey
(AR07). The model evolves the local FIR luminosity function in
luminosity with increasing redshift following the prescription of
\cite{BL02.1}. To account for the dust properties of SMGs, it also
includes a range of SED templates that have been tuned to fit their
observed submm flux distribution \citep{CH03.1,LE05.1}.
\begin{figure*}[th!]
\includegraphics[width=0.5\hsize]{Figures/zDistribution_new_RADIO}\hfill
\includegraphics[width=0.5\hsize]{Figures/zDistribution_new_SMM}
\caption{\emph{Left panel}. Histogram of the redshift distribution
of SMGs derived by \cite{CH05.1}, corrected for spectroscopic
incompleteness. This correction was implemented by interpolating the CH05
distribution in the region of the redshift desert (M.
Swinbank, private communication). The SPZC line indicates the best
Gaussian fit to the histogram. The blue solid line corresponds to the
redshift distribution of SMGs with $S_{850~\mu m} >$ 5~mJy and $S_{\rm
1.4~GHz} >$ 30~$\mu$Jy predicted by the semi-analytic model presented
in \cite{SW08.1}. The SPZ curve presented in Figure \ref{fig:zd} has
being included for comparison. \emph{Right panel}. The same
histogram, also corrected for radio incompleteness using CH05
evolutionary model. The blue solid line corresponds to the redshift
distribution of SMGs with $S_{850~\mu m} >$ 5~mJy predicted in
\cite{SW08.1}. The CHMC line indicates the best Gaussian fit to the
histogram. The SPZ and CHM curves presented in Figure \ref{fig:zd} have
being included for comparison.}
\label{fig:z_comparison}
\end{figure*}
In order to investigate the effect of this high-$z$ tail on the
predicted number of arcs, we used three different analytic expressions
to characterize the redshift distribution of SMGs in our calculations
(see Figure \ref{fig:zd}). One of them (CHM) corresponds to the best
Gaussian fit to the distribution predicted by the CH05 evolutionary model,
as quoted in CH05. The other two (SPZ and PHZ) were obtained by
fitting the CH05 and AR07 histograms with the following analytic
function, usually adopted for optical strong lensing studies
\citep{SM95.1},
\begin{equation}\label{eqn:zd}
p(z_\mathrm{s}) = \frac{\beta}{z_0^3 \Gamma(3/\beta)} z_\mathrm{s}^2 \exp \left[ -\left( \frac{z_\mathrm{s}}{z_0} \right)^\beta \right],
\end{equation}
where $\Gamma(x)$ is the complete Euler-gamma function evaluated at
$x$, $z_0$ is a free parameter that broadly selects the position of
the peak, and $\beta$ is another free parameter that defines the
extension of the high-redshift tail. Note that, unlike the histograms, this function drops to zero at low redshift. However,
the contribution to the global lensing optical depth coming from
sources at $z \lesssim 1$ is likely negligible, due to the geometric
suppression of lensing efficiency (see also the subsequent discussion
in Section \ref{sct:results}). The resultant best-fitting parameters
of these three functions are summarized in Table \ref{tab:par}.
\begin{table}[]
\caption{Parameters of the redshift distributions presented in
Figures \ref{fig:zd} and \ref{fig:z_comparison}.}
\label{tab:par}
\begin{center}
\begin{tabular}{clcccc}
\hline\hline
\noalign{\smallskip}
Nickname & $z_0^{(1)}$ & $\beta^{(1)}$ & \emph{rms$^{(2)}$} & $z_\mathrm{p}^{(3)}$ \\
\noalign{\smallskip}
\hline
\noalign{\smallskip}
SPZ & $1.99$ & $2.81$ & $-$ & $1.76$ \\
PHZ & $2.51$ & $13.3$ & $-$ & $2.18$ \\
CHM & $-$ & $-$ & $1.30$ & $2.30$ \\
\noalign{\smallskip}
\hline
\noalign{\smallskip}
SPZC$^{(4)}$ & $-$ & $-$ & $0.64$ & $2.05$ \\
CHMC$^{(4)}$ & $-$ & $-$ & $0.81$ & $2.25$ \\
\hline
\noalign{\smallskip}
\multicolumn{5}{l}{$^{(1)}$ best fit parameters of Eq. (\ref{eqn:zd}).}\\
\multicolumn{5}{l}{$^{(2)}$ width of the best Gaussian fit.}\\
\multicolumn{5}{l}{$^{(3)}$ peak position of the distribution.}\\
\multicolumn{5}{l}{$^{(4)}$ the parameters associated with these}\\
\multicolumn{5}{l}{distributions, provided by M. Swinbank,}\\
\multicolumn{5}{l}{were misquoted in SW08 and CH05.}\\
\end{tabular}
\end{center}
\end{table}
The SPZ curve constitutes a good representation of CH05 data not
corrected for spectroscopic incompleteness\footnote{Due to the lack of
strong spectral features falling into the observational windows, it is
not possible to measure the spectroscopic $z$ of sources in the range
$z=1.2-1.8$ (the so called "redshift desert")}. The PHZ curve, on the
other hand, does not describe the AR07 distribution very well, failing
to reproduce its $z\sim3-4.5$ tail. This is a consequence of how the
function in Eq. (\ref{eqn:zd}) is constructed. In particular, to
accommodate the low-$z$ part of the photometric histogram in Figure
\ref{fig:zd}, the function needs to raise very steeply and hence, by
construction, it must also drop steeply at high-$z$. Despite the function
in Eq. (\ref{eqn:zd}) not being a good choice for fitting the
photometric data, we nevertheless included the PHZ curve in our
calculations because it highlights the consequence of choosing a
distribution that is truncated at $z\sim3$. Finally, the CHM curve
allows us to predict the number of expected arcs if the CH05 histogram is
corrected for spectroscopic incompleteness and high-z SMGs without
radio counterparts (radio incompleteness). We stress that at this
stage we are not interested in using the best possible representation
for the true source redshift distribution, but only to adopt a few
motivated choices that broadly cover the range of realistic
possibilities, in order to check the corresponding effect on the
abundance of arcs.
To show more clearly the different behavior in the high-redshift tail of our three choices, we
present their cumulative distributions in the right panel of
Figure \ref{fig:zd}, namely
\begin{equation} \label{eqn:pz_cum}
P(z) = \int_0^z p(\xi)d\xi.
\end{equation}
In particular, when $P(z) \simeq 1$ for SPZ, at $z \sim 3.5$, we still
have $P(z) \simeq 0.8$ for CHM, implying that $\sim 20\%$ of the
SMGs still can be found at $z \gtrsim 3.5$ using the latter distribution.
In order to further show that this family of three functions cover all
the reasonable possibilities, we have compared them with the
predictions of one of the semi-analytical models that have been
developed to explain the properties of SMGs (see \citealt{SW08.1} and
references therein). The histogram in the left panel of Figure
\ref{fig:z_comparison} shows CH05 data corrected for spectroscopic
incompleteness. Note that the SPZ curve is very consistent with the
semi-analytic model prediction (SWR), although both curves peak at
slightly lower redshift ($\Delta z_\mathrm{p}=0.3$) than the best
Gaussian fit of the histogram (SPZC). However, as pointed out in
\cite{SW08.1} (SW08 hereafter) , the CH05 distribution is expected to
be uncertain by at least $\Delta z \sim 0.25$, which is the
field-to-field variation between the seven sub-fields in the CH05
sample due to cosmic variance. Therefore, we can consider SPZ as a
good representation of the current observations, despite the fact that
it comes from a histogram that was not corrected for spectroscopic
incompleteness.
After the computations of the number of arcs were completed, we
became aware of the fact that the parameters quoted in CH05 for the
best Gaussian fit to their simple evolutionary model (CHM, see Table
\ref{tab:par}) were incorrect (M. Swinbank, private
communication). As it is shown in the right panel of Figure
\ref{fig:z_comparison}, the CHM distribution has a higher-$z$ tail as
compared to the correct Gaussian fit (CHMC) and the prediction of the
semi-analytical model (SWS). Since the true high-$z$ tail of the
redshift distribution of SMGs is expected to be in between the cases
considered in our calculations (SPZ, PHZ and CHM), and (as it will be
discussed in Section \ref{sect:arc_results}) the final effect of the
source redshift distribution on the number of arcs is small given the
many uncertainties involved, we considered it unnecessary to repeat the
calculations for CHMC.
\subsection{Source number counts}\label{sct:counts}
The final ingredient needed to estimate the number of arcs produced by
SMGs is the observed surface density of this source population, both
at $1.4$~GHz and $850~\mu$m. Let $n_0(S)$ be the differential number counts, defined as the surface
density of unlensed galaxies per unit flux density $S$. Integrating
$n_0(S)$ over all fluxes above a given threshold, we obtain the
respective cumulative number counts
\begin{equation}\label{eqn:cum}
N_0(S) \equiv \int_S^{+\infty} n_0(\xi) d\xi.
\end{equation}
Let $\mu$ be the lensing-induced magnification of images on the
lens plane, and $\mu_+ \equiv |\mu|$. If $P(\mu_+|d_0)$ is the
magnification probability distribution for sources that are imaged
into arcs with $d \ge d_0$, then the magnified differential number
counts can be calculated as \citep{BA01.1}
\begin{equation}
n(S) = \int_0^{+\infty} n_0\left( \frac{S}{\mu_+} \right) \frac{P(\mu_+|d_0)}{\mu_+^2} d\mu_+.
\end{equation}
Hence, the magnified cumulative number counts read as
\begin{equation}\label{eqn:mag}
N(S) \equiv \int_S^{+\infty} n(\xi) d\xi = \int_0^{+\infty} N_0\left( \frac{S}{\mu_+} \right) \frac{P(\mu_+|d_0)}{\mu_+} d\mu_+.
\end{equation}
As can be seen in Eq. (\ref{eqn:mag}), the lensing magnification bias
has a twofold effect. On one side, sources that would be too faint to
be detected without the action of lensing are amplified, and hence the
respective images are brought above the detection threshold. On the
other side, the unit solid angle is stretched by lensing
magnification, implying that the number density of sources is
decreased. Which one of these two effects wins depends on the local
slope of the unmagnified cumulative number counts. In particular, if
$N_0(S) \propto S^{-\alpha}$ and $\alpha > 1$, the number density of
sources will be increased, while if $\alpha < 1$ it will be
decreased. It should be noted that, while for the unmagnified
counts $N_0(S)$ the flux density is derived by integrating the surface brightness over the
area of the source, for the magnified counts $N(S)$ the integral is performed over the area of the resulting arc.
Since our main motivation was to provide predictions for the abundance
of giant arcs to be detected in surveys carried out with future
instruments, we needed to provide the predicted number of arcs as a
function of the surface brightness, instead of flux density. The
reason is that we are working under the assumption that arcs are
resolved structures, and therefore they are observed as extended
objects. Under these circumstances, the flux integrated over the
resolution element of the instrument (seeing, PSF, pixel or beam) is
no longer the total flux of the source (as in the case of unresolved
sources), and it may therefore be below the limiting flux although the
arc as a whole is not. In other words, arc detectability under these
circumstances is not limited by the flux density but rather by the
surface brightness.
In order to take this into account, we had to convert the observed
number counts as a function of flux density into number counts as a
function of surface brightness. Assuming that the size of sources
is given by $R_\mathrm{e}$, and that the surface brightness is
constant across it, then $N_0(B) = N_0(S/\pi R_\mathrm{e}^2)$. Note
that, since the surface brightness is not affected by lensing, the
magnification bias will manifest itself only through the solid angle
stretching. Therefore, the cumulative magnified number counts (as a
function of surface brightness) can be written as
\begin{equation}\label{eqn:mag_B}
N(B) = N_0(B)\int_0^{+\infty} \frac{P(\mu_+|d_0)}{\mu_+} d\mu_+.
\end{equation}
Among other things, this implies that the magnification bias will
always decrease the cumulative number counts, irrespective of the
shape of the unmagnified ones.
In the following we used the magnification distribution given by
\cite{FE08.1}, which is represented by the superposition of two
Gaussians. In particular, we adopted the $P(\mu_+|d_0)$ function for
$d_0 = 10$, but the result is virtually the same also for the case
$d_0 = 7.5$. Note however, that this (conditional) magnification
distribution was computed for a background population of sources that
have different morphologies than SMGs (see Section
\ref{sct:shape}). In principle, the bimodality of the magnification
distribution is expected to be preserved because it only depends on
the caustic structure \citep{LI05.1}, but it can be affected by the
source morphology in two opposite ways. On one hand, since SMGs are
smaller than in \cite{FE08.1}, we expect large arcs to form closer to
the critical curves, and therefore to have larger magnifications on
average. On the other hand, the fact that SMGs are more elongated will
favor the formation of large arcs in regions of lower
magnification. Given the uncertainties in other parts of the
calculation, we consider that the use of a magnification distribution
derived for optical sources will have a marginal effect on the derived
number of arcs produced by SMGs. For a comprehensive review of the
many effects that could affect the estimation of arc abundances by
galaxy clusters, see the discussion in \cite{FE08.1}.
\subsubsection{Submm number counts}
For the latest and most complete estimate of the submm number counts
at $850~\mu$m we refer to \cite{KN08.2} (hereafter KN08), who carried out a
combined analysis of the counts derived from the
Leiden SCUBA Lens Survey (LSLS) and the SHADES survey. With
an area of 720 arcmin$^2$, the SHADES survey is the largest
blank-field submm survey completed to date, and therefore the least
affected by cosmic variance. It provides the best constraints for the
submm number counts in the flux density range $2-15$ mJy
\citep{CO06.1}. On the other hand, the LSLS survey targeted
$12$ galaxy cluster fields which cover a total area of $71.5$
arcmin$^2$ in the image plane. It provides the deepest constraints at
the faint end of the submm counts ($0.11$~mJy, after correcting for
the lensing magnification). In their analysis, KN08 used two functions
to characterize the combined differential number counts from both
surveys: A double power-law,
\begin{equation}\label{eqn:dpl}
n_0(S) = \frac{n_{0,*}/S_*}{\left( S/S_* \right)^{\alpha} + \left( S/S_* \right)^{\beta}}
\end{equation}
and a Schechter function \citep{SC76.1},
\begin{equation}\label{eqn:schechter}
n_0(S) = n_{0,*}\left( \frac{S}{S_*} \right)^{\alpha+1} e^{-S/S_*}.
\end{equation}
\begin{figure}[]
\includegraphics[width=1\hsize]{Figures/obsCounts}\hfill
\caption{Comparison between observed and predicted cumulative number
counts. The red and black solid curves corresponds to the
best-fit double power-law (DB) and the best-fit Schechter function
(SB) derived by \cite{KN08.2} for the combined $850~\mu$m cumulative
number counts from the LSLS survey \citep{KN08.2} and the SHADES
survey \citep{CO06.1}. The black dashed line indicates the shallowest
Schechter function consistent with the data of these two surveys
(SM). The blue solid line indicates the cumulative number counts
predicted by the semi-analytic model presented in \cite{SW08.1} for
SMGs with $S_{850~\mu\mathrm{m}} > 5$~mJy. Model predictions for SMGs
with $S_{850~\mu m} > 5$~mJy and $S_{\rm 1.4~GHz} > 30~\mu$Jy, and
SMGs with $S_{850~\mu m} > 5$~mJy and $S_{\rm 1.4~GHz} > 0.5~\mu$Jy
are indicated by the cyan solid and dashed lines, respectively. Note
that the cyan dashed line and the blue solid line are almost
indistinguishable.}
\label{fig:counts_swinbank}
\end{figure}
\begin{table}[t!]
\centering
\caption{Parameters for the $850~\mu$m differential number counts.}
\begin{tabular}{cccccc}
\hline\hline
\noalign{\smallskip}
Name & $S_{*}$ (mJy) & $n_{0,*}^{(4)}$ & $\alpha$ & $\beta$ \\
\noalign{\smallskip}
\hline
\noalign{\smallskip}
DB$^{(1)}$ & $9.6^{+0.3}_{-2.12}$ & $658\pm48$ & $2.12^{+0.14}_{-0.08}$ & $6.22^{+0.51}_{-0.34}$ \\
SB$^{(2)}$ & $4.30\pm0.08$ & $1039\pm69$ & $-2.62\pm0.10$ & $-$ \\
SM$^{(3)}$ & 4.22 & 970 & -2.52 & $-$ \\
\hline
\noalign{\smallskip}
\multicolumn{5}{l}{$^{(1)}$ best fit double power-law function, Eq. (\ref{eqn:dpl}).}\\
\multicolumn{5}{l}{$^{(2)}$ best fit Schechter function, Eq. (\ref{eqn:schechter}).}\\
\multicolumn{5}{l}{$^{(3)}$ shallowest Schechter function consistent with the data.}\\
\multicolumn{5}{l}{$^{(4)}$ expressed in deg$^{-2}$ for DB and in deg$^{-2}$ mJy$^{-1}$ for SB and SM.}\\
\end{tabular}
\label{submm_counts}
\end{table}
\noindent
Moreover, when fitting the observed cumulative number counts, they
added the supplementary constraint that the integrated light well
below $0.1$ mJy should not be higher than the extragalactic background
light \citep{PU96.1,FI98.1}. The resulting best-fit parameters are
summarized in Table \ref{submm_counts}.
\begin{figure*}[th!]
\includegraphics[width=0.5\hsize]{Figures/counts_SMM}\hfill
\includegraphics[width=0.5\hsize]{Figures/countsSB_SMM}\hfill
\includegraphics[width=0.5\hsize]{Figures/counts_RADIO}\hfill
\includegraphics[width=0.5\hsize]{Figures/countsSB_RADIO}
\caption{The cumulative number counts of SMGs at $850~\mu$m (top
panels) and 1.4~GHz (bottom panels), as a function of flux density (left panels)
and surface brightness (right panels). The conversion from flux density into
surface brightness was done assuming that the emission at both submm
and radio wavelengths is homogeneous and have $R_\mathrm{e} =
0.25\arcsec$. Thin lines correspond to $S_{1.4 \mathrm{GHz}} =
S_{850~\mu\mathrm{m}}/50$, while thick lines assume $S_{1.4
\mathrm{GHz}} = S_{850~\mu\mathrm{m}}/100$. The magnification pattern
used to compute the magnified number counts is the one for arcs with
$d \ge d_0 = 10$. SM indicates the shallowest Schechter function that is consistent with the data, while DB represents the best fit double power-law (see the text for more details).}
\label{fig:cc}
\end{figure*}
Figure \ref{fig:counts_swinbank} shows the (unmagnified)
cumulative number counts derived from the best fit Schechter function
(black solid line) and the best fit double power law function (red
solid line) presented in KN08 using Eq. (\ref{eqn:cum}). Note that,
whereas both curves behave almost identically at the bright flux end,
their predictions for the low flux number counts differ by a factor of
$\sim 2.5$ at $0.1$~mJy. Since the low flux tail of the submm counts
dominates the number of SMGs that could potentially be lensed, we
computed predictions for arcs produced by SMGs at $850~\mu$m for the
two following cases: (i) the shallowest Schechter function consistent
with the combined LSLS and SHADES data (also shown in Figure
\ref{fig:counts_swinbank}) and (ii) the best fit double power law
function, hereafter refered to as SM and DB,
respectively. The first one provides the minimum expected number of
arcs consistent with observations, whereas the second one gives the
number of arcs predicted by the best fit to the data (see Table
\ref{submm_counts}).
The cumulative number counts derived for these two cases as a function
of flux density are shown in the top left panel of Figure \ref{fig:cc}, including
the corresponding counts corrected for magnification bias using
Eq. (\ref{eqn:mag}). In the same Figure, the top right panel shows the
cumulative number counts as function of surface brightness. The
corresponding counts corrected for magnification bias (which will be
used to compute the number of arcs) were derived using
Eq. (\ref{eqn:mag_B}).
\subsubsection{Radio number counts}
Figure \ref{fig:counts_swinbank} also shows the cumulative submm
number counts predicted by the SW08 model (blue solid line)
compared with the results from different $\rm 850~\mu$m SCUBA
surveys. Note that, although the model tends to over-predict the
counts at faint fluxes compared with the best fits provided by KN08
(red and black solid lines), it is consistent with the observational
errors. The cyan solid line indicates the predicted counts for SMGs
with radio counterparts assuming $S_{\rm 1.4~GHz} > 30~\mu$Jy. The
fact that its shape is different from the shape of the blue solid
curve is because current observations only detect radio emission from
$\sim 60 \%$ of the observed SMGs. However, if we allow the
sensitivity threshold to go down to the $\mu$Jy level expected for
\emph{e}-MERLIN, the SW08 model indicates that it would be
possible to detect all the radio counterparts of SMGs with
$S_{850~\mu\mathrm{m}} > 5$~mJy (cyan dashed line).
Since SMGs seem to follow the FIR/radio correlation
\citep[e.g.][]{KO06.1}, the $\rm 1.4~GHz$ number counts of SMGs (which
we need to predict the number of radio arcs) could be derived by
scaling the $850~\mu$m number counts introduced in the previous
section (DB and SM). As shown in Figure 7 of CH05, the ratio between
the $850~\mu$m flux density and the $1.4$~GHz flux density shows a
broad scatter (up to one order of magnitude), which is probably a
consequence of the strong influence of the dust temperature on the
SEDs of SMGs. However, most of the points in this Figure are located
between redshift 2 and 3, and have an average $S_{850~\mu\mathrm{m}} /
S_{1.4~\mathrm{GHz}}$ ratio between $50$ and $100$. Therefore, we
decided to use these two scaling factors to derive first order upper
and lower limits of the radio number counts of SMGs. The resultant
cumulative radio number counts are shown in the lower panels of Figure
\ref{fig:cc}. Note that the values of $50$ and $100$ chosen for
the submm/radio flux density ratio are meant to be indicative, since
there are still many sources that display a ratio below $50$ or above
$100$. The reader interested in results given by different values of
this ratio can scale the curves appropriately in the upper panels of
Figure \ref{fig:cc}. Also, exact numerical values can be made
available by the authors upon request.
\section{Strong lensing optical depth}\label{sct:model}
To compute the total optical depth for lensed SMGs, we constructed a
synthetic cluster population composed of $q = 1000$ cluster-sized
dark-matter halos with masses uniformly distributed in the interval
$[10^{14},2.5 \times 10^{15}]~M_\odot h^{-1}$ at $z=0$. Note that it
is not necessary to extract these masses according to the cluster mass
function, since this is already taken into account in
Eq. (\ref{eqn:tau}) by weighting the cross sections with the function
$n(M,z)$. The structure of each cluster is modeled using the NFW
density profile (\citealt{NA95.1,NA96.1,NA97.1}), which constitutes a
good representation of average dark-matter halos over a wide range of
masses, redshifts and cosmologies in numerical $n$-body simulations
\citep{DO04.1}. Several studies of strong lensing and X-ray luminous
clusters also show that these are well fitted by an NFW profile
\citep{SC07.2,OG09.1}. This profile also has the advantage that its
lensing properties can be described analytically \citep{BA96.1}.
To account for the asymmetries of real galaxy clusters, the halos are
assumed to have elliptically distorted lensing potentials. However,
instead of considering a single ellipticity value to describe all the
synthetic cluster lenses, we derived an ellipticity distribution from
a set of numerical clusters extracted from the \emph{MareNostrum}
simulation \citep{GO07.1}. The strong lensing analysis required to
generate this ellipticity distribution was taken from Fedeli et al.
(2009, in preparation), as described in Section \ref{sct:shape}. For
each simulated cluster, the lensing analysis along three orthogonal
projections was performed, computing the cross sections for arcs with
$d \ge d_0 = 7.5$ and sources with $z_\mathrm{s} = 2$. For each of
these projections, we found the ellipticity $e$ of the NFW lens whose
cross section is closest to the cross section of the numerical
cluster, i.e., we found the ellipticity that minimizes the quantity
\begin{equation}\label{eqn:dist}
r(e) = \left|\sigma_{7.5}^{\mathrm{(n)}} - \sigma_{7.5}(e)\right|,
\end{equation}
where $\sigma_{7.5}^\mathrm{(n)}$ is the cross section of the numerical
lens, and $\sigma_{7.5}(e)$ is that of the NFW lens for a given potential ellipticity $e$.
\begin{figure}[t]
\includegraphics[width=\hsize]{Figures/ellDistribution}\hfill
\caption{The distribution of NFW lens ellipticities fitting the cross sections of
a sample of numerical clusters. The red dashed line
represents the best fit log-normal distribution, whose median and
dispersion are labeled in the top-right corner of the plot.}
\label{fig:ed}
\end{figure}
Figure \ref{fig:ed} shows the distribution of the ellipticities that
minimize the quantity $r(e)$ in Eq. (\ref{eqn:dist}) for all clusters
in our numerical analysis. The dashed red line is derived by fitting
the distribution with a log-normal function of the kind
\begin{equation}\label{eqn:lognormal}
p(e)de = \frac{1}{\sqrt{2\pi}\sigma_\mathrm{e}} \exp\left[ -\frac{\left[\ln(e) - \ln(e_0)\right]^2}{2\sigma_\mathrm{e}^2}\right] d\ln(e),
\end{equation}
where the best-fit parameters are $e_0 = 0.31$ and $\sigma_\mathrm{e}
= 0.23$. The ellipticity values used to
characterize the potential of the synthetic NFW cluster lenses were then
randomly extracted from the above distribution.
Elliptical NFW profiles are a good representation
of realistic cluster lenses only when the clusters do not undergo
major merger events \citep{ME03.1}. Since the merger
activity of galaxy clusters is known to have a significant effect on
the statistics of giant arcs \citep{TO04.1,FE06.1}, it has to be taken
into account in the construction of the synthetic cluster
population. For this reason, we used the excursion set
formalism\footnote{Also referred to as the "extended \cite{PR74.1}
formalism"} developed by \cite{LA93.1} (see also
\citealt{BO91.1,SO99.1}) to construct a backward merger tree for each
model cluster at $z = 0$, assuming that each merger is binary
(see discussion in \citealt{FE07.1}). When a merger happens, the event
is modeled assuming that the two merging halos (also described as
elliptical NFW density profiles) approach each other at a constant
speed. The duration of the merger is set by the dynamical timescales
of the two halos (see \cite{FE07.1} and \cite{FE08.1}
for a detailed description of the modeling procedure).
With the synthetic cluster population constructed in this way, the
total average optical depth was derived by computing individual cross sections with the semi-analytic
algorithm developed by \cite{FE06.1}, especially designed to estimate
the strong lensing cross sections of individual lenses in a fast and
reliable way. The optical depth for a discrete set of lenses can be recast as
\begin{equation}\label{eqn:discrete}
\tau_{d_0}(z_\mathrm{s}) = \frac{1}{4\pi D_\mathrm{s}^2} \int_0^{z_\mathrm{s}} \left[ \sum_{i=1}^{q-1} \bar{\sigma}_{d_0,i}(z) \int_{M_i}^{M_{i+1}} n(M,z) dM \right] dz ,
\end{equation}
where the masses $M_i$ ($1 \le i \ne q$) have to be sorted from the
lowest to the highest at each redshift step, and the quantity
$\bar{\sigma}_{d_0,i}(z)$ is defined as
\begin{equation}
\bar{\sigma}_{d_0,i}(z) \equiv \frac{1}{2} \left[ \sigma_{d_0}(M_i,z) + \sigma_{d_0}(M_{i+1},z) \right].
\end{equation}
This effectively means that, for all the clusters with mass
between $M_i$ and $M_{i+1}$, we assume the average cross section of
the model dark-matter halos with masses $M_i$ and $M_{i+1}$. The
algorithm of \cite{FE06.1} for computing strong lensing cross sections
consists of first assuming sources as point-like circles, and then
introducing the effect of source ellipticity according to
\cite{KE01.1}. The source finite size is taken into account by
convolving the local lensing properties over the typical source size.
The total average optical depth is calculated by integrating
Eq. (\ref{eqn:discrete}) over the source redshift
distribution. Effectively, the $p(z_\mathrm{s})$ weighting is avoided
since we assigned individual source redshifts (randomly extracted from
the distribution $p(z_\mathrm{s})$) at each of the $q$ halos in the
cluster sample and evolved their merger trees back in time until the
respective source redshift. Given the large number of synthetic
dark-matter halos used, this approach allows one to omit $p(z_\mathrm{s})$
in Eq. (\ref{eqn:av}) when the redshift integral is discretized.
Despite the fact that the ellipticity distribution used to model the
synthetic cluster population was derived for $d \ge d_0 = 7.5$, the
best fit parameters of Eq. (\ref{eqn:lognormal}) can be used to
compute the cross sections for arcs also with $d_0 = 10$ without
compromising the results. The reason is that, although there might be
a mild dependence of the distribution of lensing ellipticities on
$d_0$, it is the overall caustic structure that defines the abundance
of arcs above a certain $d_0$, regardless of its precise value. In
fact, the criterion used to determine the ellipticity distribution is
based on the similarity between the cross sections of the NFW lens and
the numerical lens, which is an indirect way of comparing the overall
caustic structures produced by both kinds of lenses. To verify this
argument, the ellipticity distribution was re-computed using a
criterion that is directly related to the caustic structure, that is,
by defining the best fitting ellipticity as the one that minimizes the
modified Hausdorff distance\footnote{This parameter constitutes one of
the best ways to quantify the morphological difference between two
sets of points \citep{DU94.1}. See also \citealt{RZ07.1} for a
different application to gravitational lensing.} between the critical
lines of the numerical and NFW lenses. The ellipticity distribution
obtained in this way is very similar to the one depicted in Figure
\ref{fig:ed} ($e_0 = 0.30$, $rms = 0.34$).
The median of the ellipticity distribution derived in this work using
the lensing cross section ($e_0 = 0.31$, see Figure \ref{fig:ed}) is
fully consistent with the one obtained by \cite{ME03.1} comparing the
deflection angle maps ($e \sim 0.3$, using lenses placed at $z \sim
0.3$ and a source population at $z_\mathrm{s} = 1$). Even though these
two criteria are arguably tightly related, the former is a quantity
that is more directly related to observables than the latter, hence it
is reassuring that they give comparable results. In addition, this
result extends the previous one by quantifying the scatter around the
median ellipticity and dealing with lenses that are distributed in
redshift.
\section{Results} \label{sct:results}
\subsection{Arc redshift distribution }
\begin{figure*}[t]
\includegraphics[width=0.5\hsize]{Figures/diffOpticalDepth}
\includegraphics[width=0.5\hsize]{Figures/opticalDepth}\hfill
\caption{\emph{Left panel}. Differential redshift distributions of
SMGs producing large gravitational arcs, corresponding to the
cumulative distributions reported in the right panel. \emph{Right
panel}. The cumulative redshift distributions of SMGs producing radio
arcs with $d \ge d_0 = 10$ for input source redshift distributions SPZ
, PHZ and CHM (see the text for more details). Lines are the best fit
functions given in Eq. (\ref{eqn:zArc}) and Table \ref{tab:zArc},
according to the labels in the plot.}
\label{fig:op}
\end{figure*}
The redshift distribution of arcs with $d \ge d_0$ (arc redshift
distribution hereafter) is expected to provide information about the
redshift distribution of the background source population that is
being lensed. However, it will also be distorted by the fact that the
abundance of massive and compact galaxy clusters evolves with
redshift, and that the lensing efficiency depends on the relative
distances of sources and lens with respect to the observer.
To assess the potential of this approach to gather
information about the intrinsic redshift distribution of SMGs, we
derived the arc redshift distribution associated with each of the
three source redshift distributions used as inputs in our calculations
(see Figure \ref{fig:zd}). This was done by computing, for each input
distribution, the average optical depth
$\bar{\tau}_{d_0}(z_\mathrm{s})$ for several different values of
$z_\mathrm{s}$. That is, we excluded in the computation of the average
optical depth those model clusters (and their respective chain of
progenitors) whose associated source redshifts were $>
z_\mathrm{s}$. The resultant cumulative arc redshift distributions,
obtained after normalizing the optical depth for each $z_\mathrm{s}$
to the total average optical depth $\bar{\tau}_{d_0}(+\infty) =
\bar{\tau}_{d_0}$, are shown in the right panel of Figure
\ref{fig:op}. The lines correspond to the best fit for each
distribution provided by the simple function
\begin{equation}\label{eqn:zArc}
\frac{\bar{\tau}_{d_0}(z_\mathrm{s})}{\bar{\tau}_{d_0}(+\infty)} = 1 - \exp \left( -\frac{z_\mathrm{s}}{z_{\mathrm{s},*}}\right)^\gamma,
\end{equation}
where $z_{\mathrm{s},*}$ indicates where the transition between the extrema $0$ and $1$ occur,
and $\gamma$ indicates how sharp this transition is. The best-fit
parameters for each of the three input source redshift distributions
are summarized in Table \ref{tab:zArc}. The corresponding differential
arc redshift distributions are shown in the left panel of
Figure \ref{fig:op}.
\begin{table}[t!]
\caption{Parameters of the arc redshift distributions shown in Figure \ref{fig:op}.}
\label{tab:zArc}
\begin{center}
\begin{tabular}{ccc}
\hline\hline
\noalign{\smallskip}
$p(z_\mathrm{s})$ & $z_{\mathrm{s},*}$ & $\gamma$\\
\noalign{\smallskip}
\hline
\noalign{\smallskip}
SPZ & $2.64$ & $4.31$ \\
PHZ & $2.31$ & $8.20$ \\
CHM & $3.53$ & $3.53$ \\
\hline
\end{tabular}
\end{center}
\end{table}
Once more, these arc redshift distributions have been shown for arcs
with length-to-width ratio larger than $d_0 = 10$ only. As we verified, since the relative contribution of individual model clusters to the total average optical depth is the same for both $d_0 = 7.5$
and $d_0 = 10$, the resulting arc redshift distribution also does not change significantly between the two choices.
\begin{figure*}[t]
\includegraphics[width=0.5\hsize]{Figures/arcCountsSB_SMM_short}\hfill
\includegraphics[width=0.5\hsize]{Figures/arcCountsSB_SMM}\hfill
\includegraphics[width=0.5\hsize]{Figures/arcCountsSB_RADIO_short}\hfill
\includegraphics[width=0.5\hsize]{Figures/arcCountsSB_RADIO}
\caption{The total number of arcs with $d \ge d_0 = 7.5$ (left panels)
and $d \ge d_0 = 10$ (right panels) that are predicted to be observed
in the whole sky above the surface brightness reported on the
abscissa. Results for each of the three input source redshift
distributions as well as both source number counts adopted in this work are shown, according to the
labels. The two top panels refer to surface brightness at $850~\mu$m,
while the bottom panels refer to $1.4$~GHz. In the bottom panels, thin lines refer to $S_{1.4~\mathrm{GHz}} = S_{850~\mu m}/50$, while thick lines refer to $S_{1.4~\mathrm{GHz}} = S_{850~\mu m}/100$. Please note the difference in scale on the abscissa between top and bottom panels.}
\label{fig:arcCounts}
\end{figure*}
\begin{figure*}[t]
\includegraphics[width=0.5\hsize]{Figures/arcCountsSB_SMM_short_mass}\hfill
\includegraphics[width=0.5\hsize]{Figures/arcCountsSB_SMM_mass}\hfill
\includegraphics[width=0.5\hsize]{Figures/arcCountsSB_RADIO_short_mass}\hfill
\includegraphics[width=0.5\hsize]{Figures/arcCountsSB_RADIO_mass}
\caption{The total number of arcs with $d \ge d_0 = 7.5$ (left panels)
and $d \ge d_0 = 10$ (right panels) that are predicted to be observed
in the whole sky above the surface brightness reported on the abscissa. Only
clusters with mass $M \ge 5 \times 10^{14} M_\odot h^{-1}$ are
included in the calculations. Results for each of the three input
source redshift distributions and both source number counts adopted in this work are shown,
according to the labels. Top panels refer to submillimeter number
counts, while bottom panels refer to radio number counts (notice the
different scale on the horizontal axis). The difference between thin and thick lines is as in Figure \ref{fig:arcCounts}.}
\label{fig:arcCounts_mass}
\end{figure*}
A comparison between Figure \ref{fig:op} and Figure \ref{fig:zd} shows
that, as expected, the arc redshift distributions reflect the general
properties of the source redshift distributions used as input, but
there are also some noteworthy differences between them. For instance,
the arc redshift distribution associated with CHM tends to zero at
very low redshift, unlike in the case of the original CHM distribution. The reason is that low
redshift sources do not produce many arcs, because (i) they have
very few potential lenses at their disposal, and (ii) the lensing efficiency
of those lenses is very low due to geometric suppression. This
results in a lack of low redshift arcs in the distribution, which
shifts its peak to higher redshifts compared with the CHM peak (from
$\rm z_{p}=2.3$ to $\rm z_{p} \sim 3.2$). Similarly, the peak of the arc
redshift distribution corresponding to SPZ is shifted from
$z_\mathrm{p} = 1.76$ to $z_\mathrm{p} \gtrsim 2$.
On the other hand, the arc redshift distribution corresponding to PHZ
is not significantly shifted but visibly narrowed. As in the previous
cases, low-redshift sources are removed from the distribution because
they cannot produce arcs, but the distribution could not shift at
higher redshift because the input source redshift distribution is
immediately truncated at $z_\mathrm{s} \lesssim 3$. In other words,
there is too little room between the drop due to lensing
efficiency and the one due to the cutoff of the input distribution to
allow a significant shift in its peak, and the only possible
consequence for the distribution is to shrink and increase the peak
height in order to preserve the normalization.
In general, it is apparent that the differences between different
source redshift distributions are somewhat enhanced when it comes to
the arc redshift distribution. Therefore, assuming that redshift
information is available for arcs, this approach can in principle be
used to obtain some information about the general characteristics of
the source redshift distribution, although it will probably not allow one to
distinguish between redshift distributions that are very similar.
\subsection{Number of radio and submm arcs} \label{sect:arc_results}
In this section we present and discuss the main results of this work:
the predicted number of arcs produced by SMGs at radio and submm
wavelengths. To that end, we computed the total average optical depth
for each of the three source redshift distributions presented in
Section \ref{sct:redshift} (PHZ, SPZ and CHM), and for arcs with
length-to-width ratio higher than both $d_0 = 7.5$ and $d_0 = 10$.
These quantities were then multiplied by the magnified cumulative
source number counts presented in Section \ref{sct:counts} (SM and
DB), to obtain the arc number counts as function of surface
brightness. The results, extrapolated to the whole sky, are shown in
Figure \ref{fig:arcCounts}. A detailed list with the predicted number
of submm and radio arcs for different sensitivities is presented in
Tables \ref{arcs_submm_all} and \ref{arcs_radio_all}, respectively.
Note that the arc number counts given by the source redshift
distributions SPZ and PHZ are almost indistinguishable on the scale of
Figure \ref{fig:arcCounts}, irrespective of the length-to-width
threshold $d_0$ adopted. As expected, SPZ produces more large arcs
than PHZ because it peaks at higher redshift, but only by a factor of
$\sim 7\%$. The redshift distribution CHM, on the other hand, produces
more large arcs than the other two by a factor of $\sim 2$. Since, as
mentioned in Section \ref{sct:redshift}, the distributions CHM and PHZ
can be considered as upper and lower limits to the true redshift
distribution respectively, we can conclude that the uncertainty
introduced by the redshift distribution in the predicted number of
arcs is less than a factor of two.
In terms of the length-to-width threshold, the number of arcs
predicted for $d_0 = 7.5$ is larger than for
$d_0 = 10$ (as was also expected). However, the ratio
between the number of arcs with $d \ge d_0 = 7.5$ and $d \ge d_0 = 10$
is not exactly equal to the ratio in the respective optical depths, since the
magnification distributions for the two kinds of arcs are also
different (see the discussion in \citealt{FE08.1}).
Finally, when it comes to comparing the results from the two adopted
source number counts (DB and SM), we see that the difference in the
predicted number of arcs is negligible for submm surface brightness
limits greater than $5$~mJy arcsec$^{-2}$. However, at
$B_{850~\mu\mathrm{m}}=0.5$~mJy arcsec$^{-2}$, the function DB
predicts $2$ times more arcs than SM, and the difference becomes a
factor of $5$ for $0.1$~mJy arcsec$^{-2}$. In the radio domain, the
difference between DB and SM is negligible for $B_{1.4 ~\mathrm{GHz}}
= 50~\mu$Jy arcsec$^{-2}$, a factor $\sim 2$ for $10~\mu$Jy
arcsec$^{-2}$, a factor $\sim 3$ for $5~\mu$Jy arcsec$^{-2}$ and a
factor $\sim 8$ for $1~\mu$Jy arcsec$^{-2}$. Therefore, the
uncertainty in the predicted number of arcs is clearly dominated by
the uncertainty of the source number counts at the faint surface
brightness end.
Considering an all-sky submm survey with enough resolution to resolve
individual arcs with $d \ge d_{0}=7.5$ ($\sim 0.2\arcsec$), and a
sensitivity of $B_{850~\mu\mathrm{m}} = 1$ mJy arcsec$^{-2}$, our
calculations predict between $\sim 500$ (PHZ SM) and $\sim 600$ (SPZ
DB) arcs with a signal-to-noise ratio (SNR) larger than
$5$. In the case of $d \ge d_{0} = 10$, the expected number of arcs
would be between $200$ and $250$. If the sensitivity is reduced to
$0.1$ mJy arcsec$^{-2}$, these predictions can vary between $\sim
3400$ and $\sim 8300$ for $d_{0}=7.5$, and between $1400$ and $3600$
for $d_{0}=10$.
In a similar way, an all sky radio survey with a sensitivity of
$B_{1.4 ~\mathrm{GHz}} = 0.1$~mJy arcsec$^{-2}$ would detect between 8
and 50 arcs for $d_{0}=7.5$ (between none and $25$ for $d_{0}=10$) at
SNR $\ge 5$, with the main uncertainty given by the
$S_{850~\mu\mathrm{m}}/S_{1.4 \mathrm{GHz}}$ ratio used to obtain the
radio number counts by scaling the observed submm counts. If the
limiting radio surface brightness is reduced to $\sim 10~\mu$Jy
arcsec$^{-2}$, the predicted number of arcs could be increased to
$\sim 500 - 1300$ for $d_{0}=7.5$ ($200 - 600$ for $d_{0}=10$). In
order to have excellent statistics with a few thousand giant arcs
with SNR $\ge 5$, it would be necessary to go as deep as
$S_{1.4 \mathrm{GHz}} = 1~\mu$Jy arcsec$^{-2}$. The largest
number of arcs is given by the CHM source redshift distribution, which
is about a factor of 2 larger than the number of arcs predicted by SPZ
and PHZ.
It is plausible that future radio and submillimeter surveys of galaxy
clusters would focus on the most massive objects, since the center of
attention of many multiwavelength studies is on X-ray bright
clusters. To roughly evaluate the effect of this kind of selection, we
re-computed the optical depths by including only those clusters in our
synthetic population with mass $M \ge 5 \times 10^{14} M_\odot
h^{-1}$. The resulting arc number counts are presented in Figure
\ref{fig:arcCounts_mass}, where we used the same scale and line types
as in Figure \ref{fig:arcCounts} to ease comparison. The corresponding
numbers of submm and radio arcs predicted for different sensitivities
are listed in Tables \ref{arcs_submm_massive} and
\ref{arcs_radio_massive}, respectively. The most interesting feature
about these new plots is that the relative difference in the arc
number counts produced by the CHM distribution on the one hand, and PHZ
and SPZ on the other, is significantly reduced. This is due to the
fact that massive clusters are found mainly at low redshift, hence
lower-mass higher-redshift lenses, that are accessible only to the CHM
distribution, become unimportant.
The order-of-magnitude reduction in the abundance of giant arcs when
focusing only on clusters with mass $M \ge 5 \times 10^{14} M_\odot
h^{-1}$ is in agreement with the fact that the bulk of the lensing
signal actually comes from low-mass clusters, since the optical depth
is obviously dominated by the lowest mass objects that are capable of
producing a non-vanishing cross sections (see Eq. \ref{eqn:tau}). Note
also that, unlike the previous case, PHZ produces slightly more arcs
than SPZ. This is due to the fact that we are including in the
calculations only low-$z$ clusters, and PHZ actually has more sources
with, e.g., $z_\mathrm{s} > 1$ than SPZ (see Figure \ref{fig:zd}).
Considering again an all-sky submm survey with enough resolution to
resolve individual arcs with $d_{0} = 7.5$ and sensitivity of
$B_{850~\mu\mathrm{m}} = 1$ mJy arcsec$^{-2}$, we predict $\sim 20$
arcs \textbf{with $\rm SNR \ge 5$} (8 if $d_{0}=10$). This number can
increase to $100 - 250$ $(40 - 90)$ if $B_{850~\mu\mathrm{m}} \ge 0.1$
mJy arcsec$^{-2}$. In the case of a radio survey, it would be
necessary to push the limiting flux density down to $\sim 1~\mu$Jy
arcsec$^{-2}$ to detect few hundred arcs (between $40 - 200$ if
$d_{0}=10$).
\section{Comparison with previous work}\label{sct:relations}
The probability of strong gravitational lensing due to background
sources at radio and submm wavelengths has been a poorly studied issue
in the past years. In addition, the few works available in the
literature usually involve cosmological models, deflector mass ranges,
and modeling approaches for the source and lens populations that are
different from the ones used in the present work, making the
comparison between them difficult and often not possible. With this
note of caution, we tried however to make some of these tentative comparisons in
the following. This required us to repeat the calculations in the last
section using the number counts as a function of flux density instead
of surface brightness. The results are shown in Figure
\ref{fig:arcCounts_comparison} only for arcs with $d \ge d_0 = 10$.
\begin{figure*}[t]
\includegraphics[width=0.5\hsize]{Figures/arcCounts_SMM}\hfill
\includegraphics[width=0.5\hsize]{Figures/arcCounts_SMM_mass}\hfill
\includegraphics[width=0.5\hsize]{Figures/arcCounts_RADIO}\hfill
\includegraphics[width=0.5\hsize]{Figures/arcCounts_RADIO_mass}
\caption{The number of arcs with $d \ge d_0 = 10$ predicted to be
observed in the whole sky as a function of the submm flux density at
$850~\mu$m (top two panels) and radio flux density at 1.4~GHz (bottom
two). The left panels refer to all clusters in the sample, while the
right ones shows results when only clusters with mass $M \ge 10^{14}
M_\odot h^{-1}$ are considered. Different line styles and colors refer
to different number count models and source redshift distributions. In
the two bottom panels, the thin lines assume $S_{1.4 \mathrm{GHz}} =
S_{850~\mu \mathrm{m}}/50$, while the thick lines refer to $S_{1.4
\mathrm{GHz}} = S_{850~\mu \mathrm{m}}/100$.}
\label{fig:arcCounts_comparison}
\end{figure*}
\subsection{Submm wavelengths}
Given the poor resolution of current submm instruments, observational
studies of submm arcs have not been possible so far, with only one
submm arc candidate reported until now. This arc is supposed to be the
brightest region of the extended submm source SMM J$04542-0301$,
located in the core of the cluster MS$0451.6-0305$
(\citealt{BO04.1,BE07.1}; Berciano Alba et al. 2009, in
press). However, higher resolution submm observations are required in
order to confirm this hypothesis, and meaningful estimates of the
length and width of this source, unfortunately, cannot yet be done. On
the theoretical side, gravitational lensing of SMGs due to galaxy
clusters was first studied by \cite{BL97.1}, using a circularly
symmetric model of the cluster A2218 and the submm counts predicted by
different galaxy evolution models. More recent studies \citep{CO99.2,
PA09.1} also have been focused on predicting the number of submm
lensed sources, but predictions for the abundance of submm arcs have
never been attempted before.
For instance, in the work of \cite{PA09.1}, the authors employ the
strong lensing analysis of the \emph{Millennium Simulation} performed
by \cite{HI07.1} (see also \citealt{HI08.1}) in order to compute (i)
the average magnification of SMGs as a function of flux density, and
(ii) the contribution to the differential number counts given by
sources with different redshifts and magnifications. Hence, their
results cannot be compared with ours in a straightforward way.
The only work with which we could try a tentative comparison is the
one by \cite{CO99.2} (CO99 hereafter), where the author provides
number counts of (among others) gravitationally lensed submm sources
as a function of their magnification. The clusters were modeled as
Singular Isothermal Sphere (SIS henceforth) density profiles, which
means that the image magnification equals its length-to-width ratio,
as long as sources are circular and point-like. Since the sources that
we are using are not circular, nor point-like, the following
comparison should be taken with caution. The background submm
sources were described by means of the redshift and number
distributions observed in the Hubble Deep Field (HDF). Using a
$\Lambda$CDM cosmology, and considering cluster lenses with $M \ge 8.8
\times 10^{14} M_\odot h^{-1}$, CO99 predicted $\sim 500$ submm
sources in the whole sky with lensing magnification larger than $10$
and $S_{850~\mu m} \ge 2$ mJy.
On the other hand, our results indicate that, if no mass selection is
applied and for $S_{850~\mu m} \ge 2$ mJy, we should find a few
thousand arcs with $d \ge d_0 = 10$ in the whole sky. Restricting the
cluster mass range to $M \ge 5 \times 10^{14} M_\odot h^{-1}$ reduces
the number of arcs to $\sim 100$ at most. Matching the mass range of
CO99 would only reduce the number of predicted arcs even further,
hence being discrepant with CO99 predictions. Assuming that the source
population we are considering is the same, we ascribe at least part of
this disagreement to the fact that CO99 considers a very high
normalization of the power spectrum ($\sigma_8 \simeq 1.2$), which was
based on old studies of the cluster temperature function
\citep{VI96.1}. As shown in \cite{FE08.1}, this results in greater
strong lensing optical depth, and therefore to an over-prediction of
the number of lensed images.
\subsection{Radio wavelengths}
The first observational search for radio arcs in galaxy clusters dates
back to \cite{BA95.1}, where the authors considered a cluster sample
of 46 objects with $z \lesssim 0.3$ observed, among others, at a
wavelength of $20$ cm with a sensitivity of $\sim 1$ mJy. They claimed
a systematic tangential alignment of radio images with respect to the
cluster centers, and concluded that these are arclets or even giant
arcs produced by background flat-spectrum radio sources. While their
resolution was too poor to reliably measure arc
morphological properties, these findings were subsequently questioned
by \cite{AN98.1}, who performed a similar analysis on the
\cite{AB89.1} cluster sample (ACO henceforth) with sources taken from
the FIRST (Faint Images of the Radio Sky at Twenty-centimeters)
catalogue \citep{WH97.1}, finding no evidence for a preferential
alignment of radio images in the core of massive galaxy clusters. They
also report a rough estimate of the abundance of strong lensing events
that should be seen in ACO clusters, finding that for a statistically
significant detection, the limiting flux density should be lowered to
$\lesssim 0.1$ mJy, in agreement with previous, more detailed
estimates \citep{WU93.1}. More recently, \cite{PH01.1}
searched for strong lensing events with large angular separations in
the FIRST catalog, but none of their candidates turned out to be a
real gravitational lens.
About $40\%$ of the clusters included in the sample of \cite{BA95.1}
have velocity dispersion $\sim 1000$ km s$^{-1}$. Assuming that cluster
galaxies have the same velocity dispersion of the dark-matter
particles (\citealt{GA04.1,BI06.1,FA06.1}, see however
\citealt{CO00.1}), and adopting the simulation-calibrated scaling
relation of \cite{EV08.1}, this corresponds to a mass of at least
$\sim 8 \times 10^{14} M_\odot h^{-1}$. The rest of their clusters
should have a mass $\gtrsim 4 \times 10^{14} M_\odot h^{-1}$. Assuming
a limiting flux of $\sim 1$ mJy at $1.4$~GHz, our predictions in
Figure \ref{fig:arcCounts_comparison} give $\lesssim 100$ giant radio
arcs in the whole sky when the entire cluster population is
considered, and only $\lesssim 1$ inside clusters with mass $M \ge 5
\times 10^{14} M_\odot h^{-1}$. Therefore, we find it quite
unlikely that the detection claimed by \cite{BA95.1} is due to the
radio emission from SMGs.
The previous considerations suggest the need to go to flux densities
fainter than $1$ mJy in order to detect large radio arcs in galaxy
clusters. This kind of implication is also supported by the results of
\cite{CO98.1}, which showed that the radio emission corresponding to
large optical arcs in three out of the four cases he studied is $\lesssim 0.5$
mJy. In the only optical arc with a secure radio counterpart in that
work, namely arc $A0$ in cluster $A370$, the radio counterpart does not seem to be
arc-shaped, which may be due to the radio emitting region being offset
with respect with the optical emission or to resolution issues.
On the theoretical side, the statistics of radio arcs was
first investigated by \cite{WU93.1} (WU93 hereafter). Their
predictions were made using the evolutionary model of \cite{DU90.1} to
describe the radio luminosity function (dominated by starforming
galaxies and AGNs preferentially located at $z \lesssim 1$) at $2.7$~GHz
assuming a cosmological model with $\Omega_{\mathrm{m},0} = 1$. Conversely,
we focus on the radio counterparts of SMGs (preferentially
located at $z \sim 2$) at $1.4$~GHz in a more modern $\Lambda$CDM
cosmology. As pointed out in \cite{BA98.1}, the optical depth for optical
arcs produced by sources at $z_\mathrm{s} \sim 1$ grows by about one
order of magnitude in going from an Einstein-de Sitter universe to a
$\Lambda$CDM one. Therefore, we can use this prescription for comparison between
both predictions. Note that, since the SED of SMGs is rather flat at
radio wavelengths (spectral index $\sim 0.7$, \citealt{CO92.1}), we
expect only a small change in the flux density between $2.7$~GHz and
$1.4$~GHz.
In their calculations, WU93 only considered clusters with $z \lesssim
0.6$ and a galaxy velocity dispersion $> 800$ km s$^{-1}$, which
corresponds to a mass $\gtrsim 3.5 \times 10^{14} M_\odot
h^{-1}$. After applying the cosmology correction mentioned before,
their predicted number of giant radio arcs for the whole sky is (i)
$\sim 1000$ if $S_{2.7~\mathrm{GHz}} \gtrsim 10~\mu$Jy, (ii) $\lesssim
200$ if $S_{2.7~\mathrm{GHz}} > 0.1$~mJy and (iii) very small if
$S_{2.7~\mathrm{GHz}} > $ a few mJy (such that none should be detected
in surveys in the literature at that time). Considering only clusters
with mass $\ge 5 \times 10^{14} M_\odot h^{-1}$ (which have a redshift
range comparable to the one used in WU93), our predicted number of
radio arcs with $d \ge d_0 = 10$ produced by SMGs in the whole sky is
(i) $\sim 100 - 1000$ if $S_{1.4~\mathrm{GHz}} > 10~\mu$Jy, (ii) few
tens if $S_{1.4~\mathrm{GHz}} > 0.1$~mJy and (iii) very small if
$S_{1.4~\mathrm{GHz}} > $ a few mJy.
Our results may thus seem compatible with those of WU99, considering
that the number density of SMGs is certainly smaller than the number
density of the entire radio source population. This inference is
however not conclusive, since WU99 are using sources at rather
low-redshift. We cannot say whether considering their same redshift
distribution and number counts would lead to a discrepant result.
In CO99 there is also a study about strongly magnified radio sources,
analogous to the submm sources. It is found that $\sim 20$ sources
with amplification larger than $10$ should be found with
$S_{1.4~\mathrm{GHz}}\ge 10~\mu$Jy. For the same parameters, we find
in our high-mass cluster study a number ranging from $\sim 100$ up to
$\sim 1000$, which is much larger than the findings of CO99. This
discrepancy should be even more enhanced if the two calculations are
reduced to the same $\sigma_8$. The origin of this discrepancy is not
clear, although it might be related to the higher mass threshold that
they adopt, and the fact that the redshift distribution considered by
CO99 peaks at $z \sim 1$ instead of at $z \sim 2$. It should also be
noted that CO99 attribute their finding many fewer radio arcs than
WU93 to the different number count evolution adopted.
Our calculations of the
abundance of radio and submm arcs are more accurate than the works
discussed above for different reasons, mainly the different modeling
of the cluster population. To start with, in the literature, investigators
often consider all lenses as isolated, spherically symmetric density
distributions. \cite{WU93.1} investigate the effect of elliptical mass
distributions, but only on the magnification pattern and not on the
efficiency for the production of large arcs. On the other hand, we
included the effect of asymmetries, substructures and cluster mergers,
that all have been found to be important to augment arc
statistics. Next, we used an NFW density profile to model individual
lenses, which is a good representation of average dark-matter dominated
objects like galaxy clusters, while other works have often considered
SIS or SIS-like profiles, which are more suitable for galaxy
lensing. While for a SIS lens model the image magnification equals the
length-to-width ratio, it is known to produce fewer gravitational arcs
with respect to the more realistic NFW profile \citep{ME03.1}.
\section{Summary and conclusions}\label{sct:conclusions}
The advent of the high resolution submm facilities ALMA and CCAT, and
the major technological development that radio interferometry is
currently undergoing (e.g., \emph{e}-MERLIN, EVLA and SKA) will make possible the
study of radio and submm giant arcs produced by clusters of
galaxies. In particular, the study of giant arcs produced by submm
galaxies (SMGs) seems particularly promising for at least two reasons.
\begin{itemize}
\item[$\bullet$] It provides the opportunity to detect and spatially resolve the
morphologies and internal dynamics of this population of dust obscured
high-redshift star-forming galaxies, which is very difficult to study
in the optical.
\item[$\bullet$] It can provide information about the formation and evolution of
the high redshift cluster population, by means of arc statistics studies.
\end{itemize}
To assess the prospects for these kind of studies, we provided
theoretical predictions on the abundance of gravitational arcs
produced by the SMG population at radio ($1.4$~GHz) and submm ($850~
\mu$m) wavelengths, greatly improving the accuracy of the results with
respect to the first few studies carried out a decade (or more)
ago. The advantage of radio observations is that the angular
resolution and sensitivity provided by interferometers like
\emph{e}-MERLIN and EVLA are already (or will very soon be) at the
level required for these kind of studies. However, these frequencies
do not benefit from the same favorable K-correction as mm/submm
wavelengths do, which will make the latter a more interesting
tool for studying high-redshift clusters as soon as the resolution of
sub-mm observations is good enough. The calculation of the
number of arcs produced by a background source population requires
four main ingredients: (i) the source shape and size (ii), the source
redshift distribution, (iii) the cumulative source number counts, and
(iv) a model of the cluster population.
The model of the cluster population used in this work was based on the
extended \cite{PR74.1} formalism and made use of an NFW dentity
profile to describe each cluster lens. It also included the effect of
asymmetries, substructures and cluster mergers, which have been found
to play an important role in arc lensing statistics.
Based on current radio/CO observations and the FIR/radio correlation,
we have characterized the typical size of the radio and submm emitting
regions of SMGs with an effective radius $R_\mathrm{e}=0.25\arcsec$,
and an axis ratio that varies within the interval $b/a \in
[0.3,1]$. Resolving all the arcs produced by this kind of sources will
require $\sim 0.2\arcsec$ resolution.
Since the most accurate redshift distribution of SMGs available
\citep{CH05.1} is based on observations of the radio detected members
(which is biased against $z \ge 3$ sources), we used three different
functions to quantify the effect of a high redshift tail on the
predicted number of arcs. The results indicate that this effect is
less than a factor two if we consider all simulated clusters during
the calculations, and negligible if we only consider massive
clusters.
The submm source number counts used in this work correspond to the
joint fit of the (bright) SHADES survey counts and the (faint) Leiden
SCUBA Lens Survey counts presented in \cite{KN08.2}. To account for
the uncertainty in the low flux end, predictions were made for the
best fit to the data, and the shallowest fit consistent with the
data. Note that, although only $\sim 60\%$ of the observed SMGs have
being detected in radio, the next generation of radio interferometers
will be able to detect the radio counterparts of all SMGs with
$S_{850~\mu\mathrm{m}} \ge 5$~mJy. Therefore, the radio number counts
of SMGs have been derived by scaling the submm counts using
representative upper and lower limits of the
$S_{850~\mu\mathrm{m}}/S_{1.4~\mathrm{GHz}}$ ratio for SMGs at $z \sim
2$ taken from \cite{CH05.1}.
Our calculations show that a submm all-sky survey with a sensitivity
of $1$~mJy arcsec$^{-2}$ will detect hundreds of arcs with a $5\sigma$
significance. In the radio, this number can be achieved with a
sensitivity of $10-20~\mu$Jy arcsec$^{-2}$. Obtaining a statistically
significant sample of thousands of arcs would require sensitivities of
$0.1$~mJy arcsec$^{-2}$ in the submm and $1~\mu$Jy arcsec$^{-2}$ in the
radio. However, if only massive clusters ($M \ge 5 \times 10^{14}
M_\odot h^{-1}$) are considered in the calculations, the predicted
number of arcs is reduced by about an order of magnitude.
Besides the many uncertainties involved in the theoretical predictions
presented here, the main challenge in designing a future survey for
radio/submm arc statistics studies will be in finding the best
compromise between survey area, depth and resolution, three issues
that affect the arc detectability in different manners. We believe
that this work provides a significant step forward in this direction.
\begin{table*}
\centering
\caption{Predicted number of submm ($850~\mu$m) arcs produced by SMGs
for an all-sky survey, using all the synthetic cluster population to
compute the optical depths (see Figure \ref{fig:arcCounts}).}
\label{arcs_submm_all}
\begin{tabular}{c|cc|cc|cc|cc}
\hline\hline
\noalign{\smallskip}
$B_{850~ \mu\mathrm{m}}^{~(1)}$ & \multicolumn{2}{c|}{$\rm 5~mJy ~arcsec^{-2}$} & \multicolumn{2}{c|}{$\rm 1~mJy ~arcsec^{-2}$} & \multicolumn{2}{c|}{$\rm 0.5~mJy ~arcsec^{-2}$} & \multicolumn{2}{c}{$\rm 0.1~mJy ~arcsec^{-2}$} \\
\noalign{\smallskip}
$d_{0}^{~(2)}$ & $7.5$ & $10$ & $7.5$ & $10$ & $7.5$ & $10$ & $7.5$ & $10$ \\
\noalign{\smallskip}
\hline
\noalign{\smallskip}
SPZ DB$^{~(3)}$ &575 &250 &3792 &1650 &8275 &3600 &50767 &22075 \\
PHZ DB$^{~(3)}$ &550 &233 &3575 &1533 &7800 &3342 &47892 &20517 \\
CHM DB$^{~(3)}$ &1142 &517 &7425 &3325 &16200 &7267 &99458 &44592 \\
\noalign{\smallskip}
\hline
\noalign{\smallskip}
SPZ SM$^{~(3)}$ &542 &233 & 2208 &958 &3567 &1550 &9658 &4200 \\
PHZ SM$^{~(3)}$ &508 &217 & 2083 &892 &3367 &1442 &9117 &3900 \\
CHM SM$^{~(3)}$ &1058 &475 & 4317 &1933 &6992 &3133 &1058 &475 \\
\noalign{\smallskip}
\hline
\noalign{\smallskip}
\multicolumn{9}{l}{$^{(1)}$ surface brightness limit used to determine the number of arcs.}\\
\multicolumn{9}{l}{$^{(2)}$ arc length-to-width ratio thresholds.}\\
\multicolumn{9}{l}{$^{(3)}$ redshift distribution and number count function, as introduced in Figures \ref{fig:zd} and \ref{fig:cc}.}\\
\end{tabular}
\end{table*}
\begin{table*}
\centering
\caption{Predicted number of submm ($850~\mu$m) arcs produced by SMGs
for an all-sky survey, using only clusters with $M \ge 5 \times
10^{14} ~M_\odot h^{-1}$ to compute the optical depths (see Figure
\ref{fig:arcCounts_mass}).}
\label{arcs_submm_massive}
\begin{tabular}{c|cc|cc|cc|cc}
\hline\hline
\noalign{\smallskip}
$B_{850~\mu\mathrm{m}}^{~(1)}$ & \multicolumn{2}{c|}{$\rm 5~mJy ~arcsec^{-2}$} & \multicolumn{2}{c|}{$\rm 1~mJy ~arcsec^{-2}$} & \multicolumn{2}{c|}{$\rm 0.5~mJy ~arcsec^{-2}$} & \multicolumn{2}{c}{$\rm 0.1~mJy ~arcsec^{-2}$} \\
\noalign{\smallskip}
$d_{0}^{~(2)}$ & $7.5$ & $10$ & $7.5$ & $10$ & $7.5$ & $10$ & $7.5$ & $10$ \\
\noalign{\smallskip}
\hline
\noalign{\smallskip}
SPZ DB$^{~(3)}$ &17 &8 &125 &42 &267 &92 &1633 &550 \\
PHZ DB$^{~(3)}$ &17 &8 &133 &42 &283 &92 &1733 &583 \\
CHM DB$^{~(3)}$ &25 &8 &150 &50 &325 &108 &2008 &683 \\
\noalign{\smallskip}
\hline
\noalign{\smallskip}
SPZ SM$^{~(3)}$ &17 &8 &75 &25 &117 &42 &308 &108 \\
PHZ SM$^{~(3)}$ &17 &8 &75 &25 &125 &42 &333 &108 \\
CHM SM$^{~(3)}$ &25 &8 &83 &33 &142 &50 &383 &133 \\
\noalign{\smallskip}
\hline
\noalign{\smallskip}
\multicolumn{9}{l}{$^{(1)}$ surface brightness limit used to determine the number of arcs.}\\
\multicolumn{9}{l}{$^{(2)}$ arc length-to-width ratio thresholds.}\\
\multicolumn{9}{l}{$^{(3)}$ redshift distribution and number count function, as introduced in Figures \ref{fig:zd} and \ref{fig:cc}.}\\
\end{tabular}
\end{table*}
\section*{Acknowledgments}
{\small We are grateful to M. Bartelmann, A. Blain and
L. V. E. Koopmans for reading the manuscript and for many useful
comments. We also would like to thank M. Swinbank, for providing us
the histograms presented in Figure \ref{fig:z_comparison}, their
Gaussian fits, and the predictions from his evolutionary model, and
K. K. Kundsen for providing us with the observational data presented
in Figure \ref{fig:counts_swinbank}. We also acknowledge stimulating
conversation with M. Bonamente, M. Brentjens, M. Joy, A. F. Loenen and
I. Prandoni. We wish to thank the anonymous referee for useful remarks
that allowed us to improve the presentation of our
work. C. F. acknowledges financial contributions from contracts
ASI-INAF I/023/05/0 and ASI-INAF I/088/06/0.}
{\small
\bibliographystyle{aa}
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School-to-Prison Pipeline: Are Students Getting Prepped for Jail?
By Rich
By now you've probably heard the phrase "school-to-prison pipeline" used to explain the challenges urban students of color have to overcome to finish school, but what does it really mean? A group of students in Washington D.C. armed themselves with cameras to illustrate what it really looks like when your school treats you more like an inmate than a scholar.
In the nation's capital, Black students are six-times more likely to be suspended or expelled from their school than their white counterparts. Nationwide, 16 percent of African Americans students were suspended for minor infractions in 2012, compared to just five percent of whites, according to a report by the Department of Education. Moreover, recent data found that many teachers have lower expectations for students of color than their white peers, sometimes before they even enter the classroom. With so many obstacles stacked against minority students, it's a wonder most of them go on to finish school at all.
But what exactly are kids up against? Through Critical Exposure, a D.C.-based non-profit group, students in the 2012-2013 fellowship program created a multimedia project to show the difficulty many of them face just to get a diploma.
The eye-opening project showed city schools with airport-like metal detectors, iron security gates, bars on the windows, and armed guards. One student said he felt like a criminal just by attending school, and another student photographer admitted, "Coming in the building feels like turning in my stuff before entering a jail cell."
Malik Thompson, a 19-year-old student who says he was kicked out of D.C. schools, credited Critical Exposure with helping him get back on track.
"I think more programs like Critical Exposure should exist where young people have avenues to begin to experience their own power, to work collaboratively together with adult supporters in order to make change in their world."
Thompson finished high school through a home-school program and currently interns with the Gandhi Institute in Rochester, New York, advocating for social justice. None of it would have been possible without being involved in the photography fellowship.
"Critical Exposure was essential to me becoming the person I am today,"
While schools should be a place of knowledge, empowerment, and learning for our youth, far too often it's nothing more than a pit stop on the road to the legal system. If we're serious about cutting off the school-to-prison pipeline, as programs like Critical Exposure show us, it's important to listen to the experiences of our youth to be sure we're meeting their needs.
Feature image: Critical Exposure, Photographer: Karl L.
What do you think should change in the way these schools are set up?
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using (FileStream fs = new FileStream("abc.txt", FileMode.Create)) {
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}
{
FileStream fs = new FileStream("abc.txt", FileMode.Create);
try {
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using var fs = new FileStream("abc.txt", FileMode.Create);
//https://pt.stackoverflow.com/q/163768/101
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"redpajama_set_name": "RedPajamaGithub"
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National Maritime Museum (NMM) w Greenwich w Londynie jest najważniejszym muzeum morskim w Zjednoczonym Królestwie i jednym z największych muzeów tego typu na świecie. Historyczne budynki − wraz z Królewskim Obserwatorium Astronomicznym i XVII-wiecznym pałacem Queen's House − zostały wpisane na listę światowego dziedzictwa UNESCO. W roku 2012 królowa Elżbieta II podpisała dekret, na mocy którego National Maritime Museum, Queen's House, Królewskie Obserwatorium Astronomiczne i żaglowiec Cutty Sark zostały objęte wspólną nazwą Królewskich Muzeów w Greenwich (Royal Museums Greenwich). NMM jest sponsorowane przez Ministerstwo Kultury i Sportu Wielkiej Brytanii. Wstęp, jak w innych muzeach publicznych Zjednoczonego Królestwa, jest bezpłatny, jednak za wstęp na niektóre wystawy czasowe opłaty są pobierane.
Oficjalne otwarcie
Muzeum zostało utworzone na podstawie National Maritime Act z roku 1934. Podstawą zbiorów była darowizna sir Jamesa Cairda (1864–1954). Król Jerzy VI dokonał oficjalnego otwarcia placówki 27 kwietnia 1937 roku, w czym towarzyszyła mu córka, księżniczka Elżbieta, późniejsza władczyni Zjednoczonego Królestwa, z którą odbył podróż Tamizą z Londynu. Pierwszym dyrektorem NMM został sir Geoffrey Callender.
Zbiory
Od najdawniejszych czasów podlondyńskie Greenwich związane było z żeglugą morską i nawigacją. Tu w starożytności lądowali Rzymianie, tu przebywał często król Henryk VIII, tu powstawały zręby Royal Navy, a Karol II Stuart założył w roku 1675 Królewskie Obserwatorium, "dla znalezienia długości geograficznej miejsc". Miejsce lokalizacji czasu uniwersalnego i południka zerowego, od roku 1884 było centrum badań astronomicznych, a nawigatorzy na całym świecie regulowali swe zegary zgodnie z czasem Greenwich.
NMM zawiera największą na świecie kolekcję przedmiotów związanych z historią Wielkiej Brytanii na morzu (w sumie ponad dwa miliony okazów), w tym dzieła malarstwa marynistycznego, tak brytyjskiego, jak i holenderskiego z XVII wieku, historyczne mapy, manuskrypty, plany i modele dawnych statków i okrętów, instrumenty nawigacyjne i naukowe oraz przyrządy astronomiczne (prezentowane w obserwatorium). Zawiera też kolekcję portretów osób tak ważnych dla historii brytyjskiej marynarki, jak np. Horatio Nelson czy James Cook.
Pewien cień na działalność National Maritime Museum rzucają dzieła sztuki zabrane z Niemiec po zakończeniu II wojny światowej, w tym modele okrętów i obrazy. Muzeum było często krytykowane za bezprawne posiadanie, jak to określano, "zrabowanych dzieł sztuki". Muzeum twierdzi jednak, że te obiekty kulturalne to "zdobycz wojenna" należąca się Wielkiej Brytanii na podstawie ustaleń konferencji poczdamskiej.
Galeria zbiorów NMM
Uwagi
Przypisy
Muzea i galerie w Londynie
Royal Borough of Greenwich
Atrakcje turystyczne w Londynie
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Johann Wigand, latinisiert Joannes Wigandus, (* 1523 in Mansfeld; † 21. Oktober 1587 in Liebemühl) war ein evangelischer Theologe und Reformator.
Leben
Nach dem Besuch der Schule in Mansfeld kam Wigand 1538 an die Universität Wittenberg, wo er unter anderem Luther und Melanchthon hörte. Er unterbrach aber seine Ausbildung und wurde 1540 Lehrer an der Sebaldusschule in Nürnberg. Nach Wittenberg zurückgekehrt, erwarb er am 1. September 1545 den akademischen Grad eines Magisters, wurde 1546 Pfarrer in seiner Heimatstadt und 1553 Superintendent in Magdeburg. Hier begann er auf Anraten des Matthias Flacius Illyricus (1520–1575) zusammen mit Matthias Judex mit der Bearbeitung der Kirchengeschichte aus protestantischer Sicht, den sogenannten Magdeburger Centurien.
Nach einem Zwischenspiel als Professor der Theologie zu Jena begab sich Wigand als Superintendent nach Wismar, wo er mit botanischen Studien begann, aber auch zusammen mit Matthäus Judex an den Centurien weiterarbeitete. Am 12. Juli 1563 wurde Wigand an der Universität Rostock zum Doktor der Theologie promoviert. Eine zweite Wirkungszeit in Jena endete 1573 mit seiner Absetzung und Ausweisung.
Nach kürzeren Aufenthalten in Braunschweig und Wolfenbüttel folgte er einem Ruf an die Universität Königsberg, von wo er den Kampf gegen die Philippisten fortsetzte. Der samländische Bischof Tilemann Hesshus weihte Wigand 1575 in Königsberg zum Bischof von Pomesanien. Da Hesshusius 1577 als Irrlehrer abgesetzt wurde und dann eine Theologieprofessur in Helmstedt annahm, wurde Wigand zusätzlich Bischof des Samlandes. Beide Ämter versah er bis zu seinem Tode 1587. Obschon die Drucklegung der Centurien 1574 nach dem Erscheinen des 13. Bandes aussetzte, arbeitete er an dem Projekt weiter. Es sind handschriftlich Skizzen zu einer Fortsetzung bis ins 16. Jahrhundert erhalten.
Wigand war einer der Hauptvertreter der Gnesiolutheraner. Er beteiligte sich an allen wichtigen Lehrstreitigkeiten, die nach Luthers Tod in der evangelischen Kirche ausbrachen.
Werke
Vitae theologorum Prussicorum. Da das Königsberger Exemplar der Biogramme von Wigand seit 1945 verschollen ist, muss das Wolfenbütteler Dokument (Cod. Guelf. 6. 5 Aug. 2°) als Unikat gelten. Abb., Abb.
Christliche Erinnerung Von der Bekentnis der Theologen in Meissen vom Abendmal. Jetzt newlich auszgangen. Königsberg, J. Daubmanns Erben, 1574; bis 1575 folgten drei weitere Ausgaben
De Jesu Christo Deo et Homine. Königsberg, 1575
Corpus Doctrinae unsers Herrn Jesu Christi und der Apostel. Mühlhausen, 1562
Methodus oder Heubtartikel christlicher lere. Magdeburg, 1557
Ob die Newen Wittenberger stets bis daher einig mit den alten geleret, Vnd Ob Lutheri vnd Philippi schrifften durch aus gantz einig vnd einhellig. Wie die Vngenanten Scribenten itzt zu Wittenberg in offentlichem druck schreiben in der Vorrede vber die Smalkaldischen Artikel. Königsberg, 1575
Synopsis Antichristi romani spiritu oris Christi revelati. Jena, 1560
Welche Religion die elteste sey, unter der Euangelischen und der Bepstischen. Erinnerung und untrericht [!] für einfeltige Christen. Jena, 1587
Vera historia de succino Borussico. Jena, 1590 Digitalisat
Einzelnachweise
Weblinks
Adam, Melchior: Vitae Germanorum Theologorum qui superiori seculo Ecclesiam Christi ... propagarunt ... - Frankfurt <Main>: Jonas Rosa; Heidelberg: Johannes Georgius Geyder, Acad. Typogr., 1620.
Zu den Centurien
Ecclesiastica historia (Magdeburger Centurien) Digitale Version der "Bibliothek der Monumenta Germaniae Historica"
Literatur
Kurt Wein: Johannes Wigand (1523–1587): Preußens erster Botaniker in: Sudhoffs Archiv 35 (1942/43), S. 160–205
Realenzyklopädie für protestantische Theologie und Kirche, Band 21 Seite 270
Wigand's Autobiographie in: Fortgesetzte Sammlung von alten und neuen theologischen Sachen. Leipzig 1738, 601–620.
Wilhelm Preger: Matthias Flacius Illyricus und seine Zeit. Erlangen 1859–1861.
Heinz Scheible: Die Entstehung der Magdeburger Zenturien. Ein Beitrag zur Geschichte der historiographischen Methode. (Schriften des Vereins für Reformationsgeschichte 183), Gütersloh 1966
Michael Bunners: Johann Wigand (1523–1587), lutherischer Geistlicher und Gelehrter in Wismar von 1562–1568 – ein homo universalis – Hauptautor der Centurien. (In: Die Magdeburger Centurien. Band I: Die Kirchengeschichtsschreibung des Flacius Illyricus, hrsg. von Eckart W. Peters, Dößel 2007, S. 91–108)
Hochschullehrer (Friedrich-Schiller-Universität Jena)
Lutherischer Theologe (16. Jahrhundert)
Lutherischer Bischof (16. Jahrhundert)
Rektor (Albertus-Universität Königsberg)
Rektor (Friedrich-Schiller-Universität Jena)
Person des Christentums (Ostpreußen)
Person des Christentums (Magdeburg)
Botaniker (16. Jahrhundert)
Person (Wismar)
Geboren 1523
Gestorben 1587
Deutscher
Mann
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info(at)texasliving(dotted)com
What Makes Us A Better Choice
Lenders Page
Dutch and Cheryl Wiemeyer
806 S. Hwy 377
Aubrey, Texas 76227
940-365-4687 info(at)texasliving(dotted)com
Home » Area Lakes
Lake Ray Roberts
Website: http://www.swf-wc.usace.army.mil/lewisville/RayRoberts.htm
Lake Ray Roberts is a 30,000 acre reservoir. It offers two state parks (Isle du Bois and Johnson Branch), six satellite parks (Jordan Unit, Pond Creek, Pecan Creek, Buck Creek, Sanger, and Elm Fork), Wildlife Management Areas, wetlands, waterfowl sanctuaries and the 20 mile Ray Roberts Lake/Lake Lewisville Greenbelt Corridor. Birdwatching, water sports, riding horses or backpacking along a scenic trail, Ray Roberts has something for everyone.
The lake tends to attract fisherman with some recreational boaters, mostly around the southern section of the lake.
The lakeside communities we service include Pilot Point, Sanger, Tioga, Mountain Springs and Valley View.
Lake Lewsiville
Website: http://www.swf-wc.usace.army.mil/lewisville/Lewisville_Lake.htm
Surrounded by 9,000 protected acres of nature, Lewisville Lake spans 23,280 acres and has 233 miles of shoreline. With an average depth of 25 feet, Lewisville Lake is large enough for all kinds of water sports and still leaves room for some of the biggest fish this side of Moby Dick. (Well, this is Texas after all.) Catch the big one in the morning, then take a walk on our wild side and explore miles of scenic trails all around Lewisville Lake.
Lewisville Lake is a Corps of Engineers reservoir that is immensely popular for water sports and outdoor recreation in the Dallas-Fort Worth area. The City of Lewisville manages Lake Park on the south shore of the lake: picnic area, RV and tent camping, pavilion, 24-hour fishing barge, swimming beach and excellent public facilities. Marinas, boat rentals, launch ramps and angler's supplies are also available. Fishing on Lewisville Lake includes large-mouth bass, crappie, catfish, white bass and spectacular hybrid white/striped bass. Swimming, water skiing, jet skiing, sailing, sail boarding, camping, biking and picnicking are all part of what makes Lewisville Lake so much fun.
The lakeside communities in our market area include Oak Point and Cross Roads, which border the lake on the northeast side.
Lake Texoma
Website: http://www.laketexoma.com/home.asp
This 89,000 acre lake on the Red River is shared by Texas and Oklahoma. It is widely recognized as a top fishing lake, and is one of the most popular recreation destinations in the Southwest. Lake Texoma was built by the Corps of Engineers in the 1940's, and was stocked with black bass and crappie along with the native white bass in the Red and Washita Rivers.
The lake area includes two wildlife refuges, two state parks, fifty four U.S. Army Corps of Engineers-managed parks, twenty-six resorts, hundreds of campgrounds and a variety of excellent golf courses. Power boating, power sailing, personal watercraft, water skiers and wind surfers all consider the lake an excellent place to have fun. Lake Texoma has become a huge sailing center based on the lake's size, depth and miles of sailing shoreline.
Although Lake Texoma attracts people from all over the Metroplex, the communities we service include Whitesboro.
Property Type Property Type Single Family Residential Commercial Lots and Land Lease Multifamily Residential City or ZIP Code Beds Beds Any Number Studio 1+ 2+ 3+ 4+ 5+ 6+ 7+ 8+ 9+ 10+ Baths Baths Any Number Studio 1+ 2+ 3+ 4+ 5+ 6+ 7+ 8+ 9+ 10+ Minimum Price Min. Price $50,000 $75,000 $100,000 $110,000 $120,000 $130,000 $140,000 $150,000 $160,000 $170,000 $180,000 $190,000 $200,000 $225,000 $250,000 $275,000 $300,000 $325,000 $350,000 $375,000 $400,000 $425,000 $450,000 $475,000 $500,000 $525,000 $550,000 $575,000 $600,000 $650,000 $700,000 $750,000 $800,000 $850,000 $900,000 $1,000,000 Maximum Price Max. Price $50,000 $75,000 $100,000 $110,000 $120,000 $130,000 $140,000 $150,000 $160,000 $170,000 $180,000 $190,000 $200,000 $225,000 $250,000 $275,000 $300,000 $325,000 $350,000 $375,000 $400,000 $425,000 $450,000 $475,000 $500,000 $525,000 $550,000 $575,000 $600,000 $650,000 $700,000 $750,000 $800,000 $850,000 $900,000 $1,000,000
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Serica calignosa är en skalbaggsart som beskrevs av Dawson 1932. Serica calignosa ingår i släktet Serica och familjen Melolonthidae. Inga underarter finns listade i Catalogue of Life.
Källor
Skalbaggar
calignosa
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/*!
* Yamm!3 - Yet another megamenu for Bootstrap 3
* http://geedmo.github.com/yamm3
*
* @geedmo - Licensed under the MIT license
*/
.yamm .nav,
.yamm .collapse,
.yamm .dropup,
.yamm .dropdown {
position: static;
}
.yamm .container {
position: relative;
}
.yamm .dropdown-menu {
left: auto;
}
.yamm .yamm-content {
padding: 20px 30px;
}
.yamm .dropdown.yamm-fw .dropdown-menu {
left: 0;
right: 0;
}
.yamm .dropdown.yamm-hw .dropdown-menu {
left: 25%;
right: 25%;
}
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No more hassle to drop off your rackets and waiting for them to be restrung. Stringr lets tennis players get stringing services delivered to the location of their choice.
We are currently starting our service in Los Angeles area but will be expanding across the country in the upcoming months.
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Artwork Commemorating Cherry Blossom Festival, Ja...
Category: Memorials/Tributes; Outdoor Sculpture; Sculpture
Hanami is a Japanese celebration where people celebrate the flowering of the Cherry Blossom trees. The celebration originated in Japan, yet the celebration has been able to inspire Macon, Georgia to have a similar celebration with identical trees. The Cherry Blossom Festival in Macon is called the "International Cherry Blossom Festival", and Macon is known to be the Cherry Blossom Capital of the World because 300,000 sakura (meaning Cherry Blossoms) trees grow in the city. The trees bloom in late March. The festival last for ten days which consists of activities, carnivals, food venders, music, parades, and street performances. The streets are filled in downtown Macon. A replication of the Japanese lantern commemorates the Cherry Blossom Festival. Origins:Cherry Blossom trees are not native to the South. Willian A. Fickling Sr., a local of Macon, enjoyed the one Cherry Blossom tree in his backyard, but he only could identify his tree after a trip to Washington DC where he was able to careful compare the two trees. After careful scrutiny between his tree and the cherry blossom trees in Washington DC, he was able to identify the two as identical trees. In 1973, 500 Cherry Blossom trees were planted around Macon and quickly became popular in the Macon community. The first festival began in spring of 1982. ?
Benches Commemorating Second Annual Cherry Blossom...
Central City Park Bell
Category: Memorials/Tributes
Eternal Flame Memorial
This memorial is dedicated to veterans of wars from Macon and Bibb co. on the occasion of the 50th anniversary of the American Legion. It was repaired and reworked in 1993 with funds from American Legion. The eternal flame burns on the Poplar Street side of the City Hall building at the foot of the two grand staircases that flank the building's white-columned portico. In 1837, city hall was built as headquarters of the Monroe Railroad and Banking Co. before serving as the seat of government for the city of Macon. During the Civil War, it was a military hospital. Its greatest notoriety during the civil war came in November 18, 1864, when Governor Joseph E. Brown, fleeing the Union army's advance into Milledgeville, moved the state capital to Macon and set up an office at City Hall. The General Assembly met in the building the following February and March, the last legislative session under the Confederate States of America. The building ceased to serve as capitol on March 11, 1865 . Two city council chambers are located in the building. The Eternal Flame commemorates the building. 2014 conditions: a little wear and tear to it and could use a fresh coat of paint
In Memory of Carl Vinson
Carl Vinson served in the United States House of Representatives for 50 years — the longest continuous service in history — from 1914 to 1964, a tenure that extended during the terms of nine presidents from Woodrow Wilson to Lyndon Johnson. He was a fervent believer that peace can only be maintained if the country's defenses are strong. Mr. Vinson was known as one of the nation's most stalwart and influential supporters of a strong national defense. He was chairman of the House Naval Affairs Committee for 16 years and of the Armed Services Committee for 14 years. In matters of national defense his influence came to be regarded as second only to that of the President. From 1951 until his retirement the congressional district he represented included Macon and Bibb County, and he was instrumental in the location within the middle Georgia area of many projects of great benefit to Macon. He was primarily responsible for the construction of Robins Air Force Base in Warner Robins and played a leading role in assuring that I-75 and I-16 passed through Macon. Mr. Vinson was a leader in founding the Mercer Medical School, and his efforts were vital to the construction of Lake Tobesofkee, the construction of Cochran Field (now Macon's Municipal Airport), the new Federal Building on College Street in Macon, and the Naval Ordinance Plant, the reactivation of Camp Wheeler near Macon during World War II, and the naming of a dirigible and naval vessel for the city of Macon, all came about primarily as a result of his efforts. Carl Vinson was born November 18, 1883, near Milledville, Georgia, and spent his formative years in that city. After his graduation from Mercer University Law School in Macon in 1902, he practiced law, was appointed Baldwin County Court Solicitor, was elected to two terms of the Georgia Legislature, and served as Judge of Baldwin County Court. A life-long Democrat, he was elected in 1914 to the U.S. House of Representatives and was sworn in November 5 of that year as the youngest member of Congress. From 1917 until his retirement, Mr. Vinson was a member of first the Naval Affairs Committee and then the Armed Services Committee into which the Naval Affairs Committee was merged. Throughout that time he played a leading role in defense matters, and his influence was enhanced in 1931 when he became chairman of the Naval Affairs Committee and in 1949 when he became chairman of the Armed Service Committee. Not only did Mr. Vinson believe that a strong national defense is essential to peace, he regarded national defense as a non-partisan matter: "… My country and its safety come ahead of any party…" These two principles and his belief in civilian control of the military guided him throughout his career. Condition: Great Funded By: Friends of Carl Vinson-$30,000-private funds.
In Memory of Dr. Martin Luther King Jr. Visits to ...
Memorializes Dr. King's visits to Macon.
Memorial Magnolias Plaque
Category: Historical; Memorials/Tributes
Inscribed on the Memorial Magnolia Plaque, "In grateful appreciation of those of our own families and friends who gave their lives in War World II. That the Ideals they cherished more than life might not perish from the earth. We, the citizens of Bibb County, have caused their names to be engraved upon this tablet and have surrounded it with rare magnolias. A living memorial to their unfaltering devotion." The memorial is situated in the open grass area in front of the Mercer Law School. Condition in 1993: good Condition in 2014:
Middle Georgia's Veteran Memorial
"In honor of the men and women of the Armed Forces of the U.S. who served in WW!, WWII, Korean, and Vietnam" is the inscription on the monumant. There are six black granite columns on either side of the larger red granite column which holds the eagle. The names of the people from all wars are inscribed at the bottom. Condition as of January 2014: Excellent, slight weathering and one flag has minor tears.
Monument Commemorating the Fourth Anniversary of t...
Category: Historical; Memorials/Tributes; Sculpture
The Monument Commemorating the Fourth Anniversary of the Signing of the Armistice is "In memory of those of the 151st Machine Gun Battalion." In France, the 151st Machine Gun Battalion where soldiers came mostly from three Macon companies of the Georgia National Guard. There was much causality during the period of service. "Dulce et Decorum est Pro Patria Mori" is inscribed at the bottom of the plaque. In English the phrase means "It is sweet and right to die for your country". This phrase was widely understood by many people during World War I. These lines originated from a poem expressed by the Roman lyrical poet Horace's Odes. Designer: Captain A. Sidney Brown; Builder: Schneider Marble Co. of Americus. 1993 condition: the sculpture needs cleaning but is otherwise in good condition.
NewTown Macon Compass Rose
Category: Memorials/Tributes; Outdoor Sculpture
This engraved brick and granite compass rose commerates the NewTown Macon organization's 1999 Big Picture Campaign. The generous donor's names surround the compass rose.
Sergeant Rodney M. Davis Memorial Monument
Rodney Maxwell Davis (April 7, 1942 – September 6, 1967) was a United States Marine who posthumously received the Medal of Honor for his heroism during the Vietnam War. Davis was born on April 7, 1942, in Macon, Georgia to Gordon N. Davis and Ruth A. Davis. He attended elementary school and high school there and graduated from Peter G. Appling High School, May 29, 1961. Shortly after graduation, he enlisted in the United States Marine Corps in his hometown, August 31, 1961 Ordered to the Republic of Vietnam in August 1967, he was assigned duty as a Platoon Guide with Company B, First Battalion, Fifth Marines, First Marine Division. On September 6, 1967, he was operating with his unit in the Quang Nam Province on a search and clear mission during Operation Swift, when they were attacked by a large North Vietnamese force. Elements of the platoon were pinned down in a trench line by mortars, heavy automatic and small arms fire. He went from man to man encouraging them on and also returning fire at the same time. An enemy hand grenade fell in the trenches his men were fighting from and without hesitation he threw himself upon the grenade. He saved his fellow Marines in this selfless act and thus earned the nation's highest military decoration: the Medal of Honor. Presentation of the Medal was made posthumously to his widow, Mrs. Judy P. Davis, by Vice President Spiro T. Agnew in his office. The Presentation is "in the name of the Congress of the United States."
With Honor They Served
Memorials to Macon Police Officers, Macon-Bibb Firefighters and Bibb County Deputy Sheriffs fallen in the line of duty. Located in Messenburg Park.
Category: Historical; Memorials/Tributes; Outdoor Sculpture
The memorial was erected in 1937. It is in the shape of an obelisk. There are etchings around the top of the memorial. The base has three narrow steps around it. The memorial is dedicated "in honor and loving memory of those brave men and women of Bibb County, Georgia, both the living and the dead, whose heroic service and supreme sacrifice in the cause of liberty during the World War (A.D. 1917-1918) and gave us the full meaning of patriotism. This memorial was made possible through private subscription of loyal friends in Bibb County where Mrs. William Oscar Kinney was the General Chairman. 1993 condition: good.
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Call of the Wetland: Image No. 1 of 11
In Calgary, more than 90 percent of the city's pre-settlement wetlands have been lost due to urban growth, pollution, fragmentation and climate change.
See larger image (253.9 KB)
Bordering Tsuu T'ina Nation lands on the west side, and continuing its journey through several areas of significance for the Blackfoot and other First Nation communities, the Rotary/Mattamy Greenway travels through over 55 Calgary neighborhoods, and reflects the diversity of the city's population.
The Miistakis Institute plans on sharing the collected data with the City of Calgary and Alberta Environment and Parks, in the hopes that it will help influence important decisions on future urban development and planning.
Parks Foundation Calgary's Rotary/Mattamy Greenway, a nearly complete 138-kilometer urban pathway that encircles Calgary, is an ideal backdrop for this amphibian monitoring program, with its series of 12 interpretive wetlands, off-leash dog parks, memorial gardens, family fitness parks and nature-inspired playparks along its route.
The boreal chorus frog, Alberta's smallest amphibian, has a healthy population across the province. But in Alberta, the northern leopard frog is a species at risk. So is the long-toed salamander. In fact, of the six amphibians that live in the rural areas surrounding Calgary, three are at-risk—and very little is known about amphibians in the city itself.
Wetland losses significantly impact biodiversity and ecosystem services important to human well-being, notes the Miistakis Institute.
There are more than 4,000 wetlands within the Calgary city limits, and Call of the Wetland has identified 60 of those wetlands for regular amphibian surveying from volunteers.
"It's a bit early to tell, but we see momentum already building toward a community that we expect will champion wetland protection and restoration," says Tracy Lee, project coordinator for Call of the Wetland.
The Rotary/Mattamy Greenway, whose construction began in 2010, links parks, natural areas, greenspaces, river valleys and people. The Rotary/Mattamy Greenway connects to Calgary's already extensive pathway system, forming the largest pathway network in the world with more than 1,000 kilometres of trails.
Call of the Wetland: Image No. 10 of 11
Wetlands represent natural infrastructure that plays a significant role in contributing to the rain cycle, filter sediments and pollutants, and lessening the impacts of floods and drought.
Call of the Wetland aims to engage Calgarians in understanding the health of wetlands through monitoring of amphibians and enabling a connection to nature in the city.
See larger image (171 KB)
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# LOVE AND DEATH IN SAVING EUROPE
_A novel_
Rita Dulci Rahman & Jose Miguel Andreu
LM Essential Publishers
_To our grandchildren: Kaj, Leonardo, Fae, and Federico_.
_With all our love and hope for their good future_.
**Colophon**
---
2012© | Rita Dulci Rahman & Jose Miguel Andreu
Publisher | LM Essential Publishers
Cover Design | Raul Behr, Professional IT Services, Paramaribo
ISBN | 978-94-91480-01-0
No part of this book shall be reproduced, stored in a retrieval system or transmitted by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission from the authors and publisher.
Contact: info@leonon.nl
Book can be purchased as a printed book, eBook and streaming book in all (Web)Bookshops, Amazon.com, Bol.com, Yindo and KOBO
### Authors Note
This novel was born out of our concern over the future of Europe. It is a fictitious and humorous love-and-life story with a perspective of solving the current European crisis.
Needless to say that none of the characters, or the circumstances or events in the book have anything to do with reality or with current politicians and governing functionaries in Europe.
Any conceived resemblance by readers is based on coincidence. The book is meant to entertain while it may contribute to fresh thinking on long-term success for the European project, creating a better future for current youngsters and generations to come.
### Contents
1. The call that changed the life of the president
2. Lost love illusions but moving forward in Berlin
3. A French-German initiative is overcoming turmoil
4. Love and foul-play in Dubai
5. Sharing cooks but missing soups brings love back
6. Voluntary federating the best and angering the rest
7. A rainy night in Brussels
8. From Russia with love
9. A birthday party in the Basque Country
10. Blunt truths in the Spanish Parliament
11. Ibrahim is set free but the triumph is for Perrier
12. Florence in chaos with protesting beauties and new
13. The tragic end of Bopoulos
14. Passionate loss for the makers in the first federal elections
15. Celebrating the fifth anniversary of the federation
### One
### The call that changed the life of the president
"I have told you a thousand times that when someone calls and I'm in the bathroom, you have to say that I'm in a top meeting and cannot be disturbed."
Jacques Perrier, President of France, upset for the disturbance and nervous from having to rush out of the bathroom, was hardly in control of the telephone through which he screamed at his middle-aged secretary on the other end of the line. Meanwhile his eyes caught the digital clock at his desk showing 11.06 hours.
It happened on a chilly morning in October, and none of the involved could have then imagined that this telephone call would be the beginning of the end of the career of the President, and of his, in those days, rather frequent happiness.
"But sir, the Chancellor of Germany is on the line and it is very urgent. She needs to speak to you now. Please, may I put you through?"
"Ok, go ahead, but from now on, be attentive."
So, to put things in the right order, before the call from Berlin came in turning Jacques Perrier's life upside down, the man had first been observing from the windows of his office, that in only minutes, everything around the Palace L'Elysee was disappearing under a white blanket while he could hear frosty drops falling softly from the roofs. What struck him most about the scenery was the deep silence of the normally bustling streets, as if Paris itself had stopped breathing. With the image of his city wrapped in silence, he had gone to the bathroom for even more mindful reflections, when suddenly the phone rang.
He sharply remembered his first encounter with Marlein Ditch, the German Chancellor. Although the persistent rumours about her moodiness and sudden, angry outbursts facing aides and colleagues alike, had reached him long before his election as President de la Republique, at their first meeting her look—lips pressed together, no lipstick, grey suit, no jewellery other than a tiny golden cross on a fine chain, and a somewhat manly handshake—had confirmed his provisional reference to her: a German spinster coming in from the cold.
"Dear friend, my dearest Jacques, sorry for disturbing you, but I had to, it is urgent. Things are really running out of control. You will not believe what I am going to tell you now. I have just been informed by my Ambassador in Rome that the PIGS1 have initiated a move to create a political federation of four countries inside the Euro zone. It is our friend from Spain, who, unable to run his own ransacked federated country, has convinced our Italian colleague, another dud, to jointly create a new state of 120-million people, just transforming themselves and the other two neighbouring losers into the biggest country of the EU. Unbelievable! I am furious with this Mafiosi way to put pressure on us. We need to stop this immediately."
"Holy Christ, Marlein, first the EU generously helped the Spaniards to develop their country over the past twenty years, and now, out of thanks, our foolish colleague is taking advantage by pulling failing powers to his side. It is a bitter joke that those with today's weakest economies, those who perhaps should not have been admitted to enter in the Euro zone, want to steal us the show and put us in minority. Frankly speaking, I am fed up with this Machiavelli believing he could force us to either abandon the Euro or to fall in his presumed leading strings. What a group of crippled countries! We should have ignored them from the very beginning. You can never trust beggars."
By now also Jacques Perrier was furious and, without in any way wishing to be diplomatic, both leaders used strong language to clear their minds bogs, but to be fair to the reader one has to know that the thinking of Perrier in the bathroom, just before the phone rang, although similarly upsetting, had little to do with the Euro crisis and attempted economic shortcuts.
No, until the call from Berlin came in, the thoughts of Perrier in the intimacy of the small room with its colourful tiles and the unmistaken scent of bitter almonds had been of a totally different nature. Lingering on a breathless, quiet Paris, Perrier moved his reflections to the death of his father four months ago and the deep sorrow and emptiness it had left inside him.
As Jacques Perrier had always been a very nervous man, these were feelings he was unable to cope with, but slowly he was learning to control them during the day, sometimes even in the bathroom.
Gone was the man whom he had been meeting so discreetly when both knew that the end was near. In those days, the palliative treatment for lung cancer had made his father serene in facing his last curtain. It was of no use to challenge old Perrier with anything other than fate since he used to refer to almost all subjects as "for God to decide." This caused Jacques to become overwhelmed by the burden of disillusion, as he could no longer demonstrate his extended knowledge of modern political life or on the economic future of Europe in the wake of emerging Asia, issues that for years had been the flavour in routine, catch-up meetings between Jacques Perrier and his father, the late Perrier Sr. from Bayonne.
After the funeral Jacques deeply suffered from sombre moods and many nights he left his tears run freely in his pillow while feeling regretful, also for the fact that not even his extraordinary electoral victory for the presidency of France made it possible to prolong the passing away of his father.
Jacques Perrier Jr. admired his father most for having worked his entire life to maintain and upgrade his family despite his little education. So much so, that by the time Jacques Jr. was a teenager, the family no longer suffered from the stigma of refugee carried by Perrier Sr. from the moment he had fled the Franco regime in Spain at the age of twenty. Thereafter, Perrier Sr. had managed, with little more than the clothes he was wearing, to illegally cross the border and in few weeks to start a Brazilian coffee grinding and retail company in Bayonne.
No wonder, that Jacques Perrier Jr. expected far more compassion from above the skies for his simple-minded but more spiritual father instead of him ending with an incurable disease.
Even more annoying were the persistent telephone calls the President had been receiving in the past weeks, including this morning at 10:00 hours from a mysterious Martha. The woman presented herself as originating from Cahors, but for the last twelve years living in La Defence, and when speaking about her parents, both alive and well, her voice would become remarkably affectionate and clearly driven by love. When this Martha for the first time managed to get hold of the French President directly on the phone (she presented herself as his sister living in Lyon to get through) Jacques Perrier was hard hit by the intimacy of her information over the behaviour of his mother.
Mysterious Martha requested the president to keep his mother away from dating her old father, since this was hurting Martha's mother.
Picture it: his seventy-nine-year-old mother in her full, black, traditional widow's dress, travelling six or more hours from Bayonne down to Paris to meet a eighty-two-year-old married man in a luxury hotel room in the heart of the capital, simply to have a passionate night before travelling back all alone to Bayonne and probably at peace that no Sunday paper journalist had been alerted by a gossiping bellman over the hosting of the President's mother, dressed in full mourning, for a love night with an unknown, old guy.
The image of his wrinkled and slightly overweight mother passionately making love in a hotel bed near L'Elysee with an old, rickety man—whose growling, wasted wife was crying herself to sleep that night—was outrageous. The image had blown his mind as misfortune piled on misfortune, and the echo of Martha's explanations repeated in his ears. According to Martha, the two paramours had officially been engaged in 1951, just before Martha's father left for Algiers to re-embody the French Legionary army. But when her fiancée returned six years later, Jacques" mother was already married for three years with coffee broker Perrier from Bayonne and had to present herself as the proud mother of two, half-Catalan, half-French children, a boy of two and a girl of ten months. In those days of course she could not dream of the possibility that her little son would once become the first half-immigrant President of the Republic.
Perhaps because of not being able to dream this unthinkable dream, his then twenty-seven-year-old mother had soon after, stubbornly left father Perrier and his two, small children in their factory cum house in Bayonne, and started a new life in Cahors with her uniformed hero. Certainly, it must have broken her poor little heart when few months later—based on a seldom-used article in the Civil Code—the Gendarmerie took her out of the house in Cahors, and straight back to the factory of her immigrant husband in Bayonne.
In all the following decades, Jacques Perrier Jr. never got any information, if true, about this part of the personal life history of his parents, neither from them nor from his Spanish grandmother who had always been living in the room next to his father's office in the constantly-expanding factory cum house in Bayonne.
Only when the mysterious Martha got hold of him three months after the dead of his father, Jacques was forced to wonder if he had ever observed any warm romance between his parents, or better, if he had ever caught them in any intimacy in the twenty-two years that he passed in the house in Bayonne.
However, knowing his mother, Perrier Jr. was almost sure that if it had not been for the bills, neither Martha, nor her mother would have found out that the two old-aged paramours were dating in Paris. In fact, according to Martha, the old man, suffering acute disorientation, once got lost on his way home from the hotel near Place Clichy. When questioned at the police station in the early hours of a rainy Sunday morning, he took a hotel bill from his pocket and explained that his fiancé was waiting there for him.
The detailed and frank communications of mysterious Martha hit Jacques like a bullet straight through his stomach. How long had this love affair gone on? Had his father been blind all these years? Or did his father just hide his heart-breaking secret in the man-to-man conversations the two had over the past thirty-three years? Was he really to speak now to his mother on her detached marriage, dreaming and longing for decades for her Romeo from Cahors, or should he simply decide to send her a spy to catch her in the act and thereafter confront her?
* * *
The alarming telephone call from the German Chancellor, within an hour from the last call of mysterious Martha, plus the communications on the move of the Machiavelli were the last things Jacques wanted on this chilly morning. Consequently, his anger was out of control and his answers were firm, but Chancellor Ditch was also in full power in her reaction.
"Mais mon ami, Jacques, keep calm! Do you really believe that these two Latin conspirators—forgive me to say, but I do not consider you Latino—can do more than spend the money of the others, I mean of ours? I suggest us to have an urgent meeting with the president of the European Commission to shorten the legs of these Latino PIGS-mies. Far from things being lost, I actually see great opportunities for Germany and France. This is the right moment to once and for all reintroduce rationality in the political structure of the Union. I am sure that if we play well, we may have a fluke and get rid of the deadwood of the European Union, including the mistake of the acceptance of most of the twelve new comers. I still cannot digest that we have swallowed the monstrous enlargement sold to us by the Brits and their transatlantic nephew. Let's meet in Brussels tomorrow. I am calling the PresCom2 now."
"Marlein, I see your point. I fully agree to seek the opportunity. Let us meet tomorrow at ten."
After hanging the phone, a now bewildered _President de la France_ continued staring at the white, softened Paris landscape. He had a good face, handsome in a bony sort of way, and eyes wide and bright, often with little sparks of excitement dancing in the centers of them. But he had condemned himself to maniacal pursuits, running from one event to another from the first day of his inauguration. However, today's phone calls certainly had put his eyes in lower spirits. With his nose almost touching the glass of the window, he had to confess to himself that first his mother had gone out of her mind and now the Spanish Machiavelli. Frankly, no one seemed to care about the fact that he had far more important things to worry about!
He remembered his early days after being elected President of the Republic. With what foresight he went to work those days. What great expectations—expressed by so many Frenchmen—faced him. But then, his first exchanges with populist press, who in the name of the man in the street had even dared to address him as The Great Conqueror of Europe, were all courtesy and humility. He was aware of the risks and actually considered himself like an amateurish marathon runner, all knees and elbows prepared to sooner or later hit the grit, but still keeping the iodine and plasters as much as possible out of sight for a public with great prospects.
Perrier Jr., still over thinking the uncongenial communications of the past hours, left the window and moved to his gigantic, mahogany desk, flopped into his oversized chair and started reshuffling some papers piled in the left corner. He was an easily overwhelmed person and while his memory was ordering the events of the morning, before and after the call from Berlin, things became rather clear to him.
How often had he repeated to himself in the early days of his presidency: _Man, oh, man, I do not, with any army, need to conquer and sophisticate the separate countries of Europe; they have already started their own unification process! This is a circumstance, which should have made Bonaparte envy me_.
At the beginning, it seemed to him that he could easily push forward in the European Union with merely smart diplomacy and some logrolling. In his understanding in those days, his only and real challenge was to control his impatience and strategically maneuver to reach the Olympus. The more annoying was the content of the Berlin call just now. So much so, that Perrier Jr. started swinging in his oversized chair and fledging his hands while admitting to himself that within a year of his presidency, things had become far more difficult. To start with, the Euro system with its ill architecture and currency fluctuations proved less solid than proclaimed by his predecessors. Secondly, his projected strong French leadership of a Union of twenty-seven, veto-owning countries soon became a nightmare. Recently more experienced, the image playing in his mind whenever thinking of the European Union, or of what had come out of Delors' project, was one of a slow march of a crippled, blind elephant.
At several moments he had almost bemused observed the majority of middle-ranged intelligent member-state leaders who behaved as self-appointed captains on the EU boat. Remarkable, since none of these pretended captains had either navigation maps or skills, while they all seemed to have different, final harbors in mind. Even more, no one wanted to pay for the trip although pretending to do so, thus preferring free riding over allegedly being misused by the others, as they systematically complained.
What caca! These were the things that irritated him most in his European Union affair. In particular, the British position of not wanting to pay; not entering in the Euro but continuing to influence the system; and finally pushing for a mega-enlargement with mainly poor, less-developed nations, promising them full financial support, once again to be paid by others and not by London.
Moving his fingers through his voluminous and still rather dark hair, Perrier tried once more to put his thoughts straight. Come to think of it, in this context of headwinds, even Bonaparte would not have made much progress. Personally disappointing was the fact that no French-German initiative suggested by France in the past years for deepening the Union had progressed. Nothing was possible with the current Chancellor of Germany. Although perhaps the absurd move of the Spanish Machiavelli could create a new opportunity to seduce the spinster to establish a selective European Federation constructed by him, Jacques Perrier.
Put at ease by the new perspective, Perrier finally could relax so he glided out of his chair and walked over to the bookshelves next to the window. Yes, there it was, the little, blue book left behind by his predecessor.
While walking closer to the bookshelves and pulling out _Overcoming the EU Crisis_ , he remembered the repeated conversations he had with his minister of European Affairs, a leftist intellectual he included in his government just to marginalize the socialist opposition. In those days, both men, although coming from different political backgrounds, considered the proposal of the blue book to establish a voluntary federation of main Euro zone countries on a French-German initiative as something worthwhile, but any attempt to speak on the matter with the German counterpart was set aside by her with the explanation that she was not ready to exorcise federation ghosts in Germany.
* * *
Minutes later, with a cold wind snapping at the old windows of L'Elysee, Jacques Perrier, returned to his desk. Decisively placing the blue book on his desk and passing his eyes over the things he liked most—his photo in silver frame with the American President together inspecting troops in Afghanistan; framed in wood, him in New Delhi at the Presidential Palace with the dark skin, Indian President discussing the nuclear arms race while offering him French mirages; and finally on the ground in front of his desk, the Persian carpet his wife Alexandra recently bought him in Istanbul. He concluded that the Spanish-Italian maneuver gave him the best pretext to demolish the current political architecture of the Union and once and for all to get rid of the abundance of traitors, free-riders, and beggar states accumulated over the last four decades in the hulk of the EU vessel.
______________________
1 PIGS here stand for Portugal, Italy, Greece and Spain. Note that Ireland has been left out.
2 The President of the European Commission is often referred to as PresCom.
### Two
### Lost love illusions but moving forward in Berlin
One day later, with some delay due to heavy rains in greater Berlin, a chartered jetliner took off for Brussels with on board Chancellor Marlein Ditch and her advisors.
Perhaps her entering the plane at the military airport of Berlin could be the best place to describe her appearance. Marlein Ditch was a small, pretty, skinny, dark blond creature with the kind of skin that quickly tans so that she always looked quite healthy. Light, green-grey eyes under full, dark eyebrows were constantly scrutinizing counterparts to detect uncertainty, hesitance, or half-truths.
Plausibly, she would be far more attractive if she would take better care of her make-up and permit herself more feminine dresses, as currently her facade was nothing more than the manifestation of a plain Jane – the reason why French colleague Perrier could only think of her as the German spinster, while her staff in office had long lost their appetite to examine her extra casual presentation.
* * *
As soon as the fasten-seatbelt-signs in the jetliner went off, the dark-suited senior advisor on EU matters of Fraulein Ditch pulled out of his seat and, standing as straight as possible in the low roofed plane, politely presented the files he prepared for the extra Brussels meeting of the two state-leaders with the PressCom on the issue of the federation of the Southerners.
Lamentably, the bundle of papers in the grey file had no lucky landing on the table in front of the Chancellor, as she, in one, rushed movement threw them into the air while screaming with a high-pitched voice to her dark suited aide.
"Do you really think that I should now review all these documents? How many times have I repeated that I want a minimal twenty-four hours to prepare myself? And presented in bullet points. I am not a bionic woman!"
Racing down on his knees to catch the papers flying around and quickly stuffing them in the copy file in his hands, the aide contained his slight anger.
"Madam Chancellor, excuse me please, but you have called me only twelve hours ago to arrange for the meeting. I am sorry. Were it not for our colleagues in Brussels and Paris like me always willing to overwork ourselves, there would have been little news to report. I apologize, but as I also have been forced to study their inputs, would you mind me instead verbally briefing you now?"
The Chancellor in a new outcry: "No, you cannot! Although I am grateful for your considerate suggestions, to my knowledge you have not presented me with one, single, original idea in the past, three years. Believe me things are too important now for cutting and pasting. I can hardly trust my French colleague, let alone the rest of the bunch."
The civil servant in Hans Schmidt was in obeisance as he neglected her mood and, with his bowed head almost touching the ceiling of the curving plane, remarked with playful gentleness.
"But Mrs. Chancellor, what is it of great importance that you want to pose in Brussels?"
"Mr. Schmidt, tell me. Is there much choice left for me with the mess I have inherited from my predecessors? Please, sit down. I will explain it to you. I am not telling you anything new if I say that this European Union is not a Union. But on the other hand, to speak the truth, I am not at all interested in a Union with this bunch, many of them dreaming of Germany as a Treasury Island, ready to be looted. Believe me, some of them would not even mind the Euro zone returning to inflation rates near those we suffered in times of the Weimar Republic. But as long as I am here, the European Central Bank will have to behave as the Bundesbank in the days before the Euro system. We are no longer feeding beggars."
Moving with greater confidence since the Chancellor was closing in on a subject on which Hans Schmidt had his views and projections clear cut, he sat down opposite Frau Ditch convinced that his one-liner had touched the right string and that even her lavish answer would be easy to ward off. He only was to listen careful and then answer strategically.
"Listen Schmidt, my French colleague has offered me insistently to create a federation formed only by stable countries of the Euro zone. Of course these countries should be pre-selected by him and me before involving anyone else. And frankly, due to the circumstances, I consider his approach at this time in history the right one. Yesterday night I was thinking and rethinking what would be my own pre-selection and believe me, this was far from easy. Let's see. Apart from France and Germany, we have the Dutch, Austria, and Luxembourg. More?
Counting on Belgium in its current political stalemate is absurd. So is Ireland. And of course I have strong doubts on Italy, although pulling them out of the PIGS would fortunately blow the plans of Spain. But then, the Italians are not trustable at all since they love both the underground economy and spending money without paying taxes.
What complications!"
From take-off, thick, dark clouds surrounded the plane and probably the chosen altitude to fly into Brussels would mean continued turbulence. Certainly not Herr Schmidt's favorite flying weather, but as he could observe from the nervous moves of the German Chancellor opposite him, neither hers. He was now bowing slightly in her direction to create a more relaxed atmosphere and started speaking at lower voice.
"So, Mrs. Chancellor, if I hear you well, you are suggesting that France is going to be our only trustworthy counterpart for solving the current financial and political crisis in the EU."
"My dear Schmidt, I would like your deduction to be correct, but the naked truth is that not even the French can be my betting horse. You know, to me all French political parties, except of course the extreme right are tilted to the left, and you know what that means in the current circumstances: increased public expenditure financed by fresh, printed money."
The plane bumped more aggressively and Frau Ditch flung forward to him while her hands anxiously grabbed the arms of her chair. So much so that Herr Schmidt could suddenly smell her perfume or maybe it was just her body lotion. Unmistakably spicy, although he would not have thought her ever using more than the scent of ice, he reflected with a hidden smile while Frau Ditch continued expressing her views on the future of the EU.
"Herr Schmidt, you will agree with me that the current intentions of EU policy makers could take us, if we are not very cautious, to an inflationary process that we Germans strongly detest."
He was aware that he should immediately take a distance from his too personal reflections on the Chancellor and replied. "Madame, if you allow me, and with all my respect, it is my humble view, although shared by some European governments, our Trans-Atlantic friends, Britain, China, India, and others alike, that having public deficits in times of recessions or slow growth will not necessarily be inflationary.
Perhaps, what differentiates the Euro zone situation for the worst is that we have only one Central Bank shared by seventeen nations, which does not enable decision making in relation with printing money since this was forbidden at the construction of the Euro zone. To my understanding, there is only one way out: to change the statutes and make possible that the European Central Bank finances the recovery of the economic activity in the Euro zone without exaggerated, inflationary concerns."
At his last words, the plane entered an even heavier zone of turbulence, seemingly passing an airbag and falling down quite some meters. This time, Schmidt could not avoid crossing eyes with Frau Ditch. Green-grey, they became filled with a dog's fear. During the bump her face came close to his and he could see a pale, satin flush creeping up from her neck and covering her cheeks. In great contrast was her strong reaction on his frank remarks.
"But my dear advisor, you should first and foremost read books of German economic history and you should know that we, the Germans, produced an economic miracle also in the times of Chancellors Adenhauer and Erhard at all times correctly balancing our public budgets. Even now we have only small deficits and we are growing much faster than the French and others."
Schmidt, with his eyes following the line of her cheeks and small shoulders, was now amiably calm. "But madam, if I may say so, note that in times of the former German miracle, we received a strong impulse from the Marshall Plan and that now in reality we are merely living from the budget deficits of the Americans, Chinese, and other EU members. I think that economists like Stieglitz and Krugman, both Nobel Laureates, are right in defending public deficits in times of unemployment. Probably, if the Americans, Chinese, and Europeans would have acted like us, even Germany would now be in cero growth or even worst."
By now the turbulence was so bad that Frau Ditch had to lean backwards and with her eyes in her frozen face staring at the table between them, she signaled with her hand that the conversation was over. Marlein Ditch had been saved by the bell and in order not to be overwhelmed by fear she closed her eyes, leaned backwards, and set herself to pass the rest of the bumpy flight in silence. But first there was a quick glimpse on her watch, which made her figuring out that they would have at minimum another twenty minutes before landing.
Anxious, she decided that instead of restlessly having to count the seconds and minutes till touchdown, she would rather reflect on the arguments of advisor Schmidt.
First of all, she had to admit that Schmidt's opinions were far away from those regularly expressed in her Council of Ministers meetings. But the difference was quite understandable since the latter were mostly defending the traditional way of doing politics in Germany. On the other hand, Schmidt's arguments were, as one could expect, not at all original.
Really, in the past three months, she had been reading the same arguments in most mainstream international weeklies, of course outside of Germany. Could it be just a matter of envy of these internationals with the "German miracle"? Or could it be that they would prove to be right and that her Council of Ministers was mistaken?
If the outsiders were right, the Euro zone would need a Central Bank with statutes similar to those of Central banks in the big, independent, or federal nations. Although, the Euro zone was not one nation so Schmidt and Jacques might be right that the only way to solve the problem of creating jobs without significant inflation would be to establish a Federal European State of several, Euro zone countries.
Nice thought, but not easy for the spirit of Germans, completely averse to systematically having to feed the beggars of the South. Logically, Jacques Perrier repeated several times, " _By just merging interested countries with more or less the same per-capita income, that is to say, homogeneous countries in the Euro zone, thus sidelining free-riders and beggars_."
He could be right. Federating five, relevant, Euro-one countries could create a 175-million-people state to start with. But for her, it would probably be more difficult to actively promote this idea. If Germany would promote a super EU state this could also wake up some ugly ghosts of the recent past in the continent.
* * *
Thinking of ghosts, jittery Marlein Ditch in cloudy skies was being knotted slowly by the remembrance of far more unpleasant experiences in her past. Although she had long learned to push matters far to the back of her memory, once in a while, mainly in situations of stress or tension, the nasty events came back to her. And they were coming back to her now.
The story is difficult to tell, for to tell it from the point of view of Marlein would almost certainly end up downgrading it. One has to understand that today, for most people, in modern, united Berlin, Marlein Ditch is a philologist and feminist—never married, no children—who after a hardly visible, unfruitful career as policy staff in a small institution in East Berlin, turned her boring, invisible life upside-down by entering into politics. And then she surprisingly managed to reach the highest level by becoming the second female Chancellor of a United Germany.
Frau Ditch became the chief of the largest country in the EU but hardly anyone around her in modern Berlin or in Brussels would know anything or seemed interested in her past in Leipzig and Dresden, or to be more precise, in the story of her dramatic experience as one of the happy few selected talents for the elite athletic program of the German Democratic Republic.
For the interested reader, one could reflect on Marlein's life story by highlighting the three episodes she was firmly keeping secret. One could state that she had symbolically buried any unwelcome content of her life under the many stones of the Berlin Wall when it collapsed in 1989. At that very moment in time, she effectively seized the opportunity to cross from East into West without her past.
* * *
_First: the Leipzig period: 1968—1972_
In 1968, the 13-year-old Marlein, coming from a small village twenty-four kilometers east of Weimar was admitted to a Training School for Olympic Athletes at the outskirts of Leipzig.
Marlein Ditch was one of the happy few who successfully passed the selection at the annual nationwide competition to enter into the elite athletic program of the German Democratic Republic. The training school itself, beside preparing students to keep up the extremely high level of golden medals GDR athletes used to take home from worldwide competitions, was also the greenhouse for coaches in training at the prestigious Deutsche Hochshule fur Korper Kultur und Sport (currently the University of Leipzig) in the center of the city.
What a glorious day it was, the morning Marlein entered the office of the Rector with her parents and her aunt Frieda. In those days, the latter was a member of the city counsel of Weimar, and consequently a middle cadre of the Socialist Unity Party in the country.
Only two hours later, on the same serene morning, Marlein was able to empty her suitcase, filled mainly with training dresses, in the closet of her new room. It was an artic room on the top floor of the three-story building with a dormer window spreading some daylight on the two, small beds, one for Marlein and the other for another "coming" athlete, who had also been placed in the same class room of the Sport Lyceum.
All the buildings of the Institute (the hostel, the sport-halls, the classrooms, canteen, first-aid, and library) were located in a spacious and hilly, green park with the statue of Karl Marx at the entrance.
Aunt Frieda, a person with a visionary mind, not only supported the admittance of Marlein to the prestigious school, but she also, with an eye on the future, designed elegant nametags and name cards for her soon-to-be-famous niece, ready for use immediately after Marlein would win her first golden medal for excellence, be it on the asymmetric bars, the vault horse or the balance beam.
As it later would appear, the ideas of Aunt Frieda were very premature since Marlein would leave the Sport Lyceum in Leipzig at the age of seventeen and short of any gold medal as she had to skip the Games of 1972 with a chronic fracture and continuing pains in her slightly deformed left knee. All this caused by a serious fall from the balance beam in the second year of arriving at the school and compounded by continued exercising.
In the months after the accident, the fracture in her knee could not cure since from the moment of the fall—Marlein tumbled from the beam during a regional championship in Minsk—until her departure from the school, she continued competing, forced by Coach Friedrich, although endlessly being put on the pain rack. Subsequently her life became a real nightmare in the following twenty months as she could not share her misfortune with anyone.
Condemned to silence by Friedrich with a body stuffed with painkillers, she continued training and competing in at least two more championships for young athletes in Dachau and Moscow.
As she later reflected on these dark days of her youth, it had not only been a matter of performing while passing all torture landmarks, but also the experience of being trapped in a pitch-black tunnel filled with the many false expectations of Aunt Frieda and her parents on the one side, and the lethal pressure of Friedrich on the other.
So when she left the institution at the age of seventeen, not only had her body aged too fast, but also her illusions had swiftly crumbled and, deathly tired, she settled for a gloomy life as a housewife with Friedrich. He was an irresponsible man more than twice her age who offered his small apartment for her to come to terms with her innocence lost and her dreams evaporated.
* * *
_Second: the Dresden period: 1973—1978_
To survive the disappointment of only marginal recovery from the—at her age exceptional—osteoporosis, Marlein completely lost herself in her philology studies at the University of Dresden. There she was, a shy, eighteen-year-old youngster, too small and perhaps too skinny for her age, already married and on rainy days often walking with a slight hobble.
Yet, she surprised professors and deans of the faculty by following classes of two years in one and finalizing her master studies one year ahead of the normal scheduled time. And although it was understandable that she rarely found time to participate in the vibrant student life of the beautiful city with its abundant, historic buildings along the Elbe, it was remarkable that she strongly held back to any mingling in her private life or in her life story, while the opposite would have been something quite natural in a faculty of philology.
As the reader may understand by now, it must have been a deliberate choice of Marlein, who instead of trying to come to terms with her past was probably more occupied, be it in silence, with the preparations of a huge turnaround in the next stage of her life.
No one will definitely know, but fact is that her quiet behavior at the faculty in Dresden secured that nobody would be able to remember anything special of the young, hard-working, loner student by the time she was inaugurated as German Chancellor.
At most, some neighbors in the apartment building in the Garten Strasse in the center of Dresden would be able to recall that, in April, a week before Good Friday in 1978, the husband of Marlein, a forty-year-old sports coach suddenly died during a trip to Moscow, thus leaving his young widow in disarray.
Perhaps these neighbors would also remember that Marlein, who herself informed them of the death of her husband by sticking a note on the information board in the entrance hall of the building block, did not open her door in the days after for anyone ringing in an attempt to show compassion and offer support to the far-too-young widow.
Those who approached Marlein around Good Friday had to settle for her firm refusal, followed by the announcement of a well-balanced, young widow that she was busy packing to leave for East Berlin. As she explained monotonously through the intercom, she had applied for a job as policy staff at the Hendrik Kreamer House in the Linden-Strasse in East Berlin, the only community center of the Dutch Protestant Church in the GDR. The vacancy was brought to her attention already in February by the Vicar of the Kreuzkirche and she was thankful for his support. It had resulted in her appointment to this somewhat exclusive institute in East Berlin. With her voice slightly cracking, she would add that her misfortune with the loss of her husband had thus become more bearable.
Nevertheless, the reader should be informed that neither Marlein's parents or her Aunt Frieda, let alone the neighbors and her colleagues at the faculty in Dresden were aware of the truth that the man who Marlein proclaimed dead, was alive and well in Potsdam, some 150 kilometers from Dresden, preparing to leave on a scholarship to Moscow.
In the wa-wa hours of the night of the Monday before Good Friday, with the knowledge and stimulation of Marlein, Friedrich had unnoticeably moved out. He was lucky that he could temporary settle in a small apartment in the compound of the athletic training institute of Potsdam. Even more, the next day, he was happy to start living in his scarcely furnished studio with a young, well-proportioned, Cuban woman he actually picked from the streets two weeks before in Dresden. It is also objective to state here that things worked out far less-fortunate for Friedrich since only days after settling for his new love life with the Latino and her jiggling buttocks and artificially-oversized breasts; he found out that his new partner was living on a daily dose of lithium to balance her bi-polar moods. The situation was unbearable in the confinement of the small studio in Potsdam but it was already far too late for him to solicit a welcome back in Dresden.
Little did he know that the announcement of his alleged dead was already made, including the information that his funeral was taking place in Warsaw, which not only was half-way from Moscow to Dresden, but also, according to his presumed widow, his hometown.
All that takes us back to reflect a little on the marriage life of the couple over the past five years.
Marlein started being disappointed after the first three years as she expected far more interest for her academic endeavors from the coach and, if not, at least some more sophistication in his behavior.
Certainly Marlein had not imagined that she would find Friedrich at the sofa in their living room with the Vietnamese cleaning maid of the faculty, or that he would repeat his extra-marital affairs with other cleaning maids, which as far as she knew happened repeatedly, and which she cynically categorized as his favorite group to hunt.
Coach Friedrich was in his way also disappointed with his wife. Perhaps he expected far cozier homecomings, but instead his young spouse buried herself in her study and preferred reading books till the early morning hours. In these circumstances, he fell asleep alone in the double bed, dreaming of making love with Marlein before a post-orgasmic daze would wake him up. Yet, Marlein from her side was determined not to compromise to the needs and wants of what she considered routine of primitive man. So while one could explain Friedrich's disappointment and misbehavior as the result of his slowly but steadily exclusion by his academically advancing wife, one could also consider that Marlein from her side was convinced that Friedrich was regularly seducing young, female athletes at the institute in Dresden, or if not, exotic, cleaning maids from overseas, socialist countries and she would not want to expose herself to the risk of any sexually transmitted diseases.
By the time the fourth youngster made her appearance, this time from Cuba, Marlein coldly asked Friedrich to step out of her life, preferably as soon and invisibly as possible! Subsequently, the sports trainer walked out of Marlein's life just before dawn with only a few of his clothes and shoes.
In the same week, Marlein calmly announced his dead at the faculty and asked for two weeks off for attending his funeral in Warsaw. As she explained, having been prescribed good tranquilizers, there would be no problems with her traveling alone.
Just one week before the announcement of Friedrich's passing; the Vicar of the Kreutz Kirche had brought her the positive news on her application for the vacancy at the Hendrik Kreamer House. Showing only restrained delight with being accepted, Marlein timidly asked the Vicar if she could donate some of her things to the church when leaving for Berlin.
The first week of her leave to attend the faked funeral in Warsaw was quietly passed by Marlein in a small hotel up in the north of Rostock; and in the second week, dressed in dark colors for the occasion, she stayed at her family home in the outskirts of Weimar.
Yet, the tears she shed with Aunt Frieda and her mom, both in no doubt over the fact that Marlein had just returned from entombing poor Friedrich, were real as was her somber mood. Together back home in Weimar, the three women grieved over Marlein's misfortunes over the past seven years, starting with the failure of becoming a gold medal athlete. And afterwards, the three prayed together in the St Peter and Paul Church for seven, better years to come for the young Marlein. It is fair to say that also these prayers were for real.
* * *
_Third: the East Berlin period 1978—1989_
Time left a hole in her memory concerning the East Berlin period, except for the fact that the years went by quiet and the people in the Kreamer House were very trustworthy. In 1982, Marlein, for the first time in her life, spent two months in the West. The Ecumenical Community of Berlin negotiated and paid for her knee operation in the academic hospital of Leiden, the oldest university city of the Netherlands. After a successful, ultra-modern implantation, she passed another month for her revalidation in the Hendrik Kreamer House in Oegstgeest, the sister house of the institution she was working for in East Berlin. In Oegstgeest, Marlein was surprised by the existence of hundreds of Christians preparing for trips to Eastern Europe in their campers and mobile homes stuffed with bibles, all destined for forbidden Christian gatherings in Romania and Hungary. How things had changed!
* * *
At the announcement of preparing for landing in Brussels, a slightly emotional Marlein Ditch abandoned her reflections, opened her bag, and pulled out her lipstick she might have bought years ago but hardly used since it was against her convictions as a feminist. Perhaps it could be of some help today. One never knows, but sometimes a colorful smile could suddenly move the will of translators, aides, advisors, or even the PresCom in a good direction for the preparation of a voluntary federation of Euro zone countries.
### Three
### A French-German initiative is overcoming turmoil
Brussels was cold with some porous sunlight in a distance when Chancellor Ditch arrived at Berlaymont, the EU Commission premises in the Rue de la Loi. Approaching the monstrous building in steel and glass panels, Marlein knew for sure that one of her predecessors would have agreed with the construction of this-to her taste-ugly building, and then again right in the capital of the most politically dysfunctional member of the European Union, but it would probably not have been her choice.
Entering the building-in her view also furnished with bad taste-the ambiance converted even cooler when the Chancellor surprisingly ran into the British Prime Minister. He certainly was the last person on earth she would want to meet this morning.
"Madam Chancellor, what a pleasant surprise. How are you doing? Looking good as usual."
"Do not flatter me. I am fine, but what on earth are you doing here my friend? Meetings?"
"No, no, nothing formal, I just met some of my parliamentarians and I have to admit that I have used the opportunity to meet the PresCom over breakfast. And as you may understand, I have of course insisted on cutting the British contribution to the EU budget."
"Dear friend, so you continue with the same demarche of your predecessors who tried to pull the legs of the European Council. And this even after the blow Britain received on this issue with twenty-four votes against."
"Madam Chancellor, dearest Marlein, this is simply what the British people want. Do I have another choice as a democratically elected Prime Minister than to honor the view of the people?"
"Dear Prime Minister, would you agree with me that even the British people, as by the way also the German people, could change their view provided that they were well-informed on their long-term interests?"
While taking off his glasses and hooking them in the top pocket of his jacket, the Brit produced one of his well-known, diplomatic non-answers.
"Changing the subject, what is the cause of your sudden visit from Berlin? Is it to the PresCom?"
"Yes. I just wanted to have a first-hand account of the move of the Southerners. You may be aware."
"Madam Chancellor, I have to confess that I have been informed a week ago by my four ambassadors _in situ_ about the Spanish initiative, but actually, I do not see any matter for concern. One should expect many wild ideas, given the current problems in the Euro zone. Fortunately Britain is not part of it. As you know, we over and over again warned about the instability of the monetary union created in Maastricht."
"But dear colleague, perhaps things would have developed far better if Britain and some others had not opted out. To say the truth, you have not entered the Euro zone, but in exchange you have presented us the gift of the omnibus enlargement of 2004. I am still mad about the trick, but I have no time now to go into discussion. So, let us agree to disagree, I have to rush."
As Marlein abandoned the company of the British Prime Minister, she concluded that the Brits, irrespective of their political color, were behaving the same in relation to the EU: they probably joined to kill the project as, years ago, de Gaulle suspected.
At arrival at the door of the PresCom office, Frau Ditch still felt disturbed over her unexpected encounter and the prickly open-ended conversation over the political crisis in the EU. And all that, in his mother tongue, an asymmetric situation Marlein more and more detested.
Subsequently, the man in the marine blue and yellow outfit, full of golden tassels and stripes, waiting for her to clear the way to the President of the Commission, was at first almost overlooked by Marlein. Only when the bogus lackey announced that both the President of France and the PresCom would join them with some minutes delay, Marlein granted him a look to immediately turn her eyes off while remarking in clear disturbance—and this time, in German—to Hans Schmidt.
"Thank God, with our Federation, this whole theater of phony monarchy lackeys will be something of the past."
After the Chancellor and her aide took a seat in the _ante-chambre_ , they started hearing the loud, incomprehensible, and agitated speaking of the President of France in the room next door. Jacques Perrier was apparently on the phone and in bad temper.
* * *
"Alexandra, listen. You cannot do this to me, and certainly not in this way. I married you, just before my inauguration as President of the Republic. I expect you to fulfil your duties and to let me terminate my first mandate before any act of divorce. Really, this is a blow under the belt. Something I have never received from the opposition in the National Assembly, or from any of the unfriendly friends in my party." On the other side of the line, his wife Alexandra pretended to apologize while explaining in a serene voice.
"It is not me leaving you, Jacques; it is you who has systematically left me from the first days of our marriage. Yes, I could understand that you did not sleep with me when you tripped to the US or China and I had to remain home. But what is not acceptable to me is that you did not stay with me and left for Le Havre to confront some unimportant, striking port workers, or because you had left for Val d"Isere to inaugurate a petty snow canon in the ski-station of one of your friends. Your hyper-activity and lack of priority is simply absurd for a man with so many ministers at his disposal. Ah, and do not think that I have invented this argument; all Frenchmen say the same.
Anyway, to make sure that you are not unpleasantly surprised by information coming from your ambassadors, or that you have to read rumours in glossy magazines, I prefer to inform you that I am currently in Istanbul, accompanied by a man of my age, perhaps a little younger, of Turkish nationality."
" _Merde_ , you call me in Brussels to say that you are cheating me with a Turkish lover-boy?
What the hell is going on?"
"Calm down please. Do you remember the guide who the Turkish president offered us to show us around in Istanbul when we were visiting Ankara and you suddenly preferred to remain in the hotel to make a thousand calls to Paris to satisfy your micro-management?
I felt very alone then, but paradoxically these two days turned into very nice after the guide cheered me up. In reward, I invited him to Paris for a visit, which totally unplanned ended up in us developing a relationship. I know it may be very painful for you. I am very sorry.
And although at this moment, I would prefer living with him, I can promise you that I will remain with you till the finish of your term."
"Enough, Xandra, I cannot hear this. I will not talk to you any longer. I am in a meeting."
An angry and humiliated President of France, at the brink of a nervous breakdown but simultaneously also aware that he had some time to react before any divorce, caught himself thinking about possible solutions for getting rid of the Turkish guide while walking slowly towards the _ante-chambre_.
Come to think of it, he recognised that he might have committed mistakes the first years of his presidency, in particular his endless rushing from here to there to wave his flag. But this in no way justified the behaviour of Alexandra. Would he ever understand women? Thank God she had given him some breathing space till the end of his first term.
Perhaps he would be able to recover his skills to charm the young writer he married shortly before his electoral success. Nevertheless, provoking the disappearance of the Turkish guide from her side was a very urgent issue. At all costs, he should elude that the media would in one way or another become aware of any affair of Alexandra, which would certainly affect his career. Not to mention the fact that, of all existing possibilities, she had chosen a Turk.
* * *
Having waited for more than five minutes, an impatient German Chancellor started stretching, when at that very moment her irritated glance hit a worried French President who was hasting towards her. As Perrier was trying to camouflage his furious screaming of some minutes before, he drew up an artificial smile on his bony face and discreetly tried to wipe off the sweating on his forehead. Yet, Frau Ditch was boiling with curiosity to know what his emotional conversation had been about.
"I hope it was not bad news you got, Jacques. Be assured that we could only hear you speaking without understanding a word."
Jacques Perrier was quick with his response, "My wife has called me, first to say she loves me and secondly to complain about her relation with my eldest son who's becoming more and more difficult. And I have understood that if things do not change, I will have to make a choice between him and her. I am sure the last observation was pure bluff of Alexandra. Anyway, it was a debate of minor importance but, nonetheless, frequent among couples. Luckily for you, Marlein, you have none of these problems. You see, even becoming president of France does not guarantee a happy family. Perhaps you did well not to marry."
Marlein decided to drop the conversation by answering, "Absolutely my friend, for me, the grass was never greener on the other side. Alas, few people understand the constraints of combining state leadership with family life, but as far as I know, our combination is far more difficult than the family life of movie stars, as we are also supposed to show high morals and set the example."
In the following minutes, the two top politicians used the waiting time to exchange views on the morning news, in particular on the headlines concerning the bluffs of the Iranian president in relation to Israel, fresh political protests in Tunis and Cairo, and the euro-dollar fluctuations, when suddenly another lackey, again in full EU colours, yellow stars and cavalry head, opened the double doors to the PresCom office and announced, "The President of the European Commission."
While Carlos Bopoulos, the PresCom was approaching in a completely hassle-free way, he started talking.
"Dear friends, sorry for the delay, but as you may imagine my meeting with the Budget Commissioner has lasted far longer than expected. Ach, you all know how the Union finances are faring. I have explained a thousand times in several forums that with our squalid EU budget we cannot reach much progress. I would have liked to see the two of you in my place, suffering with available funds of only one-percent of the EU GDP, when at the same time everybody travels to Brussels for showing me his or her hand palm as did the medieval monks of Mendicant Orders. Yet, conversely to the latter, the current begging hand is accompanied by extreme urgency and arrogance as if the money they demand was their indisputable right."
Contrary to the French President, PresCom Bopoulos was 1.90 meters high and extremely wrinkled in forehead and around the eyes and ears. His curly hair had notoriously been rejuvenated with an overdose of shiny, black dye that should match his dark eyes behind fashionable framed glasses, but under his severe overhanging eyelids his eyes were almost fully invisible. To complete the picture, his sky blue tie could have been a gift from Aznar, while his deep blue shirt, undoubtedly Italian, could have been a gift from Prodi. However, the origin of his buttons was clear: marine blue flags with the usual ring of yellow stars in the middle in great harmony with the uniforms of his lackeys. One should note that these buttons were typically part of the small presents that his secretary kept for third-world country visitors or journalists.
The last odd detail of the PresCom in full ornate were his shoes;
almost cherry red, they were in stark contrast with his cream suit.
Certainly the multicolour appearance of Bopoulos well reflected his political past. Before becoming European PresCom, the man had shifted several times and even from one extreme of the political spectrum to the other in the various political parties of Greece. An experience which probably made him rather acceptable to the diverse EU member states who crowned him as President of the Commission only after four years of being EU Commissioner of Sport and Culture.
On the other hand, one should not neglect either the fact that his fluency in more than eight languages, including Flemish and Serbian, might have contributed to his popularity in the European Parliament and even so in the European Council, but perhaps the mere fact that he had no enemies was most outstanding. He had a fame of being completely relaxed, someone who never splashed a single drop outside the pot. Immediately after Marlein and Jacques—with their respective aides at back benches—had seated themselves, the French President expressed his agreement with the budget remarks of the PresCom at entrance.
"You are right, Carlos. I have also said in many forums that if the EU wants to be a serious institution with full political capacities, it should count at least on six to eight-percent of its joint GDP. In reality this is not a big figure in comparison to the federal budget of the US government or even the national budgets of our member states.
Actually, I felt disgusted when some minutes ago the German Chancellor reported to me the content of her conversation with our friend, the Prime Minister of Britain, who openly revealed to her that he had been pleading once again for the check rebound. Let us not forget that Britain shamelessly started demanding the rebound already some few months after entering in the Union in 1973. This is exactly as some pinchpenny grooms do, claiming back the rings and jewelleries from their wives one day after the marriage to deliver them to the pawnbroker under the threat of immediate divorce."
This time the German Chancellor reacted itched. "Six to eight-percent of EU GDP, what are you saying, Jacques? Let us be frank. Do you really believe that after Germany is contributing almost two-percent of its GDP while others prefer free-riding, any German would agree to increase our EU burden with a single Euro cent? Should I remind you that we Germans have paid double for our own unification: first from our own national budget and secondly by our extra contribution to the EU? And all this while member-states complained in those days about our increased power, and others started their economic miracle by diverting our capitals to their territories, by means of lowering the rate of their corporate tax. As you may understand, I am referring here to the Irish miracle which finally turned into a nightmare."
At Marlein's last words, President Perrier, erecting from his armchair as a tiger and requesting his aide to retrieve the blue book on solving the EU crisis, quickly responded, "My dear Marlein, you have not fully understood my remark. With my proposed budget I was referring to that of the federation. This budget would be equivalent to six to eight-percent of the joint GDP of the federating countries, which would be a magnificent business for Germany, France and all who join us. Note that the participating countries, by joining their services, could save huge sums on their defence and security budget, on foreign representation, as well as on public finance, and on other costly sectors such as infrastructure development. The value of these joint services would be well over the six to eight-percent. Believe me, serious studies have figured out a total saving of two-percent on the collective GDP."
As his aide placed the blue book in front of him, Jacques started waving it in the air, adding, "But listen, we are speaking about a serious study and not about a figure of half-a-percent that the architects of the Euro promised us when they delivered the current mess we have nowadays."
By now, Carlos Bopoulos, who kept silent but clearly showed disagreement by moving his head like an Indian Sadhu, decided to intervene and change the subject.
"Colleagues, I had understood that you were here to be informed first—hand on the situation of the attempted federation of our dear member states of the south. Let me assure you that there is no reason to worry whatsoever. I think that the attempt of the Spaniards and Italians is nothing more than a _fuite-a-l'avance_. Although their merger could alter the power play within the EU, thus provoking strong reactions, I have already dealt with the matter. No one less than the Russian Prime Minister, hinting at a possible, future agreement on a free-trade zone with the EU, has informed me that he has rebalanced the problem. As he explained to me, in a recent Russia-Italy bilateral top, Russia expressed great concern over the negative impact on Russian gas exports to the EU following the federation of the Southerners. If I understood well, some Eastern diplomacy is on its way to blow up the operation."
"Monsieur, speaking from the view of France," said Perrier, "I may agree that this so-called threat of the PIGS is no more than a bluff, which will melt faster than two pieces of ice in a whiskey on the rocks." But the reaction of German Chancellor Ditch was far more reserved.
"Really, I do not want to offend anyone, but I feel that what is hidden under this manoeuvre is a pressure on the rest of the EU member states to lend them the money they cannot borrow on the open, international markets. So, I think that if we guarantee them the money they need, this projected federation of Southerners, who have only in common their tendency to parasite us, would vanish as a soap bubble. But my dear friends, I cannot risk my government falling. As you all know, there is not a single German willing to put more money in any of the bankrupted countries of the Euro zone. Really, in these days of Facebook and Twitter, I will not move in that direction.
Indeed, what has become clear with this absurd business of the PIGS is the kind of people we are dealing with. We cannot continue cooperating with leaders who are constantly bargaining with principles, cheating on their deficit figures, and dividing instead of adding. We can no longer accept that Mister PresCom, I think that the moment of putting our house in order has finally arrived. You will have to agree with Jacques and me that with all these purported drivers, the EU project is practically arrested and in need of a radical restatement in its architecture. Although I initially hesitated about the proposal of Jacques, every minute I am more convinced that he is right. The bunch of twenty-seven is unmanageable as most of them have different economic and political interest than the core countries like us. Even more, you must remember that the Germans established clear criteria in the Maastricht Treaty for countries to be part of the monetary union. But at least three countries that did not fulfil the rules were still admitted to enter, and you see how they are now. Others have not only overcome the deficit figures of the Stability Pact, but have reached levels three or four times on top of it, which is the case of Spain and Portugal. And here we have it, the full picture of the PIGS. Prescom, you will agree with me that we cannot continue in such an unstable situation in which every two months another weak brother may fall if we don't advance money. Consequently, Jacques and I believe that the strongest and most courageous countries of the Euro zone should turn the page of the current stalemate and make a rapid move towards a political union of a selected group of member states, thus fulfilling the dreams of Monet, Schuman, and others."
Carlos Bopoulos, who during the intervention of Marlein became visibly restless with his face growing congested, was cracking his fingers and slowly weighing his words in his answer.
"Dear friends, I have listened attentively to both of you and I do understand your concerns and some anger. Yet, you may understand that as PresCom for twenty-seven member states, I will have to look at things from a broader perspective. First of all, one should never oversee the fact that Europe has experienced its longest, peaceful period in its turbulent and frequently violent history. This is the most important achievement of the Union, not to mention the fact that our diversity has anchored the average political behaviour of member states in a more centred and lukewarm position, far away from the dangers of fascism, communism, and extreme capitalism. The things you both have described to me are certainly worrisome, but are not more than stones on the way. On the other hand, I think that one of the most important values of the Union is solidarity and I think that at this historical moment in time, it would be wrong to abandon to their own survival those who are less affluent than the core countries, or those who have committed some serious economic mistakes. I am certainly convinced that in the near future the current, economic slowdown will be overcome, and that in two decades all of us will be citizens of a Mega Union of more than 600-million people, just doubling the population of the USA. Madam et Monsieur, I see no reason whatsoever why Germany and France should not cooperate for the consolidation of this Mega Union, in which Germany and France will always play a leading role while overtly profiting from a huge market."
The last words of the PresCom were the sign for the President of France to leave. He felt outraged over what he considered the continuous, hollow mantra of Bopoulos cum suits. Jacques pondered that he had heard the same arguments many times in different forums since the commemoration of the fiftieth anniversary of the Treaty of Rome. Clearly, this PresCom, like so many other second-rate EU politicians, lacked a theory on the future of Europe. It was a waste of time to continue listening to things that would only convince those working in Brussels, fearing to lose their jobs.
Thus, Jacques aggressively gathered his belongings, looked at his Rolex, and announced, "I will no longer jeopardize the future of France and its great citizens for village politics of small, backwards countries that are hardly interested in a common destiny. I am off, but I will immediately start initiating the promotion of a voluntary, self-selected federation of five to six, economically-homogeneous countries who are already in our monetary union. Bonjour a tous."
At his last words he was at the door followed by the German Chancellor who was quickly apologising to the PresCom for having to leave as well, but thanked him politely for his views concerning the feasibility of the PIGS project.
On their way out and no longer in hearing distance of the PresCom or his proxy lackeys, the German Chancellor at low voice invited the French President to meet at the German Ambassador's Residence in Brussels for a _tête a tête_.
The German Ambassador—pink tie, dark suit—was standing at the gate of the residence with his partner and all the servants in white jackets forming a straight line. Nothing unusual except perhaps for the male partner of the Ambassador; a Caribbean, muscle-bound ex-boxer with curly, dark hair and a bright smile in his ebony face, who on top of all counted visibly some twenty years younger than his spouse, the Head of Mission.
At the stop of the two diplomatic cars in front of the Residence, the German Ambassador subtly signaled to the German Chamber Orchestra, on tour in Brussels, to start playing the Marseillaise.
However, Jacques Perrier, trying to quickly move out of the car, lost his equilibrium and unexpectedly landed in the strong arms of the ex-boxer, who with his extremely, high-pitched voice, started screaming
"Oh what an honor to receive the president of France in my arms!" The German Ambassador swiftly turned to the scene and was gazing severely annoyed at his partner before he ordered him to immediately put the French president down and join the ranks of the servants for listening to the anthems.
"But Dieter, darling, I have only instinctively helped him not to fall", jested the ex-boxer. Correcting his suit and tie, and picking off a curly hair from his hand, the French president produced a smile on his face as he exclaimed to the German Chancellor, "My dear colleague, have not you just understood from the PresCom that our two countries are in peace since 1945? So why would you provoke a political raw, by playing the French anthem even before I could stand in position?"
Meanwhile, the German Chancellor was throwing an angry eye on her ambassador before hastily bending over in the direction of the president of France and apologizing to him. At low voice so her ambassador who stood at attention for the German anthem could not hear, she reflected on the more and more overt exhibition of same-sex relations in diplomacy, military army, and parliament. In these days of ultra-liberty, ethical relativism, and political correctness, being sexually opposite was almost provocatively promoted while, at the same time, even the most humble, religious symbols were being forbidden.
* * *
The library of the Residence was a room with dark oak woodwork and bookshelves on all but one wall, leaving only space for one large window; and a very modern fireplace in an iron box which was hanging from the ceiling. On the comfortable sofas on one side of the library the tête a tête would take place.
After the coffee had been served and both political leaders were able to glance around, commenting politely on some book titles while enjoying their aromatic cups, the conversation started. The German Chancellor was the first to speak.
With secret undertones and looking straight in the eyes of Jacques Perrier, she remarked, "Believe me, I had not expected a different reaction from the PresCom. In my view, although he may experience the EU"s top-level inefficiency and non-governability on a daily basis, he will cling to his position cost what cost."
"You are right, Marlein. My experience with him is one of merely a puppet of Downing Street. Perhaps we should no longer lose our time with him and others alike. I feel that Europe has lost precious time in the last two decades while China and India are economically churning out. Even the US with respectively a second-rank actor, two Texans and a saxophone player, not to mention the current, legal modernist has economically grown faster than us. All this wasting time has to stop, which is why we should start the EU federating process right now. What about a secret bilateral of the two of us _en marge_ of the inauguration of the new plant for French Mirage 29? We have to move firm and fast with our federation."
### Four
### Love and foul-play in Dubai
Although it was 06.30 hours in the morning, the international airport of Dubai was full of pilgrims trying to board planes to go to Mecca when Ibrahim arrived from Istanbul.
In contrast to the fasting horde, his first activity back on the ground was the gobbling of two cakes and two croissants before he entered the public bathroom at the airport to drink some cool water. All activities were meant to refill his empty stomach and to recover from dehydration caused by the low-budget flight in which nothing was offered for free, not even water, after a four-hour delay at Istanbul airport. Not to mention the fact that taking a seat at the airport had also been impossible. The extreme hardship of the trip had raised his appetite to boiling levels. He was eager to finally embrace Alexandra with whom he would meet at the Sheraton Creek Hotel in central Dubai at midday.
After trailing his luggage up to the taxi stand, he boarded a yellow taxi alike to those rushing in New York. It was his first time in Dubai, but if things with Alexandra developed positively, visits to Dubai could become a regular part of his existence.
* * *
On the way from the airport to the hotel, Ibrahim started a conversation with the driver who appeared to be from Pakistan. The driver, a young man in his twenties, was eager to know more about the life in Istanbul. In particular, he mentioned his desire to visit the Sofia Mosque. However, such a visit might be no more than a dream since, as the driver explained, he had to send all his earnings to Karachi and consequently he had to live in a room of forty square-meters with just one bathroom, together with around twenty roommates. Changing the subject, the conversation moved to the objective of Ibrahim's visit to Dubai.
The driver asked, "Business or holiday, sir?"
"Let us say, holiday. Four days touring with my fiancée."
"Oh sir, so lucky you are. These Dubai women, much money have and father always want Muslim man come from Istanbul, for husband. Too much nice."
"No, no, my fiancée is neither Arab nor Muslim, she is French."
"Ha-an, sir, even better. Never mind sir, I say, too much sexy have these French ladies. No problem virginity losing before marriage. Pak family much more difficult. My father-in law too much me control no sex before marriage, but me much clever. This girl, my wife now, me take to other village. Hi-hi. You also other village take now Sir, hi-hi?"
"Ok, I see it is taking time for you to take me to the hotel. My information is that this trip should not cost more than eighty Dirham and your meter is already showing seventy-four. So are we near?"
"But sir, no problem, everybody knows crisis have in America and Europe, and also in Dubai, inflation coming everywhere. Now Arab also democracy want oil price more up. But you my brother, sir, you pay eighty Dirham and my tip as per your own convenience."
* * *
In his hotel suite, rented by Alexandra, Ibrahim took a long warm bath with Mediterranean salts, ordered a full American breakfast at room service, and waited for the food in his white gown and slippers while sitting in front of the window facing the creek.
Letting his eyes pass over the water and the small boats with cargo and tourists crossing, Ibrahim reflected on the complications of his relation with Alexandra. First of all, he was sincerely in love with her, and he was convinced that she had similar feelings for him. However, they were living in worlds apart. She was the wife of no one less than the President of France and Ibrahim was no one more than a young and clever economist employed by the Turkish president as a personal advisor. In this position, he was regularly asked to accompany state leaders and their wives to visit the monuments of Ankara and Istanbul, while explaining the splendid future of Turkey and the added value it would offer when entering into the EU.
Although he was excitedly waiting for Alexandra, he was also overrun by a certain discontent. Picture it, his greatest love of all would be landing in some hours at the Dubai airport, but he could not be there to close her in his loving arms. It was a sad and miserable situation ever since, as a cover up, she would be accompanied by two old classmates with whom she would be visiting a fashion show in the famous seven-star hotel Bourg Al Arab. Given that she would be staying in that hotel, he would have to settle for seeing her only when it would fit in her program and she would be ready to take a cab to visit him in the Sheraton Creek Hotel. The mere fact that he would have to wait passively, not knowing if and when she would be coming to meet him, made his humiliation more intense.
* * *
A telephone ring woke him up. He probably had fallen asleep while waiting for Xandra. A quick look at his Omega, a present from his father, confirmed that it was midday and that he had been sleeping more than four hours.
"My love, how are you? Alexandra sounded cheerful. "I am now in a cab on my way to you. My mates are having their lunch in Bourg Al Arab."
"Darling, you caught me in the middle of a pleasant dream. Of course, my dream was with you in the center, lighting up my life.
Oh, how I have missed you. Upon arrival, please come up directly to my room, 421. I will impatiently be waiting for you. I am hungry for your touch and full of energy."
"Oh, I feel the same but cannot speak freely now. Notice my low voice. I have a Pak driver in the cab who, after me asking for the Sheraton Creek Hotel and detecting that I am French, has remarked that he delivered a man to the same hotel in the morning, a brother Muslim from Istanbul who confessed to him having a French fiancée. I trust you have not entered in more details about us."
"No darling, nothing, although believe me, I would like nothing more than to scream across the streets that I am in love with you."
"Keep quiet. Your time will come. The cab driver himself is going to help you. Ha-ha. You know that this man is now praying to Allah because he considers that the coincidence of first driving you, and then driving me, is a sign of good luck. Darling, I have to hang because our Pak friend has big ears, also literally, hi-hi."
At arrival at the Sheraton Creek Hotel, a good-tempered Alexandra offered a splendid tip to the still praying Pak driver and rushed to the lift. Minutes later at the fourth floor, she softly knocked on 421.
An elated Ibrahim flung the door open. "Be welcome my beautiful and smart queen. Oh, you look better than ever, darling; come, let me hold you. I have a fantastic wine waiting for us and all my loving."
A passionate deep kiss averted her from answering him. "How I have longed for your lips," she murmured while being fervidly carried by him into the suite. As they took refuge in each other's warmth, long kisses followed, only to be suspended for breathing.
Minutes later, as the first heat was receding, Alexandra recovered some rationality.
"Lovely Ibrahim, being with you is paradise to me, but we should take care not spoiling it. I mean, you should not talk with strangers about your feelings, let alone our love."
"Believe me, darling, I have neither mentioned your name nor have I shared any other information with that cab driver. Besides, his English was not easy to understand and I guess mine for him was as well difficult."
"It was probably enough for this creepy man to keep on trying to touch my hand when I was leaving the cab as if we were sharing a secret. In no part of the world you should trust taxi drivers and certainly not in the Middle East. According to Jacques, some of them are confidents of anyone for little money, be it Taliban or FBI."
"I am sorry, darling, but my mind was so full of you that I could not keep my lips sealed. By the way, do me the favor from your side not to mention your husband's name when we are together. I often pray for our relation to have a happy ending. Try to understand, I am tired of this secrecy. I beg you, leave him, please! Oh, I plea, come with me to Istanbul. I love you!"
"Don't break my heart, Ibrahim, I cannot leave him now. He married me shortly before his inauguration and I will not leave him before his turn is over. And now I am with you, okay?"
At her last words she started nervously looking into her Gucci bag for a cigarette, but was stopped in the act by Ibrahim who, whilst unbuttoning her blouse, started kissing her breast and consequently the two bodies moved compellingly to the bed.
Two hours later, they both had had their showers after the passionate encounter, Alexandra was again looking for a cigarette and this time discovered that she had forgotten the package in Bourg Al Arab. A gratified Ibrahim now offered to go down to the lobby to get her a new package.
* * *
Ibrahim was not the only man waiting for the lift to take him down to the lobby. Two men, apparently Europeans, left the room next door and joined the waiting in the corridor. According to their clothes, they were on their way to the fitness center in the basement of the hotel.
After an almost involuntary greeting, there was a silence among them till the lift arrived, but when the two men and Ibrahim entered the lift, the taller and thinner indifferently asked if Ibrahim was going to the lobby, before presumably pressing the buttons of the lobby and the fitness. Seconds later—the lift had surprisingly not stopped at the lobby—Ibrahim found himself standing in front of the open lift in the basement, overseeing the entrance to the fitness on the left and the garage to the right. As he had planned to go to the lobby, he moved backwards to let the two gentlemen pass, but suddenly he felt the cold metal of a pistol in his neck while he was being pushed softly by the longer man who murmured, "Do not resist, keep calm, keep silent and nothing will happen."
He was pushed in the direction of a white, four-wheel-drive Toyota, waiting for them in the middle of the garage with the engine on.
When all three men were inside, the car started driving away slowly and Ibrahim was forced to smile to the guard at the entrance, the gun pushing hard and cold in his back.
* * *
The clock in the lobby showed 15.32 hours when a nervous-looking Alexandra made her entrance. She had been waiting for more than fifty minutes for Ibrahim to return with cigarettes and had become very concerned. Rushing from one shop to another in the shopping corridor of the hotel and not finding any sign of Ibrahim made her a prey of fear, even more so as she could not ask for him without leaving traces of their secret affair.
Finally she decided to start looking for Ibrahim outside the hotel, and as the reader may imagine, suddenly the Pak taxi driver walked over to her and, with his smile from ear to ear, jovially remarked, "Ha-an madam, little problem, I see. Never mind me saying madam, love with Arab man always difficult. Just me sleep in parking garage in cab when I see this, your almost husband, quickly leaving with Arab friends. This one problem, me know. Always Arab mansab every evening go coffee shop with friends and madam home stay alone."
"Please, I have no time for jokes. Who were these men that left with Ibrahim? Arabs? What did you see, please tell me! When did you see it happen? Please, where have they gone?" The questions were rolling out of her mouth while she feared the worst.
"Madam, these Arab men, much European looking; no white _kurta pajamas_ wear, but European suit. First me see men parking in garage with motor running, little bit strange. Also me see no number plate, car all cover with black plastic. Much clever, these men, no camera see plate."
"Okay, tell me, what direction did they take? Tell me please."
"This one me not know, madam. Garage left, all me see."
Alexandra took a deep breath, moved her hands over her eyes, and waited three seconds in silence before she requested the taxi driver to take her back to Bourg Al Arab.
* * *
On the way back, her mind was full of conflicting thoughts. Had Ibrahim been kidnapped? My God, could Jacques be involved in this? Should she call him to find out? But, if Jacques was not involved, by calling him, she would reveal the reason of her trip to Dubai.
A puzzled Alexandra left the cab and included a twenty-dollar tip to the driver with a friendly smile and a wink.
"Thank you for the service and do not forget, this was nothing but business."
The taxi driver, looking somewhat confused, shrouded his shoulders and repeated: "Yes madam, just business."
While Alexandra walked intently towards the coffee shop at the beach of Bourg Al Arab, where she planned to have a whiskey to calm down before meeting her friends, a noisy helicopter flying above the sea caught her attention. Little could she know at that time that this helicopter was carrying Ibrahim, handcuffed and blindfolded. Nor that he was on his way to a private plane at a nearby small airport, which would take him to a secret destination for thorough investigation. And although Ibrahim could not see the faces of his captors, he unmistakably recognized their accent as American.
### Five
### Sharing cooks but missing soups brings love back
Three weeks after the meeting in Brussels with the PressCom, German Chancellor Ditch received a report from her advisors concerning the voluntary federation, as proposed by the president of France.
The most remarkable conclusions in the German report were: 1) that the number of countries that had provisionally been considered in the meeting of Marlein and Jacques at the German Ambassador's Residence in Brussels was too small and should include a minimum of one, large country south of the Euro zone to make a round territory, climatically diverse with a total population well over 200-million people and, 2) that the countries joining the federation should be economically homogeneous, which would not exclude Spain, Italy, Slovenia, and Finland. But after reading the report, Marlein considered that she would only accept that Spain and Italy entered in the Federation, if these two countries would correct their high imbalances in a reasonable period of time. And of course, on the condition also that these countries would not continue with their outlandish idea of establishing the Southerners" Federation.
In Marlein's view, the Italians were having a long history of lacking solidarity with the rest of the European Union and within their own society. She could remember the two or three times in the past when they had left the cooperation process, in particular in the case of the serpent and the European monetary system. And then, again, she remembered the short duration of many governments in Italy as a consequence of the various breakaway fractions and strategic games by which they used to make politics.
The Spaniards, although far more sympathetic, Marlein considered little more than a group of _bon vivants_ and fun-makers. Nice chaps to go out for drinks and tapas, but not much inclined for hard working and fulfillment of commitments or contracts, particularly with women. Not to mention that they continuously had problems with breakaway Basques and Catalans, something that could produce severe headaches in the Federation.
Reflecting on the cases of Finland and Slovenia, both also members of the Euro zone and with good behavior records in their young membership, she would not mind including them, but they should be invited to join, similar to Spain and Italy, only after the five core members would have agreed on the main lines of the Federation.
The eight, resting countries3 of the Euro zone, plus ten more EU member states4, she judged as being far from mature for this initiative. Indeed, they either misbehaved or they hadn't reached the desired economic homogeneity, so for now they should be sidelined.
* * *
At a thousand kilometers distance, but more or less at the same time, French president Perrier received his own advisory report. In this report, the candidacy of the Italians was straightforward rejected by his aides while Spain was not even mentioned. In line with his initial proposal, the report focused entirely on the five countries, suggesting three layers of excluded Euro zone member countries. First, there was the layer of the bad performing countries such as Ireland, Greece, and Portugal. Second layer was formed by the states with doubtful behavior, Belgium, Spain, and Italy. And third, the little populated states of the periphery as Slovenia and Finland. In the French report, all the excluded countries could have an opportunity to enter the Federation after a ten-year period, provided they behaved economically well. The report suggested also that none of the initially excluded Euro zone countries should receive bad treatment from the Federating core members. Even more, it was underlined that the excluded countries could remain in the Euro zone provided that they renounced to form part of the board of the European Central Bank, hence of the monetary policy and decision-making.
Having finished reading the one-page summary of the report with satisfaction and in full agreement, Jacques Perrier started cleaning up his desk to rush to the helicopter that was to take him to Gap in order to chair a local event. He was to give the winning trophies for
"Snowboarding for juniors" in the French championship.
However, at the moment he was closing the door of his office, his private Blackberry rang, disquieting him. This could only be a close contact, so he answered, be it impatiently: "Yes, Perrier ", but then again, before being able to ask who was on the other side of the line, some overlapped, Arab and English words caught his ears. Puzzled he requested, "Who is calling?" The silence on the other side was only interrupted by heavy breathing. Jacques repeated at louder voice
"Who are you?"
Silence again, but then he was capable to hear at a distance someone, probably chewing bubblegum with grinding jaws, confirming to another person that Jacques Perrier was on the phone.
This was the signal for whoever was calling to start speaking to Jacques. Few words... before hanging, and with a grave voice:
"Monsieur le President, we have served your cause" and the line went cold.
In the silence that followed, Jacques tried to find the logic of what he just heard. Unquestionably, his Blackberry was accessible only for a very close circle of people. Besides, although the number of the caller was blocked, the call had unmistakably come from long distance.
Moreover, he felt that he had been connected to the Arab world.
Albeit, his connections with the Arab world were restrained to Lebanon, Iraq, and the Maghreb, the caller had been someone or an institution unrestrained in the possession of his secret number.
Besides, his closer network was all French-speaking, while those calling him just now were clearly Anglophone, not to forget that he could catch the chewing of bubblegum.
Making memories, he started returning to his desk to look for a business card while remembering a confidential meeting he had in Cairo with the president of Egypt and his Chief of Intelligence. At that meeting, a US Senator and an Afro-American lady in her forties-who appeared to be the Vice Councilor for Security of the American president-were attending. At the end of the informative conversations, Jacques spontaneously invited the two Americans for dinner at the French residence in Cairo.
* * *
During the aperitif they toasted to French-American cooperation with a breathtaking view on the Nile and the Vice Councilor for Security explained that she had just arrived from Afghanistan and was worried that the NATO partners were not progressing fast enough, thus losing public support in the US. And all this while victory seemed to move further and further away. During her speaking, Jacques had problems not being distracted by the fact that she, from time to time, showed a piece of pink gum that she was chewing.
Thereafter, as she had been placed opposite him at the dinner table, he could observe during the entire, copious meal that she did not get rid of her chewing gum. At first, it intrigued him more than annoying him that she managed to eat a second course of prawns in a sauce of garlic butter and cognac while occasionally and totally comfortable moving the chewing gum from one cheek to another, but finally it made him nervous and he lost the thread of her story about the difference in approach between the US and the EU in combating terrorism.
Come to think of it, he suddenly feared that someone working in the security cloaks of the US or an allied Arab country might have called him just now. But why behaving so secretly and what was he to do with the remark, "We have served your cause"?
Back behind his desk, he decided to attempt a reality check and impatiently opened his computer to send a confidential e-mail to his own Security Advisor. Typing fast, he ordered the latter to contact the Afro-American vice Councilor, currently in office in Washington. He also requested his Security Advisor to use his best diplomatic skills to find out cautiously if the Afro-American Security Deputy knew anything about the whereabouts of a certain Ibrahim Orzgol, a Turkish, top-level civil servant, who according to Downing Street, disappeared during a visit to Dubai one week ago.
"Please keep it all between these walls to preserve good-neighborhood policies with Ankara," was Jacques written instruction to his Security Advisor, before he rushed out from his office and to the patio of L'Elysee, where his helicopter was already geared up for departure.
But long after entering the helicopter and putting his helmet on to soften the noise of the engines, the last words of the clandestine call kept on hammering in his mind and during the trip Jacques Perrier repeated to himself that there had not been any Arab connection involved in anything he had arranged to separate the worlds of his wife and her Turkish lover. So he had to keep calm.
* * *
Two hour-and-a-half later and looking back at what he used to call a successful performance as _President de la Republique_ at one of his many "meet the people" functions, Jacques Perrier decided to forget about the Ibrahim case and instead to share his good mood with his wife Alexandra.
As far as he had observed in the past week, Alexandra had not shown any sign of uneasiness with him; she had never strayed her eyes away as they spoke, and although Jacques was curious to find out if she knew anything about the kidnapping of her presumed boyfriend, he avoided even the slightest hint in that direction.
Thus Jacques decided to call her at the spot and to propose to have a nice dinner together, considering that if Alexandra knew something about the kidnapping, her overall mood of the past week had been more like wanting to forget about it and reshape her life with her husband, instead of blaming him. However, the possibility that she did not know about the disappearance of Ibrahim could mean that the whole affair was already over when the man vanished. The best would be for Jacques to keep all the real subjects off limits tonight.
"Salute, Jacques, where are you?" she answered.
"I am entering the helicopter, sweetheart. I am on my way back from Gap. I will be home in about seventy minutes. Miss you disproportionably."
As Alexandra did not immediately react to his flirt, he continued, "I am looking back at a very good performance this evening. Polls show my strong recovery so a good reason to celebrate my comeback.
Wonder if we could have a cozy diner together. I feel a second term much nearer than two weeks ago."
"Nice for you, but I may remember you that I do not consider myself bond to you for a second term," was her blunt answer.
Ignoring her mood, he insisted amicably, "My darling, we have had a thousand cozy diners together during which we had good times commenting on all the idiots we met along the day. Why change a winning horse? I promise you not only an amusing diner but also a sparkling desert. And, surprise, I have in my pocket a box of third-generation blue pills. Wow!"
A slowly defrosting Alexandra answered, "Jacques, frankly speaking, I am not interested in your third-generation pills, but I will wait for you. Do your best to make me comfortable. See you."
At the last words, Alexandra put off her Blackberry and walked over to the window of her bedroom. She actually had been lying in bed when the phone rang. Come to think of it, she was not in any mood for dinner with Jacques. She was almost sure that Jacques was the instigator of the disappearance of Ibrahim, but she decided not to say anything to him till she had hard facts, for which she had undertaken her own secret research. And although Ibrahim had at times expressed some doubts about the future of the relation, she was convinced that the probability that he had opted for a French farewell was almost nil.
* * *
Jacques private Secretary made the last-minute arrangements for the meal between the President and the First Lady with the kitchen staff of L'Elysee; something less and less common in the Palace since, as a consequence of the hectic life of the couple, joint dining was almost entirely reserved for representative banquets with official guests. The instruction to the kitchen staff and attendants were to create an intimate atmosphere in the small, blue dining room near the President's bedroom and to prepare a light, but haute cuisine, three-course meal with champagne.
So, when Alexandra arrived, the dimmers of the blue room were all on low and a dozen candles in the antique silver candleholders created an intimate atmosphere. Yet she was still not in the mood and more concerned with not seeing much in the darkness, in particular not seeing Jacques.
Without looking around she walked straight to the table and requested the attendant, "Any idea if the President is going to be on time?"
"Yes, the President will be in time" was the joking answer of Jacques jumping from the little Victorian sofa in the corner.
"Sorry, I could not see you in this complete darkness. Why have you turned off all lights? Is this your new energy policy in the residence to please the green party"?
"Sweetheart, don't be so arrant. Things are far less complicated than you think. Let's say that I simply wanted to have a comfortable dinner with my beloved wife. I have selected your favorite music."
At Jacques" last words, Andrea Botticelli's caressing voice started warming the room and Jacques called for the champagne and some exclusive canapés before inviting her to sit next to him.
Cheering up, he raised his flute for a toast, "That our good luck continues."
A sarcastic answer from Alexandra followed; "I really do not know what good luck you are referring to. Certainly not mine in the last week."
"But Xandra, look at you, look around you. You are a young woman in your early-forties. The best time of your life and you are the First Lady of France, one of the most important republics in the world."
With a skeptical look at him, she shared another prod.
"Yes, fine. That is why I have to share you with 65-million French people, who by the way are more and more critical of you. I have to see them voting you in again."
"Ah darling, stop complaining. You are not black, you are not poor, and you are not a Muslim. This means that you not only belong to the Western society as a select collective of sixteen-percent of the global population, but also to the small, exclusive peak, one-tenth of a percent of that sixteen who by the way still rule the world. Being in this position and then complaining is like defying destiny.
A destiny that, Let's be honest, has treated us exceptionally well. So if I may suggest, just enjoy the evening with me, let us bring back the good, old days."
Alexandra turned off her face, took a slow sip from the flute, and started staring at the candlelight in front of her. She was upset with the fact that he had prepared this show as if nothing had happened since she informed him of her relation with Ibrahim. Even more, no doubt that Jacques played a central role in the abduction of Ibrahim. Against this background, it was annoying to sit by him with his candles and champagne.
"So, you Jacques, you are toasting on our good luck. Probably, for you and the exclusive peak of the happy few to which we belong, good or bad luck can be arranged. This sounds to me as if you all have been granted the role as the left hand of God."
"You are flattering me, Xandra. Believe me..., you are giving me far more power than I actually have. Take it from me; I am far more limited. Not only by the opposition in the National Assembly, or by some fools in Brussels, or by the whims of the Americans, but also by all the national and international rules that we have to fulfill. You know quite well that people like me are scrutinized around the clock, and darling, I hope that you keep in mind that this scrutinizing also happens with the First Lady."
Meanwhile the soup, as a first course, was served and without speaking further they both moved from the sofa to the table.
Immediately after being seated, Jacques placed his spoon in the soup and bowed it softly forward, but he pulled back surprised when the spoon appeared to be capable of standing upright alone in the viscose substance. In the next second he signed to the attendant to approach him and mildly raising his voice remarked that the soup was not a consommé. The butler was quick in his answer.
"But Mr. President, as far as I know, this is a Chinese noodle soup prepared by your new Chinese team in the kitchen. May I remind you that you recently have agreed with your Chinese colleague on an exchange of presidential cooks for three weeks?"
"So, call my guest cook. I will have to explain him something. What is his name? I guess at least he speaks English."
Within two minutes, a nervously bowing, white dressed, and pale-to-almost-yellow Chinese cook made his audience in front of the president, sure to suffer a reprimand.
"Excuse me, Lee. Your name is Lee, is not it? May I say, I have been served several-thousand of soups in my life, of course French soups mostly, but I cannot understand what you have served me today as a soup? This is neither a soup nor a cream." The president skimmed the edge of the soup's surface repeatedly with his spoon.
With a trembling voice, the Chinese cook, who hardly spoke any other language than Mandarin, answered the President.
"But Sir, this not French soup, sir. This Chinese noodle soup."
"Please, do not use the word soup for this dish. Do you know the definition of a soup? As my Catalan grandmother used to say when serving the soup at Christmas, a soup has to be minimally sixty-percent liquid, irrespective of the ingredients you put in it. Consequently, if my spoon can stay upright like now, this is not a soup. Understand?"
"But this famous Chinese noodle soup, sir! President Hu always likes this Chinese soup!
Perrier, increasingly agitated, continued pointing at the spoon standing upright in the soup as he repeated, "Per definition, a soup is minimal sixty-percent liquid. This is not a soup, and if you do not understand that, you are not much of a cook."
This was the moment for a slightly irritated Alexandra to intervene.
"Jacques, please stop it. You cannot lecture him about Chinese soups. On top of that, you speak Franglais and he speaks Chinglish so you two will never understand each other while you are discussing an irrelevant matter as Byzantium priests used to do when they were discussing on the gender of angels."
At her last words, Alexandra herself burst out in laughing, but Jacques did not seize the opportunity.
"Fine, then I will have a French soup. Please bring me a French consommé. Otherwise, bring me some caviar," he ordered the cook.
Alexandra had now laid her hand in a comforting gesture on the hand of Perrier while saying, "My dearest Jacques, there are moments like now that I really do not understand you. Are you aware that sometimes you behave to anything but the President? Extraordinary! Just like some days ago. Please, may I refresh your memory? Listen, remember your "meet the people" discussion with that rightist barkeeper in Clichy-Sur-Blois? The man was complaining that the neighborhood was being poured by brown shit of sparrows, which according to the barkeeper was the result of the sparrows being fed by the immigrants from the Maghreb with Arab baguettes. His complain was utterly nonsense and full of prejudice. But my God, Jacques, I will never forget how you seriously tried to gain political support out of such idiocy and in such an absurd way. It was a perfect piece for a theater play. Nothing more! And how I suffered a lot in those moments because I wanted to cry out laughing, but I could not."
"So, darling what did I do? I cannot remember."
"Let me revive the event for you Jacques. I will do it like a script of the play it was:
The barkeeper: "Mister President, we are confronted with a new phenomenon in this neighborhood: sparrows shitting dark in huge quantities. This is because these birds are now being fed by Muslims from Maghreb countries and with Arab baguettes."
You: "Really? Tell me more. This is another serious problem of non-Western immigrants in France. It is too bad that these people who refuse to speak good French and who dress with headscarves and burkas are now even changing the flora and fauna of our neighborhoods. But what is it about the sparrows? It's the first time I'm hearing about this detail."
The barkeeper: "Mister President, these poor birds are now forced to eat multicultural bread. That bread makes them shit brown. Before, they would have been fed with our French baguettes and they would shit white. Do we also force our sparrows to adjust to these intruders? It is really horrible. Every restaurant I enter and ask for a tea, they will ask me first if I want Moroccan or mint-tea, and even if I ask for coffee. I am first offered Turkish coffee."
You: "I fully understand your complaint. What do you suggest: no more non-French bakeries in Clichy-Sur-Blois, no more Turkish bread, no more Arab baguette, no more pitta and whatever they call it? I agree. I fully agree. From now on, bakeries in Clichy-Sur-Blois should sell only French baguettes for the people and for the sparrows alike. You have my support."
Another attendant at the meeting: "But, Mister President, a Moroccan baguette costs forty Euro cents and a French baguette eighty. So, I shall buy the Moroccan as long as I am unemployed, right? And believe me, Excellency; these cheaper baguettes taste fine, while at the same time, I personally did not observe any change in the color of my shit."
You (as you always claimed the last word, instead of laughing aloud): "The Moroccan baguette does not comply, I mean in weight and compact, with a real, French baguette. So, a Moroccan baguette is not a baguette."
"My God, Jacques, I could not keep my laughing, but I had to keep up appearances. Jacques, I have to say it, you are often just an idiot, but you certainly are my idiot!" She was now leaning towards him, closer and closer, and started caressing his arm. "In the end I could only hope that I could walk away and laugh as I am doing now."
Jacques was surprised. Unbelievable, but Alexandra's mood had totally changed and he believed she was—figuratively speaking—ready to eat out of his hands. Some pleasant though savage instinct took hold of him.
This time, Jacques" observation was correct. After Alexandra had spontaneously reflected on the Byzantium habits and the idiocies of Jacques, and she was to admit to herself that, truth be told, the life as First Lady might not always be romantic but it could be rather funny while in his own clownish way, her husband was willing to put her on a pedestal. She also knew that contrary to what she had said to Jacques, she had never been sure about leaving him. Let's say he was the boss of all the civil servants in France, why would she leave him for a middle-rank civil servant in a hybrid East-West country where women were still fighting to be put on a pedestal?
The candles lit Alexandra's attractive, oval face; her artistic, modern haircut partly overhanging one eye; the rather small but well-shaped nose and her beautiful upper lip under a pearl pink lipstick matching with the bronze eye-shadow which further accentuated her big and sparkling, brown eyes. Hence, Jacques was slowly moving in the direction of her lips but he was also half-expecting her to fear up while reminding him of the presence of the serving staff in the room when the little beep of his phone broke the glamour with the honking information that he received a new message in his inbox. In putting the phone off to avoid further disturbance, his eyes caught the first line of the message originating from his security advisor: _the suspect you informed about, is already one week in an overseas Information Treatment Centre in Africa, according to trustable source_.
It was a simple but scary line which Jacques immediately was trying to move as fast as possible to the back of his memory in order to let life leap over oblivion, since almost at the same instant Alexandra surprisingly took the initiative to cover his lips with hers. The mixture of scents of sweet honey, cinnamon, and anisette overwhelmed Jacques. Her tender lips warmed his heart up and melted his mind.
_____________________
3 The eight excluded Euro-zone countries would be Belgium, Ireland, Portugal, Greece, Malta, Cyprus, Slovakia, and Estonia
4 The remaining ten non-Euro-zone member states would be Britain, Denmark, Sweden, Poland, Hungary, Czech Republic, Romania, Bulgaria, Lithuania and Latvia.
### Six
### Voluntary federating the best and angering the rest
The Press Conference had been scheduled for Friday at 11:30 am in the ballroom of Hotel Negresco in Nice, Cote D'Azur. Actually, since the days of the Treaty of Nice in 2000, it was the first time that this elegant city in the south of France was once again hosting several, top European politicians and advisors. They all arrived sometime on Wednesday afternoon and immediately on the first evening started their negotiation on a selective and voluntary European Federation.
By now, the reader may wonder who "they" were, but this was certainly not a question for the many journalists who had already awaited the participants of the selected EU integration meeting at the airport of Nice on that rainy Wednesday. Even more, the rumors of the event had previously spread in all the twenty-seven capitals of the European Union and even far beyond.
Hence it was no surprise for the journalists at Nice-Cote D'Azur airport, be it Terminal One or Two, to register over the day the arrival of the German Chancellor and the Prime Ministers of The Netherlands, Austria and Luxemburg.
Most guests came by chartered planes and one could observe slightly stressed expressions on the faces over the complicated landing in the pouring rain: landing-gear almost touching the sea water before touching down on the tarmac amidst a strong, eastern wind.
Nevertheless, as soon as they were safe and sound in the VIP arrival lounge, all would agree that even with the sun hiding behind clouds, the grey overshadowed bay of the main city of the blue cost remained beautiful as ever. The last to arrive was the President of France, Jacques Perrier, who at a blunt question of a British journalist,
"Mr. Perrier, why have you not invited your British colleague?" resolutely answered, "Regrettably, we have not invited those who opted out from the Monetary Union."
Another journalist, challenged by the answer of the French President, remarked, "But what about the remaining twelve countries of the Monetary Union who are also absent?"
Again Jacques Perrier, walking stiff to the car waiting for him, was firm in his reply. "We will inform you on Friday why we are five and what we have agreed, if any."
Yet, his answer was not accepted by the journalists crowding around him and an Italian TV reporter decided to put things more sharply,
"Is it possible to agree on anything in absence of twelve of the partners of the Euro zone? This smells like as a _coup d'Etat_. Are "the five" here for blowing up the Union because you do not want to be in solidarity with member states in financial problems or economic delay?"
The President of France, pretending not to hear the last question, entered his car and left for Hotel Negresco where, except for a few rooms, almost the entire three stories had been reserved for the participants and their accompanying aids.
The moment the French President arrived in front of the lobby of the hotel, the rain stopped but the masses Jacques silently had hoped to see welcoming him were absent. At best there was no need for a slightly disappointed Jacques Perrier to show his IDs to the two bellmen in sixteenth-century uniforms. However, for the press conference on Friday, journalists would have to pass a second filter with probably better screening equipment than the White House.
* * *
Friday morning, the big day of the press conference, was cheered up by a hesitating, morning sun glazing over the bay in contrast to the two past days which yielded mild but persistent raining. At 10:30, the ballroom of Negresco was already fully occupied with excited journalists.
There were newspapers and TV reporters, not only from the twenty-seven member states but also from USA, Russia, China, India, Indonesia, and several countries from the south of the Mediterranean Sea including Egypt. Turkey was also represented. The room started bustling as most journalists were still puzzled about the objective of the Nice-Top-for-Five and they were left sharing rumors from Wednesday evening onwards. To pop up the expectations some journalist started broadcasting interviews with other reporters.
South African TV was asking the editor of _The Economist_ to express his view on the exclusion of Italy and Spain from the top, just when the two were near to request bailout support. The answer of the editor was short and clear. Spain went too far with the housing bubble and could become practically a corpse in the coming decade.
Concerning Italy, the editor believed that in the last, two decades Italy lost gas and its electro brain scan had become almost flat.
Consequently, both countries could become an unbearable burden for the Euro zone.
* * *
At exactly 11:25 all eyes in the ballroom turned to the left side door through which the hosts of the press conference made their entrée. As one could have expected, first there was the French President Perrier, followed by the German Chancellor Ditch and, two steps behind, the Prime Ministers of the Netherlands and Luxembourg with Austria closing the parade.
Immediately after the hosts seated themselves behind the table at the podium, the French President started reading the press briefing from the five initiators of the projected European Federation. Contrary to his normal practice, Jacques Perrier was reading calm and skillful, given that the text was also prepared by the five and their aides, weighing word after word.
_Ladies and Gentlemen_ ,
_In the current, economic crisis and taking into account the industrial shift to Asia combined with the fact that the growth rate of the EU twenty-seven as a whole will remain extremely low and condemned to an almost jobless growth for the coming decade, we, the five countries of the Euro zone here represented have considered it high time to take a drastic initiative to pull the future of our nationals out of the dip._
_Having experienced also that the governance of twenty-seven countries on the basis of consensus has become extremely time-consuming and severely indecisive, and considering that the architecture of the Euro zone is hardly operative, we, the five, most stable Euro zone members have taken the initiative to break the stalemate by working out the possibility of moving forward and setting up a political federation among some Euro zone members: those who have a real European vocation and are economically homogeneous. This is no more than our duty towards workers and employers and young and old in our societies, who since the introduction of the monetary union, have observed their living conditions and the future of their children become bleak_.
_During our deliberations, we have decided to also invite Italy, Spain, Slovenia, and Finland to embody in the future European Federation. So if these four Euro zone members join us, it is our intention to set up at short-erm, a federated state of around 300-million people, a figure similar to the population of the United States of America and with a per-capita GDP significantly higher than that of the current EU Twenty-Seven_.
_In our view, the construction of a political and economic Federation of nine states containing 300-million people will have huge advantages for the participating countries such as:_
_1. Economies of Integration of different branches of our public sectors, which, as figured out, would generate a saving up to two-percent of the joint GDP of the federated countries, from which one point of the joint GDP will be saved through the integration and reorganization of the current national armies into one federated army. Mentioned financial savings could be devoted to tax reductions and stimulation of jobs creation inside the European Federation (EF)_.
_2. Other dynamic advantages would include a jump in research and technology to improve the productivity per hour of the workers of the European Federation without increasing working time, thus enabling a more human life for the population of the Federation._
_3. It is our intention that the economy of the Federation moves on the coordinates of the Social Economy of Market, which means that the current social advantages, mainly pensions and insurances of unemployment and health, will converge at a Federal level into unique systems, after a transitory period of twenty-five to thirty years._
_4. The Federation will finally enable, within its borders, the arrival of a real, unique European market, while at the same time it will provide a federal wide security net for those expelled from this unique market._
_5. The Federation will also enable the recovery of the effectiveness and sustainability of the economic policy, thus overcoming the defective organization, fragmented policies and lack of control in public finance as practiced in the last ten years in the Monetary Union. It is well known that the coordination between the European Central Bank and the Finance Ministries of the Euro zone States has been chaotic, particularly since the last crisis started in 2008_.
_Ladies and gentlemen, after admitting that some serious mistakes were made in the construction of the Europe project in the past twenty years, the five countries here represented have decided to correct the direction and speed of the project. For your information, we are in full agreement that: first, the current deficient architecture of the Euro system is unworkable; second, the admission of twelve newcomers in 2004-2007, most of them lacking maturity in economic and political development although well intended in terms of keeping peace in Europe, was premature; and thirdly, that several attempts for a soft, economic, and political reorganization of Europe have ended up in an unsolvable conundrum_.
_In front of the deadlock, we, the five, represented member states, have, after careful deliberations, concluded that we had two options: either to continue as we are, or to set up a selective Federation. In our view, the first option would drive us towards further jobless, slow economic growth and progressive, economic divergence in relation to the USA and emerging Asia. Observe that this option and its expected outcome will be inconsistent with the economic aspirations of our nationals and will undermine the desire of our countries to continue playing a global role_.
_Taking into account that for the five of us the first option was a blind alley, we have decided to put in common some precious parts of our sovereignty in exchange of finally achieving the dreams of the founders of European Project. We are sure whatsoever that with the formation of the Federation, our economy will step up its rhythm of growth as a consequence of a far better governance, which will benefit the EF citizens_.
_And of course, the Federation will play an international, political role, much more relevant than before, according to the size and power of a big, federal state of 300-million people. Finally, the five member states here represented, declare solemnly that our Federation will be born with a vocation of integration of the Euro zone members. Although some may remain out for the time being, they will always be welcome to join the Federation, provided that they fulfill the required economic homogeneity with the pioneers_.
_Note also that the selected Federation is certainly not intending to abandon the rest of the EU-Twenty-Seven. Indeed, all the economic treaties signed until now by the federating countries will continue ruling with the remaining EU countries. However, these remaining EU countries will not intervene in any form in agenda-setting and decision-making of the Federation. I thank you for your patience and welcome your questions_.
While Jacques Perrier was reading the joint statement, one could observe growing nervousness among the participating journalists as the majority started using their Smartphone and IPods to inform their headquarters.
The more in contrast was the silence after Jacques Perrier's concluding statement. For a few seconds, no one moved, no one spoke, no one reacted, and just when an overwhelmed Marlein Ditch reached for her bag, the audience started applauding endlessly.
At this point, a far more confident Hans Schmidt, the aide of the German Chancellor on EU matters stood up and while walking to the reading desk in the corner of the podium, signaled for silence with his hands waving in the air. Smiling happily, this time he personally claimed some of the victory. Hans Schmidt announced to the participating reporters that under his guidance they now had the opportunity to put questions and seek clarifications.
So the German advisor was fully in charge when he granted the first question to a female journalist from New York Times and the New Yorker played straight with her question.
"So finally, the magic word "federation", feared by many Europeans and worshiped by others, has appeared in a proposal for the future by two of the most powerful members of the EU. Is it your intention to become a global player at the same level as the US and China?"
This time Marlein Ditch, the German Chancellor, could finally daze with a determined answer, "Of course, this is our intention, as part of our ambition to contribute to the creation of a multi-polar, globalizing world. Indeed in the past twenty years, we have lived in a context in which there existed only one hegemonic power and one emerging challenger. We do believe that this has not been good for the social and political stability of the world. You have to accept that the more distributed is the power, the more balanced will be the global, economic progress, the more equitable will be solutions of global problems and less probable will be the abuses coming from the powerful, large countries. Next question please."
A Hungarian journalist from HTV had a question for Jacques Perrier. "Reflecting on your meeting, one may clearly deduce that France and Germany have masterminded this restrictive, federating project. Would you confirm this? And if you confirm, my second question is, do France and Germany consider themselves to be entitled to take an initiative that could exclude the majority of EU-27 countries? And my third question: is the restrictive federation a way for Germany and France to halt the financing of the newcomers of 2004 and 2007?"
Jacques Perrier replied, "Of course, the magnum projects of mankind are always planned by minorities. In relation to Europe, and from the very beginning in 1951, France and Germany have been the main animators of the different steps of the integration process of Europe.
And in the current EU crisis we have again decided to take the steering wheel for changing the orientation of the project. As to your second question: for decades the EU project gained in a balanced way both geographical extension and economic and political integration.
Regrettably, the EU project got derailed in the 1990s when some member states opted out of the Euro while others entered without fulfilling the conditions or even lying on provided data. On top of that, between 2004 and 2007, many newcomers have entered the EU without economically being mature and at the same time having big, financial needs. All this has transformed the up-to-the-Maastricht Treaty workable governance of former EU-12 into a consensus based unmanageable mess of twenty-seven countries with different economic positions, interests, and political ambitions. Since the financial crisis in the West, which started in 2008, it has become crystal clear that the countries of the Euro zone, for their own economic survival and to complete their aspirations, need to politically integrate into a unitary state. Finally, the mere fact that we have bailed out several Euro zone countries proves our being in solidarity with them. Even more, we do believe that the economies of scale, raised by the Federation, will result in important budget savings which will also enable us to increase the budget for economic cooperation with EU members and non-members."
The next question was again addressed to Perrier. A representative of the Italian Corriere de la Sera submitted, "Sir, what about the sovereignty given up by the member countries entering the Federation? Are you conscious that your federation project, if put into referendums in each of the nine nations at this critical moment in time, could get some majority rejections?" Perrier was visibly relaxed. The Italian reporter had put an expected question to him, one he had discussed over and over again with his advisors.
"My dear friend, in the last twenty years, we have been trying in the EU to make omelets without breaking eggs but this, as anyone knows, is impossible. We cannot be a political union and at the same time be all of us independent. In fact, the citizens of the nine countries of the Euro zone called to form part of the federation, when time arrives, will have to dramatically decide between only two options: either they give up part of the remaining sovereignty or they remain in the current stalemate. But given the fact that the referendum will take place at the same day and time in all the nine countries, a majority "no" vote in one country may mean that this country should stay out of the federation for at least ten years or more, due to the fact that we cannot build a federation with hesitating countries. And note that a period of ten or fifteen years at the current, critical moment of history has a galactic dimension. In fifteen years, our world will have changed dramatically, and if we do not radically change our political organization now, we may lose the train. The balance, you know... Jesus Christ!
In few seconds, while Perrier was talking, three, totally naked women, only a rope around their waists suddenly fell from the ceiling of the ballroom. The effect was stunning. Perrier could not but stare at the naked bodies in front of him: nipples affected by the exposure to cold air, flat bellies, bushy triangles, a serious sisal rode. The three women, their blonde hair covered with big boinas, started screaming in chorus, "Gora Euzkadi Azkatuta", "Long live a free Bask Country" and "Vive le Pays Basque livre."
From different corners of the ballroom, hastily German and French guards emerged as photo cameras and Smartphone's started splashing their lights while the ladies entered into the next stage of their protest and ignited small strings of fireworks.
"ETA Attack! ETA Attack!" shouted some journalists who worriedly started rushing out of the ballroom or looking to hide somewhere in case of an explosion. Some guards, now with their revolvers up, were speedily approaching the naked women and if it was not for the cool and decisive reaction of Marlein Ditch, things could have ended far worse.
"Stop, do not shoot. No one is armed" she was screaming, placing herself swiftly between the activist women and the guards. "Are you mad! You want to be killed?" she continued yelling to the Bask activists who started moving to the side door left. And to the journalists, who were busy rushing out of the ballroom, thereby almost provoking a stampede, Marlein ordered, "Please calm down.
Nothing serious is going on. How things have radicalized after September 11th. These three women could have been killed for a simple protest like we all used to organize in the 60s and 70s."
These were miraculous words of the German Chancellor since simultaneously a team of four, special agents of the Gendarmerie, fully armed with automatic long guns stormed the ballroom.
"Freeze!"
As it appeared, the first journalists who left the ballroom not only informed outside guards of an ongoing terrorist attack in the ballroom, but someone also spread the rumor that the Dutch and Austrian Prime Ministers had been abducted by ETA terrorists; a rumor that in seconds had reentered the ballroom.
While everyone was freezing somewhat, a heavily sweating and completely distressed Perrier, who had been hiding under the table and lost all control of the situation from the moment the naked women landed in front of him, cautiously reappeared. Looking around somewhat bewildered and speaking to himself, "My God, the three terrorists and the two Prime Ministers are missing! What bad luck I have: two Prime Ministers taken hostage by ETA terrorists in Nice, during a ceremony organized by me. Horrible; how will this end?"
And then directed to the Special Forces he shouted, "I am the President of the Republic. I order you to use all means you have to rescue my guests from Holland and Austria."
"No, wait, we are sound and safe." A smiling Dutch Prime Minister and his Austrian colleague were returning to the ballroom from backstage, accompanied by the three, female activists who were no longer naked but wrapped in ballroom curtains to cover their bodies. The Dutchman explained, "As you can all see, we have been using our soft diplomacy skills and convinced the ladies that they should go home quietly since the future of some regions in the Federation will be reconsidered by us."
"Thank God my guests are safe, but these three activists will have to face French court" affirmed Jacques Perrier.
Meanwhile Hans Schmidt had exited the ballroom and was trying to gather the journalists for a continuation of the press conference, but as the Spanish and Italian TV teams remarked, "Could we have any more spectacular news? First, an exclusive federation and then a terrorist attack by ETA combined with a sex show. We are going back to cut and paste for the evening news. Bye, bye."
### Seven
### A rainy night in Brussels
It was a dark, rainy night in Brussels, not unusual for the time of the year, but still the type of weather that would keep many people off the streets. Yet, the radio presenter of a nocturnal music program reminded the occupants of the Volkswagen Polo that it was 1:30 in the morning and that the day had long past.
The two people in the car had defied a rain storm that showed no sign of stopping, persisting for hours and hours pouring monotonously from the clouded skies. No wonder that the roads near the Grand Palace, primarily tiled with stone cobbles, had changed in a slippery, shining dark surface. Nonetheless, the young lady behind the steering wheel of the small car exposed a remarkable imprudent driving style, clearly against the logic of physics, which could only annoy the person sitting next to her. At times... compelling her to drive more careful, "My love, please slow down, you are taking us straight to the emergency if not worse," but then again almost aloof as this man had to divide his attention between the young driver and the piling professional problems he had, no one less than Bopoulos, the PressCom of the European Union, was sitting as the company of the young lady.
However, the more Bopoulos expressed concern about the dangerous driving style of Clara, the more inclined the twenty-five-year-old waitress was to speed up the engine and cut off corners by running over the pavements. Clara was showing her anger with the thirty-five-year-older Bopoulos as all initial promises concerning the future of the relation had slowly dissipated into smoke. The two had met by incidence in a bistro in the center of Brussels. Bopoulos, the president of the EU Commission, exceptionally happened to participate in the birthday party for his secretary, and Clara, a substitute waitress, young, good-looking and forthright, had been charming in a naïve way. So when Clara, while serving coffees, bluntly remarked that she had no clue what the EU was, everyone laughed. Even more, she underlined—with a broad smile showing quality teeth—that this was the first time in her entire life that she had heard the words European Commission.
Listening to her, Carlos Bopoulos was swayed and quickly offered to tell her the whole history, background, and possible future of the European Union whenever she was ready for a cup of coffee.
Much to his surprise Clara did call the next day and a date was fixed. Certainly his normally attentive secretary did not pay much attention to Clara's call as probably no one signaled any sexual undertone in the spontaneous invitation of Bopoulos to educate the young waitress on the European Union.
The truth is that the history of the EU was never explained to Clara, not on their first afternoon encounter and never thereafter. On their first coffee date, they both instinctively bypassed the EU history lesson and immediately started flirting by playful interviewing each other about their private life. Exchanging glances and warmly closing in, they talked to each other, gauging one another's proclivity for commitment. Of course, all this was not arbitrary. They were both, for different reasons, exploring the options for a more intimate encounter.
Carlos Bopoulos was staggered by the intense attraction of her young body, something he had been dreaming of from the moment he started noticing grey hairs growing out of his ears and nose, his arms getting shaggy, and the mirror in his bathroom showing the hairs on his chest becoming grey and brushy, as were his disheveled eyebrows.
For Clara, although not clear what the European Commission stood for, the mere fact that she was having coffee with a president created visions of being cared for as a princess in wealthy surroundings by an old, odd-dressed rich man. Subsequently, the initial, innocent coffee appointment on that first Thursday afternoon ended suddenly in making love ardently in the pied-a-terre of an Italian Parliament member and good friend of Bopoulos who had left some days for Milan.
Thereafter, Clara and Carlos met for more than four months, usually only on Thursday evenings, taking advantage of the fact that Bopoulos" wife, the so-called, "Duchess of Algarve", would generally go see her parents who were living in Algarve Thursday mornings and return the next day in the evening, while on Thursday the Italian Euro-parliamentarian would also travel to his family in Milan.
Yet, as remarked earlier, the intentions of the two in the affair were totally different. For Bopoulos, his double life at the weekly, one-day love encounter, which he more and more tried to limit to the confines of the pied-a-terre of his Italian friend to avoid uninvited eyes, was first and foremost to set hard proof for a man of sixty that he continued being able to seduce and sexually satisfy a beautiful youngster.
Nonetheless, his victory feeling at Thursday evenings was momentary as by Friday evening home with his wife—who was known for her remarkable, social character but uncompromising classiness—he felt increasingly ashamed and well aware of the disastrous consequences things could have if his affair would ever be known by her. The family would certainly fall apart, and with some influence of their mother, his two children could totally turn their back on him. Even more, as almost all the luxury and wealth he enjoyed in his private life originated from his wife, or better said from his father-in-law, breaking up would also have severe financial consequences for him.
Breaking up with Clara, rational the best option, seemed easier when she was not around, as the minute they would meet, he would lose rational and go for the immense satisfaction of his lover boy victory. So his main challenge was to keep both balls in the air but invisible to one another.
For pretty Clara, at first sight, she was like a real life copy of Barbie—the projected scope of the relation was a more lasting one, preferably concluding with her marriage to a well-known man with a good income. So her hopes were that Bopoulos would leave his wife and secure her a more wealthy future.
As the asymmetric interests were becoming more manifest to Clara due to the lack of interest of Bopoulos to even extend their meeting days, but on the contrary opting for more and more secrecy and almost solely locking themselves within the confines of the apartment and the bed of his Italian friend, Clara started becoming less compliant on the Thursday evenings and it happened more often that she would completely lose control and would start shouting in repetition what her expectations were and that he had to leave his wife.
So that rainy night in Brussels, Clara was once again near freaking out as Bopoulos spent almost the entire evening—from the moment she picked him up at the side door of a motel restaurant in Brussels South, on their way to the pied-a-terre to making love in the apartment of the Italian, to now on her way to drop him off again—making endless phone calls over a subject she could not and did not want to understand. She was outrageous over his lack of attention for her company and the words popping up repeatedly in his phone conversations, "federation" and "PIGS", caused her temper to flare. So, when he warned her to slow down on the slippery road, her tone became scolding and her behavior hysteric. "I have given all I have, Carlos, but you are too fucking egoist to even worry about my feelings. If it is not your work, it is your wife. If it is not your wife, it is your Commission. I am only good for Thursday evenings in bed behind close curtains. Go to hell!"
The more she screamed, the harder she hit the pedal. Carlos was trying to calm her down by speaking softly. "Please Clara, slow down, the roads are slippery. You will kill us both."
"You would deserve that. You have taken everything from me. It is time for your wife to know the truth. I am tired of playing cat-and-mouse with your Federation nonsense."
"Please Clara, slow down."
"I will if you leave your wife and marry me. Say it, say it now."
As Clara raised her voice even more, his phone started ringing and the car started slipping. Carlos, with his left hand also on the wheel, was trying hard to keep the car on the right side of the road when there was a loud bang followed by a human body, presumably a man, flying over the front of the car followed by the remains of a bicycle that was crushed under the front left wheel. Clara's screams were blood-curdling, but slowly ebbed away.
In the total silence that followed the crash, Carlos Bopoulos saw his future as in a movie falling apart: first, his wife walking out on him; next, his children hatefully accusing him; next, his office staff making a mockery of him; and finally Clara changing into a hysteric witch. Only this last image was real since the road accident provoked an explosive wrath in Clara.
While no longer accusing her of reckless driving, Bopoulos had to make all efforts to cool her down and drag her from behind the steering wheel. She started blaming him loudly for the accident and her whole, misfortunate life. It was his refusal to commit to her that made her to understand that she had to give up, to move on and run away. She was screaming. Although the streets were rather empty at this time of the night, some people living in the neighborhood heard the bang of the crash and started looking through their windows while calling the police. Considering the short arrival of police and emergency services and perhaps even a delayed journalist, Bopoulos was painfully aware of his possible recognition which could be followed by an exposure to awkward questioning. And of course, the appearing journalists would focus on the fact that he was in the company of a hysterical youngster who easily would be identified as not his wife. This could severely damage his career as well as his family and all that just for not controlling his aging hormones. Thenceforth, he understood that he had no other choice than to quickly disappear from the scene and as far as possible away from the hysteric youngster.
A few cars were already passing by the place of the accident, rolling down windows, and observing the details of a fresh crash with probably one victim. Misfortune over misfortune, one of the cars, having a diplomatic plate, was driven by the British Consul who a couple of minutes before abandoned a disco-bar in the neighborhood.
Instantaneously, the Consul identified Bopoulos, the PresCom, in a heated debate with a young woman who certainly was not the so-called "Duchess of Algarve" meters away from the bleeding victim. The police had not yet arrived.
In a bright second, smelling scandal, the British diplomat decided to pass and stop his car around the first corner, got out, and walked back stealthily to observe what was going on.
Meanwhile Bopoulos regained his calm and was trying to overrule Clara to solve the accident business without him.
"Dear Clara, you were driving. So you are responsible for what has happened. Please, you have to explain things to the police when they arrive, in particular that you were alone in the car. It would make things worse, also for you, to say that you were with me. You hear me, you were alone! We will meet tomorrow and I will compensate you abundantly, so please do not spoil my career. Be assured, I will compensate you generously, very generously!"
Although Clara did not fully believe what he was saying remembering that he often had remarked cynically that, "promises were to be broken", she decided to go along by saying to the police that she had been driving alone. Maybe this would change her position with him for the better. And besides, spoiling the career of the president of the EU Commission, although she was only vaguely aware of what it stood for, could also be inconvenient for her future, not in the least since from now on he would owe her.
"Okay, you can go, but where do we meet tomorrow?" was her quick and calm reaction. Carlos Bopoulos confirmed an appointment at midday at a café in Grand Place, although it was passing his mind that the next day, first thing in the morning, he would have to be in Strasbourg and thereafter in the afternoon and evening he would have to share his time with his wife and children in the residence in the historical Sonian Forest in Brussels. He could not escape any of these arrangements. The meeting in Strasbourg with the European Parliament was about a financial support for Ireland and hence utterly important as was the family dinner with his two daughters, all university students, who as usual would be traveling home from campus in Gent and Paris to share family life for at least one weekend. This was something their father insisted on, supported by his wife even though Carlos was sure that she would have enjoyed passing the weekends with her parents in Algarve.
* * *
Eleven minutes after the accident, an ambulance and a police patrol arrived on the spot to find the nervous, young waitress in tears explaining that she, being aware of the slippery state of the cobles, had been driving very careful and all alone on a dark, rainy night in Brussels when, all of a sudden and out of nowhere, an unfortunate cyclist crossed her path, probably he himself in a slip with his cycle.
Although Clara did all she could to avoid an accident, he ran into her car and severely hurt himself.
"What misfortune for both of us," she ended her story wiping of tears from her innocent, sparkling, blue eyes.
As there were no eyewitnesses and the cyclist was in coma, her story seemed to convince the two policemen. The elder among them even started apologizing for the misfortune that the Greek goddess Ate, daughter of Zeus, installed on poor, little Clara and offered her a glass of water brought in by one of the neighbors while all the bystanders, including the British Consul, attuned in nodding their heads and sighing that such a poor, little girl did not deserve such misfortune.
The ambulance people had already picked up the victim—who as they explained was in very bad condition and one should pray for his life—and left for the nearest hospital. The policemen hereafter invited a much calmer Clara to accompany them to the police station for deposition, but they both repeatedly explicated in full harmony with the bystanders that Clara had nothing to fear and suggested even that she was already acquitted, while the second-hand Polo, an hour earlier recklessly driven by annoyed Clara, was towed away.
* * *
In spite of the smoothness of police handling at the accident spot, for Carlos Bopoulos things worked out less fortunate. First, the British diplomat did not go home when the spot of the accident was cleared, but instead at nearly 2:00 in the morning, he returned to his office to report to his level at the Foreign Office, but with copy to the High Commissioner, over the things he had witnessed past midnight near Grand Place: the involvement of the EU PressCom in the company of a young woman in a car accident, the flight of the PressCom before the police arrived, and probably under instruction of the PressCom, the make-up of the story by the youngster in order to wipe off any involvement of the PressCom. This led to the closing comment in the report of the British Consul that the car accident probably coincided with a case of adultery by the PressCom. This event, according to the written comment of the Consul, would certainly have a tail and one should see his report as wagging the tail in order for the political staff at the embassy to scan for more information, and henceforth the interpretation of possible consequences.
* * *
Bopoulos, from his side, continued his flight from the scene by jumping into a cab and ordering the driver to just drive him around on the ring of Brussels till further instruction, and not as the readers might have thought, to his residence in the Sonian Forest, close to the center of Brussels. Carlos Bopoulos preferred to quietly reflect how to escape the problem of hysteric Clara having him now somehow in her grip.
And of course, he would have to find a way to avoid any damage on his career and on his comfortable family life. How was he to divide himself between the three constraints awaiting him tomorrow? What an idiot a man could be in front of sexual attraction! And then, what was he to do next? First and foremost, he had to get rid of the waitress in good harmony, regardless of the cost. Perhaps a job as some low-ranking assistant in an EU Delegation office in Ouagadougou would help.
* * *
Things got even more complicated when Bopoulos was woken up on Friday morning by his Blackberry ringing. The call came from none other than the British Prime Minister.
"My dear Carlos, sorry for disturbing you so early but knowing you will be flying to Strasbourg, and things being urgent, I took the liberty to intrude on your privacy. To put things straight, I have to ask you to immediately convene a meeting for at latest on Monday with the European Commission. It is on the issue of Nice and the proposed fractioning of the European Union by France and Germany, that is to say, on the issue of the five to nine voluntary federation, clearly aimed at sidelining the UK."
A sleepy Bopoulos walked to the closet with the Blackberry between his shoulder and jaw. On the way, he took his shirt from last night from the dress boy and he routinely started checking his collar on lipstick stains next to smelling the shoulders to disclose female perfume, his routine on Friday morning in order not to alarm anyone.
Meanwhile listening to the Brit, his first reaction was to take away any prominence of the Nice rendezvous of the five EU member states by calmly answering.
"Let me be frank too, if I were you mister PM, I would not give much importance to the issue. Nothing concrete will happen. The whole thing is too complicated! I have to see these countries progress a single step forward in the development of a political federation. The best would be to wait and see. Believe me, it is highly unlikely that the citizens of even the initiating two countries, France and Germany, having been enemies again and again for the last ten centuries, will finally give up a serious part of their sovereignty-remember that they even talked in Nice of integrating their armed forces in exchange for just promises of a more prosperous future."
"I'm not so sure about what you're saying Carlos", was the quick reply of the British PM who continued. "Correct me if I am wrong, but I think that they may be right in their economic appreciations at this very moment of globalization and economic slowdown in Europe. To form a federation of nine countries, as they have expressed in Nice, would give them an immense potential. This would be a community of 300-million people with a very high level in human capital and infrastructure. And it would give them space for weighty positions in international issues, which certainly could also cause fractions in the, till now, unitary positions of the West in international affairs. You will agree with me that in a time in which the economies of China and India are churning out, the West should not become fragmented, neither economically nor politically. Believe me, if this federation proposal would change into a fact, our American friends—and I know this first hand—would feel rather offended as the federation, which perhaps would have been useful in times of the Cold War, now may result very counterproductive."
"Yep, I could not have analyzed things better, but our union of twenty-seven states, which I proudly co-manage as head of the commission—and this is also thanks to past, full-fledged, British support to my candidacy—represents a market far wider and stronger with all Europeans in their distinct, cultural history, united under one, unique project. Indeed, I am so convinced of what I'm saying, that I promise you my full cooperation to abort this plan for the creation of a selective federation of the nine. But as I said before, no need to act now. We should not start shooting our cannons to kill ants."
"Dear Bopoulos, prevention is better than curing. Even more, I suggest you to urgently make all efforts to dissuade Italy and Spain from entering the club of the five core countries. I would not have called you personally if things were not urgent. By the way, dear PressCom, I have received information from my High Commissioner in Brussels of your unfortunate car accident last night. I hope you have resulted unscathed. You were not driving, I understood."
His last remarks struck like a bomb. For seconds Carlos Bopoulos was speechless. Someone probably not only had seen what had happened, but had already leaked it into diplomatic circles. He would give a fortune to know who else was involved, but knowing the rules of the game he reacted with composure.
"I may have overlooked some things, I am sorry. I will have to deeply rethink the issue of the five-to-nine federation, and of course I am most willing to order an urgent meeting of the commission on Monday in order to jointly analyze the different alternatives in front of us."
"My dear Carlos, I will be happy to hear the outcome. In the meantime, convey my warmest regards to your better half."
After ending the conversation with the British PM, which left Bopoulos with an acid taste in his mouth, he had a quick look at his missed calls. He recognized the number of Clara and, before going into the bathroom, he decided to immediately delete all messages in his voicemail without listening to them.
In front of the mirror, while brushing his teeth, he had a closer look at his face with the two, deep-set dark eyes. He had grown older overnight since, even after taking two tranquilizers, he had remained awake, turning from one side into another.
But, there was no time to lean back now that things were closing in on him. Slowly he started weighing the options he had for today and in the near future. Perhaps he could keep things secret for his wife, but this would mean that he would remain feeble in the hands of the British and anyone else they would inform while there was a chance that Clara would try to find a way to inform his wife.
Indeed, a constant pressure from these two sides could seriously affect his health as he was suffering from high blood pressure for already more than a decade. Besides, he had no clue what could happen if he would inform his wife of his affair with Clara. In all the thirty years of their marriage, his wife, or the Duchess, had never hidden her conviction that she would return back to the family castle in Algarve if things did not work out to her satisfaction. And more than once she had explained to Carlos that her bossy father repeatedly hinted that he was in standby to help reorganize the life of his daughter, if her Greek husband was not behaving. Carlos Bopoulos did understand the threat of his father-in-law, repeated also towards him, be it in a more subtle formulation. It would not only have financial consequences, it could also hurt his career.
The reader should know that the father-in-law of Bopoulos, known among friends and family as the "Duke of Portugal" was actually not a duke and his daughter was not a duchess either. In reality, the old man was a retired banker who, after leaving his posting in Swiss at the age of sixty-seven, settled with his shrewdly procured wealth in an impressive castle in Algarve.
And the retired Portuguese could well afford himself the aristocratic nickname, "Duke of Portugal" since he was not only a very wealthy man, but also a person with highly influential friends among entrepreneurs, politicians, and bankers in most countries of Europe.
Not surprising since, besides belonging to a historically influential Portuguese family—with Jew ancestors who in times of the rule of the Augsburg in Spain and Portugal had become bankers of the Castile Crown—the Duke of Portugal had in the first years of the Second World War succeeded in becoming vice president of a bank in Swiss. A success directly related to the fact that he had been one of the masterminds of opening the bank to "foreign gold deposits."
Although not proven, Bopoulos was aware of rumours that his father-in-law could have been one of the bankers facilitating that Jews could secretly deposit gold. Most of these Jews had never come back to request their savings as they lost their lives while their inheritors could not be traced or did not possess any proof of the existence of the accounts of their ancestors and consequently some middle men became the final gainers.
False or true, the position of his father-in-law as vice president of the bank had over the years provided him with innumerable contacts with people who after the war had ended, reached important functions and positions in all the governments of Central Europe, particularly in Holland, France, Germany, and Luxembourg.
So after the war, the man was endowed with a network of contacts covering almost all important persons and positions in the war-torn continent. This gave him the opportunity to act as an independent host for the secret meetings in his residence in Zurich between top French and German civil servants, all in preparation for the European Cooperation institutions that preceded the EEC and subsequently the EU.
No wonder that when Bopoulos married the only daughter of the "the Duke of Portugal", his father-in-law instantly helped him to climb up, first in the Greek administration and later in the European Commission in Brussels. All this meant that Carlos Bopoulos had to count even harder with the old man to solve the mess of his affair with Clara.
Finally, there was Clara. She might at first have presented herself as a spontaneous, naïve, and adventurous youngster with no strings attached, but along the four months of their Thursday sex affairs, she slowly changed into a spoiled and angrily pressing beauty who wanted to get good value for her attractive appearance, even by settling with an old, presumed rich guy.
Summing up, he had caged himself and escaping was not going to be easy. Looking at his decadent image in the mirror he started speaking to himself, "Well, well, who could have imagined that such an intelligent, strategic, life-loving, and charming man would end up being sandwiched between three attackers? And that for the petty prize of enjoying a young body?" While shaving, he finally decided not to decide, to leave the things just as they were—although progressively getting rid of Clara—and trusting his own good luck which always favored him during his career.
At his arrival at the office in the Rue de la Loi, PresCom Carlos Bopoulos already devised a strategy to block the embodiment of the two, main, southern countries into the voluntary Federation of nine as initiated by the five in Nice. Best for him would be to visit the top leaders of the two countries at stake beginning with Spain. If he left today for Spain immediately after the meeting in Strasbourg, he would not have to meet or talk to Clara, nor would he have to face his wife and daughters.
* * *
But once again Ate, the goddess of misfortune as Carlos learned in primary school in Athens, had put her desires on him. Little time after arriving in Madrid in the afternoon, actually immediately after shaking hands at the Palacio de la Moncloa in Madrid, the Spanish Prime Minister informed Bopoulos that after the revolutionary gathering in Nice of the five Euro zone countries and their challenging final declaration, things had drastically turned around in Madrid and Rome, and consequently Spain and Italy wholeheartedly decided to form part of the selective Euro zone Federation initiated by the German Chancellor and the President of France.
"Believe me, Bopoulos, having read the project of Marlein and Jacques as presented in Nice, I first became silent though deeply impressed and finally I turned into a fanatic supporter of their very timely project. The world is changing and so should we. I'm convinced that they are right. I'm also grateful, and so is my cabinet, that they have invited Spain to form part of the federation of nine. Certainly to belong to a state of 300-million people with a common army, a common Ministry of Finance, etcetera, is something that the Spaniards will appreciate as you will witness in the corresponding referendum"
"So, you are abandoning the boat of the EU-27 to join the German-French adventure. Have you also considered that if the federating project fails it will blow up the whole EU-27 project in exchange of nothing? It seems to me not a very rational initiative."
"My dear Carlos, I think that at this historical moment, Marlein and Jacques have found the correct roadmap for our continent. I agree with them that the European Project as it was developed in last decades, had already years ago entered in a blind alley. Really, our current organization, although it may make that some member states—those who recently entered in the union, I mean in 2004-07—felt happy with their embodiment, the reality is that today with the issues of unanimities and different speeds of embodiment of newcomers, it is very difficult to almost impossible to take any decision and move forward. Indeed, of late, we have only succeeded in issues of international trade while our international, political capacities have practically not progressed in the fast-changing world we live in. And this means that if nothing is done, we will continue with our current decadence while we lose track of main, global developments and fight among ourselves over marginal things. I feel too responsible to my people to leave things untouched."
Bopoulos felt growing anger as he was listening to the Spanish Premier and he considered with some disgust that some months ago this same man had been defending a federation of the four, just to get more power within the EU-27. Could one think this man to be trustable? Or was he just someone playing to the best bet, irrespective of principles?
As the Spanish Premier observed some concern in the face of Bopoulos, or perhaps repulsion, and taking into account that the PressCom was Greek, and Greece was not in the list of nine, the Spanish leader even dared to make one of his typical summersaults by offering Carlos Bopoulos a bargain.
"You may imagine that when the new federation becomes a fact, there will be a new common nationality and passport for the citizens of the nine federated countries. In my view, up to now you, Carlos, have acted as a European citizen and you therefore would deserve to be among the first to receive a real European passport as a citizen of the Federation. However, being Greek, the only way out for you would be to apply for the Spanish nationality as soon as possible. And I can assure you now that I will personally see to it to happen. Let us not forget your new nationality would also create opportunities for you in reaching once again a top-ranking, civil servant position in Europe, this time in the federation of nine."
He continued, "I say nine since you may have heard dear colleague that the other three invited countries have already informed Spain of their considered positive reaction to the extraordinary opportunity offered by the five of Nice."
A depressed Bopoulus, incapable of grasping why his breaking attempt on instigation of the British PM was bound to fail, had only one last question, "Do you the federating countries really believe that the rest of the current EU members, in particular the more powerful like the UK, will take no action against your group? Do you think that the British will do nothing? Just remember that when finally the CEE was created in 1957, the British reacted by creating EFTA. And why would they not attempt to construct a simple, common market with the rest, or with a selection of the rest, and thereafter renegotiate the common market rules with the federation, excluding f.i. movements of people?
And do you think that the Americans will be happy with your exclusive club? My friend, do not forget, your federation could damage unity in the West!
"Carlos, I suggest you to be realistic. Instead of opposing the formation of the federation of nine, you should try to convince the others that far from losing, they will all profit from the existence of the federation of nine. It will be far more prosperous for them to remain in a position of common market with the federation"
* * *
When Carlos Bopoulos left Moncloa, Madrid enjoyed splendid spring weather and the streets were bustling, full of jolly people, but he felt deeply down in the dumps. He was to board a plane for Rome at 8:30 pm, but instead, accepting his defeat, he took one for Brussels at 9:10 pm, well aware of the fact that he still would have to face his wife—a late sleeper—around midnight.
* * *
Early Saturday morning, a broken Bopoulos finally arrived at the Sonian Forest residence. After a gruff farewell to his driver and a surly hello to the guard, he entered the house. At every step in the corridor underway to the living room, he was fully aware of the fact that he would have to overcome a lot of difficulties to fulfill the will of the British PM to stop the formation of the federation of nine. Not to mention the other problems in his private life.
Carlos Bopoulos found his wife impatiently waiting for him in the living room and with yet another set of unanswerable questions.
Sitting at the edge of the sofa in the spacious living room, the "Duchess" hardly answered his quick greeting kiss, but affectionately started explaining to the still-standing Carlos that from seven o"clock onwards on Friday evening, a certain Clara repeatedly called to the residence and asked for him. The housekeeper first explained to the caller that Mr. Bopoulos was not home and that, for business-related issues, the PressCom preferred calls to his office in the Rue De La Loi, where there would also be a weekend service telephone for urgent matters.
However, at the sixth, stubborn call, once again patiently and also unrelentingly answered by the housekeeper, Madam Clara had become rather hysterical and insisted that she in that case wanted to speak immediately to Mrs. Bopoulos. Of course "the Duchess" refused when asked by the housekeeper, but this did not stop the undisclosed Clara from calling over and over again. Actually, her calls did not stop until the "Duchess" gave permission to the housekeeper to take the phone off the hook at around ten.
As his wife gently explained, it crossed her mind to call for the police to stop the stalker, but something told her that it was better to leave third parties out and to wait first for clarification from Carlos.
At her last words, the Duchess pierced her light brown eyes in the dog-tired eyes of Mr. Bopoulus, at which wacked Carlos, with his shoulders down and sweat running in his back, could do little more than begging his wife to let him clear up the issue by tomorrow, amplifying that it was certainly not what she was thinking but that he was too exhausted now to touch the story of stalking Clara.
Carlos Bopoulos hastily explained that he mistakenly had left his high blood-pressure pills home when traveling to Madrid, and that he should be going to the bedroom to take one immediately, and added that Madrid had also been a disaster.
"Please darling, if you do not want me to drop dead right now and here, I beg you, let me go upstairs for my medicine and give me time to explain things tomorrow. Believe me. It is not what you think and it can wait till tomorrow. I am sorry for the trouble it caused and believe me, I am exhausted."
Without awaiting her confirmation, he stumbled up the stairs to their bedroom.
### Eight
### From Russia with Love
The banquet and dancing offered by the Russian President in honor of the German Chancellor in the Kremlin's Catherine Hall was about to start when Marlein Ditch got the shock of her life. Of course she highly appreciated the whole glamorous event in the Kremlin and she was well-aware that this gesture of the president to her was somewhat over prescriptions from protocol, but neither she, nor the Russian President would deny a certain warm sympathy in the way both were filling in the Russian-German relations, which taking history into consideration, was almost a paradigm shift.
Although the Chancellor of Germany was on a bilateral working visit to Moscow, the Russian President offered her a state banquet for which he invited G-20 ambassadors and the top representatives from the Russian society: political leaders of three parties, the business community, bankers, the academic world, religious leaders, and even some famous artists: musicians, dancers, film actors, and writers.
Actually, the Russian President invited the same group as he usually invited for the biggest party of the political calendar in Moscow: Kremlin's New Year's banquet in which some 1000 guests would socialize and network while enjoying exclusive food prepared by twenty top cooks from all over the world.
It was Marlein's first visit to the antique and artful, decorated area of the Kremlin Palace, and as she heard rumored, the palace had recently been restored by the current Russian President to its 1906 decoration and design by the last Tsarina, Alexandra Feodorovna, wife of Nicolas II, the last Tsar of Russia.
Although not showing, a rather impressed Marlein agreed that after the toast of the Russian President on her behalf. She would in a short speech explain to the guests the why of the voluntary federation and what would be the positive opportunities for the Russian society once the nine candidate countries would have made the leap forward in their political integration. Of course, Marlein was not planning to say more than trivial statements since the referendum was still pending, but saying no would have been impossible after the fruitful, German-Russian deliberations of the day for which both parties spent their precious time in a remarkable, open atmosphere.
* * *
Looking back, the one-day program was well-invested. After a working breakfast in the Germany Embassy in Moscow following her arrival at 8.45 in the morning at the airport, Marlein Ditch left the Embassy for a first meeting with the Russian Premier accompanied by the German Ambassador; advisor Hans Schmidt; and Peter Baum, a top, German diplomat specialized in Russian issues.
As usual, the first meeting started with looking into the future perspectives of Russian-German trade and investments, in particular gas and other raw materials before touching down on foreign relations and international politics.
Since about eighty-percent of the exports of Russia consisted of raw materials and half-fabrics, particularly petrol, gas, and globally scarce minerals, German interest was to balance the Russian raw materials exported to Germany with exports of luxury cars and other exclusive manufactures to the Russian market.
One should not forget either that the absolute number of billionaires and millionaires living in Moscow and St. Petersburg was one of the largest in the world. Marlein shrewdly informed the Russian Premier that the expectations for Germany were good in relation to investments and budget cuts already done, which together would continue triggering growth in Germany in the midst of the ongoing financial crisis in the West.
In fact, this information of Marlein was against the advice of Hans Schmidt who, during the preparatory breakfast, pointed out that, in the next-quarter, the economic growth rate of Germany could converge to the average low growth rate of Europe.
So all went well in the first meeting, but it is fair to say that for Marlein, the big thing was yet to come: deliberations with the Russian president, something she considered the summit of her working visit.
* * *
No wonder that punctual Marlein felt embarrassed when the delegation arrived almost an hour too late at the Kremlin, but the delay should be attributed utterly to the complete failure of the escorting police. These four, Russian policemen on heavy Chinese motorbikes were outright incapable of smoothly leading the delegation through the horrifying traffic jams near the Red Square. Clearly, no Russian car, bus, or motorbike driver was even slightly impressed by the four policemen in their somewhat over-decorated uniforms nor was any attention paid to their gesturing with arms and hands in order to make way for the two Mercedes Benz with diplomatic sign plates and country flags.
Most cars and busses did not only completely neglect the somewhat conflicting signals of the four policemen, but also aggressively continued looking for any small space in front to quickly move in, thus transforming a four-lane road in six to seven rows of cars, closing in on each other and constantly changing lanes. Thereafter it was simply impossible for anyone to move an inch forward.
"It is absurd, they should all be stripped of their driving license" was the repeated snappily remark of the German Chancellor to aid Hans Schmidt, while looking at her watch to find that they were already forty minutes or more too late on appointment.
Were it not for the Russian President—who broke the ice at their arrival with a lively narrated story of a police escort in Palestine—Marlein would have held consultations with the President tied up to the roof with nerves. The Russ told them that when he was visiting the Occupied Territories last year, the policeman escorting his car, had half—way run out of gasoline and his motorbike suddenly halted in the middle of the road, after which he was literally scooped by the car he was escorting. Luckily, the policemen survived with only some scratches while they all watched his motorbike falling from the cliffs.
So while the whole delegation was in laughter over the ridiculous accident, Chancellor Ditch restored herself and the session took off with some polite exchanges.
As soon as the routine was over, the Russian President cut short by expressing his real interest in the German-Russian consultations.
Surprisingly, this was not related to the Israel-Palestine issue, or with the recent developments in the Arab world, and not even with the financial crisis in the West or the Euro instability, but it dealt almost exclusively with Russian economic interests on the North Pole.
In brief: as the economy of Russia was still mainly driven by the export of raw materials and given the fact that climate change was progressively making possible the exploitation of huge deposits of raw materials in the North Pole, the Russian President was interested in knowing the view of Marlein Ditch concerning the ownership of these deposits.
According to him, Russia with its two-hundred-mile zone along the coast of the North Pole was without any dispute one of the main owners of these deposits, but much to his concern, the Russian President had noticed that countries with less linear coasts such as the US and Canada, seemed to believe that they were in their right to exploit the wealth of the entire Pole, irrespective of the length of their lineal coast on the Pole. Even more, Denmark, using theoretical rights on Greenland was queuing with the claimants. And then Britain and Iceland, having hardly a coast to the Pole, had also appointed themselves as candidates to accede the supposed rich stock of raw materials hidden under the ice cap. Having explained his concerns, the Russian President had put a direct question to the German Chancellor.
"Dear Marlein, soon the discussion over this issue will have to arrive at the UN since this would be the only way out of the conflicting interests. So could you, without going into detail, enlighten me at forehand on what position Germany will take? Would Germany support the Russian position? Would you abstain? Or would you support the doctrines that is basing ownership on the order of arrival of the exploiters to the territory and on their exploitation capabilities? Let us not forget that this doctrine had in the past resulted in many bloody wars in times of colonialism. Something no one should want to repeat."
Marlein was taken by surprise. It was the last thing she would want to discuss during her visit: risking to disturb German-Russian relations on an issue with little direct German interest, but great German concern in terms of protecting the planet.
Putting all her charms in the bascule, she answered, "My dear friend, really you have caught me on an unprepared domain. So let me give you my personal view since this issue has yet to be discussed in my Council of Ministers and the German Parliament. And if the European Federation is alive and well, the issue of strategic raw materials will be high on the agenda of our international policies as will our concern with sustaining the environment of our planet. But for now, frankly speaking, I think that although in the current UN legality the Russians would have a majority ownership right, if we seriously consider the new environmental and social circumstances of the world today, we will be forced to globally reschedule ownership and exploitation of natural resources, irrespective of whether they are in the seas or on land. Not in the least because the exploitation of natural resources of the North Pole will become possible only if we continue with our suicidal global warming and hence the reduction of the iced surface of the Pole. By the time we have reached that state, I fear life on the planet may have changed so much that even exploitation of the deposits at the Pole could become irrelevant.
On the other hand, the parallelism observed in relation with the race for the wealth of the North Pole—consisting of rushing to take advantage over the others without any general agreement or concern on the issue—reminds me of the so-called "Scramble for Africa", in which the Western countries—including Germany—distributed sub-Sahara Africa among themselves in an urgent, imprudent, and irrational way and without any knowledge or concern about the geography and sociology of its inhabitants. It was blatant colonizing euphoria and nothing less."
"Come on Marlein, I do not think that the German concern over global warming will be sufficient to stop the ambitions of the interested countries to start exploitation. On the other hand, I have no doubt that the global warming problem will be rebalanced very soon by using technologies now already well under research in Russia. Do not forget that the quality in research comes from the quantity and the absolute number of Russian academic graduates is currently higher than in any other European country."
"If you don't mind, Mr. President, I could introduce a different argument, the social one. Taking into consideration the fact that the global population has multiplied almost per three in the last sixty-five years, and will continue to grow, production and prices of strategic raw materials cannot be dependent on the will of a single country, or a group of them forming a cartel, let alone from multinationals and speculators.
This is an issue so serious—provoking numerous economic disturbances in the last forty years—that the production and distribution of strategic raw materials will have to be controlled by the United Nations."
"Marlein, should I expect Germany to say so because you are destined to stay out of the Security Council club of permanent members? Anyway, I would be able to agree with you, but only on one condition: real power sharing in the United Nations. Do you really believe that production of the Russian oil reserves should depend on a UN dominated by the West and western interests? Russia could only agree with you, with Germany, on the condition that this UN would be democratic. And you, Marlein, know what this implies: that the West, currently with only sixteen percent of the global population, would lose control of the UN. Do you think that the West would give up its current, oversized, international power and the profits stemming from it in exchange for nothing?"
"Of course," answered Marlein, "I am not talking in terms of the next five to ten years, but current economic trends suggest that in around twenty to twenty-five years, the economic and military dominance of the West could be over without being replaced by another dominating region or nation. As you and me will both be on retreat by then, I can only dream of how things may evolve. But my dear friend, as usual it has been a great pleasure for me talking with you."
And so the bilateral consultations between the two countries were over faster and in greater harmony than expected, and Marlein and her team could sigh released and prepare for a joyful evening in the Catherine Hall of the Kremlin; but it was there that Marlein got the shock of her life.
* * *
As Hans Schmidt, aid for European affairs, explained to the Chancellor on their way to the party, the Banquet Hall had undergone a huge facelift ordered by the current, Russian President, who probably wanted to bring back the glamour and chic of the pre-Soviet days.
Even more, his example had been followed by the Russian society.
Not only the hall with its eighteenth century ceiling paintings and decorated arches; its high roof windows, some with glass in lead and others with heavy brocade curtains; and chairs and sofas in Louis XIV-style, had been recovered and upgraded with a winkle to the days of Nicolas II, but also the dresses of the women, accompanying their husbands this evening in black tie, portrayed that the Russian ladies had seized the opportunity to glitter in Tsarina-style. Consequently, on the evening offered to her as chief guest of honor, Marlein Ditch was sadly condemned to look more plain Jane than ever, although for the first time she had dressed in pink Thai silk with a for her style very remarkable low décolleté and a fancy collier with some small stones.
During the reception in anticipation of the diner, some guests were personally introduced to the German Chancellor by the seemingly rather popular Russian President and Marlein managed to use some socializing words in Russian she still remembered from her days in school in Weimar. Meanwhile the Russian Symphony Orchestra was sweetening the memories of the guests by playing romantic, Russian composers including Modest and Tchaikovsky and the colorful guests, greatly wrapped in rustling chiffon, were sipping on glasses with cocktails based on vodka, while mingling around.
So, love was in the air when the President announced, with a jolly smile all over his face, that he was going to introduce Marlein to someone very dear to him. This person was the most successful Russian businessmen of the post-Jeltsin period, and besides his ancestors originated from Germany.
And there he was! Friedrich Greber, Marlein's former husband from Dresden, was standing eye in eye with the German Chancellor. For at least ten seconds, Marlein froze and had to make strong efforts to recover breathing. Friedrich, looking rather well cared with a body shaped by sport and elegantly dressed, introduced himself to her as Friedrich Pechov and his Russian wife, a stylish blond on extremely high heels, as Anastasia.
"How very nice," Marlein said quietly while slowly coming forward. Friedrich took her hand, raised it to his lips and bowed, before humbly waving away the compliments of the Russian President over his success in business and his outstanding support for cultural events in Moscow.
"My support is not more than my duty as a citizen," Friedrich said,
"but meeting the Chancellor in person tonight is for me a real honor." And smiling at Marlein he continued, "Madam, I am overcome by your performance in meetings and press briefings. You really are the most convincing and the most involved of all political leaders of the European Union." "You are flattering me, Mr. Pechov.
But really, I would swear we have met before," a fully recovered Marlein asked sharply as she gave Friedrich an understanding smile.
Friedrich, looking around first at the Russian President and perhaps also at his wife Anastasia was careful in responding, "Yes, come to think of it, must have been some thirty years ago in Minsk. You, Madam Chancellor, if I remember well, were participating in a youth championship of athletes and I was a young freelance trainer who had been contracted contemporary by the team from the German Democratic Republic, as one of the official coaches fell ill." Friedrich was now looking mainly at his wife and the Russian president while he was trying to hide the former intimate relation with Marlein. Crossing eyes with Marlein, he continued, "What days they were. No one could dream in those days in the stadium of Minsk that Germany would years later be united, or that the small _Osi_ girl fighting for the trophy would finally become the Bundeskanzler for East and West."
Marlein replied sarcastic as it was clear to her that Friedrich did not want to recount their past. "Equally, who would have thought in Minsk that the young trainer for some days would become a millionaire in oil? I am very impressed."
And then smiling mean, she decided to give him a low blow. "Dear Mr. Pechov, excuse me my blunt question, but have you also been capable of profiting from the fast privatization in Russia during the transition under President Jeltsin?"
It sounded false even in Marlein's own ears and she started looking at the hands of Friedrich and his Russian wife to detect, as unnoticeably as possible, if the couple was wearing marriage rings. Of course they did! The word bigamy crossed her mind as she was looking straight into the eyes of the now rather uncomfortable Friedrich. They had never filed for divorce and they both were aware of that at the very moment of Marlein's mean remark.
"Madam Chancellor, as you may well know, the privatization or dismantling of state firms under president Jeltsin was for the full one-hundred percent policy devised by IMF and WorldBank, the so-called Washington-consensus. These policies, stemming from the so-called international society, were simply imposed on the Russian society. So tell me, Madam Bundeskanzler, who profited most, the Russians or the international speculators financing Russian intermediaries?"
Friedrich was losing control, something also noticed by the Russian President who hastily introduced a new guest to Marlein in order to stop further quarreling between the two.
* * *
As the table setting clearly dated from before their mutual, verbal aggressions, Friedrich had been honored with a seat at the main table and opposite Marlein, be it two places away to the left. But as the overwhelmingly French dishes on the menu were served— _blinis au caviar beluga; fois gras, daube de bœuf a la Beaujolais, tarte au fromage et pommes en Calvados_ —they could easily avoid any eye-contact between them.
In her speech, made just before the last course was served, Marlein called upon Russia, its government and its active population to support the European Federation in the making as it would create greater opportunities for stabilizing Russian exports to Europe and perhaps one day the cooperation would result in a common market.
The Chancellor's words were welcomed by the guests with an ovation and a second toast at which Friedrich reached out to touch her flute. A sign of settling for unconditioned peace, which he had decided to repeat by asking her to dance with him at the moment the third Viennese waltz of Joseph Lanner was played by the orchestra some time after the last course.
During dancing they did not speak, but as he appeared to be a well-experienced waltz dancer, she hung elegantly in his arms, and with her eyes fixed to a detail of a ceiling painting she gave herself fully to be led by him and becoming slightly lenient by the mixture of the musk scent of his aftershave and the cognac he was breathing out. For a fraction, it was like the first weeks of their life together in Dresden when she still fully trusted him.
So on the way back to her chair she became entirely willing to listen to his warm voice. He remarked, "Marlein, I think the best for us is to keep me dead. I am now Friedrich Pechov, a naturalized, Russian businessman, married, and with two, adolescent children. Any other format would have negative consequences for both of us."
Marlein was flabbergasted by the cold way in which Friedrich broke the enchantment. He solely seemed to be interested in averting problems with his wife. And of course, she was also surprised by the fact that he seemed to know that she had announced him dead when she forced him to step out of the relation. As to the bigamy business, he was clearly not interested in that. So, she nodded without saying a word, thus giving him the conduct in the conversation.
"Besides Marlein, have I told you that you are looking gorgeous tonight and that you have become a great dancer? I have sincerely enjoyed our dancing." And my dear Friedrich, have I told you that you have become an even greater liar? You must be on cloud nine with your new family wanting to keep the truth out? What about your women hunting addiction?"
"Marlein please, do not be mean for no reason. That is not you. I have become a cheerful, respected, sophisticated businessman and you have become the German Chancellor. What else would we want? Please let us burry the past tonight forever. Would you accept my invitation to be guest of my family in our residence just some meters away from the Red Square before you return to Berlin?"
"No Friedrich, not at all. Are we to sit with your wife and lie? As you have remarked just now, let us forever lay our joint past to rest. And let us both never more say to anyone that we knew each other in our past lives. It is probably for you no problem to live in bigamy, is it?"
"Do not use this ugly word, Marlein. After so many years, it would have no value in any judicial system. After killing me, would you now be resurrecting me? Starting clearance would have more negative consequences for you than for me. I take the deal. I will, from now on, say that we met for the first time in the Kremlin because you should not think that you will never meet me again. I will be in Berlin next week to meet your minister of energy. So a decent solution would be: _It has been a pleasure to meet you, Madam Chancellor and my heartfelt thanks for the opportunity to dance with you_."
As they were now in hearing distance of the guests still sitting at the tables, Marlein softly and restricted murmured, "It is a deal, Friedrich; from Russia with love."
### Nine
### A birthday party in the Basque Country
By and by, the summer was arriving at L'Elisée and Jacques Perrier had acquired a bronze tan that matched well with the sunny weather in Paris. However, his tan had been picked up overseas, as the couple had made an official trip to Martinique on the occasion of the official memorial service in Fort-de-France for the famous French-Caribbean poet and politician Cheshire. This man was to be the first black French politician and artist to be honored with one placate in the Pantheon.
Alexandra, French First Lady and herself being a writer, had gladly accompanied Jacques, something he highly appreciated since it was well known that he and Cheshire had been on bad terms for more than a decade as politicians who were almost on different ends of the political spectrum. So Alexandra, with her charm and impressive knowledge of colonial and post-colonial history and art had been of great help to Jacques in encountering the friends and relatives of Cheshire under the wicked eyes of French media, and in bridging the lack of sympathy of the black Caribbean community for the President of the Republic. Even more, thanks to the good behavior of Alexandra during their touring in Martinique and Guadeloupe, the press reporting of the trip of the President to the oversea departments was not only mild but unvarying positive.
Accordingly, Jacques Perrier was in an excellent mood when the couple returned and as Alexandra did not show any sign of being upset with him, Jacques felt released to conclude that his problems, one after the other, were already on track for resolution. The fact that the former lover of his wife had vanished without any political cost or personal implication and surprisingly ended up in the strong hands of the transatlantic friends further supported his euphoria. Then there was also the hazard of the Southerners, the PIGS, which had been dissolved almost automatically when Italy and Spain enthusiastically agreed to abandon the PIGS faction and enter into the Federation of Euro zone countries as proposed in Nice. And although there were some adverse reactions to the European Federation, mainly from Britain, almost all editorials of important newspapers, including London-based weeklies, reminded the British that they themselves took a sideline position by rejecting to join the single currency a decade ago. Definitely, the Americans seemed to be too busy with internal budget quarrels between Democrats and Republicans and the growing influence of China, to get involved in political events in Europe.
Only one thing kept worrying the President of France and tempering his good humor: the affair of his mother with a married man in Paris who also appeared to be an old official of the Legion Etrangére. No wonder that Perrier seized the opportunity of the celebration of the eighty-first birthday of his mother to travel to Bayonne, the city of his childhood, in an attempt to set things straight.
Thought and done. Jacques Perrier left Paris in the very morning in his official airplane, under the pretext of inaugurating a "new" five-star hotel directed by an old schoolmate. This hotel had, after minor reconstruction, changed its former name—Hotel Belle Vue, into Hotel de la Federation—immediately following the press release in Nice, thus proving that the owner had a sharp wisdom for business.
Having finished the official act at 12:15 and after checking by cellular that Alexandra was at friends in Paris, he was quickly driven to the birthday party which was to be celebrated with a lunch offered in a picturesque restaurant at the outskirts, some four kilometers from the old centre of Bayonne at the seafront of Anglet. The three-story restaurant was built on cliffs with on one side a wonderful view on the Atlantic Ocean, and on the other side looking down on the historic city of Bayonne with the Church of Saint André, the Synagogue, the Basque Museum, and the great Gate of Spain all along the meandering Gascon River.
When Jacques Perrier made his entrée, the party had already started and much to his surprise was pepped up with around thirty people standing in groups, bustling and full of laughter with champagne glasses in their hands in a reserved spacious room at the top floor of the restaurant. The room had the best view in both directions and Jacques noticed that because of his participation, the restaurant was duly but discretely examined by the Gendarmerie.
His mother, clearly the _grand madam_ of the party was dressed in a lilac, deux piece with light, purple lace and covered her grey hair under a spectacular Elizabeth Taylor hat with an attached artificial bouquet of lavender flowers and yellow daisies.
"I had hoped you would come, mainly as a dream not to disappoint myself, but here you are for real. Welcome my son, I am honored and so are my friends. Dear friends, may we welcome my son, the President of the Republic!"
She spoke loud and clear and had now all the attention of the participants, which forced Jacques to say something, even if his words would be worth little more than twenty-five, potential votes. After expressing his appreciation for the long-lasting friendships his family had enjoyed in Bayonne, he ended up by pointing out that in a few months from now, Bayonne and Anglet would become border cities of the European Federation, the new state of 300-million inhabitants.
After a fresh round of champagne and canapés served with both Basque and Perigord flavors, and after Jacques toasted to the health and wealth of his mother, an impatient Perrier Jr. made a first rushed attempt to take his mother apart for some minutes in order to talk about the Legionnaire affair, but failed as she resolutely refused.
Slightly annoyed by his insistence to have some minutes alone with her in the middle of her birthday party, she quickly got rid of him by means of introducing him to a couple of Tunisians, who many years ago had become French citizens, and had lived since then as neighbors of the Perrier family. Mr. Suleiman, a sixty-one-year-old man was a medical doctor and his wife Leila of fifty-eight was proud to announce that she was a professor of Contemporary History at the University of Toulouse, faculty of political science.
Suddenly, Jacques, following his political instinct, forgot for some minutes the leitmotiv of his participation in the birthday party and started a conversation with the neighbors of his mother about the so-called Tunisian Jasmine Revolution, a political process which resulted in overthrowing already two, dictators in the Middle East and North Africa. A remarkable revolution since its overthrowing power was formed by popular street protests of mainly unemployed youngsters, mobilized via Facebook and Twitter. These uprisings of youngsters were rapidly spreading throughout the Arab world and, although in essence welcomed as a wave of democracy almost similar to the one in the former Soviet Union and satellite countries, Perrier observed a strong tempering in solidarity among his constituency in France. This happened from the moment that large groups of economic refugees started leaving North Africa for Europe in particular for France and Italy.
In order to update his insights in the problem, Jacques Perrier swiftly decided to invite the French-Tunisians to go out with him to the balcony to enjoy the views and the refreshing breeze from the ocean.
Without any preamble because—as he proclaimed from his first sentence—he was very concerned with the unexpected migration flows after things politically improved and the dictators were thrown out, and so he requested the guest of his mother for some sort of personal advise. It was fully logical—he affirmed—given the historical implication of France in Tunisia, independent from the French only since 1956, that Tunisians were attracted to immigrate to France; but that would have been more understandable before throwing down the dictator then thereafter. Just at the moment when things had become far more promising to join hands to build their own country democratically, people were risking their lives to flee to Europe. Without any pause, he directly requested the doctor and his wife.
"My dear Mediterranean friends... imagine you are me. Tell me, how would you explain to the French society that we should give asylum or safe haven to thousands of young Tunisians who have actually stopped being endangered by authoritarian government? And then just at the very moment in history when unemployment in France is also hitting young educated French. To make things worse, it is a fact that young Maghrebians who have been living for decades in the outskirts of Paris are making life in these areas more and more unsafe and unpleasant for the original French population. I simply have no clue."
The medical doctor was overwhelmed and speechless but his wife, the historian was ready to react.
"Mr. President, the news we receive every day from Tunis are frankly still very worrisome. Demonstrations continue, successive, provisional governments have fallen, political parties make extremists remarks today and deny their remarks tomorrow, single-issue interest groups pop-up daily: pro and contra Sharia, pro and contra scarves, pro and contra privatization of public firms, etc. Clearly, the country will not be stable for the coming five years if not more. We were all happy the first days after the flight of the dictator, but as the French have themselves experienced, in some few days after the euphoria, things appeared to be much more complex. Let us not forget that it took almost one-hundred years in France and many bloody battles among different interest groups, before the French revolution resulted in a sustained democracy in the country. Today in Tunis, I am sure things will not take another one-hundred years, but much will depend also on the outside support. And to be frank, that worries me most. Real interest in developments is very short lived in our days of modern mass media. In some hours, news items could completely disappear not only on TV screen but also on agendas of parliaments and governments with huge negative impacts on aid and solidarity."
While Mrs. Suleiman was talking, Jacques was becoming more and more impatient and as he sensed some accusation towards him at her last words, he interrupted her rapidly but joyful, "But, Madam, all sounds to me like an academic speech; are you lecturing me?"
In reaction the black eyes of his mother's neighbor perforated Jacques friendly smiling brown look, and with a slight rise in her voice she continued, "I would not dare lecturing you Mr. President, but please, let me explain. I remember visiting Tunis some years ago. This was for me to speech at a UN seminar titled, _Roads To Sustainable Democracy in the Arab World, The Roads of Tunisia_. After the seminar in which quite a number of civil servants participated, I had a very interesting lunch with the two women who initiated the seminar.
These two women had written a paper on global experiences with sustaining democracy in developing countries in an evolutionary and not in a revolutionary way. Starting with analyzing necessary and sufficient conditions for democratization processes to sustain, they distanced themselves from, for instance, the Iraq experience of external military interference. Learning also from the French revolution they proposed a step-by-step involvement of international cooperation in countries where some necessary conditions were fulfilled like in Tunisia. More than other countries in the region, in Tunisia some important development goals had been achieved such as the participation of women at the labor market, and reproductive rights.
But as the two ladies explained to me, one could compare the democratization process with a plane taking off. While taking off, all seatbelts have to remain fastened, but when the plane has reached its cruise level, the purser will announce the possibility for passengers to free themselves from their seatbelts. Similarly, as these women explained, at initial take off in a country after independence, some seatbelts could be tightened in terms of liberal politics, for instance forbidding political parties which could cause factions, but if thereafter not released timely, stability would not remain. The two women predicted in their conference document that the protests against the ruling one party was going to increase fast as the redistribution of personal income had too long been limited via patronage to rank and files of the ruling party, while more and more educated youngsters were unemployment, food prices were rising, and access to modern media was denied. Consequently, it was better to loosen the seatbelts step-by-step in the development plane of Tunisia, because if not, a more radical change could also cause throwing the child with the bathwater.
But the two women were shouting in the desert as the opportunity got lost. Mr. President, as things are now, we need far more help from France and fast."
"Madame, please, you have missed some crucial points. First, we French did help and are still helping Tunisia. From the independence onward, yours has been one of the countries receiving the biggest chunk of our development aid budget. And not least than 800,000 Tunisian immigrants live and study in France, of whom almost thirty-percent are unemployed enjoying social services and other benefits to which they originally did not contribute. But enough is enough. When is our historical debt over? Do my children have to compensate wrong doings of their ancestors in the nineteenth century? Absurd! It is time for you, the former colonized, to take on own responsibility for your life and future." Jacques spoke slightly irritated and probably had raised his voice, hence it was Mr Suleiman who, having kept silent till so far, was ready to intervene, "Please Mr. President, my wife and me are full-fledged French citizens and our reaction to your question is a reaction of compatriots, even if we sometimes express ourselves in a way which seems as if we were still immigrants."
Mrs. Suleiman stubbornly claimed the last word by adding, "As the French society still enjoys the fruits of colonialism, they will have to share opportunities with former colonies in order to create win-win situations. If you allow me, Mr. President, I have to stress that most colonial powers for long-took capital (raw materials and lives) and now are hardly willing to pay the interest. Note, Mr. President that refusing to pay interest for capital taken is contrary to the normal practice of capitalism."
Luckily the _grandee dame_ arrived at the spot just in time to restore peace at the balcony by explaining with a big smile, "Dear friends, my son is himself an immigrant, so do not worry. He is very much in favor of multicultural France as we all are. Actually, if I would now ask all my guests to tell me where their grandparents or great-grandparents originated from, we would suddenly find out that the whole gathering here is multicultural with grandmothers or great-grandfathers from Sweden or from Germany or from Vietnam or from Italy or from Croatia or from Spain or from Lebanon and so on and so on. So not a big deal, if we add Tunisia or Egypt to the list. Jacques, dear, let my guests enjoy the good food I am offering and let me enjoy your company for the little time left because such is the life of the mother of the President of France. She hardly sees her son other than on the television screen."
Mrs. Suleiman said, "No problem, Mrs. Perrier. I just wanted to establish an interesting dialog with the President of the Republic. For me it has been an honor and an opportunity to talk with your son.
And perhaps, I silently hoped, he would agree with my opinions." Jacques, a little bit puzzled by the indecisive discussion, and remaining with neither a direct answer to his question nor a tête a tête with his mother on her affair with a married man, finished his drink, and was about to see himself out even before the guests joined the table, when suddenly his mother joined him in leaving the balcony.
Softly speaking, he remarked, "As I said before, Mom, I will not stay for the lunch, but could we have a little chat for a minute?"
"Depend on what it is about. Tell me."
"I need to talk about your adventure with that man from Cahors."
His direct answer embarrassed her, so much so that her head first hurriedly turned to left and right to make sure that no one was overhearing any of his words before she somewhat aggressively whispered, "These are things of my privacy and you have no right to enter in it."
"Yes, as long as it does not interfere with my career! As my mother you are also in the spotlight."
"So is your wife. Please stop this nonsense. I will not answer your questioning as I consider it offensive. Truth be told, I will not talk about this but with my confessor, Father Martin."
"Mother, you don't understand how hard people play in politics. Even Father Martin could make and break, perhaps unwillingly, by incidentally placing some generic observations without quoting names and sources—thus preserving the essence of the confession secret—which at the end of the day, and after some investigation, could lead to me and provoke severe cracks on my political career."
"My dear son, you are the President of the Republic, but you have no power over my private life, particularly after all these years without visiting me. I will not forget this. What do you think, that you may force me to do this or that, because it is of convenience to you, when I personally may count with just 1300 days more of average life expectancy?" The two of them had now arrived in the room with the tables set for the thirty guests, which was still empty. In the faraway corner they continued murmuring their unfriendly conversation.
"At least you will have to let me know what Father Martin has advised you in relation with the Paris issue."
"Do I have to tell you that Father Martin has his canonic secret obligations, and my sins are only known by God and I. Father Martin is just a very safe intermediary; I fully trust him. And I will not continue with this issue. Really I cannot understand why you have come to my birthday celebration to spoil it. Why do you seek to make me feel nasty at my eighty-first birthday with all this questioning on something belonging to my private life? Business finished.., no more words. If you ask me, your career seems to be more in danger with the problems you have with your wife. Some weeks ago, Alexandra called me to say-something that I could not understand well that you were doing terrible things and that you were possibly involved in the elimination of a Turkish politician. True or not—I have never trusted writers since they often confuse reality with fiction—you had better give your attention to her instead of on my presumed, committed mistakes.
This is my thing and you should keep your distance. Perhaps time for you to confess my son."
The last remarks of his mother were a shot in the rose. He was unpleasantly touched by the fact that Alexandra had called his mother and suggested that he was eliminating love competitors. Who was imagining things, his wife or his mother? Best would be to let bygones be bygones. "Mom, do enjoy your party and forget all I have said just now. A kiss, please!" With a warm embrace and passing his hand palm softly over her cheek, he said farewell and felt sorry for the fact that he had somewhat misbehaved by first being impatient with the Tunisians and thereafter putting pressure on his mother to discuss something she perhaps herself felt ashamed over. Mission impossible! Oh, how would he have loved to just have a dive in the beautiful sea and swim away as far as possible!
### Ten
### Blunt Truths in the Spanish Parliament
If anyone had told Hans Schmidt that he would one day hold Chancellor Ditch in his arms and lightly kiss her ear, he would have laughed over so much fantasy and so little sense. One should know that, with the exception of his mother, Hans Schmidt had kept the other gender at great distance all along his thirty-nine years. So the closing in did happen, be it by incidence, and consequently thereafter he felt somewhat bruised by the sharp corners of reality.
All started with the fact that his boss, Marlein Ditch, agreed to personally address the Spanish Parliament two hours before the latter would have to vote on the draft constitution of the European Federation. Parliamentary agreement with the Federal constitution in all nine candidate countries, with voting occurring simultaneously at the same time and day in all nine parliaments, was the first step.
Thereafter an all member-states-wide referendum would give the societies at large the chance to participate more directly, paving the way for the takeoff of the Federation with a caretaker government. Ten months later the first, federal elections would follow, creating the opportunity for the federated societies to democratically elect a federal parliament and to form a first government of the European Federation.
Learning from history, the Spanish Prime Minister had accepted the suggestion of the German Chancellor to organize an information-exchange parliamentary session in Madrid before the voting and with herself as guest speaker. Indeed all the leaders involved in preparing the Federation were well aware of the risks of a rejection vote in Spain due to the highly complicated Spanish governing system and the weak financial situation in the country, not to speak of the ongoing protests of outside parliament opposition of young unemployed.
"A bad result in Italy and Spain could send us down the boulevard of the broken dreams, so to speak," Marlein repeatedly expressed in different conversations to Jacques Perrier as well as to her aid Hans Schmidt. She had clarified that the dream of constructing a state with around 300-million people under one federal government, who would be in control of the federal finances, socio-economic, foreign policy, and security needs and expectations of the collective would vanish like a soap bubble in the hands of a child if large candidate countries like Spain or Italy would go their own way, merely as a consequence of internal, political turmoil or misunderstandings."
"I am not so worried by the Italians—Frau Ditch would continue explaining—because, frankly speaking, though most of them are overtly inclined to superficiality, the Italians have a sixth sense—a sense of survival—that has guided them ever since the times of the Roman Empire. In my experience, they are generally more interested in maximizing pleasure over the rest of civilization aims, particularly in comparison with for instance Dutch and Germans so I consider that if they in any moment have entered in negotiations with the Spaniards over a Southerner's Union, it was just because it would have given them the opportunity to exercise leadership in that group. But today, having given warranties and offering them the selective federation project, their participation in the European Federation will actually save them from their own inclinations to superficiality and liberate them from their unstable internal policies with all its negative outcomes up to the recent past."
"Voila, Marlein, so what you consider worrisome is the case of Spain, is not it?" Jacques replied, giving the German Chancellor the opportunity to restate her slightly-biased opinion on Spanish governance. But Frau Ditch remained very steadfast in her strong opinions.
"Gentlemen, Spain is a country sociologically inclined to the left and to the siesta, even at sunrise. We have experienced this even these days when our team had to call to the Spanish Ministry of Foreign Affairs for feedback on the classified draft-constitution. Until ten in the morning, no one responsible answered any phone at the ministry. And then again, let us not forget that Spain is a country partially divided between the so-called historical communities and the rest.
Perhaps one should be Spaniard to understand the commotion among communities. As far as I know, many historical communities are self-proclaimed candidates to be future mini-states, though with no feasibility at all. This is in particular true for the Basque autonomous community. Let's not forget that although there are many regional ethnic groups in Europe who proclaim their uniqueness, the Basques in Spain are among the few who have taken up arms and use terrorist attacks to fight for their independence."
"Marlein, you are right," Jacques answered. "By the way, you remember how shocked I was with the sudden appearance of these three naked Basque ladies in Nice. We do have to contain Spain's participation in the Federation in a right way. Really, you should go and speak to them in parliament in your own outspoken and intelligent way."
Aid Hans Schmidt, letting aside his slight embarrassment over the blunt and somewhat stereotyping remarks of his boss, had taken the liberty to add, "According to our ambassador in Madrid, some of them, those from Bilbao, the main, Basque city, use to say—half-yoking—that they are the only ones in the world that have been born where they wanted. Also according to our German ambassador, the legal Basques political parties have been utterly intelligent in using the ETA threat in their negotiations with national parties in the post-Franco times when establishing Spanish democracy. I have also understood—although we will seriously have to check it when the European Federation is established—that the Basques do not pay taxes in net terms to the central government. So the Spanish army, foreign representation, and other national, public goods are for free for them and paid by others."
"Jacques, wish me luck. Hans help me! I will have to find the right words to clarify in Spanish Parliament that neither the Catalans nor the Basque, nor any other regional ethnic group in any of the candidate federating member-states, be it the Friezes in Holland, the Sorbs in Germany, the Corsicans in France or the Laps in Finland, should dream of becoming an independent member-state in the context of the European Federation. And of course we will continue and improve the protection of the cultures and the languages of all ethnic communities in the Federation, but it would be totally against the spirit of the Federation to give independence to breakaway factions. We are building a Federation to improve and simplify the administration, thereby creating economies of scale."
Was it not for another volcanic outburst in Iceland with ash clouds causing hundreds of flights from Berlin to be cancelled, the German Chancellor and her team, consisting of aide Hans Schmidt and two, tall, and bold security guards would have left for Madrid in a jetliner and the whole story of Schmidt accidently kissing her ear would never have happened.
But with the ash clouds throwing their dark shadows over the European sky, the Chancellor insisted on taking a high-speed train from Berlin to Madrid. According to the Secretary of Frau Ditch, the alternative of a long drive in car would be a bad signal to the public, so short after the German Cabinet banned nuclear power stations and was calling for less cars and more public transport. And although it was on his lips to inquire about the airplanes, Hans Schmidt meekly prepared for early departure from the Hauptbahnhof of Berlin.
* * *
Probably, Hans Schmidt was the most humble, civil servant of the German Ministry of Foreign Affairs. Being a career diplomat going into forty, he was extraordinary content with the fact that he had been appointed to assist the German Chancellor in all issues concerning the European Union for a period of four years. Son of a German ambassador, it was his mother who had insisted that he should join the ranks of the Foreign Service, but probably not with the intention that her only son would become a well-dressed, super-intelligent recluse, building his private life entirely and obsessively around papers, books, theaters and wines, and apathetically avoiding contact with the other gender.
By the time he was nineteen, Hans had left for campus in Bonn while his parents were enjoying their new posting in Kuala Lumpur, including the residence with the luscious garden full of mango trees and various types of palms.
But by the time he was twenty-two, his visits to home in Kuala Lumpur were overshadowed by complaints and self-pity of his mother, the ambassadress, who was fighting against the fact that her husband prematurely entered the age of decline.
As she repeatedly explained to Hans, "Your father is going off.
Though both his cholesterol and his blood pressure have been diagnosed too high, for which he was overwhelmingly medicated, he refuses to moderate his gin and tonics in receptions, and consequently we regularly have to depart shortly after arrival, with him being soaked in his head and at times also in his pants. And then there is the problem of his acute memory failures. I am partly doing his job together with his secretary, poor woman, but I do not know how long we can hide his fall out for headquarters in Bonn.
Nonetheless, the more legless he is, the more he hangs out the young provocateur he once was, making statements and expressing opinions fully anti-system or becoming a playboy by underhand pinching the Muslim waitress.
I really do not know where this will end. It is highly excruciating. I fear the worst for his career as he still has another seven years ahead. Really, I am afraid he will have to pass these seven years as a wreck in the basement of the Ministry, ordered to make reports no one will ever read, if even he can make them.
This is not what your father deserves, after all the hardship we suffered. Remember us moving from hot to here every four years, including hostile places like Dhaka, Mogadishu, and Karachi. Too much stress, too much uncertainty, and too much adjustments under very unstable circumstances, not to mention the heroic involvement of your father in humanitarian assistance when Dhaka was flooding and his attempted peace negotiations in Mogadishu with bullets flying all around him. Few people back home are aware of this. That is the tragedy of diplomatic life. For most people back home or at least for many journalists, who, when having to fill their columns, nastily and recklessly will portray ambassadors as nothing more than well paid party-goers reporting gossips in classified messages, your fathers job is useless and too costly. This is very unfair."
So it was odd that just in those days of severe complaints of his mother, she also started pressing him to apply for the Foreign Service, which he did, be it with the adjustment that he had decided not to complicate his life with forcing any partner to have to observe the monsoon from behind second quality windows, while the overpopulated, dirty city was experiencing its next electricity power-cut.
* * *
With satisfaction Hans Schmidt noted at the Central Station in Berlin, that everybody arrived well in time to board the wagon, the first of the train, reserved only for the four of them on their journey to Madrid. The Chancellor—dressed in a marine blue coat, skirt, and with a pearl necklace—arrived at the platform in the company of her driver who carried her small suitcase into the wagon, while she came over to Schmidt and gave him a friendly touch on his upper arm.
"All set for the big challenge ahead, Mr. Schmidt?"
"Yes Madame Chancellor, including as you may have seen from my reporting, a summary of the parliamentary history and the built up of the 1978 Spanish Constitution."
"Ach, ach, how serious you are, Hans Schmidt? I did not mean content, I meant personally: packing, saying farewell to your family, enjoying a good breakfast. We have a lot of hours to travel, more than enough time to prepare."
Luckily the last call for boarding released him from answering her unusual friendliness, and they rushed over to the steps to enter the train, she in front of him.
It is there that it happened. She was waving at her driver and talking to Schmidt with one foot on the first step and the other at the platform when the train suddenly moved and she fell backwards, right in the arms of Hans Schmidt. While screaming anxiously and wrestling with her hands in order to hold on to something to not fall, Hans, who also had lost balance, tried to put her back on her feet. As she tried again to restore her equilibrium, her head and shoulders changed directions and his lips softly touched her ear, not once but twice. It was his closest experience ever with a female stranger and pretty weird as she was his boss. He was aware of his blushing when he managed to put the Chancellor down, save and almost sound in the entrance of the wagon.
The first, two hours of the high-speed train trip were passed in silence. Marlein Ditch had placed her slightly swollen ankle on a cushion at the seat opposite, and had closed her eyes. Was she in pain?
The security guards had taken position near the entrances of the wagon, and were mainly looking outside at the landscape, which at times was passing by so fast, that one could hardly distinguish a thing. And aide Hans Schmidt, still feeling uncomfortable, had positioned opposite the Chancellor, but on the other side of the corridor, reading a document but from time to time stealing a look at his boss, wondering what she would be thinking.
"Hans, have I read well in your report that the majority of Spaniards, up to eighty-five-percent, vote for the two main national parties in general elections. Is this also the case in provincial elections?"
He had instantly veered up to show his attention as the Chancellor continued, "This would mean that the so-called autonomist parties—some of them even rallying for independence of their regions—are simply political opportunists. I was surprised to read that in the last decades, these parties have sometimes supported the Spanish central government, enabling the formation of parliamentary majorities when the winning national party did not gain a comfortable majority in parliament. This gave these small, autonomist parties the opportunity to act as balance of power." Losing his last bid of shyness over the boarding accident, Hans replied, "Yes Madam Chancellor, even to the absurdity of "contra nature" coalitions in terms of the left-right political contrasts or centralist-decentralist clashes. For example, the opposite interests of coalition parties in government are served in such a way that for agreeing with a law, completely contra the orientation of the regional party, the local community may have received some absurd tax reduction or central financing on a totally unnecessary infrastructure project. In simple words, bribes are paid for support. As I understood, things would have been far better if in 1978 the representation of regional parties in the Lower Chamber in Madrid were excluded and if instead these regional parties accommodation were organized by creating a political Chamber for Autonomic Regions, be it with limited competencies. It would have spared the society continuous shameful logrolling in parliament and it could have made governance more effective; perhaps, resulting in even less unemployed and less wandering immigrants."
"Herr Schmidt, as the course of history cannot be changed—she had her eyes remarkably twinkling—we will have to use all that is useful with imagination and ignore the rest. Perhaps the Spaniards will understand from my frank presentation tomorrow that the European Federation could offer a new opportunity for them, a second chance to reform their defective governing system towards a more sustainable democracy."
"Madam Chancellor, I suggest you also to pay attention to the M-15, the outside parliament opposition, I mean the movement of the many unemployed youngsters."
"Hans, we are all having this problem in Europe. I am afraid it might even drift towards Germany. What am I to say?"
"You could advise the Spanish politicians to look around. Note for instance that the employment situation in the Netherlands is far less extreme. In the past decades, The Hague introduced some creative and flexible labor policies; Spain could perhaps learn from that. And besides, the mere fact of Spain joining the Federation will give some respite as job opportunities will be up-scaled in some ways."
"Of course Hans, but provided, that Spain does not enter into the Federation with its dirty clothes still on. We will have to challenge their willingness to change the current, Spanish political style of maximal self-interests, long before the referendum and the following simultaneous voting to elect a Federal parliament and government in the nine countries."
* * *
When the German Chancellor entered the Spanish Parliament building the next morning, her ankle was bandaged and she was staggering a tad. Aide Hans Schmidt was walking one step behind carrying her briefcase. However, her grey-green eyes were sparkling and once again she had intentionally painted her lips. All-in-all, she was ready for the chase.
At first, the Spanish Prime Minister and the President of the Parliament received her and immediately took her to a room annexing the Hemicycle. As usual, the Hemicycle was the location for voting laws and hosting other inspirational parliamentary events including extraordinary plenary sessions with chief guests of honor.
The Spanish Prime Minister decided to first introduce the German Chancellor to the chairpersons of the parties in parliament, before all would be moving into the Hemicycle with the rest of the 350 representatives. The Cabinet and the media would also be present.
Hence, in the small room with its walls partly decorated with dark, wooden panels and partly with seventeen century painting in gold-plated frames, the German Chancellor was being welcomed by the party leader for each of the twelve parties in Spanish Parliament.
These twelve politicians, mainly man, were sitting at a large round table with coffee served in elegant porcelain, and all were observing Frau Ditch with interest as she hobbled in. First they politely stood up to await her seating before sitting down again, but remarkably no one rushed in towards her for a more familiar welcome such as shaking hands or embracing.
To break the ice, Marlein started talking even before taking seat,
"Ladies and gentlemen, thank you for inviting me to your deliberations before voting on the federal constitution. What a surprise for me to count just now that Spain has twelve political parties in parliament. Remarkable, as you count with only half of the population of Germany. This seems to me very challenging, but at the same time extremely complicated. Imagine, the Bundestag having twenty-four parties for my government to deal with. I would go mad."
Aide Hans Schmidt had got a little worried with Marlein's no-nonsense start, but was shortly after released when—with some delay due to awaiting the translation—all twelve started laughing and the Prime Minister, chairman of the Labor Party, rebounded.
"Madame Chancellor, we cannot deny that having twelve parties in Spanish Parliament is complicated, but what would you think of the ten parties in the Dutch Parliament with 16-million people. The Dutch example extrapolated to Germany would mean that the Bundestag would count with sixty parties, not to forget that in Holland one can find in Parliament even single issue parties such as a party only for defending animal rights."
The new round of laughter sounded much louder and aide Schmidt, remembering that he had advised the Chancellor to bring in the Netherlands as a good example, be it on tackling unemployment, started bothering over the further developments, when the Chancellor, showing full recovery, replied, "You may be right about Holland, and we are learning from that in order to design the terms for admissibility of parties in the forthcoming, federal elections.
Believe me, if our projected federation at nine progresses—and I have come here to promote it—I think that in parallel with slimming of our national administrations, with responsibilities transferred to the federal level, we will also have to slim down across countries on national, provincial, and local representations, halving at minimum the number of representatives; and if I may say so, in your case, the representation of regional or so-called autonomist parties in National Parliament. As I will explain later, only federal parties will be admitted to participate in the federal parliament, no national, regional, or single-issue (based on ethnicity, gender, age or whatever) party will be entitled to run for election."
"But Madam Chancellor I have to remind you that the high number of parties in Spanish Parliament has to do with the fact that our country is a decentralized country", answered the Prime Minister.
"Yes, too decentralized," Marlein ironically replied. "I have heard, you may correct me if I am wrong, that you have seventeen autonomous communities, served by councilors who often, in numbers, far overtake the number of ministers of the central government, and even may earn salaries and bonuses well over the salaries of your ministers in Madrid. I have also been informed that at the time of Spain"s democratic transition in 1975, the country counted with a maximum of one-million civil servants, and today one is confronted with a figure of three million. Or to make it clearer, between 2007, at the start of the financial crisis in the West, and today not less than 300.000 more civil servants joined ranks at the different levels."
During the reaction of Marlein Ditch on the remark of the Prime Minister, a growingly nervous Hans Schmidt, sitting behind the Chancellor, was flexing his fingers. He had expected outspoken critics from his boss, but not raids, and he had no clue what the outcome at voting would be in reaction to her verbal aggression. Actually, he had already tried to warn her last night to be more diplomatic when, at the dinner table in the hotel, she compared the Spanish Prime Minister with Don Quixote. According to her, the man had, in the middle of the financial crisis in the West, proclaimed that no such thing existed in Spain.
To prevent further damage Hans therefore quickly wrote a small note to the Chancellor in German, something like, _Chancellor please, careful with offending the Prime Minister, we will need his party's votes_ ; but to his further uneasiness she gave his note less than a half eye, and instantly shred it in pieces, before closing with the statement, "Dear party leaders, this really cannot go on. The Spanish population simply cannot pay your reckless political game, nor will Germany."
After the unexpected outburst of the German Chancellor with the Prime Minister flushing red and the smiles frozen on the faces of some of the party bosses: those having dreamed of the possibility that the Chancellor could have arrived with some funds for the Central Government to solve the problem of the urgent consolidation of the banks before things would really run out of hands—there was a short but deep, cold silence. Initial positions had to be reshuffled since nodding for the federation in exchange of financial support from Germany was no longer an option.
Others, the more leftist party leaders had come with little expectations, believing that the German Chancellor came to screw the Spanish workers, proposing probably to take away a huge part of the social advantages the trade unions had conquered in the last thirty-five years.
Only the conservative party boss, a man totally neutral even with himself, but fan of the rightist parties in the US, Britain, and Germany alike—and also in Saudi Arabia and China if they would have existed—dared to applaud Marlein and welcomed her once more for her visit while thanking her for her frank outburst. It was a gesture the man could afford since he knew that, without unveiling any specific problem-solving policy in the last three years, his party could easily count on a landslide victory in next national elections and he would gain the leadership in Spain without having to shoot a single bullet, so to speak. The so-called incumbent factor would work for one-hundred-percent for his party, as it had always worked in times of crisis, in Spain as well as in other countries in Europe.
As Hans Schmidt knew that Marlein Ditch asked the Spanish Prime Minister to not only have her to shake hands with the political leaders of the twelve parties in the small, annexed room, but also to give her the opportunity to present her thoughts in a brief speech _en petit committee_ before all of them would be going to the Hemicycle, he even now could not calm his nerves as the Chancellor continued.
"Ladies and gentlemen, friends, I have asked the Prime Minister to give me some minutes before we move into the big audience including journalists, TV cameras, and the whole circus. You will understand that in that setting, I will not be able to be specific. Since I consider it more relevant for my trip that you, the bosses of political parties in Spanish Parliament are well informed and have clear insight of the future of the federation, I will actually address you now. But I beg you to please be discrete on what I will say now. Our projected selective federation has far more enemies than thinkable."
With now having full attention of the twelve, Marlein Ditch started speaking from her heart, on the one hand almost building a secret coalition with them, and on the other hand, putting the same politicians with their backs against the wall.
"I have come to Madrid to promote a European Federation of nine member states. As you know, Spain has become a candidate but not in the first round, not before Nice. This is because the debt markets are all the time putting to our attention that Spain is far from a paradise today. Having said that, you will have to agree with me that with your governing system, in particular in dealing with autonomic communities, you have exceedingly politicized your economy. This has resulted, as I said before, in many unnecessary, public budget spending, lack of control on housing and bankers, not to mention the rapid growth of far too much civil servants.
My friends, you were welcomed in the European Union in 1986, but you will have to agree with me that things have changed; in the World and in Europe, and we cannot continue any longer in the same way, as if only politics counts and economics do not exist.
To make it clear, why would you build an airport in La Mancha, the fatherland of Don Quixote, if hardly ever a plane will land there?
Such a ridiculous investment should be paid personally by the promoters and not with public money. I have heard that some of your autonomous communities and some big cities simply do not want to adjust to the current times of capital, revenues, or funding scarcity. Really, you may have surmised from recent stands towards Ireland, Greece, and Portugal that the happy days are over. The leading countries in the Euro zone will leave to fall all those who do not adjust to the new financial restrictions and continue wasting time while expect miracles from us.
In Germany, Holland, Austria, France, Luxemburg, and Finland neither the populations nor the leadership are inclined to continue paying the debts of other members of the club. There is a generalized fatigue to pay to the others just because they are members of the club, in exchange of almost nothing. And please do not say to me now that Germany has exceedingly been profiting from the EU membership of Spain!
In brief, if you do not correct substantially and adjust your speed, you will exclude yourself, but not only from the Federation but also from the Euro system which, in around one year, will be the monetary system of the Federation and not of the countries not embodied into federation.
In two hours, you may vote and decide for self-exclusion from the federation, which would in the current situation automatically send you to a devaluation of your "new pesetas" by forty to fifty-percent to solve you external disequilibrium. This would mean that the euro of the new federation would cost the Spaniards around 320 pesetas, which means that your flats and assets would be bought by the citizens of the Federation for the half of their current _apparent_ value.
This would be a horrifying waking up for Spain. You will balance of course your external accounts but suddenly you will become half rich. And mainly you—emphasized the Chancellor looking at the bosses of parties, particularly to the Spanish Prime Minister who was logically there—will be the responsible of this catastrophe for your compatriots.
Dear friends, all in life has a limit. You have stretched too much the string and it is near to break. You will have to make a choice; and not even in the short term, but just in some minutes after my speech in the Hemicycle. Dear friends, take your full responsibility when you vote. Spain needs the Federation; the Federation needs Spain."
At her last words, the German Chancellor stood up from her chair and looking at the president of Parliament she remarked, "All set and done, I am ready to go to the Hemicycle."
Although the twelve politicians also stood up, they were clearly speechless after the blunt words of the German Chancellor. No applause, no approval followed her sharp wake-up call.
* * *
However, at her entrée in the Hemicycle, Marlein Ditch was encouraged by a spontaneous welcoming applaud, which only ended when the president of the parliament demanded attention and clarified the agenda: first, the German Chancellor would present her discourse, then parliamentarians could put questions for clarification and after a short coffee break the electronic voting would take place at exactly one in the afternoon. And of course the German Chancellor and her aide were most welcome to observe the election.
As agreed with Jacques Perrier, the content of the presentation of the Chancellor in the Hemicycle would be copy conform the speech of the French President in Nice. Starting with new developments in the world in the 21st Century—the shift of the global, economic gravity center towards Asia, the loss of competitiveness in Europe, the economic catching up of developing countries, in particular China and India, plus Russia, Brazil, and South Africa—the Chancellor had followed with a brief description of the stagnation in the European Union and the overwhelming problems mainly caused by the deficient architecture of the Euro System. She then briefly spoke of the past choice for enlargements with economically far weaker countries instead of further political integration of the stronger member states, which all together had transformed the European Union at twenty-seven in an almost ungovernable monster.
Hereafter the German Chancellor explored the advantages of a federation of nine countries with 300-million people to which Spain was invited to participate.
"There is so much to gain from federating, that we should not waste a single minute more. If we federate, we may save around two-percent of our joint GDP as we will be merging our armies, our foreign representations, etc. Also our nine ministries of finance will merge in a single one, which would enable us to recover our full capabilities in fiscal and monetary policy."
Concluding she added, "If we are capable of building up our federation we will form a country called to fly in some few years at the height of the US and China. And I dare to say that if we do not federate, we will be condemned to irrelevance. Note that in the current globalized world all European countries are considered small in size and population, including Germany."
After twenty-five minutes of speech, loud and clearly, perhaps a little monotonous, Marlein remembered the Spanish parliamentarians that she was always speaking within her time, because time was too precious to be wasted. She closed her file with papers and looked around smiling. And then, totally unexpected, there was no applause, but a sea of boos. It started in the corner of the Left (former Communist and others), with the chairman of the United left party screaming in Spanish.
"We do not need Germany lecturing us!"
From all sides of the Hemicycle representatives started boozing, and talking and gesturing anxiously, and as it was done in the Spanish language, the only thing Marlein Ditch and Hans Schmidt could understand were the words of the two translators who were explaining from their booths that they could not follow the speakers as they were not using the microphone. "Sorry, I cannot follow the speakers. Sorry, no translation, I do not understand what is being said."
"Order, Order, please sit down!" exclaimed the president of the parliament, repeatedly hammering on the desk in front of him. "We have enough time for you to put your questions. Who can I give the floor?" But his attempts failed and Marlein and Hans were both looking cloudy. "Madam, while you were speaking I noticed someone distributing a leaflet. I have tried to get one. Of course it is in Spanish", remarked aide Schmidt as he handed a piece of paper over to his boss.
The Spanish Prime Minister, his face again blushing, now bowed in the direction of the German Chancellor and her aide and whispered,
"The paper is an almost literally transcript of your speech during the meeting with the twelve chairs of political parties. Probably your words have not fallen well with everyone. And Madame Chancellor, as you can see, the Spanish temperament is different from the German. We simply have to wait."
"I am giving the floor for questioning" was the repeated loud remark of the president of parliament and it took him another seven minutes before the unrest was over and silence returned.
"The floor is open for questions," he repeated again but after the tumults no one seemed to be willing to cooperate, after which the president hammered out the session and announced the start of the coffee break. And once again the 350 parliamentarians were all adrift on their way out.
* * *
Marlein Ditch and Hans Schmidt left the Hemicycle in the company of the Prime Minister, who tried to explain to an astounded Marlein that all was not lost. Perhaps her words had not fallen well to everyone, but she had been so clear that he was convinced that almost all parliamentarians would vote with their mind and not with their heart. Marlein gave him a bitter look and no word. Hans Schmidt suggested that they should no longer consume the precious time of the Prime Minster, who had better be with his party men. This was the sign for the Prime Minister to apologize and to hurry back to another side of the building.
* * *
Voting at one pm would take at maximum three minutes as all was electronic and from behind the desks. "Yes" implied nodding to the new federation and accepting the draft constitution and "No" would imply that Spain would remain out of the federation.
The President of the Parliament announced, "Voting starts now; you have sixty seconds to press the button," and seconds later the voting was actually done.
Shortly after the large screens at four points in the Hemicycle projected the outcome: 348 voters were present of which 345 voted Yes, and 3 had voted No.
First there was applause and whistling and the Hemicycle hastily changed into a jubilee with parliamentarians embracing each other, including a highly relieved German Chancellor.
In the middle of the celebration, Hans Schmidt approached his boss with more good news. In all other eight candidate countries Yes votes had also triumphed.
Marlein Ditch spontaneously embraced Hans Schmidt and commanded, "Up to our high speed train, I prefer to celebrate things in my own _heimat_."
* * *
As the ash clouds propelled northwards to Siberia, flying from Madrid to Berlin once again became the least time consuming way for the German Chancellor and her aide to return home.
Now then, exactly the one thing Hans Schmidt had feared since their departure from Berlin Hauptbahnhof two days earlier—a remark from his boss over the unfortunate episode when entering the train and his distressed reaction—happened soon after the take-off of the jetliner from Barajas Airport in Madrid.
Leaning backward in her seat opposite him and with her eyes half-closed the German Chancellor first stated, "It has been a good and creative decision of us to go and motivate the Spanish Parliamentarians to accept the draft constitution of the Federation. I really feel enchanted. We have made history today. It's a pity that both of us, when arriving home tonight, will have no one waiting for us to share our delightedness."
As Schmidt did not react she continued, "These are the moments one is painfully reminded of the fact that one is a lonely number. Tell me Schmidt, any specific reason why no nice young woman managed to persuade you that she may look after you and your offspring?"
Perhaps it was the rare formulation of the Chancellor regarding marriage that created a rather wobbly feeling in his chest, forcing Schmidt to cough as the Chancellor sustained, "Sorry, it was not to embarrass you. More and more, I am thinking that perhaps after my career as German Chancellor I should at least adopt one or two children to break the cycle. What about you?"
At her last words, Hans Schmidt moved upwards in his chair and was trying to hide that he had been taken completely by the leap of his boss into his private life. While looking at his fingers that he kept twisting perpetually around each other he spelled out softly, "Perhaps living single in dignity is better than living in couple in discomfiture as my poor mother and father did for almost forty years. Right now, when arriving home, I may speak to my books and plants. And if you allow me to say truth, I have never received a humiliating answer of none of them."
"My dear advisor, one should at least have tried. As my ex used to say—it is better to have loved and lost than not to have loved at all—and I think he was right."
Marlein Ditch was now looking directly into the eyes of advisor Hans Schmidt as she calmly prolonged, "Mind you, Hans, you are from now on one of the happy few who know that I have been married once, be it long time ago. No regrets, I have no regrets as tears subside, except for not having had children. Listen, this is probably my best kept secret. My career became my baby. Should I be happy with that?"
"Madam, few people can become German Chancellor."
"Hans Schmidt, as you are a sympathetic listener, I can admit that my decision not to have children has left me today with mixed feelings. Mixed feelings since political leadership these days is fast losing its glory. Today in Europe all political leaders, regardless of our party background are standing accused of missing direction. But the truth is that the world is changing and in my experience our options for a good direction are mainly decided somewhere else. I may soon become an ex-Chancellor, whom no one will remember. Promise, you will keep my revelations for you."
"Madam Chancellor, if I may say, you have sacrificed a lot for the construction of Europe. I am sure that hundreds years from now you will still be remembered and honored just for that. No one will ever be able to despise your memory since in some decades the European Federation will have become one of the leading five states in the world and the new Euro one of the three, leading currencies. Please Madam, be assured of my loyalty and, may I say, certainly there will be a happy life for you after politics."
The Chancellor had closed her eyes and her face wore the inattentive look of a person who, precisely one minute before, fell into a deep sleep.
### Eleven
### Ibrahim is set free but the triumph is for Perrier
At 11:30 in the morning, a Japanese Sedan with a Turkish flag entered L'Elisée. It was the car of the Turkish Ambassador to Paris.
Just two hours ago, the ambassador had managed to speak to the President of the Republic by phone in order to request a most immediate meeting over a very serious issue concerning a "family problem" in relation to a Turkish citizen. On listening to the words of the Turkish diplomat, all alarms bells started ringing in the head of Jacques Perrier, and he ordered his secretary and his Chef de Protocol to immediately arrange for the meeting, even if it would mean postponing important issues on the agenda including a possible delay in participating in the extraordinary Council of Ministers meeting in Paris, related to the NATO-Libya intervention.
Those who saw the Turkish Ambassador entering L'Elisée, would have been struck by the look in his face: grave as if he was to transmit condolences or something worse. He was a man of experience, already in his sixties, and he had learned to avoid strong waves both in his career and in his personal life. Accordingly he felt heavily burdened to get involved in the personal life of others, the more so as it involved the President of France.
"Please come in, I am impatiently waiting for you. My time is limited, but this is extremely important. Have a seat", were the friendly words of Jacques Perrier standing up from behind his desk and walking towards the Turkish diplomat when the latter entered.
"Really, this is not something that ambassadors have to do" replied the Turkish Ambassador after sitting. "I am very grateful for your willingness to receive me on so short notice, and really it is very difficult for me to start. However I have to inform you that, according to our Secret Service in Dubai, a Turkish citizen, named Ibrahim Orzgol, was abducted in Dubai, some weeks ago. Till here nothing of particular in this world in which security is deteriorating fast, but the difficulty is that the kidnapped person, an attaché to the President of the Turkish Republic was abducted, probably by an American connection, just when he left a room rented by your wife at Sheraton Creek Hotel" At his last words the Turkish diplomat avoided looking at the French President and instead was facing his hands and fingernails, folded on his legs.
"Sorry Ambassador, this is impossible, and cannot be true." Perrier was waggling with his head, something between yes and no, as he explained, "My wife, what I remember, went to Dubai with some friends, old school mates, and they all stayed in Hotel Burg Al Arab."
"Mr. President, I cannot enter in the assessment of the information you have, but factual information I have received from my headquarters put the truth closer to me. And then there is a Pakistani cab driver who is also on our payroll, who reported, without names but with photos taken in his car by a hidden camera behind the central mirror, that he transferred both your wife and the Turkish attaché the same day to the Sheraton Creek hotel, while both had repeatedly suggested to him that they were going to the hotel for a love encounter. Although this was nothing rare and certainly not the type of reporting he normally provides, he started paying attention to the case when he took your wife back to the Bourg el Arab Hotel, and she was in panic over the sudden disappearance of the Turkish man. At which the Pak cabdriver had confirmed to her that he had seen her boyfriend leaving in a white four-wheel-drive with two men."
The Turkish Ambassador continued, "As far as we had his photo, it was just a matter of days to discover that the disappeared man was one of the advisors of our President. The identification of the other person involved, was even simpler. Your wife, sir, is almost weekly in many glossy magazines, so she is known all over the world; some would say even more than you. Nevertheless we have waited two months before taking any initiative in this nasty affair, hoping perhaps that things would resolve themselves. However, the family of Ibrahim Orzgol started increasing pressure on our government, reason why I am here."
A pale President of France ended by mumbling, "I'm really embarrassed. Believe me, I had a vague idea that my wife was not fully happy, but all this you have described is really unexpected. Give me some time to react. I have to cool down and re-order my mind before doing anything. I can assure you that I will come back to you, but I need some time to sort things out. And as you know, we are all occupied with developments in North Africa today, not to mention the problems of Europe with the financial crisis, and my involvement in the construction of the federation at nine. And now this complication, it is certainly too much."
"Excellency, I fully understand your constraints. The best would be for us to find a diplomatic solution, taking in consideration that a scandal would not be in the interest of the Turkish government either. Reason why the Turkish Information Service has classified everything related to the issue, including the printed material, but as outsiders have been involved, including staff of the Creek Hotel, we cannot guarantee secrecy for an indefinite period."
"Ambassador, take my words for it, I will try to resolve things as far as there is any involvement from the French side, including our collaboration in the liberation of your civil servant. But of course, I ask your government to continue with the discretion followed till now."
The Turkish Ambassador, who had listened with attention to the French President, did not seem to be convinced by the reaction of Perrier. The diplomat still had not abandoned the idea that the President of France could have devised, alone or in combination with others, a strategy to get rid of the lover of his wife by arranging his disappearance till the First Lady would have forgotten or even ........ making him disappear forever.
"Excellency, I will transmit to my government what you have said to me," replied the Ambassador, "but please keep in mind that this is for us a very delicate issue, a family is waiting for the reappearance of their beloved, and in this case we are talking about the family of an aide of our President. So, I have to ask you to do the best you can. For both of us, we should try to settle this nasty affair without major damage to any side. As I said before Mister President, there is always the risk of information ending up in wrong hands. I can assure you once more that my government would not like to be put in the position of having to disclose unpleasant information about your wife."
"Dear Ambassador, this will not happen. I would like to add that you could also transmit to your government that the French position concerning Turkey in relation to the EU is becoming softer than before, and if our federation of nine progresses, Turkey will be most welcome to integrate in a common market with us."
After formal words of farewell among the two, the Turkish Ambassador left L'Elisée, and back in his car, the man tried to lean back and relax from the somewhat unpleasant encounter. Hardly a minute had past however when his Blackberry started ringing. With a certain air of disinterests—he really had suffered enough during the unusual conversation with the President of France—he answered and immediately became aware of something that produced him a shock that hit his old heart even harder. He was informed by his headquarters that the French Ambassador to Ankara has been kidnapped by, possibly, a Kurdish separatist group.
Following the message, the Ambassador had to grasp for air as he considered that this new event could be read by the French President as a change of pieces in an unfortunate chess game unleashed by him just now to force the result Turkey desired: the devolution of Ibrahim by whoever had abducted him.
* * *
However, inside the Palace, Jacques Perrier decided to distract himself from the unpleasant message of the Turkish Ambassador, by concentrating his thoughts on federation issues, in particular on some aspects of the provisional draft of the constitution. He started carefully valuing the representativeness of the Federation Parliament. In his view the Federation would need a parliament with no more than four or five parties. Strict, proportional representation should be excluded along the first, two decades of the life of the Federation. He had to acknowledge that any step given in false could blow up the project, reason why the adopted policies should be supported by important majorities, be these supplied by one single party or by a coalition of two.
The solution was clear from the perspective of Jacques; it would be necessary to create federal parties, these being large parties formed out of the cooperation of national parties with the same ideology (conservatives, labor, Christian-democrats, liberal, green). But contrary to the existing loose groupings already formed in the current European Parliament in Strasbourg, for the European Federation the federal parties should be formal and full-fledged. Translated to the constitutional terminology of the Federation, this would mean that to enter in the federal parliament, the federal political parties should get five-percent of the total issued votes and these should have been gathered in a minimum of fifteen-percent of the federal districts, as this would give more stability to the Federal Parliament.
While Perrier continued the profiling and weighting of representative aspects of the future federation parliament, the French Minister of Foreign Affairs interrupted with a call to bring the bad news to the President that the French Ambassador to Ankara had unfortunately been kidnapped by midday while in the presence of the French Consul, just when the two were visiting the Galatas District at the outskirts of Istanbul, where the Ambassador was to inaugurate a hypermarket of an important French firm.
The French Minister confirmed that attempts of extremists had lately been less frequent in Istanbul than in other parts of the country, but according to the Turkish police—and taking into account available information—one should not exclude extremists involvement in the abduction of the French Ambassador, as the terrorists were constantly trying to attract attention from the international community.
"You have to check this information and report to me as soon as possible!" exclaimed a sweating Jacques while hiding his discomfort for his Minister. Of course he could not say more, but it crossed his mind that this could be a case of retaliation by the secret service of the Turks against him, just to force—in case that this could be possible—an action of the French President to liberate Ibrahim.
* * *
After hanging up the phone, Jacques Perrier instinctively decided to privately call the Vice Security Advisor to the US President. Maybe she would have additional or relevant information to break the cycle.
"Hello Betsy, how are you?"
"I am fine, although commotional, Mr. President" she answered,
"But I suppose you, Mr. President, may be extremely concerned at this very moment. For your information, however, we think that this event is not an issue of extremists. We have some confidents in Ankara and Istanbul who swear by the eternal paradise of all their ancestors, that this is simply an operation of the Turkish Secret Service against someone in France, not against France. Luckily, only you and I may have a clue to the problem: the unfortunate relation between your wife and the advisor of the Turkish President."
"But you said to me something enigmatic time ago in relation to this business," replied Jacques. "Could you be more explicit this time on the issue, please? I feel deeply discomforted in this case because I cannot say the truth even to my own wife! Please, by our old friendship, I pray you to explain to me all you know on the matter.
The abduction of my French Ambassador is probably a next stage in the process of hidden tensions between France and Turkey on a private issue. The last thing I need."
"Do not worry Jacques, you are adopting these days a very supportive and brave position in North Africa and the Middle East and I know that the US President is very willing to support France in any aspect connected with global matters. As a consequence, as far as I know, I can promise you that we will fully participate in solving the problem of your Ambassador without any collateral damage. When I have gathered all the information related to the case and made some calls to the Turkish Foreign Office to make a deal, I will inform you.
After a positive outcome, which as far as I know is very likely, you even could go to Turkey in a blitz trip; and perhaps only some thirty minutes after your arrival, you will be able to embrace your Ambassador in Ankara and travel back to France with him in triumph. I'm sure that if things are as we in my office believe—just a proxy-retaliation operation with exchanging purposes—at the end of the day, this nasty experience may result profitable for you. By the way, it would be convenient, when all this is finished, that you explain your ideas about the European Federation to my president", Betsy continued, "He is concerned with the influence of this project on the economy of the US and the defense system of the West.
Perhaps the forthcoming G20 meeting in Florence would be a good opportunity to have a tête-a-tête with him."
* * *
After the rather comforting conversation with Betsy, in relation to the "Ambassador kidnapping", the heart of Jacques Perrier started beating somewhat softer than before.
Even more, within an hour—and after several calls realised by Betsy to different Centres for Treatment of Information—she informed Perrier that she could certify not only that Ibrahim had already weeks before secretly been transferred to a US prison in Germany, after having been in a centre in Africa, but also that he had been cleared since he had been taken by mistake from the Hotel Sheraton Creek in Dubai.
What had happened in his case, was that Jacques Perrier had, via his Security Officer, requested information about Ibrahim, but his petition—instead of being handled as an information inquiry requested by French Intelligence to US Intelligence—had by incident been listed by staff in Virginia as a French arrest request concerning a suspect belonging to a listed Islamic organisation.
Consequently, the Vice-Advisor for National Security of the US President, after her consults, could easily order to free Ibrahim and to transfer him back to the place he had been abducted. So Ibrahim's liberation would be in Dubai, provided he agreed on the terms and conditions including no word to anyone on the places in which he had been questioned and how. In exchange, Ibrahim would receive a compensation of half-a-million dollar—over five years—on condition of remaining silent and a business class ticket to return him from Dubai to Ankara; conditions Ibrahim wholeheartedly accepted in order to be able to go home soon.
As far as these internal negotiations were successful, Betsy called the President of France two days later and greeted him in an exultant way, saying, "Dear President, I have good news. Tomorrow will be a great day for you and for France. One of your most serious domestic problems has been solved. I have not only localised where this person, Ibrahim, was but also negotiated internally the conditions and terms to set him free in Dubai, by tomorrow. The rest of my job consisted of certifying that your Ambassador in Ankara was more or less in official or semi-official hands—guess you understand me—and not in hands of any terrorist group. This has also taken little time, and finally your Ambassador will simultaneously be liberated and accompanied to the French Embassy in Ankara. In terms of timing the exchange is set for 3:00 pm tomorrow."
"Wonderful Betsy, how can I thank you? I will travel to Ankara by midday to personally welcome and comfort my ambassador. Could you keep me duly informed to be able to solemnize the operation?
Between you and me, certainly it would have been politically more rewarding if the exchange had no private base."
"But my dear friend, I guess with your diplomatic skills you will well be capable to push the information on the liberation of your Ambassador away from the Dubai part and place it in a more profitable direction for your polls. Anyway, although the operation is practically closed, we still have one loose end. A loose end—I have to confess—which is out of my and your control. This is something that will need the collaboration of your wife and the Turkish man. Your wife will have to convince Ibrahim that he should collaborate fully in staying away from her and keeping silent on the Dubai encounter.
Otherwise your political future, Mister President, could be in danger. Indeed, this short-cut initiative of the Turkish Intelligence has somewhat put us all in a difficult situation, in particular you and your beloved wife."
"I fully agree with what you are saying, Betsy. I will have to convince Alexandra to enter in touch with Ibrahim, by telephone, let us say to a number you will disclose to me at the right moment."
"I am at your service," was Betsy's smiling answer.
* * *
Taking first a deep breath and thereafter reflecting silently for some minutes, Jacques followed by calling Alexandra to update her on the good news concerning Ibrahim, but of course without giving any impression that he had been involved in his abduction or that he could have been hiding any information for her on the unfortunate case.
"Hello, Darling, I have unexpected news about your friend Ibrahim, the Turkish aide who disappeared. He is going to be liberated by his kidnappers by tomorrow. Contrary to what you hinted at to my mother, our friend was mistakenly abducted by American Middle East allies, as my Security Service has discovered.
And you may now accept that I had nothing to do with this whole unpleasant business. It has been a case of bad luck caused by an administrative error. As I understood, the US administration will compensate him well for the disturbance he suffered."
As Alexandra only heaved a deep sigh, Jacques continued, "I do not know how this information may play a role in our lives. You have accused me wrongly but understandably and believe me, I'm still deeply in love with you. I hope you feel the same way too. I am aware that I have certainly in the beginning of our marriage committed severe mistakes in our relation, mainly by not paying all the attention you deserved, but I have changed my attitude in the last months as you may have noticed and I'm determined to improve things even more."
As Alexandra kept silent, Jacques persisted, "Alexandra, I can swear to you that I have neither participated directly nor indirectly in any form in the disappearance of Ibrahim in Dubai. I was not aware of anything and as you know, such an activity isn't my style."
Finally an emotional Alexandra replied, "Jacques, I have thought and rethought about the painful developments of the past months, and I have been ashamed of myself but also of you. How could we have got involved in this? I have concluded that, without looking for an excuse, I have perhaps been attracted by Ibrahim as a consequence of your total lack of attention to me. And of course I was wrong, very wrong with my revanchist behaviour. I can assure you that this will never ever happen again. I dislike cheating, for myself and for you and believe me, I love you dearly."
Now it was time for Jacques Perrier to sigh in relief while Alexandra continued, "I will try to explain all this also to Ibrahim and hope he will understand. I think he is a good person, perhaps a little precarious of him to fall in love with the wife of the President of France, but it seemed honest. And Jacques, I would lie if I say that I did not like him, he was cheerful and I needed that so much in those days, but it was selfish of me, very selfish to compromise you and the French Republic. I hope Ibrahim will not feel offended, particularly if I promise to continue being a good friend to him. It will be just a superficial relation, a telephone call once in a while, but I will call him as soon as you order me to do so, my love."
"Okay darling, thank you for your words. Let us put a line under this nasty episode for all involved and move ahead. I feel that things between us will improve necessarily. Nothing more desired by me than that. Thank you Alexandra, my love, a kiss.
* * *
As planned, Ibrahim was released at three pm at the Sheraton Creek Hotel in Dubai by two men. As the sun was still in zenith and outside temperatures were nearing 45 degrees Celsius, Ibrahim Orzgol rushed into the coffee shop of the hotel where suddenly an old faculty friend from Ankara greeted him and invited him for a coffee. As the two were waiting for the coffee to arrive, a somewhat confused Ibrahim was looking around in the hotel lobby, where he had actually stayed only few minutes some months before.
His friend apologized for having to make an urgent call and the still-dazed Ibrahim could then hear him saying, "Ibrahim has a very good aspect," before he disconnected.
Back to Ibrahim the old faculty friend explained: "My wife, Gulay, was on the line; I just told her that I ran into you. She has gone shopping happily with the rest of the family, our two kids. Tell me Ibrahim, how are you doing? Long time, no see."
In reality, the call was to Turkey and his sentence was the agreed code to start the release of the France Ambassador in Ankara. After twenty minutes of some more familiar talks about his wife and kids whom Ibrahim hardly remembered, the two fellows embraced each other and Ibrahim left the hotel for the airport.
He started looking for a taxi at the sideway parking of the Sheraton Creek Hotel and the yellow taxi was driven by none other than the Pakistani who transported him first and Alexandra later from the airport to the hotel. With a smile, revealing his teeth that entirely lost their colours due to the use of a red, Asian chewing tobacco, the taxi driver cheerfully shouted as if he was updated on the liberation of Ibrahim.
"You, Sir....... going home after all this time? Home is the best place to stay after many bad luck. I always say my wife: the best of life is quietness. And I know: women not wife always create problems. Much problems gave, especially European madam."
This time, Ibrahim decided not to enter into any conversation with the Pakistani. He only shifted a little more comfortable in his seat and ordered to drive to the airport. During the drive at medium speed Ibrahim started reflecting silently on the obscure, useless, and painful time he spent being questioned in secret places by aggressive people. It had been a real nightmare. As he had been doing in the long, dark weeks, he tried to rationalise once again the cause of his abduction and one way or another he felt he had to blame himself.
Although the horrifying questioning—which mainly took place with him being blindfolded—had been very insistent and on issues of which he constantly and truthful had denied being involved with, he finally understood that he could only survive by letting go and not by resisting. He took for granted that he probably had fallen prey to his stupidity of falling in love with the French First Lady.
No one would ever be able to imagine what he had gone through.
The price he paid for his idiocy had been extremely high. He would not easily forget the confusing experience of losing all sense of day and night due to six, huge, halogen light balls shining on him endlessly. Or other times, when all was dark and he could not see but feel cold water creeping up from his feet till his neck or other moments when he could clearly hear the rattling of snakes or the peeping of rats very close to his naked body. With some mental exercise he taught himself to let go by swooning away as soon as the questioning started. So much so that he would remember practically nothing of the rest of the session that day or that night, except for a vague and disturbing suspicion when he regained consciousness that he had been crying.
That he all in all survived without suffering an overnight, psychotic attack or became totally insane was also thanks to the fact that he knew and prayed that his friends in Ankara would not give up on looking for him.
He could on principle have refused the compensation they offered him at the release, especially when they explained that his arrest had been an administrative mistake, but during the negotiations he became aware of the fact that they would not let him go without settling and signing. But as his professor at University in Ankara used to say quoting Einstein, " _The true sign of intelligence is not knowledge but imagination_ "; Ibrahim had imagined that a quiet life would be possible only after signing and sealing.
The compensation would perhaps make it easier for him to radically change his life, for instance by starting a quiet family life in a place near the Black Sea coast, or by going somewhere else, but where?
* * *
Meanwhile in Ankara the French Ambassador had been transferred to the back door of the Grand Hyatt Hotel and his Blackberry had been returned to him, which he immediately used to enter in touch with his staff at the French Embassy.
He thereafter took a taxi instead of waiting for his car, as the Embassy was very near and he preferred not to attract any attention from people in and around the hotel before he was back in his office, which would be the case if his black BMW with flag would arrive in front of the hotel to collect him.
Nearing the building, he noticed that there were many police cars in the neighbourhood and even a minibus of the Turkish TV parked in double line. Consequently, the Ambassador requested the cab driver to turn off and approach the private small gate of the Embassy in a narrow side street where he rushed out of the car and slipped in the garden of the building, passing under the arm of the concierge whom he had called to open the normally tightly locked door. So a first escape from the multitude of cameras of Turkish and French media had been successful.
A second escape however was impossible as the concierge had already announced his arrival to the Embassy staff and a music band in the hall of the building had set in for the "Marseillaise", while the entire staff and some relatives had lined up including the wife of the Ambassador and the President of France. Arriving from the back side of the building instead of via the front door, the welcome committee suddenly had to change positions and an emotional, gazing President Perrier turned around and rushed to embrace the liberated Ambassador, both men shedding some tears, be it each for different reasons.
After some moments of expressive greeting of the Ambassador by his wife and the entire staff, the President took the Ambassador with him to the office of the Head of Mission and behind closed doors Perrier remarked, "Dear Francois, sometimes in life we suffer the cruel arrows of destiny, or of adverse fortune, as Hamlet would have said.
Anyway, I am asking you for a very personal favour. You have to forget these days of misfortune and keep your lips sealed. We are flying together this evening to Paris. Your wife has prepared the luggage and all necessary for the two of you to enjoy three weeks of holidays quietly in Normandy, in order for you to recover from the horrible experience. Thereafter you will go back to Ankara, but only to organise your departure and prepare for your provisional posting at L'Elisée as my special advisor. Following, in the next round of appointments of Head of Missions, I can assure you that you will be honoured to represent the Republic in one of our most prestigious Embassies: Washington, London, Rome, etc."
"Okay, Sir, although I very much appreciated my assignment to Turkey, I understand that I have no choice than to surrender to your orders. You may have your reasons, and I am at your service."
"Yes, you are right. Believe me, Francois, your kidnapping has been the result of a chain of mistakes, bad luck, and political bargaining that no one of us could have imagined. But the world works in many ways out of our control. So do not think too much on it, turn the page, and start a new stage of your life. Of course, you have not been alone in your problem. As you see, the President of the Republic has been busy with all this and is now by your side. So let us return to France, and I have arranged that on arriving, we will discretely abandon the airport, without any comment to the press."
"Okay, Mr. President, I guess and hope that at one stage someone will perhaps disclose the background to me. As for now, my lips are sealed."
* * *
Two days later, in a modest apartment in Ankara, the telephone rang at 11:00 am and a still discomforted Ibrahim answered the phone to found Alexandra speaking on the other end of the line. Following a rather reserved greeting from both sides she maintained, "I have been informed in the last days that you had erroneously been abducted in Dubai. I feel very sorry for you. It must have been a horrible experience. So sorry... of course, at first I supposed that my husband was involved in it, but gladly this thinking of me was also wrong." As Ibrahim remained silent, Alexandra continued, "In the first days after the event in Dubai I suffered very much thinking of you, but thanks God, finally all this is over, so how are you?"
"I'm well now, although the people that kept me and questioned me, did not treat me careful, you understand me, do not you? It was horrifying and humiliating at the same time. On top of that I had strong emotions, thinking that our future had vanished forever and finally I deduced that our relation was driving me to the abyss."
"Oh I am so sad for you. It takes my breath away if I think of what you have gone through because of me," reacted a crazed Alexandra.
"I am the guilty. People like me, all the time exposed to the media, cannot have a complicated, private life. And if they try, as I did, they may be caught by the media, by the circumstances of the world, in this case the battle against terrorism, or whatever. I know that my love for you was beautiful while it lasted, but our circumstances were very different. I went a bridge too far, but believe me, I did not do so on purpose and I did not misuse you. I'm very sorry. I repent. I pray that we may continue being friends at a distance." said Alexandra tearfully.
"Dear Xandra, I have never in my worst moments in isolation in the centres had a single thought of you being using or misusing me.
I believe we were both sincere but perhaps naïve in our love. But I have my doubts if your new proposal will be possible. That will not be possible and also we both will be better off without any contact, I believe."
"Okay, we will see. Anyway I am glad to hear that you are well, and I feel finally better since I had been feeling responsible and guilty for what had happened to you. Believe me, during our time together I was fully sincere. I will remember it, all my life. I wish you the best, including starting a new and happy family life. Let us try to be happy over the rainbow."
"Alexandra, I wish you the same. You know that I was also very sincere with you", Ibrahim replied. "Really, in the darkest period of my life, caged as I was, I often cried myself to sleep and dreamt being with you forever", said Ibrahim emotional. "But we have both wakened up to harsh reality. Thank you for those unforgettable moments we have been together. Many people will not have lived something alike in their whole lives. Thank you. Goodbye, Xandra, goodbye."
"Friends forever, my love," replied Alexandra, while hanging the telephone.
### Twelve
### Florence in chaos with protesting beauties and new friendship to arise
It must have been around midday, when the news spread that access to the Grand Hotel at the Piazza Orginissenti in the heart of Florence, was blocked by thousands of young protestors who arrived in the capital of Tuscany from all different continents across the globe.
That June day started with temperatures well above twenty degrees Celsius and by midday the heat of the sparkling sun was all around, in particular nestling in the cobblestones of the various places of the historical city with its many touristic attractions. Even at the waterfront at Ponte Vecchio, no coolness could be found, no breeze, no snap of wind while hundreds of tourists were merging with the thousands of protestors in jointly hunting for some little shadow.
As claimed by their several, colourful spokesmen, the new generation protestors arriving from the different continents were demanding accountability of the G20 leaders, who were meeting in an extraordinary gathering in Florence, called for by the American President.
While the presidents and premiers of the G-20 countries were to stay in the Grand Hotel—a monumental building at the south bank of the river Arno dating back to the eighteenth Century with its spacious suites decorated fully antique including large frescos, thus celebrating the artistic culture of Florence—the G20 conference itself was to take place in the Palazio Pitti. This choice, made by the Italian government had high symbolic value since, as the reader may know, the gigantic Palazio Pitti was built in 1458, in the early days of the Renaissance as Residence of Luca Pitti, one of the first bankers of Italy. As both the Grand Hotel and the Palazio Pitti were located on the bank of the river Arno and near Ponte Vecchio, the G20 leaders would be able to walk the short distance between the two buildings and at the same time catch another glimpse of the facades and collections of art of Florence. But to be able to do so, the road for the short promenade had been totally cleared and besieged by a huge army of Caribinieri.
Understandable since, although not invited to the G20 meeting, thousands of youngsters had quickly mobilised and were arriving in Florence, originating from Madrid, Paris, London, Amsterdam, Berlin, Moscow, Washington, New York, Tokyo, Johannesburg, New Delhi, Beijing, Kuala Lumpur, Sidney, Oslo, Ottawa, Brasilia, and even Havana and Cairo.
The G-20 leaders were to look for joint steps to be taken urgently to shorten the financial crisis and the future of next generations was at stake since recent cracks were pointing at a more prolonged recession in Europe, US, and Japan and widespread fears were growing in relation to increased foreign indebtedness, additional losses of jobs, further decline in consumer-spending, and slimming of middle classes, particularly in these parts of the globe. Ever since the existence of wide middle classes is considered as crucial for sustainability of democracy, fears for political instability were genuinely growing all over Europe.
So the building up of the police and security force near Ponte Vecchio was going hand-in-hand with the building up of colourful demonstrations originating from all points of the compass. According to the brochures, they were distributing to passerby, the claims covered a wide spectrum of issues including: urging the implementation of a European Federation; controlling the international finance markets and banks, establishing a democratic global governing body to administrate the production and prices of scarce energy resources, rejecting nuclear energy, democratising the United Nations, and the introduction of a worldwide inheritance tax to globally finance poverty alleviation.
One of the main initiators of this Youth for Inclusive Democratic Global Governance rally in Florence was the Spanish movement May 1st, a collective formed mainly by educated, jobless youngsters counting for around forty-percent of the total volume of unemployed Spaniards. As the group had requested the Italian Premier and President to be admitted with a delegation of ten representatives from the different continents to participate in the G20 Top, at which no answer had been received, the steering group of the protestors had taken the decision that morning, to block all roads leading to the Grand Hotel and between the Grand Hotel and the Palazzio Pitti.
From ten in the morning onwards one could also see colourful banners in the adjacent streets around the two buildings, mainly addressing bankers and political leaders, reading, _If banks do not give more credits, we will go for the bankers, You will have to pay for the crisis irrespective of whether you are idiots or thefts_ , and _There is no place for private banks in future, payment systems cannot be private_. And directed to the G20 leaders banners read, " _No globalization without finances controlled by the global society_."
* * *
A more in-depth explanation to the public of the underlying background of the protest was presented on RAI-1 in the news at noon via an interview with a certain Agnani, a popular Italian sociologist currently working in Princeton but also keeping his consultancy firm in Napoli on electoral issues for left-wing politicians.
Agnani, dressed in jeans and red chequer jacket, travelled to Florence on request of the M-1 movement in order to present the demands of the movement in the media.
The first televised question posed to Agnani, was simple, "You really believe that in the twenty-first-century, your Movement for Direct Democracy has any future?"
Agnani took off his glasses and shook his curly, grey, medium long hair, arched his brows, and answered, "Frankly speaking, it will have no future because it will not progress towards institutionalisation. But we are confident that some of our proposals will be implemented at short-midterm by governments. And if I may say, what has no future at all are today's behaviour of politicians and the current architecture of democracies in the West. Many politicians are just money-makers and are not serving their populations. In many cases, the information on critical events is hidden if this is convenient for their interest. Many of them reach power by promising a future in which they hardly believe and, for some of them, it is almost irrelevant if they deliver or not. For the majority it is sufficient just to keep their seats. All this represents a clear treason to the taxpayers."
While his words were tumbling over one another, Agnani pierced his eyes in the camera and continued "Talking about the current crisis, I do think that citizens have at least the right to be informed about the gravity of the situation. As you know, no government in the West has informed citizens on the seriousness of the crisis. Consequently misinterpretations coming from multinationals and partisan academicians have flooded media which has favoured their interest."
The interviewer had quickly lifted his hands in the air, "But Mr. Agnani, are you suggesting that the media is corrupted?"
Looking away from the camera while putting a finger in his right ear and shaking it briskly, Agnani sneered, "I am not suggesting, I am just affirming categorically that corruption is all around including in the media, and politicians mainly turn a blind eye. It is rare to see someone in government resigning before conviction, a conviction that will only occur long after finishing their political term, as the juridical systems take years in finding the juridical truth. Indeed we have arrived to a situation in which many politicians have excluded themselves from their responsibilities. They spent borrowed money counting with the taxes and revenues that will be paid in future by others. This fast growing debt has become the way to escape from the unpopularity of increasing taxation, thus undemocratically halting financial sources for actions of future politicians."
"How, how, how, stop it! I have seen the pamphlets of the protestors. What has the corruption of politicians to do with the current, financial crisis?"
"Everything, politicians and central bankers are mainly captured by multinational, private banks; they have controlled neither the private banks, nor the Central Banks, thus creating a mess all over the West.
And what about the financing of the electoral campaigns, in which almost everyone looked for short cuts?"
An agitated Agnani made a short pause before he finished, "All this and many more issues should be subject for reorganising the political life in our part of the world. As the audience will agree with me, one cannot ask sacrifices from citizens, while along a durable crisis, politicians persistently show irresponsible behaviour, even allowing private bankers to increase their retributions. Indeed, with their leniency, these politicians may be excluding an entire generation from the labour market."
"Do you believe that these things can be corrected easily?"
"The problem is global and therefore needs global solutions. But it is clear that national politicians should have behaved more according to what is expectable in democracies. They should have exerted government in the name of the people and for the people and not in their own interest. If they had acted in favour of people, some European countries, today in dramatic situation, would have been spared many problems."
* * *
Amid the building up of the security on the one hand and the demonstrations on the other, the Italian Premier arrived in Florence the night before as did the President of France, who, accompanied by his wife Alexandra, first spent a day in Rome, sharing time with a visit to the Vatican to explain the progress of the European Federation to the Pope.
During the entire morning a strong cacophony of campaigns coming from the nearby streets of the Grand Hotel could be observed by the two political leaders and their staff who were all becoming rather restless in the atmosphere of waiting for a collision.
* * *
So when the American president landed at midday at Firenze Aero Porto, there was a desiccated whiff of something troublesome in the air. The man was to have a lunch at two that afternoon with the French President to be updated on the projected European Federation, but at leaving the airport, his motorcade was surprisingly halted by protestors in the steaming heat of the radiating sun. But more than the tarmac, it was the smoking of old car-tires set afire that blurred the sight. Immediately a panic stroke hit the President's own security staff who, amid the dark black smoke and unpleasant smell of burning rubber, started speaking alarmed to one another via walky-talkies and were looking for alternatives, while gunned Carabinieri were in stand-off with the demonstrators in trying to clear the street. Further escalation was avoided when two helicopters arrived and—after using teargas—a somewhat edgy, American President left for Grand Hotel via air. Meanwhile the Caribinieri were able to dissolve the rally. But the tone was set and the American president was right in fearing that there was more to come.
* * *
The working lunch of the President of France and his US counterpart, took place in a special small meeting and dining room in the mezzanine of the Grand Hotel, but even here one could hear, be it softer, the protest sounds of the demonstrations nearby. As agreed, both Presidents were accompanied by their advisors. They included an American Nobel Laureate in economics, Professor Burman, and their respective Ambassadors in Paris and Washington.
After the usual greetings and exchanges of politeness, the two delegations set on the main sides of an oval, mahogany table with three, crystal chandeliers hanging low from the ceiling.
Perrier, dressed in summer shirt and tie, began the deliberations by articulating mysteriously, "Mon chère collegue, may I first thank you for your uninterrupted support." He cryptically referred to the Turkish case and his mouth stretched wide in a silky smile, while the American President politely bowed his head. "We are really living in uncertain times in which creative leadership is vital," Perrier continued, "In this context the world is looking at us, Europe, and the USA. So before I update you on our selective Federation, I would gladly be updated by you on the situation concerning the US rating, the public deficit and debt."
In reaction the American Head of State blinked: "Dear friend, I do share your concern and can assure you, it is my nightmare. The recent downgrading of the credit rating of US government resulted not from lack of money, but from poor governance caused by the on-going Congress disruption. A number of political arguments have paralyzed policymaking and made it difficult to address pressing problems.
Unless these conditions improve, it will be difficult for elected leaders to manage the budget deficit and external debt of my country. And as everyone in the western world should know, this is for me an inherited problem coming from a former US president. His party wanted to reduce the public sector and started implementation by the sweeter part of it: reducing taxes mainly for the rich. But they have done little in reducing expenditure; on the contrary they have hugely increased military expenditure in GDP terms by getting disproportionally involved into two wars, paid at credit."
At that point, the US President passed his hand over his chin before sustaining, "So currently, the problem is not an economic but a political one. As you know, the US may easily refinance the next debt payments. But, mon ami, we were here to speak over your projected federation—the USA debt problem and its spill-over effects will be clarified in the G20 by my Secretary of Treasury—so Let's move on to the European Federation."
The American president stopped to catch his breath before inquiring,
"Entering in the subject, tell me please, what is the value added of your federation? Will it economically and politically be more than the addition of the current capacities of the nine involved countries? Are you convinced that finally Germany and France will be successful in rowing against the stream of history? Let's be frank, the candidate countries of the projected federation share a history of serious rivalries and violence including wars of a hundred-years duration." Perrier with a determined brave expression on his face, "I will start from your last observation. The German Chancellor and I do believe that if we, the nine, merge for solving "common problems" related with European public goods and services, past problems of economic wealth differences and constant begging, will simply disappear, since the nine, federating states have a very similar per-capita income. On the other hand, we are already in our seventh decade of peace in Europe, and Europe has changed enormously in that period. The people in general, and above all, the university students move in Europe very at ease. We are now not only neighbours—as it happened before the Second World War—but friends. And if we are friends and have the same purchase power, problems will not come from the social perspective."
And with his forehead wrinkled into deep corrugations right up to his hairline he continued, "At the same time, having a Central Bank for the Federation and a consolidated Ministry of Finances, we will ultimately solve our current problems with the Euro-System, while we may save a lot of money coordinating our most important policies and functions, mainly our defensive system which by itself will enable a saving of one-percent of our collective GDP."
"Your economic arguments are convincing," replied the American President, who previously noticed an indication of approval by Professor Burman who was sitting at his left, "but I don't think that building up a constitution in which every country will have to give up some sovereignty may be an easy thing. There have historically been cases of constructed federations that have not worked because at the end of the day the additional profits for the new, federated states, were not as visible as the sovereignty they gave up in exchange. And let us not forget the so-called enemies of federation: a mountain of people—mainly politicians and civil servants of the current EU-27—who clearly will suffer with the change, being this the same case that normally occurs in mergers and acquisitions in the field of private firms. They will be in for sabotage. But let us listen, if you do not mind, to Professor Burman, who apparently has something to say."
"If you allow me," said Burman, "I would remind you that in the private world. There are professional mediating firms whose activity is to facilitate mergers and acquisitions, and for long they have been successful all across the world. In the domain of federating or joining nations we have less experience, but in moments of distress—and this is clearly one of them, let us not forget that we are for the moment in the second most serious crisis since the Industrial Revolution, coinciding with an accelerated, industrial shift towards Asia. I think that movements towards federation among economically similar countries could be successful, particularly if the transferred competencies were just the core ones—army, foreign representation, and finances—that is to say, just those that do not affect culture, language, and things like that."
At this time Perrier interjected, "History may have played negatively in some cases as President Leonard rightly remarked, but if carefully treated, things may evolve satisfactorily. We do believe that the real problems of our project are not coming from the countries that will become federal members, but from those who in principle will remain out, and these nations are the majority of the current EU-27. It is certainly a matter of concern that the rest of countries, eighteen, will have to remain connected to us, but _only at economic level_ , while they will be absolutely out of the political decision making process of the Federation. Certainly, in the Federation we will make our own independent political decisions, not at all conditioned by our recent past of having been members of the EU-27. And those whom my American colleague has called "the enemies of federation" are of the same nature as the "enemies of private mergers." Consequently, compensations may be paid to them at licensing. Observe also that our federation will be in essence a public services merger, something easier to manage as we will not have minimum profit limitations, typical for private firms, while we count with a Central Bank."
"But Jacques, if you allow me to talk more familiar to you," said the US President. "I do not see well how you are forming a common parliament, with people of so different origins, cultures, languages, etc."
"To answer you properly, Leonard, may I remind you that today, we already have an experience of meetings and deliberations in the different EU-27 bodies with representatives with different languages and cultures. We have become used to speaking in many languages and we are not unique in that; the same happens also in the Indian parliament, the Lok Sabha. More important in your remark is the question of democratically establishing a federal parliament. In other words, like your Congress in Washington, representing all Americans regardless of in which state they live. This means that we will have to establish a federal parliament representing the population of all nine member states, regardless of where they are living and what language they speak. Look, we are thinking of building up what we call Federal European Political Parties, conservatives, social-democrats, liberals, greens, etc."
Leonard interrupted with a smile. "Why not just two parties as in the US?"
"As you are experiencing now, the US system is not optimal. And taking in consideration that we are starting from another position than the US, we need a careful and inclusive built-up. First of all the federal parties in the European Federation will have to pass the threshold of obtaining minimal five-percent of all issued votes; and second they should have obtained seats in at least fifteen-percent of the 120 electoral districts, every one of them containing at around two million voters. This will guarantee their representativeness at federal level."
"This sounds well, and what about the _economies of scale_ , you emphasized so much in your presentation in Nice?
"Dear President, it is the economy! We have done the tally, and we do believe that, due to the fact that our countries spend in defence around two-percent of our collective GDP, we may save by federating our defence systems around one-percent of our GDP. It will be saving and improving at the same time. Let's be frank, defence budgets are not popular in Europe. So why should we replicate by nine our rather imperfect defence systems, knowing that after merging them, we will tremendously increase effectiveness and reduce costs.
The same will count for our foreign representation. We will be able to move from several small embassies in hosting countries—one for every of the nine members—to one, big Federation embassy per hosting country; at the end of the day, much less expensive but far more influential. But perhaps most important to overcome the current Euro zone crisis will be the merging of the nine finance ministries into the Federal Ministry of Finances in order to control the accountancy of all public institutions in the Federation and implement federal fiscal policies connected with one, single monetary policy. At the same time, the national parliaments in the member states—responsible for the non-transferred competencies of the state governments—will be in charge of controlling the accounts and procedures of the Federal Ministry of Finance. So in brief, the more functions or ministries are merged, the more economies of scale we will achieve. But, Leonard, to start with, we will initially only merge vital, common services and administrate the common federal public goods." Prof. Burman started applauding by thumping with the knobs of his fingers on the table, but the US President was still not fully convinced as he inquired, "Okay, but if you do not mind, can you clarify somewhat on the international politics of the European Federation? Is our transatlantic partnership to be continued?"
"Well Leonard, I may ensure you that we will remain in the NATO although, we will ask for a new treatment in accordance with our new economic and political size. On the other hand, looking into the new realities of the twenty-first century, you will agree with me that the international agreements on issues that are affecting us all, referring to global warming, need of global economic regulation, etc, can only be solved by effective global governance.
In the past twenty years, the economic structure in the world has changed and it will be changing even more in the next, three decades. It is not easy to admit, but all signs point to the fact that in GDP, in international exports, industrial production, and even in defence expenditure of the developing world will have overtaken the current industrial world, that is to say what we call the West. These new global economic structure will have to be complemented with new global political institutions in which the "global society", that is to say the 192 countries of the United Nations, will have to play a more balanced role."
"Although I do agree with you, in the current American political context, it is extremely difficult for me to present this global economic perspective and the consequences for the West, not even in my yearly State of the Union address. I guess you and the German Chancellor are in a similar position. Believe it... I have already started giving hints, in particular making clear that we will no longer be able to continue with our role of policemen in the world. Our military expenditure should decrease in merit of maintaining infrastructures and improving human resource development in my country."
"Yep, my observation concerning global problems," responded Perrier, "was to launch the idea of democratic global governance, for instance, to correct the current, deficient administration of the seas, fisheries, and all that to protect rainforests and to control the production and prices of strategic raw materials as petrol and others. A lack of global governing that already for decades has induced severe economic cycles.
We will have to democratize the UN and give it capacity of enforcement, which means the constitution of an UN army that may intervene when necessary under the command of the new democratic UN."
"Jacques, how brave of you, but it sounds to me little realistic. Are you suggesting the introduction of a majority system in the UN Assembly and taking away veto rights in the Security Council? Come on, that would induce giving, for example, China and India with their huge populations a leading role in global governance decisions. Mind you, China, the largest undemocratic country in the world... that would really be a major setback for civilization."
"I do not think so. Observe, dear Leonard, that in the coming twenty to twenty-five years the population in China will see an increase in their average income per head of up to 25.000 US dollars. At that level, the society in China will count with an extended middle class, which, combined with an expectable high level of education of its citizens—already millions are annually graduating at academic level—will doubtlessly produce a national democracy. As proven in the history of Europe, middle class, levelled education and income will inevitably produce democracy."
The American President was probably losing patience and his voice sounded slightly irritated. "Oh come on Jacques, stop dreaming. My political advisors say that the Communist Party of China will never give up power to the people because in that case China would fall apart in several pieces. I fully endorse their insight. Do not forget that China was an empire in other times with a lot of colonial territories."
"Leonard, I beg to differ. Observe that most Chinese citizens are today already very conscious of the fact that their country is on its way to become the most powerful economy on earth. The position of China as superpower is only some years away. In the light of that, the act of splitting away and diverting from the centre, in a world in which progressively only large entities count, would be to abandon a promising future and a very profitable business. And on top of that, why abandon a socialist empire in transformation to a modern social democracy, just when all the efforts have been done and the harvest is at hand? That would be as to give up exactly what you and your parents have for long fought for."
"Even more," added Perrier, "China will be economically powerful, but I do not think that we have to fear their attempt to become a hegemonic power. Those ambitions are something of the past, when the power structure in the world was far simpler. Today already it is becoming clear that to be hegemonic is giving you more responsibilities than the spoils you may obtain. That is why some intellectuals in the US, take Professor Stiglitz, are fighting for America giving up on policing the world and going for a significant reduction of US defence expenditure."
Now going slightly red, Perrier bent forward and with a boyish smile to the American President concluded, "Besides, do what you do, Leonard, your defence expenditures will finally be overtaken by those of China, and without any special effort by its citizens, just the outcome of China"s rapid growth rate for another two decades. So, the better would be that we persuade China to embrace global demo..."
BANG...NG...NG.
A strong explosion followed by repeated gunshots brought the meeting to standstill and paralyzed the participants. The silence in the mezzanine was in contrast to the screaming which could be heard, probably coming from the Piazza Orginissenti in front of the hotel or from the narrow streets between the Grand Hotel and the Pitti Palace. It was the signal for the presidents and their bodyguards as well as the rest of the men around the table to jump up in terror and rush to the reception area of the hotel.
* * *
In the reception hall of the hotel some more delegates for the G20 top anxiously gathered and all eyes were on the hotel manager and the Italian police inspector who were trying to calm things down. As the hotel manager explained, the explosion was caused by huge firecrackers that had been placed in a barrel. He had been informed that the Carabineers were using plastic bullets to dissolve the rallies and clear the area, in order to make it possible for the delegates to replace themselves to the Pitti Palace, as the top was to start in less than two hours.
While the manager was speaking, one could hear continued shooting but also sirens of ambulances, fire-fighters, and people screaming, as well as the lancing of more primitive projectiles as cobblestones.
"The instruction to the police is to avoid escalation," continued the hotel manager. "Taking into consideration that we all have once been young and have once protested, we should try to clear the area without hurting anyone. Several arrests have been made. As the police inspector explained to me just now, all is under control. No reason for the delegates to worry. I suggest we use the Montebello-1 meeting room as information centre to keep you update before leaving for Palazzio Pitti."
"There, good Lord, let them in please." Alexandra, the first lady of France, was pointing at two, young protestors who were trying to enter the hall by pushing at the door, even bobbing on the glass. The two young women were looking rather fragile with their eyes expressing fear while begging to come in.
"I think we should let them in," Alexandra repeated while all eyes moved in the direction of the two timorous-looking youngsters women of around twenty. Jacques Perrier supported his wife in her call to assist and to give refuge to the protestors. So did President Leonard, at which the Italian Premier affirmed while neglecting the rejection of the Indian Prime Minister.
But the latter raised his brushy Indian brows and looking rather disturbed, he made the observation. "Once you join the protest, you should have the courage to fight your way home as the others do. A rally is not a tea party."
At which the Italian Premier reacted, "Have you always been so cynical?"
"No, it took me years!" was the smiling reply of the Indian leader.
As soon as the youngsters were inside the hall, the American president took the lead and started making an effort to calm them down.
"Ladies, you may stay here till the roads are cleared for you to go home. All of us here have once rallied when we were young. We went to the protest gatherings even though we were afraid since it was considered a necessary part of the transition from adolescence to grownup. In a more popular version my mother used to say,
"Eighteen and no socialist, you have no heart, thirty and still a socialist, you have no brains." However, for most of us the real challenge in our participation was being heard without letting things run out of hands. It is an art to find effective ways to express different points of views and to be heard. If my colleagues allow me, I will now give the two of you some minutes to speak out your demands in front of us. Consider it your lucky day, historically only you two will have been able to address your concerns directly to G20 leaders. Signorinas, we are all ears."
One of the youngsters, smiling released, started speaking hastily, "Sir, we are not unwilling to adjust to globalisation, but we are observing growing difficulties to find suitable jobs in Europe and America while our friends in Asia are working long hours for little wages and no protection. This is unbalanced and absurd. You, the politicians, may defend globalisation as a matter of principle, and this is probably correct, but what you cannot defend is the total lack of control. The economic situation enjoyed by our parents was very favourable and probably undeserved from the perspective of non-Westerners, but what is bizarre, is that you, the global politicians have unconditionally given way for capital to gain money in developing countries, thereby condemning the current generation of Europeans, regardless of their education, to have less jobs, while the little remaining job opportunities will be more precarious and significantly worse paid. So we, the so-called best educated generation in Western history demand democratic global governance to rebalance things."
The expressions of both the French and the American presidents were ones of surprise and Perrier was the first to react, speaking enthusiastic, "What a speech, I thought that you were not politicians, but you are! Allow me a little correction. France does not fully fit in your picture.
You are right in saying that in the last three decades the world has quickly moved towards liberalism, but France has tried to keep its traditional position in relation to the control of the markets. However, with our participation in the European Union, we had to swim with the mainstream, which resulted in us joining in mistakes such as the weak architecture of the Euro, which have put us all into crisis today.
But with the European Federation which is in the making, we will repair the errors, I promise."
Leonard moved forward to push Perrier aside and with a sarcastic smile added, "And France is putting all its weight to create a new and democratic UN. As you may have understood, we politicians do have the necessary solutions in our heads, but we fail to explain them to you. So, may I thank you on behalf of all the G20 leaders for your explanation and have a save journey home."
The Chinese president, who was silent till now, commented, "As I experienced in my years in the University of Beijing, those who fail in explanation prove that they do not understand what they are talking about."
The Indian Premier nodded but added, "I fully agree with my Chinese colleague, although I hope that his experience dates from the days after the Cultural Revolution."
### Thirteen
### The tragic end of Bopoulos
Without in any way wanting to admit defeat, Carlos Bopoulos, president of the fast-declining European Commission, had been forced to accept the invitation of the German Ambassador in Brussels to attend the garden party the latter was hosting to celebrate the success of the referendum on the European Federation.
The referendum had been held in all the nine, federating countries at the same day and information and communications leading up to that moment had also been streamlined in all countries. Release and happiness was all over when, above expectations, in most of the countries the Yes vote was around a ninety-five percent. The only meagre results came from Finland and the Netherlands with a Yes percentage of respectively fifty-two and fifty-four, but this could not temper the joy among the populations.
For Carlos Bopoulos and his attempts to put a bar in the wheel of the federating process, the outcome of the referendum had been a blow, although deep in his heart he had expected that the populations in the nine countries would favour the best way out of the Euro crisis.
Sitting at the back seat of the black Mercedes in which he was being driven to the German residence, Carlos was preparing himself for the many awkward questions he might receive from other attending Ambassadors and diplomats over the future of the European Union of twenty-seven, now that the most influential member states were pulling out to join a federation. Admitting defeat was one thing; going to a celebration party to make it public was something else. That Carlos Bopoulos accepted the invitation was not only to keep all balls in the air, but perhaps also to expose that he was a man who bear setbacks without bitterness. Never know how things might in the end favour him and by that he was not thinking of the gesture of the Spanish Prime Minister who offered him the Spanish nationality.
Come to think of it, the British Prime Minister had kept his distance from the moment Carlos reported that their agreed undermining actions to halt the participation of Spain and Italy in the Federation had not been successful. Albeit, the silence of the British Prime Minister was remarkable as he at least one day had hinted at having a stick: the affair with Clara. On the other hand, it was possible that the Prime Minister had some data over the fact that the whole Clara business had dissolved itself much more easily than expected. Carlos had simply refused to answer any of her phone calls, but at the same time he had twice transferred an amount of Euros to her account, and although she had never reacted he believed that his transfers had been recognized by her as the promised compensation.
Then there was the rest of the EU-27, that is to say, the eighteen mainly small and weak countries, who—with the exception of Britain—even before the referendum, had started in a pragmatic way to look into the consequences of the European Federation for their economies, and how not to be side-lined. Those who were in the Euro zone were mainly looking into the consequences of staying in the Euro zone without having any political control on the currency, more or less in a similar position to countries using the US dollar as their currency in other parts of the world.
Others, those not in the Euro zone, were working out possibilities to join with the Federation in a common market, considering that this would be the best option for continuing the economic advantages of the EU in the past, be it now in a far better structured way.
Of course, the British were hardly participating in any of these future projections of the rest of EU-27. London was back on the island and looking for a far greater alternative. As Carlos had seen on the BBC, a new round of heated debates had started over the British decision to join the EU, about staying out of the euro, about the priority of transatlantic partnership, and about the value of the loss of British influence on mainland Europe as a consequence of the Federation.
But, over and again, the British Prime Minister on the screen tried to calm things down by suggesting waiting and seeing since putting the idea of a federation into practise was not going to be easy, as history had proven. The mere fact that in the past ten years it had been almost impossible to agree among the member states on simple things like one pension age or on the same number of holidays per year in all EU countries was proof that making the federation work would be extremely difficult, not in the least with great, inflexible countries like France.
All these debates and developments were of utter importance for the president of the European Commission, who overnight had passed from being the political boss of EU-27 with quiet a number of globally influential countries, to being the PressCom of seventeen or eighteen mainly periphery countries excluded from the centre. So every time the naked truth of this reality crossed his mind, Carlos Bopoulos experienced problems with breathing. Even more, the dominance of the new European Federation changed the terms of any negotiation on the continent, and with the exception of Britain, the future for the seventeen excluded countries under his guidance would be one of adhesion to the proposals of the Federation and not vice verse.
* * *
When the black Mercedes arrived at the residence of the German Ambassador, a dark blue BMW quickly past and thereafter stopped in front of them. In the manoeuvre with far too much speed, the side mirror of the Mercedes was hit and with a bang fall apart in many pieces. Immediately after the hit, the four men involved: two drivers, Carlos Bopoulos, President of the European Commission, and the German, Joachim Steckman, Commissioner for Competition, approached the place with the broken mirror.
Standing alongside the Mercedes, Steckman instantly started scolding the driver of Bopoulos while totally neglecting the President of the European Commission who actually was his superior. It took Carlos Bopoulos by surprise. Who would have thought that the arrogance would pop up so quickly just hours after the success of the referendum?
"Hey, hey, Steckman, the crash was caused by your driver and you know it. And wouldn't it be better to leave the matter for the two drivers to solve?" a highly irritated Carlos screamed. But instead of answering, Steckman almost demonstratively turned his back on Carlos Bopoulos and instructed his driver in German to make sure that no form was filled with any accusation in it, before he strolled away in the direction of the garden, leaving Bopoulos gasping for air.
"Monsieur le Président de la Commission, soyez le bienvenu." Unclear if the German Ambassador had observed the incident, but he was advancing amicably over the lawn in the direction of Carlos.
Bopoulos tried to put bad memory aside as he rushed towards the German exclaiming, "Toutes mes felicitations for the outcome of the referendum. This was the most successful German-French initiative in modern history!"
As they met, they embraced warmly and during the act the German Ambassador murmured close to the ears of Bopoulos that his secretary had been calling for him already twice; it was urgent.
The first reaction of Carlos was to search for—but not find—his Blackberry he probably left it in his office. Consequently he accepted the invitation of the Ambassador to use the phone in the library, and it was there that Carlos Bopoulos got the information that a police inspector was waiting for him in the office and that things were too important to wait for tomorrow. So he had no other choice than a quick farewell, promising he would eventually return and be driven back to his office. Truth be told, he was happy to be able to prematurely leave the party of the federation triumphs.
* * *
On his way back to the office, he was naturally praying that neither his wife nor his daughters were involved in an accident because this is what people usually think when a police inspector is waiting for them.
Accordingly, back in the Rue de la Loi he rushed to his office on the third floor, to find a large female police inspector in the forties waiting in the corridor. However, with her sleazy blonde hair, red apple cheeks under small watery blue eyes, and her uniform spanning tight over her belly, she looked more like a big mama than a keeper of law and order.
"Inspector Leni Boor, Brussels Police," she said pulling a plump hand in his direction.
"Brussels police," Carlos repeated, "Carlos Boloulos, sorry that I kept you waiting. Can I be of any help?"
Inspector Boor was looking straight in the eyes of Carlos as she suggested that they would close the door first and then sat down on the comfortable sofa across his desk. Carlos automatically obeyed but while he was following her orders he was only trying to read any bad news from her eyes.
"Mr. Bopoulos, I will be frank with you, it is about Clara Polar."
"What about her?" he said, and he first felt relieved that his daughters were okay before his mind started fighting with images of Clara in a car accident.
"So, can I conclude that you admit knowing Clara Polar?"
"I am sorry, is she okay? What is this all about?"
"Clara Polar is okay under the circumstances. Any chance the two of you had a sexual relation Mr. Bopoulos?"
"Inspector, I will give an answer to that, but then you will first have to explain to me what is going on."
"Clara Polar has filled a serious allegation against you at the police station in Brussels North this morning."
At the last words of the inspector, Carlos gasped and his mind was racing in all directions ending with a vile vision of Clara handing a written accusation over his presumed abuse of her, probably with the help of friends.
"Inspector, can you tell me what allegation?" Carlos tried biting back as frowns collected his forehead.
"Of course Mr. Bopoulos, that is why I am here."
Inspector Boor was now taking out some papers from a brown bag on her laps, and with her eyes moving by turn from his face to a paper in her hands she started, "According to Clara Polar, the two of you till recently had a sexual relation and over a period of four months. After you suddenly rejected further contact, she had a routine medical control a week ago and the results, presented to her two days after the check-up, shockingly diagnosed her HIV-positive. As she had no other sexual relation, neither before, nor after the love affair with you, the AIDS infection could only have come from you."
"Utterly nonsense!
"Moreover, Clara Polar is convinced that you knew that you were having AIDS and deliberately infected her. Mr. Bopoulos, this is a very serious allegation for which you could be arrested immediately, as we would have to make sure that you could not make more victims in the time between the investigations and court ruling."
"Inspector Boor, I am shocked. This woman is a criminal. This is her revenge for me breaking up with her. She is crazy. To think that I would deliberately infect her makes me a criminal. And why would the police believe her? We have not had any contact for the last months so she could have been infected by someone else."
"Mr. Bopoulos, there are two things playing against you in this case. First, you seem to have been telling Clara Polar by repetition about an affair you had in Goa, India, about a year ago with a twenty-six-year-old woman who at one stage in her life had been exposed to risky sexual activity."
"No Inspector, Clara is making things up. Yes, I have told her about a relation in Goa, but it was a simple affair of two people attracted to each other, and I swear, the Indian women had no such thing as risky sexual activity. Clara's accusations are based on revenge, lies, and fantasy, perhaps hatred. All I hear you reporting are pathetic lies and utterly nonsense from a dangerous charlatan."
"Perhaps Mr. Bopoulos, for God's sake, you should let me continue with the clarification of the allegations. I have it here on paper. These are words of Clara Polar. You will have to falsify her accusation by proving the opposite. I can assure you, the statement is rather consistent and I have personally been taking a great risk by not summoning you to the police station. But as I am a very humane person I have come to your office to give you the opportunity to give me another perspective on the case before I take any of the steps I am supposed to take as a police officer. I am hired to put the justice machinery and the victim protection procedures into working without getting involved. So are you willing to cooperate?"
An even more bewildered Carlos Bopoulos lifted himself from the sofa, loosened his tie, opened the collar of his shirt to be able to inhale some more air, and walked around the room. In reaction to Inspector Boor's advice that he should cooperate, he was nervously gesturing with his hands that he was willing to do so, as he seemed to have lost his voice.
The inspector continued, "Am I right if I say that you just confirmed, Mr. Bopoulos, that you had a sexual affair with an Indian woman in Goa almost a year ago, right?"
Carlos confirmed by nodding his head. He felt bilious.
Inspector Boor sustained, "It was a simple vendor in a small shop of handicrafts near the hotel in which you were staying with your wife and your two adolescent daughters. You need to know that according to Clara Polar—and she has given a detailed description of things as you seemed to have told her the experience more than once—from the moment you entered the shop, you were attracted by the Indian women with her beautiful, deep, velvet eyes looking mysteriously at you while you started telling her in a humoristic way about the daily life in Brussels. She had never left Goa and as very few people came into her shop, your visits and your entertaining stories were most welcome. While your wife and children were on the beach, believing that you were reading a book in the garden of the hotel, you would pass up to two hours with the vendor in her shop. Already at the first day you noted that the vendor was melting down like butter in the sun for your anecdotes; her dark eyes in laughter were following every movement of your lips, as she was leaning towards you over the counter. Next you became aware that you were almost hypnotizing her with your words as she was slightly opening her lips, and you could see her eyes glazed with a covert desire.
By the second day, it was in the air that you would end up making love with her, but it happened on the third day. It happened just after she had told you her own life history. Starting with her arranged marriage at the age of sixteen and her repudiation at the age of twenty-four as she seemed infertile, she had explained, looking shy, that she had been thrown out of the house by her mother in law after her husband had announced her repudiation to Allah. Thereafter, she wandered in the streets of Goa for many days before an older woman offered her shelter. In exchange, she cleaned the place and cooked, but after three weeks she was invited to accompany her benefactress to a bar, to find out that around six women more or less of her age were all supposed to entertain the guests physically. For three nights she was forced to do so and the fourth night she finally managed to run away and found refuge in a Catholic nunnery in the centre of Goa. The sisters helped her to start her handicraft shop some months later. So, after three days, you passionately made love to her on an old sofa behind the counter and, from then onwards, every day, till you and your family left for Brussels six days later. Ten months later, according to Clara Polar, you must have found out having been infected with AIDS, which made you so enraged that you started looking for a victim. And so you infected her, Clara Polar."
"Inspector Boor, stop it please; these are, at best, half-truths, I can assure you." Carlos recovered his voice, although his eyes were looking thoroughly frightened.
"Mr. Bopoulos, I am almost there, please let me finish. I have seen the test results of Clara Polar. No doubt, she is HIV-positive. So tell me Sir, have you at any time in the past year submitted yourself to a medical check-up and would you be able to show me the results?
Often at check-ups doctors also ask for testing on sexually transmitted diseases."
"No, inspector, I have not. I am only controlling my blood pressure."
"Okay, before anything else, Mr. Bopoulos, I want you to go for a check on sexual transmitted diseases. Tomorrow, ultimately the day after tomorrow, and if you are cleared, you are a free man. If not, your misery will start. I probably will have to arrest you. You will have to inform your wife, putting your marriage at risk. You will have to appear in court. And on top of that, with your status, media will hunt you down."
Lamely, Bopoulos returned to the sofa, and speaking now as a broken man he murmured,
"Inspector Boor, don't you see that Clara Polar is trying to break me, my family, and my career?"
"Mr. Bopoulos, first you do the test for eventual falsification of the allegations. If disappointing, you will have to find yourself a good lawyer. And for now, I want you to sign this document for me. It states that I had a first interrogation and granted you forty-eight hours to deliver a medical test report."
After a quick glance at the document, Carlos exclaimed, "I cannot, it states that I made love to the Indian women more than once. False, it was only once."
"Mr. Bopoulos, I am not convinced and it looks like you will have a hard time convincing any judge. It is common knowledge that adultery occurs, but what is still expected from all of us is that we protect those we love or make love to. They must be able to trust us for that, Mr. Bopoulos. You were, be it indirect, told beforehand in Goa that there was a risk, and nevertheless you broke the code towards your wife and Clara Polar alike. It is possible that a verdict will be built on the fact that with your behaviour you proved to be selfish and never more trustable. But I have trusted you coming to your office, so please sign here. This does not imply that you agree with the allegations of Clara Polar, but only that I have informed you on the content."
* * *
To make things worse, Inspector Boor hardly entered the elevator at the third floor on her way out when Carlos who was rushing back to his office after letting her out heard his Blackberry ringing on his desk. It was a call from the British Prime Minister.
"Hello Carlos, I have not heard from you in a while, I hope everything is well."
"Yes, I'm fine, and how can I help you?" was the cold answer of Bopoulos.
"Feel like you are running away, my friend. Is not it time for us to talk about the future of the excluding federation?"
"What is there to say Prime Minister? The referendum has been successful and things will develop independently of you and me."
"I do not believe so. For me the future of the federation is very gloomy. It is practically impossible that these nine countries may change into one single state. In fact many others have made similar attempts in history and as far as I know, no one has succeeded, at times also with a little help from outside. And believe me Bopoulos... you are in an excellent position to support the failure. Think of Italy and Spain; these two Prime Ministers could easily be persuaded by you. I have no doubts whatsoever on your skills to intrigue."
"I would not know what to say," Carlos mumbled while his face was turning red. This really was not his day, but he instantly felt that he should bounce back adding, "Sorry my friend, I am not convinced, and I cannot promise you anything. Maybe you should first give things a second thought."
"Do not give me that, Bopoulos. If you fail in your endeavour to positively correct the trajectory of Europe, a tsunami may reach Britain but also Algarve," was the enigmatic answer of the British Prime Minister.
Apparently the conundrum was rapidly understood as Carlos, with a clear warning in his voice replied, "For some time already, I had, by references and history, some idea of how you played politics, but I would never have imagined that you would in the twenty-first century play it on the man. I don't care what information you think you can blackmail me with, but I think you are in a mistake. Do not touch my family as I will pursue you till the end of the world. Hope I have been clear." At his last words, he promptly hung up the telephone in the ears of the Brit, well aware that for the first time he firmly protected his family. It seemed that he was able to freely breathe again.
* * *
That night, Carlos did not sleep. He stayed awake for the full, eight hours even after drinking a sleeping pill. Luckily, when he had arrived home from the office at 8:30 pm, he found his wife and daughters away for the cinema, so he had decided to go to bed as soon as possible, thus avoiding having to look the three women he adored into their eyes. He left a note at the table in the living room, left a copy in the dining room, explaining that he was dog-tired and therefore had decided to sleep in the guest room at the third floor, as to make sure that he would not be disturbed by their home coming.
He wished them a happy goodnight and signed by writing, _Love you all very much, Carlos_. Hereafter, he googled HIV testing places and selected two with results in twenty-four hours, deleted the history of his search, and finally took the stairs up to the guestroom.
* * *
Lying awake and constantly turning from one side into the other, he could think of nothing else than the test, it's possible results, and the consequences. I know I am not infected, he said to himself, and yet it was possible. He was painfully aware of the fact that many exercises of humiliation might be awaiting him and that he would have to show to his children how sorry and ashamed he was about the very bad things he had been doing. He thought of confession and repentance in the cathedral at Grand Place, but actually being an orthodox, this exercise was far from him. If tested positive, would he inform his wife? And would she inform her parents? What would papers head when he was arrested?
* * *
He managed to hide his identity at the clinic by: 1) paying cash and agreeing that he would personally collect the results at the end of the next day, 2) by twisting the information on the form he had to fill in to clarify where he thought he could have been infected, and 3) by selecting a clinic seventy-eight kilometres south of Brussels in a so-called sleeping suburb.
* * *
The two days he spent waiting for the results became days of constantly distorting information and communications towards his family and in his office, and this exhausted him completely.
Combined with more than thirty-six hours of sleeplessness and growing fears over what was lying ahead of him, he had started losing concentration, loosing calm, and even loosing memory. The man who in other—not faraway—times had been warm and lively, sympathetic, and highly entertaining with a remarkable capacity to speak and joke in several languages, that man had in little time changed into an extremely nervous, bad tempered, manic depressed, and sometimes rude person. This was in brief the state of mind of Carlos Bopoulos, at the moment when he finally collected the test results.
Positive... He did reread the word three times, but it did not disappear from the paper. Killingly, it stared at him... he had tested HIV-positive. It could have been in Goa or by Clara, who would know? What mattered most was that he thereafter might have infected his wife and that he had definitely blown his career, even if the latter had already reached troubled waters with the Federation.
Things now definitely turned uphill for him and sitting in his car with the test results in his hands and, his hands leaning at the steering wheel, he was confused and he could only think of a trip to nowhere, to an unknown place in Asia or Latin America, thousand miles away from home.
The nurse who gave him the test results had repeatedly explained that HIV infection had long time ago turned into a disease not causing death. Not in Europe, perhaps in Goa. Clara would survive, be it drinking medicine for the rest of her life financed via her health insurance, similarly to persons with diabetics drinking their medicine three times a day, the rest of their lives. He would have to do the same. So would his wife.
Alas, he was caught progressively in a terrible cobweb of shame and fear. He felt deeply depressed and completely deserted. Clearly, no one would believe that he had made love to the sympathetic Goa youngster mainly to help her to restore her self-esteem. Similarly, no-one would believe that not a single hair on his head had ever thought of infecting Clara with such a stigmatizing disease, and even more, he had always been a family man with deep warm feelings for his wife and daughters, and certainly he had never been interested in the life of a womanizer or a bachelor always on the hunt.
Nevertheless he was trapped in a disgraceful and unsolvable problem, in a labyrinth without exit. The wish to disappear forever before having to face any of his victims seemed to be the only way out for him, the only solution.
* * *
At 11:00 pm, in a breaking news flash on TV and radio all over Europe, the public was informed that the President of the European Commission, Carlos Bopoulos, had tragically died in a car accident on the E-19 highway from Brussels to Namur. Showing the wreckage of a black Mercedes, the newsreaders explained in the many languages that, around 10:15, pm the car hit a light mast in full speed at the E-19. The highway police considered it likely that the sixty-two-years-old PresCom fell asleep behind the wheel and confirmed that no alcohol was found at autopsy. Carlos Boloulos left behind a widow and two daughters. A number of Cabinet Ministers and Prime Ministers in the European Union Capitals were expressing grieve on TV and their sympathy for the wife and children of the deceased President of the European Commission.
* * *
The funeral of Carlos Bopoulos was solemn. In the Catholic Cathedral of Brussels, a morning mass was held. In attendance were his entire family, from Greek and the Portuguese side, and many Prime Ministers and Chief of States. The British Prime Minister was one of the speakers, as was the German Chancellor. Amid the saddened eulogies, the Brit added that the late Bopoulos was the only person who could have averted the European Union's demolition. Indeed a great loss.
### Fourteen
### Passionate loss for the makers in the first federal elections
As Aunt Frieda used to say back in Weimar, " _The first astonishment always goes deepest, and any surprise after the first, only adds to the deep impression of the first_."
So, when at 5:00 pm, advisor Hans Schmidt entered the office of the German Chancellor to bid farewell, Marlein Ditch was still digesting the experience of two hours before at the voting station, which had left her in deep astonishment, and consequently she possessed neither the will nor the energy to show much surprise at this second event.
Hans Schmidt—dressed in a colourful Hawaii shirt, creamy Levy Straus pants, and a new half-long bushy hairstyle—looked having gone through a total makeover. A correct observation since in reality, Schmidt had been making revolution in his personal life, resulting finally in his sudden resignation from his top advisor job. Even more, he was to fly out of the country the next day as he had changed from a conventional bibliophile into an innovative adventurer. More precise, he was on his way to explore his possibilities to contribute to the salvation of the Brazilian Amazon rainforest.
Clearly much of Schmidt's conversion should be attributed to the young woman who accompanied him at his farewell tour in the Chancellor's Headquarters in Berlin. With her jet-black hair with ponytail and her dark, quick and clever sparkling eyes just visible under the Asiatic eyelids, the young lady was unmistakably descending from one of the many Amerindian tribes in South America. While Schmidt was proudly introducing his fiancée, Amaras Gusto a pharmacist who specialised in research on medicinal plants and in the discovery of new healing species, the young beauty was simply smiling alleviating, showing her white teeth while eloquently bowing her head.
On invitation of Marlein Ditch, the young couple took a seat at the sofa in the Chancellor's office and drinks were ordered.
"Nice to meet you," the Chancellor babbled while taking a good look at fiancée Amaras. And without winking an eyelid she continued, "I wish you both all happiness in your new live in Brazil. I will certainly miss my faithful advisor, and I pity not even having been able to get acquainted to his fiancée," she ended looking directly at Hans Schmidt, who as usual had started redirecting the conversation away from his private live by remarking.
"What a day!" he said "I went to the polling station this morning to do my duty as European citizen, but it was rather unpleasant to have to vote for an unknown first candidate on the list of the European Conservative Democratic Party. How things have changed in the past eight months. Who would have thought, Mrs Chancellor, that neither you nor the French
President, the two founding fathers of the European Federation, would be present among the candidates to be leading the European Federation Government in the coming five years? You unquestionably deserved better."
The German Chancellor sighed and shook her head before waiving his grievances away by recalling: "This is democracy my friend. As you know, eight months ago, when fourteen parties, Christian Democratic and centre-right Conservative, in the nine federating countries had agreed to jointly form the Federal Conservative Democratic Party (FCD), we suddenly ended up in a bitter battle for the candidacy.
Between you and me, I am convinced that if Jacques Perrier had supported me instead of throwing his full weight against me at the time of list-formation, one of us would have won the primary. As they say, while two dogs are fighting for a bone, a clever third dog will run away with it. This is what happened in the Federal Conservative Democratic Party, be it behind the screens. In the end, we both failed.
Of course I could have accepted a lower ranking on the list, but that would mean opting not to become the head of the federal government, which in itself would have tremendously harmed my position inside German politics with our Chancellor Elections just months away."
"Madam, you did not deserve less than to be the Premier of the Federation," fiancée Amaras remarked.
Hans Schmidt added, "Probably Perrier was forced to make a similar judgement, and as we know, he nevertheless lost the presidential elections in France last month. Tragic that such an advanced politician should be retired at the top of his career. The two of you pushed for the Federation to bring Europe out of crisis, thereby also improving the economic perspective of Germany and France, but paradoxically time was not on Perrier's side. Let us hope that over two months the Germans vote for you with more compassion."
"Ach Hans, after my experience of this afternoon, I would not be surprised if my faith in the upcoming German election would appear analogous to Jacques. The financial crisis was in the making long before I became Chancellor, but with the water up to their lips, voters tend to blame only the incumbents. Sadly at this time of the first Federal Elections almost in all nine federal states Christian Democratic or Conservative and Liberal parties are in power. Could you imagine eleven months ago, when the flag of the European Federation was raised on all-important buildings in the capitals of the nine federating countries, that today I would be visiting a polling station to cast my vote to select a first European Federal government, and that not one single journalist, cameraman, or photographer was around. As if my role in bringing about the European Federation was something of a long grey past, a happening of a hundreds of years ago. What a rare experience to be erased completely in so little time. It was astonishing and I am still digesting it."
"In the way it is wiping off memories, time is a big traitor. Especially good services are easily forgotten while the blaming game for the bad and the stigma's remains vivid in people's minds," Amaras lyrically spelled out with her deep, sing-song voice.
Marlein Ditch sat silent and was looking away from the two young lovers while she let memory pass over the developments in the past months.
First a provisional government of the Federation, recognised as that by the provisional Constitution, had been formed eleven months ago via consensus by the top executives of the nine federating countries (Prime Ministers or executive Presidents). This provisional federal government, consisting of a provisional Federal Premier and five, provisional Federal Ministers, had as its core business the preparations of the first federal elections to select a parliament and a government for the European Federation of nine.
Already in the first month, the provisional federal government supported by the five commissions had agreed on date, rules, procedures, and infrastructure of the elections, as well as the registration period, conditions and eligibility of federal political parties and candidates. Parties on regional or single issues, as well as parties excluding some citizens of the Federation on the base of ethnicity, gender, or sexual preference, were not eligible. So quite a number of parties would be disqualified such as the Anti-Globalist party, the Non-Smokers party, the European Unemployed party, and all nationalist or religious parties.
Then there was the problem defining the electoral districts—let us remember that according to the constitution each electoral district would have around two-million electors without disenfranchising voters in the five smaller but richer states (Luxembourg, Netherlands, Finland, Austria, and Slovenia). This had been solved by introducing a period of transition of ten years in which electoral districts were defined in such a way that of the 360 elected representative for the Federal Parliament; ninety representatives would be elected in the thirty districts of these five small member states. However, the rules that parties should pass the threshold of obtaining minimal five-percent of all issued votes, and that they should obtain seats in at least fifteen-percent of the 120 electoral districts, remained intact.
Similarly, the creation of frontier voting districts between two or more federating countries, particularly in regions with some special historical connotations was temporarily allowed. All this resulted in a total of 120 voting districts, with election of three representatives per district, which, with all variations included, would provide for 360 elected federal representatives.
Soon after, the various families of parties in the different member states—social-democrats, conservatives, greens, liberals, etc.—started meetings to form federal parties on their specific characteristics, at times with large margins such as Socialists and Labour Parties.
It was logical that when the political parties of Jacques Perrier and Marlein Ditch, both belonging to the family of centrum-right parties, entered into negotiations with another to form the Federal Democratic Conservative Party, Jacques personally contacted Marlein to harmonize expectations.
"Hello Marlein, as things look now, I suppose there will be only two main political forces dominating the scene, our FDC party and the Federal Labour-Socialists. Perhaps the Greens might also enter in the Federal Parliament, but the Premier of the Federal Government will stem from FDC or FLS. In any case I do not believe that the rest of parties will overcome the thresholds of the five and the fifteen-percent, not even the liberals. Even more, bearing in mind the personal contributions of you and me, our FDC certainly has the best expectations."
"Not only, said Marlein, I just finished reading in Le Monde that you explicated in an interview on France-2 that you will probably be First Candidate on the FDC list. Premature, is not it? We have yet to talk about this issue that I understand as essential to win the elections."
"Ach, you know how journalist are. I am sorry. I may have hinted in that direction during the interview, but nothing more. And by the way, I really thought overhearing you saying weeks ago that your preference was to continue heading government in Germany, or am I mistaken?" Jacques quickly replied.
As Marlein kept silent, he continued, "We both know that the power at federation level will be far less important as in the US and this while the responsibilities at global scale will be relevant."
"For me," answered Marlein, "Germany is a business done. It does not represent much more of a challenge for me. But on the contrary, to become the first Premier of the Federation, a first Federal Premier being a woman, would historically be a breakthrough. Come on Jacques, you and I have worked well together in the last year to create the Federation. So, why would you not continue with me, if I take the executive head of the Federation?"
"Frankly speaking Marlein, it is not for us to decide. First our boards are on set, and thereafter the electorate. I will not withdraw my candidacy and suggest you should neither."
"No, you are mistaken," reacted Marlein. "We have to clarify this issue from the very beginning in order to transmit to the electorate of the Federation that we are already very prepared to execute the Federal agenda, but if we continue giving interviews with contradicting information, I mean, I could also inform the public on our dirty battle for the Premiership. This could work out in favour of our adversaries, the FLS (Labour-Socialists) and we could even loose the elections. And my friend, do not forget that most of the Federation citizens expect you and me teaming up, to solve the recent economic problems in our countries. You are now breaking the team."
"I prefer the involved boards to decide democratically on the First Candidate. Let the internal primaries speak. I think that for you as well as for me, to change the level of our activity moving up to the Federation is the best bet we may take and I would not want to exclude myself without giving it a try. Hope you can understand."
"No I cannot. Do I have to remind you Jacques that our main target was that after a transitory period of twenty-five years, just a generation, citizens of the EU Federation would have identical treatment in all aspects of social security? In the next quarter of a century, really a small period in the history of our nations of origin and in the future life of the Federation, all citizens would speak and write in their own home language and in English, besides other languages they want to learn.
Besides, all of them would have the same opportunities for personal development. We would have one federal migration rule and one, unique frontier police. Our economy would be an efficient mix economy of market, in which the risks receive compensation, but not an egoistic economy in which everyone has to look for their own survival. We both know that most traditional market economies have a per-capita income far of those typical of the social economies of market like ours. Do I have to remind you that social economies of market have recently been identified as feminine societies? Tell me, which of us would be better to lead the execution of this policy?"
"Marlein, how disappointing you sound. I cannot but consider your fragmented exposition—although containing much of our common goals—as deliberately twisting facts. It seems to me no more than an attempt to give a blow beyond the belt. Thought we had become friends, but perhaps in the power game there are no friends."
"Jacques, do not play martyr, you seem to forget who first pissed outside the pot. I did not make any statement on TV. Let us wait for the primaries, and for now, please do not call me anymore."
And so their last personal conversation ended before history took a ride with Jacques and Marlein by the nomination of a third candidate, the Prime Minister of Austria, as First Candidate on the FDC list; a development which soon after proved leaving more chances for the FLS to win.
* * *
To break the silence, Hans Schmidt had started coughing and the German Chancellor slowly turned back to reality. In an attempt to set aside the bitterness of the memories, she now focused on fiancée Amaras.
"Tell me, Fraulein Amaras, what secret prescription have you used to convince my advisor that his future is lying in the Amazon jungle of Brazil with you? I have tried long to convince him to quit his bachelor life, but thereafter I would have preferred keeping him here. Ha ha!"
At this point the Chancellor was smiling unarmed and once again Hans Schmidt made an effort to redirect the conversation, this time away from his fiancée and the relation.
"Madam Chancellor, first prognoses are coming in on my Blackberry. They suggest victory for the Federal Labour Socialist Party, but without a majority. FDC will be second. Surprisingly, favourable results are also foreseen for the Federal Green Party, who will become third. So we will have the first coalition Federal Government. Challenging!"
However, neither Amaras, nor the German Chancellor was willing this time to give in to the diplomat, and the two even started speaking over Hans Schmidt as if he was not in the room.
Fraulein Amaras, smiling contentedly, informed Frau Ditch on her first encounter with Hans and the start of the relation. As she explained, some seven months ago, she met Hans in the canteen of the Academic Hospital in Berlin, where he had visited his ill father and she had presented the outcome of the testing of new herbal medicines to medical students. According to Amaras, Hans had walked over to her and requested her company. As she later understood, he had been advised by the medical doctor of his father to contact Amaras over alternative medicines to slowdown Alzheimer. Anyway, he had been very original in his approach.
Bowing like a knight, he had added, "Madam, we have met before, or more accurate, I have met you on my computer screen in YouTube.
And truth be spoken, reality defeats the screen of my PC. Would you be willing to share some of your precious time with me, a humble diplomat? Can I offer you a coffee? It is about my father, if that does not scare you off, but perhaps also a little about me, if I am lucky."
And while Amaras and Hans were walking towards a table in the canteen, Hans suddenly remarked, "Irresistible of Givengy. I love the smell."
"Correct, how come you recognize women perfume on brand from a distance?"
"Madame, I shall tell you my secret. I have passed many waiting hours—in airports and on boring Saturday afternoons in Berlin—testing perfumes in glamorous stores and whether I like it or not, I have become an expert. And now my nose can identify the precise perfume being used by a lady walking at a distance of up to two meters from where I am." Amaras was still laughing at the memory and in reaction the Chancellor cried out, "How sweet! Not a single hair on my head would have imagined that my bibliophile advisor could be so charming. So, you had coffee with him and he ended up leaving the service to go on adventure with you in the Amazon forest"
"No, we talked a lot over the problems of his father and alternative medicines and over my research. But three days later, his father died.
My pharmaceutical suggestions were too little and too late. It was very painful for all of us, but of course mostly for Hans."
"I know, Amaras. It is a sad story. And as far as I was informed, Hans had done all he could to make life more bearable for his father. Excuse me to insist, but after the failed prescriptions, how come Hans still decided to follow you up into the Amazon tropical forest?"
"The most shocking was the fact that his father had lost all memory. This was already the case when Hans and I met. His father could not recognize his only son and it was not possible to introduce me to him," said Amaras.
Meanwhile Hans Schmidt sat humble and silent on the sofa, Marlein Ditch was stroking the back of one hand with the fingers of the other and Amaras Gusto took a deep breath before she corrected the Chancellor.
"May I take the freedom to precise on one of your question, Madam Chancellor? To be accurate, I am not a Brazilian, I am Peruvian, and the choice to go to Brazil was not mine in the first place. I am just following my partner."
With his eyes on his Blackberry, Hans Schmidt made a new attempt to divert the conversation between the two ladies by observing, "I have no doubt that our children and grandchildren will remember this day as the most important day of the history of modern Europe. The traditional democratic deficit of the EU-27 was buried today in the Federation. Perhaps my children will not understand what we are talking about, if I tell them the stories of the flop of the EU Constitution of 2004, or the frustrations over the Euro crisis starting in 2008."
"Congratulations, dear advisor, but let us stick to the purpose of your visit. Why leave the service, why go to the middle of nowhere, why force this talented young lady to follow you? What education will your children have?" the Chancellor insisted.
As their eyes crossed, Hans Schmidt remembered how irritated he used to feel when the Chancellor kept asking things over his private life.
The last time was during the flight back from Madrid on the day of the parliamentary vote on the draft constitution for the Federation.
"Madam Chancellor, remember that we often spoke about the fact that European citizens would have to adjust to the new circumstances of globalization? I mean, the industrial shift to the East creating structural loss of jobs in the West, global warming and climate change, the end of one superpower policing the world and administrating scant, raw materials, emerging superpowers in Asia influencing international politics for peace and security, etc. We agreed that Europeans would have to change much of their life style to adjust to the new, emerging world. I mean: not only their overconsumption and individualistic materialism in comparison to the rest of the world, but also their values and behaviours including revaluing family life, leisure time, and decompressing social relations. And last but not least we should actively reduce our so-called footprint to save the earth for future generations."
"I remember Hans, but do not tell me that you are going to pioneer on this necessary new lifestyle by going to the Amazon forest. What a waste of talent."
"Mrs. Chancellor, this is exactly what I am going to do. For your knowledge, we will not be living in the jungle; we will be working in Manaus, in the University of the Amazonas. As the Amazon jungle represents over half of the planet's remaining rainforest and it comprises the largest and most species-rich tract of tropical rainforest in the world, Amaras and I are proud that we will be able to contribute, be it humble, in its conservation. Besides, I will be writing as a correspondent for _Berliner Zeitung_ , so you may follow our practices.
My articles will suggest ways in which Germans can contribute in their daily life to the conservation of the lungs of our planet."
Placing three fingers of a hand under her chin, the Chancellor held,
"Dear advisor, everyone according to his merits. I am proud of you and so would your late father have been. Wish both of you success with your idealism and hope it does not turn out to have been illusionism."
* * *
Back home in his apartment, Hans and Amaras prepared themselves for the final outcome of the federal elections on TV. They made themselves comfortable on an old, green, sit-sleep sofa, one of the few things that had not been packed that morning by the movers. The sofa had been a present of the mother of Hans when he left home for campus. Although Amaras was curious to know why the sofa was not going to Manaus, she learned that speaking of anything related to the mother of Hans was a subject to be avoided in the relation.
The old, analogue television was the other thing that had not been placed in the container for Brazil. For the rest the living room was completely empty, showing only the difference in colour of the wall paint at the places were the many book cupboards had been leaning on.
Sitting close to each other on the sofa with a bottle of red wine, two glasses, and some pretzels in a small plate on a side-table—the third and last thing not packed for Brazil—they were watching the screen with the outcomes of the counting per polling district. One after another the figures came in, and what Amaras and Hans saw made them cling closer in each other's arms as it represented a pleasant surprise.
First of all, the turnout was remarkable large, in particular in the more outsized states of the Federation a majority of eighty-percent of the electorate had cast their votes. Only in Finland and Slovenia, the turnout was more in the range of sixty to sixty-five-percent. The final outcome was outstandingly in line with earlier predictions: Federal Labour-Socialist was leading with 160 seats, Federal Conservative Democrats had won 118 seats, and the Greens had managed to gather an astonishing 82 seats. None of the other participating parties had managed to pass the thresholds.
Moving ever closer to Hans, Amaras inquired, "Darling, forgive me for saying, but I heard you telling the Chancellor today that you had voted for the Conservative Democrats, correct? I thought you favoured the Greens."
While caressing her nose tip with his finger Hans admitted, "Yes, I voted green. My lovely flat nose, this afternoon was perhaps my last diplomatic meeting. From now on, it will be the truth and nothing else than the truth."
"Why lie to the Chancellor when she was not even running? I was taken by surprise as I clearly noticed some warmth between the two of you. I think she really likes you and, concerning her being out of the federal power play, I feel that you should have played fair."
"You may be right Amaras, but it was difficult, even at my farewell. Perhaps because people consider her distanced and cold, perhaps because of her plain Jane look, perhaps because I never have been open to her, even though my real experience in her neighbourhood had often been the opposite of her image. I think she is far more sensitive than she shows, but one cannot be at ease in her neighbourhood. And when she met her ex in Moscow—by the way she never even hinted at it to me, but the man himself told me the history the same evening—I sensed tangible sadness for the rest of our stay in Russia."
"I had the feeling that she was also quite sad today. And it is probably not because you leave, but because of her being side lined in the federal elections. I can imagine that, after all the energy she has put in the federation."
"Amaras, you are a good observer. It must have hurt her that she also lost the friendship with Perrier. Even I felt down at her explanation this afternoon."
"Look Hans, the future Premier of the European Federation will speak to the European citizens," Amaras said.
Both were now staring at the television on which professor Jan-Hein Escalleno, First Candidate of the Federal Labour-Socialist (FLS) party, appeared.
Jan-Hein Escalleno, an old member of the Italian socialists, counting sixty-nine years, was swaying gently from side to side as he approached the table at the podium. He was selected in primaries in the FLS as a compromise since no-one in the centre-left family of parties forming the FLS truly believed that victory in the first federal elections would move from the brave initiators in the FDC to the back benchers and even slackers in the FLS.
Don Escalleno was a remarkable person as he was born in Madrid out of the marriage between a Dutch opera singer and an Italian bank clerk, and he had past his youth in three, different European countries before he studied ethics in Florence.
The emeritus professor of ethics, looking overwhelmed, received a warm applause. He was a respected old man who had accumulated experience in Strasbourg since the birth of the first Parliament in 1979. And for a short period in between, Jan-Hein Escalleno had also been minister of education and culture in Rome. Would his multicultural experience be enough to guide the Federal ship to calmer waters?
"Darling, do you see what I see? Marlein Ditch, German Chancellor, will react to Premier Escalleno's speech via a video-conference."
"Yes, and also the French President, I mean ex-President Perrier."
The TV presenter announced that the initiators of the Federation were going to be interviewed on the historical event of today, but first the citizens of the Federation were invited to listen to the words of the first elected Premier of the European Federation.
When the emotions of Professor Escalleno and many leaders of the centre-left parties in the member-states-who either joined the podium or were reacting via video-conference-ebbed away, there was silence as the official federation anthem, taken from Mozart, was played.
Thereafter the campaign song of the Federal Labour Socialists was played, not in the least, because the script was written by Escalleno himself. In combination with a dynamic video clip, it had become a hit on YouTube, TV and radio across all nine federal states as it was sung in ten languages.
The song read: _Every state where government intervene to correct market failures; every land where justice is done to the fortunate and the less fortunate alike; every place where government considers solidarity part of daily life; any state where caring for the earth and its environment is common practise, there is my fatherland, there is where I want to live, and that is the EF_.
And the refrain: _There is my fatherland, there is where I want to live, and that is the EF lead by the FLS_.
After thanking the European citizens for the trust in him and his party, and after promising to solve the economic problems of the young Federation, the envisaged Premier of the European Federation, launched a call to the two other parties to consider coalition, as he "thought that a first federal government should have the broadest support possible of the European citizens." A big applause erupted as the camera moved away and now Jacques Perrier in a dark suit appeared on the screen.
The TV presenter requested, "Mister Perrier, the future Premier of the first federal government has invited your party to join in a coalition government. What is your reaction? And maybe you could reflect on the outcomes of the first federal elections, as your party has lost."
"Concerning FDC joining a FLS federal government, I think that for the first parliament of the Federation, the FDC should be in the opposition. The Federation is in a process of building up and we will collaborate from our points of view. I think that the Federation is not in crisis and so it does not need a concentration government. On the other hand, the provisional constitution clarifies the agenda of the Federation, to which every government should adjust. My heartfelt congratulations to Professor Escalleno and I wish him success for the good of the Federation. As to the second question, I dare to say that FDC has lost because we had a bad campaign, almost defensive instead of continuing the good start the German Chancellor and I made. In general the public is short of memory, but we should have reminded them of the pioneers work done. And of course there was the so-called incumbent factor, which also caused me now being under resignation."
As the cameras in Paris gave way to cameras in Berlin, Marlein Ditch appeared on the screen, dressed in a light blue, two-piece looking rather at ease.
The presenter requested, "Madame Chancellor, how do you feel at the results of this first federal election? Contrary to what seemed logic, the party of the makers of the Federation has lost. Do you have any explanation for this?"
"I have a slightly different understanding of reality than my French colleague. Perhaps the loss of our party has been a punishment of the electorate. A punishment we deserve. We have spent valuable energy and resources on infighting to prepare the candidate list. As we have not been able to offer an image of stability in our federal party, it has clearly been impossible to convince enough voters that we would stabilize the federation, and voters are free in their choice. Regrets, I may have a few but, then again, I wish Jan-Hein Escalleno great acumen to create the prosperous future the citizens of the federation are dreaming of."
At the last words of the Chancellor, an emotional Amaras screamed,
"Oh Hans please, it is so unfair! She sounded very near to tears."
"Come on Amaras, pull yourself together; there is nothing we can do about it. Nothing else than to accept the outcome; and Marlein Ditch was not even a candidate."
As tears were now freely running over Amaras cheeks, Hans Schmidt was trying to comfort her, putting one hand in her neck and the other on her chin while closing in to her face and whispering.
"Please I cannot see you crying, Fraulein Ditch has lost, it is sad but nothing can change that. You have no idea of how much I had wished my mother had not told my father ever that he was suffering from Alzheimer, but she did instantaneously. That day I felt most pain because the truth was a one-way situation, no return and no escape. And then, as my father was in the first stage of the illness, he could fully understand the meaning and the consequences of what my mother had just told him and he knew, or better, all three of us knew that there was no way back. I feel the same now, Amaras. The pioneers have lost and that is it. No way back. Sad, very sad, so Amaras, I beg you; please don't cry!"
### Fifteen
### Celebrating the fifth anniversary of the Federation
It was the year 2018, and 10:30 in the morning of an ordinary Thursday in Hotel Negresco in Nice, Cote d'Azur. The people moving up and down in the English pub, furnished in old brown and olive green, were waiters and waitresses busy setting tables and refilling the bar and the glass vitrines of the counter with drinks and snacks. Indeed all employees were focused on the arrival of VIP guests from all over Europe to celebrate the fifth anniversary of the European Federation.
An early arrived was sitting at the extreme of the bar of the pub, reading at the same time _Le Figaro_ and _Nice-Matin_ at the lights of a Victorian-style, green lamp. He was the sole customer, a man in progressive glasses, in black frame original from Hermenegildo Zegna, which elegantly contrasted with his white hair and beard. He was dressed in a deep green checker jacket on which one could recognize the shield of the Golf Club of Calcutta, and his olive green shirt not only contrasted with a black butterfly, but also with Levy Strauss jeans and sporty Clark shoes.
After five years of practically having abandoned public life and after having aged at a speed twice as fast as normal, and due to the effect of hiding behind thick glasses, only the person who was surveying him discretely from the entrance, his uniformed bodyguard, was able to recognize him. But as the readers may imagine, the early arrived was no one less than the ex-President de la Republique, Monsieur Perrier Jr. and son of the late coffee-retailer of Bayonne.
Wrapped in a soft, musical background with a band playing the theme of the film, _Gone with the Wind_ , Perrier was calmly reading when suddenly two, oriental girls of four and six, rushed in, pursuing a small, brown dog. The laughter and races of the girls was complemented with that of the two waitresses who were also trying to capture the dog in order to attach the lace and collier to his neck.
Finally, when the dog was under control, a sweaty and breathless lady entered the English Pub. She had her dark blonde hair carelessly tied up with a pin and was dressed in a flowered, pink and blue blouse, hanging baggy over tight black trousers. Notwithstanding her youthful dressing style and the young age of the two girls calling her mom, her wrinkled forehead and fallen neck witnessed that she apparently was in her second fifties.
With all the noise produced by the small event, Perrier had diverted his eyes from the newspapers and was amusingly observing the development of the capture of the dog. Looking at the lady, Perrier had a strong feeling of having met her before. So, while listening to the conversation between the woman and her girls, he had a closer look at her and could not believe what he was seeing. Here she was, an old friend of him, Frau Ditch, the "German Spinster", best known as the ex-German Chancellor.
Consequently, when the group of three, accompanied by a German bodyguard were near to leave the Pub, he screamed, "Excuse me, you are Marlein Ditch, are you not?"
"Yes" she said turning around. At that very moment the bodyguard of Marlein rushed to Perrier and showing his identification as a German police officer requested him to identify himself.
While showing his ID to the German police, Perrier exclaimed in loud voice to Marlein, "I am Perrier, the former president of France." And he added while walking over to her, "Haven't seen you for a hundred years."
"Jacques, how pleasant is the surprise! Although, I had somewhat expected to see you tonight, as we should all be here celebrating the Federation, meeting you just now is nice. How are you doing?"
"I am okay, but clearly less than you. You look happy, mommy Marlein! Would you be able to join me for a cup of coffee, to catch up?"
"I would love to, Jacques, but first let me introduce you to my two daughters before they leave to the garden with the nanny. Girls...this is Jacques Perrier, mommy's best friend."
"Daddy, daddy," shouted the smallest of the two dark-skinned children while she immediately grasped the leg of Jacques, who was still rather amused over the total, changed outlook of Marlein.
"I guess your daddy would look far more Indian than me," replied Jacques looking at Marlein with smiling eyes.
"You may be right, Jacques, I really do not know their parents, but I'm happy to introduce my two girls, Laksmi and Shanti, six and three. As they were without parents in Penang, in Malaysia, and the orphanage accepted me to take care of them, we are happy the three of us, building a nice family. Frankly, I myself am disproportionately satisfied," Marlein replied.
Perrier had now grasped the hand of Marlein. "Dear friend, I guess you are also in the broadcasting of tonight, I mean the Euro-News special, in celebration of five-year anniversary of the European Federation? It is live broadcasting and I think that we will perform together. Just minutes ago, I was thinking of the press conference we had here seven years ago. You remember the proxy-ETA attack coming from the ceiling? What a day. Ha-ha. We sweat blood for some minutes."
"Yes," exclaimed Marlein. "I remember you sweating, not me. I remained calm but you did not, do you recall? As to the Euro-News special of tonight, I have also been invited. I agree that we should speak with one voice Jacques. And we can speak from our hearts, since both of us have left the political arena. I am now living in Dresden with my two kids."
"You have left Berlin for Dresden?"
"Oh, yes, after we lost the general elections to the Federation and in six months time I also lost the Bundestag elections in Germany—you may recall—I resigned from all my political compromises and decided to go back to my beloved Dresden. You know, that is where I did my university studies and lost my innocence. Perhaps you are not aware...but I married young in Dresden, although sadly my husband prematurely died."
"You Marlein, married?" Jacques interjected.
"I had no children with him, and after the, let us say, lukewarm experience in marriage in Dresden I have never felt the urge to repeat it. But surprisingly, the kid part came back after I left politics, so I went for them and really they are a godsend for me. Of course I knew that you had also lost your elections in France. I should have written to you, but finally I did not. Sorry. But Jacques..., how is your life now?"
"These days, my life is horribly quiet. To the extent that I think that so much inaction may kill me in little time. I think that I have aged fast in the last years for the lack of using my adrenaline. It makes me nervous during the day and at night produces me nightmares."
"To tell the truth, Jacques, I would not have been able to recognize you. You look very elegant, but you look like another person, someone of the world of intellectuals, with your glasses, your new look...frankly, it suits you extremely well."
"Marlein, as you said before, we will be free to speak from our hearts tonight. So what will we speak about? I think that whatever questions are put before us, we should be absolutely truthful and the European citizens should know the background of the economic decisions we have made to solve the Euro crisis and to construct the federation."
"How time may change our perspectives?" exclaimed Marlein rising the cup of coffee.
After a meditative sip she continued, "Although I am extremely proud of having promoted the European Federation with you Jacques, I am no longer convinced of the correctness of the economic policies of my government in the pre-federation days in Germany.
We blindly followed the ideas of some neo-liberal economists of those days, who today, six years later, are under strong criticism.
Certainly, some of them are now in full discredit while others are considered pure malefactors. In particular top executives of Central Banks and even some Nobel Prizes of those days should today hide in shame. They made us to believe during three decades that what they preached, the goodness of the total freedom of markets, was the utter truth. And finally we have become aware that the whole bunch had been captured by Wall Street."
"But Marlein, may I deduce from your words that you have now become a Keynesian?"
"Not exactly, but today I am more flexible than in those days. Even more, I have stopped worshipping the central idea in Germany of the utter relevance of price stability, overseeing any other economic target, for instance job-creation."
"So Marlein, you are now finally on my field."
"Could be, but for me the importance of our cooperation in those days, was first and foremost the establishment of a selective European Federation. Something, which as we can see today, has been far more relevant than interested disputes over monetary stability, financed by private banks, and backed by polluted academicians."
"Marlein, although I would not say this ever in public, you and I perfectly knew that most of our fellows of those days were mainstreamers and followers. As it is said, those who move do not appear in the photo regardless of if they are from the political right or left. As far as you and I were not elected in the Federation, nor in our own national polls, this is for me a proof that with our initiative for Federation, we moved out of the box; we abandoned mainstream."
"Yes Jacques, I have continued moving out of the box, to the extent that I am now actively promoting a multicultural Europe.
Would you believe that? But ever since I went to Penang to collect my girls and I was confronted with the relaxed multicultural and multi-religious character of the Penang society, I have converted in promoting far more openness towards other cultures and religions in Europe. In Penang I have walked in streets with mosques, Christian churches, a synagogue, and a number of Hindu temples, and I felt embarrassed over my remarks on the subject years before, even though my remarks were actually provoked by the then rising populist parties."
The conversation between Marlein and Jacques continued for another half an hour till Marlein remembered that she had promised her children to take them to the attractions park at Biot before lunch. As the friendship had been restored, the two amiably said goodbye.
They would meet again at six that evening in the studio of France2 in Nice, where a live debate between the two initiators of the European Federation, and with participation of the federal Premier and two Nobel Laureates in economics, would be broadcasted.
* * *
At five to six, Marlein arrived at the TV building where she was received by the officials and taken to the broadcasting studio to be introduced to the other guests: Escalleno, Perrier, and the two economists Ackerman and Burman.
The guests were sitting around an oval glass table, microphones attached to their collars, and a glass of orange juice or water in front of them. The bottle of champagne in the silver bucket was to be opened for the toast just at the end of the program.
As a starter, the audience at home was watching a compilation of images of the past seventy years of the European unification project, arranged mainly around issues and not so much in sequence of time.
From the "Congress of Europe" meeting in The Hague in May 1948, reporters quickly mentioned the 1951 European Community for Coal and Steel, to jump to the Treaty of Rome in 1957, followed by the Maastricht agreement in 1992 which resulted in the introduction of the Euro coins and notes in 2002. Thereafter the focus was on the celebrations of the 2004-2007 omnibus enlargements, turning into the desperate Euro crisis, but leading up to the successful establishment of the European Federation in 2013. Subsequent the arrangement of positive union developments were contrasted with images of setbacks such as the no-vote in 2005 of the French and Dutch populations on the Referendum on the Constitution, and images of the bleak days of the Balkan War in the 1990s combined with images of pathetic discussions, over the need and legitimacy of an invasion in Iraq in 2003, to destroy non-existing weapons of mass destruction.
At the end of the compilation, the studio debate started with first remarks of the reporter directed to Jan-Hein Escalleno.
"Premier Escalleno, congratulations! How does it feel to have headed the European Federation in its first, successful, five years?"
"Would you allow me to transfer your congratulations for the success of the Federation to Marlein Ditch and Jacques Perrier? Without their brave and consistent efforts, we would perhaps today have remained on a ship of twenty-seven captains, totally out of course. That situation was putting at risk not only economies in Europe but also in the rest of the world. At the end of the first decade of the 21st Century, the Euro crisis and the huge externalities on a world scale had put us on a steep wounding route to deep recession and we should thank Marlein and Jacques for having turned the boat. Madame... Frau Ditch, Monsieur Perrier,...chapeau!"
At his last words, the audience in the studio, including the cameramen and the TV presenter, started applauding exhaustively.
Consequently, the program presenter lost reserve as he minutes later addressed Perrier.
"My admired and respected former president of France, Mr. Perrier, could you explain when and why you felt the inspiration to propose the creation of a European federation?
"Although there had been arguments for the formation of a federation already in the early 1970s, it was the financial crisis of 2008—mainly hitting the West, I mean Europe, US, and Japan—which gave us the opportunity to breakthrough. All of a sudden, we were confronted not only with high youth unemployment, but also with an economic decadence and a political stalemate. The EU-27 was incapable to take any decision and a number of Euro zone countries were putting the monetary union at risk. And this while we were losing the train of economic progress, and the economic gravity centre of the world was moving to Asia. Not to mention the fact that even before the Balkan war, the then EU-15 had little role in international politics except backing-or-not of the Americans in their foreign policies. It is against this background that Marlein and I launched the proposal for a selective Federation. It had to be selective since some EU members were not interested while others in the Euro zone simply did not pass the test of economic homogeneity."
A new round of applause followed the rationalization of Perrier, while cameras were turning towards the Nobel Laureate Burman, and the presenter requested, "Mister Burman, although the idea of federating could in principle be acceptable, did it not contain a great risk of creating a multicultural-multilingual monster-state, more inefficient than the old EU-27?"
Burman, a man already far in his fifties, first took a sip from his glass, then placed his fingertips of both hands against each other, and looked around as if he was trying to gain time before finally answering, "As it has been remarked at many occasions by the promoters, the federation would surely achieve huge economies of scale, mainly in relation with the external and international functions of the federation. I mean defence, international cooperation, economic and commerce policy and external representation. And as an external observer, I have to say that these assumed economies of scale have today become real even ahead of schedule."
"And what about the improvement of economic governance" inquired the reporter now watching Ackerman, the other economist, and a man more-or-less of the same age as Burman.
"Certainly," said Ackerman, specialist in dynamic economics, while looking at Perrier and Ditch, "when the two of you initiated the process, the situation of the Euro zone was really pathetic, as a consequence of the very deficient architecture of the Euro-system in the Maastricht Treaty. But you had the courage to initiate a correction, which had to be selective because many Euro zone members were totally paralyzed by the financial crisis, others could not fulfil healthy debt criteria, and some others did not want to transfer more sovereignty to Brussels. So, the two of you took the right decision: to move forward with a group of pioneers, while promising the rest that they would not be abandoned to their own survival."
Moving microphone and cameras in the direction of Marlein Ditch, the program presenter requested, "But Madame, don't you believe it highly unfair that many countries that had come a long way with the rest by belonging to the Euro-system, finally remained excluded from the federation? I am referring to Ireland, Portugal, and Greece."
At this point, Marlein Ditch arched her brows as if she was going to say something very original, before she remarked "In those days, the exclusion of these countries was motivated by the heavy load of their public debts and the difficulties of some of their banks. We believed that the inclusion of these three countries would have been very negative for the federation as we already counted with the burdens of Spain and Italy, countries with a joint population of more than 100-million people. Indeed, we felt that it was an unaffordable burden for the young federation to take responsibility for such a big debt for so scant population in these three small countries. On the other hand, the audience should remember that it was also a matter of the governments of these three countries themselves who acted in such a way that their countries had to be excluded. Come to think of it, with the experience we have now, perhaps the problem could have been solved in those days by including the three of them in the federation and paying their debts, if necessary with new printed Euros. Such an alternative approach, although additionally increasing the rate of inflation in the first two or three years, would have solved two problems: first, the rescue of these countries and second, the rebalancing of the Euro. Let me remind you all that at the moment of its birth, the Euro quoted at a rate of Euro-Dollar 1:1.17 and progressed to quotations of 1:1.50 at the beginning of the financial crisis in 2008. Of course, the overvaluation of the Euro in those days was not good for the European exports as it was wrong to keep the interest rates in the Euro zone so low for so long. I dare to say now that our Euro policy then resulted in an inefficient allocation of our investments in those years.
Similarly, I dare to say that we, the Germans, exaggerated a lot with our anti-inflationary paranoia. I feel even now that I have to apologise for this. Probably it was a matter of weighing between two bad things, the unemployment and the inflation, and not so much as we did, to stick at all costs to an inflation of maximal two-percent. I think that this was a real mistake since modern monetary controls of Central Banks are much better than those in times of the Republic of Weimar. On the other hand, to force populations to fully pay for the mistakes of their politicians, as we did with Greece, Ireland, and Portugal, was neither fair nor intelligent. As I have learned from history—I am referring to the decisions back then in Versailles, forcing huge transfers against Germany—creditors should not strangle the economies of debtors because this finally works against the creditors own interest."
The outspoken remarks of Marlein Ditch were welcomed with another exhaustive applause, while the TV presenter approached Burman by asking, "Monsieur le Professeur, and what about the countries that were left out of the Federation but kept the Euro as their currency... do they have a better economic perspective now than let us say the new comers of 2004 who did not accede to the Euro?"
"Certainly, according to the theory of economic policy, to have more instruments to correct a negative economic situation is better than to have less. Their decision to keep the Euro without being able to participate in monetary policy decisions was the best they could do under the circumstances."
For now the audience was presented with a new compilation, and this time the snapshots were about the past 5 years of the European Federation and its positive achievements for its citizens. The camera was also portraying successful foreign policy of the European Federation, starting with the Federal Embassy in Beijing, were viewers could see a variety of promotional materials and actions directed to the Chinese middle classes to encourage not only their touristic participation in cultural highlights in the nine states of the Federation, but also to raise awareness in China concerning advanced high-tech engineering, sophisticated water management and renewable energy capabilities in the European Federation.
"Last question to all of you," exclaimed the TV presenter. "Taking into account the phenomenon of long-lasting, high, youth unemployment in many countries in Europe and recalling the rioting in many capitals at the start of the Federation, have anyone of you any idea of what could be done to offer a better future to our youth?" The guests were looking slightly hesitant at each other when Burman dared to give his view.
"I know for sure that high rates of youth unemployment, wherever they occur, will coincide with the existence of discrimination in the labor markets. The context will be one in which you will find a submarket of indefinite contracts for senior workers while the young workers will have access only to temporal and part-time jobs.
Logically, when in such a context a deep economic crisis arrives, the first to be expelled from jobs will be the young workers.
Consequently, governments should first and foremost eliminate the current dualism in the labor market to improve efficiency and the expectations of the youth."
While Burman was talking three of the four remaining guests—Escalleno, Ditch, and Perrier—were shaking their heads showing profound disapproval. Consequently, the TV presenter turned to them and invited Escalleno for explanation.
"I fully disagree with Professor Burman. If we were to unify labor contracting by making all contracts only time-bound and giving employers the right to easily hire and fire, something typically requested by private employers, we would be moving backwards in history from social democracy towards traditional unfair capitalism", Escalleno clarified.
"Wrong!" interrupted Ackerman, "I think that preventing injustice by distorting markets is not the best solution. Indeed, the dualistic employment contracting in the labor market over past decades in Europe, has resulted in high unemployment rates of young workers and that is precisely a derivative of the partial dismantling of the protection of workers, by putting the stress of the adjustment only on the youth. Protecting just one segment of workers, the senior workers, is perhaps the worst of solutions. Or you protect all workers, which would be absurd from the perspective of an economy of market, or you do not protect any one, which would leave workers to their own survival in front of abusive entrepreneurs. As far as these two situations are undesirable, there must be a point of a balanced protection for all, to be defined by democratic government and without internal discriminations in markets."
"Gentlemen please, what are we talking about?" was the reaction of a slightly irritated Marlein. "We are here reflecting on the European Federation at its fifth birthday, and any of us will have to agree that in the Federation youth unemployment rates have gone down and are well under control. We have moved from figures of up to forty-percent of unemployment under youngsters—I am thinking of the case of Spain—to current maximum levels of just ten percent. And if this process has implied higher rates of unemployment in the segment of workers over fifty-five, we should also not overlook the fact that these workers are far less productive than the younger. Thanks to creative solutions initiated by Premier Escalleno, such as for instance copying good labor practices from Holland—I mean their job sharing, more flexible working hours, and more part-time jobs for older workers—Federal member states have been able to save the future of our youth.
This is what we mark today!" At the last words of Marlein Ditch the TV presenter requested his guests to raise their glasses for a toast on the economic and socio-political success of the European Federation. It was time to celebrate.
* * *
It is not enough to say that the festivity decorations along the Promenade des Anglais in Nice were abundant. It seemed as if for the celebrations of the fifth anniversary of the European Federation, which was to start at 9:00 pm in the ballroom of hotel Negresco, all decorative imagination in all member states had been tapped and no costs had been spared. The long road along the beautiful bay was meandering down to Villefranche-sur-Mer in glittering stars caused by the thousands of white and bright, little party lights at two levels, including directly at the waterfront, while in the bay itself hundreds of boats and yachts were illuminated with colorful beams. All was to bring back memories of the first announcement of the federation initiative by Germany and France in a more buoyant way, so this time the ballroom itself had been overtly decorated with artifacts and images of almost seventy years of the EU project, leading up to its centre peace, the European Federation. The exclusive invitations for the optimistic party had this time been distributed not only in wider Europe, but also in Asia, Australia, Africa and South and North America. Royalty of federal member states, ministers of the federal cabinet, ministers of member states, chiefs of the European parties, private sector representatives, top executives of the main mass media, and representatives of societal organizations and of academic institutions, had all been invited to give a _cte de presence_ at the commemoration.
By 9:30 pm the ballroom was, as they say, packed to almost overflowing; at the farthest end there was not a corner empty and elegantly dressed women of all ages were mingling with dark suited man in black tie, all looking rather optimistic. Among the guests, one could also find former premiers and presidents, even old presidents of the European Commission or their widow's such as the Duchess of Algarve, the widow of Bopoulos, who mingled accompanied by her father, an old man who had kept the brisk manners of his time as a Swiss banker during the Second World War. Contrary to her husband, Alexandra, the wife of former French President Perrier, had reserved her beauty as if her aging had stopped one decade before, and even old mother Perrier, now nearly ninety, had dared to dress in sparkling red and yellow silk to be seen. Today, to be European was very worthwhile: they had become first-class citizens governed by a first-class government, although convoyed by the long shadow of increasing China—already the largest economy of the world in GDP-PPP terms—and by rapidly emerging India, a country with no problems of ageing population, contrary to the reality in other leading countries of the globe.
* * *
Everyone began to applaud when, in the company of some Royalty, the Premier and the President of the European Federation entered the small podium at the upper end of the ball room, where also the orchestra cornered. But before any brief toasting speech could take off, the orchestra suddenly started the Turkish March of Mozart and an impressive entrée was made by a man dressed in a white and orange gala-uniform with a white turban on his dark hair and a golden sword and dagger with brilliant stones crossing his chest. All eyes now quickly shifted to observe the extravagant appearance of the man who was announced by the pianist as the Turkish Ambassador to the European Federation... but no one except Alexandra recognized him. Staring at his face with the curled moustache, she murmured "Ibrahim" and at that very moment their eyes crossed.
However, there was one other person in the ballroom who noticed the intensity of the surprising encounter of the two former lovers: the old Mrs. Perrier, who had been standing close to Alexandra. While Alexandra was recovering from the surprise, Ibrahim immediately walked over to her and elegantly kissed her hand.
"Madam Perrier...looking beautiful as ever. What a cheer to see you again and please accept me saying that time has fully respected your magnificence."
"Uh...uh " was the reaction of the old Mrs. Perrier as Ambassador Ibrahim had been speaking loud enough to be heard also by the surrounding ladies. This was the sign for some of them to move forward to introduce themselves to the charming man, who in many ways reminded them either of a younger and modern version of Rudolf Valentino or a slightly older copy of the Australian film star, George Clooney.
Although known for being shy, Mrs. Bopoulos rushed forward and with her high-pitched voice announced, "Sir, may I take the liberty to introduce myself. Benita Bopoulos. My friend, Alexandra is the wife of an ex-president, and so am I." With a broad smile all over her face she continued, "I am the widow of the former president of the European Commission. As you may recall, my husband, Carlos, was in office when negotiations with Turkey to enter into the EU started."
Ibrahim, without giving much attention to Mrs. Bopoulos, slightly bowed before directing his attention to the old man who was accompanying her. Looking at the old man in surprise Ibrahim approached his ears and murmured, "Didn't we meet in Tel Aviv some years ago? I have the recollection of our encounter at the ministry of Foreign Affairs when a delegation of the Turkish President was presenting Turkish protest in the case of the Flotilla, the Israeli attack on boats carrying humanitarian aid to Gaza."
To which the old "Duke" quickly replied, "No, I am sorry. It must have been someone else! My sole relation with the Israeli government was on banking issues. Let us say, that it was on attempts of the Israelis to recover an imagined huge amount of gold deposited by German Jews long ago in a Swiss bank where I worked."
At the last words of the old man, Ibrahim started showing his teeth and while touching the shoulder of the old man he exclaimed, "So you are the Duke of Algarve, known also in Istanbul. What a pleasant surprise. Turkey should have had a banker like you in times of the Ottoman Empire."
Jacques Perrier, who had joined the gathering of women around the Turkish ambassador, frowned at the last remark of Ibrahim. Putting his arm around Alexandra's shoulder, he started pulling her away from the group.
When they were out of hearing he inquired at low voice, "Do you know this man? What a disgusting show-off. I was surprised seeing him kissing your hand. Who is he?"
Without interrupting the waterfall of queries of Jacques, Alexandra first shook off his hand from her shoulders before answering,
"Darling, you have never met him, but you know him. Let us say, he is the man who disappeared in Dubai in the days when I was visiting the city with old classmates, some years ago. He was kidnapped from Sheraton Creek Hotel in Dubai. And as we later learned, he was kidnapped because of an administrative mistake following a request of a friendly nation."
"My love, do not confuse the things. I do not know him as I do not know anything about his kidnapping. And after having listened to him just now, I am not even interested to meet him. Please accompany me to the toast."
At that point, Marlein Ditch approached the couple. The former Chancellor looked rather buoyant, a state of mind she explained to Jacques, which was directly related to an extremely interesting discussion she had just now with the Turkish ambassador. Surely an attractive man, but even more appealing was his insight on the future of multicultural Europe.
"Jacques, you remember me telling you this morning about my new goal in life since I have received my two girls. Well, I found the thoughts of the Turkish ambassador on the topic really refreshing. I have made an appointment with him to search opportunities for our joint cooperation."
"Marlein, if I may be frank, be careful with this man. He has a history of being an unbeatable womanizer."
"Oh, but Jacques," said Marlein, "Mrs. Bopoulos, who had a quick scan on the man at the spot, be it with help of her father, informed us just now that the ambassador is not only unmarried but also he has not been spotted with any woman in the past five years. So I wonder if he..."
Alexandra interrupted, "Really Jacques, I thought you just said that you did not know him. You are confused. Anyway, it is time for our toast on the success of five years European Federation. Let us go for a refill of our glasses."
### _About The Authors_
**Rita Dulci Rahman** is Dutch born in Aruba, Dutch Antilles. In 1970, she won a literacy prize Van der Rijn—prize in the Netherlands—for her debut collection of short stories. Between 1973 and 1979, she published a number of children books and in 1983 she wrote a column for a newspaper in the Netherlands before publishing her first novel in 2001, _Love's Perfumes_. The novel has been published in Dutch (In de Knipscheer) and English (Penguin).
Besides fiction, Rita Dulci Rahman is co-author (together with Jose Miguel Andreu) of a number of non-fiction books on global, socio-economic issues (2001: _Financing Development for Human Security;_ 2004: _Responsible Global Governance; 2005: Overcoming the EU crisis_ ; 2006: _China and India, towards global supremacy?_ and 2009: _Global Democracy for sustaining Global Capitalism_ ). Rita Dulci Rahman is a career diplomat, currently posted as Ambassador of the Kingdom of the Netherlands in the Dominican Republic and for Haiti.
**Jose Miguel Andreu** is a Spaniard born in Bilbao, and professor of macroeconomic at the University of Sevilla. _Love and Death in Saving Europe_ is his first fiction book, but his non-fiction writing dates back to 1970. Between 1980 and 1999, he published a number of books on macroeconomic issues for University students in Spain, of which his book on banking is most famous. From 2001 onward, he has been writing on global, socio-economic issues (together with Rita Dulci Rahman) projecting possible solutions for contemporary global, socio-economic problems (2001: _Financing Development for Human Security;_ 2002: _A federation with Enlargement for European Prosperity;_ 2004: _Responsible Global Governance; 2005: Over-coming the EU crisis_ ; 2006: _China and India, towards global supremacy?_ and 2009: _Global Democracy for sustaining Global Capitalism_ ).
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\section{Introduction}
The state of an $n$-dimensional system is represented by an $n \times n$ density operator, which needs $n^{2}-1$ real independent parameters for its complete specification. Any density operator in its eigenbasis can be represented as $\rho= \sum _{i=1}^{n} p_{i} \hat{P_{i}}$, where $p_{i}= Tr(\rho \hat{P}_{i})$ are the fractional populations. Thus in an eigenbasis, measurement of projection operators $\hat{P_{i}}$ yields $n-1$ independent probabilities corresponding to the diagonal elements of $\rho$. The remaining $n^2-1-(n-1)$ off-diagonal elements can be accessed by expressing $\rho$ in no fewer than $n+1$ bases.
An optimal measurement strategy thus corresponds to a judicious choice of exactly $n+1$ bases, referred to as Mutually Unbiased Bases (MUBs)\cite{Schwing, woot}, such that measurement performed in each of these bases yields unique, non-redundant information about the system.
For a given system, the practical utility of MUBs is dictated by their existence, and their physical realisation in a laboratory. The question of their existence for arbitrary $n$-dimensional systems has been extensively studied, and has been answered in the affirmative when $n$ is a prime or a power of a prime\cite{Ivano, woot}. For such spaces there always exist $n+1$ sets of MUBs which are complete. In particular when $n=2^{d}$ for some positive integer $d$, it is possible to find a partitioning of $d$-qubit Pauli operators into $n+1$ disjoint maximal commuting classes, where each class consists of $n-1$ maximally commuting set of operators \cite{band, zeii}. The corresponding MUBs are the simultaneous eigenbases of the $n+1$ commuting classes. More generally, in the case of prime power dimensions, several approaches are available to construct a complete set of $n+1$ MUBs (e.g. Heisenberg- Weyl group method\cite{band}; using finite field theory \cite{woot, tdurt} ; using generalized angular momentum operators\cite{kibler}). However, the existence of a complete set of MUBs for general finite-dimension Hilbert spaces remains an open question\cite{zan, gra, weig, beng}.
When the $n+1$ sets of MUBs are known to exist, their construction and physical realization has been achieved for very specific applications such as quantum state tomography \cite{fili, fern, adam}, Mean's King problem \cite{eng, ara, hay}; quantum cryptography \cite{bou, lin}, quantum error correction \cite{cal}, entanglement detection \cite{ent}, and quantum coding and discrete Wigner function \cite{gib, bj}. Several experimental techniques to implement the complete set of MUBs in photonic systems have been investigated \cite{lima, adam}.
Some recent works have focussed on generalising the notion of MUBs \cite{amir}. However, for systems for which they are known to exist, construction of optimal measurement operators based on MUBs is critical for their wider applicability. A general construction mechanism of such operators, to our knowledge, is unavailable in the literature. Our focus in this paper is to fill this void. Specifically, we consider spin systems for which MUBs are known to exist, and:
\begin{enumerate}
\item provide a general method to construct optimal measurement operators based on MUBs that are mutually disjoint and maximally commuting;
\item identify the physical observables to which they correspond;
\item demonstrate how they can be physically realised.
\end{enumerate}
In order to concretize ideas we eschew a general exposition for arbitrary systems, and instead consider specific spin systems for which physically realizable, optimal measurement operators based on MUBs are hitherto unavailable. In particular, we construct an orthonormal set of operators based on MUBs for spin-1, spin-3/2 and spin-2 systems. We achieve this based on a construction mechanism that extends the Stern-Gerlach setup for spin-1/2 systems. Such an extension enables us to identify the corresponding physical observables, as with the spin-1/2 case. We demonstrate how the operators can be physically realised for spin-1 and spin-3/2 cases. \emph{From an operational perspective, a key feature of the construction is that it naturally classifies the operators into mutually disjoint subsets, members of which commute enabling simultaneous measurements, resulting in a optimal measurement strategy}. The circumscription of the proposed methodology to spin systems is mainly in the interest of exposition. Examination of the method of construction will reveal that it is general enough to be applicable to higher-order spin systems and to arbitrary non-spin systems of finite dimension for which MUBs are known to exist. \\
\section{Spin-1/2 density matrix}
Our technique is closely related to the case involving a spin-1/2 density matrix. It is instructive first to review this case along with the appropriate definitions. In a finite dimensional Hilbert space $H_{d}$, orthonormal bases $A= \{|a_{0}\rangle, |a_{1}\rangle,\ldots, |a_{d-1}\rangle\}$ and $B=\{|b_{0}\rangle, |b_{1}\rangle,\ldots, |b_{d-1}\rangle\}$ are said to be mutually unbiased if $|\langle a_{i}|b_{j}\rangle|= d^{-1/2}$, for every $i,j= 0,1,\ldots,d-1$.
For a spin-1/2 density matrix parameterized as $\rho=\frac{1}{2}(I_2+\sigma_xp_x+\sigma_yp_y+\sigma_zp_z)$, it is well known that the eigenbases of Pauli operators $\sigma_x, \sigma_y$ and $\sigma_z$ are the MUBs given by,
\begin{align*}
B_{1}&= \{ |0 \rangle, |1 \rangle \},\\
B_{2}&= \left\{ \frac{1}{\sqrt {2}} (|0 \rangle + |1 \rangle ), \frac{1}{\sqrt {2}} (|0 \rangle -|1 \rangle )\right\},\\
B_{3}&= \left\{ \frac{1}{\sqrt {2}} (|0 \rangle + i |1 \rangle ), \frac{1}{\sqrt {2}} (|0 \rangle -i|1 \rangle )\right\},
\end{align*}
where $|0 \rangle= \left(
\begin{array}{c}
1\\
0\\
\end{array}
\right)$ and $|1\rangle= \left(
\begin{array}{c}
0\\
1\\
\end{array}
\right)$.\\ \\
Optimal measurement operators based on $B_i,i=1,2,3$ can be constructed and physically realized with the Stern--Gerlach apparatus. A detailed analysis of Stern--Gerlach experiment and its implications are extensively discussed in the literature \cite{swift, home, tekin} and references therein. In this experiment, a particle with magnetic moment $\vec{\mu}$ passes through the inhomogenous magnetic field $\vec{B}$. The potential energy associated with the particle is $\hat{\mathcal{H}}= - \vec{\mu}. \vec{B}$, where the magnetic moment $\vec{\mu}$ is proportional to spin. Thus when the magnetic field is oriented along $z$- direction, one can measure the expectation value of $\sigma_{z}$. In terms of the projection operators $\hat{P_{1}}$ and ${\hat{P_{2}}}$ from the two eigenvectors of the operator $\sigma_z$, it is easy to see that $\sigma_{z}= \hat{P_{1}}- \hat{P_{2}}.$
The unitary matrix
{\small
\begin{align*}
U = \frac{1}{\sqrt{2}} \left(
\begin{array}{cc}
1 & 1 \\
1 & -1 \\
\end{array}\right),
\end{align*}
}
transforms $B_{1}$ to $B_{2}$. The observable $\sigma_x$ can be measured using the same apparatus if its diagonal (eigen) basis is of the same form as $\sigma_z$, necessitating that $\sigma_{x}= \hat{P'_{1}}-\hat{P'_{2}}$, where $\hat{P'_{i}}, i=1,2$ are the projection operators of $\sigma_x$. Experimentally this can be implemented by applying magnetic field in $x$-direction. In a similar manner from a unitary transformation of $B_1$ to $B_3$ we obtain $\sigma_{y}= \hat{P''_1}- \hat{P''_2}$ for appropriate projection operators, resulting in three measurements that constitute a complete set of parameters characterizing the spin-1/2 density matrix.
A key observation which we profitably exploit in the sequel is that the Pauli operators are linear combinations of projection matrices constructed from different basis vectors spanning a two-dimensional Hilbert space, related through unitary transformations that relate the basis sets of the MUBs.
\section{Spin-1 density matrix}
Simultaneous measurement of a complete set of commuting operators is equivalent to the measurement of a single nondegenerate operator by means of a maximal or complete quantum test \cite{peres}. In some cases, generalization of Stern- Gerlach experiment for spin \textgreater 1/2 is possible by using electric multipole fields along with multipole magnetic fields \cite{lamb}. Measurements of spin-1 systems require an electric quadrupole field in addition to a dipole magnetic one \cite{swift}.
To perform such measurements one requires four observables whose eigenstates are mutually unbiased; this, however, is not possible for spin components. Thus one cannot easily generalize the spin-1/2 Stern-Gerlach experiment as more number of parameters are needed.
A spin-1 density matrix $\rho$ is characterized by eight independent parameters, and can be expanded using eight orthonormal (excluding identity) operators in infinitely many ways. Extending the program used for the spin-1/2 case requires a representation of the $3 \times 3$ density matrix $\rho$ in a matrix basis that mimics the role played by the Pauli operators. Since the natural choice for spin-$j$ Hamiltonian requires a mutlipole expansion, we choose the spherical tensor representation of the spin density matrix due to Fano \cite{fano}. The density matrix for any spin-$j$ system is given by, $\rho= \sum_{k,q} t^{k}_{q} {\tau^{k}_{q}}^{\dagger}$ where the irreducible spherical tensors $\tau^{k}_{q}$s are the $k^{th}$ degree polynomials constructed out of spin operators, $\vec{J}= (J_{x}, J_{y}, J_{z})$(See Appendix for the detailed description of the representation). For a spin-1/2 system, $\sigma_{z}= \tau^{1}_{0}$. As with SU(3) generators (for e.g. generalised Gell-Mann matrices), the spherical tensor operators for spin-1 density matrix consist of two diagonal matrices $\tau^1_0$ and $\tau^2_0$ which play the role of the diagonal $\sigma_z$.
In summary, optimal measurement of a spin-1 system can be achieved by an MUB consisting of four basis sets, each of which contains two commuting operators constructed using three projection operators.
\subsection{Construction of maximally commuting orthogonal operators}
From the discussion above, and guided by the fact that there are two diagonal matrices amongst the spherical tensors, in order to extend the technique from the spin-1/2 case, we construct an orthonormal basis matrix set consisting of four sets of operators each containing two commuting operators, which enables simultaneous measurement using a single experimental setup.
Analogous to the spin-1/2 case where the Pauli operators $\sigma_x, \sigma_y$ and $\sigma_z$ are linear combinations of the projection operators, we define eight operators, comprising an orthonormal set, as linear combinations of the projection operators arising from the MUB. The coefficients of the linear combinations are chosen in a manner that ensures that the eight operators constitute the requisite maximally commuting orthogonal set.
For a $3 \times 3$ spin-1 density matrix, from each of the four basis sets comprising an MUB $\{\{\psi_i\},\{\phi_j\}, \{\theta_k\}, \{\xi_l\}, i,j,k,l= 1, 2, 3\}$, three projection operators can be constructed. In the canonical $|jm\rangle$ basis $\{\psi_1,\psi_2,\psi_3\}$ with projection operators $\hat{P}_i,i= 1, 2 , 3$, define first the commuting operators $\hat{\alpha_{1}}= \sum_{i} r_{i} \hat{P_{i}}$ and $\hat{\alpha_{2}}= \sum_{i} s_{i} \hat{P_{i}}$ for coefficient vectors $\vec{r}=(r_1,r_2,r_3)$ and $\vec{s}=(s_1,s_2,s_3)$. The two operators are orthogonal if $\vec{r}.\vec{s}=\sum_{i} r_{i}s_{i}= 0$, since
\begin{align*}
Tr(\hat{\alpha}_1\hat{\alpha}_2) &=
\sum_{i,j}r_{i} s_{j} Tr(\hat{P}_{i} \hat{P}_{j}) \\
&=\sum_{i,j} r_{i}s_{j} \delta_{ij}
=\sum_{i} r_{i}s_{i}.
\end{align*}
Furthermore, for the operators to be traceless, we require $\sum \limits_{i}r_{i}= \sum \limits_{i}s_{i}=0.$
Guided by the spin-1/2 case, we demand that the next set of operators has the same form as that of angular momentum basis $|jm \rangle $. That is, we impose the condition that $\hat{\alpha}_3$ and $\hat{\alpha}_4$ be defined with projection operators constructed with $\{\phi_i,i=1,2,3\}$ using the same coefficient vectors $\vec{r}$ and $\vec{s}$. Consequently, for a set $\hat{P}'_i,i=1,2,3$ of projection operators obtained from a second basis $\{\phi_1,\phi_2,\phi_3\}$, we define $\hat{\alpha_{3}}= \sum_{i} r_{i} \hat{P}'_{i}$ and $\hat{\alpha_{4}}= \sum_{i} s_{i} \hat{P'}_{i}$. Orthogonality requirement amongst the $\hat{\alpha}_i$ implies that the for a unitary $U$,
\begin{align*}
Tr\big(\sum_{i} r_{i} \hat{P}_{i} \sum_{j} &r_{j} \hat{P}'_j\big)=
Tr\big(\sum_{i,j} r_{i} r_{j}( \hat{P}_{i} U \hat{P}_{j} U^{\dagger}\big) \\
&=Tr\big(\sum_{i,j} r_{i} r_{j}(|\psi_{i} \rangle \langle \psi_{i}| U |\psi_{j} \rangle \langle \psi_{j} | U^{\dagger}\big) \\
&=\sum_{i,j} r_{i} r_{j} u_{ij} u^{*}_{ij}\\
&=\sum_{i,j} r_{i} r_{j} \langle \psi_{i}|\phi_{j} \rangle \langle \phi_{i}|\psi_{j} \rangle=0 ,
\end{align*}
and thus $\sum_{i,j} r_{i} r_{j}=0$. In similar fashion we have $\sum_{i,j} s_{i} s_{j} =0$ and $\sum_{i,j} r_{i} s_{j}= 0$. Using the same coefficient vectors $\vec{r}$ and $\vec{s}$, we can continue in a similar manner to suitably define $\hat{\alpha}_5$ and $\hat{\alpha}_6$ using $\{\theta_k,k=1,2,3\}$, and $\hat{\alpha}_7$ and $\hat{\alpha}_8$ using $\{\xi_l,l=1,2,3\}$. \\
\subsection{Physical interpretation}
The exact nature of the MUBs $\{\{\psi_i\},\{\phi_j\}, \{\theta_k\}, \{\xi_l\}, i, j, k, l=1,2,3\}$ were given by Bandyopadhyay et al. \cite{band}, and are of the form
{\small
\begin{align*}
B'_{1} = \left(
\begin{array}{ccc}
1 & 0 & 0\\
0 & 1 & 0\\
0 & 0 & 1\\
\end{array}\right),
\hspace{1mm}
B'_{2} = \frac{1}{\sqrt 3}\left(
\begin{array}{ccc}
1 & 1 & 1 \\
1 & \omega^{2} & \omega\\
1 & \omega & \omega^{2} \\
\end{array}\right),
\end{align*}
}
{\small
\begin{align*}
B'_{3} = \frac{1}{\sqrt 3}\left(
\begin{array}{ccc}
1 & 1 & 1 \\
\omega & 1 & \omega^{2} \\
1 & \omega & \omega^{2} \\
\end{array}\right),
\hspace{1mm}
B'_{4} = \frac{1}{\sqrt 3}\left(
\begin{array}{ccc}
1 & 1 & 1 \\
\omega^{2} & \omega & 1 \\
1 & \omega & \omega^{2} \\
\end{array}\right),
\end{align*}
}
where columns of $B'_1, B'_2, B'_3$ and $B'_4$ are $\{\psi_i\}, \{\phi_j\}, \{\theta_k\}$ and $\{\xi_l\}$ respectively, and $\omega= e^{2\pi i/3}$.
We now identify the physical observables corresponding to the operators $\hat{\alpha}_i,i=1,\ldots,8$ and discuss their implementation. Consider first $\hat{\alpha}_1$ and $\hat{\alpha}_2$. Choosing one of $\vec{r}=(r_1,r_2,r_3)$ or $\vec{s}=(s_1,s_2,s_3)$ to be in the x-y plane (say $\vec{r}$), and from the conditions $\sum_{i} r_{i}= \sum_{i} s_{i}=0$ with $\sum_{i,j} r_{i} s_{j}= 0$, the choice of vectors $\vec{r}$ and $\vec{s}$ reduce to $\vec{r}= (r, 0, -r)$ and $\vec{s}= (s, -2s, s)$, up to an arbitrary permutation.
Examining the Fano representation of density matrix, we see that $\tau^{1}_{0}= \sqrt{\frac{3}{2}} J_{z}$ and $\tau^{2}_{0}= \frac{3J^{2}_{z}-J^{2}}{\sqrt{2}}$ and their expectation values determine two of the expansion coefficients of density matrix in this representation. Explicit forms of $\tau^{1}_{0}$ and $\tau^{2}_{0}$ are given by,
{\small
\begin{align*}
\tau^{1}_{0}=& {\sqrt{\frac{3}{2}}} \left(\begin{array}{ccc}
1 & 0 & 0\\
0 & 0 & 0\\
0 & 0 & -1\\
\end{array} \right),
\hspace*{1mm}
\tau^{2}_{0}= \frac{1}{\sqrt 2} \left(\begin{array}{ccc}
1 & 0 & 0\\
0 & -2 & 0\\
0 & 0 & 1\\
\end{array} \right),
\end{align*}}
\noindent where expectation values of $ \tau^{1}_{0}$ and $ \tau^{2}_{0}$ are respectively associated with the first and second order moments of $J_{z}$, and hence constitute experimentally measurable parameters. Thus we choose $\hat{\alpha_{1}}$ to be $\tau^{1}_{0}$ and $\hat{\alpha_{2}}$ to be $\tau^{2}_{0}$. In other words, $\vec{r}={\sqrt{\frac{3}{2}}}(1, 0, -1)$ and $\vec{s}= \frac{1}{\sqrt{2}}(1, -2, 1)$.
Now the first set of commuting operators in terms of projection operators associated with $B'_{1}$ is given by,
\begin{equation*}
\hat{ {\alpha_{1}}}= {\sqrt{\frac{3}{2}}} (\hat{P_{1}}-\hat{P_{3}}), \ \ \ \hat{{\alpha_{2}}}= \frac{1}{\sqrt 2} (\hat{P_{1}}-2\hat{P_{2}}+\hat{P_{3}}) .
\end{equation*}
The bases $B'_{1}$ and $B'_{2}$ are connected by the Fourier transformation $U'$ \cite{pawel} given by,
{\small
\begin{align*}
U' = \frac{1}{\sqrt{3}} \left(
\begin{array}{ccc}
1 & 1 & 1\\
1 & \omega^{2} & \omega \\
1 & \omega & \omega^{2} \\
\end{array}\right).
\end{align*}
}
\noindent
Thus $\hat{\alpha_{3}}$ and $\hat{\alpha_{4}}$ can be written as $\hat{\alpha_{3}}= U' \hat{\alpha_{1}} U'^{\dagger}$ and $\hat{\alpha_{4}}= U' \hat{\alpha_{2}} U'^{\dagger}$.
In a similar manner, transition from $B'_{2}$ to $B'_{3}$ can be obtained by one-axis twisting, $e^{-iS^{2}_{z}t}$ \cite{kit} for $t=2\pi/3$ and from $B'_{2}$ to $B'_{4}$ for $t=4\pi/3$.
The orthonormal set of commuting observables $\hat{\alpha_{i}}$, $i= 1, \ldots,8$ is given by,
\begin{align*}
\hat{\alpha_{1}}&= {\sqrt{\frac{3}{2}}}(\hat{P_{1}}-\hat{P_{3}}), \quad \hat{\alpha_{2}}= \frac{1}{\sqrt 2} (\hat{P_{1}}-2\hat{P_{2}}+\hat{P_{3}}) ,\\
\hat{\alpha_{3}}&= {\sqrt{\frac{3}{2}}}(\hat{P'_{1}}-\hat{P'_{3}}) , \quad \hat{\alpha_{4}}= \frac{1}{\sqrt 2} ( \hat{P'_{1}}-2\hat{P'_{2}}+\hat{P'_{3}}) ,\\
\hat{\alpha_{5}}&= {\sqrt{\frac{3}{2}}}(\hat{P''_{1}}-\hat{P''_{3}}) , \quad \hat{\alpha_{6}}= \frac{1}{\sqrt 2} ( \hat{P''_{1}}-2\hat{P''_{2}}+\hat{P''_{3}}) ,\\
\hat{\alpha_{7}}&= {\sqrt{\frac{3}{2}}}(\hat{P'''_{1}}-\hat{P'''_{3}}) , \quad \hat{\alpha_{8}}= \frac{1}{\sqrt 2} (\hat{P'''_{1}}-2\hat{P'''_{2}}+\hat{P'''_{3}}),
\end{align*}
where projection operators $\hat{P_{i}}, \hat{P'_{i}}, \hat{P''_{i}}, \hat{P'''_{i}}$ ( $i=1,2,3$) are respectively associated with the bases $B'_{1}, B'_{2}, B'_{3}, B'_{4}$. The new orthonormal operator basis is explicitly given by,
{\small
\begin{align*}
\hat{{\alpha}_{1}}&= {\sqrt{\frac{3}{2}}} \left(\begin{array}{ccc}
1 & 0 & 0\\
0 & 0 & 0\\
0 & 0 & -1\\
\end{array} \right),
\qquad
\hat{\alpha_{2}}= \frac{1}{\sqrt 2} \left(\begin{array}{ccc}
1 & 0 & 0\\
0 & -2 & 0\\
0 & 0 & 1\\
\end{array} \right),\\
\hat{\alpha_{3}}&= {\frac{1}{\sqrt{2}}} \left(\begin{array}{ccc}
0 & -i\omega & i\omega^{2}\\
i\omega^{2} & 0 & -i\omega\\
-i\omega & i\omega^{2} & 0\\
\end{array} \right),
\quad
\hat{\alpha_{4}}= \frac{1}{\sqrt 2}\left(\begin{array}{ccc}
0 & -\omega & -\omega^{2}\\
-\omega^{2} & 0 & -\omega\\
-\omega & -\omega^{2} & 0\\
\end{array} \right),\\
\hat{\alpha_{5}}&={\frac{1}{\sqrt{2}}} \left(\begin{array}{ccc}
0 & -i & i\omega^{2} \\
i & 0 & -i \omega^{2} \\
-i \omega & i \omega & 0\\
\end{array} \right),
\quad
\hat{\alpha_{6}}=\frac{1}{\sqrt 2} \left(\begin{array}{ccc}
0 & -1 & -\omega^{2}\\
-1 & 0 & -\omega^{2} \\
-\omega & -\omega & 0\\
\end{array} \right),\\
\hat{\alpha_{7}}& ={\frac{1}{\sqrt{2}}} \left(\begin{array}{ccc}
0 & -i \omega^{2} & i\omega^{2} \\
i \omega & 0 & -i\\
-i \omega & i & 0\\
\end{array} \right),
\quad
\hat{\alpha_{8}}= {\frac{1}{\sqrt{2}}} \left(\begin{array}{ccc}
0 & -\omega^{2} & -\omega^{2}\\
-\omega & 0 & -1\\
-\omega & -1 & 0\\
\end{array} \right).
\end{align*}
}
\noindent
The new operator basis provides an expansion of $\rho$:
\begin{equation*}
\rho= \frac{1}{3}(I + \sum \limits_{i=1}^{8} a_{i} \hat{\alpha_{i}}),
\end{equation*}
where $a_{i}= Tr(\rho \hat{\alpha_{i}})$. The expansion based on the operators constructed using the MUBs in a certain sense constitutes an optimal measurement strategy---complete state determination amounts to determining the $a_i$, which is optimally done using the maximally commuting orthogonal operators $\hat{\alpha}_i, i=1,\ldots,8$.
\subsection{Physical realization} In addition to dipole magnetic field in the Stern- Gerlach apparatus, if one applies an external electric quadrupole field, the resulting Hamiltonian in the multipole expansion is given by,
\begin{equation*}
\hat{\mathcal{H}}= \sum \limits_{k=0}^{2} \sum \limits_{q= -k}^{+k} h^{k}_{q} {\tau^{k}_{q}}^{\dagger}.
\end{equation*}
When the electric quadrupole field with asymmetry parameter $\eta=0$ is along the $z$-axis of the Principal Axes Frame(PAF) of the quadrupole tensor and the dipole magnetic field is oriented along the same $z$-axis \cite{swarna}, $\hat{\mathcal{H}}$ takes the form
\begin{equation*}
\hat{\mathcal{H}}= \sum \limits_{k=0}^{2} h^{k}_{0} \tau^{k}_{0}.
\end{equation*}
In this experimental setup, one can measure the expectation values of $\hat{\alpha_{1}}$ and $\hat{\alpha_{2}}$. Implementation of unitary transformations namely Fourier transform and one-axis twisting in the lab leads to the measurement of all the observables $\hat{\alpha_{3}},\hat{\alpha}_4,\ldots,\hat{\alpha_{8}}$.\\
\section{Construction for a spin-3/2 system}
For a spin-3/2 system, the MUBs comprise five basis sets given by,
{\small
\begin{align*}
B''_{1} = \left(
\begin{array}{cccc}
1 & 0 & 0 & 0 \\
0 & 1 & 0 & 0\\
0 & 0 & 1 & 0\\
0 & 0 & 0 & 1\\
\end{array}\right),
\qquad
B''_{2} = \frac{1}{2} \left(
\begin{array}{cccc}
1 & 1 & 1 &1 \\
1 & -1 & 1& -1 \\
1& 1& -1 &-1\\
1& -1& -1 & 1\\
\end{array}\right),
\qquad
B''_{3} = \frac{1}{2} \left(
\begin{array}{cccc}
1 & 1 & 1 & 1\\
i & -i & i & -i \\
i & i & -i &-i \\
-1 & 1 & 1 & -1\\
\end{array}\right),
\end{align*}
}
{\small
\begin{align*}
B''_{4} = \frac{1}{2} \left(
\begin{array}{cccc}
1 & 1&1 & 1\\
i & -i & i& -i \\
1 & 1 & -1 & -1\\
-i & i & i&-i\\
\end{array}\right),
\qquad
B''_{5} = \frac{1}{2} \left(
\begin{array}{cccc}
1 & 1 & 1 & 1 \\
1 & -1& 1& -1\\
i & i & -i & -i \\
-i & i & i & -i\\
\end{array}\right) .
\end{align*}
}
Thus we construct five sets of mutually disjoint, maximally commuting set of operators $\hat{\beta}_{i}$, $i= 1, 2, \ldots,15$. Fano expansion of spin-3/2 density matrix consists of three diagonal operators $\tau^{1}_{0}$, $\tau^{2}_{0}$ and $\tau^{3}_{0}$ in the $|3/2 \ m \rangle$ basis where $m= -3/2, \ldots,+3/2$. Along the lines of what was done for the spin-1 case, we choose $\hat{\beta_{1}}$, $\hat{\beta_{2}}$ and $\hat{\beta_{3}}$ to be $\tau^{1}_{0}$, $\tau^{2}_{0}$, $\tau^{3}_{0}$, given by,
{\small
\begin{align*}
\tau^{1}_{0} = \hat{\beta_{1}} = \frac{1}{\sqrt{5}} \left(
\begin{array}{cccc}
3 & 0 & 0 & 0 \\
0 & 1 & 0 & 0\\
0 & 0 & -1 & 0\\
0 & 0 & 0 & -3\\
\end{array}\right),
\qquad
\tau^{2}_{0}= \hat{\beta_{2}} = \left(
\begin{array}{cccc}
1 & 0 & 0 & 0 \\
0 & -1 & 0 & 0\\
0 & 0 & -1 & 0\\
0 & 0 & 0 & 1\\
\end{array}\right),
\end{align*}
}
{\small
\begin{align*}
\tau^{3}_{0}= \hat{\beta_{3}} = \frac{1}{\sqrt{5}} \left(
\begin{array}{cccc}
1 & 0 & 0 & 0 \\
0 & -3 & 0 & 0\\
0 & 0 & 3 & 0\\
0 & 0 & 0 & -1\\
\end{array}\right),
\end{align*}
}
\noindent
where $\tau^{3}_{0}= \frac{1}{3\sqrt{5}} [4J_{z}^{3}- (J_{z} J^{2}_{x}+ J^{2}_{x} J_{z}+ J_{x} J_{z} J_{x}) (J_{z} J^{2}_{y}+J^{2}_{y} J_{z}+J_{y} J_{z} J_{y})]$.
In terms of projection operators obtained from the canonical basis,
\begin{eqnarray*}
\hat{\beta_{1}}= 1/{\sqrt{5}} (3\hat{P_{1}}+\hat{P_{2}}-\hat{P_{3}}-3\hat{P_{4}}), \\
\hat{\beta_{2}}= \hat{P_{1}}-\hat{P_{2}}-\hat{P_{3}}+\hat{P_{4}}, \\
\hat{\beta_{3}}= 1/{\sqrt{5}} (\hat{P_{1}}-3\hat{P_{2}}+ 3\hat{P_{3}}-\hat{P_{4}}).
\end{eqnarray*}\\
Similarly remaining four sets of operators each containing three commuting operators are constructed from their respective projection operators employing the same linear combinations as above.\\
Thus spin-3/2 density matrix can be expanded in the new basis as
\begin{equation*}
\rho= \frac{1}{4}(I + \sum \limits_{i=1}^{15} b_{i} \hat{\beta_{i}}).
\end{equation*}
With the suitable application of quadrupole electric field, dipole and octopole magnetic field, one can obtain $\hat{\beta_{1}}$, $\hat{\beta_{2}}$ and $\hat{\beta_{3}}$. As the unitary transformations connecting different MUB sets are known, implementation of these transformations results in the measurement of rest of the observables.
\section{Construction for a spin-2 system}
For spin-2 system, with $\omega=e^{2 \pi i/5}$, the six sets of MUBs are given by
{\small
\begin{align*}
B_{1} &= \frac{1}{\sqrt{5}} \left(
\begin{array}{ccccc}
1 & 0 & 0 & 0 & 0\\
0 & 1 & 0 & 0 & 0\\
0 & 0 & 1 & 0 & 0\\
0 & 0 & 0 & 1 & 0\\
0 & 0 & 0& 0 & 1\\
\end{array}\right),
\qquad \quad
B_{2} = \frac{1}{\sqrt{5}} \left(
\begin{array}{ccccc}
1 & 1 & 1 & 1 & 1 \\
1 & \omega & {\omega}^{2} & {\omega}^{3} & {\omega}^{4}\\
1 & {\omega}^{2} & {\omega}^{4} & {\omega} & {\omega}^{3} \\
1 & {\omega}^{3} & {\omega} & {\omega}^{4} & {\omega}^{2} \\
1 & {\omega}^{4} & {\omega}^{3} &{\omega}^{2} & {\omega} \\
\end{array}\right),
\\
B_{3}& = \frac{1}{\sqrt{5}} \left(
\begin{array}{ccccc}
1 & 1 & 1 & 1 & 1 \\
\omega & \omega^{2} & \omega^{3} & \omega^{4}& 1\\
{\omega}^{4} & \omega& \omega^{3} & 1 & \omega^{2} \\
{\omega}^{4} & \omega^{2} & 1 & \omega^{3} & \omega \\
{\omega} & 1 & \omega^{4} & \omega^{3} & \omega^{2}\\
\end{array}\right),
\quad
B_{4} = \frac{1}{\sqrt{5}} \left(
\begin{array}{ccccc}
1 & 1& 1 & 1 & 1\\
\omega^{2} & \omega^{3}& \omega^{4} & 1 & \omega\\
{\omega}^{3} & 1&\omega^{2} & \omega^{4} & \omega \\
{\omega}^{3} & \omega & \omega^{4} & \omega^{2} & 1\\
{\omega}^{2} & \omega & 1 & \omega^{4} & \omega^{3}\\
\end{array}\right),
\\
B_{5} &= \frac{1}{\sqrt{5}} \left(
\begin{array}{ccccc}
1 & 1 & 1& 1& 1\\
\omega^{3} & \omega^{4}& 1& \omega& \omega^{2} \\
{\omega}^{2} & \omega^{4}&\omega & \omega^{3}& 1\\
{\omega}^{2} & 1 & \omega^{3} & \omega & \omega^{4}\\
{\omega}^{3} &\omega^{2} & \omega & 1 & \omega^{4} \\
\end{array}\right),
\quad
B_{6} = \frac{1}{\sqrt{5}} \left(
\begin{array}{ccccc}
1 & 1& 1& 1& 1 \\
\omega^{4} & 1 & {\omega} & {\omega}^{2}& {\omega}^{3}\\
{\omega}& {\omega}^{3} & 1 & {\omega}^{2}& {\omega}^{4}\\
{\omega}&{\omega}^{4} &{\omega}^{2} & 1 & {\omega}^{3}\\
{\omega}^{4}& {\omega}^{3}& {\omega}^{2}& {\omega} & 1\\
\end{array}\right).
\end{align*}
}
In this case, the four Fano spherical tensors, in terms of the projection operators, are given by,
\begin{eqnarray*}
\tau^{1}_{0}= \hat{\gamma_{1}}= {\sqrt{\frac{5}{4}}} (\hat{P_{1}}-\hat{P_{2}}+\hat{P_{4}}-\hat{P_{5}}), \\
\tau^{2}_{0}= \hat{\gamma_{2}}= {\frac{1}{\sqrt{2}}}(2\hat{P_{1}}+\hat{P_{2}}-2\hat{P_{4}}-\hat{P_{5}}), \\
\tau^{3}_{0}= \hat{\gamma_{3}}= {\frac{1}{\sqrt{2}}}(\hat{P_{1}}-2\hat{P_{2}}-\hat{P_{4}}+2\hat{P_{5}}), \\
\tau^{4}_{0}= \hat{\gamma_{4}}= {\frac{1}{2}} (\hat{P_{1}}+\hat{P_{2}}-4\hat{P_{3}}+\hat{P_{4}}+\hat{P_{5}})
\end{eqnarray*}
In similar fashion the remaining five sets of commuting operators can be obtained by operating the unitary transformations connecting MUBs in the angular momentum basis to rest of the MUBs. Consequently, spin-2 density matrix can now be expressed as
\begin{equation*}
\rho= \frac{1}{5}(I + \sum \limits_{i=1}^{24} c_{i} \hat{\gamma_{i}}).
\end{equation*}
\section{Concluding remarks}
We have provided a mechanism to construct mutually disjoint, maximally commuting operators for dimensions where MUBs are known to exist. Since these operators are maximally commuting, measurements with them correspond to optimal determination of the parameters characterizing the density matrix of the state of a system.
Our construction rests on a key observation that the Pauli operators used in a Stern-Gerlach experiment for spin-1/2 particles are linear combinations of projection operators constructed from different MUBs. Leveraging this observation, we construct Pauli-like operators with eigenbases that are MUBs for spin-1, spin-3/2 and spin-2 systems. For prime and prime power dimensions $d$ (where $d= 2j+1$), using the fact that there always exists a complete set of $d+1$ MUBs, we have constructed $d+1$ sets of mutually disjoint operators, containing $d-1$ commuting operators in each set in the following manner:
\begin{enumerate}
\item Consider the first set of MUBs as canonical basis.
\item Consider an orthonormal set of $d^{2}$ matrices, with $d$ diagonal matrices which includes the identity $I$.
For example, if the angular momentum basis is used as the canonical basis, then the diagonal matrices can be identified as the Fano spherical tensor operators $\tau^{k}_{0}$s with matrix elements $\langle jm |\tau^{k}_{0} | jm \rangle= \sqrt{2k+1} C(jkj; m0m)$, where $k=0 \ldots d-1$ and $C(jkj; m0m)$ are the Clebsch-Gordan coefficients.
\item Express each diagonal matrix (excluding identity) as a linear combination of projection operators of the canonical basis.
\item Identify the unitary transformations $U_{1}, U_{2}, \ldots, U_{d}$ that connect the first set of MUBs with the rest of MUB states.
\item Implementing $U_{i} \tau^{k}_{0} U^{\dagger}_{i}$, where $i= 1, \ldots, d$ and $k=1 \ldots, d-1$, generate the complete set of mutually disjoint, maximally commuting set of operators.
\end{enumerate}
Inspection of our method reveals that the main requirement for extension to higher-order spin systems and arbitrary density matrices representing non-spin systems is that the MUBs are known to exist and are available. For non-spin systems, expansion of the density matrix $\rho$ in an operator basis different from the spherical tensors can be considered. Physical realization then amounts to the identification of a suitable Hamiltonian that plays a role analogous to the multipole fields used in spin-$j$ systems.
Spin-5/2 is an intriguing case as it corresponds to the lowest composite dimension $d=6$ that is not a power of a prime for which the existence of a complete set of MUBs is yet to be established. It has been conjectured by Zauner \cite{zan} that for $d=6$ the maximum number of MUB sets is three. If the conjecture is true, then one cannot construct seven sets of mutually disjoint, maximally commuting set of operators.
There have been numerous attempts to detect entanglement/correlation by using minimal number of experimentally viable local measurements. Recent works\cite{chris, bin} show that MUBs, as well as Mutually Unbiased Measurements(MUMs), can be efficiently used to detect entanglement in bipartite, multipartite and higher dimensional systems. In principle, our method of constructing mutually disjoint, maximally commuting set of operators may be harnessed to detect entanglement, since the eigenbases of our operators are MUBs. Since the constructed operators are maximally commuting, the detection mechanism would require a minimal number of measurements. This work will be taken up elsewhere.
\section*{Appendix}
The density matrix for a spin-$j$ system can be represented as
\begin{equation*}
\rho(\mathbf{J}):=\rho := \frac{1}{(2j+1)} \sum_{k=0}^{2j}\sum_{q=-k}^k t^k_q \tau^{k^\dagger}_q,
\end{equation*}
$\tau^k_q$ are irreducible tensor operators of rank $k$ in the $2j+1$ dimensional spin space with projection $q$ along the axis of quantization in the real 3-dimensional space. The matrix elements of $\tau^{k}_{q}$ are
\begin{equation*}
\langle jm' |\tau^{k}_{q}(\vec{J}) | jm \rangle= [k] C(jkj; mqm'),
\end{equation*}
where $C(jkj;mqm')$ are the Clebsch--Gordan coefficients and $[k]=\sqrt{2k+1}$. $\tau^{k}_{q}$s satisfy orthogonality and symmetry relations,
\begin{equation*}
Tr({\tau^{k^{\dagger}}_{q}\tau^{k^{'}}_{q^{'}}})= (2j+1)\,\delta_{kk^{'}} \delta_{qq^{'}}, \quad \tau^{k^{\dagger}}_{q} = (-1)^{q}\tau^{k}_{-q},
\end{equation*}
where the normalization has been chosen so as to be in agreement with Madison convention.
The Fano statistical tensors or the spherical tensor parameters $t^k_q$ parametrize the density matrix $\rho$ as expectation values of $\tau^k_q$: $Tr(\rho\tau^k_q)=t^k_q$. Because of hermiticity of $\rho$, ${t^{k}_{q}}^{*}= (-1)^{q} t^{k}_{-q}$.
The importance of irreducible spherical tensor operators lies in the fact they can be constructed as symmetrized products of the angular momentum operators $\mathbf{J}$ following the well-known Weyl construction
as,
$\tau_{q}^{k}(\mathbf{J}) = \mathcal {N}_{kj}\,(\mathbf{J}\cdot \vec{\bf{\nabla}})^k \,r^{k} \,{Y}^{k}_{q}(\hat{r}),$
where
\begin{equation*}
\mathcal {N}_{kj}= {\frac{2^{k}}{k!}}{\sqrt{\frac{4\pi(2j-k)!(2j+1)}{(2j+k+1)!}}},
\end{equation*}
are the normalization factors and ${Y}^{k}_{q}(\hat {r})$ are the spherical harmonics. The tensor operators are traceless but not Hermitian, and cannot in general be identified with generators of $SU(N)$. Also, the tensor operators $\tau^{k}_{0}$s are the physical observables which have the physical interpretation. That is, the expectation values of $\tau^{k}_{0}$s correspond to the statistical moments and thus are measurable physical quantities.
\section*{Acknowledgements}
HSS thanks the Department of Science and Technology(DST), India for the grant of INSPIRE Fellowship. KB's research is partially supported by NSF DMS 1613054 and NIH R01 CA214955.
\vspace*{-10pt}
\section*{References}
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 7,566
|
\section{Introduction}
\label{sec:intro}
A strongly interacting matter is expected to be produced,
instead of a weakly interacting gas,
at RHIC and LHC energies as the shear viscosity
of the matter thus produced is exposed to be very small.
This was concluded by the hydrodynamical
simulations~\cite{Romatschke1,Heinz1,Roy,Niemi,LHC_Hydro1,LHC_Hydro2}
as well as some transport calculations~\cite{Xu1,Greco1,Greco2,LHC_Transport}
to explain the elliptic flow parameter observed at RHIC and LHC.
According to the investigations conducted in
Refs.~\cite{Hufner,Csernai,Gyulassy,Kapusta:2008vb,Chen1,Purnendu,Chen2},
the shear viscosity to entropy density ratio, $\eta/s$ may reach a minimum
in the vicinity of a phase transition, which is also indicated by some
lattice QCD calculations\cite{Lat1,Lat2,Lat3}.
The minimum value of $\eta/s$
may be very close to its quantum lower
bound, commonly known as the KSS bound~\cite{KSS}.
Owing to these interesting issues, a growing interest in the
microscopic calculation of shear viscosity for the
QGP phase~\cite{Arnold,QGP2,Moore,Basagoiti,Arts,SG_NJL} and hadronic
phase~\cite{Dobado1,Dobado2,Muronga,Nakano,Nicola,Itakura,Gorenstein,Greiner,SPal,Toneev,Prakash_2012,Buballa,Weise,SSS,Krein,Prakash_2013,Denicol,Bass,HM}
has been noticed in recent times,
though the transport coefficient calculations of
nuclear matter started somewhat
earlier~\cite{Gavin,Prakash,Toneev_7,Toneev_8,Toneev_9,Toneev_10}.
Importance of knowing the explicit temperature dependence
of shear viscosity for hadronic phase has been pointed out in
a recent work by Niemi et
al.~\cite{Niemi}. They have shown that the extracted
transverse momentum $p_T$ dependence of elliptic
flow parameter, $v_2(p_T)$, of RHIC data is highly sensitive to the temperature
dependent $\eta/s$ in hadronic matter and almost independent of the viscosity in
the QGP phase.
Being inspired by this, we have studied
the shear viscosity of pionic medium~\cite{GKS} and
then extended our study to the pion-nucleon
system~\cite{G_N}. To calculate shear viscosity of
the pionic component via Kubo relation~\cite{Zubarev,Kubo},
the thermal correlator of viscous stress tensor for pionic constituents
has to be derived, where a finite thermal width of pion
should be included for getting a non-divergent value of correlator
in the static limit~\cite{Nicola,Weise,G_IJMPA}. In Ref.~\cite{GKS}, the pion
thermal width is estimated from the pion self-energy
for different mesonic loops, which are obtained in the formalism of
real-time thermal field theory (RTF). Similarly, the thermal correlator
of viscous stress tensor for nucleonic constituents is obtained in
Ref.~\cite{G_N} to calculate the shear viscosity of nucleonic component,
where different pion-baryon loops are taken into account to determine the nucleon
thermal width. Now, in the two component nucleon-pion system,
pion propagation may also have some baryonic fluctuations besides
the mesonic fluctuations. This contribution, which was absent in our
previous studies~\cite{GKS,G_N}, is considered in the present work
to revisit our shear viscosity calculation for two component nucleon-pion system.
In the next section, the formalism
of shear viscosity for pionic and nucleonic components are
briefly described, where their corresponding thermal widths
are discussed in three different subsections. In the subsection~\ref{subsec:pi_bar},
we have elaborately deduced the pion thermal width in baryonic medium
by calculating the pion self-energy for different baryonic loops
in the formalism of RTF. In the next two subsections, the relevant
expressions of pion thermal width due to different mesonic loops
and nucleon thermal width from different pion-baryon loops are
briefly addressed as the detailed deduction of these expressions
are already provided in the previous studies~\cite{GKS,G_N}.
The numerical outcomes are discussed in Sec.~\ref{sec:num}
and in Sec.~\ref{sec:concl}, we have summarized and concluded this article.
\section{Formalism}
\label{sec:form}
Owing to the famous Kubo formula~\cite{Zubarev,Kubo},
the spectral function of two point viscous-stress tensor,
$\pi^{\mu\nu}$ can determine
the shear viscosity in momentum
space by the standard relation~\cite{Nicola}
\begin{equation}
\eta=\frac{1}{20}\lim_{q_0,\vq \rightarrow 0}\frac{1}{q_0}
\int d^4x e^{iq\cdot x}\langle[\pi_{ij}(x),\pi^{ij}(0)]\rangle_\beta~,
\label{eta_Nicola}
\end{equation}
where $\langle \hat{O}\rangle_\beta$ for any operator $\hat{O}$
denotes the equilibrium ensemble average;
$\langle \hat{O}\rangle_\beta={\rm Tr}\frac{e^{-\beta H}\hat{O}}{{\rm Tr}e^{-\beta H}}$.
The simplest one-loop expressions of Eq.~(\ref{eta_Nicola})
for pion and nucleon degrees of freedom
are respectively given below~\cite{G_IJMPA}
\begin{equation}
\eta_\pi=\frac{\beta I_\pi}{30\pi^2}\int^{\infty}_{0}
\frac{d\vec k\vk^6}{{\omega^\pi_k}^2\Gamma_\pi}n_k(\omega^\pi_k)
\{1+n_k(\omega_k^\pi)\}
\label{eta_pi}
\end{equation}
and
\begin{eqnarray}
\eta_N&=&\frac{\beta I_N}{15\pi^2}\int^{\infty}_{0}
\frac{d\vec k\vk^6}{{\omega^N_k}^2\Gamma_N}[n^+_k(\omega_k^N)\{1-n^+_k(\omega^N_k)\}
+n^-_k(\omega^N_k)\{1-n^-_k(\omega^N_k)\}]~.
\nonumber\\
\label{eta_N}
\end{eqnarray}
Their schematic diagrams are shown in Fig.~\ref{eta_pi_N}(a) and \ref{eta_N_piB}(a)
respectively.
Hence, adding the pionic and nucleonic components, we get the total shear viscosity
\begin{equation}
\eta_{\rm T}=\eta_{\pi}+\eta_N~.
\end{equation}
In the above equations, $n_k(\omega^\pi_k)=1/\{e^{\beta\omega^\pi_k}-1\}$ is
Bose-Einstein (BE) distribution of pion with energy
$\omega^\pi_k=(\vec k^2+m_\pi^2)^{1/2}$ whereas
$n^{\pm}_k=1/\{e^{\beta(\omega^\pi_k\mp \mu_N)}+1\}$ are Fermi-Dirac (FD) distributions
of nucleon and anti-nucleon with energy $\omega^N_k=(\vec k^2+m_N^2)^{1/2}$.
The corresponding thermal widths, $\Gamma_\pi$ and $\Gamma_N$
for pion and nucleon can be defined as
\begin{eqnarray}
\Gamma_\pi&=&\sum_B\Gamma_{\pi(NB)} + \sum_M\Gamma_{\pi(\pi M)}
\nonumber\\
&=&-\sum_B{\rm Im}{\Pi}^R_{\pi(NB)}(k_0=\omega^\pi_k,\vec k)/m_\pi
-\sum_M{\rm Im}{\Pi}^R_{\pi(\pi M)}(k_0=\omega^\pi_k,\vec k)/m_\pi
\nonumber\\
\label{Gam_pi}
\end{eqnarray}
and
\begin{equation}
\Gamma_N=\sum_B\Gamma_{N(\pi B)}=-\sum_B{\rm Im}\Sigma^R_{N(\pi B)}(k_0=\omega^N_k,\vec k)
\label{Gam_N}
\end{equation}
respectively, where ${\Pi}^R_{\pi(NB)}(k)$ is pion self-energy for different
nucleon-baryon ($NB$) loops (shown in Fig.~\ref{eta_pi_N}(c) and (d)),
${\Pi}^R_{\pi(\pi M)}(k)$ is pion self-energy for different pion-meson ($\pi M$)
loops (shown in Fig.~\ref{eta_pi_N}(b))
and $\Sigma^R_{N(\pi B)}(k)$ is nucleon self-energy for different
pion-baryon ($\pi B$) loops (shown in Fig.~\ref{eta_N_piB}(b)).
The superscript $R$ stands for retarded component of self-energy
and subscripts represent the external (outside the bracket) and
internal (inside the bracket) particles for the corresponding
self-energy graphs as shown in Fig.~\ref{eta_pi_N}(b), (c), (d)
and Fig.~\ref{eta_N_piB}(b).
\begin{figure}
\begin{center}
\includegraphics[scale=0.52]{eta_pi_N.eps}
\caption{The diagram (a) is a schematic one-loop representation of viscous-stress
tensor for the medium with pionic constituents. The double dashed lines
for the pion propagators indicate that they have some finite thermal
width, which can be derived from the pion self-energy diagrams (b), (c) and (d).
The diagram (b) represents pion self-energy for mesonic ($\pi M$) loops.
Direct and cross diagrams of pion self-energy
for $NB$ loops are represented by (c) and (d) respectively.}
\label{eta_pi_N}
\end{center}
\end{figure}
\begin{figure}
\begin{center}
\includegraphics[scale=0.52]{eta_N_piB.eps}
\caption{The diagram (a) is a schematic one-loop representation of viscous-stress
tensor for the medium with nucleonic constituents and
the diagram (b) represents nucleon self-energy for $\pi B$ loops.}
\label{eta_N_piB}
\end{center}
\end{figure}
Adoption of finite thermal widths $\Gamma_\pi$ and $\Gamma_N$ in Eq.~(\ref{eta_pi})
and (\ref{eta_N}) respectively
is a very well established technique~\cite{Nicola,Weise},
which is generally used in Kubo approach
to get a non-divergent value of the shear viscosity coefficient.
In this respect this treatment is equivalent to quasi-particle approximation
or relaxation time approximation.
Again, this one-loop expression of $\eta_\pi$ or $\eta_N$
from Kubo approach~\cite{Nicola,Weise,S_rev} exactly coincides with the
expression coming from the relaxation-time approximation of
the kinetic theory approach~\cite{Gavin,Prakash,SSS,S_rev}.
Hence, the thermal width of medium constituent plays a vital
role in determining the numerical strength of shear viscosity of the medium.
Next we discuss the calculations of thermal widths from different one-loop self-energy
graphs as shown in Fig.~(\ref{eta_pi_N}) and (\ref{eta_N_piB}).
\subsection{Pion thermal width for different baryonic loops}
\label{subsec:pi_bar}
Let us first concentrate on the pion
self-energy calculations for different possible baryon loops {\it i.e} ${\Pi}^R_{\pi(NB)}$.
During propagation in the medium,
pion propagator can undergo different intermediate NB loops,
where $B=\Delta(1232)$, $N^*(1440)$, $N^*(1520)$,
$N^*(1535)$, $\Delta^*(1600)$, $\Delta^*(1620)$, $N^*(1650)$,
$\Delta^*(1700)$, $N^*(1700)$, $N^*(1710)$, $N^*(1720)$ are
accounted in this work.
The masses of all the 4-star baryon resonances (in MeV) are presented inside the brackets.
The direct and cross diagrams of pion self-energy
for $NB$ loops have been represented
in the diagrams~\ref{eta_pi_N}(c) and (d).
In real-time formalism of thermal field theory (RTF), self-energy becomes
$2\times 2$ matrix with $11$, $12$, $21$ and $22$ components. From any of
the components, one can found the retarded part of self-energy, which is
directly related with physical quantity - thermal width (inverse of thermal
relaxation time).
Let us start with the $11$-component of in-medium pion
self-energy for $NB$ loop :
\begin{equation}
\Pi^{11}_{\pi(NB)}(k)=i \sum_{a=-1,+1}
\int \frac{d^4l}{(2\pi)^4} L(k,l)
E^{11}_N(l) E^{11}_B(l-a k)
\label{Pi11B}
\end{equation}
where $E^{11}_N(l)$ and $E^{11}_B(l-ak)$ are
scalar parts of the nucleon and
baryon propagators respectively at finite temperature.
In RTF this expression is as follows
\begin{equation}
E^{11}_N(l)=\frac{-1}{l^2-m_N^2+i\eta}-2\pi i\{n^+_l\theta(l_0)
+n^-_l\theta(-l_0)\}\delta(l^2-m_N^2)~,
\label{de11}
\end{equation}
where $n^{\pm}_l(\omega^N_l)=1/\{e^{\beta(\omega^N_l \mp \mu_N)}+1\}$
are the FD distributions of nucleon and
anti-nucleon for energy $\omega^N_l=(\vec l^2+m_N^2)^{1/2}$
and $\mu_N$ is the chemical potential of nucleon which is
supposed to be equal with the chemical potentials
of all the baryons considered here.
The two values of $a$ in Eq.~(\ref{Pi11B}) correspond to the direct
and crossed diagrams, shown in Fig.~\ref{eta_pi_N}
(c) and (d) respectively, which can be obtained from
one another by changing the
sign of external momentum $k$.
Let us first discuss diagram (d) for which $a=+1$.
Integrating Eq.~(\ref{Pi11B}) over $l^0$
and using the relation,
\begin{equation}
{\rm Im}\Pi^{R}_{\pi(NB)}(k)={\rm tanh}(\beta k_0/2){\rm Im}\Pi^{11}_{\pi(NB)}(k)~,
\end{equation}
the retarded component of the in-medium self energy (imaginary part)
can be expressed as
\begin{eqnarray}
{\rm Im}{\Pi}^R_{\pi(NB)}(k)&=&\pi\epsilon(k_0)\int\frac{d^3l}{(2\pi)^3}
\frac{1}{4\omega^N_l\omega^B_u}
\nonumber\\
&&L_1[\{1-n_l^+(\omega^N_l)-n_u^-(\omega^B_u)\}\delta(k_0 -\omega^N_l-\omega^B_u)
\nonumber\\
&&~~+\{n_l^+(\omega_l^N)-n_u^+(\omega^B_u)\}\delta(k_0-\omega^N_l+\omega^B_u)]
\nonumber\\
&&~~+ L_2[\{-n_l^-(\omega^N_l) +n_u^-(\omega^B_u)\}\delta(k_0 +\omega^N_l-\omega^B_u)
\nonumber\\
&&+\{-1+n_l^-(\omega^N_l)+n_u^+(\omega^B_u)\}\delta(k_0 +\omega^N_l+\omega^B_u)~,
\label{Pi_a}
\end{eqnarray}
where $n^{\pm}_u(\omega^B_u)=1/\{e^{\beta(\omega^B_u \mp \mu_N)}+1\}$
are also FD distribution functions
for baryon and anti-baryon with $\omega^B_u=\{(\vec l-\vec k)^2+m_{B}^2\}^{1/2}$
and $L_{1,2}$ denote the values of $L(l_0,\vec l,k)$ for
$l_0=\omega^N_l$ and $-\omega^N_l$ respectively.
The different $\delta$ functions in Eq.~(\ref{Pi_a}) create the regions of
different branch cuts in $k_0$-axis viz.
$-\infty$ to $-\{\vec k^2+(m_N+m_B)^2\}^{1/2}$ for unitary cut in negative $k_0$-axis,
$-\{\vec k^2+(m_B-m_N)^2\}^{1/2}$ to $\{\vec k^2+(m_B-m_N)^2\}^{1/2}$ for Landau cut and
$\{\vec k^2+(m_N+m_B)^2\}^{1/2}$ to $\infty$ for unitary cut in positive $k_0$-axis.
In these different kinematic regions,
the imaginary part of the pion self-energy becomes non-zero.
Among the four terms in the right hand side of Eq.~(\ref{Pi_a}), the third term
contributes in pion thermal width for baryonic loops,
$\Gamma_{\pi(NB)}$ because the pion pole ($k_0=\omega^\pi_k,\vec k$) is
situated within the Landau cut $(0$ to $\{\vec k^2+(m_B-m_N)^2\}^{1/2}~)$
in the positive $k_0$-axis.
From the Eq.~(\ref{Gam_pi}), using the relation,
\begin{equation}
\Gamma_{\pi(NB)}=-{\rm Im}{\Pi}^R_{\pi(NB)}(k_0=\omega^\pi_k,\vec k)/m_\pi
\end{equation}
and adding the relevant Landau cut contributions of both diagrams (c)
and (d), the total thermal width of pion for any $NB$ loop is given by
\begin{eqnarray}
\Gamma_{\pi(NB)}(\vec k,T,\mu_N) &=& \frac{1}{16\pi|\vec k| m_\pi} \int^{\omega^N_{l-}}_{\omega^N_{l+}}
d\omega^N_l\times
L\left(l_0=-\omega^N_l,\vec l,
k_0=\omega_k^\pi,\vec k
\right)[\{-n^+_l(\omega^N_l)
\nonumber\\
&&+ n^+_u(\omega^B_u=\omega^\pi_k + \omega^N_l)\}
+\{-n^-_l(\omega^N_l)
+ n^-_u(\omega^B_u=\omega^\pi_k + \omega^N_l)\}]~,
\nonumber\\
\label{G_pi_NB}
\end{eqnarray}
where
\begin{equation}
\omega^N_{l\pm} = \frac{S^2_{\pi(NB)}}{2m_\pi^2}
\left(- \omega^\pi_k \pm |\vec k| \, W_{\pi(NB)} \right) ,
\end{equation}
with
\begin{equation}
S^2_{\pi(NB)}=m_\pi^2-m_B^2+m_N^2
\end{equation}
and
\begin{equation}
W_{\pi(NB)} = \left(1- {4m_\pi^2m_N^2}/{S^4_{\pi(NB)}}\right)^{1/2}~.
\end{equation}
Lagrangian densities of spin $J_B=1/2$ and $3/2$ baryons can be written as
\begin{equation}
{\cal L}_{\rm Baryon}=\sum_B\left[{\cal L}^{free}_{B(J_B=1/2,3/2)}
+ {\cal L}^{int}_{B(J_B=1/2,3/2)}\right]~,
\end{equation}
where free parts of Lagrangian densities for baryonic fields with spin
$J_B=1/2$ and $J_B=3/2$ are
\begin{eqnarray}
{\cal L}^{\rm free}_{B(J_B=1/2)}&=&\sum_{B(J_B=1/2)}{\overline \psi_B}(i\gamma^\mu\partial_\mu-m_B)\psi_B~,
\nonumber\\
{\cal L}^{\rm free}_{B(J_B=3/2)}&=&\sum_{B(J_B=3/2)}-\frac{1}{2}{\overline \psi^\mu_B}
(\epsilon_{\mu\nu\alpha\beta}\gamma^\alpha\partial^\beta-im_B\sigma^{\alpha\beta})\psi^\nu_B
\nonumber\\
&&{\rm with}~\sigma^{\alpha\beta}=\frac{i}{2}\left[\gamma^\alpha,\gamma^\beta\right]
\end{eqnarray}
and their interaction parts are~\cite{Leupold},
\begin{eqnarray}
{\cal L}^{\rm int}&=&\frac{f}{m_\pi}{\overline \psi}_B\gamma^\mu
\left\{
\begin{array}{c}
i\gamma^5 \\
1\!\!1
\end{array}
\right\}
\psi_N\partial_\mu\pi + {\rm h.c.}~{\rm for}~J_B^P=\frac{1}{2}^{\pm},
\nonumber\\
{\cal L}^{\rm int}&=&\frac{f}{m_\pi}{\overline \psi}^\mu_B
\left\{
\begin{array}{c}
1\!\!1 \\
i\gamma^5
\end{array}
\right\}
\psi_N\partial_\mu\pi + {\rm h.c.}~{\rm for}~J_B^P=\frac{3}{2}^{\pm},
\label{Lag_BNpi}
\end{eqnarray}
Here $P$ stands for parity quantum numbers of the baryons. The coupling constants
$\pi NB$ interactions are fixed from the experimental decay widths of
$B\rightarrow N\pi$ channels~\cite{G_pi_JPG}. They are $f/m_\pi=15.7$, $2.5$,
$11.6$, $1.14$, $3.4$, $1.22$, $1.14$, $9.5$, $2.8$, $0.35$ and $1.18$
for $\Delta(1232)$, $N^*(1440)$, $N^*(1520)$,
$N^*(1535)$, $\Delta^*(1600)$, $\Delta^*(1620)$, $N^*(1650)$,
$\Delta^*(1700)$, $N^*(1700)$, $N^*(1710)$, $N^*(1720)$.
Using (\ref{Lag_BNpi}), we have found the vertex factors~\cite{G_pi_JPG}:
\begin{eqnarray}
L(k,l)
&=&-4\left(\frac{f}{m_\pi}\right)^2[2(k\cdot l)^2-a(k\cdot l)k^2
-k^2(l^2+m_Nm_B)],~~ {\rm for}~ J_B^P=\frac{1}{2}^{\pm},
\nonumber\\
&=&-\frac{8}{3m_B^2}\left(\frac{f}{m_\pi}\right)^2[m_Nm_B+l^2-a(k\cdot l)]
[(l\cdot k-ak^2)^2-k^2m_B^2],
\nonumber\\
&&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~{\rm for} J_B^P=\frac{3}{2}^{\pm}~.
\end{eqnarray}
\subsection{Pion thermal width for different mesonic loops}
\label{subsec:pi_mes}
To calculate the mesonic loop contribution of pionic thermal width
$\Gamma_{\pi(\pi M)}$, we have
evaluated pion self-energy for $\pi M$ loops, where $M$ stands for $\sigma$
and $\rho$ mesons. This contribution estimated in our previous work~\cite{GKS}
elaborately. Following that~\cite{GKS}, the expression of pion thermal
width from the mesonic loops is given below
\begin{eqnarray}
\Gamma_{\pi(\pi M)}(\vec k,T) &=& \frac{1}{16\pi|\vec k| m_\pi} \int^{\omega^\pi_{l-}}_{\omega^\pi_{l+}}
d\omega^\pi_l L\left(l_0=-\omega^\pi_l,\vec l,
k_0=\omega_k^\pi,\vec k
\right)\{n_l(\omega^\pi_l)
\nonumber\\
&&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~- n_u(\omega^M_u=\omega^\pi_k + \omega^\pi_l)\}~,
\label{G_pi_piM}
\end{eqnarray}
where $n_l$, $n_u$ are BE distribution functions of $\pi$, $M$
mesons respectively and the limits of integration are
\begin{equation}
\omega^\pi_{l\pm} = \frac{S^2_{\pi(\pi M)}}{2m_\pi^2}
\left(- \omega^\pi_k \pm |\vec k| \, W_{\pi(\pi M)} \right) ,
\end{equation}
with
\begin{equation}
S^2_{\pi(\pi M)}=2m_\pi^2-m_M^2
\end{equation}
and
\begin{equation}
W_{\pi(\pi M)} = \left(1- {4m_\pi^4}/{S^4_{\pi(\pi M)}}\right)^{1/2}~.
\end{equation}
Lagrangian density of pion, sigma and rho mesons can be written as
\begin{equation}
{\cal L}={\cal L}^{\rm free}_\pi + {\cal L}^{\rm free}_\sigma + {\cal L}^{\rm free}_\rho
+ {\cal L}^{\rm int}_{\pi\pi\rho} + {\cal L}^{\rm int}_{\pi\pi\sigma}~,
\end{equation}
where free parts of Lagrangian densities for pseudo-scalar ${\vec \pi}$, scalar $\sigma$
and vector $\rho^\mu$ fields are
are
\begin{eqnarray}
{\cal L}^{\rm free}_\pi&=&\frac{1}{2}\{(\partial_\mu{\vec \pi})\cdot(\partial^\mu{\vec \pi})-m_\pi^2{\vec \pi}^2\}
\nonumber\\
{\cal L}^{\rm free}_\sigma&=&\frac{1}{2}\{(\partial\sigma)^2-m_\sigma^2\sigma^2\}
\nonumber\\
{\cal L}^{\rm free}_\rho&=&\frac{1}{2}\{(\rho_{\mu\nu}\rho^{\mu\nu})-m_\rho^2(\rho_\mu\rho^\mu)\},~
\rho^{\mu\nu}=(\partial^\mu\rho^\nu-\partial^\nu\rho^\mu)
\end{eqnarray}
and their interaction parts are~\cite{Weise_Lag,GKS,SSS}
\begin{eqnarray}
{\cal L}^{\rm int}_{\pi\pi\rho} &=& g_\rho \, {\vec \rho}_\mu \cdot {\vec \pi} \times \partial^\mu {\vec \pi}
\nonumber\\
{\cal L}^{\rm int}_{\pi\pi\sigma}&=& \frac{g_\sigma}{2} m_\sigma {\vec \pi}\cdot {\vec\pi}\,\sigma~.
\label{Lag_pipiM}
\end{eqnarray}
The coupling constant $g_\rho=6$ and $g_\sigma=5.82$ are fixed from experimental
decay width~\cite{GKS} and physical masses of pion, sigma and rho mesons are taken
as $m_\pi=0.140$ GeV, $m_\sigma=0.390$ GeV and $m_\rho=0.770$ GeV.
Using (\ref{Lag_pipiM})
we have obtained the vertex factors:
\begin{eqnarray}
L(k,l) &=& - \frac{g^2_\sigma m_\sigma^2}{4},
~~~~~~~~~~~~~~~~~~~{\rm for}~M=\sigma~,
\nonumber\\
&=& -\frac{g^2_\rho}{m_\rho^2} \,
[ k^2 \left(k^2 - m^2_\rho\right) +
l^2 \left(l^2 - m^2_\rho\right)
- \, 2\{ (k\cdot l) \, m^2_\rho + k^2 \,l^2 \}],~{\rm for}~M=\rho~.
\nonumber\\
\end{eqnarray}
\subsection{Nucleon thermal width}
\label{subsec:N}
In order to calculate the nucleonic thermal width
$\Gamma_{N(\pi B)}$, we have
evaluated nucleon self-energy for different possible $\pi B$ loops,
where $B$ stands for all the baryons as taken in pion self-energy
for baryonic loops.
This contribution is rigorously addressed in our previous work~\cite{G_N}.
Hence taking the relevant expression of nucleon thermal
width for any $\pi B$ loop from the Ref.~\cite{G_N}, we have
\begin{eqnarray}
\Gamma_{N(\pi B)}(\vec k,T,\mu_N) &=& \frac{1}{16\pi|\vec k| m_\pi} \int^{\omega^\pi_{l-}}_{\omega^\pi_{l+}}
d\omega^\pi_l L\left(l_0=-\omega^\pi_l,\vec l,
k_0=\omega_k^N,\vec k
\right)\{n_l(\omega^\pi_l)
\nonumber\\
&&~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~+ n_u(\omega^B_u=\omega^N_k + \omega^\pi_l)\}~,
\label{G_N_piB}
\end{eqnarray}
where $n_l$ and $n_u$ are BE and FD distribution functions for $\pi$ and $B$ respectively.
The relevant limits of integration in Eq.~(\ref{G_N_piB}) are:
\begin{equation}
\omega^N_{l\pm} = \frac{S^2_{N(\pi B)}}{2m_N^2}
\left(- \omega^N_k \pm |\vec k| \, W_{N(\pi B)} \right) ,
\end{equation}
with
\begin{equation}
S^2_{N(\pi B)}=m_N^2-m_B^2+m_\pi^2
\end{equation}
and
\begin{equation}
W_{N(\pi B)} = \left(1- {4m_N^2m_\pi^2}/{S^4_{N(\pi B)}}\right)^{1/2}~.
\end{equation}
The vertex factors~\cite{G_N}:
\begin{eqnarray}
L(k,l)&=&-\left(\frac{f}{m_\pi}\right)^2\left\{\left(\frac{R^2}{2}-m_\pi^2
\right)l_0 -Pm_\pi^2m_B\right\}
~{\rm for}~J_B^P=\frac{1}{2}^{\pm}~,
\nonumber\\
L(k,l)&=&-\left(\frac{f}{m_\pi}\right)^2\frac{2}{3m_B^2}
\left\{\left(\frac{R^2}{2}-m_\pi^2\right)^2
-m_\pi^2m_B^2\right\}(k_0-l_0+Pm_B)
~{\rm for}~J_B^P=\frac{3}{2}^{\pm}
\nonumber\\
\end{eqnarray}
can be deduced by using the $\pi NB$ interaction Lagrangian
densities from Eq.~(\ref{Lag_BNpi}).
\section{Results and Discussion}
\label{sec:num}
The detailed Landau cut contributions of pion
self-energy for mesonic loops and nucleon self-energy
for different $\pi B$ loops are investigated in the earlier
Refs.~\cite{GKS} and \cite{G_N}, where their corresponding
contributions in the shear viscosity are also addressed.
Now in the two component pion-nucleon system, another
contribution to pion thermal width can arise from
the pion self-energy with baryonic loops, which was not
considered in our previous studies of the shear viscosity~\cite{GKS,G_N}.
The main purpose of the present work is to
include these baryonic loop contributions in the pion thermal width and
to revisit the shear viscosity results.
\begin{figure}
\begin{center}
\includegraphics[scale=0.35]{self_M.eps}
\caption{$\Gamma_{\pi(NB)}(M_k)$ for different $NB$ loops
in their Landau regions, which contain the pion pole $M_k=m_\pi$,
denoted by straight dotted line.}
\label{self_M}
\end{center}
\end{figure}
\begin{figure}
\begin{center}
\includegraphics[scale=0.35]{gm_T_piN.eps}
\caption{The on-shell thermal widths (upper panel) and mean free
paths (lower panel) of pion for $\pi M$ loops, $NB$ loops and their total
are represented by dotted, dashed and solid lines respectively while
dash-dotted line denotes the same results for nucleon component with
all possible $\pi B$ loops.}
\label{gm_T_piN}
\end{center}
\end{figure}
\begin{figure}
\begin{center}
\includegraphics[scale=0.35]{gm_mu_piN.eps}
\caption{Same as Fig.~(\ref{gm_T_piN}) along the $\mu_N$ axis.}
\label{gm_mu_piN}
\end{center}
\end{figure}
\begin{figure}
\begin{center}
\includegraphics[scale=0.35]{gm_k_piN.eps}
\caption{Same as Fig.~(\ref{gm_T_piN}) along the $\vec k$ axis}
\label{gm_k_piN}
\end{center}
\end{figure}
Let us first zoom in our attention on the $\Gamma_{\pi(NB)}$.
Fig.~(\ref{self_M}) represents the Landau cut contributions of
different $NB$ loops on the invariant mass axis $M_k$, which can be numerically
generated by replacing $\omega^\pi_k=(\vec k^2+M_k^2)^{1/2}$ in Eq.~(\ref{G_pi_NB}).
For a fixed set of parameters $\vec k$, $T$ and $\mu_N$,
the $\Gamma_{\pi(NB)}(M_k)$ for baryons $B=\Delta(1232)$, $\Delta^*(1650)$,
$N^*(1440)$, $N^*(1700)$ in the upper panel,
$B=N^*(1520)$, $\Delta^*(1620)$, $N^*(1535)$, $\Delta^*(1600)$
in the middle panel and $B=N^*(1720)$, $\Delta^*(1700)$
in the lower panel are individually presented in the Fig.~(\ref{self_M}).
The Landau cut regions, where $\Gamma_{\pi(NB)}(M_k)$ for different $NB$
loops have attained their non-zero values, are clearly observed
in the invariant mass axis. As an example, for $N\Delta$ loop
the Landau region is from $M=0$ to $(m_\Delta-m_N)=0.292$ GeV.
The straight dotted line denotes position of pion pole (i.e. $M_k=m_\pi$),
which indicates the on-shell contribution of $\Gamma_{\pi(NB)}$ for
different baryonic loops. Here we identify $N\Delta$ loop as a leading
candidate to contribute in the pion thermal width among all the baryonic loops.
Adding the on-shell contribution of all $NB$ loops, we get the
total thermal width of pion for baryonic loops, which is plotted
against temperature by dashed line in the upper panel of
Fig.~(\ref{gm_T_piN}). Using Eqs.(\ref{G_pi_piM}) and
(\ref{G_N_piB}), we have also generated the numerical values of
total $\Gamma_{\pi(\pi M)}(T)$ (dotted line) and
$\Gamma_{N(\pi B)}(T)$ (dashed line) by
adding their corresponding loop contributions for a same set
of input parameters ($\vec k=0.3$ GeV, $\mu_N=0$). Following
Eq.~(\ref{Gam_pi}), the solid line represents the $T$ dependence of
total thermal width of pion, $\Gamma_\pi(T)$ after adding the
mesonic and baryonic loop contributions.
All of the $\Gamma$'s are monotonically increasing function but with different
rate of increment.
The corresponding results of
mean free path, defined by $\lambda=\vec k/(\omega_k\Gamma)$, are
presented in the lower panel of the Fig.~(\ref{gm_T_piN}).
Being inversely proportional to the thermal width, the mean free paths for all of the
components monotonically decrease with $T$ and exhibit divergent nature
at low $T$.
Along the $\mu_N$ axis, $\lambda$'s ($\Gamma$'s) for all of the components
also decrease (increase) with different rates as shown in the lower (upper)
panel of Fig.~(\ref{gm_mu_piN}). Here we see that independent nature
of pion thermal width ($\Gamma_{\pi(\pi M)}$) or mean free path ($\lambda_{\pi(\pi M)}$)
for mesonic loops is transformed
to an increasing or decreasing nature when the baryonic loop contribution
is added.
Moreover, the divergence problem of $\lambda_{\pi(NB)}(\mu_N)$ at low $\mu_N$
is also cured in the total mean free path for pionic component $\lambda_\pi(\mu_N)$.
A mild $\mu_N$ dependence of the nucleonic component is observed.
At fixed values of $T$ and $\mu_N$, the momentum distribution of
thermal widths (upper panel) and mean free paths (lower panel) for
all of the components have been displayed in Fig.~(\ref{gm_k_piN}).
Being equivalent to the momentum distribution for the imaginary part
of optical potential (see e.g.~\cite{G_pi_JPG,Rapp_pi}), thermal width
of pion for any mesonic or baryonic loop exhibits a non-monotonic
distribution with a peak structure along the $\vec k$ axis. The mathematical
reason can roughly be understood from the relevant
Eqs.~(\ref{G_pi_piM}) and (\ref{G_pi_NB}) as described in Ref.~\cite{G_pi_JPG}.
After adding the different $NB$ loop contributions, each of which has similar
kind of momentum distribution with different numerical strength, we get
a multi-peak complex structure of $\Gamma_{\pi(NB)}(\vec k)$.
When we add it with the $\Gamma_{\pi(\pi M)}(\vec k)$, which
contains a dominating profile with one peak (due to $\pi\rho$ loop mainly),
then a well behaving momentum distribution with less complex structures (solid line)
is obtained. The $\Gamma_N(\vec k)$ (dash-dotted line) approximately appears
constant with a mild reduction with $\vec k$.
Though we notice a divergent nature of $\lambda_{\pi(NB)}(\vec k)$
out side the range of $\vec k=0.1-1$ GeV
but the total $\lambda_\pi$ in the entire momentum range
remains non-divergent or finite with an well-behaved distribution.
\begin{figure}
\begin{center}
\includegraphics[scale=0.35]{eta_s_T.eps}
\caption{Temperature dependence of shear viscosities (upper panel)
and entropy densities (middle panel)
for pionic (dotted line), nucleonic (dashed line) components and
their total at two different nucleon chemical potentials:
$\mu_N=0$ (solid line) and $\mu_N=0.5$ GeV (dash-dotted line).
In the lower panel, the ratios of total viscosity to entropy density
are represented as a function of $T$
at same set of $\mu_N$'s, taken in the upper and middle panels.}
\label{eta_s_T}
\end{center}
\end{figure}
\begin{figure}
\begin{center}
\includegraphics[scale=0.35]{eta_s_mu.eps}
\caption{The $\mu_N$ dependence of same quantities as Fig.~(\ref{eta_s_T})
at two different temperatures: $T=0.12$ GeV (solid line)
and $T=0.15$ GeV (dash-dotted).}
\label{eta_s_mu}
\end{center}
\end{figure}
\begin{figure}
\begin{center}
\includegraphics[scale=0.35]{ref1.eps}
\caption{Dashed and dotten lines show $\eta_\pi$ without and
with baryonic fluctuations in pion propagation respectively.}
\label{ref1}
\end{center}
\end{figure}
Using the total thermal width for pionic component, $\Gamma_\pi(\vec k,T,\mu_N)$
in Eq.~(\ref{eta_pi}) and
for nucleonic component, $\Gamma_{N}(\vec k,T,\mu_N)$ in Eq.~(\ref{eta_N}),
we have obtained shear viscosities $\eta_\pi(T,\mu_N)$ and $\eta_N(T,\mu_N)$.
They are plotted by dotted and dashed lines respectively as functions
of $T$ and $\mu_N$ in the upper panels of Fig.~(\ref{eta_s_T}) and (\ref{eta_s_mu}).
After exhibiting a soft peak structure in the low $T(<0.1$ GeV), $\eta_\pi(T)$
monotonically increases with a very mild rate in the high $T(>0.1$ GeV) domain.
When a monotonically increasing function $\eta_N(T)$
is added with this pionic component, the total shear viscosity
$\eta_T$ in high $T$ domain
enhances with slightly larger rate of increment, which can be noticed
by solid line in the upper panel of Fig.~(\ref{eta_s_T}).
Another curve of $\eta_T(T)$ at $\mu_N=0.5$ GeV is shown by dash-dotted
line, which faces a rapid increment after $T=0.06$ GeV. The reason of this
drastic enhancement can be well understood from the $\mu_N$ dependence
of the two components $\eta_\pi(\mu_N)$ and $\eta_N(\mu_N)$. The upper
panel of Fig.~(\ref{eta_s_mu}) exposes a rapidly increasing function
$\eta_N(\mu_N)$ and a soft decreasing function $\eta_\pi(\mu_N)$.
Remembering the Fig.~(\ref{gm_mu_piN}), we can understand that the origin
of soft decreasing nature of $\eta_\pi(\mu_N)$ is coming from the baryonic
loop contribution of pion as its mesonic loop contribution is independent
of $\mu_N$. Right panel of Fig.~(\ref{ref1}) is zooming this fact more distinctly,
where we see how inclusion of NB loops in pion self-energy makes $\eta_\pi$
deviate from its independent (dashed line) to dependent (dotted line) nature
with $\mu_N$. This is the main and dramatically important contributions of
the present article as an extension of earlier works~\cite{GKS,G_N}. After
including it, providing a complete picture of shear viscosity calculation
for pion-nucleon system is the main aim of this present investigation.
The dotted lines in the left and right panel of Fig.~(\ref{ref1}) are
exactly same as dotted lines in the upper panels of Fig.~(\ref{eta_s_T})
and (\ref{eta_s_mu}) respectively. Still those curves are repeated for
elaborating the effect of baryonic fluctuations in pion self-energy.
As the phase space factor of Eq.~(\ref{eta_pi}) does not depend
on the $\mu_N$, so only thermal width $\Gamma_\pi(\mu_N)$ controls on the
$\mu_N$ dependence of $\eta_\pi$. Now between two components $\Gamma_{\pi(\pi M)}$
and $\Gamma_{\pi(NB)}$ of $\Gamma_\pi$, the latter one has only the dependency
of $\mu_N$ as exposed in Fig.~(\ref{gm_mu_piN}).
The decreasing nature of $\eta_\pi(\mu_N)$
is solely governed by the increasing (decreasing) nature of function $\Gamma_\pi(\mu_N)$
($\lambda_\pi(\mu_N)$).
Whereas, in case of Eq.~(\ref{eta_N}), nucleonic phase space factor depend
on $\mu_N$ so strongly that it makes $\eta_N(\mu_N)$ be an increasing function
after dominating over the opposite action of $\Gamma_N(\mu_N)$ or
$\lambda_N(\mu_N)$ on the $\eta_N(\mu_N)$.
Middle panels of Fig.~(\ref{eta_s_T}) and (\ref{eta_s_mu}) represent
the $T$ and $\mu_N$ dependence of entropy densities for pionic and
nucleonic components by following their ideal expressions:
\begin{equation}
s_\pi = 3\beta\int \frac{d^3\vec k}{(2\pi)^3} \left(\omega^\pi_k+\frac{\vec k^2}{3\omega^\pi_k}\right)
n_k(\omega^\pi_k)
\label{s_pi}
\end{equation}
and
\begin{equation}
s_N=4\beta\int\frac{d^3\vec k }{(2\pi)^3}
\left(\omega^N_k+\frac{\vec k^2}{3\omega^N_k}-\mu_N\right)n^+_k(\omega^N_k)~.
\label{s_N}
\end{equation}
Using these numerical results of entropy densities (middle panel)
as well as for shear viscosities (upper panel) for
pionic, nucleonic components
and their total , we have presented their
corresponding ratios in the lower panels of the graphs, where straight
horizontal (red) lines stand for KSS bound of the ratio.
The decreasing nature of ratio is sustained for both $\mu_N=0$ (solid line)
and $\mu_N=0.5$ GeV (dash-dotted line) in the entire $T$ axis.
The former is dominating over the later in magnitude for $T\leq 0.12$ GeV
and then an opposite trend is followed beyond $T=0.12$ GeV.
Therefore, the ratio in the $\mu_N$ axis at $T=0.15$ GeV (dash-dotted line)
and $T=0.12$ GeV (solid line) are exhibiting a nature opposite
to each other (up to $\mu_N\approx 0.4$ GeV), which can be observed in the
lower panel of Fig.~(\ref{eta_s_mu}). Nevertheless, both of them increase
in high $\mu_N$ domain ($\mu_N>0.4$ GeV).
Most of the earlier work~\cite{Itakura,Denicol,Bass}
showed a reducing nature of ratio along the $\mu_N$ axis, which is
also found in the present work up to $T\approx 0.12$ GeV but
beyond $T=0.120$ it is not found. It indicates that our approach
has some deficiency with respect to the earlier work~\cite{Itakura,Denicol,Bass}.
This deficiency may be the mixing effect of two component system~\cite{Itakura},
which have been taken care in our further investigations and discussed in next paragraph.
\begin{figure}
\begin{center}
\includegraphics[scale=0.35]{etamix_T_piN.eps}
\caption{Upper panel: Temperature dependence of shear viscosities of
pionic (dotted line), nucleonic (dashed line) components and their
total (at three different values of $\mu_N$) in presence of mixing effect.
Lower panel: The ratios of total viscosity to entropy density vs $T$
at $\mu_N=0$ (solid line), $0.3$ GeV (dash-double-dotted line) and $0.5$ GeV
(dash-dotted line).}
\label{etamix_T_piN}
\end{center}
\end{figure}
\begin{figure}
\begin{center}
\includegraphics[scale=0.35]{etamix_mu_piN.eps}
\caption{upper and middle panels show the $\mu_N$ dependence of same quantities
as in Fig.~(\ref{etamix_T_piN}) at two different temperatures: $T=0.12$ GeV (solid line)
and $T=0.15$ GeV (dash-dotted).
Lower panel: The different points of ($T$, $\mu_N$), where $\eta^{\rm mix}/s$
is approximately equal to the KSS bound.}
\label{etamix_mu_piN}
\end{center}
\end{figure}
We have adopted a rough mixing effect~\cite{G_N},
which can generally be expected between two components of a mixed
gas~\cite{Itakura,mix}. From the Eqs.~(\ref{eta_pi}) and (\ref{eta_N}),
one can clearly notice that the phase space factors of
$\eta_\pi$ and $\eta_N$ do not face any mixing effect of
pion density, $\rho_\pi=3\int\frac{d^3k}{(2\pi)^3}n_k(\omega_k^\pi)$ and
nucleon density, $\rho_N=4\int\frac{d^3k}{(2\pi)^3}n^+_k(\omega_k^N)$.
Although their thermal widths $\Gamma_\pi$ and $\Gamma_N$ contain
this mixing effect as they depend on thermal distribution functions
of both, pion and nucleon. Following
the approximated relation~\cite{Itakura,G_N,mix}
\begin{equation}
\eta^{\rm mix}_{\rm tot}=\eta^{\rm mix}_\pi +\eta^{\rm mix}_N~,
\label{etamix_tot}
\end{equation}
with
\begin{equation}
\eta^{\rm mix}_\pi=\frac{\eta_\pi}{1+\left(\frac{\rho_N}{\rho_\pi}\right)
\left(\frac{\sigma_{\pi N}}{\sigma_{\pi\pi}}\right)\sqrt{\frac{1+m_\pi/m_N}{2}}}
\label{etamix_pi}
\end{equation}
and
\begin{equation}
\eta^{\rm mix}_N=\frac{\eta_N}{1+\left(\frac{\rho_\pi}{\rho_N}\right)
\left(\frac{\sigma_{\pi N}}{\sigma_{NN}}\right)\sqrt{\frac{1+m_N/m_\pi}{2}}}~,
\label{etamix_N}
\end{equation}
where the cross sections of all kind of scattering are simply taken as constant
with same order of magnitude ({\it i.e.}
$\sigma_{\pi\pi}\approx \sigma_{\pi N} \approx \sigma_{NN}$).
In presence of this mixing scenario, the $T$ dependence
of $\eta^{\rm mix}_\pi$ (dotted line), $\eta^{\rm mix}_N$ (dashed line) and
their total $\eta^{\rm mix}_{\rm tot}$ at $\mu_N=0$ (solid line),
$\mu_N=0.3$ GeV (dash-dotted line) and $\mu_N=0.5$ GeV
are shown in the upper panel of Fig.~(\ref{etamix_T_piN}).
The corresponding results along the $\mu_N$ axis for two different
temperatures are presented in the upper panel of Fig.~(\ref{etamix_mu_piN}).
Lower panels of Fig.~(\ref{etamix_T_piN}) and middle panel of
Fig.~(\ref{etamix_mu_piN}) are displaying the viscosity to entropy density
ratios as a function of $T$ (at three different values of $\mu_N$) and
$\mu_N$ (at two different values of $T$). One should comparatively notice
the dash-dotted line in the lower panel of Fig.~(\ref{eta_s_mu}) and the middle
panel of Fig.~(\ref{etamix_mu_piN}), which are exhibiting an opposite
nature in the low $\mu_N$ region. Hence the approximated $T$-$\mu_N$
range, where viscosity to entropy density ratio reduces, is transformed
from ($T=0-0.12$ GeV, $\mu_N=0-0.5$ GeV) to ($T=0-0.15$ GeV, $\mu_N=0-0.5$ GeV)
due to the mixing effect.
Being closer to the earlier results~\cite{Itakura,Denicol,Bass}, specially
the result of Itakura et al.~\cite{Itakura}, the mixing effect appears to be very
important. Though the ratios in both cases, without and with mixing effect
increase beyond the $\mu_N\approx0.5$ GeV but the conclusion of
our results, based on the effective hadronic
Lagrangian, should be concentrated within regions
of $0.100$ GeV $<T<0.160$ GeV and $0<\mu_N<0.500$ GeV.
The lower panel of Fig.~(\ref{etamix_mu_piN}) shows
the $T$-$\mu_N$ points where the ratios are approximately
equal to its KSS bound. From this plot we can get
a rough idea of $T$-$\mu_N$ region, where our shear
viscosity calculations for the pion-nucleon system
may be considered as a reliable estimation by using
the effective hadronic model.
\section{Summary and Conclusion}
\label{sec:concl}
The present work is an extension of our previous studies~\cite{GKS,G_N} of
the shear viscosity calculations for pionic~\cite{GKS} and nucleonic~\cite{G_N}
components, where pion thermal width due to different mesonic fluctuations and the nucleon
thermal width due to different pion-baryon fluctuations are respectively
considered. However, in the two component pion-nucleon system, pion thermal
width may also be originated from different baryonic loops, which
is not taken in our previous investigations~\cite{GKS,G_N}.
Considering this baryonic loop contribution, we have addressed
a complete picture of pion and nucleon propagation via
all possible meson and baryon quantum fluctuations at finite
temperature and density, from where their corresponding
contributions to the shear viscosities have been found.
Following the traditional technique of Kubo relation~\cite{Nicola,Weise,S_rev,G_IJMPA},
the shear viscosities of pion and nucleon components can be deduced from
their corresponding correlators of viscous stress tensor in the static limit,
which will be non-divergent when a
finite thermal width will be introduced in their free propagators.
These finite values of pion and nucleon thermal widths have been
estimated from the RTF calculations of the pion self-energy for different mesonic and baryonic
loops and the nucleon self-energy for different pion-baryon loops.
Thermal width and its inverse quantity, mean free path for each component
is numerically generated as a function of the momentum $\vec k$ of the constituent
and the medium parameters, $T$ and $\mu_N$. They show very non-trivial
momentum distributions, which have been integrated out by the Bose-enhanced
and Pauli-blocked phase space factors of pion and nucleon, respectively, to calculate
their corresponding shear viscosities. We have plotted the shear viscosity
of each component and their total as a function of $T$ and $\mu_N$, where
one can observe a distinct and important effect of
pion thermal width for baryonic loops, which is the main finding
of the present investigation to demonstrate a complete
picture of shear viscosity calculation for pion-nucleon system.
Actually the $\mu_N$ dependence is entering in the shear viscosity
of pionic component via this baryon loop contribution of pion thermal
width. This additional contribution makes the shear viscosity of pionic
component reduce with $\mu_N$ and increase with $T$.
By adopting a rough mixing effect of pion and nucleon densities
between two components, we have tried to present a numerical estimation of total
shear viscosity for a mixed gas of pion-nucleon constituents.
Normalizing by the ideal expressions of entropy densities for pion
and nucleon gas, we have obtained the viscosity to entropy density ratios for each
component and their total. In the relevant $T$-$\mu_N$
region of hadronic domain, this ratio for
the pion-nucleon gas mixture reduces and approaches toward
its KSS bound as $T$ or $\mu_N$ increases.
{\bf Acknowledgment :}
This work is financed by Funda\c{c}\~ao de Amparo \`a Pesquisa do Estado de
S\~ao Paulo - FAPESP, Grant Nos. 2012/16766-0.
I am very grateful to Prof. Gastao Krein for his academic
and non-academic support during my postdoctoral period in Brazil.
|
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Q: Oracle to cassandra data comparison Table in oracle is having one column having values in json string, the same tables with the column values in json needs to be validated in cassandra. But don't know how to do it?
|
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В физике конденсированных сред и физике чёрных дыр, модель Сачдева — Йе — Китаева (SYK) — это точно решаемая модель, которую первоначально предложил Субир Сачдев и Джинву Йе, а затем модифицировал в общепринятую в настоящее время форму Алексей Китаев. Считается, что эта модель помогает понять суть сильно коррелированных материалов, а также имеет тесную связь с дискретной моделью AdS/CFT и фермионным кодом. Модель поддаётся цифровому квантовому моделированию с новаторскими экспериментами, реализованными в установке ЯМР.
Модель SYK
Пусть — целое число и — чётное число такие, что , рассмотрим набор майорановских фермионов которые являются фермионными операторами, которые удовлетворяют условиям: (1) эрмитовы ; (2) cоотношение Клиффорда . Выберем случайную величину такую, что ожидание удовлетворяет: (1) ; и (2) , тогда модель SYK определяется как
.
Обратите внимание, что иногда добавляется дополнительный коэффициент нормализации.
Самая известная модель — это когда , тогда модель принимает вид
,
обратите внимание, что здесь фактор добавляется для совпадения с обычно используемой формой.
Ссылки
Физика конденсированного состояния
|
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{"url":"http:\/\/math.wikia.com\/wiki\/Pi","text":"FANDOM\n\n1,099 Pages\n\n This is a disambiguation page: a list of articles associated with the same title. If you arrived here from another page, you may wish to go back to that page and change the link to point directly to the intended article.\n\nPi, the 16th Greek letter, lowercase \u03c0, uppercase \u03a0, can refer to:\n\n\u2022 pi (constant) - \u03c0 \u2248 3.141592653589793238462643383279502884197169399375105820974944592307816406286208..., an irrational number representing the ratio of a circle's circumference to its diameter (also known as Archimedes' number)\n\u2022 Product operator \u03a0 \u2014 e.g., $\\prod_{i=0}^n f(i)$. (See also product of a sequence.) It is functionally similar to summation notation, using $\\sum_{i=0}^n$, which is the sum of a sequence.\n\u2022 Prime counting function \u03c0(x). (See also prime numbers.) A function defined to return a value equal to the quantity of prime numbers less than or equal to its inputted value. (eg $\\pi(8) = 4$ since only four numbers: 2,3,5,7 are all the prime numbers less than or equal to 8.)\n\u2022 The transformation (horizontal shift) of the Gamma function: $\\Pi(x) = \\Gamma(x+1)$.\n\u2022 The reciprocal of its capitalized counterpart: $\\pi(x) =\\frac{1}{\\Pi(x)}$.\n\u2022 The upside down capital represent Coproducts: $\\coprod_{j \\in J}$","date":"2018-03-24 16:05:44","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 6, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.9554685950279236, \"perplexity\": 917.8644613393438}, \"config\": {\"markdown_headings\": false, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 5, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2018-13\/segments\/1521257650730.61\/warc\/CC-MAIN-20180324151847-20180324171847-00248.warc.gz\"}"}
| null | null |
Filmografia
Cinema
Ghost Ship, regia di Achira Nokthet (2015)
Sweet Boy, regia di Niroon Limsomwong e Sathanapong Limwongthong (2016)
Ton dai took tee - cortometraggio (2017)
SisterS (2019)
Televisione
Run phi Secret Love - serie TV, 8 episodi (2016)
My Dear Loser - Rak mai aothan - serie TV, 10 episodi (2017-2018)
Please... sieng riek winyarn - serie TV, 6 episodi (2017)
YOUniverse - Chakkrawan thoe - webserie, 4 episodi (2018)
Love Songs Love Series - serie TV, 4 episodi (2018)
The Gifted - Nak rian phalang kif - serie TV, 13 episodi (2018)
Happy Birthday - serie TV, 13 episodi (2018)
Our Skyy - Yak hen thong fah pen yang wan nan - miniserie TV, 1 episodio (2018)
He's Coming To Me - miniserie TV, 8 episodi (2019)
Samee See Thong (2019)
BLACKLIST (2019)
Programmi televisivi
Rod rong rian (GMM 25, 2018)
Beauty & The Babes Soo Taai My First Date (YouTube/Line TV, 2018)
Note
Collegamenti esterni
Attori televisivi thailandesi
|
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El Comitè de Bioètica d'Espanya és un òrgan col·legiat, independent i de caràcter consultiu sobre les matèries relacionades amb les implicacions ètiques i socials de la Biomedicina i les Ciències de la Salut. El comitè va ser creat per la Llei 14/2007, de 3 de juliol, de Recerca Biomèdica i està adscrit al Ministeri de Sanitat i Consum d'Espanya. Té la seva seu en l'Institut de Salut Carlos III.
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Els Comitès de Bioètica formen part del compromís institucional que assumeixen els establiments on es realitza recerca en éssers humans, amb les instàncies reguladores, els participants en les recerques i en general amb la societat en el seu conjunt. La inclusió dels aspectes ètics en els protocols de recerca és un indicador de qualitat equiparable al rigor metodològic d'una recerca científica, on els Comitès de Bioètica han de ser els garants que la recerca respongui, des de la valoració dels aspectes ètics, als interessos i a les necessitats de la ciutadania.
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El Ministeri de Sanitat, Serveis Socials i Igualtat nomena als 12 membres, triats entre persones acreditadament qualificades del món científic, jurídic i bioètic per un període de quatre anys renovables per una sola vegada, d'aquesta forma: sis a proposta de les comunitats autònomes, segons el que s'acorda a aquest efecte en el si del Consell Interterritorial del Sistema Nacional de Salut, una pel Ministeri de Justícia, una altra pel Ministeri d'Educació i Ciència, tres pel Ministeri de Sanitat i Consum i una final pel Ministeri d'Indústria, Turisme i Comerç. El Secretari del Comitè és un funcionari amb rang de Sotsdirector General pertanyent a l'Institut de Salut Carlos III, que actua amb veu i sense vot.
Membres del tercer Comitè (2018- )
Federico De Montalvo Jääskeläinen (president), jurista
Rogelio Altisent Trota (vicepresident), metge
Vicente Bellver Capella, filòsof del dret
Fidel Cadena Serrano, fiscal
Pablo Ignacio Fernández Muñiz, metge, conseller de salut del Principat d'Astúries
Álvaro de la Gándara del Castillo, metge, paliativista
Encarnación Guillén Navarro, pediatre, genetista
Nicolás Jouve de la Barreda, biòleg, genetista
Natalia López Moratalla, bioquímica
Manuel de los Reyes López, cardiòleg
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Jose Miguel Serrano Ruiz-Calderón, jurista
Emilia Sánchez Chamorro (secretària), epidemiòloga
Membres del segon Comitè (2013-2018)
Carlos Alonso Bedate, Membre del Centre de Biologia Molecular del CSIC.
César Nombela Cano, catedràtic de Microbiologia de la Facultat de Farmàcia de la Universitat Complutense de Madrid.
Carlos María Romeo Casabona.
Nicolás Jouve de la Barreda, catedràtic de Genètica de la universitat d'Alcalá.
Vicente Bellver Capella, Doctor en Dret i professor titular de Filosofia del Dret a la Universitat de València.
Federico Montalvo Jaaskelainen, Professor de Dret Constitucional de la Universitat Pontifícia de Comillas.
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José Miguel Serrano Ruiz Calderón, professor titular de Filosofia del Dret de la Universitat Complutense de Madrid
Javier Arias Díaz (fins a juliol de 2015), catedràtic de Cirurgia de la UCM, Sotsdirector General de Teràpia Cel·lular i Medicina Regenerativa, ISCIII, actuant com a Secretari del Comitè.
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Emilia Sánchez Chamorro
Membres del primer Comitè (2008-2012)
Carlos Alonso Bedate Membre del Centre de Biologia Molecular del CSIC
Yolanda Gómez Sánchez catedràtica de Dret Constitucional en la UNED i membre del Comitè Internacional de Bioètica de la Unesco
Carmen Ayuso cap associada del Servei de Genètica i sotsdirectora de Recerca de la Fundació Jiménez Díaz, de Madrid
José Antonio Martín Pallín magistrat del Tribunal Suprem
Victoria Camps catedràtica d'Ètica a la Universitat de Barcelona i integrant dels comitès ètics de l'Hospital Vall d'Hebron i de la Fundació Esteve, de Barcelona
Jordi Camí catedràtic de Farmacologia de la Universitat Pompeu Fabra, de Barcelona, i director general del Parc de Recerca Biomèdica de Barcelona
Maria Casado directora del Centre de Recerca Observatori de Bioètica i Dret de la UB-Parc Científic de Barcelona
César Loris president del comitè Ètic de Recerca Clínica d'Aragó i cap del Servei de Nefrología Infantil de l'Hospital Universitari Miguel Servet, de Saragossa.
César Nombela catedràtic de Microbiologia de la Facultat de Farmàcia de la Universitat Complutense de Madrid.
Marcelo Palacios fundador de la Societat Internacional de Bioètica-SIBI.
Carlos Romeo Casabona director de la Càtedra Universitària Fundació BBVA-Diputació Foral de Biscaia de Dret i Genoma Humà de les universitats de Deusto i del País Basc.
Pablo Simón Lorda màster en Bioètica per la Universitat Complutense i professor de l'Escola Andalusa de Salut Pública.
Javier Arias Díaz catedràtic de Cirurgia de la UCM, Sotsdirector General de Teràpia Cel·lular i Medicina Regenerativa, ISCIII, actuant com a Secretari del Comitè.
Referències
Enllaços externs
Comitè de Bioètica d'Espanya
Nomenament dels membres del Comitè de Bioètica d'Espanya
Bioètica
Ciència a Espanya
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 6,410
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/**
* This code is mostly from the old Etherpad. Please help us to comment this code.
* This helps other people to understand this code better and helps them to improve it.
* TL;DR COMMENTS ON THIS FILE ARE HIGHLY APPRECIATED
*/
/**
* Copyright 2009 Google Inc.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS-IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
var padutils = require('./pad_utils').padutils;
var padmodals = (function()
{
var pad = undefined;
var self = {
init: function(_pad)
{
pad = _pad;
},
showModal: function(modalId, duration)
{
$(".modaldialog").hide();
$(modalId).show().css(
{
'opacity': 0
}).animate(
{
'opacity': 1
}, duration);
$("#modaloverlay").show().css(
{
'opacity': 0
}).animate(
{
'opacity': 1
}, duration);
},
hideModal: function(duration)
{
padutils.cancelActions('hide-feedbackbox');
padutils.cancelActions('hide-sharebox');
$("#sharebox-response").hide();
$(".modaldialog").animate(
{
'opacity': 0
}, duration, function()
{
$("#modaloverlay").hide();
});
$("#modaloverlay").animate(
{
'opacity': 0
}, duration, function()
{
$("#modaloverlay").hide();
});
}
};
return self;
}());
exports.padmodals = padmodals;
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 5,070
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Nasookin was a sternwheel-driven steamboat that operated on Kootenay Lake in British Columbia from 1913 to 1947. Nasookin was one of the largest inland steam vessels ever to operate in British Columbia and the Columbia River and its tributaries. Nasookin became surplus to its original owner, the Canadian Pacific Railway, and was transferred to the British Columbia Provincial government which used it as an auto ferry until 1947. Negligent mooring of the steamer in 1948 led to irreparable damage to its hull, and it was later scrapped. Portions of the upper works were salvaged and used as a house.
Name
The name Nasookin was reported to mean "Big Chief." The name was selected by CPR in Montreal on the recommendation of A.D. Wheeler, of Ainsworth, to continue the plan of using First Nations names for all of its steamers on the lake.
Design
Nasookin was the sister ship of two other vessels, Bonnington operating on the Arrow Lakes and Sicamous, on Okanagan Lake. Nasookin was the second to be built, with Bonnington having been the first. Nasookin was nearly identical to Bonnington. Nasookin had a steel deck, whereas that of Bonnington's was of wood. The hull design was slightly different on Nasookin and its engines were more powerful.
Main deck
Nasookin had four decks. The main deck housed the boiler and the engines, and had space for cargo. The crew accommodations were also on the main deck. On the left side of the main deck was a galley, a pantry, the crew's mess, cold storage, and cabins for the cook. On the right side was a bathroom, lavatory, storeroom, waiter's room, express room, and mail room. Also on the main deck were six cabins with bunks for 12 men.
Saloon deck
Next above the main deck was the saloon deck, which was devoted almost entirely to passenger accommodations. In the center of the saloon deck was a dining room which could seat 60 people at its six main tables. The ceiling of the dining room extended through the next deck, creating an impressive effect, similar to ocean-going or coastal steamships of the time.
Forward of the dining room on the left side was the steward's office and room, and on the right side was the purser's office. There were also 14 staterooms on the saloon deck, and, in the forward area, a smoking room with curved sides and large windows. At the rear of the saloon deck was the ladies' saloon.
Gallery deck
Above the saloon deck was the gallery deck, so named because of the gallery around the interior of the deck that overlooked the dining room on the saloon deck. The gallery deck had 25 three-berth staterooms. Forward on the gallery deck was the ladies' observation lounge, while to the rear on this deck was another men's smoking room. The chief engineer also had a cabin on the gallery deck.
Texas deck and pilot house
Above the saloon deck was the texas deck, so named because of a cabin structure, called a texas that was built on this deck. The texas housed a further 18 three-berth staterooms, as well as cabins for the captain and officers, and a room for the boat's watchman. The pilot house was located on top of the texas, just above the captain's cabin.
Construction
The steel hull of Nasookin was built by the Western Drydock and Shipbuilding Company of Port Arthur, Ontario. The hull was then disassembled for shipment by rail to British Columbia to be reassembled for service on Kootenay Lake.
Assembly of Nasookin began in the fall of 1912 at the CPR shipyard at Nelson, British Columbia. Several hundred men were reported to be at work on the vessel. Construction was supervised by the chief engineer of the CPR's Lake and River Service, David Stephens. James M. Bulger master shipbuilder, and J. French, yard foreman, also managed the work.
Dimensions
When built, Nasookin was the largest sternwheeler in British Columbia and the largest sternwheeler north of San Francisco. Nasookin was reported to have been long, exclusive of the extension of the main deck over the stern, called the "fantail", on which the stern-wheel was mounted. Including the fantail, the length overall was .
The beam was , which would have been exclusive of the long protective timbers running alongside the top of the hull, called guards. Nasookin was projected to draw about 5 feet of water.
From the top of the pilot house to the waterline was about 50 feet. Overall size of Nasookin was 1869 gross tons 1035 net tons, with ton in this case being a measure of volume and not weight. Nasookin was reported to have cost $200,000 to build. Nasookin was capable of carrying 550 passengers on day trips, with overnight accommodations for 170.
Engineering
Nasookin was propelled by a stern-wheel turned by twin compound horizontally-mounted steam engines, each with cylinder bores (high pressure) and (low pressure) and a piston stroke of . Another source reports slightly larger piston bore diameters. The boilers produced steam at a pressure of 200 lbs P.S.I. The boilers were coal-fired.
According to one source, the stern-wheel shaft was , with a core. A contemporaneous source reported the stern-wheel was about 20 feet wide, with a diameter of 24 feet. Each paddle blade, called a "bucket" was 25 inches wide. Electricity for the six hundred 16 candle power lights on board was produced by a 25 watt dynamo.
Before launching, Nasookin was expected to be able to reach a speed of per hour, an hour faster than Bonnington, on the Arrow Lakes.
Launch and trial run
Nasookin was launched on April 30, 1913 before a crowd estimated at 2,000 people. The vessel was decorated with flags and bunting. Barges were moored alongside the launch site so that more people could see the launch. The steam tug Ymir and the sternwheeler Nelson also carried sightseers. The launch went well and the new steamer would be ready to run in a week or so, because much of the finish work had already been completed.
Nasookin made its trial run on May 4, 1913 under Captain McKinnon, with David Stephens acting as chief engineer. The vessel went up the west arm of Kootenay Lake to Procter and then into the main lake. The trip was a success.
The formal maiden run of Nasookin was taken on Victoria Day, May 25, 1913, with the boat embarking its full licensed passenger capacity of 550 persons.
Career
The CPR intended Nasookin to be able to handle the growing local business on Kootenay Lake as well as tourism which CPR was in the process of developing. CPR intended that at least in the summer months when traffic was at its busiest, that Nasookin replace Kuskanook on the route on the lake between Procter and Kootenay Landing, British Columbia. By August 1913, Nasookin was running between Nelson and Kootenay Landing, connecting at each point with CPR trains. J.V. Murphy was the CPR's district passenger agent in Nelson, B.C.
In September 1913, CPR offered "reduced rates" to the Spokane Interstate Fair, to be held from September 15 to September 21, in Spokane, Washington. Fare from Greenwood would be $15.15. Fare from Phoenix would be a little bit more, $15.30.
In May 1915, Nasookin was reported to be ready to return to service "as soon as traffic warrants it." On April 1, 1916, Nasookin resumed its route on the West Arm of Kootenay Lake after having been taken out of service for months because of ice on the lake. On Sunday, July 14, 1929, the town of Creston, BC had the "biggest auto tourist day" so far that year, when Nasookin loaded 26 automobiles headed west at Kuskanook, BC.
Auto ferry
By 1931, CPR had no further use for Nasookin. A railway had been completed from Kootenay Landing to Nelson, and steamboat service between the two points was no longer required.
CPR leased Nasookin to the government of British Columbia, to be used to carry motor vehicles from Frasers Landing, which was located near Proctor, on the north side of the west arm of the lake, to Gray Creek on Crawford Bay. At first, the only modification to Nasookin was to remove the extension of the passenger deck from the house to the bow, to permit larger vehicles such as buses to be carried.
First the province leased Nasookin, and then, in 1933, purchased the vessel outright. The upper decks of Nasookin had made the steamer difficult to handle in a cross wind, so it was taken to Nelson and extensively rebuilt, with the cabins on the texas deck completely removed, and the pilot house placed on top of the truncated gallery deck. The steamer became less attractive but more functional, and was able to run for another 15 years.
Disposition
Nasookin was replaced by a twin-propeller ferry in 1947. Nasookin was then sold to Norman C. Stibbs, who then transferred the steamer to the Navy League of Canada for use as a training vessel. In 1948, there were record high levels on Kootenay Lake, and Nasookin broke free from its moorings. The steamer was tied up, but no one paid much care to its location. A concrete wall, not visible under the high water, was under Nasookin's hull, and when the water level fell, the sternwheeler settled on the wall, cracking the hull beyond repair.
In 1950, Nasookin was sold to Earle Cutler, who stripped the parts out of the steamer. The hull was towed away in 1954. Portions of the upper works were made into a house.
Notes
References
Printed sources
On-line newspapers and journals
Paddle steamers of British Columbia
Passenger ships of Canada
Ships built in British Columbia
1913 ships
Ships of CP Ships
Steamboats of Kootenay Lake
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 5,953
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In the first half-hour, First Voices Radio aired an exclusive audio premiere of a new documentary, titled: "Keepers of the Pass." The documentary covers the 2-year saga of the ordeal brought by the Rampough Lenape of New Jersey and their right to pray on land they own across the road from a private community that did not want them there. The land is called the Split Rock Sweetwater Prayer Camp. "Keepers of the Pass," a Human Rights and Fifth Estate Production, was videotaped over several months during the conflict, was created to share with communities suffering racial abuses and similar encroachments on constitutional rights.
in the second half, ANNE WHITE HAT is a member of the Aske Tiospaye (clan) of the Sicangu Lakota Oyate. The Sicangu Lakota is one of the Oceti Sakowin, the Seven Council Fires of the Lakota Oyate (the Lakota Nation). Anne's father is a direct descendant of Chief Iron Shell, and her grandfather was Chief Hollow Horn Bear. Her traditional homelands encompass the Black Hills and prairies of the upper midwest, known as South Dakota. Anne has resided in Louisiana since 2010.
Anne is one of the Indigenous women who have been central to the leadership of the campaign to stop construction of the Bayou Bridge Pipeline, which is designed to carry oil from Lake Charles 162 miles across the state to St. James parish, 30 miles west of New Orleans. Anne was arrested on September 18, 2018, after leading a prayer ceremony at a boat launch near St. Martinville, Louisiana, and charged with two felony counts under La. R.S. 14:61 for unauthorized entry of a critical infrastructure that allegedly occurred on September 3, 2018, near a pipeline construction site in the Atchafalaya Basin. White Hat had been present on the property in question as a Water Protector with the permission of co-owners of the land. She engaged in a non-violent protest against, and monitoring of, the pipeline project and was trying to raise awareness about the fact that the pipeline was being constructed on the property illegally, a fact later confirmed as the company was found by a Louisiana court in December 2018 to have been trespassing at the time.
Anne is the proud mother of three amazing children as well as an experienced herbalist. During the struggle at Standing Rock to stop the Dakota Access Pipeline she returned home to treat Water Protectors at Sacred Stone, Rosebud, and Oceti Sakowin camps. Speaking of this experience, Anne said, "Folks at Standing Rock took a beating for us, every day. They suffered a lot of emotional trauma. A lot of it was trauma that had been in our DNA as Indigenous people — we had suffered these things and survived these things." She stressed the importance of "decolonizing everything … so that we can rebuild our nations and ourselves because it is possible to do that."
Anne has been featured in the media for her activism fighting to defend the earth from oil and gas pipelines, including in The Guardian, Lakota Country Times and Now This News. She is currently facing the possibility of prosecution for the two felony charges that are subject to five years imprisonment each and is a plaintiff in the Center for Constitutional Rights case, White Hat v. Landry.
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 2,358
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package de.olafdietsche.android.samples.listview_arrayadapter;
import java.util.ArrayList;
import android.app.Activity;
import android.os.Bundle;
import android.view.View;
import android.widget.ArrayAdapter;
import android.widget.ListView;
import android.util.Log;
public class MainActivity extends Activity {
@Override
public void onCreate(Bundle savedInstanceState) {
super.onCreate(savedInstanceState);
setContentView(R.layout.main);
ListView list = (ListView) findViewById(R.id.list);
View header = list.inflate(this, R.layout.header, null);
list.addHeaderView(header);
String[] names = getResources().getStringArray(R.array.names);
ArrayAdapter<String> adapter = new ArrayAdapter<String>(this, R.layout.row, names);
list.setAdapter(adapter);
}
private static final String TAG = MainActivity.class.getName();
}
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 8,541
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Белимел () — село в Болгарии. Находится в Монтанской области, входит в общину Чипровци. Население составляет 243 человека.
История
Над селом есть старое римское городище, руины которого можно увидеть и сегодня. Ещё во времена фракийцев Северо-Западная Болгария была заселена племенем трибаллов, что объясняет множество обнаруженных древних объектов, таких как украшения или орудия.
Согласно местным легендам, деревня была разрушена после Чипровского восстания в 1688 году, и его жители переехали в Бессарабию, а поселение было восстановлено 40 лет спустя. Согласно другой легенде, в селе поселились жители разрушенной после восстания деревни Клисура.
Деревня Бели Мел — родина предводителя Вырбанпенского восстания 1837 года, Вырбана Пенова. Считается, что Вырбан Пенов является прототипом Шарлая Белимелеца, героя романа Ивана Вазова «Белимелецът».
Примечания
Ссылки
Статистика населения
Сёла Монтанской области
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 330
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Q: Polynomial expectations of generic distributions Summary
Polynomial expectations depend only moments and cross moments of a multivariate distribution. I would like to use Expectation to compute polynomial expectations for generic distribution of which only the necessary moments are specified.
Some details
I would like to compute polynomial exectations with the function Expectation for variables distributed according to a generic distribution. Here is a toy example:
In[139]:= ClearAll[myDist]
myDist /: Moment[myDist[mu_, var_], 1] := mu
myDist /: Moment[myDist[mu_, var_], 2] := Moment[myDist[mu, var], 1]^2 + var
myDist /: Moment[myDist[0, var_], 4] :=
Cumulant[myDist[0, var], 4] + 2 Moment[myDist[0, var], 2]
myDist /: Moment[myDist[0, var_], 3] := 0
This few lines provide enough information about the distribution myDist so that Mathematica can compute
In[144]:= Expectation[2 x^2, x \[Distributed] myDist[0, s^2], Method -> "Moment"]
Expectation[2 x^4, x \[Distributed] myDist[0, s^2], Method -> "Moment"]
Out[144]= 2 s^2
Out[145]= 2 (2 s^2 + Cumulant[myDist[0, s^2], 4])
I would like to carry out similar calculations with several random variables. For example.
In[147]:= ClearAll[a, b, x, y]
Expectation[
a x + b y, {x \[Distributed] myDist[0, s^2],
y \[Distributed] myDist[0, s^2]}, Method -> "Moment"]
Expectation[(a x + b y)^2, {x \[Distributed] myDist[0, s^2],
y \[Distributed] myDist[0, s^2]}, Method -> "Moment"]
Out[148]= Expectation[
a x + b y, {x \[Distributed] myDist[0, s^2],
y \[Distributed] myDist[0, s^2]}, Method -> "Moment"]
Out[149]= Expectation[(a x + b y)^2, {x \[Distributed] myDist[0, s^2],
y \[Distributed] myDist[0, s^2]}, Method -> "Moment"]
In this case Mathematica doesn't carry out the computation, even though it has all the information to do so. Namely
*
*x and y are independent (this is implied in the specification {x\[Distributed]myDist[0,s^2],y\[Distributed]myDist[0,s^2]}, according to the definition of Expectation);
*the result is completely determined by the first and second moment of x and y (Provided).
One of the problems is that Expectation doesn't know (or it is pre-emped by some other rule or evaluation)
In[153]:= Expectation[
a x + b y, {x \[Distributed] myDist[0, s^2],
y \[Distributed] myDist[0, s^2]}, Method -> "Moment"] ===
a Expectation[x, x \[Distributed] myDist[0, s^2], Method -> "Moment"] +
b Expectation[y, y \[Distributed] myDist[0, s^2], Method -> "Moment"]
Out[153]= False
Notice that all-is-well when the distribution is one that Mathematica knows
In[166]:= Expectation[
a x + b y, {x \[Distributed] NormalDistribution[0, s^2],
y \[Distributed] NormalDistribution[0, s^2]}, Method -> "Moment"]
Out[166]= 0
One possible solution is to define an operator such as myExpectation that knows/uses linearity properties of the mathematical expectation, but I would rather not reinvent the wheel and leverage the power of the built in symbol Expectation (for example specializing a result to one of the built in distributions) as well as the ease with it deals with higher momenta and cumulants.
I tried (with no success)
*
*using ProductDistribution[{myDist[], 2}] instead of
{x\[Distributed]myDist[0,s^2],y\[Distributed]myDist[0,s^2]};
*definiting a generic distribution as suggested (here) with the symbol ProbabilityDistribution. In this case the delayed UpValues for the moments cannot be set.
Indeed
myDist2[mu_, var_] =
ProbabilityDistribution[myDistPDF[x, mu, var], {x, -Infinity, Infinity}]
myDist2 /: Moment[myDist[mu_, var_], 1] := mu
Out[164]= ProbabilityDistribution[
myDistPDF[\[FormalX], mu, var], {\[FormalX], -\[Infinity], \[Infinity]}]
During evaluation of In[164]:= TagSetDelayed::tagnf: Tag myDist2 not found in Moment[ProbabilityDistribution[myDistPDF[\[FormalX],mu_,var_],{\[FormalX],-\[Infinity],\[Infinity]}],1]. >>
Out[165]= $Failed
If a HoldPattern the left-hand-side of the moment delayed assignment, the command executes with no error, but it the information won't be used by Expectation. The reason for this is that Expectation first evaluates its arguments and myDist2 evaluated to
ProbabilityDistribution[myDistPDF[\[FormalX],mu,var],{\[FormalX],-\[Infinity],\[Infinity]}]
and the upvalues of myDist are from then on "invisible" to Expectation.
Some related question on how to define an arbitrary distributions are
here and here.
A: Provided you add
myDist /: Moment[myDist[mu_, var_], 0] := 1
The following (which is risky as it messes up with built in definitions) would
work
freeQ[a_, b_] := FreeQ[a, b] /; Length[b] <= 1
freeQ[a_, b_] := And @@ Map[FreeQ[a, #] &, b] /; Length[b] > 1
Unprotect[Expectation];
Expectation[a__, b__, c__] :=
Map[Expectation[#, b, c] &, a // Expand] /; Head[Expand[a]] == Plus
Expectation[a_ z_, b_, c__] :=
a Expectation[z, b, c] /; freeQ[a, b /. u_ \[Distributed] _ -> u]
Expectation[a_ , {b__, c__}, d__] :=
Expectation[a, b, d] /; freeQ[a, c /. u_ \[Distributed] _ -> u]
Expectation[a1_ a2_ , {b1__, b2__}, c__] :=
Expectation[a1, b1, c] Expectation[a2, b2, c] /;
(freeQ[a2, b1 /. u_ \[Distributed] _ -> u] &&
freeQ[a1, b2 /. u_ \[Distributed] _ -> u] )
Expectation[a_ , {b_, c_}, d__] :=
Expectation[a, c, d] /; freeQ[a, b /. u_ \[Distributed] _ -> u]
Protect[Expectation];
e.g.
Expectation[(a x + b y)^2, {x \[Distributed] myDist[0, s^2],
y \[Distributed] myDist[0, s^2]}, Method -> "Moment"]
(* a^2 s^2+b^2 s^2 *)
Expectation[(a x + b y)^3, {x \[Distributed] myDist[0, s^2],
y \[Distributed] myDist[0, s^2]}, Method -> "Moment"]
(* 0 *)
Once again this is risky and I have not checked all possible edge effects ! :-)
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 9,000
|
Nick Owen: Two Conversations with Roy Wood
Hello ... Hello ... my old friends ... It's great to see you once again! You may recall that the Nick Owen In Conversation With Roy Wood event at Birmingham Town Hall was postponed shortly before the originally intended date of Tuesday 22nd October. The good news is that not only has a new, revised date for this much anticipated event just been announced but a second date at The Garrick Theatre, Lichfield has also been scheduled in early 2014 too thus:
"Eccentric Birmingham-born rock musician Roy Wood visits Symphony Hall in December with his Rock & Roll Band, but prior to this, see him in conversation with Nick Owen. From his performance with The Move on the night England won the World Cup in 1966, to his sparkling 40th Anniversary concert, there is sure to be a lot to talk about! Nick Owen, popular radio and television broadcaster, is best known for his pioneering days in breakfast television, sharing the sofa with Anne Diamond at TV-am in the eighties. Having interviewed literally thousands of people, including six past and present Prime Ministers, showbiz figures from Bob Hope to Morecambe & Wise, members of The Beatles and many more, he visits Town Hall to delve into the career highlights of pop legend Roy Wood." (Birmingham Town Hall)
Friday 31st January
Nick Owen In Conversation With Roy Wood @ Birmingham Town Hall
Tickets: £15.00 each [*plus booking fee][less 10% if booked before 31/12/13]
www.thsh.co.uk/event/nick-owen-in-conversation-with-roy-wood
Nick Owen In Conversation With Roy Wood @ Lichfield Garrick Theatre
Tickets: £15.00 each [*plus booking fee]
www.lichfieldgarrick.com/Shows/Roy-Wood-in-conversation-with-Nick-Owen
"Roy Wood is one of the best known performers to emerge from the prodigious number of prolific musicians who've illuminated popular culture in the Midlands. Roy will be talking to broadcaster Nick Owen in this fascinating evening of stories, from performing at the Royal Albert Hall in front of Her Majesty the Queen to why he's never received a penny in royalties from one of his best known hits, Flowers in the Rain. His anecdotes are compelling and what's more, he plays enough instruments to be able to create an orchestra almost on his own!" (Lichfield Garrick)
ELO Beatles Forever [ELOBF] recommends Roy Wood to those enlightened folks who enjoy the music of ELO, Jeff Lynne, The Move, Wizzard, The Idle Race, 'Brum Beat', The Beatles and related artistes.
Caught Live [4]: Quill @ The Robin 29/12/13
Review: Greatest Failures [Baby Scream]
ELOBF Gig Guide [14]: Q1 2014
Jeff Lynne @ The Troubadour Merry Minstrel II
Caught Live [4]: Roy Wood Rockmas 2013
Second Rare Xanadu 10" Picture Disc Surfaces on eB...
Caught Live [2]: Winston's Big Brother
In Pictures: Secret Messages 2LP Acetates
Caught Live [3]: Roy Wood Rock & Roll Band
Jeff Lynne: Stream of Stars Unveiled
Recommended [2]: ELO My Favourite Band [Gee Sunray...
Remembering Roy Orbison: 25 Years On
Recommended: Rare Session 60 CD ft. Kelly Groucutt...
Caught Live: Winston's Big Brother
American Hustle: Jeff Lynne & ELO Tracks
The Trembling Wilburys: Not Alone Anymore
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 7,104
|
{"url":"http:\/\/tex.stackexchange.com\/questions\/25983\/how-and-when-to-remove-the-space-on-the-left-hand-of-the-beginning-of-a-paragrap","text":"# How and when to remove the space on the left hand of the beginning of a paragraph?\n\nI have something like that:\n\n\\section{subsection}\n...\n\\begin{figure}\n...\n\\end{figure}\ntexttexttext\n...\n\n\nIt turns out that it does not put the \"texttexttext\" on the very left hand side... it leaves some space... My questions are:\n\n1. How to remove this space?\n\n2. Generally speaking, in a technical report, when should we leave some space on the left hand side of the beginning of a paragraph? when shouldn't we?\n\n3. If we leave some space the left hand side of the beginning of a paragraph, should we leave a blank line above it to separate from the previous paragraph?\n\n4. Also, what is the best way to add a blank line? \\\\[1em]?\n\nI would like to know the convention.\n\n-\nCould you be a bit more specific about (4). That is, do you want a general skip between paragraphs of a specific length (say 1em)? \u2013\u00a0 Werner Aug 17 '11 at 19:44\n\n1. In answer to your first question, this space is 'provided' by \\parindent and indents the paragraph by a certain amount. In order to remove it, prepend the paragraph with \\noindent. Some more information on practical and not-so-practical global changes that affect \\parindent, read the UK TeX FAQ entry on 'Zero paragraph indent'.\n\n2. Your second question deals more about personal preference, since there are many documents I've seen that use either an indent or not. Regardless of the choice, even from a technical point of view, consistency should reign supreme.\n\n3. LaTeX provides some guidelines as to where this indentation occurs or not. Some macros (like sectional commands, to name one) end using \\noindent (and sometimes \\ignorespacesafterend) to drop the indent from the paragraph following the command. Perhaps as a prime example, consider the titlesec package. Adjusting the spacing around sectional commands <command> is performed by means of\n\n\\titlespacing[*]{<command>}{<left>}{<before-sep>}{<after-sep>}[right>]\n\n\nThe starred * version specifically kills the indentation of the paragraph following <command>. Again, with the choice left up to the user\/typesetter, this could be considered personal preference.\n\n4. In order to produce an empty line you could use\n\n... orci velit, suscipit quis congue at, laoreet vitae elit.\n\n\\mbox{}% Creates an empty box\n\nLorem ipsum dolor sit amet, consectetur ...\n\n\nHowever, this will necessarily create an empty-line paragraph, and therefore have a \\parskip above and below the line. Although the use of \\\\[<len>] works in text mode for paragraph spacing, is typically used in tabular and array environments. For vertical whitespace of a specific length, use \\vspace*{<len>}. You will notice LaTeX complaining about Underfull \\hbox (badness 10000) in paragraph at lines ... though, which should identify incorrect usage of spacing associated with line breaking.\n\n-\n\nThe \"space\" you are referring to is the paragraph indent, and it is automatically added to each new paragraph (which in your LaTeX source is created by adding a blank line between pragraphs.) It may also be added automatically at the end of certain environments.\n\nThe default for most document classes is to indent every new paragraph except for those immediately following a chapter\/section\/subsection heading.\n\n1. To remove the indent in a single paragraph, use the \\noindent command. You shouldn't generally need to do this, however. If you find indented paragraphs after an environment (e.g. displayed math) that you don't need, you should make sure there is no blank line in your source after the environment. It's helpful to insert a % on a line by itself in these cases to make your source more readable.\n2. When to break a paragraph and when not to is a writing question: it has no direct objective answer, although roughly a paragraph corresponds to a single idea. Here is a link to a reasonable explanation: Paragraphs and paragraphing.\n3. If you are indenting new paragraphs, there is no need to insert blank lines in the output between paragraphs. (Of course your source document will use blank lines to separate paragraphs.)\n4. In general, you shouldn't use \\\\ to create blank lines. The \\\\ command inserts a line break within a single paragraph. As Werner says in his answer, line spacing around headings should be done by the heading definition, and not manually. If you do need to make a blank line, on an exceptional basis, you can insert space with the \\bigskip commands (or \\vspace{}) command, or but generally you shouldn't have to do this. See What is an elegant way to insert a skip between two paragraphs?.\n\nFor some documents (not regular reports\/articles\/theses\/books) it is sometimes appropriate to have no paragraph indentation, and separate paragraphs with blank lines. If you need this kind of format, you should use the parskip package.\n\n-\nTo add to this wonderful answer: I use \\setlength{\\parindent}{0in} in the preambel to eliminate the need for \\noindent altogether. \u2013\u00a0 kongo09 Aug 17 '11 at 20:59\n@kongo09 Unfortunately I don't think this is really a good idea. You need some way to separate paragraphs in your text; either you use a non-zero \\parindent or you use a blank line and no par indent. In the latter case, you should use the parskip package, rather than setting \\parindent to 0. Also, one of the problems with this latter scheme is that it can lead to ambiguous paragraph breaks at page breaks. (Not as big a problem as people like to claim IMO, but still an issue.) \u2013\u00a0 Alan Munn Aug 17 '11 at 21:04\nYou are totally right with respect to normal books or scientific publications (which is the main playground of TeX). However, there are plenty of use-cases where the question of inter-paragraph spacing is totally separate from the indent question. Think, e.g. of a photo collage book without any text or paragraphs. \u2013\u00a0 kongo09 Aug 17 '11 at 21:18\n@kongo09 Perhaps, but if that's the case, you can use \\parskip and just not put any blank lines in your source. :-) \u2013\u00a0 Alan Munn Aug 17 '11 at 21:21","date":"2014-07-11 15:08:25","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.9559561610221863, \"perplexity\": 1403.039355712339}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2014-23\/segments\/1404776427615.55\/warc\/CC-MAIN-20140707234027-00051-ip-10-180-212-248.ec2.internal.warc.gz\"}"}
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The Darkness II
An intense first person shooter that delivers a twisted and gripping narrative of tragedy, modern crime drama, and supernatural horror.
Developer: Digital Extremes Publisher: 2K
Languages: English, French, German, Italian, Japanese, Spanish - Spain, Russian
Tags: FPS (423), Action (364), Gore (345), Shooter (231), Dark (230), Singleplayer (214), Co-op (199), Horror (194), First-Person (161), Violent (137), Multiplayer (132), Atmospheric (127), Story Rich (117), Supernatural (112), Comic Book (101), Short (93), Multiple Endings (79), Adventure (76), Nudity (63), Funny (37)
Category: Single-player, Co-op, Steam Achievements, Partial Controller Support
Release date: Feb 9, 2012
Old userscore: 91% Metascore: 77%
Owners: 1,000,000 .. 2,000,000
Playtime in the last 2 weeks: 59:21 (average) 59:21 (median)
Geography over time (Share)
1 Hook Jan 25, 2015 $1.99 N/A (N/A) 200,000 .. 500,000 0% 00:00 (00:00)
2 SOMA Sep 21, 2015 $29.99 N/A (N/A/84%) 1,000,000 .. 2,000,000 1.28% 03:46 (02:18)
3 Pixel Puzzles: Japan Apr 17, 2014 Free N/A (N/A) 200,000 .. 500,000 0% 00:00 (00:00)
4 Killing Floor - Toy Master Oct 16, 2014 Free N/A (N/A) 500,000 .. 1,000,000 0% 00:00 (00:00)
5 Passing Pineview Forest Nov 21, 2014 Free N/A (N/A) 200,000 .. 500,000 0% 00:00 (00:00)
6 Resident Evil 0 Jan 19, 2016 $4.99 N/A (N/A) 500,000 .. 1,000,000 0% 00:00 (00:00)
7 Magnetic: Cage Closed May 26, 2015 $4.99 N/A (N/A/61%) 50,000 .. 100,000 0% 00:00 (00:00)
8 Five Nights at Freddy's 3 Mar 2, 2015 $7.99 N/A (N/A/68%) 500,000 .. 1,000,000 0% 00:00 (00:00)
9 Spooky's Jump Scare Mansion Jul 28, 2015 Free N/A (N/A) 500,000 .. 1,000,000 0.68% 01:26 (00:28)
10 Wrack Sep 30, 2014 $9.99 N/A (N/A/66%) 50,000 .. 100,000 0% 00:00 (00:00)
11 Super 3-D Noah's Ark Jan 1, 1995 $7.99 N/A (N/A) 50,000 .. 100,000 0% 00:00 (00:00)
12 TransPlan Jun 8, 2015 $2.99 N/A (N/A) 0 .. 20,000 0% 00:00 (00:00)
13 Prominence Poker Dec 12, 2016 Free N/A (N/A) 500,000 .. 1,000,000 3.85% 07:26 (07:19)
14 Outlast 2 Apr 25, 2017 $29.99 N/A (N/A/75%) 1,000,000 .. 2,000,000 0.36% 00:45 (00:15)
15 The Room Two Jul 5, 2016 $4.99 N/A (N/A) 200,000 .. 500,000 0% 00:00 (00:00)
16 Five Nights at Freddy's: Sister Location Oct 7, 2016 $7.99 N/A (N/A/62%) 500,000 .. 1,000,000 0% 00:00 (00:00)
17 Tattletail Dec 28, 2016 $4.99 N/A (N/A) 0 .. 20,000 0% 00:00 (00:00)
18 Bendy and the Ink Machine Feb 10, 2017 $19.99 N/A (N/A) 1,000,000 .. 2,000,000 1.32% 00:32 (00:10)
19 Drunken Robot Pornography Feb 19, 2014 $14.99 N/A (N/A/66%) 100,000 .. 200,000 0% 00:00 (00:00)
20 Half-Life: Opposing Force Nov 1, 1999 $4.99 N/A (N/A) 5,000,000 .. 10,000,000 0.19% 02:35 (00:51)
21 Dead Space (2008) Oct 20, 2008 $19.99 N/A (N/A/86%) 2,000,000 .. 5,000,000 1.18% 02:45 (02:37)
22 Penumbra Overture Mar 30, 2007 $9.99 N/A (N/A/73%) 200,000 .. 500,000 0% 00:00 (00:00)
23 Singularity Jun 30, 2010 $29.99 N/A (N/A/76%) 200,000 .. 500,000 0% 00:00 (00:00)
24 Amnesia: The Dark Descent Sep 8, 2010 $19.99 N/A (N/A/85%) 500,000 .. 1,000,000 0% 00:00 (00:00)
25 Duke Nukem Forever Jun 13, 2011 $19.99 N/A (N/A/54%) 1,000,000 .. 2,000,000 0% 00:00 (00:00)
26 Closure Sep 7, 2012 $9.99 N/A (N/A/78%) 200,000 .. 500,000 0% 00:00 (00:00)
27 Puzzle Agent 2 Jun 30, 2011 $4.99 N/A (N/A/63%) 500,000 .. 1,000,000 0% 00:00 (00:00)
28 Day of Defeat May 1, 2003 $4.99 N/A (N/A/79%) 5,000,000 .. 10,000,000 0.21% 00:01 (00:00)
29 Magrunner: Dark Pulse Jun 20, 2013 $19.99 N/A (N/A/70%) 200,000 .. 500,000 0% 00:00 (00:00)
30 Call of Duty: Advanced Warfare - Gold Edition Nov 3, 2014 $49.99 N/A (N/A/78%) 500,000 .. 1,000,000 0% 00:00 (00:00)
31 Splice Jun 13, 2012 $9.99 N/A (N/A/70%) 200,000 .. 500,000 0% 00:00 (00:00)
32 Far Cry 3 - Blood Dragon May 1, 2013 $14.99 N/A (N/A/81%) 1,000,000 .. 2,000,000 0% 00:00 (00:00)
33 Outlast Sep 4, 2013 $19.99 N/A (N/A/80%) 2,000,000 .. 5,000,000 0% 00:00 (00:00)
34 Amnesia: A Machine for Pigs Sep 10, 2013 $19.99 N/A (N/A/72%) 1,000,000 .. 2,000,000 0% 00:00 (00:00)
35 Among the Sleep - Enhanced Edition Nov 2, 2017 $16.99 N/A (N/A/66%) 200,000 .. 500,000 0% 00:00 (00:00)
Geography of active players over time, share:
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 7,684
|
Gait learning for soft microrobots controlled by light fields
Rohr, A. V., Trimpe, S., Marco, A., Fischer, P., Palagi, S.
In International Conference on Intelligent Robots and Systems (IROS) 2018, pages: 6199-6206, International Conference on Intelligent Robots and Systems 2018, October 2018 (inproceedings)
Soft microrobots based on photoresponsive materials and controlled by light fields can generate a variety of different gaits. This inherent flexibility can be exploited to maximize their locomotion performance in a given environment and used to adapt them to changing environments. However, because of the lack of accurate locomotion models, and given the intrinsic variability among microrobots, analytical control design is not possible. Common data-driven approaches, on the other hand, require running prohibitive numbers of experiments and lead to very sample-specific results. Here we propose a probabilistic learning approach for light-controlled soft microrobots based on Bayesian Optimization (BO) and Gaussian Processes (GPs). The proposed approach results in a learning scheme that is highly data-efficient, enabling gait optimization with a limited experimental budget, and robust against differences among microrobot samples. These features are obtained by designing the learning scheme through the comparison of different GP priors and BO settings on a semisynthetic data set. The developed learning scheme is validated in microrobot experiments, resulting in a 115% improvement in a microrobot's locomotion performance with an experimental budget of only 20 tests. These encouraging results lead the way toward self-adaptive microrobotic systems based on lightcontrolled soft microrobots and probabilistic learning control.
ics pf
arXiv IEEE Xplore DOI Project Page [BibTex]
ics pf Rohr, A. V., Trimpe, S., Marco, A., Fischer, P., Palagi, S. Gait learning for soft microrobots controlled by light fields In International Conference on Intelligent Robots and Systems (IROS) 2018, pages: 6199-6206, International Conference on Intelligent Robots and Systems 2018, October 2018 (inproceedings)
Nanoscale robotic agents in biological fluids and tissues
Palagi, S., Walker, D. Q. T., Fischer, P.
In The Encyclopedia of Medical Robotics, 2, pages: 19-42, 2, (Editors: Desai, J. P. and Ferreira, A.), World Scientific, October 2018 (inbook)
Nanorobots are untethered structures of sub-micron size that can be controlled in a non-trivial way. Such nanoscale robotic agents are envisioned to revolutionize medicine by enabling minimally invasive diagnostic and therapeutic procedures. To be useful, nanorobots must be operated in complex biological fluids and tissues, which are often difficult to penetrate. In this chapter, we first discuss potential medical applications of motile nanorobots. We briefly present the challenges related to swimming at such small scales and we survey the rheological properties of some biological fluids and tissues. We then review recent experimental results in the development of nanorobots and in particular their design, fabrication, actuation, and propulsion in complex biological fluids and tissues. Recent work shows that their nanoscale dimension is a clear asset for operation in biological tissues, since many biological tissues consist of networks of macromolecules that prevent the passage of larger micron-scale structures, but contain dynamic pores through which nanorobots can move.
pf Palagi, S., Walker, D. Q. T., Fischer, P. Nanoscale robotic agents in biological fluids and tissues In The Encyclopedia of Medical Robotics, 2, pages: 19-42, 2, (Editors: Desai, J. P. and Ferreira, A.), World Scientific, October 2018 (inbook)
Soft Miniaturized Linear Actuators Wirelessly Powered by Rotating Permanent Magnets
Qiu, T., Palagi, S., Sachs, J., Fischer, P.
In 2018 IEEE International Conference on Robotics and Automation (ICRA), pages: 3595-3600, May 2018 (inproceedings)
Wireless actuation by magnetic fields allows for the operation of untethered miniaturized devices, e.g. in biomedical applications. Nevertheless, generating large controlled forces over relatively large distances is challenging. Magnetic torques are easier to generate and control, but they are not always suitable for the tasks at hand. Moreover, strong magnetic fields are required to generate a sufficient torque, which are difficult to achieve with electromagnets. Here, we demonstrate a soft miniaturized actuator that transforms an externally applied magnetic torque into a controlled linear force. We report the design, fabrication and characterization of both the actuator and the magnetic field generator. We show that the magnet assembly, which is based on a set of rotating permanent magnets, can generate strong controlled oscillating fields over a relatively large workspace. The actuator, which is 3D-printed, can lift a load of more than 40 times its weight. Finally, we show that the actuator can be further miniaturized, paving the way towards strong, wirelessly powered microactuators.
pf Qiu, T., Palagi, S., Sachs, J., Fischer, P. Soft Miniaturized Linear Actuators Wirelessly Powered by Rotating Permanent Magnets In 2018 IEEE International Conference on Robotics and Automation (ICRA), pages: 3595-3600, May 2018 (inproceedings)
Photogravitactic Microswimmers
Singh, D. P., Uspal, W. E., Popescu, M. N., Wilson, L. G., Fischer, P.
Adv. Func. Mat., 28, pages: 1706660, Febuary 2018 (article)
Abstract Phototactic microorganisms are commonly observed to respond to natural sunlight by swimming upward against gravity. This study demonstrates that synthetic photochemically active microswimmers can also swim against gravity. The particles initially sediment and, when illuminated at low light intensities exhibit wall‐bound states of motion near the bottom surface. Upon increasing the intensity of light, the artificial swimmers lift off from the wall and swim against gravity and away from the light source. This motion in the bulk has been further confirmed using holographic microscopy. A theoretical model is presented within the framework of self‐diffusiophoresis, which allows to unequivocally identify the photochemical activity and the phototactic response as key mechanisms in the observed phenomenology. Since the lift‐off threshold intensity depends on the particle size, it can be exploited to selectively address particles with the same density from a polydisperse mixture of active particles and move them in or out of the boundary region. This study provides a simple design strategy to fabricate artificial microswimmers whose two‐ or three‐dimensional swimming behavior can be controlled with light.
pf Singh, D. P., Uspal, W. E., Popescu, M. N., Wilson, L. G., Fischer, P. Photogravitactic Microswimmers Adv. Func. Mat., 28, pages: 1706660, Febuary 2018 (article)
Chiral Plasmonic Hydrogen Sensors
Matuschek, M., Singh, D. P., Hyeon-Ho, J., Nesterov, M., Weiss, T., Fischer, P., Neubrech, F., Na Liu, L.
Small, 14(7):1702990, Febuary 2018 (article)
In this article, a chiral plasmonic hydrogen‐sensing platform using palladium‐based nanohelices is demonstrated. Such 3D chiral nanostructures fabricated by nanoglancing angle deposition exhibit strong circular dichroism both experimentally and theoretically. The chiroptical properties of the palladium nanohelices are altered upon hydrogen uptake and sensitively depend on the hydrogen concentration. Such properties are well suited for remote and spark‐free hydrogen sensing in the flammable range. Hysteresis is reduced, when an increasing amount of gold is utilized in the palladium‐gold hybrid helices. As a result, the linearity of the circular dichroism in response to hydrogen is significantly improved. The chiral plasmonic sensor scheme is of potential interest for hydrogen‐sensing applications, where good linearity and high sensitivity are required.
pf Matuschek, M., Singh, D. P., Hyeon-Ho, J., Nesterov, M., Weiss, T., Fischer, P., Neubrech, F., Na Liu, L. Chiral Plasmonic Hydrogen Sensors Small, 14(7):1702990, Febuary 2018 (article)
Acoustic Fabrication via the Assembly and Fusion of Particles
Melde, K., Choi, E., Wu, Z., Palagi, S., Qiu, T., Fischer, P.
Acoustic assembly promises a route toward rapid parallel fabrication of whole objects directly from solution. This study reports the contact-free and maskless assembly, and fixing of silicone particles into arbitrary 2D shapes using ultrasound fields. Ultrasound passes through an acoustic hologram to form a target image. The particles assemble from a suspension along lines of high pressure in the image due to acoustic radiation forces and are then fixed (crosslinked) in a UV-triggered reaction. For this, the particles are loaded with a photoinitiator by solvent-induced swelling. This localizes the reaction and allows the bulk suspension to be reused. The final fabricated parts are mechanically stable and self-supporting.
pf Melde, K., Choi, E., Wu, Z., Palagi, S., Qiu, T., Fischer, P. Acoustic Fabrication via the Assembly and Fusion of Particles Advanced Materials, 30(3):1704507, January 2018 (article)
The Impact of Robotics and Automation on Working Conditions and Employment [Ethical, Legal, and Societal Issues]
Pham, Q., Madhavan, R., Righetti, L., Smart, W., Chatila, R.
IEEE Robotics and Automation Magazine, 25(2):126-128, June 2018 (article)
mg Pham, Q., Madhavan, R., Righetti, L., Smart, W., Chatila, R. The Impact of Robotics and Automation on Working Conditions and Employment [Ethical, Legal, and Societal Issues] IEEE Robotics and Automation Magazine, 25(2):126-128, June 2018 (article)
Unsupervised Contact Learning for Humanoid Estimation and Control
Rotella, N., Schaal, S., Righetti, L.
In 2018 IEEE International Conference on Robotics and Automation (ICRA), pages: 411-417, IEEE, Brisbane, Australia, 2018 (inproceedings)
This work presents a method for contact state estimation using fuzzy clustering to learn contact probability for full, six-dimensional humanoid contacts. The data required for training is solely from proprioceptive sensors - endeffector contact wrench sensors and inertial measurement units (IMUs) - and the method is completely unsupervised. The resulting cluster means are used to efficiently compute the probability of contact in each of the six endeffector degrees of freedom (DoFs) independently. This clustering-based contact probability estimator is validated in a kinematics-based base state estimator in a simulation environment with realistic added sensor noise for locomotion over rough, low-friction terrain on which the robot is subject to foot slip and rotation. The proposed base state estimator which utilizes these six DoF contact probability estimates is shown to perform considerably better than that which determines kinematic contact constraints purely based on measured normal force.
am mg Rotella, N., Schaal, S., Righetti, L. Unsupervised Contact Learning for Humanoid Estimation and Control In 2018 IEEE International Conference on Robotics and Automation (ICRA), pages: 411-417, IEEE, Brisbane, Australia, 2018 (inproceedings)
Learning Task-Specific Dynamics to Improve Whole-Body Control
Gams, A., Mason, S., Ude, A., Schaal, S., Righetti, L.
In Hua, IEEE, Beijing, China, November 2018 (inproceedings)
In task-based inverse dynamics control, reference accelerations used to follow a desired plan can be broken down into feedforward and feedback trajectories. The feedback term accounts for tracking errors that are caused from inaccurate dynamic models or external disturbances. On underactuated, free-floating robots, such as humanoids, high feedback terms can be used to improve tracking accuracy; however, this can lead to very stiff behavior or poor tracking accuracy due to limited control bandwidth. In this paper, we show how to reduce the required contribution of the feedback controller by incorporating learned task-space reference accelerations. Thus, we i) improve the execution of the given specific task, and ii) offer the means to reduce feedback gains, providing for greater compliance of the system. With a systematic approach we also reduce heuristic tuning of the model parameters and feedback gains, often present in real-world experiments. In contrast to learning task-specific joint-torques, which might produce a similar effect but can lead to poor generalization, our approach directly learns the task-space dynamics of the center of mass of a humanoid robot. Simulated and real-world results on the lower part of the Sarcos Hermes humanoid robot demonstrate the applicability of the approach.
am mg Gams, A., Mason, S., Ude, A., Schaal, S., Righetti, L. Learning Task-Specific Dynamics to Improve Whole-Body Control In Hua, IEEE, Beijing, China, November 2018 (inproceedings)
An MPC Walking Framework With External Contact Forces
Mason, S., Rotella, N., Schaal, S., Righetti, L.
In 2018 IEEE International Conference on Robotics and Automation (ICRA), pages: 1785-1790, IEEE, Brisbane, Australia, May 2018 (inproceedings)
In this work, we present an extension to a linear Model Predictive Control (MPC) scheme that plans external contact forces for the robot when given multiple contact locations and their corresponding friction cone. To this end, we set up a two-step optimization problem. In the first optimization, we compute the Center of Mass (CoM) trajectory, foot step locations, and introduce slack variables to account for violating the imposed constraints on the Zero Moment Point (ZMP). We then use the slack variables to trigger the second optimization, in which we calculate the optimal external force that compensates for the ZMP tracking error. This optimization considers multiple contacts positions within the environment by formulating the problem as a Mixed Integer Quadratic Program (MIQP) that can be solved at a speed between 100-300 Hz. Once contact is created, the MIQP reduces to a single Quadratic Program (QP) that can be solved in real-time ({\textless}; 1kHz). Simulations show that the presented walking control scheme can withstand disturbances 2-3× larger with the additional force provided by a hand contact.
am mg Mason, S., Rotella, N., Schaal, S., Righetti, L. An MPC Walking Framework With External Contact Forces In 2018 IEEE International Conference on Robotics and Automation (ICRA), pages: 1785-1790, IEEE, Brisbane, Australia, May 2018 (inproceedings)
Lethal Autonomous Weapon Systems [Ethical, Legal, and Societal Issues]
Righetti, L., Pham, Q., Madhavan, R., Chatila, R.
IEEE Robotics \& Automation Magazine, 25(1):123-126, March 2018 (article)
The topic of lethal autonomous weapon systems has recently caught public attention due to extensive news coverage and apocalyptic declarations from famous scientists and technologists. Weapon systems with increasing autonomy are being developed due to fast improvements in machine learning, robotics, and automation in general. These developments raise important and complex security, legal, ethical, societal, and technological issues that are being extensively discussed by scholars, nongovernmental organizations (NGOs), militaries, governments, and the international community. Unfortunately, the robotics community has stayed out of the debate, for the most part, despite being the main provider of autonomous technologies. In this column, we review the main issues raised by the increase of autonomy in weapon systems and the state of the international discussion. We argue that the robotics community has a fundamental role to play in these discussions, for its own sake, to provide the often-missing technical expertise necessary to frame the debate and promote technological development in line with the IEEE Robotics and Automation Society (RAS) objective of advancing technology to benefit humanity.
mg Righetti, L., Pham, Q., Madhavan, R., Chatila, R. Lethal Autonomous Weapon Systems [Ethical, Legal, and Societal Issues] IEEE Robotics \& Automation Magazine, 25(1):123-126, March 2018 (article)
Nonlinear optical spectroscopy of chiral molecules
Fischer, P., Hache, F.
CHIRALITY, 17(8):421-437, 2005 (article)
We review nonlinear optical processes that are specific to chiral molecules in solution and on surfaces. In contrast to conventional natural optical activity phenomena, which depend linearly on the electric field strength of the optical field, we discuss how optical processes that are nonlinear (quadratic, cubic, and quartic) functions of the electromagnetic field strength may probe optically active centers and chiral vibrations. We show that nonlinear techniques open entirely new ways of exploring chirality in chemical and biological systems: The cubic processes give rise to nonlinear circular dichroism and nonlinear optical rotation and make it possible to observe dynamic chiral processes at ultrafast time scales. The quadratic second-harmonic and sum-frequency-generation phenomena and the quartic processes may arise entirely in the electric-dipole approximation and do not require the use of circularly polarized light to detect chirality: They provide surface selectivity and their observables can be relatively much larger than in linear optical activity. These processes also give rise to the generation of light at a new color, and in liquids this frequency conversion only occurs if the solution is optically active. We survey recent chiral nonlinear optical experiments and give examples of their application to problems of biophysical interest. (C) 2005 Wiley-Liss, Inc.
pf Fischer, P., Hache, F. Nonlinear optical spectroscopy of chiral molecules CHIRALITY, 17(8):421-437, 2005 (article)
Negative refraction at optical frequencies in nonmagnetic two-component molecular media
Chen, Y., Fischer, P., Wise, F.
PHYSICAL REVIEW LETTERS, 95(6), 2005 (article)
There is significant motivation to develop media with negative refractive indices at optical frequencies, but efforts in this direction are hampered by the weakness of the magnetic response at such frequencies. We show theoretically that a nonmagnetic medium with two atomic or molecular constituents can exhibit a negative refractive index. A negative index is possible even when the real parts of both the permittivity and permeability are positive. This surprising result provides a route to isotropic negative-index media at optical frequencies.
pf Chen, Y., Fischer, P., Wise, F. Negative refraction at optical frequencies in nonmagnetic two-component molecular media PHYSICAL REVIEW LETTERS, 95(6), 2005 (article)
A dynamical systems approach to learning: a frequency-adaptive hopper robot
Buchli, J., Righetti, L., Ijspeert, A.
In Proceedings of the VIIIth European Conference on Artificial Life ECAL 2005, pages: 210-220, Springer Verlag, 2005 (inproceedings)
mg Buchli, J., Righetti, L., Ijspeert, A. A dynamical systems approach to learning: a frequency-adaptive hopper robot In Proceedings of the VIIIth European Conference on Artificial Life ECAL 2005, pages: 210-220, Springer Verlag, 2005 (inproceedings)
From Dynamic Hebbian Learning for Oscillators to Adaptive Central Pattern Generators
Righetti, L., Buchli, J., Ijspeert, A.
In Proceedings of 3rd International Symposium on Adaptive Motion in Animals and Machines – AMAM 2005, Verlag ISLE, Ilmenau, 2005 (inproceedings)
mg Righetti, L., Buchli, J., Ijspeert, A. From Dynamic Hebbian Learning for Oscillators to Adaptive Central Pattern Generators In Proceedings of 3rd International Symposium on Adaptive Motion in Animals and Machines – AMAM 2005, Verlag ISLE, Ilmenau, 2005 (inproceedings)
Isotropic second-order nonlinear optical susceptibilities
Fischer, P., Buckingham, A., Albrecht, A.
PHYSICAL REVIEW A, 64(5), 2001 (article)
The second-order nonlinear optical susceptibility, in the electric dipole approximation, is only nonvanishing for materials that are noncentrosymmetric. Should the medium be isotropic, then only a chiral system. such as an optically active liquid, satisfies this symmetry requirement. We derive the quantum-mechanical form of the isotropic component of the sum- and difference-frequency susceptibility and discuss its unusual spectral properties. We show that any coherent second-order nonlinear optical process in a system of randomly oriented molecules requires the medium to be chiral. and the incident frequencies to be different and nonzero. Furthermore, a minimum of two nondegenerate excited molecular states are needed for the isotropic part of the susceptibility to be nonvanishing. The rotationally invariant susceptibility is zero in the static field limit and shows exceptionally sensitive resonance and dephasing effects that are particular to chiral centers.
pf Fischer, P., Buckingham, A., Albrecht, A. Isotropic second-order nonlinear optical susceptibilities PHYSICAL REVIEW A, 64(5), 2001 (article)
Reply to "Comment on 'Phenomenological damping in optical response tensors'"
Buckingham, A., Fischer, P.
We show that damping factors must not be incorporated in the perturbation of the ground state by a static electric field. If they are included, as in the theory of Stedman et al. {[}preceding Comment. Phys. Rev. A 63, 047801 (2001)], then there would be an electric dipole in the y direction induced in a hydrogen atom in the M-s = + 1/2 state by a static electric field in the x direction. Such a dipole is excluded by symmetry.
pf Buckingham, A., Fischer, P. Reply to "Comment on 'Phenomenological damping in optical response tensors'" PHYSICAL REVIEW A, 63(4), 2001 (article)
Phenomenological damping in optical response tensors
Although perturbation theory applied to the optical response of a molecule or material system is only strictly valid far from resonances, it is often applied to ``near-resonance{''} conditions by means of complex energies incorporating damping. Inconsistent signs of the damping in optical response tensors have appeared in the recent literature, as have errors in the treatment of the perturbation by a static held. The ``equal-sign{''} convention used in a recent publication yields an unphysical material response, and Koroteev's intimation that linear electro-optical circular dichroism may exist in an optically active liquid under resonance conditions is also flawed. We show that the isotropic part of the Pockels tensor vanishes.
pf Buckingham, A., Fischer, P. Phenomenological damping in optical response tensors PHYSICAL REVIEW A, 61(3), 2000 (article)
Ab initio investigation of the sum-frequency hyperpolarizability of small chiral molecules
Champagne, B., Fischer, P., Buckingham, A.
CHEMICAL PHYSICS LETTERS, 331(1):83-88, 2000 (article)
Using a sum-over-states procedure based on configuration interaction singles /6-311++G{*}{*}, we have computed the sum-frequency hyperpolarizability beta (ijk)(-3 omega; 2 omega, omega) Of two small chiral molecules, R-monofluoro-oxirane and R-(+)-propylene oxide. Excitation energies were scaled to fit experimental UV-absorption data and checked with ab initio values from time-dependent density functional theory. The isotropic part of the computed hyperpolarizabilities, beta(-3 omega; 2 omega, omega), is much smaller than that reported previously from sum-frequency generation experiments on aqueous solutions of arabinose. Comparison is made with a single-centre chiral model. (C) 2000 Elsevier Science B.V. All rights reserved.
pf Champagne, B., Fischer, P., Buckingham, A. Ab initio investigation of the sum-frequency hyperpolarizability of small chiral molecules CHEMICAL PHYSICS LETTERS, 331(1):83-88, 2000 (article)
Three-wave mixing in chiral liquids
Fischer, P., Wiersma, D., Righini, R., Champagne, B., Buckingham, A.
PHYSICAL REVIEW LETTERS, 85(20):4253-4256, 2000 (article)
Second-order nonlinear optical frequency conversion in isotropic systems is only dipole allowed for sum- and difference-frequency generation in chiral media. We develop a single-center chiral model of the three-wave mixing (sum:frequency generation) nonlinearity and estimate its magnitude. We also report results from ab initio calculations and from three- and four-wave mixing experiments in support of the theoretical estimates. We show that the second-order susceptibility in chiral liquids is much smaller than previously thought.
pf Fischer, P., Wiersma, D., Righini, R., Champagne, B., Buckingham, A. Three-wave mixing in chiral liquids PHYSICAL REVIEW LETTERS, 85(20):4253-4256, 2000 (article)
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Home » #deadwitness , obit , Public Official » #deadwitness City clerk Deanna Despain found dead in Oakland
#deadwitness City clerk Deanna Despain found dead in Oakland
Pete BennettNovember 17, 2020 No comments
On it's own not too far out of bounds but when San Ramon City Clerk Patricia Perry killed in Murder Suicide
Deanna Despain
City clerk Deanna Despain found dead in Oakland
January 9, 2012 12:05 pm by Lance Knobel
Update 2:35 p.m. The Associated Press is reporting that Deanna Despain's death was apparently because of a fall down a staircase in her home. She was found by her husband. There were no signs of foul play.
Deanna Despain, Berkeley's city clerk, was found dead in her home on the 4100 block of Lyman Road in Oakland at 2 a.m. on Saturday morning. The Oakland police are treating the death as suspicious.
The coroner's office is not yet releasing any information about the death, referring enquiries to the Oakland Police Department.
Despain became acting city clerk in June, 2008, with the retirement of Pamyla Means. She was appointed city clerk in May 2009. She had worked for the city for over 10 years. The birth of her child, on March 22 last year, was applauded at that evening's City Council meeting.
"Deanna was super smart, she was really on top of things," said Mark Rhoades, who worked with Despain when he was in the city's planning department. "She cared a lot about the city."
In the city offices today, word about Despain's death spread without any official news. City staff said they were working with Despain's family on an announcement, pending official word from the OPD.
Berkeleyside is awaiting information from the OPD and will provide updates as details emerge.
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{"url":"http:\/\/www.mathjournals.org\/jot\/2004-052-002\/2004-052-002-001.html","text":"Previous issue \u00b7\u00a0 Next issue \u00b7\u00a0 Most recent issue \u00b7\u00a0All issues\n\n# Journal of Operator Theory\n\nVolume 52, Issue 2, Fall 2004 \u00a0pp. 223-249.\n\nCuntz-Pimsner algebras of group actions\n\nAuthors Volodymyr V. Nekrashevych\nAuthor institution: International University Bremen, School of Engineering and Science, P.O. Box 750 561, 28725 Bremen, Germany\n\nSummary:\u00a0 We associate a $*$-bimodule over the group algebra to every self-similar group action on the space of one-sided sequences. Completions of the group algebra, which agree with the bimodule are investigated. This gives new examples of Hilbert bimodules and the associated Cuntz-Pimsner algebras. A direct proof of simplicity of these algebras is given. We show also a relation between the Cuntz algebras and the Higman-Thompson groups and define an analog of the Higman-Thompson group for the Cuntz-Pimsner algebra of a self-similar group action.\n\nContents \u00a0\u00a0 Full-Text PDF","date":"2022-07-07 17:03:52","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.21351556479930878, \"perplexity\": 1582.3027009696511}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2022-27\/segments\/1656104495692.77\/warc\/CC-MAIN-20220707154329-20220707184329-00051.warc.gz\"}"}
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{"url":"https:\/\/nrich.maths.org\/371","text":"### Triangle Incircle Iteration\n\nKeep constructing triangles in the incircle of the previous triangle. What happens?\n\n### Circumspection\n\nM is any point on the line AB. Squares of side length AM and MB are constructed and their circumcircles intersect at P (and M). Prove that the lines AD and BE produced pass through P.\n\n### Lawnmower\n\nA kite shaped lawn consists of an equilateral triangle ABC of side 130 feet and an isosceles triangle BCD in which BD and CD are of length 169 feet. A gardener has a motor mower which cuts strips of grass exactly one foot wide and wishes to cut the entire lawn in parallel strips. What is the minimum number of strips the gardener must mow?\n\n# Long Short\n\n##### Stage: 4 Challenge Level:\nDraw a circle with radius $1$ unit. Choose any four points on the circumference and join them together to form a quadrilateral.\n\nLabel the sides: $a$ is the shortest, $b$ is the next shortest, then $c$, and finally $d$ is the longest side (it is possible to have two sides of equal length).\n\nWhat is the maximum length that the shortest side $a$ could be?\n\nSide $b$ must be less than a certain value - what value?\n\nWhat is the maximum length that the longest side $d$ could be? Is it possible for $c$ and $d$ both to be this maximum length?","date":"2017-07-22 08:50:58","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.4686563014984131, \"perplexity\": 696.0192764070592}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2017-30\/segments\/1500549423927.54\/warc\/CC-MAIN-20170722082709-20170722102709-00107.warc.gz\"}"}
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{"url":"http:\/\/mathhelpforum.com\/pre-calculus\/214591-exponential-equation-quadratic-form.html","text":"# Math Help - Exponential Equation in Quadratic Form\n\n1. ## Exponential Equation in Quadratic Form\n\nI am curious as to how i am to solve and equation with a negative exponent.\nMy problem is:\n10e^x-15-45e^-x=0\nWe are suppose to use the formula that u=e^x.\nI don't know what to do since there is a negative after the 45.\n\n2. ## Re: Exponential Equation in Quadratic Form\n\nOriginally Posted by paigesisco\n10e^x-15-45e^-x=0\nWe are suppose to use the formula that u=e^x.\nI don't know what to do since there is a negative after the 45.\n$\\\\10e^x-15-45e^{-x}=0\\\\10e^{2x}-15e^x-45=0\\\\2e^{2x}-3e^x-9=0\\\\(2e^x+3)(e^x-3)=0$\n\n3. ## Re: Exponential Equation in Quadratic Form\n\nCan you explain the method you used so that i can use it on future problems? I am confused on how the x's transfered\n\n4. ## Re: Exponential Equation in Quadratic Form\n\nOriginally Posted by paigesisco\nCan you explain the method you used so that i can use it on future problems? I am confused on how the x's transfered\nTake the original equation an multiply all terms by $e^x$.","date":"2015-01-31 00:53:26","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 2, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.7450293898582458, \"perplexity\": 672.4527265247399}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.3, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2015-06\/segments\/1422122047499.45\/warc\/CC-MAIN-20150124175407-00202-ip-10-180-212-252.ec2.internal.warc.gz\"}"}
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{"url":"https:\/\/mathoverflow.net\/questions\/191241\/removing-subtrees","text":"# Removing subtrees\n\nLet $T$ be a complete infinite rooted binary tree. Is it possible to remove (infinitely many) subtrees of $T$ and get a subgraph $G$ such that:\n\n1. $G$ has no complete subtrees (the graph below any vertex of $G$ is not a complete binary tree).\n\n2. There exists some $\\epsilon > 0$ such that for any $n \\in \\mathbb{N}$ the number of vertices of $G$ whose distance from the root is $n$ is at least $\\epsilon2^n$.\n\nYes. In fact you can take the tree corresponding to all sequences $x$ of 0s and 1s such that the fraction of 1s is no more than 2\/3.\n\n\u2022 This is a good idea. The problem is that even though 1 and 2 are satisfied, I do not see why this set of sequences can be obtained by removing subtrees as I required. What you can get by removing subtrees, is the set of sequences with every prefix having at most 2\/3 1s. In this case, is 2 satisfied? Dec 22 '14 at 7:31\n\u2022 Yes, implicitly I meant that (see version before I edited the answer if you can). And yes, 2 is satisfied. Take a look at the proof of the strong law of large numbers to see why. Dec 22 '14 at 7:41\n\nI don't know if it will help you, but there is another reformulation that may be useful here.\n\nYou can model the infinite complete binary tree $\\{0,1\\}^{\\omega}$ by the interval $[0,1]$ (with the binary expansion). In particular, if you fix a finite binary string $x$, then the subtree consisting of the branch $x$ followed by a complete binary tree represents a subinterval of $[0,1]$ of length $2^{-|x|}$.\n\nSo finding a subtree satisfying your condition 1 amounts to finding a subset of $[0,1]$ with (Lebesgue) measure zero closed subset with empty interior (thanks Blass).\n\nThe condition 2 is related to Hausdorff dimension of subsets of $[0,1]$. Indeed, the collection of vertices at distance $n$ from the root can be seen as a collection of subintervals, each of length $2^{-n}$, whose union covers your subset. The number of vertices is then the number of such intervals.\n\nRoughly speaking, if you take a subset of dimension $\\theta$ (Hausdorff or a variant, I don't remember exactly), then the number of vertices of your subtree at distance $n$ grows like $O(\\theta^n)$ when $n \\rightarrow \\infty$.\n\npb\n\n\u2022 In the $[0,1]$ model, condition 1 requires the set to be a closed set with empty interior, but it can still have positive Lebesgue measure. Dec 22 '14 at 0:31\n\u2022 Oops, you're right! Dec 22 '14 at 0:57","date":"2021-11-28 03:29:59","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.8935041427612305, \"perplexity\": 149.67765143894405}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2021-49\/segments\/1637964358443.87\/warc\/CC-MAIN-20211128013650-20211128043650-00352.warc.gz\"}"}
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## _Dedication_
_To my mother, Rose,_
_another beautiful flower_
## Epigraph
What is a weed?
A plant whose virtues have not yet been discovered.
—RALPH WALDO EMERSON
## Contents
1. _Dedication_
2. _Epigraph_
3. _Contents_
4. PART I: THE OLD WORLD
1. _Introduction: The Girls in the Basement_
2. 1. Big Bad Scary Weed
3. 2. The Dutch Masters
4. 3. The Martyr and the Millionaires
5. PART II: THE NEW WORLD
1. 4. Widgets and Dabs
2. 5. The Endocannabinoid System: The Body's Supercomputer
3. 6. The World's Largest Human Trial
4. 7. Snake Oil or Cancer Cure?
5. 8. Budtenders and Sinsemilliers: Inside the Dispensary
6. PART III: FUTURE WEED
1. 9. Designing Your Highs
2. 10. The Four Enhancements
3. 11. The Next Reinvention of Weed
7. _Appendix: Beyond Stoned—Cannabis for Inspiration, Intimacy, and Other Adult Pleasures_
8. _Acknowledgments_
9. _Notes_
10. _About the Author_
11. _Credits_
12. _Copyright_
13. _About the Publisher_
# Guide
1. Cover
2. Contents
3. Chapter 1
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## PART I
## THE OLD WORLD
## ___Introduction_
## THE GIRLS IN THE BASEMENT
_New England_
Want to see my new hobby?"
It was 8:17 on a crisp Sunday morning in the autumn of 2012 when my cousin awakened me with a cup of coffee and that question. He was standing over my bed, practically panting with an anticipation that made saying no impossible. Little did I know that his new hobby was about to change my life.
I sipped my coffee, pulled on my clothes, and followed him downstairs through the garage, then behind a padlocked door that led me into a foam-insulated antechamber that housed plant food, smelled like Odor-Eaters, and hummed with machine-made white noise. He flashed me a broad smile as he unlocked another door, which led me into a basement grow room and the source of the new hobby: two floor-to-ceiling Mylar bags that, when unzipped, revealed six budding female cannabis plants, all basking in the hot yellow glow of one 400-watt high-pressure sodium lightbulb. The girls oiled the air with a skunky, grassy scent, and they looked very happy—as they should be, living in a cushy, digitally controlled 68-degree climate, bathing in a steady cloud of intoxicating CO2, and guzzling the finest organic nutrients.
I was impressed by the simple technical apparatus, but I was far more impressed by the fruits of my cousin's labor a few hours later, when I had the pleasure of sampling a strain called Super Lemon Haze. Finally, after some thirty years of smoking whatever pot came my way, I found something that seemed to complement—no, enhance—my biology. The aroma was citrusy and the taste was smooth enough. And the effect? Let's say that my brain ticked away linearly, laterally, and happily with no soporific slouch. No paranoia. No cloudy thinking. It was energizing yet soothing at the same time, as if my body were radiating sunshine from the inside out. "I need to get reacquainted with this plant," I told myself as we retired to my cousin's man cave, where freshly harvested stalks were curing on wire hangers, and long, sugar-coated "colas" (the top buds of marijuana plants) were stored in Mason jars, as if on exhibit in a museum.
On a website called 420magazine.com, my cousin showed me some extremely cool electromagnified photos of mature cannabis flowers, each tiny leaf carpeted with glistening sacs filled with resins. These sacs are called trichomes, he explained, and they are equally responsible for the plant's survival and its allure. Botanically, they produce the powerful chemicals that repel predatory insects, inhibit deadly molds, and bring humans and some animals intoxicating pleasure. In eight more weeks, the girls in his basement would mature into ladies and their sacs would be bubbling with sticky, stinky, gluey, wet resins—and that's the moment they'd be chopped down and killed. Is it an accident that men have traditionally been the keepers of this ritual, given its unavoidable Freudian connotations?
That comment elicited little more than a shrug from my cousin. Like many growers, he was more interested in talking about plants than my snarky observations on gender stereotypes. The resinous heads of the plants, which are plump with THC, plus powerful essential oils called terpenes, flavonoids, and hundreds of other compounds, are revered by breeders, who have, in the last forty years, created the strongest strains ever known. "You harvest the plants just as the trichomes start to go cloudy," my cousin explained. "That's when they're at the height of their powers."
My cousin, who once told me I couldn't write one word that would ever teach him anything, has never shown any propensity for higher education in the traditional sense. But he has always had a green thumb and a taste for this plant. That, plus his excessive desire for privacy and mistrust of law enforcement, has driven him to cultivate his pursuit in well-guarded secrecy. Even his family is seemingly unaware of what grows below its living room. He once broached the topic with his wife, a religious Christian, and the conversation went something like this:
"I have a new hobby, dear. Do you want to hear about it?"
"Not really."
And that was that.
I hadn't smoked much in the last fifteen years—as with many people in my generation, I found that weed had become too strong, too unpredictable. There were too many nights spent paranoid and unhappy, or asocial and cocooned in self-absorption, or just a blink away from sleep. If I was going to alchemize my consciousness, I wanted to go up, not down, so I moved on to other pursuits: wine, sport, meditation, yoga, single-malt scotch. But that day it struck me: If my cousin in rural New England could learn about strains, obtain the high-quality seeds and the equipment to cultivate them, and then educate himself, mainly through the Internet and in conversations with the guys who ran his local gardening store, about growing prime, organic, pesticide-free bud indoors, then a revolution of sorts had occurred in my absence. Maybe it was time I investigated more deeply.
My timing was auspicious. My great sixteen-year relationship had just ended. We had tried spackling over the problems, addressing, therapizing, ignoring them, whatever it is two people do when they sense things falling, inevitably and irretrievably, apart. We tried because we loved and respected each other, but ultimately we called it quits. It was the same with my career as a magazine editor. For years, I had been pretending to be excited by a profession that once brought me torrents of pleasure; but now it just seemed like work, with all of the drudgery and deadlines and none of the creative charge. I was, for the first time in two decades, adrift, primed for change, ready to dance, drink champagne, recharge my sex life, and reinvent the way I worked. My entire life was in need of a rethink, my vices included.
My headiest pot-smoking days had occurred in college. In the 1970s it was easy to blaze joint after joint and never become too scarily high. When I look back I wonder how it was possible to inhale that amount and still graduate from Northwestern University with a 3.5 grade point average. As it turned out, it was possible because the pot I was smoking then was baby-ass weak compared with today's varieties. The weed I smoked in high school probably averaged 3 to 5 percent THC. By the time I hit college, highly potent sinsemilla had debuted in North America, and the average THC content doubled, then tripled. Today's crops clock in at between 15 and 29 percent THC. That is a significant change, one brought about intentionally by growers and unintentionally by Ronald Reagan. But I'm getting ahead of myself.
Once back in New York, I dipped further into this subject. There are hundreds of blogs and Instagram accounts authored by all types of cannabists (a more refined title than "pothead" or "stoner," don't you think?)—people who devote themselves to the plant and its many mysteries. Endless words are spewed on techniques of growing. Topics range from soil nutrients to the most powerful and energy-efficient lights to use indoors, from the quietest ventilation systems to the ongoing debates over the benefits of sun-grown versus indoor cultivation or soil versus hydroponic. There are sites devoted to the politics of pot, hash making, oil production, rare strains, cooking with cannabis, curing cancer with cannabis, and other obscure corners of connoisseurship. The most arcane are the real-time videos of grow rooms—cameras trained on the plants and just left to run, with no irony intended. _You'd have to be really zonked to watch this_ , I remember thinking.
The more I explored, the more I discovered that the world of cannabis was in flux. There were new products that intrigued me: shatter, CBD, wax, the incongruously named butane honey oil. And there were hundreds of strains, some with evocative names like Tangerine Dream and Super Silver Haze, and others with scarier monikers such as AK-47 or Green Crack. I originally presumed these offerings were just new wrappings on age-old products, but that assumption too turned out to be just another indication of my ignorance. I read about medical marijuana, but initially thought it more of a rouse than a legitimate course of treatment that had been used for centuries in Asia and the Middle East. And then there was the surreal history of prohibition and the demonization of a plant. Once I learned that cannabis has accompanied man in his travels for as long as history has been recorded, I began pondering the larger purpose of such a magical, medical substance that grows in the earth. I had a lot to learn.
One truth came through loud and clear: For aficionados, pot is more than just a plant. It's a relationship, a commitment. Certain people—I'm thinking of growers in particular—develop a passion that borders on love for their crop. They don't simply like or revere it, as you might a rose or an heirloom tomato. They obsess over it much the way vintners fixate on their grapes. They test the soil regularly to ensure it maintains the proper pH level, so that the right minerals nourish their plants' roots. Indoor growers monitor the air temperature and humidity levels hourly. They baby their plants, inspecting them for molds or fungi that could decimate months of hard work in just a few hours. Some consult moon cycles to determine the optimal time to plant, feed, water, and harvest, and then they debate whether it's better to chop their plants in the morning or evening. They forgive their plants when a crop isn't up to snuff and extol them when it delivers. It's full-blown plantophilia.
Although I had been in close communion with this plant for decades, it struck me that I knew almost nothing about it. And I wasn't alone. Most of my acquaintances thought they understood pot, while in fact they knew nothing about how it worked in the mind or body; others blithely dismissed it as a been-there-done-that phase of their youth. Part of me harbored that attitude because I never deemed a mere _weed_ to be worthy of respect. Because of its prevalence, I just assumed cannabis wasn't very interesting.
In the ensuing weeks, I continued my halting reacquaintance with the plant, coming to a new acceptance of what I could and could not do in the enhanced state. I enjoyed watching movies but couldn't read, as my mind would wander promiscuously around the page, off the page, and into deep vortexes of thought between the first and last word of a sentence. But music . . . ahhh, music sounded richer, deeper, more textured. Food became a revelatory sensory explosion, and sex deepened to an intimate exploration of my partner's body and, at times, soul.
In those early days of Super Lemon Haze I smoked largely alone, because, as I've come to realize, I was in a cannabis closet of my own making. I guarded my secret exploration for fear of being judged as a pothead, which I was not. I used occasionally and moderately in the same way I drank, and as pretentious as it might sound, I liked to think of my usage as conscious consumption. But gradually I ventured out. I went to parties and other social gatherings where I cautiously invited certain guests to join me in a puff. To my surprise, my offerings were greeted appreciatively by men and women, friends and strangers, most often on my side of the generational divide. I assumed that I would be dismissed by my peers as a middle-aged guy desperately chasing his youth, but I was wrong. These were businesspeople, journalists, lawyers, filmmakers, entrepreneurs, and professionals, and they were delighted to partake. Even those who weren't interested in smoking were intrigued and full of questions. Many recounted a familiar trajectory: they had smoked in their twenties, got paranoid in their thirties, and now that their bodies were falling apart, or their kids had left home, or their material success hadn't delivered on its promises, they were ready to take another look at this plant. Often someone would pull me aside to discuss my rekindled pursuit in detail. Was it causing any harm? Would it help for this or that pain? Was it really an aphrodisiac? _Can you get me some?_ To my surprise, almost everyone was curious about cannabis.
One afternoon, over lunch in midtown Manhattan, I was describing this epiphany to my lawyer, one of the best and most erudite in New York City, when, in between bites of my red snapper, he stopped me. "You know, Joe, one of my favorite things to do on a Saturday night is to come home after dining out with my wife and go into my study. I turn on some music, turn down the lights, and smoke a joint." He never cared about single-malt scotch or potato vodka, and he finds the wine snob thing ridiculous. And, he added, the fact that some bureaucrats in Washington, DC, could dictate what substance he used to relax was one of the most flagrant overreaches of policing authority on the books. He told me of a party he had recently attended in LA. Most guests were in their sixties—and all of them were lighting joints or openly sucking on vaporizing pens, talking about strains and percentages of THC. "California is like a different universe," he said. "In LA, everyone is smoking or eating these candies and cookies and it has completely changed the culture."
He was, of course, correct. In 2012, before the Feds cracked down on Orange County, there were more dispensaries in Los Angeles than Starbucks franchises (but fewer than McDonald's). If you weren't cannabis inclined, this proliferation escaped your attention and had little impact on your life; but if you were a user, you could, with a doctor's recommendation, walk into a dispensary and consult a "budtender" about which strains on offer best suited your "condition." Without the stain of criminality, the dispensary system taught customers about the many varieties of cannabis and their unique properties. It was nothing short of revolutionary.
Titillated by all this fresh information, I decided to do something new and different—even if it meant reacquainting myself with something old and familiar: to submerge myself in this brave new—and yet at the same time, ancient—world. Events were unfolding at breakneck speed—the residents of Washington and Colorado voted to legalize and tax recreational cannabis. Dr. Sanjay Gupta aired his cannabis apologia, _Weed_ , on CNN and started a national conversation about the medical relevance of the plant. The Obama administration softened its antipot rhetoric, and then–attorney general Eric Holder issued the Cole memo, indicating that the Feds would not be storming the Rockies to stop legalization from going forward. And it wasn't only America that was changing its tune. Uruguay and Spain legalized and Jamaica followed suit. Would, as prohibitionists had claimed for almost a century, the fabric of these societies fray? Would their citizens smoke themselves into stupors and crowd into emergency rooms, or would society adapt more gracefully? What would the world look like once this plant became as accepted as beer?
Before diving in, I decided to establish some ground rules for myself: No stupid smoking myself silly. Be open about what I'm doing with everyone to help tear down the cannabis closet. Avoid politics, as laws were changing too rapidly to keep pace with. And keep my focus on the ways _adults_ could use this plant to their benefit. For too long now, the conversation has been hijacked by those who steer it to the harmful effects of drugs on children. I don't believe children should use substances, but experience has demonstrated that ignorance is more dangerous than intoxication and that they should be educated about the harms and benefits of alcohol, pharmaceuticals, and consciousness-altering plants.
My final determination: to see if I could harness cannabis to suit me as an engaged, responsible, and professional adult. Could certain strains or delivery methods better enhance the flow of creative ideas or intimacy in sex or empathy among friends? Could I actually take a certain dose and use it not only for play, but also for work? Could I use this weed to sprinkle a little magic onto a world that is overly reliant on data and thin on enchantment?
One day I called my cousin to thank him for launching me on this great adventure. He was already nurturing his second harvest, which he estimated would yield the equivalent of a few months' rent for a small city apartment.
"I think my wife is having a change of heart," he told me.
"Why's that?"
"The other day she said to me, 'You know that hobby of yours? I hope you do it really big. I think I'd like to plan an early retirement.'"
## ___Chapter 1_
## BIG BAD SCARY WEED
_New York City and Newton, Massachusetts_
I had always assumed there was some risk of brain, lung, or motivational damage from smoking pot, but I also knew it was far less dangerous than any other recreational substance, and that the risks could be contained with moderate use. Changing consciousness always seems to involve some risk. Certain thinkers, like Dr. Andrew Weil, have argued that human beings have a genetic predisposition to alter our states of awareness, and that it might be evolutionarily advantageous to do so, helping mankind develop spiritually and psychically. I am familiar with that urge and have always found it a worthwhile pursuit.
But here's what I didn't understand: If pot is as benign as its adherents claim, and such a miraculous and versatile medicine on top of that, how did it acquire such a bad rap? Or more accurately, so many contradictory bad raps? How did it get grouped along with heroin and LSD as a schedule I narcotic, which, according to the government, means that it has no medical benefit and is potentially lethal? And exactly which problems did it cause? Did it kill brain cells, sex drive, motivation, or sperm counts? Did it lead to lung or brain cancer, sexual compulsion, cocaine addiction, violence, or insanity? Did it grow breasts in men? And if it did unleash these horrors, how did I—and most of my generation—escape them?
According to biologists, botanists, and anthropologists, the cannabis plant, a relative of hops, debuted in the Caucasus Mountains, most likely in current-day Kazakhstan (ancestral home of Borat), some ten thousand years ago. The harsh landscape and climate forced the plant to be hearty and, to a certain extent, inventive if it was to survive. It had to grow quickly, before the short summer season ended. Animals and birds loved the seeds (cannabis seeds are still allowed in bird feed, the only cannabis product to escape the US federal ban), and they gobbled them up and then pooped them out while migrating. This is one way the plant used the feet and wings of other species to proliferate.
When humans arrived, they carried seeds out of the Caucasus along the Silk Route, and this is where the first fork in the genetic river occurred. The seeds that moved east into the colder regions of the Himalayas developed into the so-called indica strains, also known as kush strains; the high they produce tends to be more physical than cerebral. It brings on sleepiness and the condition that is perfectly expressed by the term "couchlock," that state of deep stoneyness in which even the thought of getting up to get a glass of water to soothe your parched throat is exhausting and thus unlikely to occur.
Indica plants are short and bushy, with leaves that are round. More crucially, this variety is very productive. Indicas flower quickly, in twelve to sixteen weeks, to contend with their short growing season.
Seeds that went west to the Middle East and Africa eventually became known as the sativa varieties. These warmer-climate plants are more gangly, at times stretching twenty feet tall. They have narrow, finger-shaped leaves and rangy buds that take longer to mature (some can take up to half a year). A sativa variety generally yields a more energetic high—I once heard it described as "my mind on jazz," which pretty much nails it. They stimulate talkativeness, nervousness, and those machine-gun bursts of creative flow. These are the strains I prefer.
It may sound a bit mad to call cannabis inventive or intelligent, but ethnobotanists agree that this plant has astutely inveigled its way into the lives of human beings over thousands of years. When our hunter ancestors were chased by a wild boar, they likely nibbled some cannabis buds afterward to help them forget the trauma, relax, recover, and get up the next day and hit the plains again for another day's supper. When night fell, the plant encouraged our ancestors to fall into the arms of their loved ones. Women munched the sticky flowers to ease the nausea of pregnancy and to numb and then forget the pain of childbirth so they could repeat the experience and help our species proliferate—a miraculous and evolutionarily strategic benefit, when you stop to think about it.
Once humans settled down and began to farm, cannabis seeds not only fed the animals but also yielded an oil that contains the exact ratio of essential fatty acids needed to help children thrive. The stalks provided fiber that was turned into tents and clothes. Burning the flowers in enclosed structures enabled village elders to create rituals that connected the tribe to higher powers and also helped rival factions relax; after a few minutes of sitting together in the smoky tent, they could more amicably sort out their differences. And the plant found its way into the healers' medicinal arsenal. Without healing plants, their formulary, their stature, and not to mention their patients, would have disappeared.
The ancient Chinese considered this wild grass one of the fifty fundamental herbs and were the first to write about the medical and spiritual benefits of it, over 4,700 years ago. The father of Chinese medicine, Shen-Nung, used "ma" to treat a dazzling array of illnesses including gout, rheumatism, malaria, constipation, and absentmindedness. Of the two thousand medicinal plants known in the vast field of Ayurvedic Indian medicine, cannabis is the most important among them. While members of all these cultures occasionally inhaled cannabis as smoke—presumably to get closer to God—it was most commonly used as a tincture or eaten. The Egyptians used it in suppositories and to relieve eye pain; they buried kings and royalty with pounds of pot, presumably to be presented as a housewarming gift to God once they had moved on to the next life. And the Greeks made wine steeped with cannabis, which they used to treat inflammation and ear problems.
Westerners began to view plant substances with suspicion with the advent of modern Christianity. In its efforts to break the human bond with magic plants on earth and refocus the gaze of its constituents on One God in Heaven, Catholic church elders in the Middle Ages branded plant users pagans, sorcerers, or witches—and reinforced the message through one of the religion's foundation myths: Adam and Eve were tossed out of Eden for tasting the forbidden fruit. It may have been an apple, but it could just as likely have been another plant, possibly cannabis. No matter. The message was clear: partake of a plant's pleasures, God will be displeased, and you will be punished. This realignment didn't extend solely to cannabis, but to all psychoactive plants as well. The Spanish conquistadors massacred hordes of natives in Latin America for using psilocybin, peyote, datura, morning glory, salvia, and ayahuasca, to name but a few.
Europeans remained largely ignorant about cannabis until Sir William Brooke O'Shaughnessy, an Irish inventor and physician, went to work in the hospitals of Calcutta in 1839. While there, he developed a fascination with Indian botanical medicines, primary among them a tincture of cannabis indica, also known as hemp oil. O'Shaughnessy was curious about the ways Eastern cultures, in particular those in hot, crowded regions, used botanicals to prevent diseases before they happened and then to treat them once they struck. He did the first animal studies on cannabis and noted that it effectively eased the pain of muscle spasms caused by rabies, tetanus, cholera, and many other illnesses. So convinced was he of the plant's ability to heal that he brought it back to England, where it caused a sensation. Physicians and small companies began to produce their own cannabis elixir and sell it privately and in general stores. Even Queen Victoria's doctor reportedly—perhaps mythically—used it to ameliorate the pain of her menstrual cramps.
In the following sixty years, over one hundred scientific and medical papers were written about this wonder drug that treated some old-fashioned-sounding illnesses (including neuralgia and melancholy) and many others that are still with us today (including sleeplessness, nausea, and neuropathy). In the United States, physicians began making their own hemp oil tinctures and selling them out of their offices, as did drug companies such as Eli Lilly, Parke-Davis, and Squibb. These companies are now somewhat embarrassed about their association with this maligned weed. When _Fortune_ magazine asked Eli Lilly for details on its historical cannabis sales, a Lilly spokeswoman responded, "Due to competing priorities, we . . . are unable to facilitate your query."
The primary problem with this all-purpose plant tonic was not its efficacy but the difficulty of ensuring accurate dosing. When cannabis is swallowed, it takes one and a half to two hours for the effects to come on, so early patients never knew if they had taken enough. Too large of a dose could cause harrowing anxiety, but most doctors worried about prescribing too little.
From 1913 through the 1920s, just as anti-alcohol fervor was beginning to grip the United States, twenty-seven states passed anti-marijuana prohibitions. The meticulously researched 1974 book _The Marijuana Conviction_ by two professors, Charles H. Whitebread II and Richard J. Bonnie, examined legal archives and newspaper articles from those states to learn what spurred them to take such drastic measures against a plant that was still little known on these shores. Only about fifty thousand US citizens had ever smoked the plant in the early part of the twentieth century, and this unawareness made the passing of such prohibitions almost effortless, since most people didn't connect the liquid in the brown bottles in their medicine chests with this imported green weed.
Whitebread and Bonnie quickly deduced that marijuana prohibitions were motivated less by hostility to the drug and more by hostility to the immigrants who used it. In 1914, following the Mexican Revolution, immigrants flooded into the Southwest in search of stability and better economic conditions. They labored as beet-field workers and cotton pickers, and they brought with them an herb they called "mariguano."* It was easier to carry than bottles of alcohol—and cheaper too, as it could be picked in their yards or along roads for free.
On the floor of the Texas State Senate, one legislator pronounced, "All Mexicans are crazy and this stuff is what makes them crazy." Another legislator from Montana put it this way: "When some beet field peon takes a few traces of this stuff . . . he thinks he has just been elected president of Mexico, so he starts out to execute all his political enemies." Even states in the Northeast, which had almost no Mexican immigrants, prohibited cannabis prophylactically. No one in this state uses it, the logic went, but we should ban it to prevent the drinkers who are being cut off from alcohol from coming here in search of a drug they can use.
Utah was the first US state to criminalize the use and possession of cannabis. Whitebread and Bonnie first presumed that this was due to the immigrant invasion, but further investigation revealed that Utah had only a tiny Mexican population. The antiweed laws were more influenced by that other American intoxicant, religion.
In 1910, elders in the church of Latter-Day Saints declared polygamy to have been a mistake and banned it. A number of Mormons were unhappy with this change and emigrated to northwest Mexico in hopes of setting up "traditional" communities that would convert heathen Indians to Mormonism and allow them to take multiple wives. After four years, those plans weren't panning out. The Indians weren't buying Mormonism, and the Mormon faithful were unhappy being separated from their flock. Many of them headed home, and they brought weed with them. The church elders have always opposed stimulants of any kind, including tea and coffee, so when these apostates were discovered taking a puff, Utah's legislature turned a religious prohibition into the country's first drug law in 1915. Other states quickly followed suit, including Wyoming (1915), Texas (1919), Iowa (1923), Nevada (1923), Oregon (1923), Washington (1923), Arkansas (1923), and Nebraska (1927). Despite this flurry of legislative zeal, the majority of Americans still had no idea of what marijuana was. It took an ambitious bureaucrat to exploit that ignorance.
Harry Anslinger was the thick-necked chief of the Federal Bureau of Narcotics (FBN), the predecessor to today's Drug Enforcement Agency (DEA), and the spiritual godfather of America's War on Drugs. Much like his rival J. Edgar Hoover, Anslinger seemed to enjoy steamrolling anyone in his path, and he was very effective at doing so.
During the Depression, tax revenue plummeted, which meant massive government job cuts, Anslinger's agency included. The disastrous economy—27 percent unemployment—plus the influx of two million Mexican laborers who had entered the country illegally provided Anslinger with a crisis he couldn't resist. What if he could tie that foreign loco drug to crime and convince the country that this terrible scourge could be fought only by steady, forceful action from a beefed-up FBN?
Sounds crazy? Just wait.
With financial backing from the beverage industry, which was just recovering from fourteen years of alcohol prohibition, plus the support of the archconservative newspaper tycoon William Randolph Hearst, who owned some eighty national newspapers (and who became rabidly anti-Mexican when Pancho Villa confiscated his 800,000 forested acres in Mexico during the revolution), Anslinger proposed the Marijuana Tax Act to Congress in 1937. The idea was to impose a tariff so stiff and paperwork so burdensome that no doctor would prescribe a cannabis tincture and no company would produce it.
When Whitebread and Bonnie asked the Library of Congress for a copy of the congressional hearings on the Marijuana Tax Act, the librarians couldn't locate a transcript. It took them four months to honor the request because the hearings were so brief that the slim volume containing the transcript had slid behind a bookshelf. The librarians had to dismantle the bookcase to retrieve it.
More surprising still were the file's contents. With no medical or scientific evidence backing him up, Anslinger claimed that "marihuana is an addictive drug which produces insanity, criminality and death." Speaking before Congress, Anslinger called a number of "experts," including Dr. James Munch, a pharmacologist from Temple University, who injected marijuana's psychoactive ingredient into the brains of three hundred dogs, two of which died. When asked if he chose dogs because their reactions mirrored those of humans, he replied, "I wouldn't know, I am not a dog psychologist." Nor was he much of a pharmacologist. THC wasn't discovered until 1964, so whatever the doctor thought he was injecting wasn't what he claimed it was.
Next up was Dr. William C. Woodward, a lawyer, physician, and chief counsel to the American Medical Association (AMA), who testified that his organization "knew] of no evidence that marijuana is a dangerous drug" and opposed the legislation. To which one congressman replied, "Doctor, if you can't say something good about what we are trying to do, why don't you go home?"[*
When the bill passed to the (un–air conditioned) floor of the House at 5:45 on a clammy August afternoon, the debate lasted one minute and thirty-two seconds. FDR signed it into law, and Anslinger later named the dog pharmacologist from Temple the "Official Expert of the Federal Bureau of Narcotics on Marihuana," a position he held until 1962.
His target now clearly in his sights, Anslinger cranked up his attacks. One article, "Marihuana: Assassin of Youth," published in Hearst's countrywide chain of newspapers, famously claimed that "the weed from the devil's garden" caused white women to seek sexual relations with Negroes, and caused whites and black to dance cheek to cheek. He wangled money from alcohol and pharmaceutical companies to make antipot films. _Reefer Madness_ is a cult classic today, but it succeeded then in swaying the vulnerable masses that marijuana was a portal to lewd behavior. One puff brought on irreversible insanity.
Skeptics might question how one man could wage such an effective propaganda campaign against a plant. But in the late 1930s and 1940s, five lurid murder trials came to national attention, and in each the defendants pleaded not guilty by reason of insanity from smoking marijuana—an ideal defense, since Anslinger claimed marijuana caused insanity. In the most famous trial, two women jumped on a Newark, New Jersey, bus and robbed, shot, and killed the driver. The women claimed marijuana-induced insanity, and the defense called the same pharmacologist from Temple University, who told the jury about his animal experiments, adding that he himself had tried the drug. After two puffs, he said, he turned into a bat and flew around the room until he found himself in the pit of a two-hundred-foot-deep inkwell. "Killer Drug Turns Doctor to Bat!" the next day's Newark _Star-Ledger_ howled.
The two suspects got off.
By 1941, the Marijuana Tax Act had succeeded in causing such a burden that doctors quit prescribing cannabis. It was dropped from the _American Pharmacopeia_ , and the tincture vanished from the shelves. Two years later, Anslinger, desperate for a few arrests, launched a crusade against jazz musicians. Duke Ellington, Charlie Parker, Billie Holiday, and Louis Armstrong were among the suspects. The jazz drummer Gene Krupa was busted in San Francisco and jailed for eighty-four days. The singer Anita O'Day got six months.
For some reason Anslinger had a beef with jazz. At a 1948 hearing in which he was gunning for another funding bump, one senator asked why he needed additional staff. He replied, "Because there are people out there violating the marijuana laws."
"Like who?"
"Musicians."
The senators' faces must have registered looks of disbelief, because then he added, "And I don't mean good musicians, _I mean jazz musicians_."
Seventy-six newspaper editorials slammed Anslinger; within three days the Treasury Department received fifteen thousand letters, one of which simply said, "I applaud your efforts to rid America of the scourge of narcotics addiction. If you are as ill-informed about that as you are about music, however, you will never succeed."
Sadly for cannabis users, Anslinger's zeal didn't diminish.
Except for the Beat poets and others on the fringes who extolled it, pot use declined during the cultural dry spell of the Eisenhower era. Once the 1960s counterculture began to send its green shoots into the mainstream, however, cannabis became the fuel that powered the Beatles, hippies, Vietnam War protestors, and civil rights activists. It was once again in the spotlight, but instead of an ambitious bureaucrat railing against it, now it was that most paranoid of presidents, Richard Nixon, who took up the battle and backed it with the full power of his office.
In 1968, the same year Nixon was elected to office, Dr. Lester Grinspoon was being toasted as one of Harvard's golden boys. The then-forty-year-old psychiatrist taught, saw patients, conducted research, and published papers and books—in short, he was an exemplary academic who lent burnish to the Ivy League faculty. On weekends he and his wife, Betsy, would party with fellow Harvard luminaries, including the poet of the cosmos, Carl Sagan, and the anthropologist Stephen Jay Gould. At those parties Harvard's best and brightest were trading in gin for joints, or combining the two.
Sagan jousted regularly with his white-shoe friend, urging him to smoke, assuring him it would expand his splendid but narrow mind, but Grinspoon's reply was always the same: "I'm a psychiatrist and a doctor, Carl, and you shouldn't smoke that stuff. It's dangerous." Sagan would roll his eyes and take another hit. "I'm not one of those fissured ceramics, Lester," he would say, employing his favorite phrase for "crackpot." "It won't harm you. You'll love it."
After a while, Dr. Grinspoon grew weary of sermonizing and decided to launch his own investigation into the brain-addling weed. "I'll write the definitive treatise spelling out the hazards to young people so they will stop destroying their lives," he told himself. It would be his most valuable contribution to protecting America's youth, not to mention a few of his misguided friends.
In the stacks of the Countway Library of Medicine, Grinspoon devoured the poetry of Dumas, Balzac, Baudelaire, and Gautier. He examined dozens of reports on criminality, sex, addiction, and the so-called gateway theory, which claims, with no evidence whatsoever, that "soft" drugs like marijuana are stepping-stones to stronger, more dangerous drugs such as heroin.* He read about the pharmacology of cannabis intoxication and investigated how it affects the brain in the near and long terms.
Midway through his research, Dr. Grinspoon came to an uncomfortable realization: He had been duped. All the "facts" about this plant's dangers had been disseminated by the US government or its drug enforcement agencies without one shred of historical, medical, or scientific evidence to support them. Even worse, he understood how his ignorance was passively condoning the government's jailing of its own citizens for no justifiable cause. "At that time we were arresting 300,000 people a year for using or selling marijuana," he recalls. "Now it's just under 900,000, which is terrible, and here I was being a part of that persecution."
Dr. Grinspoon published his findings in the _International Journal of Psychiatry_ , a small-circulation professional review, where they went unnoticed. Among the few who read his report, though, was the editor of _Scientific American_ , who reprinted it as the lead article in his magazine in 1969. That attracted a few more eyeballs, two of which belonged to Murray Chastain, an editor at Harvard University Press, who urged Grinspoon to expand the manuscript into a book.
Though it wasn't his primary area of interest, Grinspoon agreed—provided he could have a finished copy by March 24, 1971. That date was immutable, he explained, because his sixteen-year-old son, Danny, had been diagnosed with acute lymphocytic leukemia, and Grinspoon wanted him to hold the book in his hands before he died.
As is the case with so many marijuana advocates, it was Grinspoon's personal experience with the plant that cemented his change of mind.
Danny's chemotherapy regimen was wreaking havoc in his body and on the entire family. The minute he was off the gurney Danny was overcome with nausea, and the Grinspoons would rush their son home so he could avoid the humiliation of puking in the car. "Once in his room, he'd be vomiting or dry heaving for the next eight hours. It was awful to hear, let alone witness," Lester recalls today. "Chemo made my boy nauseous in every cell in his body. You could see that he was feeling it in his toes."
It was Lester's wife, Betsy, who suggested they try marijuana—his own research showed that it was a traditional treatment for nausea, after all—but the good doctor refused. It's illegal, he reminded her, and besides, he was wary of offending the valiant physicians who were treating his son. "It's a line I regret uttering until this day," he admitted to me.
Betsy was less concerned about ruffling the feathers of Lester's colleagues, so en route to treatment one day she stopped in the parking lot of Danny's high school and asked one of his friends to find her some pot. Once the boy overcame the shock of selling grass (as it was quaintly known) to his friend's mother, he handed her a few hastily rolled joints, which she and Danny shared.
When Lester walked into the treatment room that day he was surprised to find Danny and his wife laughing. After chemo, Lester was further startled when Danny stood up and said, "Hey, Mom, can we get a grinder on the way back to school? I'm sort of hungry."
Lester had witnessed firsthand the plant's healing capacities. "Doctors in the nineteenth century knew more about cannabis than we did in the 1970s," he recalls. "They knew nothing about its chemistry but they knew it stopped nausea and that it was not toxic."
His professional and personal insights gelled into the most famous of Grinspoon's ten books, _Marihuana Reconsidered_ , which was published on schedule in March 1971. His son didn't survive the cancer, but he did live long enough to see the book's dedication: "To Danny."
Betsy still believes it's the best line Lester has ever written.
Lester didn't sample cannabis for two more years. He suspected he might be called as an expert witness before the courts and legislatures if the book gained traction, and he didn't want to impugn his professional credibility.
Grinspoon's hunch was correct, and at one hearing in Massachusetts, an especially aggressive state senator challenged him about his personal use. "Senator, I'd be glad to answer that question if you'll tell me if an affirmative answer makes me a more or less credible witness," Grinspoon replied in his Boston Brahmin accent. The senator huffed, "You, sir, are being impertinent," and stormed out.
That night the doctor went home and lit the joint that he had stashed in his bedside table. "It was clear that it made no difference whether I did or did not smoke," he recalls. He and Betsy had a wonderful evening together, and Grinspoon has been smoking unapologetically ever since.
___Marihuana Reconsidered_ was an instant classic. The book was reprinted around the world in fourteen languages and sparked a tidal wave of discussion, primarily among the chattering classes. Lester became a hero in Cambridge; his photo occupied the entire front window of the Harvard bookstore.
But other countervailing winds were blowing at the time. Richard Nixon, who hated marijuana as much as he despised the hippie leftie pinko commies he associated with it, was determined to eradicate pot from the country's shores. He launched the first war on drugs to intercept drug shipments on land, sea, and air, and he simultaneously ordered a national study on drug abuse that he hoped would once and for all prove the dangers of the evil weed.
Nixon named Raymond P. Shafer, the conservative Republican governor of Pennsylvania, to lead the National Commission on Marijuana and Drug Abuse. He knew Shafer was itching to be appointed to the Supreme Court, so he was the ideal candidate to do his bidding. He also instructed his aides to ensure the report packed a wallop. "I want a goddamn strong statement on marijuana," Nixon instructed his chief of staff, H. R. "Bob" Haldeman (the discussions were recorded by hidden microphones Nixon had installed in the Oval Office). "Can I get that out of this sonofabitching, uh, Domestic Council?"
Haldeman reassured him (and, ever the obedient lieutenant, he didn't correct him on the name of the commission that he had appointed).
"I mean one [statement] on marijuana that just tears the ass out of them," Nixon continued. "You know. . . . Every one of the bastards that are out for legalizing marijuana is Jewish. What the Christ is the matter with the Jews, Bob? What is the matter with them?"
Nixon feared pot was becoming a white suburban problem that would lead America to ruin. No one cared if black musicians or a few poets used it, but voting parents seeing their kids lighting up—that was cause for alarm. "Do you think the Russians allow dope?" he asked Haldeman and John Ehrlichman, his domestic policy advisor. "Homosexuality, dope, immorality . . . these are the enemies of strong societies. That's why the Communists and the left-wingers are pushing the stuff. They're trying to destroy us."
Shafer's commission fanned out across the world, conducting over fifty national studies and visiting countries as wide afar as Holland, Morocco, Afghanistan, and Jamaica to study cannabis and the effects it had on societies. The final report, over four thousand pages long, was published in four volumes. It cost $4 million in 1971 dollars ($23.5 million today) and was, and remains, the most comprehensive government study of cannabis in American history.
When released in early 1971 under the title, _Marihuana: A Signal of Misunderstanding_ , the report wasn't what the White House was expecting. It concluded that the punishment for marijuana was more harmful than the drug itself and recommended decriminalizing personal possession and moving it from the restrictive schedule I category into schedule III, alongside synthesized testosterone, estrogen, and acetaminophen, and other drugs that carry "less potential for abuse." "Considering the range of social concerns in contemporary America," wrote the Shafer Commission, as the group that authored the report came to be known, "marihuana does not, in our considered judgment, rank very high."
Nixon was apoplectic. He disavowed the commission's findings and ignored its every recommendation. As a result, it received scant media attention, and the silence surrounding its findings solidified the previous forty years of disinformation, scholarly works by Harvard professors notwithstanding. Most damningly, Nixon disregarded the report's advice and kept cannabis and all of its constituents, whether psychoactive or not, shackled as a schedule I narcotic. This meant that THC and CBD, the other unsung chemical hero of cannabis, were preposterously designated along with heroin, LSD, and Ecstasy as the most dangerous drugs in existence, with a high propensity for addiction and no medical benefits. Cocaine, methamphetamine, and OxyContin are schedule II.
Needless to say, Raymond Shafer was never named a judge. And as seen in the following chart, cannabis is still classified as a schedule I narcotic, despite the fact that it has never been cited as causing one death from overdose.
* * *
US OVERDOSE DEATHS, 2001–2014
* * *
Dr. Grinspoon was eighty-six when we met at his home in Newton, Massachusetts. He suffers from "a host of medical disasters" that he has little interest in discussing, but he is one of the few medical professionals in America who is eager to talk honestly about marijuana, a subject that has captured his imagination for the last four decades.
Although he's largely homebound, his friends in the medical marijuana community stay in contact, emailing him so frequently that he can't keep pace, and sending him gifts to ease the torments of his ailing body. Amid the stacks of books on the shelves and tables in his study is a large portrait of Danny and two smoking devices that Sagan sent him while filming _Cosmos_ : an ancient opium pipe and an Egyptian hookah. His favorite new invention is his slim vaporizer pen filled with hash oil that he wears nerd style in his shirt pocket. A puff or two offers relief from the host of symptoms that plague him.
Most popular histories blame ambitious lawmakers and paranoid presidents for sounding the death knell for cannabis. But Dr. Grinspoon, a consummate researcher, told me that two other medical advances played an important role in sidelining the herb as a medicine. In 1900, _Cannabis indica_ was most often prescribed for pain and insomnia. But in 1898, Bayer created aspirin from birch bark, and shortly thereafter the first barbiturates were also synthesized. Today we take for granted the inexpensive manufacture of precisely dosed, easy-to-swallow medications, but the invention of pills and capsules that could be precisely measured in milligrams was groundbreaking at the time. Tincture of _Cannabis indica_ , which varied in strength depending on the crop from which it was derived, and was vexing to dose, suddenly seemed very old-fashioned.
Pharmaceutical companies have since tried to synthesize a drug that mimics cannabis, but they have come up short. Because the plant contains upwards of seven hundred compounds, eighty of which are thought to be therapeutic, and all of which combine synergistically to produce both the high and the healing, extracting just one compound in a lab has never proved as effective as the whole plant is. In 1985, the US government supported Unimed Pharmaceuticals in developing Marinol, a chemically derived THC, which authorities hoped would stanch all cries for legalization. "With Marinol the government was saying, you should stop pressing for legalization because we're going to have a single-bullet drug soon," which would make smoking marijuana unnecessary, says Grinspoon.
To spur sales, the government classified Marinol as a schedule II drug, which allowed doctors to legally prescribe it. When it still wasn't catching on, it was placed in schedule III in 1992. But today we know that it isn't simply THC in cannabis that causes the high and delivers therapeutic effectiveness. Hundreds of other compounds—CBD, terpenes, phytochemicals, flavonoids, and other so-called minor cannabinoids—all work together to create an ensemble, or entourage, effect.
"My experience is that the people who use Marinol are doing so because they don't want to smoke anything or they're afraid of the law," says Grinspoon. "I've yet to have a patient who smokes and prefers Marinol. Cannabis has other benefits, of course. It's the best recreational drug—you get more bang for the buck and you don't wake up with an awful hangover like you do with alcohol and [despite the unfounded claims over the last eighty years] you're not damaging liver or brain cells."
Grinspoon still smokes daily for enjoyment too. "It stimulates the frontal lobe and ideas come out of my brain like darts at a dartboard. You get more bad ideas too, but you also get more good ones. That's why I like to consider things both stoned and straight."
Throughout our conversation, Dr. Grinspoon repeatedly hit his vape pen. He let slip that he is suffering from cancer, diabetes, hemophilia, and a stomach condition that has enervated the vagus nerve that controls digestion, among other functions. He hates speaking of his own illnesses and will be cross with me for revealing them, but his vape pen is a lifesaver when his digestion goes awry.
He also swallows a high-CBD, low-THC cannabis capsule every night, sent to him by a cannabis practitioner in California. "Just like everyone took vitamin pills in the sixties and seventies, I believe that in the future cannabis will be treated equivalently. THC with CBD is a powerful antioxidant and anti-inflammatory. There's no way of proving it and it's not a scientific or medical claim, but I think it has slowed down these diseases I've been burdened with."
In 2013, Grinspoon published a lengthy article calling for the creation of a new discipline that he termed "cannabinopathic medicine." Because the safety of cannabis has been chronicled for over fifty centuries by millions of people across cultures, and because the National Institute on Drug Abuse (NIDA) has conducted hundreds of studies over forty years attempting to prove the harmful effects of cannabis, without any success whatsoever, he advocates forgoing clinical trials and perhaps reclassifying the drug as a nutraceutical (a product derived from foods or plants that is presumed to support health). These are heretical words for a scientist, but Grinspoon correctly insists that cannabis doesn't fit within the confines of traditional medications and should be treated akin to aspirin or penicillin. Neither of those medications went through clinical trials in their day, as their safety and efficacy were established before the Food and Drug Administration set up those protocols. In fact, since one thousand people a year die from aspirin-related deaths and no one in the history of recorded time has ever died from cannabis, it is, strictly speaking, safer than aspirin.
Even today, most doctors, who learn about drugs primarily from pharmaceutical companies and can still lose their licenses if caught prescribing illegal medications, remain silent, skeptical, or downright hostile to the plant. Is their silence justified in light of the legal consequences?
Though often praised for his early scholarship, Grinspoon's courage on behalf of medical cannabis is rarely acknowledged outside cannabis-centric circles.
"I didn't try marijuana until after publication, because I wanted to keep objective, but once I did try it I was honest about it," he recalls. "I was on the Barbara Walters show in 1974 with Norman Zinberg, the former head of NIDA, and Robert DuPont, the first drug czar, who now owns a lot of urine-testing patents—he makes a lot money off of that and is doing well.
"Barbara asked if we had used marijuana, and DuPont, the drug czar, said no, which I knew not to be true. He trained at my place, and while I never smoked with him, he spoke about it. Zinberg also said no, which also wasn't true, because I smoked with him the week before at his house.
"When she asked me, I replied, 'Not only have I smoked it, but I do smoke it.' Her mouth dropped open. She was not prepared.
"But I believed then, and still believe firmly, that coming out is crucial to changing the stereotype of the cannabis smoker. That was one of Carl Sagan's major contributions and regrets. He would tell me, 'I wish I could help you in this fight, Lester,' but there was no way he could come out. He was testifying before congressional committees in 1969. It would have destroyed his career, no question about it."
And what about Dr. Grinspoon's career? Did coming out as an unrepentant cannabist negatively affect his career trajectory?
"It didn't destroy it, but it sent me down a different path. In 1975, I was put up for early professorship. I had published two books, _Schizophrenia_ and _Marihuana Reconsidered._ The dean called me to his office after a promotions committee meeting and told me they didn't give me the professorship. 'They loved the schizophrenia book but they didn't like _Marihuana Reconsidered_. They said it was too controversial.'
"I said, ' _Controversial?_ We're in the academy! What about the scholarship?' People moved away from me at Harvard because of my outspokenness. But I stuck to my guns and I think I made the right decision."
By the late 1970s, it appeared that pot was well on its way to being decriminalized. Media on the left and right were calling for it, thirty states had reduced penalties for possession, and in 1977 President Jimmy Carter announced his intention to stop arresting people carrying under an ounce. The prospects for reform looked promising until Dr. Peter Bourne, Carter's drug policy advisor, attended a Christmas party thrown by the National Organization for the Reform of Marijuana Laws (NORML) in 1977. Many guests were shocked when Bourne was offered cocaine and then took two hits from a small glass vial. Though Bourne denied taking the snorts, the incident was widely witnessed and it hit the press. Bourne resigned a few months later, and Carter dropped the reform effort once his political fortunes began flagging.*
When Ronald Reagan swept into office in 1980, he distinguished himself from his "soft" predecessor by declaring drugs to be America's number one scourge. He not only revived Nixon's drug war but turned it nuclear by funneling billions of dollars away from treatment and into the police and prison industries. Within one year, law enforcement jobs at every level rose 36 percent and prison-related jobs jumped 86 percent. By 1984, his administration had upped the penalties for possession, cultivation, and sale of cannabis. Nancy took her "Just Say No" show on the road (this despite the fact that she was a chronic user of prescription tranquilizers, according to her daughter Patti Davis). The DARE (Drug Abuse Resistance Education) program indoctrinated American youth about the dangers of illegal drug use and further blurred the distinction between "hard drugs," such as heroin and crack cocaine, and pot.*
Reagan also took the drug war into the skies. US spy satellites hovered above Central and South American countries to pinpoint grows, while crop dusters sprayed deadly paraquat over Mexican fields. At home, the effort centered on the breadbasket of cannabis cultivation: Humboldt, Mendocino, and Trinity Counties in Northern California, a remote area with abandoned logging sites that attracted growers because of its heavy forestation and often-impassible roads. In a matter of years, the so-called Emerald Triangle had become the world capital of sinsemilla ("without seeds" in Spanish), and strains like Big Sur Holy Weed, Maui Wowie, and Kona Gold acquired legendary status. With its newfound potency and flowers the size of fists, North American cannabis entered its golden age of cultivation.*
The wily genius of those early breeders was in part born of necessity. Rather than cultivating the twenty-foot-tall sativa strains that were native to the Americas but grew so large they might as well have been wearing a neon sign that flashed BUST ME!, these New World growers combined North American strains with shorter, heartier indicas smuggled in from Asia. Years of studious crossbreeding enabled them to create more potent varieties that could be packed into tight spaces and that flowered in three months, not five, thus doubling their annual yield. In an indirect "fuck you" to the War on Drugs, an estimated thirty thousand citizens in all states began to grow, launching what has rightfully been called the largest underground breeding experiment in agricultural history. One of Reagan's least heralded but most enduring legacies is this: as the ferocity of the Drug Wars intensified, so did the potency of pot.
But the DEA was not deterred. Narcs in camouflage established checkpoints on roads, buzzed homes in helicopters, raided private grows, hacked up gardens, and seized property. For all intents and purposes, Northern California "rejoined, operationally speaking, the Third World," as Thomas Pynchon wrote in _Vineland_ , his novel set in the area during Reagan's rule. Of course, local cops loved it, as a river of money flowed nonstop from Washington, providing jobs and expensive equipment for their small-town forces.
October 26, 1989, is the day that changed the plant and growers' entire operation forever. Operation Green Merchant was the brainchild of one FBI agent, Jim Stewart, who two years before had noticed the number of ads in the back pages of _High Times_ placed by hydroponic equipment stores, garden centers, light companies, and Dutch seed banks. He organized hundreds of FBI agents to pose as growers and fan out across forty-six states to visit the advertised shops. After two years of undercover ops, the FBI pounced, confiscating mailing lists and sales receipts in what most legal scholars now term a gross breach of privacy laws. Then, often with TV cameras and reporters in tow, federal agents swooped down on unsuspecting private citizens, many of whom were (legally) growing orchids or tomatoes indoors to (illegally) search their homes without warrants. From 1989 to 1991, over 400 citizens were arrested, 50,000 plants were killed, 358 indoor grows busted, and $10 million in merchandise seized.* From then on, growers doubled down their efforts to move indoors.
George H. W. Bush kept the drug war going full tilt, but Clinton—he who never inhaled—spent more money on drug war activities than Reagan and Bush combined. The Clinton administration got creative about the way it drove home its antipot/antidrug messages. One covert program sponsored by the Office of National Drug Control Policy (ONDCP) offered about $25 million each year to the five major television networks to shoehorn antipot messages into the plots of their most popular prime-time shows.
Here's how this neat little scheme worked: ONDCP selected the shows most valuable to its mission, secretly vetted scripts, and then paid the networks for instituting the script alterations they suggested.
In the original script of one episode of the WB's _Smart Guy_ , two substance-using kids were depicted as cool and popular; after the drug office's input, "we showed that they were losers and put them in a utility room," said one ONDCP contractor. Other programs that had antidrug subplots woven into them included _ER_ ; _The Practice_ ; _Beverly Hills, 90210_ ; _Home Improvement_ ; _Sports Night_ ; _7th Heaven_ ; _The Drew Carey Show_ ; _Sabrina, the Teenage Witch_ ; _Boy Meets World_ ; and _General Hospital_. Bill Kovach, a media watchdog and then the curator of the Nieman Foundation at Harvard, called this sub rosa propaganda campaign a "venal . . . form of mind control."
While some of the plot switches were understated, others were as subtle as a brick through a window. _The Wayans Bros._ featured a career-devastating, pot-induced freak-out of angel-dust proportions. _Sports Night_ showed a death behind the wheel due to alcohol and pot combined. _Cosby_ showed kids caught with marijuana being pressed to name their supplier. The White House denied trying to influence content; its officials insisted that it was only trying to achieve an "accurate portrayal" of drug use. Most networks also denied collaborating with the government. But those denials rang hollow once a CBS spokesman admitted that his network "is proud to be working with the government in regard to the war on drugs."
Forty years after Lester Grinspoon realized he had been duped, I had reached the same conclusion. Now that I'd stripped away the fictions about this dangerous weed, it was time to find the facts.
## ___Chapter 2_
## THE DUTCH MASTERS
_Amsterdam, the Netherlands_
Operation Green Merchant forced growers in the United States into three different directions. They went either (1) into early retirement, (2) indoors and out of sight, or (3) to Amsterdam to ply their trade in relative peace. Ever since 1976, when the Dutch government decriminalized cannabis, Amsterdam has lured aficionados. But the escalation of the American drug wars crowned Amsterdam as the center of the pot universe, and exiles flocked there, just as literary exiles once flocked to Paris in the 1920s. I thought the Dutch capital would be an ideal place to see how that culture had flowered, as it were—but like so many aspects of cannabis and the place it occupies in modern life, so much of what I thought I knew turned out to be wrong.
My arrival in Amsterdam in November 2012 coincided with the twenty-fifth anniversary of the Cannabis Cup, the oldest such festival in the world. Since 1987, when the editors at _High Times_ magazine* inaugurated the event, "the global ganja community" has made the pilgrimage to the Cup with the same reverence as Muslims making their Haj to Mecca.
The Cup lures thousands of fans to sample and crown the best strains of cannabis and hashish grown each year. A $350 entrance badge gives participants access to the exposition hall and the "right" to purchase the strains in competition at designated coffeehouses. The badge also turns attendees into judges, allowing them to vote for their favorite strain, plus other categories including "Best Glass," "Best Booth," and "Best Concentrate." Winners receive the accolades of the cannabis community, which isn't worth all that much, and a serious marketing lift across the world, which is worth a whole lot more. A Cannabis Cup win has turned many a well-grown strain into a global superstar.
The premise of the judging baffled me—how can anyone who has inhaled several strains in an hour distinguish differences in flavor, not to mention the quality, of the highs? I was apparently alone in my concern. Few of the three thousand people in attendance seemed to question this. Most were grateful for the opportunity to simply light up in public without having to look over their shoulders.
When the Cup debuted, it was a select, invitation-only affair—or perhaps just an excuse for _High Times'_ editors to escape the office and ply their trade in a more exotic locale. In the Cup's early days, the editors invited the founders of the four biggest seed companies—the so-called Dutch Masters—to share the fruits of their harvest with the community of celebrants. Those early Cups were reportedly huge fun, involving lots of smoke plus wacky "spiritual" rituals that honored the plant's ceremonial roots.
Today's Cups are as much about cash as they are about hash, a five-day trade show thinly disguised as a celebration for seed sellers, hemp clothing makers, twenty-first-century farmers, and a lot of hopefuls looking to make a buck. Each vendor pays $4,500 for a booth that is housed in a damp, barely heated shipyard warehouse. In addition to the expo, there is a daily lecture series on topics ranging from "A Historical Perspective on the Emergence of the Cannabis Industry" to "Cooking with Cannabis." _High Times_ now sponsors just under a dozen spin-off cups in cities across the world, including Medical Cannabis Cups in California, Michigan, and Oregon. It has also spawned a circuit of competing industry events, which include CannaTrade in Switzerland, Spannabis in Barcelona, the London Hemp Fair, and Hempfest in Seattle, which in 2013 drew about 85,000 participants a day.
I arrived just as the 2012 event was kicking off, and from the crowd gathered outside I thought I had been dropped into a refugee camp for Woodstock exiles. Groups of men huddled around fires burning in oil drums, warming their hands, drinking coffee, and puffing up, or they were hunched over mounds of tobacco and pot, rolling and sparking spliff after spliff. When the purple "cannabus" unloaded another squadron of revelers in Rasta hats, dreadlocks, and tie-dye shirts, I sighed and wondered if the 1960s would ever be over. Just three weeks prior, the citizens of Colorado and Washington had voted to legalize pot, and news reports were claiming that four in ten Americans had smoked at least once in their lives. The press was painting pictures of legal weed being sold as openly as wine and implying that parents would soon be smoking at PTA meetings, but I was having difficulty reconciling the scene before my eyes with the bright vision of normalization that I imagined to be just around the corner. A vision that includes the absorption of this ragtag group into a larger legal market that makes room for people (like me) who like pot but haven't made it their lifestyle.
It wasn't until I stepped inside the hall and inhaled that fragrant secondhand smoke that I was able to loosen my guard and see past the bad fashion and unkempt appearances. In fact, some of the activities were strangely futuristic, such as people attaching five-foot-long clear balloons to Volcano vaporizers and then sucking down the clouds inside them. This method of inhalation makes smoking a joint look positively old school. Buds are ground up and placed into a bowl atop the Volcano, which resembles the bottom of a blender. A gust of hot air heated to the ideal temperature, 368 degrees Fahrenheit, melts the oils into a milky vapor that inflates the giant balloon. Once filled, the balloon is passed around and the crowd sips from the joyous cloud it contains. At about $600, this German-made digital instrument is the Maybach of vaporizers. Patients in enlightened dispensaries around the world use Volcanoes to take in the psychoactive and healing oils without irritating their lungs with plant matter. Vape pens, which sell for a fraction of the price, are an increasingly popular but far less effective delivery system.
In another booth a wide-smiling Canadian cannapreneur who called himself "Bubbleman" was holding forth with a frenetic energy largely absent in this heavy-eyed crowd. In one hand he brandished an enormous glass bong. In the other he held a pillbox of "bubble hash," small clumps of golden powder that he had produced. After a colossal hit that sent him into spasms of coughing, he wiped a tear from his eye and tilted the pipe to anyone who showed interest, which was everyone but me. It was afternoon, I was pleasantly enhanced, and I didn't want to spend my first day in a fog thicker than the mist that had blanketed the canals that morning. "I'm a lightweight," I said lamely, prompting a look of perplexed pity. What he had just sucked down was the purest, most concentrated form of THC ever created, Bubbleman told me. Most pot clocks in at 12 to 20 percent THC; his is a thonking 60 to 70 percent THC. One hit and you're up, up, and away.
"If it's so pure, what's making you cough?"
"Oh, that's just the oils expanding in my lungs . . ." _Hack, hack._ "You know what they say, 'If you don't cough, you don't get off.'"
Like many of the career enthusiasts in this hall, Bubbleman, aka Marc Richardson, was only too happy to give me a primer on his product, which is also known as "full melt" or "water hash." The plant's resins are contained in tiny glands or "bubbles" encased in a wax that sit atop skinny stalks, just as golf balls sit on tees. Magnified under a powerful close-up camera lens, the trichomes, bracts, and calyxes—the different structures that make up the flowering buds—resemble trippy and colorful underwater seascapes. When the bubbles are decapitated from their stems, collected, and pressed together, they become hashish.
For centuries, hash was traditionally collected by placing plants on screens, sieves, or silk cloths and shaking them until the glands fell off. The concentrated green, amber, or red powder was then formed into cakes, balls, bricks, or cubes, stamped with place of origin, and transported around the world. At some point in the 1980s, an American named Sadhu Sam noticed that the glands could also be dislodged by submerging whole cannabis leaves in icy water, then straining, drying, and pressing them into "water hash."
Bubbleman has taken this technique to the next level. He makes hash with his very own Bubble Bags—a twelve-bag kit that is marijuana's answer to microbrewing. They have made him a wealthy man.
To make bubble, Marc soaks about ten pounds of "trim," the lower-grade leaves that are removed before a bud makes it to market, in a tub of ice water. The cold bath freezes the waxy coating on the trichomes, knocking them off their stalks. The resins sink (oil is heavier than water) and the wet plant matter is strained through a series of filter bags with increasingly smaller holes. Ten pounds of trim yields one ounce of bubble hash.
If you're enterprising, as Marc obviously is, you might press the hash through a laminating machine. If you're adventurous (reckless?) you might then mold it into the shape of your credit card and slip it into your wallet. Plastic-coated hashish is virtually odor free and is essentially invisible to customs agents. Note to all would-be smugglers: Be sure to place your wallet in your jacket, not in your trousers, or your body heat might leave you with a gooey wad of bills and a tarry stain on your seat.
"What you have here is the ideal marijuana product for the twenty-first century," Marc announces to no one in particular. He has clearly used this line before. "It answers health, purity, and security concerns all at once. The cleaner it is, the fewer residues it leaves behind. That's why it's called full melt." He sparks up another bowl and invites me to inspect it close up. The hash froths mightily, but once inhaled there's nothing but a black smudge remaining.
Some minutes later a half dozen cops as wide as Sub-Zeroes come charging down the center aisle of the hall, which prompts a few vendors to scurry behind the curtains of their booths, grab as many duffel bags as they can shoulder, and hurtle toward the door. This year the police have capped the amount of product that one can possess at five grams, and this show of force is their way of demonstrating that they mean business.
Low attendance and increased police presence are but two indications that things are tougher today in the Dutch cannabis trade than they have been since the mid-1970s, when the Health Ministry instituted the "Tolerance Policy" that decriminalized soft drug use.
Based on research showing that young people typically find their way to harder drugs through dealers, the Dutch allowed a designated number of shops to sell cannabis and decriminalized the possession of small amounts. (Bafflingly, they made growing the plant illegal.) It has eliminated all arrests for possession but also discouraged drug use among the young. Dutch youth today use fewer drugs than those of any other European country, most likely because the familiar is always less alluring than the forbidden.
When it comes to drug policy, politics often trumps facts, even in sensible, pragmatic Holland. In 2011, locals from the more conservative, Calvinist southern counties began complaining about weekend traffic jams caused by "cannatourists"—smokers who drive across the border to purchase a week's supply and then head home. These counties passed laws that limited the amount tourists could buy to three measly grams, which hardly justified the gasoline used to make the journey. They also tried to force buyers to register their names and addresses, scaring off anyone with even the slightest mistrust of authority.
The mayor of Amsterdam signaled that he too was contemplating instituting the same "Weedpass" laws until coffee shop owners and their (unionized) workers did something unusual—they organized themselves into a coherent opposition. Some business owners, including Arjan Roskam, Amsterdam's self-anointed "King of Cannabis," argued that visitors to the Dutch capital were not coming for the weather (among the dampest in Europe, with 214 gray days a year), the food (mayo on everything), or the famously grumpy Dutch service (keep reading). They were coming for the cannabis and depositing some $2.6 billion in revenue (and approximately $500 million in taxes) into the Dutch economy for the privilege. After a pitched seven-month battle, the mayor backed off. By the summer of 2011, Weedpass in Amsterdam was dead.
Things quieted down in the intervening years, but I sensed the Dutch cannabis industry was still recoiling from the realization of just how fragile its existence is. The Tolerance Policy is, after all, nothing more than a dispensation—it's not a law—and it can be revoked as easily and quickly as it was put in place. When a group of Belgian growers turned their back on me as I entered their booth—did my short hair or open notebook finger me for a narc?—I began to question if Amsterdam was indeed the new world of cannabis or the old world in decline.
On day two I skipped the Cup to immerse myself in the city's other cannabis attractions. The first stop: The Hash Marijuana & Hemp Museum in the city's informally christened "Green Light District," just beyond the famed Red Light District (though Amsterdam is slowly scrubbing this area, replacing storefront brothels with expensive bakeries, cafes, and organic food shops. The items on display in these shop windows are far more tempting than the women flogging their flesh in street-facing brothels). The museum is a bit tatty and in need of some love, but still, the hodgepodge of smoking instruments, medicine bottles, and ephemera from around the world demonstrates just how much human ingenuity has gone into the pursuit of getting high.
The museum is owned by Ben Dronkers, who also owns SensiSeed, one of the oldest and largest seed banks in the world ("We were authentic before it was hip" is its tag line). Dronkers got into cannabis early and began collecting seeds and growing illegally. He was arrested many times for his "criminal" activity, though lenient Dutch jail sentences of two or three days for fifty pounds of pot are in stark contrast to the severe American penalties. Still, it was tiresome, so to pass the hours of incarceration Dronkers studied the Opium Act (the Dutch precursor to the Marijuana Tax Act) and learned that the seeds were excluded from the ban because they contain no psychoactive material. Dronkers went to court and won permission to grow plants for seeds, a legal loophole that allowed him to quietly produce seeds for over ten years. He cultivated plants in greenhouses on farms in the south of Holland, paying farmers twice what they earned growing tomatoes, and Sensi became the go-to source for growers around the world. Buyers today can still choose from dozens of classic strains based on price ("most affordable" to "premium"), yield ("medium" to "XXL"), plant size ("compact" to "high"), and climate ("sunny" to "cool").*
Today Dronkers is the most established cannapreneur in Holland. His family-run enterprise owns several buildings on the museum's block, not to mention a resort in Thailand, a home in Malaysia, and an eighteenth-century villa forty miles outside Amsterdam called the Cannabis Castle, a "marijuana Mecca" where gawping tour groups can "take photos and touch any of the 2,000 plants exhibited."
I spent days pursuing Dronkers in hopes that he might give me his perspective on the future of cannabis—after all, he's been in this game longer than most—but he was tough to pin down. Only after leaving messages at his shops, tacked to his front door, and on his voice mail, did he reluctantly invite me to visit him in the penthouse office of HempFlax, his two-decade-old enterprise dedicated to growing and processing cannabis's sober cousin.
I was on time for our appointment but no one answered the buzzer. I inquired in the Hemp & Hashish Museum but the kids in the ticket booth said they didn't recognize the owner's name, which was either indicative of their "I don't give a hoot" service ethic or Dronkers's skill at maintaining an unassuming profile.
Finally, after buzzing and calling, the door creaked open to reveal a Botticelli blond boy—one of Dronkers's sons. He led me upstairs to his father, a handsome man who could have passed for a politician but for the fat spliff wedged between his fingers. His minimally furnished penthouse overlooks some of central Amsterdam's most valuable property—the view from the windows a charming jumble of crooked rooflines and weather vanes. The sounds of scooters and bike bells were interrupted only by the cawing of seagulls perched atop gables. But it was the bud the size of a small sex toy lying on the table that gripped my attention.
Dronkers was polite, but not terribly interested in recounting his checkered past for some writer. He threw out a few canned lines—the SensiSeed bank "is as important as the rainforest" because it preserves old seeds. The museum "is one of his greatest gifts to cannabis culture." Its new sister museum in Barcelona is a beautiful way to show that "hemp is the crop of the future—it can save the world." Hemp fiber is more absorbent and durable than cotton and no pesticides are needed to grow it. It makes great paper—better than trees, so it can help end deforestation. It's used for soil remediation, as it helps refresh toxic land by sucking pollutants out of it. When compressed, it's tougher than metal and won't split like plastic, which is why Bugatti, Jaguar, and Bentley use it to make car doors.
In restoring hemp to the country that profited from it so mightily four centuries ago, Dronkers is completing his metamorphosis from criminal to entrepreneur to humanitarian. Like the Bronfmans, who smuggled whiskey into the United States in defiance of Prohibition during the 1920s but who later rehabilitated their family name, Dronkers appears to be focused on his legacy. Or maybe he's just sick of talking about weed.
In this way the Dronkers and Bronfman families have much in common. The Bronfmans of Montreal emerged from the dark days of dryness with a reliable brand that people trusted. Other bootleg scotches were often an unholy concoction of grain alcohol, prune juice (for coloring), and creosote (to lend the smokiness). Some fakes were spiked with embalming fluid, bleach, or even paint thinner for "kick," which had the unfortunate consequence of killing people. But Seagram's was always reliably pure, not to mention tasty.
Following Prohibition, Seagram's was first in line to secure US import licenses and go legit in order to slake our national thirst. The brand also employed a marketing tactic that tomorrow's cannapreneurs should bear in mind—they ushered in the notion of "social drinking" and encouraged intelligent, rather than uninformed, consumption by adding the phrase "Drink moderately" to their labels. Those two sobering words, plus millions of dollars donated to charities over the years, helped the Bronfmans shift from gangster bootleggers to responsible capitalists, to benefactors of the arts, to model citizens.
Perhaps it was the soggy November miasma that shrouded the city, but the coffee shops I passed by were mostly grim-looking affairs. Sparsely populated, underdecorated, neglected, and unloved, they were yet another signal that Amsterdam and perhaps the entire country was retrenching from its open embrace of cannabis.*
I decided that evening to visit one of the Green House coffee shops that are favored by a global cast of celebrities and boldface names. I walked to a shop on the south side of town, but when I arrived around nine p.m. I was surprised to find myself the lone visitor. While waiting for the party to get started I studied the menu, which was printed on laminated sheets the size of placemats. Categories included Herijuana, whatever that is, HydroWeed (grown hydroponically), Neiderweit, (low-strength Dutch homegrown), and a number of different "extractions." I had been trying to navigate the Dutch strains but I found the classifications as confusing as the terroir system for wine. At least the terroir system, which characterizes and categorizes French wines by the soil and climactic conditions of a particular region, is based on something tangible—geography. With cannabis, the names generally come from the whim and sometimes questionable judgment of the breeder. Take the highly vaunted and terribly named strain AK-47. One myth says its name is derived from the grower's initials (AK) and the number of days it takes to mature (47). Wrong! The original breeder, Simon from Serious Seeds, said he christened it after a machine gun because it delivers a powerful high that qualifies it as a true one-hit wonder. A marketing genius he is not.
"Why is this one called Blueberry Cheese?" I asked the budtender, who was robotically weighing and bagging bud behind the bar. "Cuz it must smell like cheese," he grunted. (Actually, _dude_ , it smells more like blueberry. But this sort of begrudging service was typical of what I encountered that autumn. Unlike New York, where waiter-actors frothily treat you to a thirty-second soliloquy on the family history of the cow your hamburger came from, diffidence here is the norm.)
A few stragglers wandered into Green House, bought some goods at the bar, and promptly left. I bought a plump pre-roll of Silver Haze, took a few pleasant hits, and moved inside to the main lounge, where I sank into a velvet couch and scanned the photos of famous visitors on the wall, Woody Harrelson, Pink, Quentin Tarantino, Miley Cyrus, and, puzzlingly, David Hasselhof among them. Silver Haze was pleasant enough but nowhere near the soaring high that came from the stuff that my cousin had produced. Many cannabists contend that decades of interbreeding the same seeds and strains has rendered Dutch weed unremarkable, or "one big mongrel bucket of crap," as Robert Connell-Clarke, one of the world's leading ethnobotanists on cannabis, put it.
Finally I asked the grumpy budtender if I was in the right place. Could this be the famous Green House I'd heard so much about? This is a local's spot, he said, shaking his head in disbelief about the dumbness of my question. Most people here just take away. If you want the scene you need to go to the Green House near Dam Square. "Rihanna was there a few nights ago," he offered. "She was a real mess."
The Dam Square locale was a hive of activity. An aggressively young crowd was jostling to inspect the buds and hashishes displayed below the glass-top bar, and the half-dozen smiling budtenders, mostly Spaniards, were struggling to keep up. I bought another pre-roll of something called Arjan's Super Haze #1, found a seat, and ordered a cup of peppermint tea. This was more like it. The crowd was a handsome mix of men and women. (That was unusual; the cannabis circuit is about 70 percent male today and could benefit from more female presence.) A "Strain Hunters" video was playing on the flat screen. This is a vanity project by Green House owner Arjan Roskam, the aforementioned King of Cannabis, who travels to remote lands in search of rare strains that haven't yet been imported to the West.
To my mind Arjan is a modern spokesmodel for the new world of cannabis. While Dronkers is touting hemp as a cure for what ails the planet, Arjan is trying to drag the Dutch cannabis industry out of the 1980s and into the mainstream with well-designed shops staffed by friendly, enthusiastic servers. In his own way he's a disrupter—someone who does things differently, or so he claims. When he began cultivating indoor sinsemilla in the 1980s, all the coffee shops sold hash exclusively. The cannabis in Europe was, at the time, of low quality—it often came packed in bricks—and it was so rarely found that smokers referred to it as spinach. Seeing he faced an uphill battle, Arjan gave his cannabis to coffee shops for free and urged them to give it away to customers.
The freemium marketing model didn't work. Dutch smokers shied away from bud, so Arjan struck out on his own, launching the Green House shops in 1992. Obviously born with the PR gene, he invited the mayor and the chief of police to one opening. He still has a copy of that letter and mentions it frequently as a point of pride. He also ensured that _High Times'_ editors were always greeted by a few ounces of his latest strains when they checked into their hotels.
Since then, he has racked up nearly thirty Cannabis Cup prizes. He claims that companies in California are wooing him to share his strains. Even his language is evocative and gauged to sell. "Have you tried our Sharkberry Cream?" he asks me. "It's really flowery, like spring and summer. The Lemon Haze Crystal? It's super strong. We suggest you smoke it at night."
But this well-groomed _High Times_ cover boy is more than a marketer. He's also trying to inject some new juice into a loosely aligned industry that is now facing real competition from abroad. He is a spokesperson for the Cannabis Retailers Association, which serves as a trade group for coffee shop owners. He claims the Green Light District was his concept to attract celebrity smokers from the United States. When they do show up, Arjan is first in line to snap a photo with them, which he duly posts on Facebook and Instagram.
In trying to turn cannabis from a plant into a brand it's useful to have a king, even if he is self-crowned. The Strain Hunters films—which have aired on the National Geographic Channel and on Vice TV—burnish his media profile, while his retail operations, seed company, and plant-nutrient company signal that his business is in growth mode rather than in decline. I suspect this is why he, in the midst of this dark moment for the Dutch industry, sees opportunity. "In the past we couldn't do anything because it was illegal everywhere. But now, the Czech Republic, Spain, Uruguay, even Albania . . . it's all changing. I think the best ten years are ahead. The feds and the police are finally getting tired of us."*
On the last day of the Cup I met an American in a porkpie hat with a bushy beard the size of a small animal on his face. Adam Dunn was one of those drug war refugees who moved to Amsterdam in the late 1980s and ended up developing an award-winning strain called SAGE (Sativa Afghani Genetic Equilibrium). In 2001, SAGE took second place at the Cup and elevated Dunn to a top-tier grower. Now, twelve years later, he was here trying to interest buyers in his hemp clothing line, HoodLamb, which is worn by the surfer Kelly Slater, Chuck D. from Public Enemy, and Snoop Dogg, and thus carries A-list celebrity cred.
It was nice to be back in Amsterdam to see friends, Adam says, but he's grumbly about the heightened paranoia and the sparse crowds. This was the lowest attendance in years and Adam finds the Dutch scene depressing. The place in Europe for popping seeds these days is Spain, he tells me, and the clubs in Barcelona, he hears, are especially nice. As far as growing is concerned, well, he moved to Denver last year. "There's no energy here anymore. Colorado, man, it's wide open. There's places with three thousand plants, places with two thousand lights legally. There's potential to do all the things we wanted to do in Holland but couldn't because there was no infrastructure, no space or even air conditioners. And no one wanted to invest the money.
"The lights, they're going off in Amsterdam. Denver, man, that's the future. I swear it's so much easier there," he said, white smile cracking through his facebush. "You should come to see what's going on there, man. We can hang out."
Adam was on point. With US states now going legal, what exactly would normalization look like once the fearmongering and criminality were taken away and cannabis was sold as openly as beer? That was the big question, but other questions were percolating in the back of my mind, especially regarding the medicinal side of this much-disputed weed. Namely, what exactly is the difference between medical marijuana and the stuff that people use for recreation, inspiration, or simply to get high? And what healing properties does the plant actually possess?
## ___Chapter 3_
## THE MARTYR AND THE MILLIONAIRES
_San Francisco, Oakland, California_
The father of medical marijuana in the United States was . . .
A: Thomas Jefferson
B: Sanjay Gupta
C: Dennis Peron
D: George Soros
Stoners might guess Jefferson. They'll cite his diary entries and the laws he passed exhorting American farmers to plant hemp. They incorrectly use those facts as proof that the founding fathers may have enjoyed a puff in between starting a revolution and establishing a country. Not true. All countries at the time cultivated hemp for fiber, which they used to make sails, clothing, and paper.
American television viewers would likely vote for Gupta. His 2013 documentary, _Weed_ , helped convince Americans that the plant is real medicine and showed them how it could ameliorate symptoms of severe and rare diseases, such as Dravet syndrome.
The correct answer, however, is C and D, Dennis Peron and George Soros. This proxy marriage of a Vietnam vet, pot dealer, gay activist, and onetime Republican candidate for governor of Wisconsin, and this billionaire supporter paved the way for California's Proposition 215, the world's first-ever medical marijuana law. Peron almost single-handedly reframed the plant—and the debate around it—from a reckless drug of rebellion to a botanical medicine, but his mission would likely have imploded without the deep pockets and deeper convictions of a few unwavering backers.
Until Peron, pot advocates in the United States were spinning their wheels, arguing that citizens should have the right to intoxicate themselves in any way they see fit. While this argument is valid, it's not all that persuasive: fighting for the right to get stoned never resonated with soccer moms (or dads) who didn't want their kids exposed to yet another temptation, no matter how safe or natural it was. Peron tectonically shifted the paradigm, but outside of a small coterie of California activists, his story is little known.
I tracked down the self-proclaimed "fairy godfather of medical marijuana" (MMJ) in San Francisco, where he lives in a hulking Victorian pile known as the Castro Castle. I rang the doorbell at noon as we had arranged the day before, but the gentleman who answered apologetically informed me that Dennis had to unexpectedly take his brother to the airport. He invited me into the kitchen, where I watched a bear of a chef in an apron cooking lunch for a group of men seated around a table in various states of undress, speaking different languages. The walls were a shrine to the king of this castle. There were photos of Dennis with Harvey Milk, Dennis in bell-bottoms addressing a rally, yellowed newspaper clippings of Dennis running for office. Was this a gay bordello? A commune? I didn't ask. Instead, I retired to the back garden to await my audience.
I sat myself near a grotesque mural of Brownie Mary (née Mary Jane Rathbun), one of Peron's best friends and a local legend who was known as the city's Florence Nightingale for distributing "magic brownies" to AIDS patients in city hospitals. With her gray hair and unfashionable eyewear, Mary may have looked like a kindly grandmother, but her scabrous remarks made her a cause célèbre. "If the narcs think I'm going to stop baking pot brownies for my kids with AIDS they can go fuck themselves in Macy's window!" she announced to deafening cheers at a rally following one of her several arrests. With Mary's image smiling insanely over my shoulder, I was handed a mug of tea by a handyman who informed me that the Castro Castle is in fact an inexpensive B and B frequented by travelers hungry for a taste of old-school San Francisco life.
Two cups of tea later, Peron joined me. With his short, neatly combed hair and button-down shirt, he looked more like a priest than a firebrand, and he sounded rather subdued as well. A stroke in 2010 had reduced his voice to a raspy whisper, but the impish twinkle in his eye signaled to me that this guy could still cause trouble.
Peron's infatuation with pot began, as it did for many, in Vietnam, where his Air America unit was dispatched to the Thai border to spy on the Ho Chi Minh Trail for the CIA. The Vietcong learned about the mission and rained mortar shells on Peron's unit every night for a month. Constant bombardment taught Peron two things: (1) that sleeping could be fatal—this is one reason so many Vietnam vets suffered debilitating insomnia once they returned from war—and it was safer to lie awake at night; and (2) that he was gay. It was in the trenches that he first had sex with a man.
Tour of duty over, Peron returned home with a duffel bag full of Thai Stick. He grew out his crew cut, moved to a commune, and dedicated himself to the vague goal of "helping America come to peace with itself." (OK, it was the early 1970s.) Pot was the instrument through which he hoped to execute that unlikely reconciliation.
In the late 1970s Peron flouted the law to open the Big Top pot supermarket in San Francisco, which quickly became the country's largest cannabis retailer. It was so successful that Peron had $1 million in twenty-dollar bills stashed in a closet. Just as large bundles of cash make dispensary owners vulnerable to robbery and paranoia today, they also did so back then, so when a horde of plainclothes policemen knocked down the door, Peron assumed he was being burgled. He hoisted a five-gallon water jug over his head to hurl down the stairs at his invaders, but the cops fired first, landing a bullet in his leg.
Given the looser laws of the Carter era, the 199 pounds of pot on the premises should have landed Peron in the clink for a few years. But when Officer Paul Makaveckas was asked at the trial to show the court how he fired the shot, he stood up in the witness box and aimed his pistol at Peron for a long thirty seconds. Then Makaveckas audibly lamented his faulty aim. A hit to the heart would have meant "one less faggot in San Francisco," he said within earshot of lawyers.
That untoward remark won Peron a reduced seven-month sentence in county jail, an unyielding hostility to law enforcement, and instant stature in the small but growing movement to legalize pot. Once out of jail he authored Proposition W (for "weed"), which directed the district attorney to stop arresting San Franciscans for possessing, transferring, or growing marijuana. The largely symbolic city ordinance passed overwhelmingly in 1978 with 63.7 percent of the vote.
After Mayor George Moscone and Supervisor Harvey Milk were gunned down by Dan White, a former cop who later somehow convinced a jury that an overdose of Twinkies had caused his diminished mental capacity, AIDS began its rampage and gay men began dying. The desperation was palpable. No one at the time knew what caused the scourge (it was still being misidentified as GRID, Gay-Related Immunodeficiency Disease) and there was no treatment for the Kaposi's sarcoma (KS) that scarred people with purple lesions, or the PCP pneumonia that drowned them to death in their own sputum. When Peron's partner, Jonathan West, was diagnosed in the late 1980s, there were always a few ounces of weed on hand to ameliorate his suffering.
One evening, just before midnight, ten plainclothes narcotics officers in rubber gloves showed up at Peron and West's home with a search warrant. The cops ransacked the apartment and forced Jonathan facedown onto the floor, bootjacking his neck. "Know what AIDS stands for?" one of them asked. "Asshole In Deep Shit." The cops arrested Peron for possessing four ounces of Humboldt green with intent to sell. At his 1990 trial, West—ninety-eight pounds, face mottled with purple KS lesions the size of grapes—testified that the pot was his. The judge dropped the charges and scolded the arresting officers. West died two weeks later and Peron channeled his fury into writing Proposition P (for "Peron"). It was the country's first medical-marijuana initiative, and Peron was on a roll.
Activists (and politicians and actors) are typically blessed—or cursed—with a messianic self-belief that powers them forward despite good sense and the overwhelming odds against them. Their vocabularies are absent the word "compromise." Peron, impetuous and at times bombastic and utterly uninterested in the formalities of law and regulation, is no exception. Provocation turned him on. But compassion was also a part of the equation—it's no exaggeration to say that people with AIDS had been abandoned by the medical and political establishments and were left to fend for themselves. Peron's next move was to rent a five-story building on Market Street and set up the Cannabis Buyers Club, the country's first dispensary. Tacked to the wall of the office was a sign: THIS IS A FREE-DRUG WORKPLACE.
The top two floors of the club were decked with comfortable, if raggedy, furniture. Meals cost one dollar, and liquid nutritional supplements were served to those who couldn't hold down food. But it wasn't décor or food that did the healing. George Zimmer, the founder of the clothing retailer Men's Wearhouse and an early visitor to the Buyers Club, recalled that his strongest impression was the support the patients offered each other, since so many were pariahs, shunned by their families and isolated in spheres of loneliness. Even Peron's parents supported the work he was doing. "My parents would get calls saying: 'Your son is on TV! He is selling marijuana to AIDS patients,'" Brian Peron, Dennis's younger brother, recalls. "My mom would say, 'Good, they need it.'"
By 1995, the Cannabis Buyers Club had four thousand members; the following year, membership tripled. The locale became a popular stop on the tourist circuit, and Peron kept the rules for admission loose. Anyone over fifty-five was automatically accepted—Dennis defended this practice by asking, "Don't you think people that age have the right to decide what they want to treat their aches and pains with?"
Later that year Peron altered the course of history by drafting another ballot initiative that allowed anyone suffering from any ailment for which marijuana provides relief to buy or grow the plant. The wording was intentionally vague—it allowed doctors to "recommend" cannabis for any condition they saw fit. (If the initiative had used the word "prescribe," it would have been on a collision course with the federal policy that barred doctors from prescribing any illegal substance.)
There were 433,000 obstacles to turning Proposition 215 (aka the "Compassionate Care Act") into law—that was the number of signatures needed to get it onto the California ballot by April 1996. By January, with only three months pending before the deadline, the situation was looking dire. Peron's ragtag band of volunteers was woefully behind; they claimed to have accrued 250,000 signatures, but in fact they only had 35,000, and most of them were fakes, copied out of the telephone book.
Enter Ethan Nadelmann, a Harvard-educated lawyer who had been eyeing the flailing effort from New York. Funded by the business magnate George Soros, Nadelmann's organization—then called the Lindesmith Center and today called the Drug Policy Alliance—had a goal even more quixotic than Peron's: ending the War on Drugs. And this is how the unlikely marriage between the martyr and the moneymen began, a quiet but necessary affiliation that has propelled the movement forward until this day.
In the chaos of the California ballot initiative, Nadelmann saw an opening to score a win in the big leagues of American politics. Polls showed that a majority of Americans on the West Coast agreed that the drug war had gone too far and that addicts should be treated rather than jailed. With public opinion on his side he called on Soros, who had recently earned $1 billion by short-selling £10 billion during the 1992 UK currency crisis, to get the ball rolling.
"At the time George was more of a Rockefeller Republican than liberal Democrat, but there were always a few issues he felt strongly about," Nadelmann recalls. "I was walking him through our [group's] national agenda, which included expanding access to methadone maintenance, needle exchanges to reduce the spread of AIDS, rolling back mandatory sentencing laws, and finally, medical marijuana. 'Medical marijuana?' George interrupted. 'I like the sound of that.' It was the intersection of two areas he cared deeply about: drug policy reform plus dying with dignity."
Soros ponied up $550,000, but he was hesitant to become the effort's sole backer, as he lived out of state and didn't want the Daddy Warbucks stigma of buying an election. Nadelmann dug into a few other deep pockets; George Zimmer, an Oakland resident, chipped in $250,000. Peter Lewis, the founder of Progressive Insurance, anted up $500,000, and John Sperling, whose Phoenix, Arizona–based Apollo Group owned eighty-eight private colleges, kicked in $200,000. Gail Zappa, the wife of Frank Zappa, and Larry Flynt, the publisher of _Hustler_ , chipped in more. Laurance S. Rockefeller, a brother of New York governor Nelson Rockefeller, who passed the country's first mandatory prison sentences for all drug offenses, topped it off with $50,000 at the behest of the spiritual teacher Ram Dass.
Though Soros and Sperling had sampled cannabis, legalizing the plant was not their primary aim. They were far more aggrieved by the 1.5 million US citizens arrested yearly for drug crimes, over half of which were—and still are—marijuana related. Eighty-eight percent of these arrests were for mere possession. Despite roughly equal usage rates, blacks were 3.73 times more likely than whites to be arrested for marijuana. Most shockingly, the total number of cannabis-related arrests in 2010 exceeded arrests for violent crimes, including murder, manslaughter, forcible rape, robbery, and aggravated assault.
Over the years, Soros has remained one of pot legalization's strongest backers, contributing an estimated $25–$30 million to the cause since the mid-1990s. Zimmer and Lewis were, on the other hand, both smokers and had a more personal stake. Of the two, Lewis was more outspoken about what the plant added to his life. "Marijuana being illegal is a tragedy I want to correct," he said in one of the last interviews he gave prior to his death. "I feel deeply that helping to achieve this objective is one of the best contributions I can make to the well-being of our great country."
Nadelmann understood that Proposition 215 couldn't succeed without Dennis Peron, but he also knew it couldn't succeed with him either, so he offered the money with strings: Peron had to submit to the authority of Bill Zimmerman, a pollster whom Nadelmann had appointed campaign chief. Peron agreed nominally, and in the next three months Zimmerman's army collected the necessary signatures. But Zimmerman and Peron got on like chalk and cheese. The activists thought that the politicos were shunting them aside, and Zimmerman judged Peron to be an untrustworthy liability. "His statements too often turned out to be intentional lies," he says today.
Zimmerman ordered Peron to stop speaking to the media and publicly excoriated him as a pot dealer whose chicanery would contravene the seriousness of the medical issue. But his attempts at stifling Peron only created more resistance. After months of putting out fires, Zimmerman opened the _San Francisco Chronicle_ to see Peron puffing a fat doobie, and proclaiming that "all use, whether you know it or not, is medical." Opponents of 215 had a field day. This was the logic of an addict, they screamed, more proof that medical marijuana was nothing more than a stalking horse for full legalization. "I think the medical marijuana movement has more to fear from Dennis Peron and people like him than from law enforcement," Zimmerman fumed publicly.
Whether MMJ was a ruse or not, Peron's statement was both true and confusing. It's partly due to semantics, but also due to the narrow definition of medicine that has dominated the twentieth century. Take, for instance, people who smoke pot to ease anxiety. Are they medicating? If they were to visit a doctor, they'd get a prescription for an antidepressant or Xanax, which would attack the problem from a different route. Is an antidepressant more of a medicine simply because it comes in a pill? Many would say no.
Vitamin C is another example. Most of us take it to prevent unspecified illnesses, such as colds. But if you have scurvy, a fatal condition that is annihilated by vitamin C, you bet it is medical. Perhaps the most succinct definition of medical marijuana comes from Dr. Amanda Reiman, the California policy manager of the Drug Policy Alliance: "Medical marijuana treats a specific symptom or disease. Using it more generally, say, to change your mood, is adult use."
In the lead-up to the election, Drug Czar Barry McCaffrey, plus Senators Barbara Boxer and Diane Feinstein, predicted disaster if this "dangerous" bill were to pass; they were soon joined by Presidents Ford, Carter, Clinton, and George H. W. Bush in calling for its defeat.
_Doonesbury_ , it turned out, was more in touch with California voters than those officials. Garry Trudeau, the creator of the comic, ran a two-week series poking fun at the storm 215 had whipped up. In one installment, Zonker's friend Cornell says, "I can't get hold of any pot for our AIDS patients. Our regular sources have been spooked ever since the Cannabis Buyers Club in San Francisco got raided . . ." In response, California's attorney general Dan Lungren held a press conference to rebut the cartoon. "Sure it's a comic strip, but what's the difference between advocating drugs in a comic strip or in a rap video or on the street corner?" he fulminated. "Zonker's a real person in our society. He is not fictitious. And we should put Zonker behind bars where he belongs!"
On November 5, 1996, over five million Californians voted to pass Prop 215—56 percent of voters—and, in a twist that must still have Peron smiling, his fiercest opponents were then charged with enforcing the measure.
Proposition 215 was intentionally loose. It created medical cooperatives between growers and patients and allowed anyone with a doctor's recommendation and a California ID to purchase pot. But it made no mention of distribution, sales, or taxation, and these gaps have caused a storm of confusion, lawsuits, and disagreements ever since.
For years, rumors circulated that the original bill included regulations about how to distribute medical marijuana and that the duplicitous Peron had erased the language from the ballot initiative. But 215's author, Bill Panzer, laid that rumor to rest. "We thought, 'Let's just start out with growing your own,'" he told me. "We didn't think that people were ready for distribution and that it would be going too far.
"In retrospect, I have more respect today for how Dennis read the electorate than I did then. I used to pooh-pooh the idea that all use can be medical, but he turned out to be right. And I have to laugh. You see the commercials for prescription medicines on TV and at the end they say all this or that can kill you or give you suicidal thoughts, and you realize that cannabis doesn't do any of this stuff."
When 215 became law, social apocalypse was predicted in California. Workplaces will be overrun by pot smokers! Crime will skyrocket! More drug babies will be born! Philip Morris will buy up Humboldt County! Today, twenty years after partial legalization, the results are in, and they should be examined with a hard gaze, no matter how inconvenient they may be.
Polling data show that younger adults are now substituting cannabis for alcohol, and their parents approve. California parents believe the herb is less harmful to their children's health and safety, especially when driving. Some cities have struggled to regulate the sudden explosion of dispensaries, but the fears that the pot shop on the corner would attract unsavory lurkers, traffic, and declining neighborhoods never materialized. Nor has imposing a local tax on medical marijuana, such as Oakland, San Jose, and other cities have done, driven consumers to the black market in search of cheaper prices. Buyers have demonstrated that when they are given the opportunity to purchase high-quality, clean marijuana legally, and when the experience is welcoming and respectful rather than furtive, they will return for more.
Cultivation has sparked a modest boon in some rural northern communities, creating tax revenue and cottage industries that service the cannabis industry. The old adage that the gold rush made some people like Levi Strauss, who sold pickaxes to miners, richer than those who found gold, seems to be holding true: testing labs, gardening centers, and software developers are all alive and well. Even political conservatives running for election in Riverside County were counseled by consultants that being a prohibitionist was to be on the wrong side of history.
But the biggest changes have occurred through education. People across generations, professions, and classes are reframing cannabis, not only as a promising botanical medicine, but also as an integral part of the state's economy and culture, not all that different from wine, almonds, and earthquakes.
In one tony San Francisco restaurant, I spied a party discreetly passing around a pen vaporizer between courses. Because these e-joints emit barely a hint of odor, they make public enhancement as easy as drinking a beer. At a cocktail party in Vancouver, British Columbia, seniors sucking on Pax vaporizers were discussing literature and debating the aesthetic differences between sun-grown and indoor varieties of cannabis. Indoor grows were deemed cleaner and less prone to mold, but the consensus was that pot grown under the sun has a wider spectrum of tastes and effects. "I think of indoor guys as the bodybuilder who builds his torso but still has skinny legs," one guest said. "Sun-grown flowers are looser, leafier . . . happier." A Hollywood studio head told me he has replaced sleeping pills with low-dose edibles and relies on them to ease the wear and tear of red-eye flights between the coasts. "A low-dose cannabis chocolate-covered coffee bean an hour before the plane takes off and I wake up in New York refreshed and with no hangover. It's better than Xanax."
In spite of the 1996 victory, George Soros continued to waver on legalization. He thought that decriminalization—simply removing the penalties for possession but not regulating or allowing pot's sale—was the safer route to travel. Despite the evidence that pot is less addictive or physically destructive than tobacco or alcohol, he was concerned about the mayhem that might ensue if citizens were allowed open access to "a drug." He maintained that ambivalence for over a decade but continued funding the effort to reform state laws nevertheless. By 2010 it had become obvious that decriminalization was insufficient to stop the massive number of arrests of young men of color for possession, and Soros made the case for legalization in a measured and logical opinion piece in the _Wall Street Journal_.
"Regulating and taxing marijuana would simultaneously save taxpayers billions of dollars in enforcement and incarceration costs, while providing many billions of dollars in revenue annually," he wrote. "It also would reduce the crime, violence, and corruption associated with drug markets, and the violations of civil liberties and human rights that occur when large numbers of otherwise law-abiding citizens are subject to arrest. Police could focus on serious crime instead."
Soros had finally awakened to what middle-class white kids like me have always known: When we are caught snorting a line of cocaine or smoking a joint, we get a slap on the hand, maybe a fine. A black kid gets a ticket to orange.
Nadelmann described Soros as possessing a soaring intellect, of which I have little doubt. But his writing was dispassionate and impersonal, and I was curious about the inner journey that caused him to revise his opinion. His PR man rebuffed my request for an interview, so I was left to assume that he was either tired of being associated with this disreputable plant or that he was more interested in the issues that result from pot's illegality—that is, the multibillion-dollar prison-industrial complex that he cited in the _Journal_ opinion piece. The situation has only worsened in the intervening years.
Over 2.3 million inmates are currently residing in state, federal, and private prisons throughout the country. That's a half million more people locked up in the land of the free than in China, even though the People's Republic has a population five times as large.
Ten years ago there were only five private prisons in the United States, holding 2,000 inmates. Today, there are one hundred for-profit prisons, with 62,000 inmates, and that number is projected to swell to 360,000 in coming decades. Why? Because for a state to contract a private prison, it must guarantee an 80 to 90 percent occupancy rate, and the drug wars provide a steady stream of occupants. As Soros wrote, "The roughly 750,000 arrests [local law enforcement] made each year for possession of small amounts of marijuana represent more than 40 percent of all drug arrests. This amounts to one arrest every 42 seconds and 120,000 more arrests for pot each year than for violent crimes."
Local law enforcement has also developed its own drug dependency—on pot in particular—thanks to something called asset forfeiture. Each year, the Drug Enforcement Agency funnels some $10 billion in grants to local cops, incentivizing them to seize the property of anyone suspected of producing or selling illegal substances. No proof of guilt is required—a cop's suspicion is enough to seize property. The cops tally up the value of the seized items—a house, a car, an iPad—and submit it to the DEA, which takes a 20 percent schmear off the top and then returns 80 percent in cash to the local forces, which use the boondoggle to buy advanced weaponry, new cars, or office furniture. Asset forfeiture is little more than a program of perks for cash-strapped local forces, which turns America into a giant Walmart for law enforcement. Between 2002 and 2012, marijuana arrests yielded them $1 billion, according to Justice Department data. Property owners have no recourse to the courts; even if they did, the legal costs to get back their property would often exceed its value.
Even while polls indicate that beat officers favor reforming marijuana laws, institutional forces go to the mat to maintain the status quo. In Florida, the state sheriffs' association, led by Polk County sheriff Grady Judd, became the public face opposing the medical marijuana referendum on the 2014 ballot. Judd rattled off the familiar and largely fact-free arguments against reform: the dangers of driving while high, increased workers' compensation claims, teenage addiction, and the imaginary increase in respiratory illnesses. But the annual strategic plan his office submitted to the Polk County Board of Commissioners tells a different tale, one that has nothing to do with public health. In it, Judd says that his force is "doing more with fewer resources" and that he's had to cut seventeen deputy sheriff positions due to a lack of funds. He describes seizures from marijuana grow houses as a significant revenue source, assets that help "meet eligible equipment or other non-recurring needs that could not be met by local funding, thereby putting forfeited and unclaimed funds to work in crime prevention, for the taxpayer." A Florida law enforcement newsletter describes the state's marijuana-eradication program, which nets about $1 million a year, more concisely: It is "an excellent return on investment."
Like Soros, Peter Lewis, the founder of Progressive Insurance, the nation's fourth-largest insurance company, also concluded that the drug wars are little more than a $51 billion-a-year jobs program for cops, prison guards, and piss-testing companies. "On its face, based on examination of any set of facts, the War on Drugs is a gross waste of money," Lewis observed. "Its only practical rationale is to imprison certain segments of the population so the jailers can make a living." But Lewis had a more intimate relationship with the plant, and he opened up about it toward the end of his life. His thoughts are worth recounting, as such personal revelations from the mouths of the rich and powerful are so rarely expressed.
Lewis's reign as CEO of Progressive lasted thirty-five years. Until the mid-1990s, the insurance magnate aimed his philanthropy at cultural institutions, universities, and museums. But following Lewis's divorce from his first wife, one of his sons handed him a joint to help him cope with his emotional upheaval. He took to it instantly and continued smoking unrepentantly for the rest of his life.
From all accounts, Lewis was an unusual executive, a seeker of the "unconventionally possible, a boundary breaker," in the words of his friend and former Princeton classmate Ralph Nader. He hung Andy Warhol's Mao portraits at Progressive's Cleveland, Ohio, headquarters and delighted in the anger they aroused in some employees, noting that at least the art stimulated them. Lewis felt that the legalization movement and the plant itself could benefit from reimagineering. He wanted to torch the walls of the cannabis closet to liberate pot from the constraints of its stoner image and argued for a national coming-out day, when professionals, family members—even strangers—would publicly share their experiences with cannabis.
Lewis's own coming out, however, wasn't his choice. In 1999, a former employee snitched about his smoking habits to a reporter from _Fortune_ magazine. In a prime example of mainstream media boneheadedness, the reporter patronized Lewis as a "functioning pothead," but praised his bottom-line business acumen, as if the two traits couldn't coexist in one brain. The following year, while Lewis was passing through the Auckland, New Zealand, airport, drug dogs sniffed out 1.7 ounces of pot and 2 ounces of hash in his luggage. Lewis pled guilty to the charge of importing drugs and spent one night in jail, but the charges were dropped after he agreed to "donate" $53,000 to a drug rehab center. The judge subsequently invited Lewis to stick around New Zealand to watch the challenger for the America's Cup yacht race and "enjoy the fresh air."
In 2001, at age sixty-four, Lewis's left leg was amputated below the knee because of an incurable infection. Confined to a wheelchair and in excruciating pain, he smoked constantly. "It didn't exactly eliminate the pain, but it made the pain tolerable—and it let me avoid those heavy-duty narcotics that leave you incapacitated," he said.
Like a modern-day Howard Hughes, Lewis dispensed vast sums of money to causes close to his heart. Waging his own "War on Drug Laws" was high on his list. "Our marijuana laws are outdated, ineffective and stupid," he wrote in _Forbes_. "Everything that has been done to enforce these laws has had a negative effect, with no results."
It's the rare CEO of a public company valued over $14 billion who speaks about the value of emotions in business, but in doing so Lewis initiated a conversation that needs to occur more audibly if weed is ever going to assume its rightful position alongside alcohol as a socially sanctioned intoxicant. His refreshingly candid comments reveal the ways the plant wove him into the wider fabric of life. "Running a business turns out to be a pretty lonely thing to do," Lewis said. "Marijuana would help me commune with myself. It would turn my daily collection of information into some kind of understanding of what was really going on—what the key components were, what the emotional components were. It made me better at my job. Except for activities that require physical dexterity like playing tennis, I think it basically helped me be better at almost anything I ever did."
Pot, he concluded, enabled him to stay "open to craziness, to new ideas, to stuff that no one ever thought about before. It kept me open to doing things that everybody else said you shouldn't do. . . . [It] helped me to accomplish what I set out to do, made me easier to be with and easier on myself. It allows me to be more accepting of, and caring for, other people."
Graham Boyd, who administered Lewis's philanthropy, told me that Lewis donated over $40 million of his personal fortune to marijuana reform. That money underwrote ballot campaigns, research, polling, and legal defense, and it enabled twenty-three states to enact medical marijuana laws by the time of Lewis's death in November 2013.
The movement to legalize weed is often compared with the effort to legalize gay marriage. The two have many surface commonalities. Both took root in the 1960s and waged a half-century-long battle. Advocates of both groups were vilified by pseudoscience and an unquestioning media. Before they became poster boys for Baby Bjorns and Chinese newborns, gay men were largely pictured in lipstick or in leather. Similarly, cannabists are still hampered by Harold and Kumar portrayals. Few mainstream businesspeople other than Lewis or Sir Richard Branson have spoken out about their personal use. That gaping silence allows otherwise intelligent and influential pundits, like the former _New Yorker_ editor Tina Brown, to peddle tired stereotypes without being held accountable. "Legal weed contributes to us being a fatter, dumber, sleepier nation, even less able to compete with the Chinese. Will pot be our nation's downfall?" she tweeted after the presumably fatter and dumber voters in Washington and Colorado legalized marijuana.
The thoughtful _New York Times_ columnist David Brooks climbed high onto his horse the very same day to issue this peroration: "In legalizing weed, citizens of Colorado are, indeed, enhancing individual freedom. But they are also nurturing a moral ecology in which it is a bit harder to be the sort of person most of us want to be." It's not difficult to picture him sipping his eighteen-year-old single-malt scotch when finishing that little disquisition.
While coming out about marijuana may not win elections or change the smug opinions of the chattering classes, it will demonstrate that pot is used far more widely and interestingly than is currently presumed. As Ted Trimpa, a lobbyist who worked on both gay marriage and Colorado's legalization efforts, observed: "When pot becomes not just the kid with long hair and skateboard or the guy in the beat up VW van . . . when it's the investment banker, the doctor . . . that's when things will change."
Here's a little secret: It already is the banker and the doctor. They're just not talking about it openly yet.
Lewis passed away before we could speak. So I was pleasantly surprised when George "I guarantee it" Zimmer agreed to meet. I was even more surprised because I had contacted him just after the board of Men's Wearhouse, the company he had founded in 1972 and that had grown to be the largest men's retailer in the United States, had booted him. He'd left without a struggle.
Zimmer was called "the most interesting man in fashion," in part because his interests reached far beyond suits, sales, and spreadsheets. A member of the board of the Institute for Noetic Sciences, he has been a student of consciousness studies for decades. He practiced a form of compassionate capitalism that centered around one tenet: happy employees attract happy customers. Make no mistake, I'm not attributing Zimmer's success to cannabis, but by his own account, it guided him to becoming a more effective leader.
One way he did that was by traversing the country to spend face time with the rank-and-file employees at their holiday parties. He wouldn't talk to the executives but spent the night on the dance floor with the troops. "It made them feel great," Zimmer told me. He also banned background checks and drug testing. Eighty-four percent of large American companies subscribe to this form of chemical McCarthyism, but Zimmer viewed drug tests and background checks as serious infringements on personal liberty, both of which are weighted unfairly against cannabis.
"If you want to have trust, you need to be trustworthy," Zimmer explained when I asked him to expand on his position. We are sitting in the bland offices of his new enterprise, Montclair Venture Partners, perched above a shopping strip in one of Oakland's wealthier suburbs. His office is impersonal and generically appointed, but two objects stand out among the drabness. One is a framed front page of the _Houston Chronicle_ announcing "Nixon Resigns!" The other is a chessboard set up with a game that he is playing remotely with a partner named Chris.
"Asking an employee to do a drug test or a background check is like saying, 'I don't trust you at all.' Besides, what am I going to find out? That some guy was stopped for a few joints when he was fifteen?" Zimmer, who has an affinity for conspiracy theories, points out that one of the largest urine-analysis companies, Bensinger, DuPont & Associates, was cofounded by Nixon's former drug czar Robert DuPont. It's a multibillion-dollar industry centered on piss, paranoia, and the fiction of a drug-free America. Lobbying for the industry is supported by Jim Beam and Anheuser-Busch, among other liquor companies—further evidence that conspiracies are typically more than theories when the subject is pot.
I wasn't sure how Zimmer would respond to personal questions about cannabis, but unlike the other, tighter-lipped members of the millionaires' club, he was loose and relaxed. He has never taken an outspoken public stance but has voiced his opinions when asked. In a 1999 article in the _San Francisco Examiner,_ he proclaimed his support for the 55 percent inheritance tax and his opposition to the War on Drugs. He also recounted how he offered his mom medical marijuana when she was undergoing chemotherapy. "She looked at me like I suggested that she blow up a building," he recalled. "She said, 'Absolutely not,' and I said, 'OK.'"
His board of directors greeted such remarks with displeasure. "They would say, 'George, there's no benefit from speaking out about pot] and there may be harm.' I would say, 'Actually, there's no harm and there may be benefit.' The rank and file loved my ability to speak truth to power."[* And apparently they liked that the boss smoked openly, which he did with employees off the clock. "After a [sales] training, sitting around a fire pit, I'd take out a joint and say, 'Since most of you had to fly here you probably couldn't bring any pot, so I'm going to light a joint.' Not everyone smoked, but you can be damn sure that a myth developed concerning my open use of cannabis."
Pot, says Zimmer, helps him "shut out noise. As long as you're not totally fucked up, pot enables you to have a sense of the small picture and macro at same time. I've always thought that being a successful businessperson is the ability to balance that focused financial statement analysis with the panoramic right brain way of thinking." It also made him more willing to collaborate while softening some of his aggressive edges. At one time, he recalls, he was type A competitive. Pot didn't make him less of a fighter. It simply provided an awareness that aggression isn't the only route to crossing the finish line first.
While his management style may be modern, Zimmer's smoking habits are defiantly old-school. He smokes three joints a day and finds it therapeutic to roll his own. The nuances of edibles, strains, and concentrates hold little allure. When I show him a menu from Harborside Health Center, the world's largest dispensary, located just a few miles down the road in Oakland, he laughs at the epicurean list of categories. "Supermelt? Shatter? Amber? Sun-grown? _Strains?_ I've never noticed the difference between strains," he says. "I've never tried to notice. The only thing people look at is the price."
"What, you'll smoke whatever comes your way?"
"Including my own roaches! I won't throw roaches away any more than I throw away my change. There ought to be a way to tip with roaches."
I am looking at this gray-haired gent being swallowed by a black leather couch, realizing again that this forthrightness is precisely what's missing from today's cannabis conversation—an American icon openly discussing rerolling his roaches. By talking about it honestly and personally, Zimmer is nudging cannabis into acceptance. It's what Peter Lewis suggested in a 2011 editorial he published in _Forbes_ : "If everyone who used marijuana stood up and said, 'I use this; it's pretty good,' the argument would be over."
I mention this to Zimmer and he smiles. "The latest polls show that fifty-eight percent of America thinks pot should be legal. As data comes out from Colorado and Washington, we'll see that the only real changes are auto-accident deaths going down and tax revenues going up. When you factor in the changes it will bring to the criminal justice system, it's enormous."
His gaze moves toward the chessboard. "It's like chess when you're up a knight. After twenty years, we're finally in a winning position. We just shouldn't fuck it up."
## PART II
## THE NEW WORLD
## ___Chapter 4_
## WIDGETS AND DABS
_Denver, Colorado_
Samuel R. Caldwell's gravestone in the Mount Pleasant cemetery in Erie, Colorado, is a sad sight. Few people in the Denver area know the name of this hapless drifter and occasional bootlegger, who, on October 6, 1937, became the first US citizen to be arrested for selling a handful of "marihuana cigarettes." Justice was swift and harsh back then. Just five days after the Marijuana Tax Act was passed, Caldwell was fined a staggering $1,000 and sentenced to four years' hard labor in Leavenworth, then the country's largest maximum-security prison. "I consider marijuana the worst of all narcotics—far worse than the use of morphine or cocaine," the sentencing judge said. "Marijuana destroys life itself. I have no sympathies with those who sell this weed."
Caldwell paid the fine with his life savings and was confined to a cramped cell on murderers' row. Less than a year after completing his sentence, he died isolated and alone. His gravestone, on a wind-scraped hill, is sinking on one side. Down the hill, a larger road is being built beside the cemetery, and dirt movers have cleared the land for new construction.
It's early 2013, and Denver is in the beginning stages of its frothy green rush—in the last election, more Coloradans voted for legalizing marijuana than voted for Barack Obama—and a new economy is being built in some part on the anticipated fortunes that marijuana will bring. But no one is naming a strain after Samuel Caldwell—the state's first marijuana martyr is long forgotten.
My first trip to Denver occurred just six weeks after medical marijuana was legalized and a year before recreational sales were to begin. Until this point, the state had fuzzy regulations that authorized some dispensaries to operate, but also allowed local governments to shut them down willy-nilly without warning or explanation. The cannabis industry was operating in the so-called gray area, which meant that operators who one day thought they were within the law found themselves out of business the next. It was a mess—until the voters decided enough was enough.
It's not outwardly obvious at this early stage that Colorado is the first fully legal medical marijuana state—people aren't gathering on street corners puffing up. But there are clues, some obvious, others more subtle, that changes are in the offing. The double-story stacks of HVAC units on the roofs of warehouses along I-70, the city's main artery, indicate that they have been converted into massive indoor grows. Billboards along downtown Denver's newly christened "Green Mile" show a man passed out with a bottle and a football on the ground. The caption reads "Marijuana: Safer Than Alcohol . . . and Football," a swipe at the NFL for its strident anticannabis stance. Where ads for sex and escorts once filled the back page of _Westword_ , the Mile High City's alternative weekly, there are now ads for dispensaries announcing daily specials. The _Denver Post_ 's "The Cannabist" is the country's most insightful blog on the business and culture of pot, stoners coyly refer to themselves as medicators, and the city that was once the healthiest in America now has the highest percentage of chronic-pain patients. Seattle can't be far behind.
The rapid birth of an industry this large makes all of Denver feel like a start-up. Businesses large and small are springing up, and if the players adhere to the laws, which they appear to be doing, Colorado could be the model that is replicated throughout the country. Pain-management clinics, "glass galleries," clone bars, hydro houses, and yes, the country's first Bud 'n' Breakfast—the range of products and services is expanding so quickly that there is a shortage of plant in the market.
I arrive at Adam Dunn's hemp clothing shop, HoodLamb, at one p.m., as agreed. The sign indicates that HoodLamb is open at noon, but the doors are locked. There's a very cool vintage Cadillac hearse parked around back but no one in sight. I call Adam, but his voice mail is full and not accepting messages. I text. No response. I'm now used to this—stoners share a notable disregard for time. Amotivational syndrome? "Atemporal syndrome" more describes my experience.
Adam finally pulls up in a beaten-up car, unaware or unconcerned about his tardiness. He hands me his card, which reads: "I may not have friends in high places but I have high friends in places," which instantly washes away any hint of annoyance and makes me smile. His beard has grown to an epic ZZ Top length since we met in Amsterdam, and I'm transfixed by the quarter-size discs in his earlobes. They are so big I could pass my forefinger though the holes.
Adam leads me through a wide aisle of loosely arranged racks of hoodies and outer jackets, stacks of old-school graffiti paintings, and a small display of Dr. Bronner's Hemp Oil Soaps into the back office.* This is the inner sanctum and it is crammed with two gold velvet sofas, a minifridge filled with IPAs and ales, a washing machine (used to wash trim), and monitors showing the security camera view of each entrance. The coffee table—the centerpiece in all stoner décor—is strewn with the remains of last night's adventures: anthills of ground cannabis flowers, massive pipes, and blowtorches of varying sizes. One glass vial contains a substance that looks like crumbled wax. It's called "budder," or "earwax," Adam explains. It's a hash concentrate that still contains the waxy trichomes that envelop the resins. (If there were more women in this industry, I guarantee that no product would ever be named after the secretions and dead skin that accumulate in the outer ear.) There are also small packets of what looks like amber candy wrapped in white paper just like cocaine used to come, called "shatter." I'm curious about every one of these new-world products, but Adam has other things on his mind.
It's official. What the car is to Detroit, what digital technology is to Silicon Valley, cannabis is to Denver—and every grower is ramping up to meet the demand. One friend was actually storing his car in his garage, Adam tells me, until he realized it would be so much more profitable to turn it into a grow. _Duh!_ His landlord agreed and helped him rewire the garage with additional amperage for lights and ventilation. Another has quit her day job as administrative assistant to the state senate majority leader to lobby for the legal cultivation of hemp. The regulatory, legal, and political structure is finally in place to do big things here. This is why growers cannot be dismissed—without growers there are no plants, and without plants there is no industry.
Adam is modest, charmingly ironic, and authentically hip without any hipster artifice. He defines himself as a "lifestyle guy." He was born in Woodstock in the summer of 1969—"How fitting, right?"—and was raised by his single mom, Adrienne, who has recently moved in with him, his wife, and their baby daughter. Adrienne does grandma duty while also tending to a few plants. She and Adam have been growing partners since he was a teenager, and they are thisclose. "She grows better than I do," he confides. "In Amsterdam, all of the Cannabis Cups I won, it was her work. I was the one out there on the front lines."
Back in Amsterdam, Adam's marketing formula was "grow it and know it before you sell it." At harvest time he'd invite people around to evaluate several new crops: How does each one smell, taste, and burn? What are the effects? What is the bag appeal (appearance)? But to discern a truly great strain, all he had to do was wait to see which sample disappeared first. "It's like food," he tells me. "It doesn't lie."
And it's the route to his success here too. "I'm looking for customers for life, so I can't separate myself from weed. Our clientele, the people who want hemp clothing, are smokers, and you can't turn your back on those people. _We only grow hemp, but we don't smoke? You kidding me?_ You're turning your back on the people who love cannabis. One thing I've learned, if you have great cannabis, everyone loves you and you'll have a great business."
Dunn envisions the day when the warm Colorado sun will be shining over fifty thousand acres of hemp. "But right now [until it becomes legal to grow hemp] we'll take an eighth of an acre of hemp and produce enough seed for five hundred acres. Next year we can produce a thousand acres. Within four years we'll have fifty thousand acres from an eighth of an acre. That's kinda nice. We'll be completely self-sufficient from a handful of seeds.
"The thing about growing is that when you produce something you get such a good high just knowing you did it all yourself. If I can say 'I was part of that,' I would feel complete."
Until that rapturous day arrives, Adam is content to occupy an almost saintly position among growers. His skills at what were recently regarded as fringe criminal activities are making him suddenly, and highly, employable. He and his buddies are the R&D guys of an emerging market.
Derek Cumings, for example, is a hotheaded, foulmouthed "hash consultant" in high demand. Besides being a proficient hash oil producer, he has devised recipes that mask the oil's bitter taste, which he is now licensing to five different edible companies. Steve is a horticulturist who last year made over four million cuttings of orchids and other noncannabis plants (in true stoner fashion, he counted). He's anticipating a busy career once recreational cannabis comes online. Educated horticulturists are valued because their knowledge of plants and plant diseases is more comprehensive than homeschooled pot growers. Chris is a trimmer in a vast industrial grow, but he's eyeing a career change. Trimming leaves off plants all day is as dull as factory work. It's making his fingers stiff with early-onset carpal tunnel syndrome, so he's gunning for a job with the twentysomething founder of Evo Hemp bars. Working in the cannabis trade is to this generation what waiting tables was to mine.
There are a few unspoken rituals that all celebrants observe here in the cannabis chapel. There are no introductions or formalities. New guests float in, exchange a nod, and park. Rarely are they acknowledged by name.
It's what they pull from their backpacks that identify and confer status on them: large glass jars of freshly cured flowers that are passed around for everyone to savor. The lone woman in the crowd has come with her husband to replenish the hash oil cartridges she uses in her vaporizing pen. She doesn't rate the prepackaged oils as highly as what she obtains here, either in taste or effects. Derek painstakingly injects them with some of the top-quality goo he manufactured that day. Not a penny changes hands.
The other rule of the windowless room seems to be: speak of nothing but pot. There is no mention of women, sex, politics, sports, love, philosophy, or food.* Cannabis is the single shared obsession. Derek has achieved a sort of hero status for keeping one citrusy smelling strain, Tangerine Dream, alive for eleven years. A while back he spread the seeds among these growers and tonight one has returned with his first harvest. Cracking open a jar of finger-length "Tanj" buds, he passes it around for inspection. Steve, the horticulturist, dunks his nose in the jar and closes his eyes, inhaling. "Aromatherapy," he utters to no one in particular.
As I'm observing these goings-on, it strikes me again that this plant holds a uniquely powerful sway over certain members of the human race. People who grow cannabis don't just like it. They love it (to the same extent that its detractors detest it). When not growing, they long for it. Another grower I know has maintained a grow in his bedroom closet for years. He doesn't smoke that much and he doesn't sell—he gives it away, because money isn't the point. The sheer act of nurturing the plants, knowing that they are in his closet sucking up electricity and doing their thing, provides the same comfort as a dog or cat, he told me.
Perfectly sane people from all walks of life have a deep, abiding emotional relationship with this plant.
I initially compared pot aficionados to wine snobs, but I'm revising that analogy. These guys are more like early Silicon Valley geeks, holed up in their garages, diddling with motherboards and circuits in near isolation. No one—maybe not even they—knew what they were up to, yet they were fueled by the conviction that they were creating something new, possibly revolutionary. Their (initial) motivation wasn't money; it was more a desire to upend the established order with something of their own creation. Both groups had questionable social skills, but their dedication was unfettered and the momentum they launched unstoppable.
Once night falls, the dabbing begins. Dabs (as in "a little dab'll do ya," Jimmy Buffett's 1970s ad for Brylcreem) are a wholly new way of taking in stratospheric amounts of THC that has taken the weed world by storm. Although hash oils have been made in the West for fifty years, they were formerly difficult to produce, messy to use, and never really caught on.* Now, with modern extraction methods and a new generation of smokers in search of cleaner superhighs, dabbing is so popular that some breathless headline writers are heralding it as "The Future of Getting High."
It's also marijuana's biggest public-relations nightmare. Even if you believe that the plant is harmless and creates only good in the world, watching someone dab may cause you to rethink your position. It makes smoking a three-foot-tall bong look old-fashioned.
Adam demonstrates. Because oils burn at a higher temperature than flowers, he first aims a blow torch—the type I've used to make crème brûlée—at a titanium nail that sits in the bowl of his giant glass water pipe called a rig (as in "oil rig") until the nail is glowing orange. With a dab stick, a metal instrument that resembles the device a dentist uses to scratch plaque from teeth, he slices a poppy seed–size dab of hardened hash oil, the aforementioned "shatter." The dab hovers above the heated nail and _whoosh_! As it melts, a lush plume of smoke swirls into the pipe. Powerful pot is 20 to 25 percent THC. A dab is a mind-stinging 70 to 90 percent THC.
That evening, Adam hits a dab every hour or so and never misses a beat. His conversation is steady, coherent, and sharp; he must have the tolerance of a giant.
Cannaoisseurs claim that concentrates are the sous vide of their evolving culture—the closest thing to a psychedelic experience one can wrest from cannabis. They also claim, perhaps rightfully, that smoking concentrates constitutes "harm reduction," as all the lung-irritating plant matter is removed, so it delivers the strongest, purest high with the lowest amount of toxins. And while dabbing is still largely an insider thing, it is filtering into the mainstream. At one cannabis fund-raiser at Bill Maher's compound in the Hollywood Hills, there was a margarita bar on one level, and upstairs, a seventy-foot dab bar with a half-dozen rigs lined up and loaded. Cannabis quenchers in grape and lemonade flavors were also served to soothe parched throats.
Critics—who range from Robert Connell-Clarke, an ethnobotanist and one of the world's experts on the plant, to anti-marijuana mothers' groups—are less sanguine about dabbing. Many articles, and far too little research, malign dabs as "a dangerous new drug" (fact: dabs are simply another form of marijuana or hashish), "the crack of marijuana" (fact: dabs are powerful but not addictive), or "increasing risk of overdose" (questionable: "overdose" is a loaded word that generally implies death; this can't happen with cannabis, but other weird and inexplicable things can, as I was soon to learn).
Armchair critics typically fail to realize that there are two ways of extracting these concentrates: with CO2 or water, like Bubbleman's bubble hash, or with more toxic solvents, such as butane. The latter category is called butane honey oil, or BHO, and herein lies the true nub of the controversy.
To make BHO, marijuana leaves are packed into a long glass tube. Liquid butane, the same solvent used in cigarette lighters, is pushed through the leaves, stripping them of their oils. This produces a green puddle of solvent and cannabinoids, which is then baked to theoretically evaporate the remaining solvent. The result is "pure" concentrated THC. The length of bake time determines if the resulting concentrate takes the form of a gooey oil or the hard candy-like substance known as "shatter."
One doesn't need a PhD in chemistry for several concerns to spring to mind.
First, butane is extremely flammable. Some amateurs may accidentally strike a match and blow themselves up, which makes the comparison to meth cooking unavoidable, but also brings with it other, more immediate dangers. YouTube is sprinkled with videos showing houses being rocked off their foundations. This is serious. Camy Boyle, the associate nurse manager for the burn unit at the University of Colorado Hospital, told the _Denver Post_ that in 2011 and 2012 he saw only one injury that could be traced to hash oil production. In 2013 the hospital's burn unit saw ten. It's not difficult to see why people don't want their neighbors or their neighbors' kids toying with this.
Second, even though baking theoretically evaporates the solvent, chances are that traces remain. This means that humans who smoke BHO are inhaling a substance that contains some quantity of benzene, a hydrocarbon refined from crude oil that has been linked to diseases of the liver, kidney, and central nervous system, not to mention cancer. Although some extractors claim to use the world's cleanest butane, even that, according to Connell-Clarke, "is full of contaminants, some present due to inefficient butane collection and others added for their odor so the butane has an easily detected smell. Some impurities and additives are slow to evaporate, become trapped, and can readily contaminate butane-extracted oils."
Third, the allure of powerful highs is undeniable, as is the need for strong medicine to treat serious illnesses, but steady dabbing strikes me like taking morphine for a headache when aspirin will do the trick. There is no research about what a constant infusion of supersize doses of THC does to the body. Unless such high doses are prescribed for specific medical conditions, their repeated use seems like an unnecessary risk until more is known.
States are now debating whether to ban concentrate production or at least limit legal production to cleaner CO2 or cold-water extraction methods in proper labs with security features. That's a sensible compromise, a far better idea than prohibiting concentrate production altogether. As the last eighty years have shown, prohibition is a superhighway to increased desire.
The following day, Adam takes me on a nickel tour of some of the start-ups fueling the cannaboom. We visit the kitchens of Incredibles, makers of cannabis chocolate bars. The company is owned by a former chef who was struggling to make ends meet behind the stove. His fortunes have changed almost overnight—his main struggle now is finding enough oil to meet the ever-increasing demand. Later we drop into a community discussion being held in the cavernous back area of a neighborhood saloon. Lawyers, former cops, and policy makers are onstage discussing how to avoid arrest for driving under the influence. The issue is a thorny one because THC stays in the body for some thirty days. Even if you haven't smoked in a month and are stone-cold sober, a urine test could still yield a positive result and you could lose your driver's license.* A lawyer reminds the one hundred attendees that the police can't force suspects to take a DUI test, and that drivers should refuse if asked. Ditto if they insist on searching the car without a warrant. These are thorny issues, ones that won't be solved overnight, but it's rather thrilling to see a group with different agendas hammering them out together. It's the way grassroots democracy is supposed to work, and it left me feeling discontented that I live in a state where such discussions are not even on the horizon. Same country, different world.
The excitement in Denver wasn't restricted to Adam's small world of craft cannabis growers and makers. If these independent operators are the cannabis equivalents of microbrewers, other ambitious players are gunning to be Coors. Dixie Elixirs is the king of cannabis-infused edibles and drinkables in Colorado and possibly the country (it's impossible to know, since there is no Dun & Bradstreet of the industry yet), and edibles is the market's fastest-growing segment. "Not everyone wants to smoke a joint," Vincent "Tripp" Keber, Dixie's cofounder and CEO, tells me as we inspect his 27,000-square-foot factory. "Some people may have had a bad experience with marijuana in youth. Others have kids and they may not necessarily want to be lighting up. We have over one hundred SKUs representing twelve different delivery systems. Our widgets allow you discretion."
Keber actually used the word "widget" to describe his goods, as if the anodyne language of manufacturing proves his claim that he holds no particular attachment to the plant. "I'm not suggesting I never inhaled, but we started this company to make money," he said. In fact, distancing his company from the pot of old is one of the routes he's taking toward legitimacy. When television crews visit the facility they're shunted away from the plants. Dixie's packaging is wisely absent the green cannabis leaf. Nor is Keber the predictable face of a cannapreneur. With his Palm Beach sports jackets and salesman's smile, he has been pegged as the Gordon Gekko of Ganja, a distinction he relishes. Being the straight man in a stoner world is radical in its own way.
Keber and company were real estate developers who hit it big by building "intergenerational resort communities" in southeast Florida. In 2009 they smelled opportunity and became passive investors in Dixie Elixirs. They'd supply the capital, hire the "talent," and then sit back and watch the business explode.
Or so they thought, until the reality of turning a crew of hobbyists into an industry hit home. In its first year, production at Dixie began to lag. When Keber stopped by one day to deliver another $250,000 funding bump, he found that his top four lieutenants were "more interested in medicating than manufacturing." He axed them and jumped in as CEO. And while his coiffed appearance may win him credibility in the business community, it didn't help him with suppliers, who viewed him with suspicion. On one early expedition to procure "raw plant material," he was instructed to meet his contact in a junkyard. Keber was wandering through the debris when the grower slinked out from behind a pile of scrap metal, spooking the hell out of him. "Couldn't we just have this meeting in an office?" he remembers thinking.
On another buying trip he was blindfolded and shoved in the backseat of a car, bookended by two Russian thugs. The GPS on his phone was disabled, he was driven in circles for thirty minutes and shunted between different cars. Upon arrival he was led into a room where the table was stacked with cash and his hosts were all packing guns. An Armenian with a long-filter Russian cigarette dangling from his lips commanded him to sit.
"You vant coffee?" Keber doesn't drink coffee, but the Czech translator tipped him off: "Whatever he offers you, accept. In our culture it's rude to refuse."
Keber drank the coffee. "I'm trying to show the soccer mom in Ohio that what we're doing is legit, that there are people who wear jackets to work and don't have dreadlocks and who are building companies that you can monetize. It was the Wild West then.
"Thankfully, I haven't heard a Russian accent in a long time."
Today, Dixie is Colorado's premier industrial-scale cannabusiness, churning out candies, sodas, chocolates, and skin creams. It has impressively fine-tuned its manufacturing to punch out one thousand brownies an hour that are consistent in dosage and flavor. It owns the intellectual property to its processes, which ensures no oil blebs or plant detritus in the formulations. Its packaging is now child resistant and tamper proof, and it's got the labeling, ingredients, and nutritional facts ready to go, so "if the FDA decides to regulate the industry, we'll be prepared."
For what, exactly? "Once eight states legalize adult use, I believe unequivocally that Big Alcohol or Big Tobacco will be asking, 'Who do we make the check payable to?'" Keber said. "And saying this makes me unpopular, but we're building a company to be attractive to the alcohol model. It's something they can absorb into their group, turn into a division, and then expand upon with their distribution."
Die-hard cannabists contend that this desire to sell out to Big Bad Corporate America betrays their decades-long struggle for legitimacy, and there's evidence that that sentiment taps a deep vein. Many consumers want to know where their products come from, if it's clean and locally grown. They want to know it's connected to their community. But surely there is room enough for both big and small in this emerging world. Mass marketers will never be able to stamp out innovative small-batch producers like Adam and his merry band of growers. Just as with chocolate, coffee, or beer, it's easy enough to envision the day when Marljuana pre-rolls are sold in a supermarket-size dispensary and Adam Dunn's more artisanal goods are for sale inside his shop and at other specialty stores.
Samuel Caldwell must be doing double flips in his grave.
"You ready to try one?" Adam is firing up a nail, goading me to relinquish my dab virginity. It's my last night in Denver. The boys have been extremely gracious about not pushing anything on me, but after days of watching these guys consume inordinate amounts of dabs, curiosity has overcome my apprehension. These guys are doing dab after dab and are energetic and focused, so I accept the offer before Adam and I head out to dinner.
Adam picks off an apple seed–size piece of shatter and hovers it above the Ti nail. An apple seed is twice the size of a sesame seed, but the distinction is so minute I think nothing of it and suck it down. It hits hard and fast. In seconds my entire being is teeming, every cell a vibrating tightrope of sensation.
The car ride is magic—I'm flying miles above the slight feeling of enhancement I've grown used to since this journey began. Once at City, O' City, the hottest vegan restaurant in Denver at the moment, we drift through the crowded dining room and land two seats at the bar. Adam is telling me about how people all over the world are using cannabis oil to treat skin cancers and I'm thinking, _Yeah, right. Tell me more when you haven't hit the bong_. But then I glance at the menu and see that the words are dancing on the page, off the page, refusing to come into focus. Within seconds the room is swerving, the floor tilting and buckling like a boat in crashing waves. Before I can identify what's happening, my skin goes clammy and I feel the color drain from my face. This isn't going to end well.
I stumble outside in hopes of the cold air slapping me straight, but it's too late. A heave rumbles in my gut, kicking its way up into my throat and out of my mouth, ending in a full Linda Blair exorcism. I can't understand how this can be happening. Cannabis is supposed to be antiemetic, and I'd eaten nothing all day.
After what seems like hours, but was more like twenty minutes, I slouch inside and explain the sidewalk disaster to Adam. Humbled and embarrassed, my mouth rancid, I ask him to deliver me to my hotel, which he does graciously, but not without two pit stops in a snow-strewn gutter along the way. My last memory of City, O' City was seeing a busboy outside unhappily mopping up my mess with a few pitchers of hot water and a broom.
Inside my room I lay on the bed in the dark for minutes or maybe an hour. In a lone corner of my mind I recall reading that drinking cold lemon water and taking hot baths are antidotes to extreme drug discomfort, but I can't muster the energy for either. I topple into an indistinct dream, fully clothed and shoes on.
What the hell happened? It would take months of searching to find out.
* * *
BRAVE NEW WEED WORDS
* * *
**Old** | **New**
---|---
Amsterdam | Denver
Pot | Meds
Stoner | Cannabist
Blasted | Dosed
Joints | Dabs
Hashish | Full melt; bubble
Wrecked | Enhanced
Bong | Rig
Buds | Flowers
Sinsemilla | Strains
Dealers | Dispensaries
Scoring | Weedmaps
Maui Wowie | Blue Dream
THC | CBD
Brownies | Edibles
Pipes | Glass
Golden Triangle | Emerald Triangle
420 | 710 (read upside-down, "710" spells oil, as in "hash oil")
## ___Chapter 5_
## THE ENDOCANNABINOID SYSTEM: THE BODY'S SUPERCOMPUTER
_Jerusalem, Israel_
The Denver disaster, as I've come to think of it, put a damper on my unbridled enthusiasm for cannabis. No matter what anyone says, too much pot can create feelings of deep discomfort. You can't stop the anguish—you must simply wait it out for what seems like a lifetime.
After a merciful sleep I woke up shaken but fine, except for a throat frayed from stomach acids flowing in the wrong direction. Still, the upheaval was a stern reminder that no plant intoxicant, benign or otherwise, is 100 percent predictable. Pot has always been known as a fickle woman. If this relationship was to continue, I needed to get a handle on her capriciousness.
The last time pot had smacked me that hard was in San Francisco in the summer of 1976, when a lover twelve years my senior told me she was pregnant with my child the very night I had planned to tell her that I was gay. We had smoked a fatty of some Hawaiian strain, and my knotted-up and confused body reacted to this emotional shock with the same testicle-squeezing retching that felled me in Denver. I always presumed that the stonking amount of THC in that Hawaiian weed had sparked the convulsion, but now I wondered if something else, such as the compound that produces the dark-green civety smell prevalent in so many of the Colorado superstrains, was to blame.
Once my head cleared from Denver, I began Googling for answers. One search turned up "cannabinoid hyperemesis syndrome," a spurt of cyclical vomiting that extends for days and is accompanied by the compulsive need for warm showers. Chronic smokers who light up six times a day complain about this, but it doesn't appear to be my problem. Message boards were dotted with amateur hypotheses about "greening out" from overeating, but the Denver dabbers never even snacked, so my stomach was consistently, and unhappily, empty. One post on Weedmaps, a strain directory and the nearest thing to WebMd for cannabis, suggested that violent coughing might have thrown my stomach into reverse peristalsis. Unlikely. Another post echoed my own confusion: If pot allayed nausea, why did it induce vomiting?
I was facing a common problem in the new world of cannabis: a dearth of consistent reliable information. Much of the "expert opinion" on the Web is produced by self-anointed experts or backyard chemists, which makes it suspect, tinged by wishful thinking, or fiction masquerading as fact. There have been an avalanche of experimental studies—over twenty thousand to date—but few definitive clinical trials. As a result, the science can seem like a thicket of contradictions. Cannabis cures cancer! It causes it! It protects the brain! It causes schizophrenia! It's addictive! It helps alcoholics wean themselves off booze! The only drug that treats _everything_ is either snake oil or a miracle, and I don't believe in miracles. So what's the truth?
My confusion, it turned out, was not unwarranted. The international prohibitions and unrelenting anticannabis propaganda, much of which is generated in the United States, has been remarkably effective at blurring the line between truth and myth. This has not happened by accident.
Not only does the schedule I classification restrict access to the plant, it also makes researching it exceedingly burdensome. It's no exaggeration to say that studying cannabis in the United States today is as politicized as studying genetics in the USSR under Lysenko was in the 1960s. Rather than send resisters to the Gulag, which is what happened to any scientist who bucked Trofim Lysenko's wacky theories, the US government uses red tape to strangle most meaningful cannabis research. That may sound like an overstatement, but it is, in fact, easier to test a known poison such as arsenic in human beings than it is to test cannabis, primarily because access to the plant has been so tightly controlled by three federal agencies—the National Institute on Drug Abuse (NIDA), the Drug Enforcement Agency (DEA), and the Food and Drug Administration (FDA)—for over forty-five years.
Here's how it works: The feds control the supply of marijuana by growing their own crop at a plantation at the University of Mississippi, where until 2014 the total production was limited to a meager forty-six pounds a year.* Scientists seeking access to the Mississippi crop must first apply to NIDA for permission. If NIDA gives the go-ahead, which it rarely does, researchers must then secure approvals from the DEA and FDA. (Until the Obama administration loosened the rule in 2015, a third approval from a public health service review board—composed of unspecified "health professionals"—was required.)
"The American study of cannabis is light-years behind the rest of the world in terms of what's been done and published," says Dr. Ethan Russo, a neurologist, ethnobotanist, and one of America's leading researchers into medical cannabis. "We have an echelon of official oversight that doesn't apply to any other drug."
A case in point was Dr. Donald Abrams's 1992 attempt to examine the effects of cannabis on what was at the time called "AIDS-related wasting syndrome," which was wiping away thousands of lives a year. In the 1990s, ten thousand skeletal AIDS patients in San Francisco were already smoking pot to maintain their appetites and weight, yet no American science was evaluating its effects.
Abrams, who is currently chief oncologist at San Francisco General Hospital, had originally planned to secure medical-grade cannabis from Holland for his study. His application went to NIDA, where it sat for nine months unanswered, until it was rejected for poor experimental design. After several revisions the application finally made its way to the DEA, which demanded Abrams scratch his plan to obtain cannabis from abroad and use the Mississippi stash instead. He complied and resubmitted his application, but it fell into a black hole until 1996, when he received two troubling letters from the independent review board. One reviewer questioned his reason for wanting to investigate such a "toxic" substance; another worried that AIDS patients might develop high cholesterol from smoking pot. In what has to be the understatement of the decade, Abrams told me that the reviewers seemed to "miss the point."
Abrams was so disheartened by the years-long obstructions that he eventually met face-to-face with the then head of NIDA, Alan Leshner, who explained that his organization was the National Institute _on_ Drug Abuse, not _for_ drug abuse, and that his congressional mandate forbade him from funding any investigation seeking to uncover any benefits of cannabis. With that in mind, Abrams recast his study yet again, this time to examine the ways cannabis might _interfere_ with the antiviral drugs that fight HIV. That won him the green light in 1997. The evidence showed that cannabis was perfectly safe for use with retrovirals; moreover, the recipients gained more weight and maintained better health than the control groups using a placebo or Marinol.
When Abrams told me this story, I thought it might have been an isolated incident. But after forty-five years and some 1,800 studies, NIDA, which allots $66 million a year to ferreting out the harms of cannabis, has failed to conclusively prove any health-threatening dangers of the plant.* That hasn't stopped it from regularly issuing studies correlating cannabis use with brain "changes" in kids, long-term memory deficits, addiction to more dangerous drugs, and increased incidence of psychosis or lower IQs. The media regurgitates these results without question.
The often-repeated claim that cannabis causes permanent damage to brain cells is equally specious. There is little doubt in my mind that sustained overuse can produce a certain dullness of thought—the bleary eyes of someone who oversmokes are a window into a blurry mind. But long-term studies show that there are no differences in brain activity between heavy and light users over time. The same goes for the endless studies on what has come to be known as "cannabis-induced psychosis." Of course smoking or eating too much pot can trigger extreme discomfort or a state that some describe as akin to a temporary psychotic episode, but the symptoms typically disappear and leave no permanent damage.
The same holds true for schizophrenia. While studies from NIDA and other groups have found that cannabis users are more likely to be at risk for schizophrenia, no study has ever established a causal relationship. It's just as likely that people prone to schizophrenia tend to self-medicate with cannabis. What's more, the incidence of schizophrenia in the United States has held steady at about 1 percent since the 1960s, while pot use has risen from 33 to 39 percent. This indicates that from the Dean Martin era through the Chris Martin era, three generations of adults have used the plant without the predicted rash of mental illness occurring.
The United States is the largest funder of medical research in the world. But until Congress releases cannabis from the confines of schedule I, American science in this area will always be viewed as second-rate and subject to doubt. The research blockade also explains why the most groundbreaking cannabis research comes from abroad—primarily from Israel. That tiny country of eight million is, in fact, the capital of cannabis science. It's where Dr. Raphael Mechoulam, the scientist who cracked the chemical code of cannabis a half century ago and then discovered the endocannabinoid system (ECS) in the human body with which it interacts, is still hard at work.
Oh, you've never heard of Mechoulam or the endocannabinoid system, the largest receptor system in the human body, even though it was discovered over twenty-five years ago? Don't feel uninformed. Ninety-five percent of American doctors haven't, either.
Hebrew University sits high above the tiny village of Ein Kerem, just west of Jerusalem. This large institution is where Mechoulam has worked for almost half a century, beginning shortly after he discovered THC in 1964. At that time, the plucky thirty-four-year-old biochemistry grad student had been researching plant medicines at Israel's Weizmann Institute. It struck him then that morphine had been isolated from opium about 160 years prior, in 1804, and cocaine had been extracted from coca leaves in 1850, but the chemistry of cannabis, which was used much more widely for health and high, remained a mystery.
The Israelis have always taken a hard line against cannabis, due in some small part to anti-Arab bias (Muslims favor cannabis over alcohol) and because a nation on permanent military alert is incompatible with what Baudelaire called the "silent, lazy, soft benevolence" of pot. But science, when not dictated or restricted by governments, knows no political boundaries, so Mechoulam forged ahead until he hit a roadblock: there was no way for him to legally obtain plant material. He asked the administrator at Weizmann if he had a contact in the police. "C'mon! Just go and pay your parking tickets!" came the response. When Mechoulam explained the nature of his inquiry, the director called in a favor from an old army pal who was number three on the force. "There are some advantages to living in a small country," the professor told me.
At the police station, Mechoulam collected five kilos (eleven pounds) of primo brown hashish, molded into two-hundred-gram bricks, shaped like shoe soles, wrapped in linen, and stamped with their place of origin: "Stambul."* Mechoulam carried his bounty to the lab on a bus in a plastic bag. The smell was very noticeable, he recalls, and very pleasant.
He and another scientist, Yehiel Gaoni, employed a new separation technology that allowed them to isolate and determine the structures of the two major components in the plant: cannabidiol, or CBD; and the psychoactive molecule delta 9-tetrahydrocannabinol, or THC. No one was terribly excited by their discovery, so the team spent the next months scrounging for additional funding to carry on. (Scientific research in Israel is funded just as it is in the West: a scientist gets an idea and must then hunt for money to support his inquiry.) They applied for a US National Institutes of Health grant but were rejected by the head of pharmacology, Dr. Dan Efron, who explained in a polite but patronizing way that "cannabis is not an American problem. It is used in Mexico and by some jazz musicians in the US, but that's about all." The NIH would consider supporting Mechoulam's research when he found another, more relevant topic.
One year later, Efron was on the phone to Mechoulam with an urgent message. A US senator's son had been found smoking pot, and the senator was desperate to know if it could damage his brain. Mechoulam extended an invitation to discuss the matter, and Efron showed up in Jerusalem the next day. By the conclusion of their meeting, Efron had packed most of the world's supply of THC—ten grams—into his suitcase. Presumably he smuggled the drug past US customs, since no official at the time knew what it was.
The NIH has funneled money into Mechoulam's lab ever since. This has allowed his team to become the uncontested world authority on the chemistry of the plant and the endocannabinoid system with which it interacts. Mechoulam himself has published over four hundred papers, edited four books, owns twenty-five patents, and has received twenty-seven honors from six countries. His findings have earned him the respect of scientists, policy advisors, doctors, politicians, growers, and other researchers around the world. Yet prohibition has effectively kept his findings and his name hidden from public awareness.
The discovery of THC solved the mystery of the high, but the more important discoveries were still to come. In 1988, an American chemist, Dr. Allyn Howlett, located a network of receptors in the brain that respond to THC. The densest concentration of these receptors—the Milky Way, as it were—is in the brain areas that coordinate movement and control emotions, memory, pain, pleasure, and reproduction.
Cannabists take this connection between THC and brain receptors as further proof of the symbiotic link between the plant and the human body. But Mechoulam doesn't think the plant has any abiding interest in the grand order of the universe. It may appear coincidental that the cannabis plant generates chemicals similar to those produced by our bodies, but such a coincidence is not without precedent. The human body also manufactures its own opiates, the endorphins, which mimic the pleasure-producing secretion from the poppy flower that becomes heroin. To Mechoulam's evidence-based mind, all plants produce tens of thousands of compounds that both attract bugs and animals to carry their seeds and also protect them from hostile insects, grazing animals, and harmful UV radiation. Cannabis very cleverly "pleasures our minds in order to use our feet," as Michael Pollan put it. These many compounds constitute the plant's immune system, and the fact that they also affect humans is little more than a happy accident.
More important, Mechoulam also knows that the human body doesn't manufacture receptors to respond to random substances found in plants. So he and his team began hunting for a compound like THC that the body itself produces to stimulate these receptors.
In 1992, Bill Devane, a postdoctoral student, and Lumir Hanus, a Czech chemist, both part of Mechoulam's lab, found a brain chemical that mirrors the effects of THC. They named this THC analogue "anandamide" after the Sanskrit word _ananda_ , for bliss (that naming convention probably wouldn't fly today). Just like THC, anandamide is thought to radiate a golden, sunny pleasure, intensify sensory experience, stimulate appetite, and temporarily blot out short-term memory.* When I asked Mechoulam why he didn't give the molecule a Hebrew name, he smiled and said, "Because in Hebrew there are more words for sorrow than happiness. . . . Jews don't like being happy." Before long, Mechoulam's lab found another brain chemical that mimics CBD, 2-arachidonoylglycerol, which they named (rather uninspiringly) 2-AG.
Shortly after Dr. Howlett located the brain receptors, other scientists in Britain discovered a galaxy of receptors that snakes throughout the entire body into every organ, gland, immune cell, and connective tissue.* Further exploration revealed this endocannabinoid system (ECS) to be the largest signaling system in the human body. Let me be clear: this is not a theoretical system that exists in the minds of a few wishful thinkers. Scientists have found endocannabinoid receptors in all vertebrates and even the most primitive invertebrates—sponges—which suggests that the system has been around for thirty-four million years.
The next inevitable question was: What the hell does it do?
Because they are invisible, neurotransmitter systems are difficult to picture and comprehend. Think of them as cell phone networks, but rather than beam signals through the air, the brain sends chemicals and electric impulses that command cells to communicate with each other. We are more familiar with other neurotransmitter systems because they were discovered first—dopamine, serotonin, histamine—but the ECS is the largest and possibly the bossiest of all. It has been called "the body's supercomputer" because one of its functions is to keep every other bodily system in balance. What's more, it is the only neurotransmitter network that communicates with cells in two directions.
Not only do commands emanate from the brain outward, but if an organ is in trouble, the endocannabinoid neurotransmitters act like an early-warning defense system, sending a cry for help back to the brain.
In the last thirty years, an entirely new class of pharmaceuticals has been formed from the basis of receptor systems. Antihistamines initially targeted receptors in the nasal passages, for example, but additional histamine receptors were later discovered in the digestive system, and that discovery gave rise to medications such as Zantac or Prilosec that treat all manner of gastric disorders. What's more, under- or overproduction of neurotransmitters is now linked to illnesses that have eluded science for decades. Too little dopamine is connected to Parkinson's disease. Overproduction is related to schizophrenia. Serotonin, which mimics the psilocybin found in magic mushrooms, mitigates depression.
As the body's supercomputer, the ECS steadies the "temperature" in every room in the body's house. It appears to regulate the flow and balance—the chi—of all of the organ systems, as well as regulating blood sugar, immune function, muscle and fat tissues, hormones, pain centers, reward centers, and metabolic functions. It maintains the heart's steady beat, the stomach's digestion, the lungs' bellows, and even the rate at which bones heal. It rewards us for eating and having sex, two activities essential to keeping the species thriving. It enables us to forget pain. And it warns the body when trouble is afoot by sending out chemicals to protect troubled areas from further damage. If you're thinking, "Wait, I thought the immune system did that!" remember that not all illnesses involve microbes, viruses, or infections. When you break a bone or bang your head, endocannabinoids act as the body's first responders by sending signals back to the brain. According to Professor Mechoulam's qualified thinking, "They may function as a parallel immune system. Maybe." At the very least they form a cellular bridge between body and mind.
I first greeted this wealth of information skeptically. How was it possible that the largest neurotransmitter system in the human body had escaped my attention? As it turns out, my ignorance is well justified. Even though a global cadre of scientists has been exploring the endocannabinoid system for two decades, prohibition has slowed the enterprise.
Studying and understanding the relationship between cannabis and the endocannabinoid system is burdensome; everything from obtaining raw plant material to sharing information to securing funding is difficult. The mainstream media, rabidly anticannabis until very recently, has passively collaborated by casting a derisive eye on the science. Mechoulam has been called "Dr. Pot," and has been described as holding "a PhD in getting high." Bill Clinton's drug czar, Barry McCaffrey, once maligned cannabinoids as "Cheech and Chong medicine." His ignorance can almost be forgiven, since most Western physicians are also unaware of the ECS for the simple reason that it isn't taught in medical schools. This is in part due to the medical profession's anticannabis bias, but also because it's impractical for medical schools to educate students about a bodily system that can be treated only by illegal compounds.
At the same time, the US government has owned patent number 6,630,507 on cannabinoids as antioxidants and neuroprotectors since 2003. These unstudied compounds are so promising that Julius Axelrod, the Nobel Prize–winning biochemist who discovered dopamine pathways in the brain, is one of the patent's three signatories. The logic of the US government owning a patent on a schedule I drug, which it defines as having _no therapeutic value_ , is beyond tortured. When it comes to cannabis, science and government policy exist in parallel universes.
Mechoulam, now in his mid-eighties, is gracious about this lapse of logic, and he recognizes the larger concerns and political pressures at hand. "When insulin was discovered in the early 1920s, it was in the clinic within six months. When cortisone was discovered some 70 years ago, it was in the clinic within two years, and it became very successful. No one has given anandamide or 2-AG to a human because the toxicology research—which costs millions of dollars [and is the first step in all clinical trials]—hasn't been done yet. I've asked the National Institute on Drug Abuse many times—I begged them actually, please do it—because a [pharmaceutical] company will not, and obviously an academic cannot do it. It's a technical thing. It's something that quite obviously should be done, yet it has not been done."
How long will it take to do safety trials on a compound that has been used without incident for thousands of years by millions of people and which mimics a compound produced by our own bodies? I wondered aloud.
"Another decade."
Science has done a good job of describing how these endogenous brain chemicals communicate with receptor cells on the microscopic level. But science has not effectively conveyed what cannabis's ability to mimic the chemicals naturally produced by our brains might mean for medicine or for humanity—poets and philosophers traditionally do a better job at that. This is another reason I've come to Israel: to get a handle on the big picture potential of this plant. Among the handful of scientists who understand these compounds on the molecular and macro levels, Mechoulam heads the pantheon.
Researchers in this small field agree that cannabinoids regulate five basic functions of existence: relaxing, eating, sleeping, forgetting, and protecting our organs. But there is more to this picture than meets the eye, and Mechoulam is beginning to weave the various strands into a coherent theory of how cannabinoids differentiate human beings from every other species.
Take, for example, forgetting. While most people view forgetting as a memory lapse, Mechoulam points out just how important it is for our brains to edit the torrent of sensory data that assaults us daily. Think about a simple task such as driving on a highway. If we couldn't block out the sights, sounds, smells, and sensory input coming at us from multiple sources, we'd be paralyzed by overstimulation, unable to drive—and miserable. Similarly, forgetting is crucial to treating incapacitating illnesses like post-traumatic stress disorder (PTSD), in which painful memories seem to lodge in the mind and haunt sufferers, often for the rest of their lives. In Mechoulam's view, certain chemicals lock in memories, but cannabinoids help unlock them. Informal studies with Holocaust survivors, plus dozens of my own interviews with Vietnam War veterans, indicate that cannabis effectively eradicates harrowing memories that turn sufferers into zombies. No other medicine does this.
Without anandamide we might not ever be able to get over trauma, phobias, neuroses, or chronic pain. Pain is one of the most difficult experiences to recall. It's impossible to remember pain the way you re-create other emotions, and that's for an evolutionarily adaptive reason—think about how many single-child families there would be if women couldn't forget the agony of childbirth. Cannabinoids allow us to forget and move on.
There are other ways that cannabinoids may enable human beings to thrive. This is an odd concept for many of us because it doesn't fit contemporary health-care models in which medicines are used only to treat illnesses; instead, cannabinoid molecules appear to be crucial to maintaining health and wellness. The distinction is profound, and further clues were unearthed in a 1990s study on the effects of cannabis on newborns by Dr. Melanie Dreher, the dean of nursing at Rush University Medical Center in Chicago.
Dreher traveled to Jamaica to investigate how the Roots Daughters, a group of rural and largely impoverished Rastafarian women, use ganja to maintain appetite, help them rest, and allay nausea when pregnant. These women also serve a mild ganja tea to their families as a daily health tonic—when you're poor (or just smart), forestalling illness is less expensive than treating it once it hits.
Dreher followed thirty Roots Daughters and their babies for five years, until the children were old enough to enter school. Her results showed that infants whose moms smoked ganja socialized and made eye contact more quickly and were also easier to engage than the babies of nonsmokers. The ganja kids were not developmentally disadvantaged. In fact, the five-year-old children of smokers scored higher on tests for verbal ability, and for motor, perceptual, and quantitative skills, and memory and mood. "Given what everyone else was finding at the same time, we thought [our findings] were pretty darned interesting and a little counterintuitive," said Dreher.
Dreher's findings, while confined to a small sample group, contravened everything that "experts" had pronounced about the plant's deleterious effects on kids. Yet they were published in 1994 to resounding silence. In the wake of that silence, Dreher applied to the National Institute on Drug Abuse for additional funding to return to Jamaica to follow the same children at age ten, but her request was denied. Instead, NIDA continued to commission more studies on rats, from which researchers concluded that exposure to excessive quantities of cannabis (up to sixty joints a day) in the womb might harm the brain, lower IQ, and damage "executive function." The same dire warnings are still being trumpeted today, all of which Dreher calls "red herrings that drag us from more important findings. Why not look at school performance, social interaction, prenatal examinations, or if these kids are participating in sports or using more alcohol than their peers?" she asks. "This is the ultimate outcome—how we live our lives—not some red herring called 'executive function.'"
A few years later, and completely independently, Dr. Ester Fride found physiological corroboration of Dreher's findings. Fride, a neuroscientist and colleague of Mechoulam's who died in 2010, was investigating the ways cannabinoids affect a newborn's development by testing them on rats that had had their endocannabinoid systems "knocked out" genetically. Her science showed that without functioning endocannabinoid systems, newborns failed to suckle or begin maternal bonding. Further investigation showed that endocannabinoids are essential to a baby's ability to thrive as it grows. Even more surprisingly, she discovered that cannabinoid receptors develop extremely slowly in babies, which is why young children don't experience psychoactivity when they take cannabis. This observation had been anecdotally reported in nineteenth-century medical reports, which noted that children could tolerate mighty doses of cannabis that would have left their parents reeling.
Dreher asks: "Is it an evolutionary accident that the two activities necessary to sustain life and perpetuate the species are eating and sex and that cannabis makes both things more pleasurable?" Or, as Dr. Allyn Howlett put it to Michael Pollan: All the things endocannabinoids do "are exactly what Adam and Eve would want after being thrown out of Eden. You couldn't design a more perfect drug for getting Eve through the pain of childbirth and helping Adam endure a life of physical toil." In other words, cannabinoids are chemicals that enable us to cope with the human condition.
The more science uncovers about endocannabinoids, the more it seems that they are responsible for functions we once mistakenly attributed to other receptor systems. Those happy feelings known as a "runner's high," for example, were for decades assumed to be generated by endorphins flooding our brain. Today, researchers know that the runner's high results from endocannabinoids beaming signals to the brain's reward centers. Evolutionary biologists suspect that these pleasure responses are also adaptive: they guide us innately to knowing that aerobic exercise is beneficial.
In 2012, three American biologists examined how exercise influences the endocannabinoid levels of two naturally athletic species, humans and dogs, and then compared the results with studies of more-sedentary creatures, ferrets. Blood samples taken after a brisk run showed that concentrations of anandamide spiked in the dogs and humans, while the ferrets showed no changes at all. In humans, higher levels of anandamide also correlated with the runner's high.
Why? One explanation comes from Greg Gerdeman, an evolutionary neurobiologist at Eckerd College in Florida. Exercise was not an option in the fields and forests where our hunter-gatherer ancestors lived. Daily life required sweat: walking for hours to gather fruit, nuts, and roots; foraging for firewood; and running miles a day in pursuit of prey. In prehistoric times, hunters were, in fact, endurance runners. Before they invented spears or weapons, our predecessors pursued prey on foot until the animal gave out. The spike of anandamide that encouraged our ancestors to pursue dinner and stay active was an evolutionary advantage that allowed them to survive.
Gerdeman hypothesizes that specific exercises might help activate particular cannabinoid receptors to alleviate depression or shift one's mood. Another study indicates that some lucky people may be less prone to anxiety because their brains produce higher levels of anandamide. Think about that: resilience to anxiety may have nothing to do with the vague and perhaps mythical qualities we call being "strong" or "tough." It may have more to do with winning the genetic sweepstakes.
For fifty years, Mechoulam has sidestepped the moralistic debates about the benefits or harms of using cannabis and has avoided adjudicating on the wisdom or folly of legalization. Legalization "is a social decision, not a medical one," he has said. "Our society says 'yes' to tobacco (although millions die of it), or high alcohol drinks (although millions die of them or become addicts), or high-stakes gambling (although it may ruin families). When our society says 'yes' to recreational cannabis it will join the above, irrespective of anything."
To him, cannabis is a brilliantly packaged factory of compounds that raise all sorts of questions that can be answered only through deeper investigation. Of the five basic functions the ECS performs, Mechoulam's researchers are largely focused on using cannabinoids to help the body protect itself from injury and repair itself more quickly after damage occurs. Before he and I met, he introduced me to his A-team, many of whom are over sixty-five, have been studying cannabinoids for decades, and are the most respected experts in this field. Most of them have never seen, touched, or smelled the plant. I tell you this because it's commonly assumed that people who study cannabis are stoners or, at the very least, advocates. Be assured that this is not the case with Mechoulam's team.
Professor Itai Bab leads a ten-person team that's investigating the ways cannabinoids heal broken bones.* When we meet in his cramped and dark office surrounded by towers of books, I explain that I've come to Israel because American cannabinoid research is so impoverished—few doctors in the United States know of his work.
"That's because the US in general doesn't know much about the rest of the world," he tells me. "Americans read American journals and go primarily to meetings in the US. And it's not only in the cannabinoid world."
Bab is by nature a skeptic—a fine quality in a scientist, especially one who is working in the politically charged realm of cannabis science. Even though his very first presentation to the International Cannabinoid Research Society won him a five-minute standing ovation, he is less convinced than his colleagues of cannabis's great promise. "This is a small, noisy field," he warns, "full of big, hot political pressures." The half smile on his face indicates that he enjoys a certain amount of friendly opposition.
Bab's investigations of animals show that CBD doesn't hasten the healing of broken bones, but it does help them heal more strongly. It also protects the skeleton against age-related osteoporosis. "It's too early to know when to administer CBD or what the correct dose is," he says. "We injected it daily starting one day after a fracture for eight weeks. At the eight-week point we saw this bone-strengthening effect."
Is it possible that CBD can possibly fortify the brittle, withering bones of the two hundred million women around the world stricken with osteoporosis? As if he can see the cogs in my brain churning, the professor moves to dampen my enthusiasm. He's been down this road before.
"Yes, it was all very exciting at first, but journalists always take this one step too far. There are two big gaps in our knowledge to date. One is dose. So many different strains of cannabis make it difficult to know the [exact] constituents, and this makes it difficult to prescribe." This is true with any plant-based medicine, but it's especially problematic with cannabis, which manufactures, at last count, over seven hundred compounds. Nor has there ever been a large-scale study that addresses adverse reactions. To illustrate, he walks me through an abbreviated history of another so-called miracle cure.
Rimonabant was a drug that was developed when one clever scientist had the idea to synthesize a THC analogue to block the receptors that ignite the munchies. A drug that reduces appetite _and_ helps overweight patients shed pounds? The French company Sanofi-Aventis recognized the appeal—and the enormous profit potential—and rushed the drug to trials.
Rimonabant worked—for a while. In trials that lasted two years, people's cravings for food, not to mention alcohol, cigarettes, and cocaine, all diminished, and the drug was approved for use in Europe. But once people began using it for a longer period, they reported feeling morbidly depressed or plagued by suicidal thoughts. It was eventually discovered that while Rimonabant makes you eat less, it also blocks receptors in all of the brain's pleasure centers. Rimonabant had the opposite effect of cannabis: it was a joy killer and a profit killer, and Sanofi-Aventis quickly made it go away.
I take Professor Bab's point, but other qualified researchers have confidently told me that the long-term effects of whole-plant cannabis are about as worrisome as those of caffeine. "Overdosing" on pot isn't deadly, nor has it ever been linked to any long-term illness. I repeat Lester Grinspoon's contention that, in very practical terms, cannabis has passed the largest human trial ever with flying colors.
"I think this argument is based on romantic reasoning," Bab counters. "It's nice to get a little stoned. Food, music, sex are better . . . it's a terrific world . . . you don't die immediately. But it's lack of knowledge that contributes to this romantic attitude. Who knows what happens after ten or twenty years of use? Maybe all that euphoria turns to depression. Who knows why you vomited? What I'm saying is that in the twenty-first century, we should not use anything where we're not sure of the long-term effects."
Spoken like a scientist who believes that false hope is the enemy of truth. Indeed, many pro-cannabis folks who proclaim pot a panacea for every illness would do well to employ some of his skepticism. But my concern is different: What happens to those who are suffering while science grinds on? Shouldn't they at least have access to a plant that, to the best of our knowledge, has never caused any long-term complications?
"Look," he says, "we know it's anti-inflammatory. It doesn't have the highest potency, which is good because potent drugs have potent side effects—and we are just starting to understand that inflammation is the beginning of many age-related diseases.
"But let's put everything in perspective. There are many important systems in the body, and this is a small portion in the scientific world. At the American Heart Association, thirty thousand people show up for meetings. In neuroscience, twenty to thirty thousand. Bones are small, about four to five thousand. The main cannabinoid conference, the ICRS, has four hundred attendees. So cannabinoids are very, very small. They're not that important in medicine or in life. The benefits are OK, but not earth shattering.
"Even if my dreams come true it will not change the world."
After a half hour, the skeptical professor admitted that cannabinoid research could maybe lead to important drugs or medicines—"A few, not many." Other scientists, most of whom have never used the plant with patients, have been similarly incredulous. Because cannabis doesn't fit neatly into established scientific paradigms, they mistakenly suspect it is little more than a placebo that fools patients into thinking they feel better because they're high. That argument baffles me for two reasons: One, CBD isn't terribly psychoactive; it doesn't make users so high that they misread their bodily sensations. Two, most medicines, with the exception of antibiotics that kill infections, are supposed to make you feel better. Isn't that the point?
The one exception to this, Bab granted, could be the way CBD ameliorates traumatic brain injury. "Esther will tell you more about that."
Professor Esther Shohami has published 244 papers on the ways cannabinoids protect the brain from injury in sports, war, car accidents, and strokes. Even though one botched clinical trial indicated otherwise, her research demonstrates that cannabis may be an excellent guardian of our gray matter, probably the best protection we have to date.
Estimates show that 1.7 million Americans suffer traumatic brain injury, or TBI, each year. Of them, 125,000 are left in a sort of cognitive purgatory, in which some brain functions work normally and others go dangerously haywire. When cannabinoids are injected into the bloodstream immediately after a brain injury, they have been shown to lessen paralysis, memory impairment, and all manner of cognitive defects. "The improvement is not marginal, it's significant," Shohami says.
Here's why: When the head sustains a blow (and it need not be one violent whack; a series of concussions on a football field can be just as injurious), the brain rattles against the skull. This jangling sets off a tsunami of glutamate, a toxic substance that wipes out neurons, leaving slurred speech, shaky movements, and dementia in its wake. This toxic surge occurs one to four hours after injury, and if left unchecked it is more harmful than the initial physical blow. Until the advent of endocannabinoids, there was no way temper the glutamate release.
Shohami has shown that cannabinoids injected within this four-hour window diminish the glutamate flood and stop the body from attacking itself. More remarkably, they stimulate healing by recruiting new stem cells to become brain cells. This last finding is crucial. Until recently, scientists believed that the brain stopped generating stem cells at birth. But today we know that they lie dormant, on alert, as it were, waiting to be marshaled into action. "Endocannabinoids direct the stem cells to become brain cells and contribute toward recovery," Shohami says.
In 1998, the Israeli pharmaceutical company Pharmos injected a synthetic CBD into the bloodstreams of sixty-seven Israeli soldiers shortly after they had suffered head trauma. Recovery rates were impressive, so Pharmos expanded the trials to other countries. But when researchers in Poland tried the same experiment, they couldn't replicate the results. What happened?
One of Shohami's key insights was that cannabidiol must be administered shortly after injury to prevent the glutamate storm from rampaging. In Israel, geographic distances are tiny, so getting the drug to the patient quickly was simple. But in places where the distance between the accident and hospital was larger, the glutamate reaction had advanced too far by the time CDB was administered. "Some of the patients were treated eight hours after the damage, and that was too late," Dr. Manuel Guzman, a biochemist at Complutense University in Madrid and a leading cannabis cancer researcher, told me. "It is essential with trauma to get to the hospital soon. If the wait time lasts longer than two or three hours, then damage is usually irreversible." Many other cannabinoid researchers have echoed his conclusion.
When the results couldn't be replicated, Pharmos pulled the plug on the trial. One failed clinical trial typically scares away other companies from investigating new drugs—the expense, insurance, and red tape are formidable—even if the flaw is in the design of the experiment and not the drug.
Shohami maintains her belief in the protective power of cannabinoids. "These compounds are very potent with TBI, and at the moment there is nothing else for this injury. If cannabidiol is taken for development by a company, I believe it would benefit these patients. Besides," she adds, "I think it is amazing that the body has the ability to protect itself and that we can give it something to enhance that mechanism."
At the moment, cannabinoids are potential wonder drugs for treating other illnesses, including diabetes and certain forms of heart disease—"potential" being the operative word.
Early-stage research shows much promise. But until the large double-blind, placebo-controlled studies that are the gold standard of pharmaceutical research are conducted, no proof can be established. Cannabinoids have never failed the test of proof; the test of proof has never been applied.
The potential to stanch the flow of traumatic brain injuries is especially significant for soldiers and other types of modern warriors, such as professional athletes. Shortly after I returned from Israel, five thousand retired players sued the US National Football League for $1 billion in damages because of the brain injuries they had sustained during their careers. They accused the league of hiding the dangers of repeated concussions and the harrowing degenerative brain diseases that result from them. Repeated head blows leave one in three football players eight to fourteen times more vulnerable to early-onset Alzheimer's and dementia than the general population, and symptoms set in as early as age forty.* One player was discovered supergluing his rotten teeth to his gums to hold them in place. Another was found urinating into an oven thinking it was a toilet. Yet another was zapping his back with a Taser gun to quell his relentless pain. The issue was thrust into the spotlight when a former Chicago Bears defensive back, Dave Duerson, committed suicide by shooting himself in the chest so he could leave his addled brain to science for dissection. His goal was to force the NFL to recant its long-standing denial about this illness.
Concerned coaches have called for a more-protective helmet design, but this is no more effective than wearing high socks to prevent a broken leg. The league also toyed with fining players who play too rough, but that caused a backlash among fans who enjoy watching their heroes going head-to-head. Cosmetic fixes won't solve the problem. Nothing can repair a brain that has turned to mush.
There has been some Internet chatter about the NFL backing research into cannabinoids to protect players. But at this point such research sounds more like fantasy football than the pro leagues, who are unlikely to challenge the status quo by suggesting that a treatment based on an illegal substance might actually help their wounded warriors.
But Dr. Ethan Russo suggests that CBD could be given as a low-dose preventative medicine, if, of course, it weren't illegal, especially as it has no side effects. "Could low doses of CBD on a regular basis significantly blunt this problem?" Russo asks. "The answer is yes, quite possibly"—but until it is removed from schedule I, we'll never know.
* * *
WHY IS CBD ILLEGAL?
* * *
The United States is pretty much alone is placing CBD in schedule I, and this is the result of a historical aberration rather than science. In 1969, Dr. Timothy Leary won a lawsuit against the government that basically threw out the legal underpinnings of the 1937 ban on cannabis. For one year there was no federal law that deemed cannabis illegal. It made no practical difference, however, because by then every state had its own law.
In 1970, Nixon appointed the Shafer Commission to determine what to do about cannabis. As a placeholder until the report's findings were released, Congress passed the Controlled Substances Act and put cannabis (and all of its constituents, whether psychoactive or not) in schedule I. When Shafer recommended decriminalizing pot and making it available for medical use, Nixon rejected the findings even before the report was printed. So the schedule I placeholder was grandfathered into law even though the scientific basis for that classification was refuted at the time and multiple times since.
* * *
If you are under the misapprehension that science occurs in gleaming white labs with sleek, modern equipment, let me assure you that Mechoulam's beige world hasn't seen a decorator, let alone a paint job, in forty years. My conversation with the father of cannabinoid research was sporadically drowned out by electricians tearing out the ceiling in the hallway to replace decades-old wiring. I had expected more distinguished surroundings for such a highly decorated researcher, but science is a painstaking affair, not a showy one, and scarce pennies are rarely spent on shiny surrounds. Most scientists would probably be suspicious of showy digs anyway.
Once the banging subsides I kick off our conversation by explaining my journey through the new world of cannabis. "Yes, it is a new world," he says. "Four or five thousand years. Not too old." Gentle admonition noted.
"But for a plant that's been around so long we seem to know so little about it."
"We know quite a bit about it," he counters. "It was used in the black populations and by jazz musicians who said that they couldn't play their jazz unless they were under the effect of cannabis, which probably has some truth. What we don't know, what no one has looked into, is whether it causes any change in the _emotions_ that make it better for musicians."
At the time that statement washed over me. Only when later reviewing my tapes did it became clear that he was talking about the potential power of endocannabinoids to affect the emotional center from which artistic expression arises. Instead, I moved on to the less savory topic of my own vomiting and asked: If cannabis is so effective in treating nausea, why can it sometimes trigger the opposite reaction?
It has a lot to do with dose, he explains. A large amount can cause an entirely different response than a small one, "and it is probably individually determined." Everyone has a different susceptibility, probably because our endocannabinoid systems vary. "The first and only time we gave it to people about fifty years ago, my wife made a cake and put ten milligrams of THC in each piece of cake. Five of our guests took the cake with THC and five took the placebo. The placebo had no effect, but all of those who took THC reacted differently. My wife felt a little bit high. She sat in her chair. Another said he felt nothing but every fifteen seconds he started talking, _pa pa pa_. Another didn't stop talking for two hours—he was a member of Parliament so it accentuated what he knows—and the fifth one had an anxiety reaction. So same dose, five different reactions."
Every few months, it seems, new reports come out associating overuse with schizophrenia. Is this fact or is this propaganda?
It depends on what part of cannabis you're talking about, Mechoulam responded. "We gave CBD to a schizophrenic girl in Brazil who displayed no psychotic symptoms as long as she got CBD orally. We couldn't do clinical trials—it takes a lot of money. In 2012, a German group reported that CBD is an extremely good antischizophrenic compound, as good as the drugs being administered today, with one exception: the potent antipsychotics given today cause nasty side effects and CBD does not. In large doses they found that CBD enhances anandamide concentrations in the brain. There are a lot of things anandamide does, all of them essentially positive."
As he's speaking, Mechoulam prints out a chart that lists the dizzying number of illnesses in which the ECS system is somehow involved. In addition to the obvious suspects, the list includes stroke, morphine dependency, Parkinson's disease, Huntington's disease, neurodegenerative disorders, epilepsy, cancer, diabetes, osteoporosis, inflammatory bowel disease, psoriasis, arthritis, and seizure disorders. It also includes so-called untreatable illnesses such as chronic hiccups, a torturous affliction that can persist for months, and Tourette's syndrome, a neurological disorder characterized by repetitive, involuntary movements and weird vocal tics.
My face must indicate incredulity because Mechoulam interrupts himself to ask, "You don't believe me?
"George Kunos, one of the heads of the National Institutes of Health in Washington, recently wrote that the endocannabinoid system is apparently involved in almost _all_ major diseases of the body. This is a very strong statement because Kunos is an excellent scientist—Hungarian, you know—and because there are very few compounds that act on everything."*
What I'm thinking is, _Pharmaceutical companies are tripping over themselves to find new drugs that heal without killing people_. But what I say is, "If anandamide or other cannabinoids do all of these marvelous things, why haven't you patented a synthetic version?"
"We did. But by the time we got people interested the patent was ten years old, and then it was too late. A patent is only good for twenty years, and by the time a pharmaceutical company completes trials they'll have just a few years left to make back their investment. And so, there we are."
If I were Mechoulam, I'd probably feel like a lone man screaming in a forest whom no one hears. Isn't he frustrated, I ask, by the political and legal hurdles that have caused his field to progress so slowly?
His warm, questioning eyes greet me with a gaze as if to say, you poor, naive layman. "Why should I be frustrated? It depends on where you start. I'm a pessimist. I didn't expect anything to happen. The first prize I got was for best publication by a young scientist at the Weizmann Institute in the 1960s. A committee made that decision, but the chairman of the academic board thought I should be doing something else and did everything to kick me out."
I don't believe he's a pessimist. Mechoulam's investigations and insights have blazed this trail for the last half century. Pessimism doesn't fuel such single-focused dedication.
Curiosity does.
"Our brains produce two hundred to three hundred anandamide-like compounds, most of which no one has looked at. When you sit around with your friends, are you a photocopy of any of them? If I see my granddaughter running toward me, I feel happy. Why is that?" What he is asking is: Could cannabis be the chemical link that translates the objective reality of the child rushing toward him into the subjective feeling of happiness?
And then he reveals his big theory: "Why the hell is the body making this many compounds at the same time? Why doesn't it make just five compounds? We have two to three hundred anandamide-like compounds in our brain, and their levels and ratios are different. Is it just possible that the interplay of these compounds causes the differences in our personalities or has something to do with our psychological setup? We know almost nothing about the chemistry of our personalities. Our body produces compounds that regulate every physiological system, so why not our personalities? People discovered the major neurotransmitters in the 1930s and '40s, but here's a new system, and we should expect new things to be discovered."
Of course, this is simply a theory, but it's as riveting as it is inconceivable that something in this much-maligned plant could actually hold the key to unlocking the brain chemistry of emotions.
According to Ethan Russo, it's generally wise to heed Mechoulam's hunches. "A great scientist doesn't just figure out the how, but the why, and Mechoulam excels at this. To outsiders it may seem that these three hundred chemicals he's discussing are extraneous, but one of his guiding principles is that nature doesn't waste energy. There must always be a rationale behind the energy the body expends to make these things, and his passion has been to uncover that rationale."
Or, in the words of this self-identified pessimist, "The anandamide story may continue well beyond what we know today. Why are we sorry? Angry? Happy? I don't know, but one has to prove a theory. It's not a big deal. For the next fifty years I need something to do."
## ___Chapter 6_
## THE WORLD'S LARGEST HUMAN TRIAL
_Tel Aviv, Israel_
Not only is Israel the nucleus of cannabis research, but the country also has twenty thousand human subjects participating in the world's largest state-run medical cannabis program. Over the last two decades, this program has won support from citizens, government officials on the right and left, and religious leaders (who have, incidentally, declared cannabis kosher). "In Israel, the government takes a role in ensuring quality and safety of the product, and supports research to further the understanding of the plant's medical benefits," said Amanda Reiman of the Drug Policy Alliance. "In the US, the government has actively prevented research from taking place and has threatened municipalities that attempt to regulate quality and safety with criminal prosecution." Seeing this program in action turned me into a believer about the power of medical cannabis once and for all.
The program sprouted up in 1995, when a subcommittee in Parliament recommended that the government allow the severely ill to have access to medicinal cannabis. The decision was not taken lightly. Israel moved cautiously, fearing that it might threaten its relationship with the United States or violate the United Nations Single Convention on Narcotic Drugs. That treaty, ratified by 185 nations in 1964, aimed to stop drug trafficking across borders "by coordinated international action" and bound individual countries to outlaw "narcotic" drugs (yes, cannabis was defined as a narcotic) except for medical and scientific purposes. Article 49 of the treaty allowed countries to gradually phase out coca-leaf chewing, opium smoking, and other traditional drug uses, but insisted that "the use of cannabis for other than medical and scientific purposes must be discontinued as soon as possible."
But with Mechoulam at the bow of scientific study, and with cannabis representing a low-cost solution to so many medical problems that have no other remedies, Israel took cautious steps forward. At the start, only one doctor in the entire country was allowed to grant licenses, and he dispensed them stingily, granting only sixty-two over the course of ten years. Cannabis was also designated a medication of last resort, meaning that patients must have exhausted all other forms of treatment before being allowed to use it. The cash-strapped state was also unwilling to take on more work and cost, so it insisted that the first five licensed patients grow their own meds—a hurdle that quickly proved insurmountable, as desperately ill people are not good gardeners. The list of applicable conditions was initially limited to asthma, AIDS wasting syndrome, and vomiting and pain associated with chemotherapy. Today, the conditions are still restricted—unnecessarily so, say advocates, who also criticize the government for banning paraphernalia like bongs and grinders—but have been expanded.*
Patients now pay a fixed price of $100 per month regardless of how much cannabis they use. The starting dosage is 20 grams (0.75 ounce) per month, but patients can get more depending on their affliction—42 grams (1.5 ounces) is the average monthly dose. That price is inexpensive by Western standards—but key to the program's success is the fact that two Israeli insurance companies partially cover reimbursement. (Holland and Israel are the only countries where insurance covers medical cannabis.) A handful of public hospitals have even purchased Volcano vaporizers for patients who can't afford to buy them. Patients can request individual mouthpieces and balloons.
Today, twenty doctors can legally prescribe cannabis, and eight tightly monitored grows distribute it on-site, through home deliveries, and in small dispensaries and hospitals. Interestingly (and smartly), all patients must undergo training about which strains and which forms—baked goods, joints, oils, or tinctures—best treat their conditions before starting treatment. They are also advised on how to optimize dosages, reduce side effects, and monitor potential drug interactions. "It doesn't matter if you've used it for forty years, you get the same training as someone who's never touched it," says Mimi Peleg, who directs cannabis training at the state's largest distribution center, MECHKAR. "People always start out laughing at me, but by the end of the training they're not laughing anymore. They're grateful. I show them how they're probably wasting ninety percent of the cannabis they've been using. The average Israeli smokes with tobacco and never leaves the cannabinoids in their lungs long enough to be fully absorbed. You need a minimum of four seconds, especially with CBD, which takes longer to absorb." Note to US medical marijuana programs: because cannabis is not a "single bullet" approach to illness, and because strains vary widely from location to location, education is crucial. Effective treatment requires more than sending a patient to a pharmacy to pick up pills or to a dispensary to buy bud.
Still, the Israeli government didn't exactly embrace this program; until 2009, it treated it the same way it treats its Dimona nuclear reactor—by pretending it isn't there—and only 1,800 patients had enrolled. Officials didn't want Israel to be known as the Amsterdam of the Mideast, and they preferred experimenting with production and distribution without the eyes of the world watching. Most Israelis were unaware of their country's program until a documentary called _Prescribed Grass_ aired on national television and blew the lid off that secret. For that, they have Zach Klein, the documentary's director, to thank.
Zach began exploring medical cannabis when his mom, Lea, was diagnosed with early-stage breast cancer. Over Friday-night Sabbath supper she broke the news to her family and explained the chemotherapy regimen she was embarking on. Strangely, she added, her oncologist had whispered something to her as she left the office: "Try to find some hashish. It will help you with the chemo." She fixed her gaze on Zach and asked, "Who here can find me some?"
Zack delivered a few grams to his mother, but Lea declined partaking. The antidrug commercials on Israeli television—very much like the Reagan-era "this is your brain on drugs" egg-frying-in-a-pan ads that blanketed US airways in the 1980s—still resonated, and she worried about the plant diminishing her mental acuity. So Zach tracked down Professor Mechoulam, who had recently been awarded the country's highest prize for scientific achievement, at a lecture and asked him, "Is it true that cannabis won't harm the brain? Does it really protect it?"
The professor flashed him a watery-eyed smile. "Didn't you hear my presentation?"
The evidence the professor laid out lit a fire under Zach, and he drove to his mom's apartment that night to share the news and a joint. A few puffs and her nausea abated; in time, sleep was restored. Then, in a stroke of bad luck, she broke her hip. The opiate-based pain meds she was prescribed sunk her into depression, so she switched to cannabis. Pain ameliorated, depression lifted.
Stirred by his mother's experiences, Zach set out to make a film about the common plant with uncommon healing properties. But there was little to shoot other than scientists synthesizing chemicals and injecting them into rats. Zach back-burnered the film, but his interest in the plant led him to Tikun Olam, the country's only cannabis farm at the time.
Tikun Olam is impressive on many levels, including its carefully crafted public image. Even its name, which in Hebrew means "healing the world through compassion, kindness, and justice," speaks to a higher purpose. It became internationally famous in 2012 by announcing it had engineered the first CBD strain that delivered all of the healing but without the "unwanted side effects"—that is, the high. In fact, Tikun Olam didn't originate the first CBD strain, but the media couldn't resist the story of a "highless" marijuana. Nor could it resist regurgitating the myth that the growing operation was started by Dorit Cohen, a biology teacher who retired to grow an herb farm in her home but switched to cannabis once she learned about its medicinal powers.
I met Dorit—she is a quiet, pleasant woman, but she is not the brains behind this operation. It was her son, Tsachi, who masterminded Tikun Olam's ascent from small grow of fifty plants in his family's home overlooking the farming village of Safed to the largest cannabis operation in the country—an eight-acre industrial garden of greenhouses, trimming machines, and different huts for baby and mother plants. Zach was so taken with Tikun Olam that he joined the operation. His first job was driving cured plants two hours away to Tel Aviv, where they were distributed to patients out of Tsachi's apartment.
Two notable aspects about the Cohens also struck me: they are an orthodox religious family, and Safed, where the operation is headquartered, is the center of Judaism's mystical Kabbalah sect. This didn't strike Israelis as odd, but the incongruity of Hassidic men trimming weed in their black hats, black coats, and side curls, davening before the plants, delighted me. In fact, farmhands play religious music for the plants (personally, I think the plants might be happier with Bach or post– _Yellow Submarine_ Beatles) and there's a synagogue on the property where the community gathers to pray. Rabbi Shimon Bar Yochai, a legendary Kabbalah mystic, is buried on a nearby hill, where his spirit guards the farm from harm.*
Thanks in large part to Sanjay Gupta's documentary _Weed_ , Tikun Olam's strains are today among the most recognized in the world. Each is named after a dead patient. Eran Almog—the namesake of a wedding dress designer who battled cancer for seven years—supposedly contains a whopping 29 percent THC. Avidekel was named for the father of one of Tikun Olam's founders; with 16 percent CBD and only marginal THC, it is a star among CBD strains.
Tikun Olam provided Zach Klein with the setting and characters he needed to begin his film. By the time shooting began he had also ascended to the role of Tikun Olam's minister of information. That position made him Israel's first legally designated joint roller (he possesses a "license to roll a dangerous drug"); he was subsequently granted a second license to chauffeur plants to industry trade shows, where he would position them next to pharmaceutical companies' products and then educate passersby about the medicine that grows in the ground and can't be patented.
Over two years Klein convinced patients and the country's top scientists to participate in his film, and the narrative crystallized. He sold a rough cut to Israeli's largest television network, Channel 2, but the network balked at including the story of one PTSD patient in the final cut. His recovery was so extraordinary, they said, no one would believe it.
The patient in question was a policeman who had witnessed the 2002 Passover massacre, in which a suicide bomber disguised as a woman exploded a massive bomb in a hotel where 250 families had gathered to celebrate the Jewish holiday. This cop's unit was first on the scene, and the carnage—30 dead, 140 wounded, limbs strewn atop tables—was trapped so firmly in his memory that no anti-anxiety medication could eradicate it.
When he first skulked into the dispensary, this ex-cop wore his cap slung low over his eyes, as if hiding. He spoke in a hushed whisper and couldn't maintain focused attention. He hadn't worked in four years, had dropped his friends, and was barely speaking to his wife and family. He was quite literally missing in action. Zach handed the cop a joint but he brushed it away. "This is a drug."
"Your psychiatrist sent you here because this is the treatment of last resort," Zach reminded him. "There's nothing more after this."
Begrudgingly, the cop smoked half of the joint and then left. Ten minutes later a woman charged into the dispensary. "I'm his wife," she announced. "What have you done to him? For the last ten minutes he's been sitting in the car laughing. He hasn't laughed in years. _What's going on here?_ "
The officer continued his cannabis treatment. A month later, his psychiatrist called Zach. "He's talking to his family. They went on holiday; he hugged his daughter; he even sat through a Passover Seder." He sent other referrals, but after the seventieth patient, the Ministry of Health clamped down and ordered him to stop. They were concerned that word would get out and that the demand for cannabis would exceed the supply.
I ask Klein why he thinks so many doctors are resistant to cannabis. He answers with a story about Ignaz Semmelweis, a nineteenth-century Hungarian gynecologist. In Semmelweis's hospital, women were dying of infections after childbirth. Semmelweis noticed that when he washed his hands before a procedure, fewer infections occurred, so he suggested that everyone in his department do the same. His colleagues derided him as crazy and eventually drove him out of the hospital. "This is the story of medicine," Zach concludes. "A lot of doctors are convinced they know everything. Others are so overwhelmed that new ideas, even simple ones, can be too much."
_Prescribed Grass_ aired November 19, 2009. The following day the Ministry of Health was barraged with so many calls it spun into crisis mode. At first it threatened to shutter Tikun Olam and import its supply of cannabis from Holland, but the Dutch rebuffed the Israeli request. Holland couldn't produce enough to satisfy a foreign market; besides, the cost would have been prohibitively expensive for average Israelis. The Israelis retreated and then sanctioned seven other grows to compete with Tikun Olam to meet the burgeoning demand. The program has since exploded and now serves over twenty thousand participants from all sectors of Israeli society.
Three months after the documentary aired, Zach received a distressed call from Inbal Sokorin, head nurse at the Haradim nursing home, one hour south of Tel Aviv. She had an extremely agitated patient with dementia whose family had just secured a cannabis license for her, but Inbal had no idea how to treat her. "I don't believe in this, but since you made this documentary why don't you come here and show us what to do?" she huffed.
They discussed the issues confronting her patients, but what they didn't discuss was her growing frustration with geriatric care in general. "I used to sit here and ask myself, 'What am I doing?'" she confesses to me once we've settled into her cubicle at the back of this surprisingly cheerful facility. "We were giving a lot of medication but there was a lot of suffering. We had to fight with patients to give them blood, to put in a feeding tube. By Jewish law you have to fight for life until the end, but I was asking myself, 'Why do we want them to live if they want to die?'
"Every day I'd come in and say 'Good morning' to one patient, and she'd growl, 'What's good about this morning? Last night I asked God to take me and now all I see is _you_.'" Inbal has a passion for her work that causes her avid, jet-black eyes to dance even when recounting its difficulties. The room gets palpably warmer when she smiles. But her conflict was real, she assures me. "I believe in nursing. I know I can help people and educate them. But we were fighting for life and no one was happy."
Zach presented Inbal with research findings about how cannabis can calm people with dementia, and then showed her how to store, administer, and dose cannabis flowers, all of which contravene the protocols of a traditional medical setting. One doctor warned her against going forward. "Be very careful. All of the cannabis patients are going to end up psychotic. It's a very dangerous drug and you're going to have a big, _big_ problem." But the initial reactions of a few patients proved him wrong.
She introduced Zach to the dementia patient whom the staff had nicknamed Tiger because of her constant roar. Her antipsychotic medication, olanzapine (Zyprexa), was creating miserable side effects including spasticity, stiff limbs, and a constant twitching of the mouth.
Zach handed her a joint, but her unyielding hand muscles didn't allow her to grasp it. With Inbal's permission, Zach jerry-rigged a bong from a plastic water bottle (remember that old trick?), took a breath, and blew the smoke into Tiger's face. After two inhalations her screaming quieted. Zach asked for her hand and she gave it to him. "The anxiety and fear melted from her eyes," Inbal recalls. "I wouldn't have believed it if I hadn't seen it."
That night Inbal couldn't sleep. She was excited and confused. "I'm not religious, but if I were I would say that God spoke to me that night. And what he said was: 'I'm giving you hope, Inbal, but it's not going to be easy.'" Her approach to nursing was about to be upended.
Zach continued treating other patients at Haradim with cannabis. He secured a Volcano vaporizer and instructed the staff how to use it. One patient, Moshe Roth, became an international poster boy for medical marijuana thanks to his soul-stirring appearance in Gupta's _Weed_. A Holocaust survivor, Roth was tormented by nightmares, which made him so cranky and irritable that his marriage had all but disintegrated. One daily joint at eleven a.m. took away his fear and anxiety. Sleep returned, as did his wife, and he began to write and paint again (chickens are his theme. After he fled the Nazis he hid in the chicken coop of a French farmer for a year).
Another ninety-seven-year-old woman was so thin (seventy pounds) that she looked like a _shablul_ , says Inbal, a snail, shrunken and coiled upon herself. She was refusing food, so she was being force-fed with a nasal tube, which was inserted into her nostril and threaded into her stomach. She felt imprisoned by this tube, and it was so painful the nurses were forced to restrain her hands to prevent her from yanking it out.
Instead, a few sprinkles of cannabis in her morning porridge stimulated her appetite so that her weight rose by almost half, to 105 pounds. Today she's off the feeding tube and is taking daily cannabis capsules to maintain her taste for food. Almost all elderly patients prefer capsules to smoking. "Nurses like them because they are easier to count out and store," says Inbal. "The elderly, they were born to capsules."
Inbal began tracking dosages, strains, and five conditions that commonly affect the elderly: spasticity, pain, agitation, loss of appetite, and depression (which includes trauma and Holocaust-related PTSD). She consulted with Hebrew University professors, who counseled her not to use THC for those who didn't enjoy feeling high. "Professor Mechoulam said to me that THC can affect short-term memory, which can be beneficial at times and detrimental at others. If they don't like getting high, they get CBD strains.
"But patients suffering from life, they get THC."
By tracking over one hundred patients, Inbal and her team confirmed the following:
• Cannabis, if administered gradually, produces no side effects. If there is no improvement, treatment is easily stopped with no withdrawal symptoms.
• Once appetite is stimulated, nutritional absorption rises to normal range. Swallowing is easier and spasticity is reduced.
• For acute conditions, smoke, not vapor, heals more powerfully.
Inbal knows that medical practitioners object to this last finding, but lung irritation concerns her less than providing the quickest analgesic relief.
"Of course, it's not good to smoke all the time, but if you have a strong, sudden pain and you smoke immediately"—she claps her hands, _chik chak_ —"the pain is reduced.
"Physicians are doubtful, but sometimes I have to remind them that they are practicing the art of healing."
It's not difficult to see why traditionally trained doctors resist using an herb that is smoked or baked into a cookie. "Take one-quarter of this ginger snap twice a day" is not a prescription that many doctors feel comfortable making. Doctors prefer single bullets that come in finely dosed pills, and mistrust anything that hasn't passed the muster of clinical trials. The concerns are well founded, but Western medicine's unilateral approach to healing dismisses much of the knowledge that other cultures have accumulated for centuries. This dismissal is not because the other systems don't work, but more because Western medicine doesn't yet understand how they work. Acupuncture is a prime example.
The American Medical Association dismissed acupuncture as voodoo until scientists discovered that poking a needle into the skin commands an endorphin to shoot out an internal opioid that stops pain. Our arrogance blinded us to centuries of statistical data culled from hundreds of thousands of patients that enabled Chinese doctors to map hundreds of pressure points. In dismissing centuries of data until they could "prove" it, Western physicians overestimated their own competence.*
Cannabis has been the victim of the same Western hubris, but since Israel now operates what is effectively the world's largest human trial, I figured there must be one specialist who had wide hands-on experience and could share anecdotal evidence about the drug's effectiveness. Luckily, Dr. Bereket Schiff-Keren picked up her phone when I called.
Schiff-Keren is a pain specialist who has prescribed cannabis to over 1,500 patients at Tel Aviv's massive Ichilov Hospital. Before I could get into her office, however, I had to first confront a highly agitated woman pacing the hall outside. She was rail thin and had a loosely draped scarf around her hairless scalp. When she learned that I was scheduled before her, her face creased with anxiety, so much so that I ceded my position in line.
Schiff-Keren later informed me that the woman, once a nurse in that very hospital, had terminal lung cancer and had refused chemo and radiation. "She's going to die and she accepts that. But she also has terrible pain in her shoulder and chest where a massive tumor has invaded. Bales of narcotics didn't work, so she came to me for cannabis. Her oncologist didn't suggest it; she came of her own accord, and I'm treating her. She needed a refill and she wasn't happy about waiting."
Bereket has a quiet, gentle voice, but she's fearless, a quality that she demonstrates every day by driving her motorcycle through Tel Aviv's snarled traffic. For over a decade she has prescribed cannabis despite shifting government policies and the opprobrium of fellow doctors. "It has made me mistrusted by some of my colleagues," she says. "They think it's a kind of antiscience. Most doctors say we don't have enough evidence yet, but my patients need results. If there comes a woman like this, thirty-five kilos, you saw her? She was very thin. She wasn't happy about waiting, but she's not happy whatsoever. Pain makes you unhappy."
Herein lies the difference between a researcher and a healer. One lives strictly by the scientific method. The other sees human beings begging for relief, which makes denying treatment difficult, if not cruel.
Dr. Andrew Weil once told me that of all modern medicine's accomplishments, one of the least advanced areas is pain relief. Does Schiff-Keren agree with this assessment?
"Absolutely. It wasn't until World War Two that people became aware that pain is a disease of its own. Until then, pain was considered a symptom of something else and would be alleviated once the something else was treated. But John Bonica [an anesthesiologist, chronic pain sufferer, and the founding father of pain management] showed that pain is a disease of its own and that we should treat it _in addition_ to the disease. And sometimes treating the disease is impossible. For example, ninety percent of incurable cancer patients live in pain. Alleviating it is the least we can do for the terminally ill."
What about those contending with the small pains of aging? Some naturopaths insist that you're not treating the source of the illness if you simply treat the pain.
"One of the things that keeps people alive is activity, and pain is very limiting. Enabling a person to go to work, have a family life, walk—walk!—sex, helps people to feel fulfilled in their lives. Chronic pain is common. Half of the people in their 'golden years' suffer joint or muscle pain, which is usually an outcome of degenerative joint diseases, osteoporosis, and those sorts of things. And now that life expectancy is getting longer, aging people want to be productive and enjoy their lives . . . and, I don't find cannabis treats only certain pains effectively. It treats every pain."
_Every pain?_
"Every pain." It works well with neuropathic pain, which causes a burning sensation along the nerve routes that makes your limbs feel as though they are on fire from the inside out, and with other pains as well. Unlike opiates, which block pain, cannabis seems to do two things: distract from it and alleviate it. And cannabis can be safely combined with other drugs: opiates, anticonvulsants, antidepressants, and anti-inflammatories. "Cannabis works with all four. It's not as strong as opiates, but every day I have patients telling me it works," Schiff-Keren says. "For me, the science is the cream on the cake. Patients telling me that it works, that counts more."
You are a very unusual doctor, I say.
"Yes, I am. Most doctors wouldn't say this. But fifteen hundred patients over ten years have taught me that cannabis is useful in most cases."
So at the risk of sounding facile, is cannabis a miracle medicine?
"It's a miraculous drug, yes. It's terrible because people are so prejudiced and frightened. But I stopped being frightened a long time ago, because the patients told me it worked."
## ___Chapter 7_
## SNAKE OIL OR CANCER CURE?
_Bodega Bay and Los Angeles, California_
Being in Israel among this elite echelon of scientists made it clear that there is so much more within cannabis than meets the eye. It's no big surprise that the plant is useful for insomnia and pain, but bone healing? Traumatic brain injury? Diabetes? Just as the ancients observed that cannabis can treat dozens of unlikely illnesses, research, when it is allowed to occur, is elucidating the mechanism of how some of these things work. The initial results are far from conclusive, but the implications are mind-blowing—especially with illnesses such as chronic obstructive pulmonary disease (COPD) and cancer. Yes, lung disease and cancer, and no, I was not stoned when I wrote that last sentence.
Keep reading.
When Dr. Donald Tashkin, professor emeritus of medicine at the David Geffen School of Medicine at UCLA, began studying how cannabis smoke affects lung function in the 1990s, he presumed that it would lead to diseases similar to those elicited by tobacco, as both plants emit many of the same gases and tars when burned. In fact, cannabis actually contains 50 percent more benzopyrene—a cancer-causing agent—than tobacco does. But after three decades of NIDA-funded studies, Tashkin, now in his seventies, concluded that marijuana smoke doesn't contribute to COPD; it has the opposite effect, at least in the short term, drastically opening the airways to allow more air into the lungs. "The effect is comparable to a classical dose of an inhaled bronchodilator," Tashkin told me. "We also found that cannabis inhibited experimentally induced asthma."*
Another report published in the _International Journal of Cancer_ in 2014 came to a similar conclusion. "Results from our pooled analyses provide little evidence for an increased risk of lung cancer among habitual or long-term cannabis smokers," the authors wrote. And a 2009 Brown University study concluded that those who had a history of smoking weed possessed a much lower risk of head and neck cancers compared with subjects who did not.
Make no mistake: smoking pot won't prevent lung, head, or neck diseases. But some element of the smoke appears to protect the lungs from damage. "THC is anti-inflammatory, and inflammation is necessary for COPD to progress," Tashkin hypothesizes.
"Marijuana contains the same carcinogens as tobacco smoke, so it should be a risk factor for lung cancer—but it isn't," Tashkin reiterated. "Studies in cell cultures and animal models have shown that THC inhibits the growth of glioma, thyroid, prostate, breast, and lung cancer—you name it. It causes cells to die off before malignancies develop, and there's less sprouting of new blood vessels that metastases need."
I have read those sentences repeatedly, and each time I come away scratching my head: Why hasn't this extraordinary information trickled down to the public, or at least been investigated in humans? Why have most mainstream news organizations ignored it? And why is NIDA spending millions more scrutinizing the "dangerous" aspects of secondhand cannabis smoke when the firsthand smoke might actually be beneficial?
The anti-inflammatory story is still unfolding; these protective effects of cannabis aren't seen only in the lungs. Gary Wenk, a professor of psychology and neuroscience at Ohio State University, has been studying aging and Alzheimer's disease in animals for over thirty years. He also tests experimental drugs for pharmaceutical companies, so he is one of the few Americans who possesses a DEA license to study the plant without having to run the bureaucratic gauntlet. Wenk and his entire research lab are so convinced of cannabis's power to slow the degeneration in aging brains that they come to work wearing T-shirts proclaiming ONE PUFF A DAY!
After a decade of experimental research, Wenk has concluded that a single daily puff bathes the brain in protective anti-inflammatories. Early evidence also suggests that people who smoked pot when they were younger have lower rates of Alzheimer's later in life. "These studies teach us that our brain's own cannabinoid system is necessary for us to maintain the processes that prevent the decline of our minds," Wenk told me from his office in Columbus, Ohio.
While one puff a day is no cure for Alzheimer's, there is a possibility that it might forestall its onset. "All we can say at this point is that it slows aging in the brain," says Wenk. "The real secrets to youth are out of our grasp, because the only known way to stop cells from oxidizing is to stop eating or breathing. THC crosses the blood-brain barrier the tight scrim that guards the brain from most chemicals carried in the blood] and it has the same addiction rating as coffee," Wenk says. "So in the future we may be wearing patches that release these drugs all day. It has never made scientific sense as to why it is a schedule I narcotic, but science was never part of the law."[*
The prohibition on controlled scientific studies plus willy-nilly state-by-state legalization has created a Wild West of medical cannabis use, ungoverned by federal laws or regulations. It is increasingly common for parents who have kids with seizure disorders or cancer to pick up and move to medical marijuana states, or to find treatment information from Facebook, which is riddled with public groups named "Cannabis Cures Cancer!" "Cannabis Oil Success Stories," or "CannaKids," and dozens of secret, invitation-only sites as well. Parents who venture into this uncharted territory are now known as "medical refugees," and they must usually operate without guidance. It's a lonely and vulnerable position to be in. They'll either get lucky and find a practitioner who knows what he or she is doing, or they'll run into some cannabis cowboy trying to make a buck—and if things go wrong, the results can be fatal.
The first hint of the plant's tumor-terminating properties appeared in a 1974 Medical College of Virginia study launched to uncover the damages cannabis inflicted on the immune system. Instead of hastening the death of mice implanted with lung cancer, breast cancer, or leukemia, cannabis actually slowed tumor growth and extended the rodents' lives by one-third. The DEA squelched that study for twenty years until some disgruntled researchers leaked a copy to the national media, which covered it halfheartedly.
Inquiry on cannabis as a tumor assailant went quiet until 2000, when Dr. Manuel Guzman, from Complutense University, injected cannabinoids into cancer cells in the brains of rats. The results were mind-boggling: cannabinoids triggered cancer cells to commit suicide—a condition known as apoptosis—and prevented blood vessels from feeding tumors. (The media ignored that story as well.) Guzman told me that further inquiry has shown that administering cannabinoids orally, especially in conjunction with the drug temozolomide, is more effective than injecting it into cells directly—cannabinoids are homebodies; they don't like to travel far when injected. But when taken orally, they surround certain types of tumors and annihilate them. Guzman, like all responsible researchers who don't want to be branded as pot docs or quacks, is quick to warn that cannabinoids have been studied only in a handful of tumors (brain, pancreatic, skin carcinoma and melanoma, and breast, primarily).* Moreover, cancer in mice (average weight: less than one pound) is far less complicated than it is in humans, which is why so many drugs that succeed in rodents fail in human trials.
That 1974 Virginia cancer study lodged in the mind of a Canadian man, Rick Simpson, back when the results were first announced. Over the years he wondered why he hadn't seen any more about it, but he assumed it was probably just another false lead in the battle against this cunning multiheaded scourge.
Then, twenty-three years later, after falling from a high ladder at work, Simpson suffered a brain injury that caused an earsplitting ringing in his ears, "about the same as having a lawn mower running in your living room," he said. "They tried every possible drug, but nothing worked. It got so bad I wanted to shoot myself."
He was taking 1,000 milligrams of tegretol, a seizure-disorder drug with powerful side effects including terrible bouts of dizziness, loss of balance, and cloudy thinking. Desperate for a less overwhelming treatment, he asked his doctor about ingesting concentrated cannabis oil. His doctor tsked away the suggestion, so Simpson unearthed some old hippie recipes that used naphtha (aka paint thinner) to extract THC—just as the Denver dabbers use butane—and began to render the high-potency oils himself.
In a few weeks one daily droplet of oil quieted the ringing in Simpson's ears and also lowered his blood pressure and restored his health, he said. A few years later when melanoma patches appeared on his face, he covered them with the oil for four days before having the skin biopsied. The tests came back negative and Simpson began crowing about the "medicine that Big Pharma doesn't want you to know about."*
Taking his message wider, Simpson made a documentary, _Run from the Cure_ , which demonstrated his extraction methods and recommended ingesting a walloping one gram a day of indica "hemp oil" to treat any and all of the two-hundred-plus varieties of cancer and tumors. This ninety-day one-treatment-fits-all regimen was to be followed by a maintenance dose of one gram a month for life. No one knows where Simpson came up with these dosages and protocols, but that didn't stop word from spreading. Today the Internet is crawling with videos of converts claiming to have cured their cancers with Simpson's oil. For those unfortunates for whom it doesn't work, well, we don't hear from them, do we?
In 2009, Canadian Mounties raided Simpson's house in Amherst, Nova Scotia, confiscating over 1,600 plants and issuing an arrest warrant for possession and trafficking. He was in Europe at the time and has been on the lam ever since, but his story has made "Rick Simpson Oil," or "RSO," a worldwide brand.
RSO offers hope—at times, false hope—to desperate people, many of whom forgo traditional treatment in favor of cannabis oil. I met one such fellow while reporting in Florida. He had a quarter-size patch of skin cancer on his leg but was uncertain if it was basal or squamous cell (the latter is more life-threatening) carcinoma or melanoma (the latter is scarier, as it more easily spreads to other organs), since he hadn't seen a doctor for diagnosis. He was painting homemade RSO on the patch with no treatment plan or medical supervision. He didn't believe in doctors (evidently he believed more in YouTube videos), and I cautioned him against the go-it-alone-pray-for-a-miracle approach.
Dr. Donald Abrams, surely one of the most procannabis oncologists in the United States, became very agitated when I asked him about the wisdom of replacing chemo or radiation with cannabis oil. "I find it sad and very devastating," Abrams told me. "The number of patients doing this is growing weekly, and it is nothing more than idealist utopian promotion that has some ugly unintended consequences." In other words, death.
Simpson doesn't sell oils and he gives the formula away for free. His goal, he says, is not profit but to spread the cannabis oil gospel to anyone who'll listen. No one knows if it works consistently or on what types of cancers, but thousands of people have sworn that it does. What is known is that squaring off with fatal diseases, especially with unproven, unregulated plant medicines of varying strengths and qualities, is risky. It's especially fraught in an unregulated environment where there is no way to discern the quacks from the healers, as many voyagers into the new world of cannabis have discovered. Angela Ryder is one of them.
Around Thanksgiving 2012, Angela's ten-year-old son, Chico, came tearing out of the bathroom, excited about the alien growth in his throat. "Hey, Mom, look at this!" he said, opening his mouth to show her his engorged tonsil. He thought it was kind of cool. When Chico left, her husband, Paul Ryder (bass player of the English alt rock band Happy Mondays), turned to her and mouthed, "Cancer!" Angela rolled her eyes—Paul is a notorious hypochondriac. A virus had been snaking its way through the household, so it stood to reason that their youngest son was next in line.
Two weeks later, Angela spotted a lump protruding from the side of Chico's neck. It looked like a swollen gland, so they visited a nurse practitioner at the local CVS pharmacy. "You don't think it could be a tumor, do you?" Angela asked the nurse.
"Oh no."
"How can you be certain?"
"I've studied medicine. These antibiotics should do the trick . . ."
Five days later, the lump on Chico's neck had ballooned to the size of a bonbon, so they headed to the doctor, who prescribed a different antibiotic. But it's odd, he said, a throat infection doesn't typically appear on only one side of the throat—both sides are normally swollen. Let's run a test for mono.
"Good news!" the doctor's assistant said when she called in the results a few days later. "It's not mono!" But Angela was not relieved. Chico was now puking uncontrollably and his heart was racing. Something was very wrong. Next stop: a head and neck specialist who biopsied the tonsil for lymphoma.
When those tests came back negative the specialist was at a loss. We don't typically see tumors in the mouths of children, he said. People who smoke and drink, yes, but not in a child.
On December 20, Chico was still throwing up. He couldn't eat. Angela took him to another specialist, who took one look at the scan and called an oncologist stat. "Christ!" she said. "They biopsied the wrong tissue." There was a tumor hidden behind the tonsil, pushing it forward. The oncologist told Angela that the hidden tumor was so large it was constricting Chico's carotid artery, which was making his heart rate go haywire.
Eventually they identified the tumor as "rhabdo" (rhabdomyosarcoma), a malignancy of the soft tissue that affects just three hundred kids in the United States each year. It's so rare and a cure so unlikely to ever turn a profit that pharma companies have never developed a treatment for it. But there was no time to worry about such existential problems. The tumor was advancing so quickly that Chico's airway would be cut off in ten days. "We're starting chemo and radiation this afternoon," Angela was told.
It was her fiftieth birthday. She texted the news to her husband, rushed home, packed Chico's bag, canceled her party, and plunged forward into the dark.
After twenty-one days of chemotherapy, Chico's tumor shrank and his heart rate stabilized. But forty-three long weeks of chemo frazzled the nerve endings in his feet. Walking was so agonizing that he was confined to a wheelchair. Twenty-eight radiation treatments desiccated his salivary glands and left his mouth and gullet a rash of burning chancres. Swallowing was so excruciating that he was fed through a plastic feeding tube inserted into his stomach. His weight plunged almost in half, from 110 to 65 pounds. His white blood cells all but disappeared.
Angela was desperate to ease her son's pain, but the oncologist warned her that almost anything—herbs, supplements, even vitamins—could interfere with the treatment. Still, she couldn't just sit by and watch Chico suffer. A naturopath gave her glutamine to eliminate the mouth sores, and Marrow Plus, a blend of Chinese herbs, to stimulate white blood cell production, and after relentless lobbying, her oncologist agreed to try them. The glutamine healed his mouth and three days of Marrow Plus gave the white cells a lift from which they never fell. The oncologist was so impressed that he began mentioning both supplements to other patients.
The only treatment that didn't work was Marinol, the synthetic cannabis. Chico was relentlessly nauseated. When a home nurse recommended the real thing, Angela persuaded the oncologist to go along. But no irritating smoke, he insisted. Only edibles or vapor.
Angela had no experience with pot, so her first visit to a dispensary felt furtive and a little exciting, like sneaking into a sex shop. The workers laughed when she showed them the recommendation written on a proper prescription pad—"pot docs" in Los Angeles rarely submit anything so professional. The owner's mom had passed away from cancer so he was sympathetic and offered her a sample of every edible on the shelves. "See what he likes, then come back and get more," he said.
Confusingly, many of the packages weren't labeled for THC content, so at Angela's request the budtenders marked them for her: three stars for strong, two for medium, one for weak. Dosing in this manner was more than a little fraught, but in the end it didn't matter, because Chico couldn't hold them down anyway. Finally, a friend loaned them a Volcano vaporizer. Sucking on those giant vapor-filled bags provided her son with relief. "It was all completely baffling but I was going with the flow," recalls Angela.
The more Angela learned about cannabis as medicine, the more questions arose. She plowed through medical abstracts, but the language of chemistry was blindingly arcane and dull. Blogs were riddled with misspellings and typos, which didn't inspire confidence. The cannabis cancer "community" is also riven with internecine disagreement—true believers railed at Angela for "killing her son with chemo." The comments were hurtful, but she knew that the only thing that chemo killed was Chico's tumor. The side effects were rough but her son was alive.
On Facebook, Angela discovered cannakid celebrities like "Baby Sophie" and "Brave Mykayla," whose tumors shrank after using oil. At conferences, their parents take the stage to share their stories and beg the government to stop treating them as criminals, while their cannakids pose for photos with other sick babies. Angela was convinced that medical marijuana was worth a try, but she had no idea where to find oil to treat her son. None of these potent concentrates were available at her dispensary, so she turned to Facebook, where she learned that buying cannabis oil online was as tricky as trading penny stocks. Prices varied widely, as did quality.
One Facebook friend led Angela to a maker of good repute. The Ryders plunked down $3,300 for sixty grams, which arrived in three unlabeled plastic pots. The consistency was tarry, as it should be, but it reeked of alcohol, not the type you drink but the kind you keep under the sink. A slip of paper indicated that it had been tested at 80 percent THC—powerful stuff. She dipped a Tums into the oil and gave it to Chico. After a week he said two words she hadn't heard in six months: "I'm hungry." In the ensuing weeks, his appetite improved and things were looking up—until one member of her Facebook support group, Cannabis Oil Success Stories, raised an alarm. The oil should smell fragrant and herbaceous, he warned her, and insisted she get it tested pronto. She did, only to learn that the oil was just 58 percent THC, one quarter less potent than advertised, and had been extracted with isopropyl alcohol.
"Isopropyl is rubbing alcohol. Is that bad?" she asked the chemist at the lab.
"It's poison," he responded. "Especially if it isn't all cooked off, which this isn't."
"Shit."
"Oh, and instead of sixty grams you only got forty."
Angela's initial foray was not unusual. Internet scams are growing as the word of this mighty oil spreads. One site is selling cannabis paste with the word "cure" in its name, made from industrial hemp of an unknown origin, taking advantage of confusing nomenclature in an unregulated market.
"It's a huge rip-off," says Dr. Russo. "The cost is exorbitant and God knows what toxins are in there because they use what's left over from hemp processing in countries like China or Romania and they don't have the same laws about pesticide use that we have. It's super-concentrated, so you're super-concentrating those toxins too. I don't trust any of it and I don't think anyone else should, either."
So many unwitting people have been duped by false or substandard "hemp oils" that Rick Simpson released a 2014 video warning about a group of "hemp oil hucksters" falsely claiming to be led by his grandson. They were creating fake domain names and MoneyGram accounts to which worried patients would wire money and receive nothing in return.
Finding quality medications proved elusive until the television host Ricki Lake, who was at the time producing a documentary about medical marijuana, led Angela to a Bay Area collective called Aunt Zelda's.
The very name conjured a character out of _Tales of the City_ in Birkenstocks and a dirndl skirt stirring a cauldron of cannabis oil made from a recipe in the _Whole Earth Catalog_. But the owner, Mara Gordon, turned out to be more mad scientist than Anna Madrigal. Mara was a process engineer who had worked for Safeway and General Electric before a botched surgery and the twenty-six medications she was taking turned her into a chemical zombie. In 2011, a friend made her some magic brownies that eased her pain and brought her unexpected pleasures. Soon this fifty-something Jewish grandmother was devising her own recipes, blending flowers into her Aunt Zelda's carrot cake recipe (the large quantity of olive oil in carrot cake speeds cannabinoid uptake into the bloodstream) and sharing slices with other baby boomers whose bodies were falling apart.
It didn't take Mara long to see that the alternative-healing world of cannabis was ripe for reinvention. At a 2011 Hempcon conference, she surveyed heavy users about why they were smoking every day. The answers gave her pause. "This one had a football injury that never healed properly, that one was so painfully shy that he couldn't leave his house. So many people had medical issues but didn't know they were medical," she said. "They didn't want to be smoking all the time. They wanted their lives back." But all had the same question for her in return: "How do you make this oil?" So rather than delivering her prepared lecture, she told them to take out their pens and follow her instructions. "Like the adage says, 'Give a man a fish, you feed him for a day; teach him to fish and you feed him for life,'" she said.
Mara isn't warm and fuzzy. The most alternative aspect about her is that her career as a cannabis consultant makes her a healer in California and a criminal in most of the other United States. She has treated thousands of patients since 2010, and in Northern California, where cannabis oil is becoming an accepted adjunct to chemotherapy, more than a few oncologists refer patients to her.
Mara immediately switched up Chico's regimen, giving him CBD in the morning to lessen his mental fog and THC at night to get him to sleep. "Taking THC and CBD together for this illness is like having two accomplished cooks in the kitchen," she told me. "They get in each other's way." And then she made Angela toss the medicine made with isopropyl alcohol. "Why would anyone mix poison into this magic plant?" she asked.
Aunt Zelda's collective was nothing like the granola rustic village I had envisioned. It was far less exotic. The collective was housed in a condominium that backed onto a golf course in suburban Walnut Creek, about an hour north of Oakland, a sterile enclave of cul de sacs lined with minivans, straight out of the opening scenes of _Close Encounters of the Third Kind_.
On my first visit I found Mara and her husband, Stewart Smith, in their spotless galley kitchen decarboxylating (frying) a fragrant strain, aptly named Pepe LePeu, in organic coconut oil. The room smelled sweet and grassy, like a Thai restaurant in a hay field. Mara beams an infrared thermometer at the green mush, ensuring that it is heated to 219 degrees Fahrenheit, the ideal temperature to infuse the oil without degrading the cannabinoids, terpenoids, and flavonoids. Once the oil is bright green and the flowers are toasted brown, she announces that it is ready to be drained.
"How can you tell it's ready?" I ask.
"It's like matzoh balls. After a while you just sort of know when it's done."
Mara is part librarian, part compounding pharmacist, part strict disciplinarian, who discovered that she has a passion for treating cancer patients with cannabis products. At the time of my initial visits in 2013, Aunt Zelda's was treating a rash of "glios," many of them children with glioblastoma, a devastating brain cancer that oncologists call "the Terminator." Glios on chemotherapy typically live for fifteen months; left untreated they're gone in a quarter of that time. Mara has been treating some glios with cannabis in conjunction with chemo for an odds-defying three years. Dr. Nicholas Butowski, a neuro-oncologist at the University of California, San Francisco, one of the physicians who refers patients to Aunt Zelda's, suspects that the oil somehow interferes with the way tumor cells divide and proliferate. What Mara does understand is that there are clues within the data that haven't been assessed, and therein lays her opportunity. She is building a database to match the compounds within the plant to the diseases they treat, so that people who don't have the luxury of waiting ten or twenty years for clinical trials will have some evidence on which to base their treatment decisions. Some people have criticized Mara and others like her as being little more than well-meaning amateurs, but when asked what qualifies her to dispense these meds, she throws her arms up in exasperation: "Who the hell else is going to do it?"
A reasonable question to which there is no reply.
Every day Mara and Stewart welcome a parade of neighbors, most of whom arrive in bright track suits, wide-brim visors, and those oversize plastic sunglasses favored by the Bengay brigade and rap stars. Today the visitors have come to inspect a newly arrived batch of "Cookies," the Girl Scout Cookies strain. There's also much buzz about AC/DC, one of the newer "highless" CBD strains that promises to ameliorate the aches and common ailments that make mortality a hot topic among this crowd. The sight of grandmas sniffing weed is deliciously incongruous, but in retrospect I'm not sure why it struck me as odd. A plant medicine that is a balm for aging and bestows a few moments of happiness—what's not to like?
One visitor, Jim, belongs to the Medical Marijuana Club at the Rossmoor senior community center, home to ten thousand retirees down the road. The club's first meeting in 2012 attracted just five members; it's now up to fifty, but Jim still can't understand why the room isn't packed.
"Last month a couple wandered into a meeting and asked, 'Is this the Church of Latter-Day Saints?' We said, 'Boy, are you in the wrong place. This is the medical marijuana club.'"
"Oh, we'd like to hear about that," they said, and even though Mormons are euphoriant averse, they sat through the entire meeting, rapt.
Jim and his wife, Mary, both septuagenarians, rely on Mara and Stewart for guidance. Jim doesn't trust Internet sites, and his allopathic doctors—most of whom have been trained to see marijuana as a use disorder—have little idea of how or what it heals. Like many suburbanites of a certain age, Jim doesn't fancy himself a cutting-edge kind of guy, yet every so often he realizes he is an unintentional pioneer.
When he went to the emergency room with a burst diverticulum, the intake nurse asked him if he used any drugs.
"Medical marijuana," he said.
"Smoke or vapor?" she asked, referring to her computerized checklist. He was impressed that a hospital would ask that question. After his treatment and upon release, he was given Marinol. "They weren't worth a damn, but at least the hospital was progressive enough to offer them. If I knew then what I know now I'd have said, 'These are fine, but Cookies are better.'"
In 2014, Mara and Stewart sold the condo and moved their operation north to Bodega Bay, the moody waterfront town where Alfred Hitchcock filmed _The Birds_. They live on Bay Hill Road, the same road that Tippi Hedren's character, Melanie Daniels, speeds along in her Aston Martin convertible in the movie's opening scenes. Stewart has converted a garage into a production facility and has taken the reins as master oil maker, and Mara serves as patient consultant. Most of her days are spent talking: to growers across the state in search of promising new strains, to researchers around the world (the United Kingdom, Spain, and the Czech Republic) in search of the latest clues and treatment protocols, and to testing labs to verify the cannabinoid contents of her preparations. She occasionally trains nurses to treat the endocannabinoid system and offers enterprising patients tutorials in organic oil making. But mostly she guides them toward using the stuff successfully themselves.
Mara has some neat tricks to enhance the efficiency and soften the side effects of cannabis oils. Eating certain types of mangos before taking THC quickens the uptake into the brain—that's an old bit of hippie lore that science has vindicated. Citicoline, a supplement that's sold in health food stores, fortifies memory and abets the brain's "attentional processing." "It's like plugging in the router when the memory Wi-Fi goes off," says Mara. "I give it to some patients [but not cancer patients, as there are some counterindications] who suddenly stop finishing sentences when they start on the oil."
It's not easy interviewing Mara without interruption. Patients call constantly, inquiring about dosing, side effects, and storage, and today she's fielding all their questions. On occasion she lets me listen in on a few consultations (with the patients' consent, of course).
Jenny is a grandmother with cervical spinal syndrome, which makes her shoulder feel as if it is being crushed in a hot vise. For seven years she's been on a brain-muddling regimen of methadone and Neurontin, a pain and antiseizure medicine, and she wants off.* Mara has created a concentrate of high-CBD Cannatonic to lessen her inflammation and lessen the pain. But Jenny, seventy-three, needs some answers.
Jenny: "Is Cannatonic an indica or sativa?"
Mara: " 'Indica' and 'sativa' are antiquated terms—sort of like 'Democrat' and 'Republican.' They don't mean that much anymore. [That's true. Though the terms are used around the world as a guide to effects, years of crossbreeding have rendered the terms meaningless. More accurate descriptions are "narrow leaf" and "round leaf" varieties.] What it has is terpenes—pharmaceutical-grade essential oils that are probably more responsible for directing the high or the effectiveness of the treatment."
Jenny: "I don't want to be stoned. I took a couple puffs off my son's vaporizer a few years ago, and [she begins to cry] . . . I am no longer myself . . . I'm sorry . . . I don't want to get emotional . . . I'm just in so much pain . . ."
Mara gently reminds her that the drugs she's taking can create confusion and then goes into a convoluted explanation of cannabinoids and receptors. Why, I ask, doesn't she simplify the science for easy consumption?
"Sometimes the elderly like to do research to make it as complicated as possible, so they don't have to admit they're using marijuana," she tells me.
Next up is a woman from Pennsylvania whose five-year-old daughter has a rare genetic form of muscular dystrophy. She weighs thirty-nine pounds. The story is heartbreaking, but the conversation revolves around the mechanics of treatment, including how to best store the medicine. "Treat it like a fine olive oil. Sunlight and heat are its enemies," Mara counsels.
The obvious question is why Mara doesn't save time and just include instructions in the packages she sends out. "By law, we can only mail the meds within California. This couple has family in the state but how the meds travel from there . . . we don't know [sly smile]. These people don't have time to wait for the laws to catch up, so we send instructions separately as a precaution, just in case the package gets waylaid . . ."
By afternoon, Stewart comes in with a few syringes of gooey Pineapple Kush oil—the rewards of his day's work. When he's not looking I surreptitiously squeeze two quinoa seed–size droplets onto my finger and rub them across my gums. Its concentrated grassy essence briefly parches my throat. When I tell Mara what I've done her eyebrows raise and she insists I spend the night. After much back and forth, I climb into my car to drive back to San Francisco. As I pull away I hear her scream, "If it's too much for you, come back! You can always sleep in the spare bed."
That droplet was about one hundred times more powerful than a joint. _I can handle this_ , I think, and for an hour I do—the only effect is an unquenchable thirst. But by the time I hit the Golden Gate Bridge, every mirror, every engine, every car in front and behind and to the side of me, not to mention the water, the sky, the lines on the pavement, is vying for my attention. To pay the toll I have to dial a number on my phone, which requires a Herculean feat of multitasking focus. The only solution is to silence the radio, hug the right lane, and crawl home like a grandma behind the wheel. The lesson? Don't toy with concentrated cannabis oil. It is powerful stuff that deserves a lot more respect than "just pot."
When the Ryders returned to England in the summer of 2014, Angela realized for the first time that there was no legal way for her to get her son's medicine into the country.
Fear of arrest led her to a network of underground makers, primarily in Scandinavia and Holland, who distribute oils to patients in need. One Dutchman, Nol van Schaik, leads a Facebook group called "Adopt a Patient," a service like Tinder that matches people in need with an excess of what the Dutch call "MediWeed."* The site accepts no ads or personal posts and offers no treatment advice, and it is filled with heartbreaking pleas from ill people begging to be adopted.
Even if you succeed in connecting with a maker, you'll soon face the problem of mailing the oils across borders. One mom in Britain ordered three shipments from abroad. The first slipped through customs but the second package arrived empty with an official letter warning her that she'd be prosecuted next time if caught. A few days later the third shipment mysteriously arrived at her home. The woman thought that some low-level official somehow understood the gravity of what was at stake and made an allowance.
But for every kindhearted soul who bends the law to help the sick, there are more dubious players who may be sneaking less pure formulations between the regulatory cracks. And if their medications turn out to be tainted, or fail to deliver the dosages they claim, the results can be, at the very least, sickening.
One company had been producing an oil made from industrially farmed hemp that may have come from China or another country with loose environmental regulations. The problems with industrial hemp are twofold: (1) Hemp is not cannabis, which means it has less of the healing terpenes, flavonoids, and powerful concentrations of cannabinoids. (2) Hemp extracts metals, pesticide solvents, and even nuclear toxins out of the earth to regenerate the soil; it was planted near and around Chernobyl after the facility's deadly meltdown in 1986. These days it is planted around factories that manufacture computer parts, in order to absorb the effluent containing lead, molybdenum, cadmium, nickel, selenium, and other noxious heavy metals.
An alarm was sounded in the medical cannabis community when one distraught mother posted in a Facebook group that her twenty-one-month-old epileptic daughter was rushed to a hospital with severe diarrhea after ingesting "hemp oil" of an unknown origin. They believed it was produced by the aforementioned company. When the oil was sent to a Colorado lab, the resulting test appeared to confirm that it was tainted with some of the same heavy metals listed above.
Just days later, however, the lab repudiated its own findings. A technician had made an error, they said, and a preliminary version of the results had been released accidentally. Although the lab concluded the oil was "safe," the retraction raised eyebrows and concern in the medical cannabis community.
Months later, an executive from this hemp oil company sent samples of its products to Brandon Krenzler for his eight-year-old daughter, the aforementioned cannakid, Brave Mykayla. Thank you very much, Krenzler replied, but Mykayla—who had been successfully treated for leukemia—was not responsive to CBD oils; THC concentrates in combination with chemo worked better for her. In spite of this, the company honcho showed up at the Krenzlers' Oregon home and presented them with $2,400 worth of oil. He asked if Krenzler would consider selling it to other families with sick children, but Krenzler declined. He also promised Krenzler a generous cut if he would allow them to rebrand their product "Brave Mykayla Oil."
Krenzler again demurred, but accepted some of the oil as a gift, which he tried on Mykala and himself. Both were beset by crippling constipation, cramping, and nausea. "Maybe I dosed it wrong," Krenzler thought, and asked two other parents with sick children to try it. One mother was forced to rush her epileptic son to the emergency room, where he was diagnosed with impacted bowel. His diet hadn't changed, so she blamed the oil. The other parent said it caused her daughter to vomit and did nothing to help her seizures.
Krenzler called the company, demanding they provide testing records, import records, and production records, "so we could prove that their product was not making us sick."
Krenzler told me his pleas went unheeded.
Worried about impurities and the composition of the oils, he sent unopened samples to a local lab in Portland to verify the accuracy of the cannabinoid content listed on the label. The results, according to Krenzler, showed the oil contained hundreds of times the .03 percent THC allowed by US law, which made it illegal to ship across state lines. When Krenzler posted the results online to warn families about the risk of federal prosecution, the lab informed him that it would no longer support its own findings. "They told me they had been threatened with legal action. At one point they even denied they had tested the product, even though I was holding their report in my hand," he says.
Is it a coincidence that two labs in different states mistakenly came up with damning results? Yes, just as it's possible that the threat of a crushing lawsuit prompted their retractions.
This emerging world of industrially produced hemp oil smacks of another oil—snake oil—that was sold by grifters until the Food and Drugs Act of 1906 regulated medicines and their formulas. Prior to that, doctors sold their own homemade medicines to patients without being subject to standards or quality controls. The Food and Drugs Act was aimed at stopping the abuses of charlatans who'd swoop into a town and make audacious claims before audiences that were planted with shills proclaiming the miraculous benefits of these snake oils. Once people bought their elixirs the peddlers would move on, never to be heard from again. And those gullible people? Well, they're still around today, congregating on the Internet, defenseless because the government cannot regulate a market it deems illegal.
Meanwhile, Chico Ryder is in remission. As of this writing, he has gained twelve pounds, is doing physical therapy to get back on his feet, and is attending school three days a week. He's still taking Aunt Zelda's oil.
## ___Chapter 8_
## BUDTENDERS AND SINSEMILLIERS: INSIDE THE DISPENSARY
_Denver, Colorado_
In February 2014, one month after recreational cannabis became legal in Colorado, Governor John Hickenlooper announced a projected $60 million tax windfall. A few months later at a Democratic Governors Association dinner in Washington, DC, Hickenlooper warned his fellow lawmakers of the "risks" of moving too quickly to legalize. "It's not a panacea," Hickenlooper said in an interview. "It's not going to solve your revenue problems." No one paid him any mind. In fact, the state ended the year with a $76 million boost from the combined tax and licensing revenue of cannabis, more than double that of alcohol.
Money is only one measure of the changes that have come quickly to what is now aptly termed "the industry." Adam Dunn still runs HoodLamb, but he is also Professor Dunn, teaching cultivation, infusion, and hemp at Clover Leaf University, "the nation's only cannabis university that is approved, regulated, and licensed by the Colorado Department of Education's Private Occupational School Board." Derek Cumings, the hash oil maker, has been made a principal in Incredibles, which is pumping out forty thousand Mile High bars a month in a dozen flavors. Sales are still being impeded by lack of cannabis oil, so Derek is building an indoor grow and extraction facility to keep production flowing. Regulation has pushed Incredibles and many other mom-and-pop start-ups to behave more like responsible businesses by measuring and labeling the THC content of their products. Until then, many had been manufacturing products with no information whatsoever—a mix of negligence, inexperience, and a lack of state-issued guidelines.
Dixie Elixir's business had also quadrupled. In 2010, cannabis-infused edibles and drinkables represented less than 10 percent of Dixie's sales. By 2014, this segment had climbed to 50 percent of their market. Tripp Keber, Dixie's CEO, was busted for possessing a small amount of cannabis in Alabama. The cops mistook the cigar he was carrying in his hand for a blunt and pulled him out of line as he entered a music festival in Gulf Shores. He broke open the cigar to prove his innocence but _oops!_ they came across a few milligrams of cannabis concentrate in the form of mints in his pocket. I called Tripp to remind him that he denied using in our initial meeting. He laughed. The bust bought him some cannabis credibility, which he realized while taking a business meeting with Willie Nelson after a concert in Newark, New Jersey. "Willie suffered and has been penalized because he's been arrested a half dozen times. That we now have in common," he said, with not a trace of irony.
The froth produced in legal cities such as Denver, Seattle, and Vancouver is just the beginning. In the vastness of the Internet, where laws have no geographical jurisdiction, it's clear that legal weed is not only here to stay but is driving all manner of new enterprises, from the electronic dab rigs to slim stash cases that hold a vape pen, an extra oil cartridge, a USB charger, plus a lighter and rolling papers (why has it taken so long to invent such a necessary accessory?). Big cultural transformations are happening now too. MassRoots.com, founded in 2013, has over 775,000 users and serves as a Facebook-like network for cannabists around the world. Ganja.girls is an Instagram photo stream of young women in scant panties and knee-high "weedsocks" sucking on lasciviously large bongs. OK, these images are not subtle, but they're not pornographic, either—the vibe is more _Girls_ than _Girls Gone Wild_. Depending on your perspective, ganja.girls is either another example of the same-old male-dominated exploitation of women—or a postfeminist embrace of a substance that is less aggressive than alcohol and more tempered by tenderness. In either case, it's another signal that the tsunami of change is unstoppable.
It's the dispensary, however, that is releasing cannabis from the cultural aspic in which it has been preserved for forty years. Whether you indulge or not, the dispensary experience is not to be missed. On your first visit, you'll find yourself in a state of giddy confusion as you take in the dizzying array of edibles, drinkables, topicals, concentrates, infused products, and perfectly manicured buds on offer. Then comes excitement once the budtender, if properly trained, guides you to products that will deliver the high you desire. In higher-end establishments, each strain of flowers will be labeled with cannabinoid content, which will either mean nothing to you or, if you're well versed, provide clues about the arc of your high. The days of consumers buying whatever some guy has in his backpack are coming to a close, and not a minute too soon.
If you're Sicilian American, as I am, and saddled with a low anger threshold, or if you are even the slightest bit political, the initial exhilaration will be followed by fury. You'll understand how the citizens of East Berlin must have felt after the Wall fell and they flooded into an electronics store in the West: Total wonder and then rage about having been kept in the dark for no comprehensible reason. In the dispensary you too will inevitably ask, "What was all that prohibition fuss about?" Why has the United States spent trillions of dollars trying to annihilate this plant, suppressing all the technology, ingenuity, and science that surrounds it?
But stick with the giddiness—it's much more enjoyable.
Dispensaries in flashier cities have a more tricked-out sense of style. San Francisco has Sparc; with its modernist, minimal lines, it is a study in Scandinavian restraint. Its free extract tastings draw enthusiastic crowds that make the place feel more like a happy hour than a store. The Apothecarium sits at the other end of the design spectrum. Flock wallpaper, marble countertops, fresh-cut flowers, and an oversize chandelier create a chic-yet-olde-world-drugstore-meets-saloon ambience. When you're handed the leather-bound menu that lists selections, the experience takes another turn toward the elegant. There are no lines and no crowds, so the purchasing experience is unrushed and relaxed.
Denver Relief, where I've volunteered to intern for a few days, reflects the modest handsomeness of the city itself. It's a small operation that purveys quality cannabis grown in its own indoor facility—Colorado law requires every dispensary to grow 75 percent of its own weed so that law enforcement can more easily track and prevent it from being "diverted" into the black market. More like a private club than a full-service health center, Denver Relief keeps its quality and prices high and patient count low (a modest three thousand) to ensure it has enough top-shelf bud to go around. Recreational sales came online a month before my internship commenced, but the owners are holding back on selling recreational cannabis to ensure their medical patients are served first.
The building itself has all the flash of a small bank branch. It's a squat brick structure nestled between a hair salon and an urgent care center on an up-and-coming block along Denver's Green Mile. By city ordinance, dispensaries must be one thousand feet away from a school, candy store, or other area trafficked by children. There are no cannabis leaves or Cheech and Chong photos in sight, no hawkers dressed in joint costumes to lure customers indoors. Even its logo, a sterile green cross, is subdued and serious.
"Our goals when we started were to be good neighbors, to progress the industry, and to have excellent product. Everything else fell into place," Kayvan Khalatbari, one of the cofounders, tells me. "We did all these things we didn't have to do to be a good face for the industry. We put ourselves on the books every chance we got. We started a dialogue with the city. Everyone else was taking advantage of loose laws. We were saying, 'Let's act right now as if we are regulated and see where that takes us.' People trusted us."
As did I, which is why I wanted to work behind their counters. Unlike meetings I attended in Amsterdam, where conversations about sensitive topics flipped into Dutch, at Denver Relief I was invited to ask questions and afforded free access to all aspects of the operation. "We have nothing to hide," Ean Seeb, Kayvan's business partner, assured me. The only caveat was that I stay within Colorado law, which meant that as a nonresident I could not touch the plant, nor could I work directly with patients. I was assigned to trail the head budtender, Scott Yoss, as he made his rounds between the dispensary and the indoor grow, where he moonlighted as a cultivator.
There are worse ways to make a living.
In dispensaries geared to pushing product, your first interaction with a budtender might go something like this:
"What do you have today?"
"Oh man, you gotta try the____."
"Is it good?"
"It's fire, man."
"Oh yeah?"
"Yeah, it really fucks you up."
Denver Relief operates on another level.
Scott is behind the counter counseling Petra, a young woman who uses pot to blunt the pain of her menstrual cramps, but who also appreciates the smooth high of carefully grown, well flushed, neatly trimmed bud. Scott is presiding over a "side by side" of two hybrid indicas, counseling Petra to let her own nose guide her to the best strain for her pain. While his method is of dubious scientific merit, his enthusiasm is infectious, another indication that I wasn't in a Dutch coffee shop anymore.
"This is our eighty-day Bio-Diesel," Scott explains. "Last year _High Times_ voted it one of earth's strongest strains. It has ten days more on the vine, which also creates a longer experience in the system. My first joint of this eighty-day beauty and I was high for four hours. The extra ten days changes the plant's chemistry. Even the flavor tastes more medicinal."
Scott, professorially handsome in his designer frames and trimmed beard, nabs a thumb-size bud from a glass Mason jar with his forceps and offers it up for appraisal. "The extra time also makes the bud open more." He squeezes the tongs to burst the oil sacs and places the sappy sample a half-inch below Petra's nostril.
"I get a whiff of asphalt plus a Band-Aid plastic strip on the inhale," he says. Petra nods vaguely, a little befuddled and maybe a little impressed. Even though she's a resident of Boulder, a onetime hippie outpost that bills itself today as "the city nestled between the mountains and reality," she's never heard a spiel like this.
"The Q3 doesn't show as well," he continues, popping the seal on another jar. "It's got a purple cast, but the nose is mild. The flavor is citrusy, and the high? It reminds me of sunshine." She whiffs and a discussion ensues about storing pot to prevent it from drying out. Scott recommends reviving dry buds by placing them in a jar covered by a damp cheesecloth secured with rubber bands. "One day should do the trick."*
The final strain is Durban Poison, which Scott describes as "smelling like the bottom of my grandmother's purse." Petra takes a deep belly breath.
"It smells less musty and more minty to me."
"I know what you mean," Scott reconsiders with a smile. "My grandmother always kept a roll of Certs in her purse."
Petra opts for Bio-Diesel, an "elite" tier, which sells for $70 a quarter ounce ("premium" tier costs $60 a quarter ounce and "special" is $50 a quarter ounce). Wielding his forceps—it is illegal to touch the meds—Scott carefully weighs out the buds on a digital scale. Protocol also discourages pouring buds out of jars, as sudden jolts can dislodge trichomes. He tips the buds into a tamper-proof, child-resistant opaque bag—"Some of our competitors charge customers three dollars for the bag, that's pretty crass"—then slides that into another paper bag as required by law, and escorts her out the door.
"Great sales job," I remark once he's back.
He shrugs. "It sells itself."
At thirty-six, Scott is the city's first (albeit self-anointed) sinsemillier, a role he takes as seriously as does a sommelier in any top-drawer restaurant. Since high school, Scott has honored the plant with the same respect that his brother, a sommelier and wine instructor with the International Wine Guild, affords the grape. The difference is that until recently Scott's passions made him a criminal while his brother's elevated him to a connoisseur.
Presiding over the counter at Denver Relief is more than a job, he says—it's a privilege. His twenty-year relationship with cannabis has helped him grapple with a depression that ran so deep that "down was up to me," and tending to the buds has provided him with unforeseen career security. "When I go to work, I don't worry about being raided, because these guys have crossed all t's and dotted all i's six steps in advance," he says. For forty-three hours of work a week, Scott earns $450, plus health benefits and a 50 percent discount on all meds. The law allows him to purchase two ounces a day. Denver Relief offers him a 75 percent discount on two ounces a month.
Like wine, beer, and coffee, the language of cannabis connoisseurship can sound riper than a moldy cheese—we've all endured fussy baristas intoning about the "wine and earth notes" in those "single-estate shade-grown beans" cultivated on some finca in the mountains of Nicaragua. On the other hand, Scott's discourse is expanding a lexicon that has been held back by eighty years of prohibition. I don't agree with or even understand all of his appraisals, but no matter—establishing a language of appreciation beyond stoner- and science-speak is an advance whose time has come.
Before manning the counter, all new budtenders at Denver Relief must train for a week, learning the law, the house rules, and what strains best treat the more common medical conditions. Newbies must also secure a $250 "support badge," which the state requires of any worker in a dispensary, grow, or packing facility, and submit to a federal background check, which includes fingerprinting and a criminal record review. Outstanding bills or warrants or past crimes eliminate you from the running.*
Denver Relief employs forty full-time workers, most of whom are CEUs: college-educated unemployeds. Their average age is thirty-one, one indication that dispensary work is usurping waiting tables as a "bridge" profession. Statistics bear this out. When Colorado's first recreational marijuana shops opened in January 2014, the state had 6,593 licensed industry workers. Five months later, that figure rose to 9,641, about the same number of Coloradans employed in law enforcement. At a marijuana-related job fair in March 2014, the crowd was so large that applicants stood in line for three hours. By the day's end, organizers were turning people away. "With this type of industry and the money that's coming in, this is the place to be right now," said one job seeker who waited for two hours, résumé in hand.
It has taken Denver Relief six years of bootstrapping to establish its good name. The business launched in 2008 with a half pound of pot, $4,000, and a memorable phone number: 303-420-MEDS. Ean was a real estate broker who, in his spare time, had been connecting patients with growers seeking to increase their patient counts. Kayvan was a co-owner of a restaurant called Sexy Pizza; Adam, their third partner, was a grower. All three knew that their current career paths were leading nowhere. Ean was bored. Kayvan had a degree in architectural engineering but found working in a firm soul-withering. He was thirty pounds overweight and surrounded by colleagues who spent their days complaining about wasting their lives. The one thing they didn't know at the time was each other—they had all met one week prior to launching the company—but they shared a vision of owning a legitimate cannabis business that would never be used as B-roll on Fox News.
Those were heady times, rich with possibilities and fraught with unknowns. Colorado had decriminalized cannabis before creating any laws to regulate it, which meant that businesses were operating without guidance as to what was legal or criminal. On January 1, 2009, the three men gathered at a bar and assessed their possibilities.
"We had no money so we couldn't just sink $150K into a dispensary," Kayvan tells me. At thirty, with his radio-smooth voice, handsome Persian features, and deep intelligence, Kayvan is among the most eligible bachelors in the industry. "I had used all my IRA and 401(k) to start Sexy Pizza and I was renting out my house and camping in a tent in the backyard. I was flat out of money, but my credit was still good . . . it was ruined by Denver Relief eventually, but that's another story."
They secured a telephone number, Ean designed a logo in Microsoft Paint, and they placed a three-line advertisement amid the sex ads on the back page of the local alternative weekly. It simply said "303 420 Meds . . . Denver Relief. We deliver."
Thus was established Denver's first door-to-door cannabis delivery service.
Deliveries began in the sweltering summer of 2009, when temperatures averaged 105 degrees. Kayvan took phone orders in his beat-up truck with no AC and with the windows rolled up so he could hear the customers. Since the law was as yet unwritten, they established their own rules, the first being that all initial patient contact should occur in public, at a Starbucks or a gas station, to preclude trouble.
Adam was the first (and last) of the three to break protocol when an unknown customer gave him a sob story about being wheelchair bound and unable to leave the house. When Adam rolled up to his driveway the guy tipped himself into the front seat and pulled a gun, hijacking the car along with patient files, cash, a credit card reader, and product.
Adam eventually got back the car, but the cash and cannabis were gone forever. So was his laxity about rules. The first month they earned $10,000; by month four they were pulling $50,000. They paid taxes (the IRS categorized their business as "wholesale, non dairy") and within a year, they signed a lease on the dispensary.
The design of Denver Relief is free of flourishes, and security was built into every aspect of the building. The walls separating patients from the inner offices are webbed with Kevlar to block a stray bullet, just in case. The roof is wrapped in industrial-gauge barbed wire to prevent thefts. There are panic buttons beneath registers. Steel doors separate rooms, windows are made with bulletproof glass, and surveillance cameras record every transaction. Only a small amount of product is kept on premises, and when not on display it is stored in a large safe within a locked room. A wooden ceiling hides the massive airflow ducts, while rows of Ona Gel, a Canadian room freshener that scents the air with "Fresh Linen," line the shelves. "We cut the stink to be nice to our neighbors," one manager, Mike Davis, explained to me.
From its start, in July 2010, Denver Relief's cannabis was twice the price of other dispensaries', but it was guaranteed free of pesticides, mold, or mildew, and powerful. One strain is raised entirely under wide-spectrum LED lamps that promise to conserve energy and increase yield. "Lost crossed" strains are older varieties that have been crossbred with newer strains to increase hardiness, potency, or medicinal qualities, similar to the way French grape varieties were hybridized to match the growing conditions of the New World. Once Denver Relief installs greenhouses in the parking lot behind its warehouse, "sun grown" flowers will join its top-shelf offerings.
"People are starting to understand the contrast between great and average marijuana," says Kayvan. "It's similar to beer. Ten years ago, craft beer was just starting to gain popularity, but now the microbrew market is taking up more room. People have tasted good beer and they're willing to pay more for it. In our business people are building massive grows to increase efficiency and lower the price, but you can't grow connoisseur quality in that environment. They'll be Coors. To grow great marijuana you have to grow small batch. That's why you'll find the finest cannabis in the basements of certain growers scattered around the country. In the future, people will build small rooms that have ideal conditions for certain strains." Sort of like _reservas privadas_.
There's one additional feature in Denver Relief that stands it apart: a donation box. Kayvan mentors two foster kids and matches every dollar patients contribute to their educations from his own pocket. He also sits on the board of the Colorado Symphony Orchestra, which, when I visited, was planning a controversial fund-raiser sponsored by local cannabis industries in support of a program, "The High Note Series." Ean donates time to the Denver chapter of the Jewish Anti-Defamation League and occasionally hosts a lunchtime lecture series. One recent topic was "Is Medical Marijuana Kosher?" ("Is the Pope Catholic?" was Ean's answer.) This is not cynical do-gooderism. Both believe that philanthropy is essential to enlarging the foundation of compassion that the medical cannabis movement was built on.
Future dispensary owners take note.
Scott Yoss got serious about expanding his cannabis vocabulary when his older brother, Matt, prodded him to put words—"tarry," "grassy," "fruity," "fuelly"—to certain smells. An understanding of the grape has deepened Scott's admiration of the bud; it has also attuned him to the finer points of presentation. Just as the base of a wine bottle has a notch that allows a server to show the customer a label when the wine is poured, Scott grips open jars from the bottom to give patients full olfactory and visual appreciation of their meds.
Scott's next patient is Nancy. She presents her ID and state-issued "Red Card" at the intake window and her patient record pops up on Scott's screen. It includes her age (forty-four), condition (insomnia and anxiety), and past purchases.
Scott greets Nancy and explains the dispensary's different promotions: "Smokeless Mondays" entitle her to 10 percent off vaporizing accessories and edibles. Tuesdays and Sundays are "heavy bag" days, which include 4.2 grams of flowers rather than the standard 3.5 grams. On "wax weekends," patients get 50 percent off their first gram of hash. Colorado's exacting laws even prescribe the way that specials can be offered. "I can say, 'Buy six for the price of five' but not, 'Buy five and get one free,'" Scott tells me.
In the dispensing area, Nancy sees jars of indica lining the shelves on the left, sativas on the right, and a small selection of edibles, drinkables, topicals, vaporizers, transdermal patches, candies, and cannabis-covered lime chili peanuts hanging in the center.
Nancy is a self-employed nurse who has steered clear of pot for the last twenty years. A few weeks ago while sipping a latte at a cafe and debating whether to take the Xanax her doctor prescribed for the anxiety that keeps her awake at night, she logged on to Leafly.com, a sort of Yelp for cannabis, and read a customer-generated review claiming that Denver Relief had "some of the best bud in the world." Leafly also offered her "nug porn" (insanely close-up photos of flowers) and strain reviews, while her GPS informed her that she was just steps away.
This is her second time in the dispensary and she has come loaded with questions. Now that she has finally sorted out the difference between a sativa and an indica, she's noticed that they don't always work as advertised. The indica she bought to help her sleep made her mind spin instead. It's too bad she can't remember the name of that strain.
"No problem," Scott tells her. He checks her last purchase and guides her toward a Ghost Train Haze. "It's larfy, but it's some of the stoniest marijuana I've smoked."
_"_ _'Larfy'?"_
"Lacking Any Real Flower. Or as some of the kids call it, Little Raggedy Ass Fucker. It has a beautiful flavor, like pineapples, and it has true medicinal qualities. It's a lesson to never judge a bud by its structure. She may be an ugly girl, but she's a great kisser."
And what about weed candy? Nancy wants to know. One friend told her that five milligrams will make her snooze like a baby.
Eating pot is like taking another drug, Scott explains, which is true but causes confusion, especially among older patients. He doesn't go into specifics about the way THC, when eaten, is processed by the liver and turned into another metabolite, Delta-11-THC, which causes a different effect on the mind and body. But he does inform Nancy that most edibles (1) take one and a half to two hours to kick in, (2) have effects that last four to eight hours depending on dose, and (3) can knock you on your ass if you take too much. He advises her to start small (three to five milligrams) on a full stomach and patiently observe the effects. She can always increase by two milligrams a day until she finds a suitable amount. This is called self-titrating.
"We also have these OMG Medicated Drinks, which enable cannabinoids to get into the system fast because they're absorbed immediately into the bloodstream rather than first routing through the stomach. One bottle hits in a record fourteen minutes and lasts three hours. If I drink a bottle and eat a fifty-milligram edible I will hallucinate."
Nancy looks confused.
"Like many drugs, cannabis is a medical substance that can be exploited as recreation," he offers.
Scott also points out the transdermal patches by Mary's Medicinals. They come in THC, CBD, 1:1 ratios, and other assorted "flavors." Scott has tried both the 1:1 THC-CBD combo and the "sativa" formulations and was impressed with how "buzzy" they were—whether this description is nuanced enough for a former nurse is another topic. "The physical patch itself is made by Dow Chemicals, so it's designed to help the cannabis absorb into the skin quickly, in about twenty minutes," he reports. Nancy is intrigued (as am I) with the idea of mixing and matching "delivery systems," but ultimately decides to stick with something she can "smoke at ten p.m. and get knocked out."
"What do you like about coming into a dispensary?" I ask Nancy as Scott packages her selections.
"I haven't smoked pot in years and before it was like, you buy an ounce in the park and you had no idea of what you were getting," she says without hesitation. "Now it's more scientific. I can see what I'm buying and I love the education I'm getting.
"Two, I don't feel like a criminal. I'm not! Three, Xanax is the only thing my doctor has to offer for anxiety and, as a recovering alcoholic, I don't want to take pills that might be addictive."
She pauses for a moment. "And seeing how normal this is has made me question . . . When I read things like, 'The brain doesn't stop growing until you're twenty-five,' well, if that's true, maybe we should be talking about changing the liquor laws first."
The dispensary is the cannabis classroom of the post-prohibition era.
Nancy's purchases—one hash oil cartridge for her O.penVape pen plus her flowers—come to $120. Since her bill tops $100, the dispensary covers the $2 debit card fee. Scott bags her goods, then escorts her back into the middle area.
It's an elegant way of personally bidding each patient adieu, but it also ensures that no one removes the medical ID sticker and patient number on the premises, which would violate the law. "Getting in and out of the dispensary is like a pilot getting a series of clearances to take off or land," notes Scott. "Here, you need the Red Card, government ID, and patient ID to enter. If you remove the labels and attempt to resell it once you've left, it's just like you're selling prescription drugs, and you're a criminal."
One afternoon Scott and I gather in the backyard of the Arts and Crafts home that his brother Matt shares with his wife, Patty. At my request Scott has prepared a "flight" of six strains for us to sample and discuss. Describing cannabis as "a potent piece of medicine" is as clumsy as "killer bud" is vacant. I'm curious to see if we can arrive at a consensus about the flavors of the different strains before getting so wasted we can't speak. A lot of people would consider this exercise fussy and adding an unnecessary complication to something as simple as enjoying well-grown weed, but I believe that the more precisely the vaporized resins can be articulated, the more accurately we'll be able to discuss their effects on the tongue, body, and mind.
When Matt kicks off a wine-tasting class, he brings in thirty-three stereoisomers (liquid scent molecules) and asks students to associate each with a word. "Saying the word creates a neural pathway in the brain and improves your ability to categorize and identify other smells that are similar but not exactly the same," he tells me. We'll see.
First up: Chem Dawg. Scott slides it out of its plastic joint holder (another simple yet long-overdue invention that enables joints to be carried without being crushed and thus prevents them from turning pockets into ashtrays), and sparks it up.
Matt is instantly struck by the effect, which is stronger than the flavor, and hesitantly takes a second hit. "I think it's a lot of cucumber."
I've never heard of any cannabis described as cucumber and I say so.
"In wine we say that if you think that that glass of burgundy smells like burned shrimp shells, goddamn it, it smells like burned shrimp shells," says Matt with a smile. "Everyone has an individual relationship to smell and taste."
"Well, I think this tastes earthy, like fresh mud after the rain," I offer. Patty is uncertain, so rather than struggling to find middle ground between dirt and cukes, we move on to the next strain, Lemon Diesel, the name of which we all agree, fits the citrusy taste.
"It's like Lemon Pine Sol," says Patti. "The previous one was more like pencil shavings."
"Yes!" agrees Scott. "Pencil shavings and cardboard."
The third strain, Bio-Diesel, causes Matt to pronounce, "Cinnamon, maybe with some bark or sawdust."
"That sourness and spice, that's the diesel," adds Scott. "It's fuelly, or like road tar or asphalt."
_Asphalt? Sawdust?_ One thing is clear: the flavor descriptions of wine are more sensual than those of cannabis.
Next up is OG 18, which Scott says is "sweet butterscotch on the inhale but leaves the room smelling of burned rubber bands."
"That's the same way I describe a South African Pinotage," says Matt. "It has a gamey character to it, like you're roasting an antelope on the plains. But I taste peppermint on the exhalation."
"Yes, she's delicate, not brutish," adds Scott. Hey, guys, I pipe in, there's a whopping difference between peppermint and smoldering rubber bands!
"Burned rubber is the smell it _leaves behind_ in the room," Scott clarifies. "But yes, the flavor of the smoke on the exhale is more eucalyptus. It's very . . . green."
Matt, sensing my frustration with the free-form nature of this exercise, reminds me that precision isn't the point. "In France there are 475 terrains, plus an amazing number of producers outside of those regions. Each terroir grows a different variety of grape, but the local soil and microclimates also contribute to the unique taste. And that's before anything even hits a barrel to age."
"That's how experts keep their jobs," I say. "They're never able to arrive at consensus!"
"And that's the best part about it!" says Matt. "It takes a lifetime to learn about the three thousand strains. That's why cannabis and wine are both so compelling. They are living things, so always changing. You can never learn enough."
I see his point, which is finally one thing we can all agree on.
At the conclusion of the tasting, Scott explains that despite our differing opinions, we did successfully identify the broad notes of each category. The first two strains he selected for their "woodsier" flavors, which our descriptions touched upon. The second pair was more sour, which we nailed as citrusy. The third pairing included two sweets, which we missed, probably because it's impossible to disassociate taste from effect, and by that time the judges were cross-eyed. The conclusion: Tasting wine is easier. With cannabis, you can't spit it out.
Monday is a slow day. In the long gaps between patients trickling in, the staff places orders, restocks shelves, and prepares some well-stuffed, perfectly formed pre-rolls. At closing, the scales are cleaned and leveled, the keyboards air-gunned to remove any stray "shake," floors are mopped and vacuumed, and keypads, door switches, and arms of chairs are swabbed with Lysol.
The staff gathers outside in a nearby parking lot for an after-work "shifty." Smoking on the clock is verboten and results in immediate dismissal. When a joint of Durban Poison comes around, Ean politely refuses. "I've got enough anxiety right now," he says. "Sativa won't be much help." He's referring to his wedding, which is coming up next month on the fifty-yard line of a football stadium in Ann Arbor, Michigan, his fiancée's hometown.
(Here's how Abbie, Ean's fiancée, announced the news to her family:
"Hey, Mom, I just got engaged! He's fifteen years older than me and owns a really great marijuana dispensary."
Silence.
"Oh, and he's Jewish."
"That's great, dear.")
Ean's statement reveals a lot about how cannabis literacy dovetails with self-awareness in the new world. He assesses his own mental state, and because he knows that the "energizing" properties of Durban Poison can exacerbate anxiety, he declines that strain. This is radical in American medicine, where "health" is generally outsourced to doctors. The notion of a patient identifying a condition, then choosing a botanical medicine that can't be patented or owned, and self-medicating? That's precisely why Dr. Grinspoon calls cannabis the true people's medicine, and why pharmaceutical companies find it threatening.
There's no question that a climate-controlled room with artificial sunlight bathing regimented rows of plants is one of earth's most unnatural environments. Brandon Kennedy, the CEO of the largest cannabis-oriented venture capital firm, Privateer Holdings, once described an indoor grow as "a bank inside of a prison filled with toasters that constantly need to cool down." I saw what he meant once inside Denver Relief's sprawling brick bunker, which had 1,200 plants crammed into 5,000 square feet with aisles so narrow I had to step one foot in front the other to proceed.
A single harvest churns about eighty pounds of bud every thirty-five days, which places the value of this inventory at any given moment at $350,000. Even with the additional 20,000 square feet of greenhouses they're planning to add, Denver Relief's operation will still be considered small to midsize. At the moment, grows occupy about 4.5 million square feet in Colorado, the equivalent of seventy-eight football fields, and the state's warehouse vacancy rate is at an all-time low. "This industry has come on so fast that initially I was uneasy—it seemed like a fad," says Brad Calbert, the president of the Colliers International brokerage. "Supply is deficient, demand is excessive, and capital is abundant. Make that cash."
The illumination in the Denver Relief greenhouse is as bright as an operating room—five hundred times the strength that's recommended for reading.* A high-power carbon air-filtration system keeps the humidity level low to discourage the growth of indoor microorganisms. The system changes the air thirty times an hour—sixty times the rate in a modern home. Carbon dioxide (CO2) levels are four times natural levels, to boost plant growth. Every system, including surveillance, is connected to the mobile phone of the master grower. Should an evening snow suddenly drive down the temperature indoors, alarms sound. According to one 2012 study, the electricity used by these grows is sucking up a shameful 1 percent of the nation's annual wattage.
The environment inside the grow is significantly more inoculated than that of a hospital. Visitors must remove their shoes at entry and wear protective booties to avoid traipsing in potentially destructive creatures, such as the dreaded spider mite, the full horror of which can be appreciated only though the lens of an electron microscope. This hirsute micromonster affixes to the underside of leaves and sticks its proboscis into a plant's veins to suck them dry. Another scourge is powdery mildew, a floury fungus that spreads so quickly it can wipe out a grow in two days if unchecked. Pestophobia is the reason well-designed grows are subdivided into smaller rooms. If one area becomes infected, the devastation is easier to contain. Losing an entire harvest can cost millions and destroy a business.
Scott serves as an assistant to Noah B., a former schoolteacher, and Kayvan's younger brother, Hassan. The four of us spend the morning snipping yellowing leaves to make tomorrow's scheduled reaping go faster. We deposit the dead leaves into black garbage bags, which Hassan holds up to a security camera for the control board to monitor. Law requires him to weigh each bag before affixing an infrared tag that tracks every gram of garbage.
Securely transporting the flowers is akin to moving gold bars. To preclude diversion into the black market, plants are weighed five times: after they are chopped; after they are dried and cured; after they are bagged and refrigerated; and before departing for the dispensary. The state requires the driver to chart his route—if he changes course, insurance won't cover any trouble, should it occur. Once the shipment reaches its destination, the bags are again weighed to ensure nothing was lost along the way.
Tomorrow is harvest day, which means one-third of this grow will be sacrificed in the morning. The plants have been snoozing for the last twelve hours in total darkness (not even a flashlight is allowed), and the three growers and I have gathered in the dark to pay our last respects before a blaze of one thousand sulfurous lights jolts these snoozing plants into one final burst of resin production.
Under the glare, the differences between strains is breathtaking. The tawny leaves of Girl Scout Cookies appear reptilian in their rigidity, giving them a prehistoric cast. Unlike most cannabis varieties, the buds of Cookies are the same size near the light and below the canopy. They are dense and wrinkled like the folds of a shar-pei's neck. Outer Space buds grow as long as a banana and as thick as a twenty-ounce soda bottle. They are so spectacular they beg to be displayed whole under glass. Tomorrow ten freelance trimmers supplied by the Hemp Temps employment agency will set to work snipping excess leaves, which will be used for oil production. Each trimmer earns twelve to fifteen dollars an hour depending on his or her skill level. (Hassan calls the skill distinction "bullshit. The best trimmers are those who learned on illegal grows because they had to do their job steadily and quickly.") Besides trimmers, Hemp Temps also provides master growers as well as "confidential consumers," who surreptitiously drop into dispensaries and supply "detailed intelligence based on their visit to the assigned location" to owners. In other words, spies.
If fighting mites or mildew excites you, if staying atop ever-changing regulations doesn't feel like herding cats, if, at this very moment, you are contemplating moving to a legal marijuana state to open a dispensary and cash in on the greenrush, don't sell the house quite yet. The obstacles to success are many.
For every Scott Yoss, there are a hundred underground "experts" who may know a lot about growing illegally but who know nothing about navigating a tough new regulatory environment. "Our idea is to bring in the best practices from other industries," says Kayvan. "Budtenders should have great retail skills. Cultivators should have managed massive greenhouses with vegetables or flowers, or have a horticulture degree. It's easier to teach someone to grow marijuana if they know how to grow other plants than it is to show an underground grower how to manage a large facility with big automated systems. We had one grower who, if you disagreed about something, would say, 'Fuck it, I'm going to cut down all the plants.' So now we generally preach, 'Don't hire within the industry.'"
You also need a high tolerance for running an all-cash business. Financial institutions that many American businesses rely on—PayPal, Swipe, Square, not to mention credit card companies—shun the cannabis trade. Doing business with an illegal enterprise is still a crime under federal law. Banks are no exception.
The final disincentive? Because cannabis businesses fall under an obscure area of the federal tax code, the law doesn't allow them to deduct operating expenses, such as rent, salaries, or equipment costs. This means they could be paying a federal income tax upwards of 70 percent.
It's a good thing they sell a product that quells anxiety.
At the conclusion of my stint at Denver Relief, I quietly cornered Scott and Ean separately to inquire about purchasing some of their product. The answer was politely and firmly delivered: "No dice!" Scott made the excuse that since he smokes about a quarter ounce a week of flowers and a third of a gram of hash, he doesn't have a lot of slack. Ean more forthrightly told me that if he were to sell to an out-of-state visitor without a Red Card he could lose his license and livelihood. Both recommended I visit another shop down the road that allows recreational sales. I'm probably one of the few Americans to have worked in a dispensary and not been allowed to buy cannabis there, a minor inconvenience for me but an excellent sign for the future of the industry.
## PART III
## FUTURE WEED
## ___Chapter 9_
## DESIGNING YOUR HIGHS
_Los Angeles, California_
One of the problems of the current world of weed is the lack of diverse opinions within it. Advocates have been occupied fighting prohibition and all that comes with it for so long that stoner culture, which is still dominated by young guys in hoodies or old guys in hoodies who act like their younger counterparts, have hijacked the conversation for a half century. As we enter the post-prohibition era, new voices are emerging, and they are countering the received wisdom.
Michael Backes is one such disrupter. Rather than joining the chorus of those who claim that cannabis is harmless in any amount and in all circumstances, he takes the more epicurean position that it is currently oversmoked and underutilized. Backes is itching to spark a new debate about how the plant can responsibly fit into a society that doesn't outlaw or demonize it. He's convinced of cannabis's untapped potential, but he's unconvinced that stoners will be leading the way to uncovering it.
"It's not macho to take massive amounts of THC," he told me over a beer near his loft in downtown Los Angeles's Arts District. "It's not a mark of pride. But thanks to prohibition, our conception of the correct cannabis dose today is based on how much we can withstand. It's Seth Rogan hitting the bong or Snoop Dogg and Wiz Khalifa smoking all day long. It's so dumb."
The post-prohibitionist argument, as he frames it, goes something like this: For thousands of years, humans raised cannabis to complement human chemistry. But in the last half century, breeders have thrown this complement out of whack by selecting plants with massive amounts of THC. Cannabis merchants and growers don't view this as a problem, as it's more lucrative and efficient to grow plants that are smaller, more productive, and pack a bigger wallop. But in terms of creating the most pleasurable, _interesting_ highs, and reaping the maximum therapeutic benefits, superweed may not be the answer.
"It's a general truism that nine percent of the pot smokers are smoking fifty percent of the pot, just as nine percent of drinkers are drinking fifty percent of the booze," Backes told me. "But the Bronfmans didn't sell moonshine when alcohol prohibition ended. They sold Seagram's. The marijuana moonshiners want to sling weed and they want more people smoking a gram of wax or an eighth [of an ounce] a day because _that's a business_. But judging pot by THC levels alone is like judging the quality of a cognac by its alcohol content. Who needs Gaston Briand if you've got Everclear?"
It's a reasonable point, one that's more often made by prohibitionists who twist it to say that today's powerpot is more dangerous than the weed of the past, and this is why we should keep it illegal _._ But Backes isn't worried about the unproven dangers of a relatively benign plant that has never killed one human being. He's an advocate who welcomes regulation, and he believes that the pleasures of pot can be enhanced by understanding the science of how it works. He has absorbed research from around the world, studied ancient uses, and combed through the three hundred patents that GW Pharmaceuticals has secured over the last fifteen years in its quest to bring Sativex to market as an FDA-approved whole-plant cannabis pharmaceutical.
As a founding member of Phytecs, the first company devoted to making plant-based medicines and nutraceuticals to treat the endocannabinoid system, he is also confident that the plant can be used to produce revolutionary medicines and nuanced designer highs. "My job is to figure out where all this is going in the next five years," he says. With his black-frame glasses and pressed shirt, Backes is more egghead than pothead. Unsurprisingly, he doesn't come from the ranks of the cannabis movement. He spent most of his career in film, as a technical consultant on the Spider-Man series and supervising the computer graphics for the control-room sequence in _Jurassic Park_ (several characters in Michael Crichton's books are admiringly named Michael Backes).
Like many in my generation, Backes smoked when he was young, quit as his paranoia increased with stronger plant genetics, and returned to it again in middle life when a friend recommended it to reduce the frequency of his hemiplegic migraines, which are accompanied by visual auras, withering pain, and nausea that no conventional medicine could address. A paper by Dr. Ethan Russo exposed him to two radical and counterintuitive ideas: (1) low doses could be more effective than larger doses, and (2) the obsession with THC was blinding users to the other powerful minor cannabinoids and terpenes that very likely determine the trajectory of every high.
"Microdosing" didn't eliminate his pain, but it did work as a prophylaxis—it slashed the frequency of attacks from several a week to one a year. This stunning outcome inspired him to eventually cut back on film work and cofound the Cornerstone Collective in 2008, an "evidence-based" dispensary of three thousand members. Cornerstone operated in an intentionally nondescript office with no signage, and it sourced rare strains grown by connoisseur growers. It was among the first organizations to collect and share information about which strains best treat specific illnesses, and it embraced mold and microbe testing to minimize health risks to its members. It shunned plastic packaging in favor of glass, because plastic, according to one study, interacts with the plant's naturally occurring solvents to form carcinogens such as formaldehyde. After five and half years, Backes severed his ties with the collective to author a book, _Cannabis Pharmacy_ , and to set up Phytecs.
Backes may be a pioneering post-prohibitionist, but he has always enjoyed dancing on the cutting edge. He imported a plasma TV from Japan years before there was HD-anything to view on it. The technology was so compelling he just had to have it. He experimented with other psychoactive substances but now avoids them because they "grab too much bandwidth." He had a brief flirtation with an esoteric tonic of wild Changbai ginseng that cost $500 a pound. "It makes the price of a truffle look like a tomato," he says. "It's pure energy. I used to go through a bottle a month."
Pot provided a similar thrill when he was growing up in 1970s Tucson. He inhaled some of the legendary landrace strains that slipped across the Mexican border—Kona Gold, Panama Red, Big Sur Holy Weed, Thai Stick, Zacatecas Purple—and their smells and flavors are ingrained in his mind thanks to his eidetic memory. This idiosyncratic gift of recall was once mistakenly called a photographic memory—Teddy Roosevelt, Sergey Rachmaninoff, Abbie Hoffman, and the film director Guillermo Del Toro also have it in common. But Backes's memory is more Proustian; it allows near-total recall of sounds, tastes, and, significantly, smells. This rare ability to catalogue scents is why "noses" in the perfume industry are paid handsomely to blend essential oils into blockbuster fragrances, the finest of which leave lasting emotional impressions. It also gives Backes a unique competitive advantage in his newfound profession.
"Give me twenty strains and chances are I could name fifteen of them," he says without bluster. "It's practice. I'm not trying to be Robert Parker, and wine experts may be full of it anyway—they've blindfolded some of them and the results were not pretty—but I can honestly remember just how different Kona Gold was." A smile cuts across his face as the scent recollection of Kona Gold filters back into his consciousness. "Kona was the best high. It smelled piney like a Christmas tree and the high was like that moment on LSD when you're filled with a suffusion of joy and diamond clarity before you start tripping.
"That's why it cost $200 an ounce in 1979 [$700 in today's dollars] and came in a redwood box. People sit on pillows in monasteries for years to get to that. That's the goal with cannabis and it has been lost over time. Most people, thanks to prohibition, don't even know it's gone."
Microdosing also inspired Backes to vary the amounts he used for pleasure. He was soon mixing and matching dosage and delivery methods (smoking or vaporizing plus edibles) to potentiate specific moods, be it clarity and focus, creative idea generation, deep relaxation, or emotional connection in sex.
In tribal times, drug journeys were shaped by shamans who knew how to avoid treacherous routes and guide followers safely into other dimensions. The finest shamans don't act on superstition. They draw on a centuries-old body of systematic knowledge, and their techniques are honed and refined over time. Backes's cannabis intelligence is drawn from botany, chemistry, neurobiology, and hundreds of anecdotal reports, a rare set of skills that so impressed me that I anointed him my unofficial shaman.
When I was growing up, a joint rolled was a joint smoked down to the roach. We continued smoking stupid no matter how potent pot became. But to get interesting highs that don't knock you flat, twenty-first-century cannabis should be consumed in a twenty-first-century way. Backes says dose control is key.
Dose is one of the few ways that cannabis mirrors alcohol. One or two drinks can act as a social lubricant; five can make you socially disconnected. Aspirin is another example. At 600 milligrams, aspirin reduces pain and inflammation. At 100 to 160 milligrams, it unclogs arteries. The relationship between dose and effect wasn't firmly established until Dr. Mark Wallace at the University of California, San Diego, injected capsaicin, the ingredient in chili pepper that burns, into the arms of volunteers and then treated them with varying doses of cannabis. At too low a dose, subjects got no pain relief. A moderate dose provided excellent relief, but too high of a dose actually magnified the pain. The conclusion? Cannabis is so dose specific that large and small amounts create opposite effects.
"Because it's nontoxic there's been no guidance and that's a problem," says Backes. "With tequila, someone might say, 'Don't drink five shots or you'll be unhappy.' No one says that with pot. They think that once you reach a certain level of psychoactivity you'll automatically know when to stop. You won't.
"A lot of people say they stopped smoking at some point because it made them paranoid. What's making them paranoid is an overdose of THC. Reduce that and it goes away. It took me a year to figure out to smoke a match head instead of a bowl." Binge smoking or oversmoking is yet another unforeseen result of prohibition, he contends, just as binge drinking became the norm in the 1920s and '30s, when drinkers would stockpile and guzzle as much grain alcohol as they could because they never knew where their next batch was coming from. "I can't help think that while science is undermining the prohibitionists' ability to support the lies about the dangers of cannabis, the dabbers are doing their best to keep it illegal," Backes says.
The second key to taming today's pot is understanding the role that the lost molecule, CBD, plays in modulating the high. Without it, aficionados claim the plant has morphed from something that produces a complex and subtle enhancement—think wine—to a powerful fuel, like grappa. CBD is often misidentified as the "highless" weed, but in my experience it creates a subtle, warm feeling—more of a flat "mid" than a rip-roaring high. This uninspiring semihigh is why growers in the 1980s and '90s bred CBD out of the plant. If the strains didn't send them flying, they would chuck the seeds to ensure they didn't produce another bum crop. It's why today's potent pot is often misconstrued as "great."
The problem with THC-only pot is that it's not what nature, in her infinite wisdom, intended. THC is a tricky chemical. It can be trippy, imparting sunny feelings of joy, but too much can create a trifecta of unpleasantness: paranoia, anxiety, and nausea. Here's why: When administered together, THC and CBD play Rock 'Em Sock 'Em Robots in the battle to fill receptors. But THC is much more adhesive than CBD; it's Superglue compared with CBD's old tape. THC usually lands first, but CBD will run interference, which tempers THC's effects. Even though they are often described as antagonists, they are more like old lovers. Yes, they fight, but overall they get on best when they're together.
One of CBD's less regaled attributes is its ability to dampen anxiety. One Brazilian research team demonstrated its usefulness in overcoming stage fright. It's a well-known dictum that people fear public speaking more than death; but when the subjects of this 2011 study were given CBD before taking the stage, it decreased their discomfort, anxiety, and sweating, and calmed their heart rates.
To support this contention, Backes reminds me of this often-forgotten bit of cannabis ephemera: The Beatles, Charlie Parker, Carl Sagan, Bob Dylan, Allen Ginsberg—all the artists, writers, and thinkers that extolled cannabis for its creative fuel—weren't imbibing 25 percent THC. Their smoke was 4 or 5 percent THC, and it very likely contained an equal measure of CBD.
"When Dylan turned on Paul McCartney, Paul asked his assistant to follow him around and record the flood of ideas that cannabis was triggering. If he had smoked that amount of today's pot he'd have been on his back. Those creative highs had nothing to do with the stony Cheech and Chong highs. In California right now you can't find anything under eight percent THC, and that's twice as strong as what they were smoking." Perhaps the real act of creativity lies in knowing how much to use to get you where you want to go.*
According to Backes, educated Californians are using cannabis more as a precision instrument than a sledgehammer. The key words here are "education" and "precision." You need to know how much to take and how to deliver it into the body. The professionals (mostly in the film industry) Backes knows use a smidgen to open the spigot of creativity and help them get out of their own way. Larger doses are reserved for revising or going deeper into material. Other execs in high-pressure industries are substituting a low-dose 2.5-milligram edible for an afternoon cocktail to soften the rougher edges of the day and maintain calm. Those are far more noteworthy ways of using cannabis than just smoking until you can't stand up.
Athletes are also toying with dosages and delivery methods to contend with the rigors of training. Avery Collins is an ultramarathon runner who uses a smorgasbord of edibles to help him through his 120-mile-a-week workout. One ten-milligram edible makes a thirty-mile trek along the mountain trails in Steamboat Springs, Colorado, tick by. After a run, he'll soothe sore muscles with a topical salve that reduces inflammation. He reserves a joint for parties and other social occasions as an almost quaint, old-world pleasure. Oh, and he has never competed while high for fear of jeopardizing his integrity or his focus. "Cannabis is a mental enhancement for me, not a performance enhancer," he says. "I need to hold on to my determination. I don't want to see all that training wash away in one day."
Backes's deep understanding of the endocannabinoid system helped explain another mystery that had been confounding me: tolerance. Although my grower buddies were imbibing all day, it turns out that they're not getting as high, because their receptors are filled to the brim.
Wake-and-bakers say that their tolerance reduces side effects, such as loss of coordination and short-term memory. It's confusing how smoking more can reduce unwanted effects, but it was demonstrated in a little-noticed 1993 study by Dr. Miles Herkenham, a principal investigator at the National Institute of Mental Health.
To understand tolerance, it's useful to understand the way dopamine, the neurotransmitter that stimulates the brain's "happy" center, works. Other drugs, including heroin, cocaine, amphetamines, alcohol, and nicotine, make us feel well by pumping up production of this pleasure juice, which titillates the brain's reward receptors. Heroin is so addictive because the brain quickly learns to treasure that pleasure and maximizes the amount of dopamine it produces. This, in turn, drives us to take more heroin, until the body requires those elevated levels to maintain homeostasis. If the body doesn't get its fix, a physiological storm moves in and certain systems go berserk, making addicts in withdrawal suffer cramps, diarrhea, and other wretchedness.
We know a lot about opiate addiction because the dopamine neurotransmitter system was discovered in the 1970s. But cannabinoid receptors weren't identified until the 1990s, and scientists simply assumed that cannabis worked in the same way—and they trumpeted their mistaken assumptions to the world. Their errors helped solidify some of the unfounded myths about cannabis addiction.
In his experiments, Herkenham gave mice different levels of radioactively labeled synthetic THC for two weeks. The strongest doses were "the equivalent of smoking a thousand joints a day," Herkenham told me. At first, the superstoned mice were catatonic, so docile that the scientists could arrange their tiny limbs in different yoga positions with no resistance. But after a few days they noticed that the mice hit with the highest doses began to regain motor control more quickly.
When the scientists dissected the mice's brains, they saw those exposed to extreme THC had the fewest available cannabinoid receptors. The body, in its infinite wisdom, had reduced the number of receptors that THC could bind to so the animals couldn't get as high.*
"Down regulating" cannabinoid receptors is the body's way of placing a ceiling on every high. It also explains how heavy users can smoke all day and go about their business, while more casual users would be drooling had they consumed the same amount.
And the reason cannabis causes virtually no withdrawal? There are no receptors in tissues that trigger withdrawal symptoms, just as there are no cannabinoid receptors in the brain areas that control the heart or lungs. "That's one of the nicest things about working with cannabinoids," Herkenham told me. "You can give ten thousand times a typical dose and it won't kill the animal." Or a human.
But here's the possible bad news: the effects of long-term down regulation are as yet unknown. If you're supplementing the body's main regulatory system with a large supply of THC in dabs, for example, and your body isn't producing as many endocannabinoids, there's a chance that you could tip your body into a state of endocannabinoid deficiency. This is speculative, but other neurotransmitter systems have diseases associated with deficiencies: dementia in Alzheimer's disease is correlated with a loss of acetylcholine; parkinsonism is associated with low levels of dopamine; and depression is associated with low levels of serotonin. Why should the endocannabinoid system, which has the greatest receptor density of all, be the exception?
As to what those unforeseen effects of down regulation might be, it's anyone's guess. There haven't been any longitudinal studies, but I have found that people who oversmoke for years on end do seem to exhibit some form of cognitive dulling. They lose some of their brightness and become disconnected from their inner lives (cannabis takes away dreams, which might explain this disconnection).
These issues are the same with any substance, and the consequences differ depending on the drug. The writer Adam Hanft published an unforgettable article about the contributions antidepressants made to the financial crisis of 2008. He found that prescriptions for Lexapro, Prozac, and Seroquel, the drugs that so many white-collar professionals rely on to fight off depression and power through their days, spiked in the years leading up to the recession and possibly numbed the ability of the managers to assess risk. In other words, derivatives look really good if you don't care about the results. I'm not drawing a parallel between cannabis and antidepressants, but as we learn more about how the ECS functions, we would be reckless to ignore what we know about dose, tolerance, and what it means to smoke smart. Sorry, stoners. Post-prohibition means it's time to get real.
To understand how to think about designing highs that can change your mind or mood in certain desired directions, you need to understand terpenes. These powerful smell molecules, the most common of which are key components in lemon, pepper, lavender, and pine, create the pungent aromas of fresh bud (see the terpene chart at the end of the chapter). We're not talking mild aromatherapy here. Terpenes in cannabis occur in pharmaceutical-grade concentrations. When dried and heated, they combine to form a chemical cascade that may direct the trajectory of the high.
"THC increases how fast terpenes cross the blood-brain barrier," contends Backes. "Kona Gold, Panama Red, Acapulco Gold, all these great seventies genetics that got you beautifully high had lower THC content than strains today, but they had a lot of terpenes." In other words, THC determines how wide the door to the brain opens; terpenes are the different paths that are illuminated once you walk through.
From a sheath of papers Backes unfolds a chromatograph that compares the terpene content of two strains, Bubba Kush and Lemon Haze. Both have comparable levels of THC, between 13 and 15 percent, but their highs are different thanks to their terpene mixes. The peaks and dips of the lines resemble the "Random Hill" profile on a stationary exercise bike, but they zig and zag in opposite directions. Bubba Kush has a higher concentration of myrcene and linalool, two terps that cause relaxation. Lemon Haze is richer in pinene and limonene, making it more uplifting and clear.
Although I've used the words "indica" and "sativa" throughout this book, they are not reliable indicators of the stimulating or sedative qualities of one strain. In fact, the best indicator of whether a strain will bring you up or down is its terpene profile. "Once you start to know the different terpenes and how they work, you can more reliably predict the effects," says Backes.
At this point, reading the terpenes is more a forecast than a road map to each high because of a complicated interplay of chemicals known as the entourage effect. The entourage effect is best understood in musical terms: Individual instruments produce lovely sounds on their own, but the majesty of a symphony can be realized only when all the instruments play together. Terpenes are the violins and flutes, and only when they mix with other cannabinoids can the symphonic complexity of the high be realized. This also explains how cannabis has outfoxed pharmaceutical companies in their attempts to isolate and patent single-molecule medicines. The sum of cannabis's chemical parts is greater than any one of its individual components. Just as with certain celebrities who walk the red carpet, the major cannabinoids need their entourages to function optimally.
Those of us who live in illegal states smoke what our dealers bring us and hope for the best. But Backes and other pioneers of the new cannabis era are hoping to combine terpenes to engineer effects that are more predictable. GW Pharmaceuticals is breeding plants that are high in one minor cannabinoid called THCV, for example, that retards appetite and may work like a diet pill. A natural, plant-based product that gets you skinny and makes you feel happy? Now there's a business!
But it's a ways away. In the meantime, I ask my shaman what he might recommend for crisp, transparent highs that will also relieve the stiffness of my lumbar and cervical spine, my occasional insomnia, and the other indignities of aging.
For physical issues, he recommends low-dose aspirin, eighty milligrams every day for inflammation, and a high-CBD cannabis strain to ease the pain.
To sleep, I'm to take a vapor hit or two one and a half hours before bed—that will allow the high to fade in time to allow the metabolites that encourage sleepiness to kick in. And he recommends a low-dose edible just before I hit the pillow. The effects will come on after an hour, which should carry me through the night.
"To counteract morning fuzzies, eat two tablespoons of almond butter before bed. That keeps your sugar level even so you wake up sharp. For some, slow-morning starts are age related, for others it's insulin resistance. In either case it works like a charm.
"For your high, a pinene-enhanced narrow-leaf variety appears to intensify psychoactivity and eliminate memory deficits. It's not much guesswork, because you are very specific: whereas most people are just getting stoned, you want to get high. A sublingual candy once a day will also extend the length of a high," Backes tells me. "I always make sure to have THC in a ratio with CBD that works for me. And remember, microdosing promotes hyperfocus and avoids bounce-back."
_Bounce-back?_
"The endocannabinoid system loves balance. If you hit yourself with a big dose, your body's going to try to balance out, so the system will swing back in the other direction. It's like riding a seesaw. Two people of the same weight can balance but if some big guy jumps on one end, the little guy on the other end is going to lose his teeth. When you dabbed, you got hit in the teeth.
"What you probably want is something that goes up and comes down smoothly without a peak. Personally, I don't want an intense high. I want a gentle onset, a long-lasting effect, and then something that just disappears."
Lester Grinspoon learned forty years ago that everything he knew about cannabis was wrong because of official lies. Now that science has refuted the lies, the fog is lifting. Guiding the high is the next frontier.
Backes turned out to be a superb shaman, but he wasn't, alas, a guru: microdosing and mixing delivery systems (one five-milligram edible plus one or two hits on a joint) is an excellent way to eke out different nuances from a high, but it didn't curtail my vomiting response. Nor did specifying the origin of the strain—puking occurred with buds from California, Colorado, and homegrown East Coast varieties, too. A bong, a joint, a pipe—every method of smoking except for vaporization—brought it on, and sometimes after just two modest hits.
Nor did "set and setting" make a difference. This term, coined by Dr. Timothy Leary, explains that all drug experiences are shaped by mind-set as well as physical setting. My eruptions occurred under diverse conditions—alone, in small groups, once at a dinner party I was hosting in my own apartment. Believe me, when the host of the party disappears abruptly into the bathroom for twenty minutes and emerges ashen-faced, his credibility as poster boy for the New World of Weed is shot.
My adverse reaction, as I learned in talking to other users, isn't all that uncommon. It just hasn't been properly addressed in the literature. Something else in the plant was triggering it, as Dr. Brian Becker, an integrative physician who runs a dispensary in Tucson, Arizona, explained to me. Becker suggested that a component of certain sativa strains that I favored could be bombarding the "chemoreceptor trigger zone" (CTZ) in the medulla oblongata of my brain, an area that's also packed with cannabinoid receptors. His solution, if I wish to continue using pot (which I do), was to switch to an indica strain with a different terpene mix, or to find something with an equal ratio of THC and CBD. "CBD is your life raft," he told me.
Nice idea, Doc, but I live in the old world. Even if people in New York knew what CBD was, such a specific strain was almost impossible to obtain. It wasn't until I read a blog post by Dr. Allan Frankel irresistibly titled "How to Extend Your High from Two Hours to Six" that I found one of the life rafts that Becker spoke of.
Frankel is a warm, possibly brilliant, and at times volatile character—like many people on the forefront of cannabis exploration, he's an outsider who has battled the authorities, as well as his own demons. Marcus Welby he's not.
For thirty years Frankel was an openly procannabis internist with a busy practice on Wilshire Boulevard in Los Angeles. But he ran into trouble with the Medical Board of California for prescribing OxyContin to his girlfriend without keeping clinical notes (sin #1) and then popping some of those opioid painkillers himself (sin #2). When the board got wind of his ethical breeches, it suspended his medical license for fifteen months. Sympathetic cannabis advocates portray Frankel as a victim of pot politics, but medical professionals across the board assured me he was sloppy, perhaps not thinking clearly, and in clear violation of medical ethics. In the service of my investigation, I suspended judgment and paid him a visit.
Frankel has since reinvented himself as a $175/hour consulting cannabis physician. He has absorbed an enormous amount of information from botany, chemistry, and medical studies, which led to the invention of a concentrated whole-plant spray that works like Sativex but is far less expensive—270 sprays of Sativex costs about $700 in the United Kingdom, where it is sold, whereas an equivalent amount of Frankel's formula sells for about $200. Frankel claims that his formula includes all of the terpenes and compounds that occur in nature and is easy to use—a few spritzes under the tongue, and it hits the bloodstream in fifteen minutes. Some people call this a joint in a bottle. Frankel refers to it more grandiloquently as his Golden Oil.
Frankel's oil is designed to appeal to doctors conversant in the post-prohibitionist world of receptor medicines. It is prescribed in precise milligrams rather than grams, which is standard in medical practice. He brags about the successes he's had with weight loss, certain psychiatric conditions, and even some cancers. A half dozen patients I spoke to supported his claims, but frustratingly he hasn't documented his findings, so there's no objective evidence by which to evaluate them. Mavericks, especially in the weed world, are not always organized.
But here's where his system really succeeds. The meds are calibrated on a psychoactivity scale of one to ten. Number one is almost all CBD, with just a smidgen of THC. Frankel recommends every smoker keep a bottle in the medicine chest as an antidote to uncomfortable THC moments. Numbers seven and above are high in THC and used for severe sleep disorders.
"People don't usually come to me with problems like yours," he told me when we met in his Santa Monica office. "They're more like, 'I have cancer that's eating my face.' And, I would prefer you use the term 'overmedicating' to 'overdosing.' 'Overdose' is such a loaded word."
For one of those bell-ringing clear highs Backes had extolled, Frankel suggested number five, which has CBD and THC in equal ratios. "Do you want to be more focused, smiley, feel less moody, happier? Would feeling awesome for six hours be acceptable over being stoned for two?"
Who could say no? I opened wide and lifted my tongue.
Two sprays and thirty minutes later, a warm fizzle spread through my body. I was energized yet grounded and clear. The high wasn't nearly as enveloping as smoking—it was more of a gentle, warm kiss that even allowed me to read. It's what awesome feels like.
And it's efficient. A joint sends 80 percent of the cannabinoids up in smoke; a pipe, 50 percent. With extracts like Frankel's you get 100 percent absorption. Extra bonus: oral spray is no scarier to use than a minty breath spray. "Anyone who isn't comfortable smoking a joint for their medical health—that's my niche," Frankel says.
Not only are the sprays less frightening for the inexperienced, the extracts have no odor and come in small brown bottles that make them undetectable when traveling. So I carried home a few bottles and offered them to my ninety-four-year-old mother, who hasn't had a full night's sleep in ten years but who refuses tranquilizers or sleeping pills because they make her dizzy and prone to falling. Believe me, this is a woman who abhorred marijuana, but before I could finish explaining how the extract is produced, she was pumping some into her mouth. The first few nights were a bust, but by the end of week one she had a few delicious nights of uninterrupted sleep and was noticeably more peppy during the day. And then, out of nowhere, her caregivers stopped the meds.
"Why on earth did you stop?" I asked them.
"She's just not herself. She's running around, washing dishes. She's almost giddy, and we're afraid she might fall."
I was left, as I seldom am, speechless.
I liked the Frankel system. I enjoyed the clear high that came with no adverse side effects. But it's impractical if you're not a Californian, since US law forbids shipping cannabis meds across state lines. I was back to square one until I stumbled upon what turned out to be another life raft, the Plenty vaporizer.
Until the Plenty, vaporizing technology left me (and many users) unimpressed. Sure, vaporizers are convenient and fit neatly into a pocket, but their temperature controls are unreliable—you can often taste burning plant along with the vapor, which scratches the throat. Plus, they just don't deliver a satisfying high. You take off but you never soar.
The Plenty is neither convenient nor sexy, and it definitely attracts attention. It requires an electrical outlet, and it looks like a hybrid of a Black & Decker drill and a Flash Gordon ray gun. But don't let its clunky appearance fool you. The Plenty unleashes a generous draw, a full aromatic burst of flavor, and a sunny high with far less facepunching cognitive disturbance than you'll get from a joint.
This power tool for cannabists is the brainchild of Markus Storz, half of Storz & Bickel, the same German company that produced the Volcano in 2001. For over a decade, the company has successfully marketed its devices to the worldwide medical community, while maintaining a strict silence about what herbs its machines vaporize so as not to run afoul of strict American import laws. Both Storz and his partner, Jürgen Bickel, shun publicity and have never revealed themselves to be cannabists. They needn't. The way their inventions coax flavors from the plant makes their proclivities abundantly clear.
Unlike standard-issue vaporizers that use conduction heat only, the Plenty blends conduction with convection to deliver a higher quality of satisfaction. Conduction is created by a small heating element (an internal oven, as it were); convection moves the hot air away from the heat source. This combination makes the Plenty the world's first precision vaporizer, because the temperature can be accurately controlled. It can reach 420 degrees Fahrenheit (wink), but the coiled mouthpiece ensures a cool draw.
In the same way digital technology has disrupted the "delivery system" of the cable television or music businesses, advanced vape technology could alter the way people have smoked for centuries. A vaporizer high is qualitatively different from a smoking high. It leaves users feeling less tired, forgetful, disoriented, and nauseated. Many smokers complain that it isn't the sort of face slap they are familiar with, and they are correct. There is less cognitive interference than one gets from smoking a joint or a bowl, simply because terpenes and cannabinoids melt at lower temperatures than those required to burn the plant. What's more—and this is crucial—smoking includes tars and toxins, the culprits responsible for couchlock and other adverse reactions, very likely including vomiting. I have used the Plenty for ten months and never felt even the threat of nausea.
As we learn more about the inner workings of the plant, we may one day find it possible to set the temperatures of these precision vapes to extract specific cannabinoids for different effects. Once the vaporization points of terpenes are identified, these instruments may allow us to extract more limonene for mental clarity, say, or more linalool to get to sleep, or any number of different compounds that might help the sick heal. This isn't to say the joint or the pipe are dead, but science, technology, and curious minds are allowing us to tap the complex botanical factory inside this plant to produce specific effects that until now we've never been able to control.
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HOW TO READ A TESTING LABEL
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For people who enjoy reading food labels, the lab testing of marijuana is a revelation. This label, produced by the Werc Shop in Pasadena, California, for the Laguna Woods retirement community, provides an analysis of the Blue Headband strain. Is it definitive? Not as definitive as the marketers of cannabis products would like us to believe, according to the Werc Shop's founder, Dr. Jeffrey Raber. All the studies on terpenes and cannabinoids to date have been done on single molecules, but no breakdown of individual compounds can predict the entourage effect that these chemicals produce when heated and mixed. Understanding the numbers means you're not flying quite so blindly, so it's best to think of these labels as guides, not definitive road maps to your high.
The results of this test indicate that the high would be stony and likely to end in a powerful sedative crash.
******Aerobic, Entero-bacteria, Yeast and Mold** : These are all microbiological screens. A gold rating passes with flying colors; silver is questionable. Bronze means trouble.
**Pesticides:** Any pesticides detected would "fail" and not be salable.
**THC Max:** 17.99 percent is powerful but not extraordinarily so by today's standards.
**THCA:** This is a measure of the THC acid on the leaf before it is burned and becomes THC. THCA is a strong anti-inflammatory and is not psychoactive. This percentage correlates with the amount of THC and is also a mark of freshness.
**CBD Max:** Coming in at 0.27 percent, there's not much here. High-CBD strains are now available in most medical markets, with ranges rivaling the high-THC plants in the mid to upper teens, and occasionally as high as 20 percent.
**CBG:** Another nonpsychoactive cannabinoid with some painkilling benefits. Dr. Raber calls this a good level.
**THCV:** This is a THC analogue that is involved in the appetite cascade, but it does not have psychoactive properties. Concentration is low.
**CBN:** CBN indicates if the bud is old, which this isn't.
**Terpenes:** The smell molecules that help determine the trajectory of the high.
**Myrcene:** A terpene that purportedly contributes to the couchlock and sleepy "indica" effect. Anything over 8 or 10 will potentially produce a noticeable effect.
**Pinene:** This terpene dilates the bronchial tubes in the lungs. It is stimulating and enhances focus. An appreciable number is present here.
******Beta-caryophyllene:** The back-notes in black pepper and cloves, beta-caryophyllene is in high concentration, which indicates that it will activate more receptors in the body.
**Limonene:** A terpene that's anti-inflammatory, antitumor, and antifungal. It is purported to produce feelings of clarity in some strains. This Blue Headband sample has a negligible amount.
**Linalool:** The small amount of this terpene indicates it may be slightly sedative, but this effect could also be overwhelmed by the larger amounts of other terpenes present.
* * *
TERPENES: FORECASTING THE HIGH AND THE HEALING
* * *
Source: http://www.alternet.org/drugs/same-compounds-behind-marijuanas-distinctive-stinky-smells-give-clues-about-kinds-high-youll
## ___Chapter 10_
## THE FOUR ENHANCEMENTS
_Inside the mind (wherever that is)_
Ineffability is the hallmark of any consciousness-changing pursuit, which makes it powerful to experience but difficult to discuss. Because most of marijuana's powers are not as immediately obvious as its capacities for fun or relaxation, and because we tend to oversmoke the plant, it seems preposterous at first glance that this mere weed might be a route to higher cognitive functioning.
It's difficult not to conjure up those cartoons that feature a shaggy-haired stoner, gazing at a smartphone uttering something banal, like "Oh wow, man!" Dumbfounded by the obvious, inarticulate to the extreme, that's the perception of the cannabis user. But I have come to think that even those words "Oh wow, man!" contain a key attribute of cannabis consciousness: an expanded receptivity to the world. Cannabis opens the reducing valve that is our brain. The taste of food, the embrace of a lover, the colors of the sea—the world is more vibrant, more amplified in the enhanced state. A more intriguing question might be, "Is there more to being high than an amplified state of receptivity?"
I began to explore the idea by examining recent studies with psilocybin and people facing the end of their lives. These studies concluded that psychedelics can create powerful and permanent changes in hearts and minds. Of course, cannabis confers a far more attenuated experience than psilocybin does, and I'm not comparing them head-on. But both substances are classified as psychedelics, not because they cause hallucinations, but because, as the Greek root of the word indicates, they both reveal the mind ( _psych_ _ē_ = mind, and _d_ _ē_ _loun_ = to make visible, to reveal). Unlike those of psilocybin, however, the effects of cannabis are inconsistent. I've long thought this inconsistency is the primary reason that people who like control shy away from pot and veer toward more predictable substances.
Opiates lull users into a pleasant reverie. They blunt the senses, bringing relief but little palpable joy. Cocaine, meth, and amphetamines rev us up by dumping massive amounts of dopamine in the brain. They make us feel powerful, but they don't tie us to anything beyond our own temporarily bloated egos. Alcohol is socially lubricating in small amounts, but drink too much and the effects become depressive or disinhibiting, and you tune other people out. Psychedelics and cannabis (dosed properly) enhance our receptivity to other humans, animals, and maybe to something sacred. The effects of cannabis are not nearly as dramatic or life altering as those of psilocybin, DMT, or LSD, which is one reason why it is used less often in shamanic and other holy rituals.
Most organized religions make little mention of the plants that yoked humans to the divine, even though, as Richard Schultes, the godfather of psychoactive plant research, noted, cannabis "may have introduced man to an otherworldly plane from which emerged religious beliefs, perhaps even the concept of deity. The plant became accepted as a special gift of the gods, a sacred medium for communion with the spiritual world, and as such it has remained in some cultures to the present."
Scholars agree that as organized religions exerted their sway over more followers, they demonized the spiritual connection between plants and people. Priests in the Middle Ages labeled plant users sorcerers or witches who relied on potions to cast spells on others. The Spanish Conquistadores brutalized _curanderas_ in Mexico who used psilocybin and peyote to open doors to a secreted world. Unlike the Rastafarians and Hinduism's Shiva sect, both of which still use pot as a gateway to the divine, most Western religions shun mind-expanding substances in favor of prayer, confession, repentance, and suffering—methods of redemption that keep the flock corralled and reinforce the church's authority.
Pot famously supplies an extra measure of perspective, and perspective is very threatening to those who don't want their authority questioned.
The yoga sutras, written in Sanskrit a few hundred years before Christ, cite "herbs" as one of five methods of piercing the veil between the conscious and unconscious mind. Conventional religious scholars contend the "herbs" in question refer to everyday cooking items. But Mark Haskell Smith, the author of _Heart of Dankness: Underground Botanists, Outlaw Farmers, and the Race for the Cannabis_ _Cup_ , is fairly certain that the sutras weren't talking about cardamom. A yoga practitioner for over twenty years, Smith said a few puffs before practice guides him "more deeply into the poses." Not I. Except for activities that I perform on autopilot—swimming, cycling, or skiing, say—pot has never aided my physical prowess. Nor has it ever brought me closer to God, whoever she may be.
And while neuroscience has described the mechanics of molecules' crossing certain synaptic gaps to couple with proteins to activate receptors, those explanations are far less compelling than the effects the substances yield. Science can provide a partial answer, but I have found the reports of poets, philosophers, and astronomers far more insightful about how the states of expanded consciousness _feel_.
Carl Sagan captured the many-faceted sensations of being high in a breakthrough essay he wrote in 1969 as Mr. X. "I do not consider myself a religious person in the usual sense, but there is a religious aspect to some highs. The heightened sensitivity in all areas gives me a feeling of communion with my surroundings, both animate and inanimate. Sometimes a kind of existential perception of the absurd comes over me and I see with awful certainty the hypocrisies and posturing of myself and my fellow man. And at other times, there is a different sense of the absurd, a playful and whimsical awareness. . . ."
Communion with nature and with other beings, an existential perception of the absurd, a distance that yields perspective: these are the experiences that I find interesting. They are also the areas that empirical science has the most difficulty describing.
Around the same time Sagan was exploring pot, Dr. Andrew Weil wrote in _The Natural Mind_ that altering consciousness was a fundamental urge in human beings, and that we use all sorts of substances to change our minds—caffeine, sugar, alcohol, tobacco, among them. Aldous Huxley and Timothy Leary had previously flirted with similar ideas, but Weil, the father of integrative medicine in the West, surveyed cultures globally and included meditation, dancing, fasting, yoga, and prayer in his methods of altering consciousness. Weil also pointed out that this urge occurs in children as well. As kids, both he and I were addicted to hyperventilating and spinning in circles, an indulgence I pursued until the age of eleven, when I succeeded in blacking out and cracking my skull on the sharp edge of a table as I crumbled to the floor. Thus I learned to proceed cautiously when altering consciousness, for it is not always possible to predict where you'll land.
But it isn't only our species that seeks an altered state. Dr. Ronald Siegel, a psychopharmacologist who was an associate research professor in the Department of Psychiatry and Biobehavioral Sciences at UCLA, posited that the urge to transcend our everyday minds is a fourth drive in humans, followed only by the drives for drink, food, and sex, and that this fourth drive is shared by all creatures. Certain butterflies get drunk by sipping on the alcohol produced by fermented fruits on vines or trees; cats get sexually charged by catnip; coffee beans drive goats into ecstatic states that frequently end with them temporarily abandoning their guard against predators and tumbling down hills. "In every country, in almost every class of animal, I found examples of not only the accidental but the intentional use of drugs," Siegel wrote. "After examining thousands of cases, I conclude that the action of an animal in seeking out intoxicants was a natural behavior in the animal kingdom."
Siegel's observation, while fascinating, isn't wholly accurate as far as the motivation of insects is concerned. Newer research indicates that their tiny brains lack pleasure centers, so the "intoxication" they feel may simply be agitation. Nor is their "intention" an act of free will, as the concept of agency or mind can't be applied to insects. But the human brain is far more complex. Its topography is as baffling as the way it functions. Recent theories describe the brain as an infinite number of chemical pathways—neural maps—that traverse different areas when firing. Robin Carhart-Harris, a British neuroscientist who is using fMRI technology with patients on psilocybin journeys, is one such cartographer of consciousness.
By planting microelectrodes inside the brain, he is able to see changes in blood flow and oxygen levels of different areas. But he takes this one step further by talking to patients who are tripping on psilocybin and then correlating what he sees on scans with what people are experiencing. He is literally opening a window into the mind—or, more accurately, the brain, since we have no idea where the human mind resides.
We tend to think of our brains as sponges that absorb sensory data, but the brain functions more as an editor that prunes the heaps of sensory input of our daily lives so that we can make sense of it all. In _The Doors of Perception_ , Aldous Huxley compared the brain to a reducing valve that shuts out most of the information flooding into our senses. When Carhart-Harris looked at the results of his fMRI scans that pinpointed the areas that the drugs were affecting, he saw that Huxley was onto something. Psychedelics substantially reduced brain activity in the various interconnected areas known as the "default-mode network," rather than opening up the floodgates of perception.
The default-mode network was first described in 2001, and it has since become the favored metaphor by which neuroscientists discuss the structure of consciousness. In the beginning of the twentieth century, Freud described the architecture of consciousness in terms of ego, id, and superego. In the 1980s, it was left-brain/right-brain thinking. But the default-mode network is the first neural structure that scientists have actually been able to see at work.
Basically, it comprises a hub of brain activity that activates when we are at a state of wakeful rest. It's on when we are not attending to the world or to a task, and it "lights up" when we are daydreaming, ruminating, or removed from sensory processing. It's akin to what is commonly referred to as right-brain thinking. It is however, self-referential, which means it always maintains a concept of the bounded self.
Carhart-Harris discovered that blood flow and electrical activity in the default-mode network shut down significantly when people are on psychedelics. Since he was able to speak to the patients as he was viewing these neurochemical changes, he listened to them consistently describe the loss of self and the merging with the universe that occurs while tripping. When the default-mode network shuts down, activity in other brain regions is unleashed, and things hidden from view during normal waking consciousness come to the fore: emotions, memories, wishes, and fears. Regions that don't ordinarily communicate directly with one another strike up conversations.
Carhart-Harris agrees with Freud that the psychedelic state resembles the psychological condition of the infant who has yet to develop a sense of himself as a bounded individual. Psychedelics loosen the ego boundaries that separate us from the rest of the world and allow the workings of the unconscious mind to rise above the surface. They remove a filter that hides much of reality. It's possible—probable even—that cannabis does the same thing, but to a lesser extent.*
This sort of enhanced thinking can help people by relaxing the grip of our overbearing egos and the rigid rationality they enforce. By adulthood, the mind has learned to predict and anticipate the way the world works based on past experiences. Such habitual thinking saves us a lot of mental energy, since we don't have to approach every situation with what the Buddhists call beginner's mind. Rote thinking—doing things on autopilot—enables us to survive and navigate our complex environments.
Up to a point. In Carhart-Harris's view, adults pay a steep price for order. "We give up our emotional lability, our ability to be open to surprises, our ability to think flexibly, and our ability to value nature," as Carhart-Harris puts it. The ego can become despotic. This becomes clear when we are depressed. The self turns inward and the uncontrollable introspection gradually grays out reality.
Carhart-Harris contends that people suffering from mental disturbances characterized by excessively rigid patterns of thinking, such as addiction or obsessive-compulsive disorders, could benefit from psychedelics, since they "disrupt stereotyped patterns of thought and behavior." In his view, these disorders are ailments of the ego. He also suspects that psychedelically induced disruptions could lead to more creative thinking—some brains could benefit from a little less order. Whether cannabis can take them there is yet to be proved, but there is ample evidence that it is one way of "pulling back the veil of consciousness, to paraphrase William James, to open us to a different way of greeting the world.
Even if you've never taken a substance, this less mediated way of thinking will feel vaguely familiar—we call it intuition or daydreaming. Those who are more prone to being hypnotized or who are more plugged into the voices inside their heads—and I'm not one of them—rely on intuition more than their reason-based minds. When people do something "without thinking about it," or when they are in the "flow," they're letting go of some cognitive processing and accessing some of these other, more instinctive forms of awareness.
Western culture favors rational thinking over this more mysterious or "spiritual" thought. You don't have to be a religious person to recognize this. But by stressing the rational, we sacrifice a certain amount of receptivity to the natural world around us. I'm not arguing that cannabis will help us contend with climate change or the eradication of certain animal species, but there is little doubt that it affects the way we see our place in life's grand order. This enhanced receptivity, not to mention insight, empathy, and awe, are but a few of the cognitive functions that cannabis underscores. I refer to them as the Four Enhancements.
RECEPTIVITY
Cannabis enhances our responsiveness to the world around us and inside our own bodies as well. When high, all of our senses—touch, taste, sound, sight, smell—become _italicized_ , in Michael Pollan's phrasing, as if we are capable of absorbing more color, flavor, and scent.
Increased receptivity means that we are, as the poet bell hooks put it, less amputated from our emotional lives. This may explain why more men gravitate to pot than women. Forgive the generalization, but women typically appear to be innately more emotional and intuitive than men. Men, for many reasons, favor the rational and logical over the more inward-facing side of themselves, and thus can lose touch with it. Pot, used mindfully, can reconnect them with their more nurturing aspects.
Experienced smokers don't resist these states. Like a skier coursing through moguls, they lean into them and ride them to deeper pleasures. I'm thinking in particular of two cognitive functions that pot famously distorts: short-term memory and one's sense of time. When these cognitive disruptions occur, thoughts and feelings bullet through our brains more quickly than we can process. Verbal acuity sometimes flies out the window, perhaps because we're taking in so much more. When we're more open, we're less invested in being on top of things, and this can be misinterpreted as being vulnerable, gullible, less aware—even though we may well be absorbing more than otherwise.
The first thing that nonsmokers notice when high is the short-circuiting of their short-term memories, a state I call memory interruptus. This state of thoughts darting in and out of the brain so quickly that they can't be grasped can make anyone feel just one step away from early-onset Alzheimer's. It doesn't last long, and no long-term effects on memory have ever been demonstrated. Still, it can be disconcerting when it's not hilarious, as it often is, as this snippet from the cult comedy classic _A Child's Garden of Grass_ illustrates:
VIRGINIA: "Are you hungry?"
ANDY: "No (long reflective pause). Wait a minute. Did you mean am I hungry for food or am I hungry in the abstract, like hungry for knowledge or adventure?"
VIRGINIA: "What were we talking about?"
ANDY: "You asked if I were hungry."
VIRGINIA: "Did I?"
ANDY: "Yes."
VIRGINIA: "Well, are you?"
ANDY: "Am I what?"
As Sebastián Marincolo points out in _High: Insights on Mari_ _juana_ , his brilliant book that examines the benefits of pot as opposed to the detriments, and to which I am indebted for much of the thinking in this chapter, experienced users can turn memory interruptus to their advantage.
Marincolo says that memory interruptus may to some degree be caused by mind racing, which could lead to a sort of buffering problem in the brain. If you take a rapid series of photos—of athletes performing, say—the camera eventually needs a moment to save the images, and at that instant the "stream" breaks. This could very well happen with our thought stream during a high. It's less of an "impairment" of short-term memory than an overflow of input. Marincolo also suggests that the pre-synesthetic effect of the high allows for wider associative leaps in thinking, so conversations travel far beyond the original subject; this makes it hard to recollect where you started and easier to lose the thread.
But when users quiet down and allow their receptivity to increase, they can access different types of memory—associative and episodic among them. A skilled user can relax and let go of his rational mind and allow other memories buried deep in the vaults to rise to the surface. In fact, before cannabis was banned in the United States, psychiatrists from the American Medical Association testified to Congress that memory retrieval was one of the most promising uses of the herb in psychotherapy.
There's one additional benefit of memory interruptus, which is one of cannabis's greatest unheralded pleasures: it can create a more childlike way of viewing the world. This, in turn, results in a renewed sense of awe, an ideal remedy for jaded adults in need of fresh eyes.
Picture a child who's greeting the world for the first time. Everything tickles him. But for adults to experience awe, we must first forget our preconceived notions. Cannabis assists that, and it offers one additional benefit: it is gentle. It lifts us out of our everyday minds without making us lose our minds.
The writer and art dealer Mark Wolfe marshaled some of that childlike "Oh wow, man!" awareness to help him contend with some of the rougher patches of fatherhood. He discovered that cannabis, which he had been using to alleviate back pain, had one amazing off-label benefit: parental attention–surplus syndrome.
After a long day at work in his gallery, Wolfe found himself to be a dutiful, but not especially enthusiastic, dad to his three daughters. Fatherly obligations felt like chores, mostly because he was exhausted and couldn't shake off his work stress. That stress was making daily rituals like putting the kids to bed interminable. Here was a typical evening exchange between Wolfe and his oldest daughter before he rediscovered pot:
CHILD: Daddy, can you show me how to make a Q?
FATHER: (sipping bourbon and soda, staring at iPad) Just make a circle and put a little squiggle at the bottom.
CHILD: No, show me!
FATHER: Sweetie, not now, OK? Daddy's tired.
Enhancement led to this exchange:
CHILD: Daddy, can you show me how to make a Q?
FATHER: (getting down on the floor) Here, I'll hold your hand while you hold the pen and we'll make one together. There! We made a Q! Isn't it fantastic?
CHILD: Thanks, Daddy!
FATHER: Don't you just love the shape of this pen?
"I swear it has made me a more loving, attentive and patient father," Wolfe wrote in the _New York Times_. "I am able to become a kid again, to see things through my daughters' eyes and experience, if I'm lucky, the wonder of each new game, each new object and sound, as they do." Of course, his more task-oriented mind would prefer he use meditation or yoga to achieve these states, but the realities of modern parenthood have tempered his ambitions. "If I had a full-time staff of cooks and nannies I'd give that a whirl. But . . . my wife and I are raising multiple tots on modest incomes in a small space in a very expensive city. No time for Tantra."
I stumbled upon the benefits of awe renewal quite unexpectedly when fighting the depression that accompanied a midlife crisis that didn't hit me until my fifties. I'm not big on making generalizations based on age, but I found that in our twenties and thirties, trudging up the mountain of life, our focus is forward; we're excited and challenged by life's possibilities. From our dreams we build the narrative of our selves. Somewhere in our forties we typically confront one of two possibilities. We've achieved success—material wealth, families, houses, education—but it's not all it was cracked up to be. The soundtrack to this reckoning is Peggy Lee's "Is That All There Is?" Those who haven't reached their goals must instead reconcile their shortcomings. They can stay on the path they've been treading or attempt an about-face and forge a new direction. Their soundtrack might be John Lennon's "(Just Like) Starting Over."
I got hit with the double-whammy combo platter. I had found success as a magazine editor but I found the work dispiriting. I was spending countless hours producing publications that had no connection to my life and, in the process, time was hurtling by, leaving me in its wake. Adrift from the passions that once stoked my fires, I sank into a vortex of depression for the first time in my life. It took me months to identify it. All I knew was that some part of my spirit had gone missing.
Eventually, with the help of twenty milligrams of Lexapro (plus talk therapy and an erratic Vipassana meditation practice), I stumbled into a new path forward. But it was a years-long slog. I was lucky enough to be experimenting with cannabis at the time, and it was one of the routes that helped bring me back to myself, perhaps by loosening some of the ego lock that Carhart-Harris speaks about and reconnecting me with that state of wonder. It helped me see the world and myself anew.
I was noodling this while driving around Los Angeles on one of my several trips there. Passing through the cluttered landscape of asphalt roads, billboards, and unremarkable concrete buildings that is LA, I was struck by just how difficult it is to grasp the heart and soul of the city through a car window. Only when flying ten thousand feet above can I take in the extraordinary terrain that makes up this megalopolis between the mountains and the sea. Seeing the whole requires perspective, and that's what pot can provide: a perch from which I can stand back from my thinking and get a wider vantage than what I can normally see at close range.
As one friend put it, "Feeling more fully present is the most important first step to everything in life. If I'm in a bad mood my world feels narrower, my judgment is more cynical. I need to attend family gatherings that I know won't be that much fun, so rather than sitting back with my arms folded and being grumpy about what's going on at the table, I take a puff or two. It makes me more accessible and engaging and more in touch with the humor of the situation. By letting go of some of my mind-based judgments, I have a better time. Some people may call this an emotional crutch, but a crutch is a tool that also enables people to walk, so depending on how it's used cannabis provides a sort of freedom."
Perspective offers relief from our everyday selves, but it doesn't occur by simply lighting a joint. It took me a long time, and a lot of wasted weed, to figure out how to choose the proper strain, dose, and setting to get where I wanted to go. Ignoring these elements makes it too easy to overindulge, veg out, and ultimately lose track of your priorities. Cannabis can be a famously placating substance, which is both its great strength and failing. It makes people content to be where they are. Unlike cocaine, say, which the writer David Lenson terms a "drug of acquisition that makes users hunger for more," pot generally makes everything in front of you just fine, which can be both good and terrible. The rock goddess Chrissie Hynde expressed this best: "Smoking while vacuuming makes vacuuming better but smoking while sitting on the couch makes vacuuming harder." Complacency is one reason cannabis is seen as demotivating. If you want to get to awe, it's crucial to know how much to smoke, when to smoke, and when to skip it altogether. A bit of awe is awesome; too much can be awful.
DEEP FOCUS
Along with memory interruptus, the other common effect of cannabis is time slowdown, that pleasantly languorous experience of the hands of the clock pushing through honey. Musicians have famously extolled time slowdown, as it seems to provide them with more space between notes in which the next phrases seem to originate. Some find it heightens sound perception, so chord formations seem easier to analyze.
Time slowdown induced from a strain high in pinene or limonene can create a state of extreme attention or mind racing that Marincolo calls hyperfocus. Such extreme attention can magnify one detail of a painting until it occupies the entire frame. It also allows us to make rapid-fire associations, and neuroscience has shown that the mere fact of the brain ticking along quickly causes feelings of joy.
Here's how Carl Sagan described hyperfocus in his Mr. X essay:
I can remember one occasion, taking a shower with my wife while high, in which I had an idea on the origins and invalidities of racism in terms of Gaussian distribution curves. It was a point obvious in a way, but rarely talked about. I drew curves in soap on the shower wall, and went to write the idea down. One idea led to another, and at the end of about an hour of extremely hard work I had found I had written eleven short essays on a wide range of social, political, philosophical, and human biological topics. . . . I have used them in university commencement addresses, public lectures, and in my books.
It was his conclusion, though, that struck me: "I am convinced that there are genuine and valid levels of perception available with cannabis (and probably with other drugs) which are, through the defects of our society and our educational system, unavailable to us without such drugs. Such a remark applies not only to self-awareness and to intellectual pursuits, but also to perceptions of real people, a vastly enhanced sensitivity to facial expression, intonations, and choice of words which sometimes yields a rapport so close it's as if two people are reading each other's minds."
Here was a great scientist expounding on matters that can't be measured but that he found immeasurably useful. Lesser minds might dismiss them because they can't be quantified.
Deep focus, or hyperfocus, also explains why certain professions, such as computer programming, attract cannabis smokers. One blogger, Corpus Callosum, explains hyperfocus hyperlogically: "Lets [sic] say you have 1000 units of brain processing power per second. Normally you could put 200 units to 5 different things thereby handling 5 things simultaneously, but on a more superficial level. Pot can let you focus 950 units onto whatever you are doing or thinking about so you can do that one thing better." Chaz Carlson, a writer at _Tech Noir,_ put it in less mechanistic terms: "You are able to focus on details you might not notice before, your brain connects ideas that it might not otherwise, and you can get fully immersed in something."
If there's any doubt about this, let me point out that in 2014, the FBI changed its no-tolerance drug policy to attract more cannabists to its cybercrime-fighting ranks. "I have to hire a great workforce to compete with those cyber criminals and some of those kids want to smoke weed on the way to the interview," FBI director James Comey said at a conference of the White Collar Crime Institute in Manhattan. When one conference-goer asked the FBI chief about a cannabis-smoking friend who had shied away from the agency because of the policy, Comey replied: "He should go ahead and apply." Comey later recanted that comment, but the message had already been publicized around the world. Mission accomplished.
INSIGHT
Norman Mailer counseled his kids to finish their educations before they began using cannabis. The more you know, the better the flow of ideas when high, he contended. "You think associatively on pot, so you can have real extraordinary thoughts. But the more education you have, the more you have to put together . . . the more wonderful connections there are to see in the universe." I cannot prove that theory, and it hints at a correlation between intelligence and better highs, which seems dubious. All the same, there seems to be some grain of truth about pot expanding the number of associative connections and, more interestingly, linking thoughts that seem to have no common thread.
In the 1850s, the members of the Club de Hashischins ( _hashashin_ is the Arabic word from which "assassin" is derived—more bad press for cannabis) dressed in robes and gathered at a hotel on the Île Saint-Louis in Paris to investigate the "intellectual intoxication" sparked by hashish. They suspected it was preferable to the "ignoble heavy drunkenness" of alcohol but wanted to test this exotic new substance for themselves. Hash, like tobacco, was a novelty in Europe at that time; Napoleon's troops had brought it back from North Africa, and the intellectuals of the day, including Charles Baudelaire, Victor Hugo, Alexandre Dumas, and Théophile Gautier, gathered regularly to ingest massive amounts of it, which they prepared as a "marmalade." Based on their descriptions of the hallucinatory spirals they slipped into, it appears that they were spiking the hash with opium, that other popular Eastern import of the day.
Baudelaire, the most prolific writer in the group, concluded that hashish didn't spark any new ideas. He deemed it little more than a magnifying glass to the thoughts already present in a user's mind; he and I (and Sagan) will have to agree to disagree on that. But almost as an afterthought, he made one observation that caused Sebastián Marincolo to take notice: hashish made "sounds take on colors and colors contain music." Marincolo traced the connection between this 160-year-old observation and one of the oddest illnesses known to man, synesthesia, and uncovered recent findings in neuroscientific theory to explain how cannabis might trigger the type of insight that leads to creativity.
Synesthesia is a cross activation of the senses in the brain. Russ, the synesthetic character played by Matthew McConaughey in the first season of the television series _True Detective_ , does a superb job of explaining his illness: "Synesthesia is a misalignment of synaptic receptors and triggers. . . . It's a type of hypersensitivity. One sense triggers another sense, like sometimes I'll see a color and it'll put a taste in my mouth. A touch, a texture, a scent, can put a [musical] note in my head." This cross activation of the senses occurs ten times more frequently in creative personalities. Duke Ellington, Leonard Bernstein, and Vladimir Nabokov were famous synesthetics, as is David Hockney. Nabokov used to cry when he saw certain numbers printed in the wrong color, a complaint that only his mother understood because she too had the disorder.
The synesthetic connection to creativity makes even more sense once you understand that the brain areas that process our senses are not fixed or surrounded by firm borders. In normal brains, these areas are loosely kept apart by chemical fences that block neurons from triggering neighboring regions. But when Dr. V. S. Ramachandran, the neuroscientist who heads the Center for Brain and Cognition at the University of California, San Diego, investigated these areas further, he saw that when the inhibiting molecules malfunction, some sense signals activate neighboring regions. In less enlightened times, psychiatrists called hearing colors or tasting shapes a sort of hysteria. Today we know better.
Uncovering the mechanics of synesthesia led Ramachandran and his coresearcher E. M. Hubbard to believe that they had inadvertently opened "a window into the nature of thought." This is most easily grasped by the way we use metaphor, one of our most abstract forms of thinking. Metaphor can be seen as a simple presynesthetic response. We all understand "feeling blue" seeing "loud colors" and tasting "sharp flavors," for example. And if you think that metaphors are arbitrary, they aren't. "Loud shirt" or "sharp taste" makes sense to us; "bitter touch" doesn't.
Cannabists know that when we're high, interesting links often form between unrelated concepts and events. The high famously connects certain music with deep feelings, or, in Sagan's case, explained the roots of racism via a complex statistical equation. A connection was created that had previously eluded his rational thinking. This linking of disparate ideas is one of the reasons so many people enjoy a puff before viewing art or listening to music. Cannabis allows previously unnoticed associations to rise to the surface. Some of these insights are visual, others are intellectual, and sometimes they involve all the senses.
In his 1966 essay "The Great Marijuana Hoax," Allen Ginsberg, the father of Beat poetry, detailed how smoking a joint enabled him to finally understand the motivations behind certain paintings that had always eluded him. "I first discovered how to see Klee's Magic Squares as the painter intended them (as optically three-dimensional space structures) while high on marijuana. I perceived ('dug') for the first time Cezanne's 'petit sensation' of space achieved on a two-dimensional canvas (by means of advancing & receding colors, organization of triangles, cubes, etc. as the painter describes in his letters) while looking at 'The Bathers' high on marijuana."
If Sagan and Ginsberg are reliable guides to inner experience (and I believe they are, especially as they approach it from such different perspectives), then it stands to reason that pot can be used to inspire fresh insight, perhaps by loosening the boundaries that constrain our task-oriented rational thinking. Illumination, in my experience, rarely comes from drugs, but drugs can introduce users to see possibilities where previously they saw none.
Creativity, of course, occurs in many forms and crosses disciplines. I conducted a small, unofficial survey of several associates from different professions to test the hypothesis. Joseph S., a venture capitalist who funds socially progressive start-ups, told me that he uses cannabis to help him reframe problems. "During a board meeting we use our linear minds when it comes to strategy and oversight. But an after-dinner enhancement can bring other dimensions that we may not have considered. Great ideas often come out, but our rule is to make no decisions until the next day."
Alan G., an architect, was designing an urban renewal project to combat sprawl in a small Southern city. By day, his team attacked the project with plans and schematic drawings. But at night they'd take a few puffs and then explore the neighborhood and surrounding wilderness on foot, interacting with the local fauna and exploring the ways residential and commercial (and animal) behavior intersected. Rather than approaching a neighborhood solely as a grid of streets and sidewalks, his team used cannabis to help envision it more broadly as a complex ecosystem, more like a garden, in which every element plays an equal role. This more holistic attention helped new patterns emerge. In their final plan they moved backyard vegetable gardens to front yards, designed corner lots to be pocket parks with benches, turned intersections into play areas, and altered traffic patterns to accommodate the changes. The project won national acclaim.
"We were able to see how you can make a big cultural impact in a complex urban environment by a changing a few simple things," the architect told me. He envisions the day when businesses use guided cannabis workshops to explore creative problem solving. "It's in the interest of all cannabis activists in the post-prohibition era to make sure this sort of education happens safely and successfully," he says. "It could be enormously useful."
INTIMACY, EMPATHY, AND SEX
Cannabis has been vaunted as an aphrodisiac for at least three thousand years, since the Persians brought it to India and extolled the ways it boosted sensual pleasure through Tantra. It loosens inhibition, intensifies touch, and some even claim it extends the duration of orgasm—all of which enables one to get lost in an embrace.
Cannabis has shown itself to be more than just herbal Viagra; it famously magnifies feelings of communion with a sexual partner. This is one of its great powers. In my experience, it opens the door to something beyond physical pleasure: real and deep intimacy. "After a while, sex for some couples is problematic," says Dr. Nick Karras, a sexologist and the author of an unpublished book, _The Passionate High: A Lover's Guide to Cannabis_. "You tell them to drink a glass of red wine or to have a date night, but what really needs to happen is that you have to reframe what sex is. Cannabis is great for enhancing your imagination and increasing your empathy."
Karras is on to something: cannabis undoubtedly expands feelings of empathy, and empathy has many benefits, not only interpersonally and societally, but also evolutionarily. The ability to imagine what another is feeling has worked to our advantage as a species. It's essential to almost every social interaction and has enabled us to advance by cooperation. It makes us sympathetic friends, good negotiators, loving parents, and responsive citizens. It also makes us fierce and strategic opponents. Without empathy, we couldn't estimate our enemy's next move (presumably Machiavelli was a highly empathetic statesman, but one you wanted to keep on your good side). Modern Western cultures that stress efficiency and technology tend to undervalue empathy, often to their detriment, and there's an explanation for why that occurs that will shortly become apparent.
One clue about the way empathy works in the brain came with the discovery of mirror neurons. In the early 1990s, Giacomo Rizzolatti and his research team at the University of Parma in Italy set out to investigate a type of brain cells—motor neurons—that transmit the electrical impulses that control movement. He attached microelectrodes to cells in a monkey's brain to see which neurons fired when the animal reached for a peanut.
The motor neurons went off as expected, but something odd happened when the monkey saw a lab assistant reach for the peanut: the very same motor neurons fired again. The scientists thought their wiring had come undone. The monkey hadn't moved, so why were his motor neurons afire? Further tests revealed that the monkey's motor neurons were "mirroring" the activity being performed by someone else.
"Mirror neurons tell us that we're literally in the minds of other people," says Marco Iacoboni, the director of the Brain Mapping Center at UCLA, and chances are they demonstrate that we're molecularly wired to take other people into account. When we see someone in pain, for example, we imitate her expression of grief without thinking. Yawning is contagious. When a toddler sees a friend crying, his tears flow almost automatically. All are the result of mirror neurons.
Some scientists think that a malfunctioning mirror neuron system may be a determining factor in autism. And since cannabis has been shown to somewhat ameliorate the effects of this disease, thinkers like Marincolo have speculated that cannabis use may stimulate mirror neurons and, consequently, play a crucial role in enhancing empathy.
Marie Myung-Ok Lee, a writer and professor at Columbia University, documented her experiments with cannabis on her severely autistic young son. J. was having three hundred tantrums a day and appeared to be in such constant pain that his only response to affection was violence. When his grandmother once attempted a hug, he struck her. Other behaviors were inexplicably odd and potentially fatal. He'd bang his head against a porcelain tub until he bled. He ate his clothing, which caused as much pain going in as it did coming out, and drove his parents to buy him edible shirts.
Marie contacted a grower, a controversial decision given her family's traditional Korean antipathy toward cannabis. After a few months of use, J. began to react to other people. He laid his grandmother's shoes out before her. When she smiled, he smiled back, and then he allowed her to hug him. One of his big breakthroughs occurred one evening during supper. Typically, meals ended with plates being frisbeed against walls, so Marie and her husband would often leave J. alone to finish eating. One night, they were in another room and heard their son leave the table to go into the kitchen. Rather than the sound of porcelain crashing, they heard a mysterious splish-splashing. J. was washing his bowl in the sink and then loading it into the dishwasher—he was imitating his parents' actions for the first time. While these small acts are hardly the powerful displays of affection his parents had hoped for, they do indicate that cannabis helped create an awareness of others that had previously been absent.
In _Bowling Alone_ , Robert Putnam, the sociologist who has been called "the poet laureate of civil society," points out that the most telling sign of happiness isn't wealth or health, but one's connections to other human beings. Cannabis used intelligently can build bridges of connection. In fact, a 2014 study from the University at Buffalo examined 634 couples in their first nine years of marriage and found that those that smoked together were happier and less prone to domestic violence than those that didn't. One newspaper trumpeted this story with the headline "Could Smoking Marijuana Be GOOD for a Relationship?" Hyperbolic, yes, but that's one headline you'd never see topping an article about gin.
PRICKLES AND GOOS
Not everyone is prone to using cannabis for inner explorations, and plenty of people deem empathy or associative thinking irrelevant to everyday life. Thinking about the way we think or feel doesn't appeal to everybody. One of the earliest and most entertaining explorers of consciousness, Alan Watts, described different personality types as prickles and goo. Prickles want rigor and precise statistics; they're edgier, introspection-averse personalities who see gooier types as hopelessly vague. Goos accuse prickles of being overly literal and cut off from inner experience. Prickles, they say, know the words but not the music. Of course, few of us are exclusively prickles or goo; as Watts said, it's gooey prickles and prickly goos, and most of us veer between these two poles.
Another way of discussing these disparities is in terms of right-and left-brain thinkers. No matter what you call them, the point is the same: the brain has several lenses through which it perceives the world.
In a footnote to _Dragons of Eden_ , his Pulitzer Prize–winning book about the evolution of human intelligence, Carl Sagan postulated that marijuana suppresses left-brain activity, the ruler of our rational minds, in favor of activity in the right hemisphere, which is more inclined to favor connection and the interdependence of things. And Iain McGilchrist's magisterial book _The Master and His Emissary_ sets forth a fascinating reevaluation of the right/left brain divide and how the struggle within the brain determines human consciousness. This weighty tome reads like a thriller; it's so rich with ideas I had to reread it immediately after finishing it the first time.
The concept of the divided brain entered the mainstream in the 1980s and launched an industry of scientists, authors, and marketers, all trumpeting the idea that different areas of the brain control specific senses and mental processes. The right hemisphere was considered the silent, less intelligent partner, content to preside over the gooier areas like art, music, and our inner selves, while the left hemisphere controlled the more prickly domains of rational thought. Advanced imaging technology has debunked that idea. "It's not simply 'emotion on the right, reason on the left,'" McGilchrist says. "There are plenty of both aspects in both sides of the brain."
The brain is far more "plastic" than originally thought, and MRI studies of brains damaged in accidents have shattered the idea that any one hemisphere is ever in control. The brain isn't divided by function; instead, it's more a difference of perspective, of conflicting ways of seeing the world. This dual perspective enables us to see both close-up and broad versions of reality, and to think both linearly and abstractly at the same time. To illustrate this ongoing dance between the right and left hemispheres, McGilchrist relies on Nietzsche's fable about the master and his emissary, from which he derived the title of his own book.
In this story, there was a wise ruler who presided over a vast kingdom. This ruler didn't want to lose touch with the different areas of his kingdom, so he appointed an emissary to travel the kingdom to report back on what he saw. In doing so, the emissary learned about the defense systems in each realm; he understood minute problems and figured out a way to exploit the unhappiness of some locals. He also realized just how powerful he was, which enabled him to easily usurp the ruler.
Here's how this translates: the right brain, the ruler, prefers to sit back and take in the whole picture. It rules areas that preside over empathy and imagination. It also controls metaphor, which McGilchrist calls "the associations by which we come to know the world."
If the right brain provides a floodlight on experience, the left hemisphere provides the spotlight. It allows the focused attention we need to survive. It enables us to parse the mechanics of how things work: how we get our food, build our houses, make our laws. The left hemisphere dissects things into their component parts so that we can understand them. The left side also controls language, and it is largely responsible for knowledge, which is why it was originally considered the "smarter," more calculating side. Simply writing that sentence convinced me that the left brain is more important to survival, which is exactly what it wants me to think.
It was impossible to read McGilchrist's book and not wonder if cannabis stimulates right hemisphere thinking—Sagan seemed to think it did—so I contacted him through his website for further discussion. He graciously declined my invitation to talk, but unlike most of the scientists I spoke to in researching this book, he had no compunction revealing his own experience with the herb (and other substances). "I am not an expert on cannabis, and, very oddly, however much of it I take—and I have tried probably 10 times and by different routes—it does absolutely nothing for me. Nothing! A cigar does far more. Ditto in combination with magic mushrooms and ketamine, which I have also tried under supervision." (McGilchrist wrote to me from South Africa, where he was working, so I encouraged him to try Durban Poison, a native South African sativa strain, to see if it would change his fortunes with the plant. I never heard back from him.)
Still, his explanations of how the two hemispheres differ reads to me like a playbook for cannabis-induced consciousness: "The right hemisphere . . . sees things in context, it understands implicit meaning, metaphor, body language. . . . It understands individuals, not just categories; it has a disposition for the living rather than the mechanical. It experiences the connections between things. Expanded attention, which is driven by the right brain, is more connected to the broader world. It's about relationships. It allows us to stand back, to gain _perspective_ [italics mine]. It is responsible for vividness of experience. It provides depth, a more 3-dimensional take on reality. It allows us to read the expression on someone's face. It helps us 'feel' music, and 'read' the tone of a conversation [ _metaphor_ ]. It's the glue that connects us to other sentient beings [ _empathy_ ] and enables the spiritual yoking."
McGilchrist ambitiously expands his insights on the divided brain to suggest why Western society is going off the rails—and he indirectly makes an argument for embracing the sort of "mosaic" thinking that cannabis can bring about. He contends that when modern Western civilization began in the Reformation, the two hemispheres were more balanced, both in physical size and in terms of function. But as time has passed and our world has grown increasingly complex, the balance has drifted further to the left hemisphere's point of view—so much so that it now occupies more volume than the right. This reliance on rational, mechanistic thinking robs us of the ability to see life's interconnections. "Nowadays we live in a world which is paradoxical," McGilchrist writes. "We pursue happiness and it leads to resentment, and unhappiness . . . we pursue freedom but we are more monitored by CCTV cameras and . . . our daily lives are more subjected to what de Tocqueville called a network of small complicated rules that cover the surface of life and strangle the freedom we crave. We have never had more information, yet wisdom seems to be further out of our grasp. We prioritize the technical and the virtual over the real. All of our technical connectedness makes us ever more lonely."
The reason we find ourselves in this pickle? Because the left hemisphere—"the Berlusconi of the brain" in McGilchrist's terminology—writes and directs the narrative of what's important to human progress. Because it governs rational thought and is in charge of language, it preaches the benefits of the rational over those of interconnectedness. And because the right hemisphere doesn't have as loud of a voice, it has more difficulty being heard.
McGilchrist is a soaring intellect who makes it abundantly clear that he doesn't oppose reason or linear thinking—he relies on it daily and couldn't have researched his book without it. It's just that he's more passionate about the more intuitive mode, and he longs for mankind to return to a more balanced view of ourselves and of the world. He echoes the concern of that other great left-brain thinker Albert Einstein, who said: "The rational mind is a loyal servant and the intuitive mind is a sacred gift. We have become a society that honors the servant but has forgotten the gift."
In addition to using cannabis to put us in touch with awe, empathy, and creative insight, it's possible that we may, in time, learn to employ it as an ambassador in the struggle between the rational and the intuitive. Perhaps this is another explanation for the plant's enduring relationship with human beings. If Sagan was correct, that cannabis temporarily suppresses left-brain perspective, and if McGilchrist is correct about the struggle for civilization being reflected in our divided brains, then, as Marincolo argues, it seems possible that this plant is one way of temporarily returning us to a more balanced state of mind (and body). If nature maintains an equilibrium inside the physical body, is it not possible that nature has also given us a plant to balance the emotional and intellectual sides of our minds?
If that's the case, I'd say that qualifies as "Oh wow, man!"
## ___Chapter 11_
## THE NEXT REINVENTION OF WEED
_New York City_
It's remarkable just how effective eighty years of propaganda, woolly science, and high moral dudgeon can be. Americans doubt the government is capable of doing anything effectively, but it has succeeded magnificently in sowing first fear and then confusion around a generally agreeable weed. By issuing claims unsupported by evidence and twisting science to their own ends, the authorities have deflected attention from another, more interesting question: How might the components inside this magic weed be used to benefit our health and minds? This book is but a preamble to that question; subsequent generations will tackle it with much more lucidity. They'll also look back at prohibition and ask: What were they thinking?
Even after three years of immersing myself in the unfolding world of cannabis, I must admit that forty-five years of NIDA studies dutifully disseminated by an unquestioning media have made an impact. Every so often, a little voice in a corner of my mind asks, "Might your thinking be clearer, quicker, or more insightful without cannabis? Could those cannabinoids stored in your fat tissue for thirty days be causing some lingering, imperceptible effect?" Would I, as Professor Bab wondered, be more depressed "once all that euphoria wore off"?
There was only one way to find out. So before my journey ended, I made one more stop—into stone-cold sobriety.
The first leg of that expedition began in my kitchen. Above my refrigerator there's a small cabinet where I've stashed some of the souvenirs I've collected along the way.* Cabinets above refrigerators are terrible places to store cannabis. The heat emitted from the motor desiccates the oils, aging them before their time. Once terpenes are gone, they never come back. It was time to attend to that.
I spread the contents of my cupboard across my dining room table and took stock. My first response was shame. Knowing now how much labor, sweat, and risk it takes to cultivate, harvest, cure, test, and label these plant products, I felt that my collection should look more dignified. The motley assemblage of bottles and plastic pill containers had no aesthetic coherence. No self-respecting host keeps a bar this untidy.
My second response was to marvel at how many different forms this plant now assumes. In addition to a half-dozen jars containing beautiful buds, I found ampoules of golden hash oil, two crumbly blobs of water hash, and two quarter-size slabs of amber shatter. A plastic syringe contained five milliliters of medical-grade organic hash oil that I occasionally smooth on my gums. I had forgotten about a liqueur called Cannalua made by a physician in California. Made of cannabis oil drowned in Kahlua, it was surprisingly tasty. So many varieties, so little time to try them all. I taped Boveda moisture-control packs inside the tops of the jars to maintain the humidity at a steady 62 percent, the ideal level for keeping flowers fresh and mold free, and stowed everything in an antique toolbox.
Next, the instruments. In bolts of fabric I wrapped the beautiful bong that Tsachi Cohen gave me while in Israel, plus a few vape pens that I had largely abandoned. The propylene glycol used to thin the mass-market oils scratched my throat, and the middling high they delivered was never exciting enough to justify the irritation. A small dab rig that a seller at a convention gave me when he learned I was writing about his favorite plant—again unused—followed, as did a butane torch that I had loaded but never fired.
I had forgotten about my Magic Flight, but it remains one of the few compact vaporizers I like. Handmade by a group of Burning Man artisans in San Diego, this nifty wooden instrument is as small as a bar of travel soap and heats flowers with a rechargeable AA battery. It's lo-fi, low cost ($100), and it gets the job done. Back in its box it went.
I set the toolbox in a dark drawer in my study. Then, in true twelve-step fashion, I announced my decision to several confidantes. "Receptor cleanses are the best!" one friend wrote back. Who knew that the passive act of "not smoking" had been elevated to an active "cleanse"? Another assured me that my first post-cleanse high would be spectacular, reminiscent of my first orgasm. It was something to look forward to, but orgasmic wasn't the point. I simply wanted to gauge if my thinking, once free of cannabis, would be sharper.
When I began this project I focused away from politics, but knowing what I now do, it became impossible not to think about cannabis without politics, especially since the supposed solution to drug abuse has ended up being far worse and stratospherically more expensive than the problem itself. So while on my cleanse I began to explore how prohibitionists have adapted their arguments in light of the inevitable march toward legalization. The target of the scaremongering has changed: the plant is still bad, but the corporations that are plotting to push legalized pot on young kids, turn them into addicts, and usher in the decline of Western civilization are far worse. Users don't need prison, they now say, the poor things need treatment. Old messages, new twists.
"Legalization is not about someone's individual right to smoke marijuana," Kevin Sabet, the great white hope of the anti-legalization lobby, told me. "It's about creating Big Tobacco all over again." The issue isn't that marijuana kills, he says, "the issue is really about getting a small number of people rich."
Sabet, along with former congressman and OxyContin addict Patrick Kennedy, leads Project SAM (Smart Approaches to Marijuana). Project SAM's narrative goes like this: Once tobacco companies muscle their way into cannabis, they'll crank up their PR machines to downplay the health concerns just as they did with tobacco. This will result in more kids dropping out of school, more workplace and road accidents, and more psychotic episodes. "I'm not saying these things will happen," Sabet clarified, "but it greatly increases _the risk_ , and this is what I'm worried about. That's why I'm trying to formulate a more nuanced social policy, something between Richard Nixon and Colorado."
Sabet's motivations have puzzled and enraged reformers for years. A former social policy advisor in the Clinton, Bush, and Obama administrations, he cofounded Project SAM in 2014. Though he presents himself more as a drug diplomat than as a drug warrior, Sabet's past reveals him to be a long-standing pot opponent. As an undergraduate at Berkeley, Sabet was leafleting and warning students against it, according to fellow classmates. He even tried unsuccessfully to have People's Park, the symbolic epicenter of the anti–Vietnam War protest movement, razed to make way for a student dorm, a proposal that was overwhelmingly shot down by his peers. Today, he's still getting off on standing well outside the popular clique.
Sabet is understandably cagey about his past as a drug warrior. In 2007, he served on the board of an organization called Drug Free America Foundation. This group is supported by the notorious antidrug crusaders Mel and Betty Sembler, who are also the masterminds behind Straight, Inc., the Abu Ghraib of drug treatment programs. In lawsuits, the victims of Straight's "rehabilitation" methods testified about being sleep deprived, gagged, and pinned on the floor for so long that they soiled themselves. When one journalist asked Sabet if he had worked for the Semblers, he flatly denied it. When the journalist later confronted him with an annual report that listed him on their advisory board, he dissembled. "I was on the advisory board along with Jeb Bush, Bob DuPont, and others for a few years—that's all unpaid." Such trademark Sabet doublespeak provokes his opponents to describe him as obnoxious or bullying. Post-prohibitionist Michael Backes calls SAM "the Westboro Baptist Church of drug policy and Kevin Sabet their Shirley Phelps-Roper."
What they don't call him is dumb. I reached Sabet at his home in Princeton, New Jersey, where he lives with his wife. We spoke for about an hour, during which he laid out his arguments, calmly and rationally. He clearly believes what he is saying; the problem is that the "facts" he lays out don't add up. Consider some of his well-worn pronouncements:
**Pot is stronger today and therefore more dangerous.** Yes, pot is stronger, but cannabis has never appeared on a morgue report. While the jury is still out on the long-term consequences of steady dabbing, dabs are not the cannabis equivalent of crack, no matter what headline writers say.
******New forms of pot, such as edibles, have caused a "huge upsurge" in the number of ER visits by people who ate too** **much.** Edibles are no more harmful than smoking, though confusion about and inaccurate labeling of THC strength is indeed an issue. Foes quote alarmist headlines like those that appeared in the journal _Clinical Pediatrics_ that reported that between 2006 and 2013 there was an "upsurge of over 147%" in children under six who ate their parents' edibles when they inadvertently thought they were candy. That sounds like an enormous jump, but it's a tiny change when the raw numbers are examined: from 100 in 2006 to 250 in 2013.
**Western society is better suited to alcohol because we have a longer history with it.** Sound familiar? It should—it's little more than a redux of the same xenophobia that Harry Anslinger used to attack Mexican immigrants and their "loco weed" in the 1930s. An identical argument could be made against green tea: Because it's from the East and more foreign than coffee and therefore less understood, be wary.
**If pot is legalized, teen use will skyrocket.** Sabet claims that one in six kids will get hooked on pot, a fact he bandies about with not one shred of supporting evidence. In fact, studies in Holland, which decriminalized cannabis in 1976, and Portugal, which decriminalized all drugs in 2002, show just the opposite. Holland has the lowest teen use of any European country, and Portugal's youth have not started to smoke with abandon.
**The pot lobby has spent over $100 million over the last twenty years to legalize all drugs, and the anti side doesn't get one tenth of that.** This extraordinary half-truth ignores the trillions of dollars the US government has spent in the last forty years to demonize cannabis. According to the Office of National Drug Control Policy, the US federal government spent over $15 billion in 2010 prosecuting the War on Drugs, at a rate of about $500 per second.
******Secure and contented people aren't heavy consumers of psychoactive substances.** Meaning, pot is something that intelligent adults outgrow. Older adults are the fastest-growing group of cannabists, as they are searching for more natural, less toxic, and less expensive ways of protecting their minds and bodies from the ravages of age.
And finally, my all-time favorite disputation: **There is no proof that cannabis works as a medicine.** Sabet, who has no medical training, made this blindingly tautological claim in the _Huffington Post_ in 2014. Of course, there is no "proof" of the plant's medical efficacy, but that is not because it has ever failed to meet the standard of proof. Rather, the tests required to demonstrate its efficacy have never been allowed because of the schedule I restrictions.
Our conversation spooled on for over an hour, and throughout it struck me that Sabet was describing a monster that bore no resemblance to the cannabis I know. So I asked: Has he ever sampled, just once, the substance that he has spent his entire adult life battling against?
"No," he replied. "I know people are kind of interested in that question and it's kind of a fun thing but I agree with serious scholars that it's a really dumb question for policy. We don't ask cancer doctors to get cancer or we don't ask people whether they think jumping off a roof is bad idea if they've never done it. So it's kind of a weird question but I understand why you ask it. A lot of people do."
Condescension noted and the linking of cannabis to cancer duly ignored. "I don't think everything that everyone is working on is something that they have to experience themselves to be able to comment on it," he continued. "I think, you know, my PhD from Oxford, an undergraduate degree from Berkeley, working in three administrations, and speaking to the top researchers in the world has somewhat qualified me to be able to talk about this from a public policy perspective. And I actually think if you're a regular marijuana user you're disqualified from talking about the issue because you're clearly biased. It's hard for you to acknowledge that this could be a problem, hard for you to acknowledge that something you enjoy doing might not be good for your brain. I don't think we can count on an objective point of view from somebody who might be under the influence of a psychoactive substance at the time of trying to critically reason about it."
But if he is so concerned about the evils of drugs, why not fight a real slayer like meth?
"I got into this field in my early teens because I saw issues of mental health and marijuana addiction being swept under the rug. People didn't want to confront it because they didn't want to confront a problem in their family or because they didn't think it was a big deal. And in reality, some of my friends growing up did have a lot of problems with marijuana and alcohol and other substances, and that actually drew my curiosity, seeing other smart, otherwise athletic friends not reach their potential."
You can see the problem here: I am disqualified from having an opinion because I use pot, yet his opinions were based only on hearsay and the recitations of discredited drug war science. I concluded that Sabet is a man who relishes being a lone wolf, staking out the unpopular position. But it begs the question of who is funding his lonely battle. Is it Big Alcohol that fears pot will wipe away some of its market?
"Ha," he said. "We don't get any alcohol, pharma, or tobacco funding. If anything, the alcohol folks don't like what we say about their industry targeting people who drink heavily, because that's what the marijuana industry would do, too. Our funding is mainly from volunteers. We just had a summit where a few treatment centers gave us five thousand dollars.
"The National Association of Drug Court Professionals have given us money for our summit."
"How about Big Pharma? Are they backing Project SAM?"
"I'm waiting by the mailbox eagerly for the check. I don't know where people who say this get their information from."
I do. The most vocal antipot groups, Partnership for Drug-Free Kids* and the Community Anti-Drug Coalitions of America (CADCA), receive funding from federal grants worth some $90 million, and from pharmaceutical companies, who contribute undisclosed amounts. So while it's ostensibly true that Project SAM receives no funds from the government or pharmaceutical companies directly, the local chapters of CADCA regularly hire Sabet at $3,000 a pop to deliver lectures and inspire the beleaguered troops in their war of diminishing returns.
Even more indicting: the two largest corporate funders of these antilegalization groups are Purdue Pharma, the maker of OxyContin, and Abbott Laboratories, the maker of Vicodin. Both of these opioid painkillers are among the most addictive drugs known to man. Opioid painkillers now cause more deaths than heroin and cocaine _combined_ , according to the Centers for Disease Control. OxyContin has been linked to thousands of overdoses since it came to market in 1996.
The antipot groups funded by these two pharmaceutical giants predict that legalizing cannabis will lead to delinquency, addiction, and death, yet they are conspicuously silent about limiting access to opioids. When such legislation is floated in Congress, they lobby to kill it and have done so successfully for years. They also oppose removing cannabis from schedule I.
Why? Because the profits of Abbott and Purdue (and the government funding of anticannabis groups) depend on maintaining the status quo. OxyContin has raked in more than $27 billion since 1996. Purdue has no intention of ceding market share to a mere plant that also happens to relieve pain, is not addictive, and can be grown in the backyard. It may be an underhanded way of enforcing one's agenda, but it's not surprising given that corporations have a legal obligation to their shareholders to defend their markets.
Is it coincidental that Sabet's agenda aligns so neatly with these pharma companies' or that he argues that no plant can be a true medicine, as he did in the _Huffington Post_? One thing is certain: it makes conspiracy theories about drug companies' fear of cannabis sound a lot less like stoner paranoia.
OK, so let's imagine that these vested interests run out of steam, more states vote to legalize, and the federal prohibition lifts. What will this unfettered world of cannabis look like? You don't need a crystal ball to see this future, and it looks nothing like the doomsday scenario that Sabet and others paint. The experience of other countries, plus the United States' history of ending alcohol prohibition, are fine guides to how the future will unfold.
When cannabis becomes more widely available, usage typically spikes a few percentage points, but it levels off once the curious get their kicks. This is what occurred in Portugal, where that debt-burdened nation decriminalized possession of _all drugs_ in quantities less than ten grams in order to move from an imprisonment paradigm to a less costly treatment paradigm. To be clear, Portugal has not legalized drug use, it has simply decriminalized it. The number of drug addicts who have undergone rehab has increased dramatically, while the number of drug-related HIV infections has decreased in kind. The country hasn't suffered an outbreak of societal pandemonium. In Colorado, there hasn't even been an outbreak of laziness. In its first year of recreational sales, ten thousand people were at work in the industry.
Legalization and regulation will, of course, create new problems, but none of them, as we can see from Colorado and Washington, are unsolvable. Big Tobacco and Big Alcohol will likely swoop in and eventually come to dominate the mass market, just as they do now with beer, cigarettes, and wine. All sorts of claims will be made, with various levels of truthiness, as is the case with food supplements—but this is endemic to capitalism, not pot. Celebrities large and small will muscle into the act. Willie Nelson has formed Willie's Reserve, though no one quite knows what the company will be doing or selling. Snoop Dogg engaged Pentagram, one of the world's most established branding firms, to craft the "California cool" visual identity of his "Leafs By Snoop" range of products; Melissa Etheridge is developing marijuana-infused wine (sounds disgusting); Whoopi Goldberg has launched a line of topical rubs and bath products aimed at women suffering from menstrual cramps; even the reality TV star Bethenny Frankel is supposedly working on a strain of Skinnygirl weed that she hopes will leave users free of the munchies. All advertising and marketing will undoubtedly be restricted and reined in, just as it is with alcohol and tobacco today.
But legalization will allow researchers and others to investigate how we might use the plant to make our lives better. It will allow us to solve more vexing issues than it will create.
Take dosing, for instance. Today we almost intuitively know that one 1.5-milliliter shot of vodka has roughly the same alcohol content as a 5-ounce glass of wine (18 milliliters) and a 12-ounce bottle of beer (20 milliliters). Those standards enable everyone to moderate his or her intake without having to do any math. I can't wait for the day when a label will tell me that a 5-milligram edible is the equivalent of three hits on a joint of Blue Dream (but that the effects won't kick in for an hour and will last twice as long). It will also make some of the puzzling adverse reactions less puzzling. In the normalized world, imaginary increases in psychoses and other red herrings will take second place to real problems (mold, pesticides, inaccurate dosing and testing, maybe even vomiting) that are currently underreported because of prohibition.
Until that occurs, cannabis will continue to be the world's noisiest flower. All people, whether they use it or not, whether they are excited by or deny the science, whether they favor or abhor legalization, have an opinion about this weed. The century-long demonization has magnified cannabis to the point where it is seen as either magical or monstrous, and this is yet another distortion. Pot is peripheral to life, not essential to it. It belongs on the sidelines, not in the spotlight. I can't wait until it becomes boring and normal.
Another benefit of legalization: it will allow a culture that has been trapped in time to mature. New ideas will blossom, and those who have been marginalized can be ushered into the mainstream. This is occurring in Northern California, where the members of the Emerald Growers Association (EGA), a group of eight hundred farmers who are concentrated in Mendocino, Humboldt, and Trinity Counties, are demanding to be recognized as producers of top-tier, sun-grown organic cannabis, rather than being sidelined as criminals.
Pressing for regulation in a state that has been legally vague for two decades is a risky position. Many of the EGA's fellow cannabis farmers are dead set against coming out of the shadows to work within the system. They fear reprisal from the government, which is still raiding their grows, and they mistrust corporations, fearing they will buy up their farms and knock them out of business, just as they did with small tobacco farmers. Their concerns are not unwarranted.
But there is no future in staying outlaw. "When you're illegal, this year is always the last year," says Casey O'Neill, the chair of the Emerald Growers Association. "There's no way to plan for the future, no reason to make infrastructure upgrades." The EGA may be the only group in America that wants to pay taxes, and if they did, the boon would be undeniable. There are an estimated fifty-three thousand cannabis farmers in California, who raise a crop estimated to be worth $32 to $36 billion a year. This raises the question of what is the bigger crime: growing and taxing the sale of a plant, or asking a state that can't afford to keep its libraries open to forgo the estimated $2.5 to $3.5 billion in new annual tax revenues?
There's a larger issue at stake. In Northern California, most of these cannabis farmers also grow organic broccoli, tomatoes, zucchini, and every other vegetable that their hot microclimate will produce. But vegetables can no longer sustain small farmers or their families. Cannabis provides a "fulcrum crop," which brings in half to two-thirds of their yearly income. This steady income allows growers to join the economy, escape the black market, and pay their workers twice what a typical farmhand earns. "Small farms are part of the American dream, but the economics are no longer there," says O'Neill. "Today, we have two choices. We can levy taxes and give small farmers a subsidy, but I'm not asking for a handout. Or we can allow small farmers to grow organic, heritage strains that create dollar potential, maintain the environment, and thrive rather than subsist."*
To secure this future, the EGA is also taking unprecedented steps to protect the heritage of its growers' strains by establishing a controlled appellation system similar to that of French wine makers. In thirteenth-century Burgundy, the monks who grew grapes noticed that certain soils and climates produced wines of unique character that couldn't be produced elsewhere. The terroir is what made certain varietals of Burgundy good and others outstanding. The EGA is hoping to replicate that system once granted legitimacy, and the idea is spreading to other cannabis-growing regions around the world. It's not unimaginable that we could see top-tier cannabis wars in the near future: sun-grown Humboldt Green versus Blue Mountain Jamaican. Take your pick!
When prohibitionists hear this, they paint a picture of a drug-induced free-for-all. They envision strain reviews next to wine reviews in the _New York Times_ , chalkboards beseeching patrons to smoke up in the same way that bars encourage drinking (One recent favorite: "Has your dog died? Worried about the size of your penis? Found out your husband's gay? . . . You can numb any of these problems temporarily with the help of Booze. Remember: The more you drink the less you worry!"), or foresee the day when cannabis owns basketball the way that beer owns football. But I see a different picture, one in which a maturing market benefits from regulation and control, and in which educated customers demand pesticide-free pot, grown in small batches, and in which the profits get tied back to the local community. My forward-facing picture is based in part on the fact that Big Agriculture, Big Tobacco, and Big Pharma have fallen into disrepute, and that a sizable number of weed users are the same people who prefer organic, chemical-free food and resist popping pharmaceuticals for every minor ache and pain. They will demand that their pot is grown sustainably, cleanly, and in line with their do-gooder values.
But the other part of my picture is formed by looking back through the rearview mirror at the end of alcohol prohibition. Lifting the prohibition on alcohol in 1933 put the brakes on the anything-goes atmosphere created by speakeasies and bootleggers, says Daniel Okrent, the author of _Last Call: The Rise and Fall of Prohibition_. It established closing hours, age limits, and Sunday blue laws. It created regulations that stopped people dying from tainted slush masquerading as alcohol, and it mandated physical distance between bars or liquor stores and schools, churches, or hospitals. "Just as Prohibition did not prohibit, making drink legal did not make drink freely available," Okrent concludes.
Perhaps the most radical change legalization will bring about is what might be termed the Fourth Reinvention of Pot, from sacrament to botanical medicine to intoxicant to wellness product. It may seem like a stretch at this moment to regard what Ronald Reagan fingered as "probably the most dangerous drug in the United States" as something that promotes health, but science can be denied for only so long. Once companies like Michael Backes's Phytecs are up and running and integrate empirical evidence into a viable health regimen, products that tickle the receptors of the endocannabinoid system will likely be viewed much the way vitamins or common over-the-counter remedies are today, with one significant difference: they'll be more effective. A few examples of these speculative health-altering meds include:
• THCV, which retards the appetite rather than inducing the munchies. This endocannabinoid also boosts metabolic rate, which reduces fat buildup in the liver and the amount of bad cholesterol in the blood. As an estimated 40 percent of Americans are obese and diet pills are a bust, the consequences could be profound. THCV also affects cells that produce insulin. Diabetes, in all its many forms, is endemic in China and most of the West, and it will drain the US health-care system of an estimated half trillion dollars in the next decade. If this plant-derived chemical proves effective, that's a game changer.
• CBG. Achy joints and back pain are the most commonly reported medical complaints. CBG synergizes with THC to relieve pain just as Aleve, ibuprofen, and Advil do, but without side effects. Who wouldn't prefer a safer, botanically derived Advil?
• CBD. New studies are linking the long-term use of anti-anxiety meds like Xanax, Ativan, Valium, and Klonopin to dementia and Alzheimer's. It appears that a mere two milligrams of CBD may keep us calmer and protect our brains against aging at the same time.
• THCA. An acid that appears on the raw leaf before it is heated, THCA is one of the most powerful anti-inflammatories known to man. According to Kymron deCesare, chief research officer of Steep Hill Labs, it has twice the potency of hydrocortisone taken internally with none of the side effects. One week of this treatment noticeably diminishes pains and aches associated with joint diseases.*
Even old weed can be useful. CBN, an oxidation product of THC commonly found in dried-out stashes left in the garage over the summer, is an excellent sleep remedy. "CBN is about six times as effective as any other cannabinoid," says deCesare. "If you light up old weed, the first effect is a yawn, next your muscles relax, then the sedative kicks in and your brain wants to shut down."
Viewing cannabis as a wellness product does not constitute some arbitrary marketing shift. Rather, it's a profound reincarnation of the plant and a negation of everything we have been taught about it in the last century of demonization. Prior to my journey, I might have said that everything you put into your body incurs some risk, but pot is less harmful than cigarettes or alcohol. After all, smoking kills five million people worldwide each year. Alcohol kills almost 88,000 Americans a year and is linked to domestic violence, brawls, car accidents, rape, homicide, and a high percentage of suicides. But science is showing that pot, used intelligently, may actually be good for you. The evidence is mounting; it's time to learn the truth.
We've lost a century prosecuting this war on weed, and the result has been exactly the same as every other war America has conducted during my lifetime: pointless. A decade trying to prevent communism in South Vietnam resulted in a communist government the minute we pulled out. Another decade in Afghanistan and Iraq have given birth to regional instability and ISIS, with no end in sight. Obviously, war incurs all sorts of unintended consequences, and the war on weed is no exception. What began as America's Sisyphean attempt to wipe out the plant ended up turning the United States into the world's largest cannabis producer. Trillions of dollars spent, hundreds of thousands of citizens jailed, and countless lives ruined to eradicate a plant that turns out to help kids with cancer, like Chico Ryder, or elders in Israeli nursing homes, or stressed-out executives in search of a little calm.
Why?
Whether you like weed or hate it, it's time to let science take the lead in posing new questions and answering them. As we hurtle into the twenty-first century, our on-demand lives are creating a new set of stressors. Smartphones and twenty-four-hour news cycles are bombarding us with five times as much information than we received in 1986. Isn't it comforting to know that something grown in the earth can bring relief to our overloaded brains and help us confront the loneliness of our screen-based world? People are swarming into cities at a frightening pace, and this mass migration and the resulting overcrowding is predicted to continue until 2030. Isn't it reassuring to know that there's a plant that can, for a few hours, heighten perceptions so that we can more closely observe the fluttering of a butterfly's wings or find new beauty in the scent of a pine tree? Something that, when used intentionally, can help us appreciate the subtleties in our increasingly mediated, fractalized lives?
After sixty days, twice the length of time necessary to empty my receptors, I ended my cleanse. Unsurprisingly, none of the "withdrawal symptoms" that could supposedly affect heavy users when quitting—constipation, heavy perspiration, and sleeplessness—surfaced. Cannabis sobriety was, for me, as it is for most people, a nonevent of spectacular proportions. Yes, I missed the aphrodisiacal qualities in bed. I missed the relief that comes from "taking away the mind," the joyous spurts of associative creative thinking, and of course, the lovely ritual of sharing a puff with friends. But unlike a digestive cleanse that wreaks havoc on so many bodily functions and washes away motivation, the receptor cleanse caused no noticeable differences in my physical or mental acuity. The only change I observed was an uptick in my alcohol intake. Rather than one glass of wine at night I had two, occasionally supplemented by a shot of vodka or scotch. The sugar metabolized from the alcohol disrupted my fragile sleep patterns and left me with mental cobwebs in the morning, which were eventually wiped away by a jolt or two of tonic made from that other popular botanical, coffee.
So on May 1, 2015, I unpacked my toolbox and selected two sticky fingers of a Mendocino sun-grown strain called XJ 13. I pulverized the aromatic green and scooped it into my Plenty vaporizer. When the dial hit 360 degrees Fahrenheit I took three deep draws, felt the cool mist swim into my lungs, and thought, _Maybe I am hooked on pot after all_. We have a relationship, this plant and I. Some people love weed, but love is a powerful connection that can also be accompanied by aching, longing, and obsession. For me, reuniting with pot has been more like reuniting with an old friend. The relationship is flexible and it allows me to come and go as I please. It's familiar, yet full of mystery, and it's one that takes a lifetime to truly know.
## ___Appendix_
## BEYOND STONED
_Cannabis for Inspiration, Intimacy, and Other Adult Pleasures_
When I began this book I mistakenly thought everyone knew how to use pot. I was very wrong. My generation lacked knowledge of what made the plant work and how it interacted with our bodies. The current generation is lacking information on how to best use this new, unfolding knowledge to its benefit, which is one reason I've written this book.
If you simply want to cripple your mind—to forget about yesterday, today, and tomorrow—spark up a fat joint and smoke it to the roach. If you want to use it to get creative, interesting highs that crack open doors of insight and emotional connection, that's another story. Humans have altered cannabis, but the ways we use it haven't kept pace. Here are a few twenty-first-century ways to use this twenty-first-century plant.
BEFORE
_Know the dose that makes you happy._
Pot is dose-dependent and biphasic. In other words, smoke too much, and feelings of increased sensitivity can turn to paranoia, or an ecstatic journey can end in couchlock.
**Mind-s** **et:** "Set and setting" refers to the way mind-set and environment can influence any journey on any substance. I'll add __this: cannabis is, as Baudelaire put it, "the mirror that magnifies" what's already going on in your mind. If you're depressed, cannabis can sink you lower; if you're feeling energetic, you might get a boost. Smoke a puff or two, wait three minutes, and evaluate the direction things are heading. Stop if you've taken the wrong road.
**Setting:** When using cannabis to hack into or expand your consciousness, try being in a quiet place where you can control the lighting, the music, and the company. Also, marijuana tends to make whatever one is doing while smoking more interesting, but it makes switching from one activity to another more challenging.
**Do what you know:** Save learning new activities for another time. For me, swimming while enhanced, especially outdoors, is sensory bliss. Tennis, at which I'm less accomplished, is overwhelming. Following the ball, appraising my opponent's next move, second-guessing the angle of my racquet . . . it's all too much. So learn what you enjoy and, more important, what you don't enjoy, in the enhanced state. This is key to knowing how to be high.
**Strains:** The strains matter, but they are not 100 percent accurate predictors of your high, especially if your cannabis hasn't been tested. If you are affiliated with a dispensary that tests, ask a knowledgeable budtender to explain the meaning of those numbers. THC, CBD, and terpene profiles are more likely to predict the effects of the high than strain names or categorizations such as "indica," "sativa," or "hybrid." Try strains that have both THC and CBD if you can find them and note the difference. And get to know your terpenes, as they help predict the trajectory of your high.
INHALATION
_Know your delivery methods._
A bong is efficient, as it delivers the largest intake to the lungs, and you will not watch half a gram go up in smoke as you will with a joint. I find coughing deeply unpleasant, so I monitor how much smoke fills the stem and adjust my inhale accordingly. When you lift the bowl out of the pipe, you will get a rush of smoke. You don't need to take it all.
Vaporizer pens are discreet and odor free; however, the mass-market oils that fit pens like the O.penVape are generally of lower quality and made with propylene glycol, which can irritate the sensitive tissues of the throat. Vaporizers such as the Pax that burn flowers are better, but the ceramic heating element burns at hotter, less controlled temps, so you are frying some of the oils before they get to your lungs, which makes the high flatter, less nuanced, and less colorful.
The beauty of a precision vaporizer like the Plenty is that the temperature can be adjusted. The vapor is cool, the flavor robust, and the high is crystal clear. Extra bonus: it's so strange-looking you are guaranteed to be the hit of any party you bring it to.
Dabbing is for more experienced smokers. If you're going to dab, be sure to try it with people who know what they are doing and be sure that they are starting you out with a small, _sesame seed–size_ dose. Remember, you are smoking an extremely potent concentration of THC and cannabinoids, so this is one case where size really does matter.
My rule is simple with oil: Avoid anything made with solvent. Butane is toxic, so why risk it? Water or CO2 processing is clean and does the trick.
A joint is, in fact, the least efficient way to smoke. About 50 percent of what you roll will simply perfume the air, which is not necessarily a bad thing. That said, there's something old-school and reassuringly simple about a joint, though I suspect they may be going the way of the roll-your-own cigarette as newer technologies come online. Still, rolling is a skill worth knowing.
When lighting a pipe, position the flame far enough away from the bowl to lightly kiss the top of the green. Do not torch the plant. Too much fire annihilates the resins. Serious cannoisseurs prefer matches to cheap lighters, as they say they can taste the butane.
EDIBLES
Again, dosing is key. The days of Alice B. Toklas randomly dumping a handful of fried weed into brownies and you eating a square are thankfully over. Most home cooks have no idea about portions, so it's up to you to know what you're doing. Unless you're experienced and have a tolerance, five milligrams or less should be enough to create a sunny inner state. Too much and you'll be horizontal and possibly paranoid for far too long. Try a few test runs; ingest a specified amount, and wait one to two hours to evaluate. If nothing happens after two hours, you need more, but remember it will take another one to two hours to kick in. Alternatively, you can just add inhalation or vaporization to extend the high or add new textures. Oh, and by the way, cannabis doses have no relation to your body weight. A big guy can be flattened just as easily as a small woman on the same amount.
ETIQUETTE
Just a puff or two to start, then take a break. Sharing a joint or a bowl is a lovely ritual, but the tendency is to oversmoke. Best to start slowly, take a break, and then resume if you want to go further.
• Respect silence. Words don't work quite as well when stoned, although ideas and feelings can still be communicated. Sometimes pot makes me talkative and helps my emotional connection to those around me. At other times, I prefer solitude. This social/antisocial swing is difficult to predict. If uncertain, I suggest smoking one or two puffs before entering a crowd. You'll know immediately if you need to sit in a corner or if you can dive into the group.
• Notice nuance. As Sebastián Marincolo writes: "While high, the taste of eating chocolate or drinking red wine usually is not only more intense but also more complex." Attend to these extra dimensions.
• Don't insist that others around you smoke, even if you think they'll enjoy it. Let them ask you to try it. They'll be happier if it's their choice, and you'll avoid blame should things take a wrong turn. With newbies it's good to say something like, "I can't predict your response, but chances are you'll enjoy it. If not, I'll be there to support you whatever comes up."
• Avoid mixing pot with spirits. It's difficult to avoid, given that both are seen as party favors, but I recommend keeping them distinct to really understand the difference between these two wildly different substances. Pot can be used to party, but it is a less predictable social lubricant than alcohol.
PAIN
In general, cannabis relieves neuropathic (nerve) pain, not the kind of pain that happens when you stab yourself with scissors. If something bothers you persistently, get it checked out to learn the root of the problem. If it's fixable, get it fixed. Pot won't heal it. If it's not fixable, figure out how to use pot so that it enables you to function without going into a black hole. Experiment with CBD strains if you can find them.
MAINTENANCE
• Cleanse your receptors regularly. Twenty-eight days of abstinence will scour your endocannabinoid system, and you'll get you more pleasantly high when you pick up again. Should you have trouble stopping for a month, you might want to think about how much you're smoking and why.
• Take notes. Just as recording your dreams can help you meaningfully integrate them in your waking life, writing down your insights while high can be useful for revivifying your inner life.
• Don't make it a habit. Habits are done without thinking and are not as much fun as activities that are done occasionally. Think about what you want to get from your highs and set your intentions accordingly. Fun, laughter, silliness, and joy are all fine intentions, by the way.
• Remember, the best thing about pot is also the worst thing about it: It makes everything in front of you seem OK. Don't lose track of your priorities. If you find this is happening, stop. Don't sacrifice discipline and focus. And if you can't stop, ask yourself why you can't, and maybe find some help doing so.
• And of course, stay curious and enjoy the journey. It's a brave new world of weed out there, and there's much to learn and explore.
## ___Acknowledgments_
In addition to the people profiled in these pages I am so happy to know and to thank Valerie Corral, a hero in the cannabis world, for helping end-of-life patients through their transition and for helping me navigate the history of medical cannabis in California. Al Byrne and Mary Lynn Mathre are the fantastic founders of Patients Out of Time, the first organization to hold world-class conferences for world-class scientists studying cannabis and the endocannabinoid system. Heroes. These people are heroes.
Drs. Donald Abrams, Ethan Russo, Jeffrey Block, Sunil Aggarwal, Brian Becker, Julie Holland, Jeff Guss, Erin Zerbo, Andrew Weil, Allen Frankel, Jeffrey Raber, and Lumir Hunis each spent hours explaining the chemistry of cannabis and making it comprehensible. They were always wise, measured, and available to answer questions. Roy Upton and Michael Fratis were huge helps on the botanical front.
Ethan Nadelmann, Amanda Reiman, Ted Trimpa, Joe Brezny, Brian Vicente, Christian Sederberg, and Graham Boyd were my spirit guides through the ever-changing political and legal landscapes, while Sebastián Marincolo, Jonathan Teysko, and Zach Klein served as my spirit guides in general.
For shelter, wisdom, and support: Mark Matousek, Jocelyn and Bill Zuckerman, Jack Millam and Brad Stamm, Henny Garfunkel, David Binder, and Marco Calvani were always there, as was my beloved family, Lynn Dolce and Tee Minot and Susan and Chipper Moore.
I must also thank Leslie Bocskor, Daniel Okrent, Barbara Ehrenreich, Joel Solomon, Linda Solomon, Justin Hartfield, Lea Klein, Michael Martin, Casey O'Neill and Amber Cline, Ellie Sapir, Carl Olsen, Kristin Nevedal, Richard Lee, Brandon Kennedy, Diane Goldstein, Peter Christ, John English, Josh Wurzer and Alec Dixon, Tsachi Cohen, Maayan Weisberg, Martin Lee, Nate Jackson, Riley Cote, Robert Forte, Steve D'Angelo, Andrew D'Angelo, Tim Blake, Matt Stang, Douglas Johnson, and Lindy Speakman.
And thanks to my publishing dream team: Sarah Murphy, Brian Perrin, Dave Kass, Amrit Judge, and Hannah Robinson. Milan Bozic created the year's best book jacket; my agent, Bob Levine, encouraged and sustained me through my doubts; and my two great loves, Karen Rinaldi and Jonathan Burnham, gave me the best birthday gift imaginable by agreeing to publish this book.
## ___Notes_
CHAPTER 1: BIG BAD SCARY WEED
. J. C. Callaway, "Hempseed as a Nutritional Resource: An Overview," _Emphytica_ 140 (2004): 70.
. Ethan Russo, "Cannabis in India: Ancient Lore and Modern Medicine," in _Cannabinoids as Therapeutics_ , ed. Raphael Mechoulam (Boston: Birkhäuser, 2005), www.drugpolicy.org/docUploads/Russo_CannabisInIndia_Mechoulam2005.pdf.
. Roger Parloff, "How Marijuana Became Legal," _Fortune_ , September 18, 2009, http://archive.fortune.com/2009/09/11/magazines/fortune/medical _marijuana_legalizing.fortune/index.htm.
. Evan Morris, "Pot," _The Word Detective_ , 2016, www.word-detective.com/2008/07/pot/.
. Charles Whitebread, "The History of the Non-Medical Use of Drugs in the United States," _Schaffer Library of Drug Policy_ , www.druglibrary.org/schaffer/history/whiteb1.htm.
. Jacob Sullum, "How Many Daily Heroin Users Are There in the US? Somewhere Between 60,000 and 1 Million. Maybe," _Forbes_ , March 10, 2014,www.forbes.com/sites/jacobsullum/2014/03/10/how-many-daily-heroin-users-are-there-in-the-u-s-somewhere-between-60000-and-1-million-maybe /#2596a437eb43.
. The information in this table, with the exception of the cannabis total overdose deaths, was compiled by the National Institutes of Health and the National Institute on Drug Abuse. No cannabis overdose deaths have been reported. See National Center for Health Statistics, "Overdose Death Rates," _National Institute on Drug Abuse,_ December 2015, www.drugabuse.gov/related-topics/trends-statistics/overdose-death-rates.
. Ronald Shaffer, "Unnamed Witnesses Say Bourne Used Pot, Cocaine at Party," _St. Petersburg Times_ [Florida], July 21, 1978.
. Patti Davis, _The Way I See It: An Autobiography_ (New York: Putnam, 1992).
. Peter Gorman, "Operation Green Merchant: An Overview," _Peter Gorman Archive_ , n.d., petergormanarchive.com/green_merchant.html.
. Daniel Forbes, "Prime-Time Propaganda: How the White House Secretly Hooked Network TV on Its Anti-Drug Message," _Salon,_ January 13, 2000, www.salon.com/2000/01/13/drugs_6/.
. Ibid.
. Ibid.
CHAPTER 2: THE DUTCH MASTERS
. "Hempfest: Thousands Attend Opening of Three-Day Pot Festival in Seattle Park," _Daily News_ [New York], August 17, 2013, www.nydailynews.com/news/national/hempfest-thousands-attend-three-day-pot-festival-article-1.1429555.
. "Will Banning Marijuana Sales to Foreigners Hurt Holland's Economy?," _The Week_ , April 27, 2012, http://theweek.com/articles/476012/banning-marijuana-sales-foreigners-hurt-hollands-economy.
. "Big Serious Seeds Cultivation Showdown: AK-47 Regular vs Feminised," seriousseeds.com, last modified February 2016, www.seriousseeds.com/grow-ak47.
. Ibid.
. Besar Likmeta, "Europe's Marijuana Capital Isn't Amsterdam," _GlobalPost_ , August 16, 2013, www.globalpost.com/dispatch/news/regions/europe/130815/europe-marijuana-capital-lazarat-albania.
CHAPTER 3: THE MARTYR AND THE MILLIONAIRES
. Paul DeRienzo, "Dennis Peron: The Marijuana Mouse That Roared," _High Times_ , August 1998.
. Michael Pollick, "A Medical Pot Pioneer's Story," _Herald-Tribune_ [Sarasota, Florida], July 26, 2014, http://marijuana.heraldtribune.com/2014/07/26/medical-pot-pioneers-story/.
. Eric Bailey, "6 Wealthy Donors Aid Measure on Marijuana," _Los Angeles Times_ , November 2, 1996, http://articles.latimes.com/1996–11–02/news/mn-60512_1_medical-marijuana-measure.
. "Marijuana Prosecutions for 2010 Near Record High," _NORML.org_ , September 29, 2011, http://norml.org/news/2011/09/19/marijuana-prosecutions-for-2010-near-record-high.
. US Department of Justice, "Uniform Crime Reports—Crime in the United States, 2000—Table 29: Total Estimated Arrests in the United States," _FBI.gov_ , October 22, 2001, www.fbi.gov/about-us/cjis/ucr/crime-in-the-u.s/2000/toc00.pdf.
. Julie Holland, ed., _The Pot Book: A Complete Guide to Cannabis_ (South Paris, ME: Park Street Press, 2010), 386.
. George Soros, "Why I Support Legal Marijuana," _Wall Street Journal,_ __October 26, 2010, http://online.wsj.com/news/articles/SB10001424052702303467004575574450703567656.
. Andy Kroll, "This Is How Private Prison Companies Make Millions Even When Crime Rates Fall," _Mother Jones,_ September 19, 2013, www.motherjones.com/mojo/2013/09/private-prisons-occupancy-quota-cca-crime; Vicky Pelaez, "The Prison Industry in the United States: Big Business or a New Form of Slavery?," _El Diario-La Prensa, New York and Global Research_ , March 10, 2008, www.globalresearch.ca/the-prison-industry-in-the-united-states-big-business-or-a-new-form-of-slavery/8289.
. Lee Fang, "The Real Reason Pot Is Still Illegal," _The Nation,_ July 2, 2014, www.thenation.com/article/anti-pot-lobbys-big-bankroll/.
. Ibid.
. Ralph Nader, "The Boundary-Breaking John Lewis—A CEO Who Mattered," _Cleveland.com_ , December 5, 2013, www.cleveland.com/opinion/index.ssf/2013/12/the_jolting_peter_lewis_a_ceo.html.
. Peter Lewis, "Billionaire Peter Lewis: My War on Drug Laws," _Forbes_ , September 21, 2011, www.forbes.com/sites/clareoconnor/2011/09/21/billionaire-peter-lewis-my-war-on-drug-laws/#5aa8c4447575.
. Isabel Macdonald, "The GOP's Drug-Testing Dragnet," _The Nation,_ April 3, 2013, www.thenation.com/article/gops-drug-testing-dragnet/.
. Mike Riggs, "Four Industries Getting Rich off the Drug War," _Reason_ , April 22, 2012, http://reason.com/archives/2012/04/22/4-industries-getting-rich-off-the-drug-w.
CHAPTER 4: WIDGETS AND DABS
. Sadie Gurman, "Hash Oil Explosions Rise with Legalized Marijuana," _Seattle Times_ , May 6, 2014, www.seattletimes.com/seattle-news/hash-oil-explosions-rise-with-legalized-marijuana-1/.
. Robert Connell Clarke, _Hashish_ (Los Angeles: Red Eye Press, 1998), 111.
CHAPTER 5: THE ENDOCANNABINOID SYSTEM
. Donald Abrams, "Medical Marijuana: Trials and Tribulations," _Journal of Psychoactive Drugs_ 30, no. 2 (April–June 1998): 163–69.
. Michael Pollan, "Cannabis, Forgetting, and the Botany of Desire," _Occasional Papers of the Doreen B. Townsend Center for Humanities_ , no. 27, (Berkeley: Doreen B. Townsend Center for the Humanities, University of California, 2002), http://townsendcenter.berkeley.edu/sites/default/files/publications/OP27_Pollan.pdf.
. David Jay Brown, _Mavericks of Modern Medicine: Exploring the Future of Medicine with Andrew Weil, Jack Kevorkian, Bernie Siegel, Ray Kurzweil and Others_ (Petaluma, CA: Smart Publications, 2006).
. Melanie C. Dreher, Kevin Nugent, and Rebekah Hudgins, "Prenatal Marijuana Exposure and Neonatal Outcomes in Jamaica: An Ethnographic Study," _Pediatrics_ 93, no. 2 (1994): 254–60.
. Melanie C. Dreher, "Marijuana Use in Pregnancy," The Ninth National Clinical Conference on Cannabis Therapeutics, YouTube video, posted December 6, 2015, www.youtube.com/watch?v=YWr8QDHCFos
. Ester Fride, "Cannabinoids and Feeding: The Role of the Endogenous Cannabinoid System as a Trigger for Newborn Suckling," _Journal of Cannabis Therapeutics_ 2, no. 3/4 (2002): 51–62.
. Leo Hollister, "Health Aspects of Cannabis," from _Pharmacological Reviews_ , 1986, www.druglibrary.org/schaffer/hemp/medical/hollis 1.htm.
. Pollan, _"Cannabis."_
. Christine Del'Amore, "Runner's High Hardwired in People and Dogs," _National Geographic,_ May 11, 2012, http://news.nationalgeographic.com/news/2012/05/120510-runners-high-evolution-people-dogs-science/.
. Richard Friedman, "The Feel-Good Gene," _New York Times_ , March 6, 2015, www.nytimes.com/2015/03/08/opinion/sunday/the-feel-good-gene.html _._
. Anthony Wile, "Dr. Raphael Mechoulam: The Promise of Cannabis," _The Daily Bell,_ October 19, 2014, www.thedailybell.com/exclusive-interviews/35732/Anthony-Wile-Dr-Raphael-Mechoulam-The-Promise-of-Cannabis.
. "Facts and Stats," _International Osteoporosis Foundation,_ last modified 2015, www.iofbonehealth.org/facts-statistics.
. Ken Belson, "Brain Trauma to Affect One in Three Players, N.F.L. Agrees," _New York Times_ , September 13, 2014, www.nytimes.com/2014/09/13/sports/football/actuarial-reports-in-nfl-concussion-deal-are-released.html.
. Jeanne Marie Laskas, "Bennet Omalu, Concussions, and the NFL: How One Doctor Changed Football Forever," _GQ,_ September 14, 2009, www .gq.com/story/nfl-players-brain-dementia-study-memory-concussions.
. F. M. Leweke et al., "Cannabidiol Enhances Anandamide Signaling and Alleviates Psychotic Symptoms of Schizophrenia," _Translational Psychiatry_ 2, e94 (2012), doi: 10.1038/tp.2012.15.
. P. Pacher and G. Kunos, "Modulating the Endocannabinoid System in Human Health and Disease—Successes and Failures," _FEBS Journal_ 280, no. 9 (2013): 1918–43.
CHAPTER 6: THE WORLD'S LARGEST HUMAN TRIAL
. "Why Bedrocan Is Selling Cannabis in Canada: Q&A with CEO Marc Wayne," _Leaf Science_ , January 26, 2014, www.leafscience.com/2014/01/26/bedrocan-selling-cannabis-canada-qa-ceo-marc-wayne/.
. Howard Markel, "In 1850, Ignaz Semmelweis Saved Lives with Three Words: Wash Your Hands," _PBS News Hour_ , May 15, 2015, www.pbs.org/newshour/updates/ignaz-semmelweis-doctor-prescribed-hand-washing/.
. E. Aso et al., "CB2 Cannabinoid Receptor Agonist Ameliorates Alzheimer-Like Phenotype in ABPP/PS1 Mice," _Journal of Alzheimer's Disease_ 35, no. 4 (2013): 847.
. "Cannabis, Alzheimer's Marijuana Helps Calm, Restore, Harmonize," _ALZConnected.org_ , October 7, 2014, www.alzconnected.org/discussion.aspx?type=carecenter_footer&g=posts&t=2147509906.
. J. S. Han, "Acupuncture and Endorphins," _Neuroscience Letters_ 361, no. 1–3 (2004): 258.
CHAPTER 7: SNAKE OIL OR CANCER CURE?
. L. R. Zhang et al., "Cannabis Smoking and Lung Cancer Risk: Pooled Analysis in the International Lung Cancer Consortium," _International Journal of Cancer_ 136, no. 4 (2015): 894–903.
. C. Liang et al., "A Population-Based Case-Control Study of Marijuana Use and Head and Neck Squamous Cell Carcinoma," _Cancer Prevention Research_ (Philadelphia) 2, no. 8 (2009): 759–68.
. Raymond Cushing, "Pot Shrinks Tumors; Government Knew in '74," _Alternet_ , May 30, 2000, www.alternet.org/story/9257/pot_shrinks_tumors%3B_government_knew_in_%2774.
. "Rick Simpson's Hemp-Oil Medicine," _High Times_ , November 30, 2013, www.hightimes.com/read/rick-simpsons-hemp-oil-medicine.
. "Neurontin," _WebMD_ , n.d., www.webmd.com/drugs/2/drug-9845–8217/neurontin-oral/gabapentin-oral/details#uses.
CHAPTER 8: BUDTENDERS AND SINSEMILLIERS
. Sean Williams, "7 Stunning Figures That Sum Up Colorado's Marijuana Market," _Motley Fool_ , March 8, 2015, www.fool.com/investing/general/2015/03/08/7-stunning-figures-that-sum-up-colorados-marijuana.aspx; Wil Hylton, "Willie Nelson's Crusade to Stop Big Pot," _New York_ , November 1, 2015, http://nymag.com/daily/intelligencer/2015/10/willie-nelson-crusade-stop-big-pot.html.
. Michael Backes, _Cannabis Pharmacy_ (New York: Black Dog & Leventhal, 2014), 58–60.
. Eli Stokols, "Welcome to America's Drug Laboratory," _Politico_ , May 13, 2014, www.politico.com/magazine/story/2014/05/colorado-marijuana-americas-drug-laboratory-106624; Jesse Sarles, "Job Seekers Swarm Marijuana Career Fair as Colorado's Green Rush Continues," _CBSDenver.com_ , March 14, 2014, http://denver.cbslocal.com/2014/03/14/job-seekers-swarm-marijuana-job-fair-as-colorados-green-rush-continues/.
. Fred Barbash, "Pot Sales Spark Warehouse Boom in Colorado," _Washington Post_ , March 11, 2014, www.washingtonpost.com/news/morning-mix/wp/2014/03/11/pot-sales-spark-warehouse-boom-in-colorado/.
. Steve Raabe, "Pot-Growing Warehouses in Short Supply as Demand for Weed Surges," _Denver Post_ , March 11, 2014, www.denverpost.com/marijuana/ci_25316132/pot-growing-warehouses-short-supply-demand-legal-weed.
. Evan Mills, "Energy Up in Smoke: The Carbon Footprint of Indoor Cannabis Production," Energy Associates, n.d., http://evan-mills.com/energy-associates/Indoor.html.
CHAPTER 9: DESIGNING YOUR HIGHS
. Ethan Russo, "Clinical Endocannabinoid Deficiency (CECD): Can This Concept Explain Therapeutic Benefits of Cannabis in Migraine, Fibromyalgia, Irritable Bowel Syndrome and Other Treatment-Resistant Conditions?," _Neuroendocrinology Letters_ 29, no. 2 (2008): 192–200.
. Michael Backes, _Cannabis Pharmacy_ (New York: Black Dog & Leventhal, 2014), 60–62.
. S. Malhotra et al., "Effect of Different Aspirin Doses on Platelet Aggregation in Patients with Stable Coronary Artery Disease," _Internal Medicine Journal_ 33, no. 8 (2003): 350–54.
. Mark Wallace et al., "Dose-Dependent Effects of Smoked Cannabis on Capsaicin-Induced Pain and Hyperalgesia in Healthy Volunteers," _Anesthesiology_ 107, no. 5 (2007): 785–96.
. Mateus Bergamaschi et al., "Cannabidiol Reduces the Anxiety Induced by Simulated Public Speaking in Treatment-Naïve Social Phobia Patients," _Neuropsychopharmacology_ 36, no. 6 (2011): 1219–26.
. Angelica Oviedo, John Glowa, and Miles Herkenham, "Chronic Cannabinoid Administration Alters Cannabinoid Receptor Binding in Rat Brain: A Quantitative Autoradiographic Study," _Brain Research_ 616, no. 1–2 (1993): 293–302.
. Ibid.
. Russo, "Clinical Endocannabinoid Deficiency," 192.
. Adam Hanft, "Anti-Depressant Nation," _Daily Beast_ , October 5, 2008, www.thedailybeast.com/articles/2008/10/05/did-antidepressants-cause-the-mortgage-crisis.html.
CHAPTER 10: THE FOUR ENHANCEMENTS
. Julie Holland, ed., _The Pot Book: A Complete Guide to Cannabis_ (South Paris, ME: Park Street Press, 2010).
. Laurie Winer, "A Yoga High with a Little Help," _New York Times_ , December 5, 2012, www.nytimes.com/2012/12/06/fashion/marijuana-and-yoga-pairing-up-in-classes.html.
. Carl Sagan, "Mr. X," marijuana-uses.com, April 20, 2009, http://marijuana-uses.com/mr-x/.
. Ronald K. Siegel, _Intoxication: The Universal Drive for Mind-Altering Substances_ (Rochester, Vermont: Park Street Press, 2005), 13.
. David O. Kennedy, _Plants and the Human Brain_ (New York: Oxford University Press, 2014).
. Michael Pollan, "The Trip Treatment," _New Yorker_ , February 9, 2015, www.newyorker.com/magazine/2015/02/09/trip-treatment.
. Robin Carhart-Harris, "The Entropic Brain: A Theory of Conscious States Informed by Neuroimaging Research with Psychedelic Drugs," _Frontiers in Human Neuroscience_ , February 3, 2014, http://journal.frontiersin.org/article/10.3389/fnhum.2014.00020/abstract.
. Janet E. Joy, Stanley J. Watson Jr., and John A. Benson, _Marijuana and Medicine: Assessing the Science Base_ (Washington, DC: National Academy Press, 1999).
. Mark Wolfe, "Pot for Parents," _New York Times_ , September 7, 2012, www.nytimes.com/2012/09/08/opinion/how-pot-helps-parenting.html.
. Anonymous, "The Effects of Marijuana on Consciousness," in _Altered States of Consciousness_ , ed. Charles T. Tart (New York: Doubleday & Co., 1972).
. Sagan, "Mr. X."
. Matthew Klickstein, "Does Pot Enhance Your Ability to Code?," _iTechPost_ , March 7, 2013, www.itechpost.com/articles/6198/20130307/pot-enhance-ability-code.htm.
. Charles Levinson, "Comey: FBI 'Grappling' with Hiring Policy Concerning Marijuana," _Wall Street Journal_ , May 20, 2014, http://blogs.wsj.com/law/2014/05/20/director-comey-fbi-grappling-with-hiring-policy-concerning-marijuana/.
. Sebastián Marincolo, _High: Insights on Marijuana_ (Indianapolis: Dog Ear Publishing, 2010).
. Jonathon Green, "Spoonfuls of Paradise," _The Guardian_ , October 11, 2002, www.theguardian.com/books/2002/oct/12/featuresreviews .guardianreview34.
. Marincolo, _High_ , 74.
. Vilayanur S. Ramachandran and Edward M. Hubbard, "Hearing Colors, Tasting Shapes," _Scientific American_ , May 2003, http://cbc.ucsd.edu/pdf/SciAm_2003.pdf.
. Allen Ginsberg, "The Great Marijuana Hoax," _Atlantic Monthly_ , November 1966, www.theatlantic.com/past/docs/issues/66nov/hoax.htm.
. Jasen Davis, "Cannabis and Sexology: A Coach for Couples and Cannabis," _Culture_ , February 4, 2016, http://ireadculture.com/cannabis-and-sexology/.
. Sarah Griffiths, "Could Smoking Marijuana Be Good for a Relationship? Less Domestic Violence Found Among Married Couples Who Use Drugs, Study Claims," _Daily Mail_ (UK), August 27, 2014, www.dailymail.co.uk/sciencetech/article-2735566/Could-smoking-marijuana-GOOD-relationship-Less-domestic-violence-married-couples-use-pot.html.
. Iain McGilchrist, "The Divided Brain" (TED Talk, October 2011), www .ted.com/talks/iain_mcgilchrist_the_divided_brain.
. Iain McGilchrist, _The Master and His Emissary: The Divided Brain and the Making of the Western World_ (New Haven, CT: Yale University Press, 2012): 29–31.
. McGilchrist, _The Master._
CHAPTER 11: THE NEXT REINVENTION OF WEED
. Tony O'Neill, "We Need to Talk About Kevin Sabet," _Substance.com_ , January 21, 2015, www.substance.com/we-need-to-talk-about-kevin-sabet/19316/.
2. Bridget Onders et al., "Marijuana Exposure Among Children Younger Than Six Years in the United States," _Clinical Pediatrics_ , June 7, 2015, http://cpj.sagepub.com/content/early/2015/06/03/0009922815589912 .abstract.
. Maia Szalavitz, "Drugs in Portugal: Did Decriminalization Work?," _Time_ , April 26, 2009, http://content.time.com/time/health/article /0,8599,1893946,00.html.
. Lee Fang, "The Real Reason."
. Ibid.
. Kevin A. Sabet, "California Medical Association's Decision Not Based on Public Health," _Huffington Post_ , October 21, 2011, www.huffingtonpost.com/kevin-a-sabet-phd/cmas-decision-not-based_b_1024471.html.
. Wiebke Hollerson, "This Is Working: Portugal, 12 Years After Decriminalizing Drugs," _Spiegel Online International_ , March 27, 2013, www .spiegel.de/international/europe/evaluating-drug-decriminalization-in-portugal-12-years-later-a-891060.html.
. "1,000–2,000 New Marijuana Jobs in Colorado," _Marijuana Business Daily_ , May 21, 2014, http://mjbizdaily.com/1000–2000-new-cannabis-jobs-in-colorado/.
. Daniel Okrent, _Last Call: The Rise and Fall of Prohibition_ (New York: Scribner, 2011), 374.
. Bari Adams, "Cannabis Compounds THCV and Cannabidiol Linked to Metabolic Rate," _Examiner.com_ , July 10, 2012, www.examiner.com/article /cannabis-compounds-thcv-and-cannabidiol-linked-to-metabolic-rate.
. Paula Span, "Study Links Anxiety Drugs to Alzheimer's Disease," _New York Times_ , September 24, 2014, http://newoldage.blogs.nytimes.com/2014/09/24/study-links-anxiety-drugs-to-alzheimers-disease/.
. Richard Alleyne, "Welcome to the Information Age—174 Newspapers a Day," _The Telegraph Online_ , February 11, 2011, www.telegraph.co.uk/news/science/science-news/8316534/Welcome-to-the-information-age-174-newspapers-a-day.html.
## ___About the Author_
**JOE DOLCE** is the former editor-in-chief of _Details_ and _Star_ magazines, and he has written for many of the world's leading publications, including the _New York Times_ , _Gourmet_ , and _Travel + Leisure_. He is the CEO and founder of Joe Dolce Communications, a presentation and media-training company based in New York City. He is not a stoner.
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## Credits
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## Copyright
As of publication, cultivating and consuming cannabis are criminal offenses in many states and illegal pursuant to federal law. This book is intended to enlighten and inform and does not encourage or advocate the unlawful use of cannabis. It is not intended to provide guidance for any particular course of medical treatment incorporating cannabis, which should only be pursued under the care of a physician in states where such use is permitted by law. The author and publisher disclaim any responsibility for loss or liability caused as a result of the use or application of material in this book.
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* Origins of the antonym "pot" are more obscure. One urban myth says the term came from the Mexican Spanish _potacion de guaya,_ or "drink of grief," a sort of wine beverage mulled with marijuana buds and leaves. The problem with this theory is that no one has yet found _potacion de guaya_ actually being used in Spanish cultures. A different theory posited by TheWordDetective.com harks back to another slang term for the stuff: "tea." This writer thinks that dried marijuana leaves resemble those of tea and that eventually they became a pun on "teapot." One Wikipedia entry on jive slang says "tea" is a "short name used for the mysterious potted plants that musicians always traveled with in the 1930s and '40s."
* Perhaps lawmakers were ruder back then, or perhaps this congressman felt Woodward's testimony was a sore loser's response to Franklin D. Roosevelt's 1936 landslide reelection. FDR brought with him two Democrats for every Republican, almost all of whom had pledged to support the New Deal. The AMA, however, had opposed every piece of New Deal legislation since Roosevelt was first elected in 1932, so by 1937 this Democratic-controlled congressional committee was probably fed up with hearing the group's opinions.
* This theory has never been proved, and the evidence indicates that the opposite is more likely the case. According to a 2014 study by the RAND Drug Policy Research Center on national drug use and health, the amount of marijuana consumed in the US likely increased by about 30 percent from 2006 to 2010, while the amount of cocaine decreased by about half.
* Some claim that Bourne's bust was singly responsible for the change in pot's legal fortunes, but that is as simplistic as crediting the television show _Will & __Grace_ for the acceptance of gay marriage. Carter had many reasons, among them gasoline shortages, high inflation, and the Iran hostage crisis, to steer clear of another difficult battle.
* The results of the DARE effort were, at best, mixed. In 1992 researchers at Indiana University found that DARE grads had significantly higher rates of hallucinogenic drug use than those who hadn't entered the program.
* According to DrugScience.org, cannabis is still the United States' number one cash crop—despite the $51 billion the DEA spends each year prosecuting the drug wars. Revenues for cannabis are greater than that of all other US-grown commodities, including wheat, soy, and corn. It is one of the few remaining products that is truly made in America.
* Some of that merchandise was never to be seen again. George Warren, who owned six hydroponic stores in the Northeast, was never arrested or associated with any crime, but still had over $200,000 in lighting equipment confiscated. When he inquired about having it returned, FBI agents told him that it was going to be sold at auction. "You mean they confiscate my merchandise because they _think_ some people are going to grow pot with it and then they sell it to someone else?" he asked in astonishment. "That's how it works," he was told.
* The magazine has become to old-school cannabis lovers what _Playboy_ once was to past generations of men: a dying standard-bearer, courageous and provocative when it began, but a bit of an artifact today. It regularly includes centerfolds of "nug porn," magnified buds and calyxes, dripping with juicy resins that dedicated readers pore over, cut out, and tape to their walls as if they were forbidden carnal pleasures.
* In fact, many companies got away with selling seeds by stating that they were for "collection purposes only." They were to be held and not sprouted until the laws changed.
* This may, in fact, be the case. Today, Holland has about 750 coffee shops, half the amount of a decade ago.
* In the Albanian village of Lazarat (population 7,000) farmers last year sowed 300,000 cannabis plants on 60 acres. The haul was estimated to yield 500 tons, which was on track to earn the town $6 billion. When the cops attempted to burn the crop a few colorful reports claim they were met at the village gates by grandmothers taking aim at them with machine guns and antitank missiles to protect their harvest.
* There's no doubt that pot fosters irreverence toward authority. Nixon sensed this, and if he had been a student of literature he would have known that it had been mentioned for centuries. _The Arabian Nights_ recounts the tale of a king who dressed as a commoner and went to town to ask people what they thought of his rule. He ran into a few hash smokers and peppered them with questions. In response, one stood up and imitated the king giving a pompous speech. The king realized that to be loved by the common man, he should speak to them more directly. Somehow pot pulls back the curtain on authority: It's "I am you and you are me and we are all together" in this human endeavor. Authority senses that; insecure authority fears it.
* David Bronner, a grandson of the founder of the liquid soap company, has been an outspoken supporter of hemp and legalization efforts.
* Not once in the four days I spent here did anyone mention food. I plan my dinner over breakfast but these smokers were utterly uninterested in eating, which is odd, given pot's well-established connection to the munchies. These guys also drank very little alcohol—water, energy drinks, and the occasional Corona Light were the mainstays. Serious smokers know that pot and gallons of alcohol don't mix.
* Cannabis oil (aka hash oil) briefly spiked in popularity in the 1960s, when hippies painted it on joints to boost highs. We now know that that application was an utter waste of material because oil burns at a different temperature than flowers. What's more, the goo was messy to use and stuck to clothes like tar, so it fell out of favor.
* The law has since been rewritten. If THC is identified in a driver's blood in quantities of 5 milligrams per milliliter or higher, "such fact gives rise to permissible inference that the defendant was under the influence."
* Production was increased to 1,433 pounds per year in 2014.
* According to the NIDA budget office, the total budget for NIDA in 2015 was $1.016 billion, and the marijuana research budget was $66 million. When asked to clarify the precise numbers, the National Institute on Drug Abuse told me, "Please keep in mind that this is for the NIDA budget. NIDA is one of 27 Institutes within the National Institutes of Health. There are other institutes who conduct marijuana research."
* Even smugglers, whose identity relies on not being known, identify place of origin. Why? Branding!
* This is the assumption, at least. Anandamide has never been administered to a human being due to legal restrictions, so there is no proof.
* Receptors in the brain are known as CB1 receptors; receptors in the body's other organs are called CB2 receptors.
* Sadly, Professor Bab died shortly after my interview with him.
* Until 2012, the league denied that any brain injury resulted from football.
* In May 2013, George Kunos and Pál Parcher wrote in the _FEBS Journal_ that "modulating endocannabinoid system activity may have therapeutic potential in almost all diseases affecting humans, including obesity/metabolic syndrome, diabetes and diabetic complications, neurodegenerative, inflammatory, cardiovascular, liver, gastrointestinal, skin diseases, pain, psychiatric disorders, cachexia, cancer, chemotherapy-induced nausea and vomiting, among many others."
* The expanded list includes chronic pain, orphan diseases (i.e., diseases and conditions that affect only a small number of people and for which few pharmaceutical drugs are developed), HIV, fibromyalgia, anorexia, multiple sclerosis, Parkinson's disease, malignant cancers, and Crohn's disease (but mystifyingly _not_ irritable bowel syndrome).
* I was refused official access to the farm. The government once freely permitted reporters to visit, but after the BBC, CNN, the Associated Press, Reuters, and the _New York Times_ descended on Tikun Olam in November 2012, media access has been denied. Instead, I was treated to a Skype tour. Note to government apparatchiks: digital technology renders travel bans irrelevant.
* Ethan Russo also points out that the key indication of good health in Ayurveda is balancing three elements: ether, fire, and water. These ideas can be easily translated to modern science but rarely are: Ether is the central and parasympathetic nervous systems; fire is thermogenesis, heat production, and metabolism; water refers to thermotaxis, heat regulation, and the formation of preservative fluids like synovia and mucus. They are more rudimentary terms for similar functions that science has vindicated as long-standing truths.
* Folk medicine has recorded this effect for centuries. Sitting in a cannabis smoke–filled room was long considered by Indian doctors to be an effective asthma treatment. What does appear to correlate with symptoms of bronchitis—namely cough, phlegm production, and wheezing—is the ash produced from smoking a joint (or any substance, for that matter). The ash accumulation can be somewhat ameliorated by using a bong, which traps ash in water, or a vaporizer.
* According to Wenk, who is also the author of _Your Brain on Food_ , two additional nutritional changes can decelerate biological aging. First, restrict calories to 1,500 a day. "My rats on calorie-restricted diets, their hair doesn't fall out, their eyes don't fog with glaucoma, they get fewer tumors, their kidney's don't fail, they're smarter. . . . It's astonishing, there's so much evidence." But calorie restriction is no fun for humans. Instead, Wenk suggests inverting the way we consume food. "Eat everything—meat, gluten, dairy—but eat less of it and take your biggest meal at the beginning of the day," he says. His mantra? "Breakfast like a king, lunch like a prince, dinner like a pauper."
Second, eat more purple and dark-colored fruits and vegetables. They are both high in antioxidants, which scavenge the body for free radicals and put the brakes on aging. Certain orange foods, like turmeric, do the same. Indian elders have fewer incidents of Alzheimer's than their Western counterparts in part because they eat a lot of this anti-inflammatory spice that apparently also causes new brain cells to flourish. The NIH is currently investigating turmeric (but is still largely snubbing cannabis).
* Other researchers have learned that CBD is a potent inhibitor of breast cancer cells, metastasis, and tumor growth. Backed by NIH grants and with a license from the DEA, Dr. Sean McAllister, a biologist and pharmacologist at the Pacific Medical Center in San Francisco, reported in 2007 that cannabidiol kills breast cancer cells and destroys malignant tumors by switching off the ID-1 gene, a protein that appears to be a cancer cell conductor. This gene makes a brief cameo appearance during human embryonic development, but turns off thereafter. In breast cancer and several other metastatic cancers, the ID-1 gene gets turned on, causing malignant cells to invade. McAllister postulates that CBD's ability to silence the ID-1 gene could be a breakthrough anticancer medication.
* One popular conspiracy theory accuses Big Pharma of holding back cancer cures because there is more money to be made by not curing a disease but treating it partially. I'm less cynical—or more naive, depending on your point of view—about this industry's bad intentions. The mechanisms of many diseases remain elusive.
* Side effects of Neurontin include drowsiness, dizziness, loss of coordination, tiredness, blurred/double vision, unusual eye movements or shaking (tremor), swelling of the hands/ankles/feet, signs of infection (such as fever, cough, persistent sore throat), depression, suicidal thoughts/attempts, changes in mood, thoughts about harming yourself, unusual fever, swollen glands, yellowing skin/eyes, unusual tiredness, dark urine, change in the amount of urine, chest pain, rash, itching/swelling (especially of the face/tongue/throat), severe dizziness, trouble breathing.
* Holland has one licensed distributor of MediWeed, the pharma company Bedrocan. All of its four strains are registered as drugs, available by prescription and reimbursed by the Dutch national health insurance. Coffee shops are entirely different entities.
* This is a dubious solution. As Michael Backes reports in _Cannabis Pharmacy_ , when marijuana is dried, its oils lose volatility, and its aroma and potency diminish forever. Moisture cannot revive dried oils, but it can create mold. Best is to store cannabis in a glass jar in a cool, dark place with a Boveda moisture packet taped into the lid. Refrigerators work best for short-term storage; for longer bouts, freeze buds. Never refreeze once thawed.
* This is a contentious issue in other states, California especially. Growers who have been busted argue that they should not be banned from the industry today for past activities that were considered crimes during the drug wars.
* Colorado offers a power subsidy to new businesses, reducing Denver Relief's electricity bill to $6,500 a month.
* The Sanskrit Vedas counsel passing the chillum (the vertical pipe that Indian sadhus are often pictured cupping in their palms) three times and stopping for a while before taking in more.
* In fact, the most highly dosed animals had the greatest decrease in receptors (up to 80 percent), the lowest-dosed animals had the lowest reduction (up to 50 percent), and the middle-dosed group exhibited an intermediate reduction (up to 72 percent), as shown in the previously cited study by Angelica Oviedo, John Glowa, and Miles Herkenham.
* I don't want to overstate the effects of cannabis or equate it with the power of psilocybin. The cannabis experience is hugely different than that of psychedelics, not just in terms of degree but of quality. Dr. Erin Zerbo, an assistant professor in the Department of Psychiatry at Rutgers New Jersey Medical School, clarified this: "The brain is such a complicated system with lots of parts. It's also possible that activated cannabinoid receptors in the hippocampus and elsewhere in the brain might impair memory formation [not everyone agrees that this is an "impairment"], so perhaps that alone creates the feeling of living 'moment to moment,' of going forward without knowing where you just were."
* Even though the dogs once trained to sniff for pot have mostly been reassigned to bomb squads, I prefer to not take foolish chances. To transport souvenirs without incident through airports, I followed the advice of a blogger who once worked for the DEA. Lore has it that stashing flowers in a bag of ground coffee masks the smell, but like many myths, this one is not to be trusted. In fact, the terpenes in cannabis are far more powerful than those in coffee. My DEA advisor suggested vacuuming-sealing fresh buds. Also, while TSA officials are not overtly looking for illegal substances, if found, they are required to call local law enforcement, and you'll be prosecuted under the laws of that state. The US mail is another option, but it is unreliable depending on your point of origination. In my limited experience, packages mailed from California have a greater chance of arriving without a hitch; several small parcels I sent from Colorado went missing. Unsurprisingly, postal authorities in tightly regulated states are stricter about allowing illegal packages to cross their borders.
* Formerly the Partnership for a Drug-Free America, the group that produced the powerful and memorable "this is your brain on drugs" ads of the 1980s.
* Sun-grown cannabis requires few pesticides and is among the least thirsty crops grown in drought-ravaged California. One pound of beef requires 1,500 gallons of water. Almonds suck 1 gallon per nut. A bottle of wine takes 200 gallons. One avocado, 35 gallons. One eighth of an ounce of cannabis—the standard retail unit—takes a mere 2 gallons.
* Here's a handy recipe for an anti-inflammatory THCA-infused oil that you can make at home: Grind 10 grams of top-shelf flowers in a new coffee mill. (Do not use an old one. Coffee is an alkaloid, which interacts negatively with terpenoids.) Then combine with 10 grams of olive or coconut oil—oils enable faster and fuller absorption into the intestine. The mixture will resemble cornmeal mush. Let it sit twenty-four hours. Take 1 gram of the infused material twice a day. Reduce your intake to once a day as symptoms dissipate.
|
{
"redpajama_set_name": "RedPajamaBook"
}
| 461
|
\section{Introduction}
BERT has achieved unprecedented performance on text understanding~\cite{devlin2018bert}. However, BERT is hard to deploy due to its computation cost. Adaptive Neural Networks (ANN)~\cite{huang2016deep,huang2017multi} solve the problem by adding an exit for each block and allows early-exit for simple examples to save computation time. Inspired by ANN, DeeBERT~\citep{Xin2020deebert} proposed multi-exit BERT, which inserts additional classifiers for each layer of the Transformer~\cite{vaswani2017attention}. DeeBERT adopts a two-stage training style: it first fine-tunes BERT on downstream tasks as usual, and then all exits are trained jointly with the main branch of Transformer frozen. However, the dilemma between performance and computation cost still exists. Although DeeBERT demonstrates the feasibility of ANN on BERT, it suffers from the following problems: 1) Significant drop of the performance for early exits, and 2) Freezing the BERT backbone limits the expressive power of BERT for early exits.
To solve the above problems, we propose RomeBERT based on gradient regularized self-distillation. In RomeBERT, we jointly train the weights of BERT backbone with multi-exit classifiers. However, simply unfreezing the BERT backbone will introduce gradient conflicts during training, and thus hurt the performance of both early and late exits. RomeBERT introduces two techniques for robust training of Multi-Exit BERT, namely Gradient Regularization (GR) and Self-Distillation (SD). SD allows early exits to mimic the soft label of the final exit, and thus enables the consistency across different exits. As a result, SD can increase the performance of early exits while keeping the performance of the final exit comparable to the origin model. Besides SD, we adopt a novel GR approach to balance the gradients for early and late exits.
Extensive ablation studies have been performed on GLUE~\cite{wang2018glue} with the pre-trained BERT model. Experimental results demonstrate that RomeBERT achieves much better balance between efficiency and performance than DeeBERT.
\section{Related Work}
Transformer has achieved success on both visual and textual understanding~\cite{devlin2018bert,wang2018non,tan2019lxmert,geng2020character,geng2020spatio}. However, Transformer has fixed structure and is hard to deploy in practice due to the high computation cost. Many variants of Transformer have been proposed for improving the computation efficiency by means of feature clustering~\cite{vyas2020fast,zheng2020end,kitaev2020reformer}, low rank approximation~\cite{choromanski2020rethinking}, attention sparse regularization~\cite{gao2021fast}, and reversible architecture~\cite{kitaev2020reformer}. Among these variants, we focus on improving Transformer using adaptive architecture. Depth-adaptive neural networks~\cite{figurnov2017spatially,graves2016adaptive,gao2020multi,Xin2020deebert,zhou2020bert,liu2020fastbert} can perform adaptive inference by only activating part of the network thus can reduce computation cost of Transformer. During training, multi-exit classifiers with various depths are trained together. DeeBERT~\cite{Xin2020deebert} tests the feasibility of depth-adaptive inference on multi-exit BERT by exiting early if the confidence criterion is met. PABEE~\cite{zhou2020bert} takes into consideration the agreement among multi-exits and explores inference with multiple classifiers.
Knowledge Distillation (KD) \cite{hinton2015distilling} is a technique for network compression. It has been widely applied in CNN based models~\cite{furlanello2018born,xie2019self,yang2019training}. Recently, DistilBERT \cite{sanh2019distilbert} applies knowledge distillation on the BERT model. Different from knowledge distillation across models in DistilBERT, self-distillation transfer knowledge from late exits to early exits within a model. FastBERT~\cite{liu2020fastbert} proposes a similar structure as DeeBERT by adding knowledge transfer from deep exits to shallow exits. However, knowledge transfer across multi-exits is weak in FastBERT because the whole BERT backbone has been frozen for training stability. In contrast, our RomeBERT jointly trains the BERT backbone and multi-exit classifiers and adds a novel gradient regularization to solve the training stability problem. RomeBERT aims at improving earlier exit classifiers to reduce the performance imbalance among multi-exits. Our gradient regularization is highly motivated by the Gradient Episodic Memory (GEM)~\cite{lopez2017gradient} for life-long learning and Gradient Surgery~\cite{yu2020gradient} for multi-task learning.
\section{Robust Training of Multi-Exit BERT}
\subsection{Revisit DeeBERT}
DeeBERT proposes a two-stage training strategy for fine-tuning the BERT model on downstream NLP tasks. For efficient inference, it inserts an extra classifier (also called \textit{off-ramp}) after each intermediate Transformer layer. Given a data-label pair $(x, y)$ and a pretrained BERT model with $k$ layers. We can denote the output logits of the $i$-th classifier $f_i$ as $f_i(x;\theta_i)$, where $\theta_i$ is the parameters related to $f_i$.
The fine-tuning process of DeeBERT consists of two stages. First, the original BERT components (including BERT embeddings, all Transformer layers, and the final classifier) are fine-tuned with a cross-entropy loss from the final classifier $\mathcal{L}_{ce}(y, f_k(x;\theta_k))$.
Afterwards, all parameters fine-tuned in the first stage are frozen, and all intermediate classifiers but the final one are fine-tuned with the following loss: $\sum^{k-1}_{i=1}\mathcal{L}_{ce}(y, f_{i}(x;\theta_i))$. During inference, DeeBERT can dynamically determine when to early exit according to the confidence of a certain example by setting an entropy threshold $S$. If the entropy of the input example at the $i$-th off-ramp is below $S$ for the first time, the example will exit instantly at layer $i$.
\begin{table*}[htp!]
\scalebox{0.78}{
\begin{tabular}{ccccccccccccc}
\toprule
& \multicolumn{2}{c}{\textbf{SST-2}} & \multicolumn{2}{c}{\textbf{MRPC}} & \multicolumn{2}{c}{\textbf{QQP}} & \multicolumn{2}{c}{\textbf{QNLI}} & \multicolumn{2}{c}{\textbf{MNLI (m/mm)}} & \multicolumn{2}{c}{\textbf{RTE}}
\\
\cmidrule(lr){2-3}\cmidrule(lr){4-5}\cmidrule(lr){6-7}\cmidrule(lr){8-9}\cmidrule(lr){10-11}\cmidrule(lr){12-13}
Methods & Acc$\%$ & Time$\%$ & $\mathrm{F}_{1}\%$ & Time$\%$ & $\mathrm{F}_{1}\%$ & Time$\%$ & Acc$\%$ & Time$\%$ & Acc$\%$ & Time$\%$ & Acc$\%$ & Time$\%$ \\
\cmidrule(lr){1-13}
BERT-base & 93.5 & 100 & 86.9 & 100 & 71.3 & 100 & 90.8 & 100 & 84.1/83.5 & 100 & 69.4 & 100 \\
\cmidrule(lr){1-13}
DeeBERT & 90.5 & 46.6 & 87.4 & 73.9 & 69.7 & 42.6 & 87.1 & 49.3 & 83.4/82.3 & 73.1 & 67.9 & 94.8 \\
DeeBERT+SD & 91.2 & 45.9 & 86.7 & 65.4 & 70.1 & 44.6 & 86.6 & 47.9 & 83.4/82.6 & 73.7 & 67.6 & 90.6 \\
RomeBERT & \cellcolor{cyan}\bf90.6 & \cellcolor{cyan}\bf26.8 & \cellcolor{cyan}\bf86.7 & \cellcolor{cyan}\bf69.1 & \cellcolor{cyan}\bf70.8 & \cellcolor{cyan}\bf34.8 & \cellcolor{cyan}\bf88.7 & \cellcolor{cyan}\bf34.1 & \cellcolor{cyan}\bf83.3/82.6 & \cellcolor{cyan}\bf53.5 & \cellcolor{cyan}\bf69.5 & \cellcolor{cyan}\bf89.4 \\
\cmidrule(lr){1-13}
DeeBERT & 89.0 & 39.2 & 86.4 & 65.7 & 67.8 & 35.3 & 85.5 & 42.4 & 79.2/78.3 & 59.3 & 67.6 & 90.9 \\
DeeBERT+SD & 88.7 & 35.3 & 86.7 & 65.4 & 68.5 & 37.2 & 85.4 & 43.1 & 79.8/78.5 & 59.3 & 67.4 & 86.9 \\
RomeBERT & \cellcolor{cyan}\bf89.0 & \cellcolor{cyan}\bf19.8 & \cellcolor{cyan}\bf86.2 & \cellcolor{cyan}\bf62.7 & \cellcolor{cyan}\bf69.7 & \cellcolor{cyan}\bf22.8 & \cellcolor{cyan}\bf86.1 & \cellcolor{cyan}\bf24.0 & \cellcolor{cyan}\bf82.2/81.4 & \cellcolor{cyan}\bf38.9 & \cellcolor{cyan}\bf68.9 & \cellcolor{cyan}\bf69.2 \\
\cmidrule(lr){1-13}
DeeBERT & 87.7 & 33.4 & 83.6 & 41.0 & 59.1 & 19.3 & 82.4 & 34.0 & 76.3/75.5 & 53.9 & 66.1 & 79.0 \\
DeeBERT+SD & 88.2 & 32.9 & 84.4 & 40.4 & 59.9 & 20.0 & 81.7 & 34.3 & 76.6/75.4 & 52.8 & 66.3 & 71.0 \\
RomeBERT & \cellcolor{cyan}\bf88.7 & \cellcolor{cyan}\bf15.0 & \cellcolor{cyan}\bf83.8 & \cellcolor{cyan}\bf33.1 & \cellcolor{cyan}\bf67.7 & \cellcolor{cyan}\bf15.2 & \cellcolor{cyan}\bf83.2 & \cellcolor{cyan}\bf19.2 & \cellcolor{cyan}\bf77.6/76.9 & \cellcolor{cyan}\bf21.4 & \cellcolor{cyan}\bf66.9 & \cellcolor{cyan}\bf45.2\\
\bottomrule
\end{tabular}
}
\caption{Performance comparison on the \textsc{test} splits of the GLUE benchmark between DeeBERT and RomeBERT.
}
\vspace{0.2cm}
\label{tab:main}
\end{table*}
\begin{table*}[t]
\scalebox{0.78}{
\begin{tabular}{ccccccccccccc}
\toprule
& \multicolumn{2}{c}{\textbf{SST-2}} & \multicolumn{2}{c}{\textbf{MRPC}} & \multicolumn{2}{c}{\textbf{QQP}} & \multicolumn{2}{c}{\textbf{QNLI}} & \multicolumn{2}{c}{\textbf{MNLI (m/mm)}} & \multicolumn{2}{c}{\textbf{RTE}}
\\
\cmidrule(lr){2-3}\cmidrule(lr){4-5}\cmidrule(lr){6-7}\cmidrule(lr){8-9}\cmidrule(lr){10-11}\cmidrule(lr){12-13}
Methods & Acc$\%$ & Time$\%$ & $\mathrm{F}_{1}\%$ & Time$\%$ & $\mathrm{F}_{1}\%$ & Time$\%$ & Acc$\%$ & Time$\%$ & Acc$\%$ & Time$\%$ & Acc$\%$ & Time$\%$ \\
\cmidrule(lr){1-13}
BERT-base & 92.1 & 100 & 90.1 & 100 & 87.8 & 100 & 91.3 & 100 & 84.4/85.0 & 100 & 71.1 & 100 \\
\cmidrule(lr){1-13}
DeeBERT & 89.7 & 44.8 & 89.8 & 72.2 & 85.5 & 45.7 & 87.0 & 50.1 & 83.3/83.6 & 72.7 & 68.2 & 94.2 \\
DeeBERT+SD & 89.7 & 46.2 & 89.5 & 78.0 & 85.0 & 49.3 & 87.1 & 49.0 & 83.3/83.7 & 73.3 & 69.0 & 90.7 \\
RomeBERT & \cellcolor{cyan}\bf90.5 & \cellcolor{cyan}\bf26.8 & \cellcolor{cyan}\bf90.2 & \cellcolor{cyan}\bf66.7 & \cellcolor{cyan}\bf85.8 & \cellcolor{cyan}\bf42.9 & \cellcolor{cyan}\bf89.2 & \cellcolor{cyan}\bf34.6 & \cellcolor{cyan}\bf83.3/84.0 & \cellcolor{cyan}\bf52.7 & \cellcolor{cyan}\bf70.8 & \cellcolor{cyan}\bf88.9 \\
\cmidrule(lr){1-13}
DeeBERT & 87.4 & 37.3 & 89.3 & 64.9 & 83.0 & 37.7 & 85.0 & 42.8 & 78.8/79.3 & 58.7 & 67.9 & 90.0 \\
DeeBERT+SD & 87.7 & 37.2 & 88.8 & 70.1 & 82.8 & 40.8 & 85.3 & 43.8 & 78.8/79.6 & 58.2 & 68.6 & 87.9 \\
RomeBERT & \cellcolor{cyan}\bf88.5 & \cellcolor{cyan}\bf18.6 & \cellcolor{cyan}\bf89.3 & \cellcolor{cyan}\bf59.1 & \cellcolor{cyan}\bf83.8 & \cellcolor{cyan}\bf26.7 & \cellcolor{cyan}\bf86.3 & \cellcolor{cyan}\bf24.7 & \cellcolor{cyan}\bf82.1/82.8 & \cellcolor{cyan}\bf38.6 & \cellcolor{cyan}\bf71.1 & \cellcolor{cyan}\bf69.4 \\
\cmidrule(lr){1-13}
DeeBERT & 85.9 & 31.1 & 86.0 & 39.5 & 70.4 & 20.5 & 81.5 & 34.4 & 75.9/76.1 & 53.4 & 66.4 & 78.7 \\
DeeBERT+SD & 85.5 & 31.5 & 85.7 & 39.5 & 69.9 & 21.6 & 81.4 & 34.7 & 75.7/76.6 & 51.8 & 67.5 & 71.9 \\
RomeBERT & \cellcolor{cyan}\bf86.6 & \cellcolor{cyan}\bf14.2 & \cellcolor{cyan}\bf86.6 & \cellcolor{cyan}\bf32.7 & \cellcolor{cyan}\bf81.6 & \cellcolor{cyan}\bf16.5 & \cellcolor{cyan}\bf83.8 & \cellcolor{cyan}\bf20.1 & \cellcolor{cyan}\bf78.1/78.2 & \cellcolor{cyan}\bf21.1 & \cellcolor{cyan}\bf67.5 & \cellcolor{cyan}\bf43.9 \\
\bottomrule
\end{tabular}
}
\caption{Performance comparison on the \textsc{validation} splits of the GLUE benchmark between DeeBERT and RomeBERT.}
\label{tab:valid}
\end{table*}
\subsection{Self-Distillation (SD) for RomeBERT}
DeeBERT freezes the BERT backbone when training the multi-exit classifiers. This strategy stabilizes the training process of multi-exit Transformer at the price of limiting the expressive power of BERT for early exits. To utilize the expressive power of BERT backbone, we propose to train intermediate classifiers with the final classifier jointly in one stage. However, naively unfreezing the BERT backbone may lead to conflicts between different exits, which will result in performance degradation for all exits. To solve the problem, we propose an additional consistency regularization for all exits beyond the original final-layer cross-entropy supervision from $\mathcal{L}_{final}=\mathcal{L}_{ce}(y, f_k(x;\theta_k))$. Specifically, we enforce the prediction of early exits to mimic the soft prediction of the final exit. The SD strategy can regularize the prediction consistency between all exits and transfer knowledge from the late exit to early exits, thus we can stabilize the training process and enable significant performance improvements for early exits. The SD strategy is shown in the left part of Figure~\ref{fig:model}, all the intermediate exits are supervised by both the soft label (i.e., logit) of the final classifier and the ground-truth label. Specifically, the SD loss ${\cal L}_{sd}$ contains two components: multi-exit cross-entropy loss ${\cal L}_{multi}$ and Kullback-Leibler divergence (KLD) loss ${\cal L}_{kld}$, it can be written as:
\begin{align}
{\cal L}_{sd} & = {\cal L}_{multi} + {\cal L}_{kld} \nonumber \\
& = \sum_{i=1}^{k-1} [ (1-\gamma) \cdot {\cal L}_{ce} (y, f_i(x;\theta_i)) \nonumber \\
& + \gamma \cdot {\cal L}_{kld}^{(i)} (f_k(x;\theta_k) \parallel f_i(x;\theta_i), T) ], \nonumber
\end{align}
where $\gamma$ is a coefficient to balance the two loss terms and $T$ is the temperature of the KLD loss.
\begin{figure*}
\begin{center}
\includegraphics[width=0.99\linewidth,trim={0cm 0cm 0cm 0cm}]{image/DeeBERT+SD.pdf}
\end{center}
\caption{Performance comparison on the \textsc{validation} splits of the six GLUE datasets among DeeBERT, DeeBERT+SD and RomeBERT.}
\label{fig:curve}
\vspace{-0.3cm}
\end{figure*}
Suppose there are $\mathcal{C}$ classes in a classification task, we can denote the $i$-th layer Kullback-Leibler divergence loss ${\cal L}_{kld}^{(i)}$ as:
\begin{align}
{\cal L}_{kld}^{(i)} = - \sum_{c \in \mathcal{C}} p_k(c\mid x;\theta_k, T) \log\frac{p_i(c\mid x;\theta_i, T)}{p_k(c\mid x;\theta_k, T)} ,\nonumber
\end{align}
where $c$ is a class in $\mathcal{C}$, $T$ is a temperature value, and $p_i(c\mid x;\theta_i, T)$ can be computed as:
\begin{align}
p_i(c\mid x;\theta_i, T) = \frac{\exp(f_i(c \mid x;\theta_i)/T)}{\sum_j \exp(f_i(j \mid x;\theta_i)/T)}
. \nonumber
\end{align}
It is worth noting that FastBERT also adopts self-distillation to transfer knowledge from late to earlier exits. However, FastBERT follows the two-stage training paradigm of DeeBERT, where the BERT backbone is frozen during self-distillation in the second stage. In this paper, we implement DeeBERT plus self-distillation (DeeBERT+SD\footnote{Code is available at \url{https://github.com/romebert/DeeBERT-SD}.}) to reproduce the performance of FastBERT.
\subsection{\mbox{Gradient Regularization for RomeBERT}}
Self-distillation can stabilize training by enforcing consistent regularization over all exits. However, we still observe performance degradation on some GLUE tasks, i.e., RTE, QNLI and MRPC. We hypothesize that self-distillation can ease the conflicts among the training objectives of different exits but the new ${\cal L}_{sd}$ may still suffer from gradient conflicts with the final-exit training objective in these tasks.
Built upon the hypothesis, Gradient Regularization (GR) is proposed to further facilitate self-distillation in RomeBERT.
As shown in Figure~\ref{fig:model}, gradient conflict will arise when the angle between gradients computed by the final-exit loss and the combination of multi-exit loss and KLD loss is larger than $90^{\circ}$.
We denote the gradients of the final-exit loss and the self-distillation loss as $\mathbf{g}_f = \frac{\partial \mathcal{L}_{final}}{\partial \theta}$ and $\mathbf{g}_s = \frac{\partial \mathcal{L}_{sd}}{\partial \theta } =\frac{\partial (\mathcal{L}_{multi} +\mathcal{L}_{kld})}{\partial \theta }$, respectively.
To alleviate gradient conflict, GR will project the gradient of $\mathbf{g}_f$ to the normal direction of $\mathbf{g}_s$ when the angle between $\mathbf{g}_f$ and $\mathbf{g}_s$ is larger than $90^{\circ}$, i.e., $\mathbf{g}_f \cdot \mathbf{g}_s < 0$.
The projection can be formulated as:
\vspace{-0.2cm}
\begin{align}
\mathrm{Proj}(\mathbf{g}_f) = \mathbf{g}_f - \frac{\mathbf{g}_f \cdot \mathbf{g}_s}{\left \| \mathbf{g}_s \right \|^2} \cdot \mathbf{g}_s. \nonumber
\end{align}
$\mathrm{Proj}(\mathbf{g}_f)$ decreases the gradient from the final-layer exit loss while not hurting SD, which can help to produce better intermediate exits.
The modified gradient $\mathbf{g}^\star = \mathrm{Proj}(\mathbf{g}_f) + \mathbf{g}_s$ will then be used to update the model parameters.
In the other case (when the angle between $\mathbf{g}_f$ and $\mathbf{g}_s$ is less than $90^{\circ}$, i.e., $\mathbf{g}_f \cdot \mathbf{g}_s > 0$), the original gradients $\mathbf{g}_f$ and $\mathbf{g}_s$ will be kept as Case 2 shown in Figure~\ref{fig:model}.
\begin{figure}[htbp!]
\begin{center}
\includegraphics[width=1.02\linewidth,trim={0cm 0cm 0cm 0cm}]{image/BIG-QNLI_9.pdf}
\end{center}
\caption{Exit-layer distributions of DeeBERT, DeeBERT+SD and RomeBERT on QNLI validation split.}
\vspace{-0.2cm}
\label{fig:qnli}
\end{figure}
\begin{figure}[htbp!]
\begin{center}
\includegraphics[width=1.02\linewidth,trim={0cm 0cm 0cm 0cm}]{image/BIG-QQP_9.pdf}
\end{center}
\caption{Exit-layer distributions of DeeBERT, DeeBERT+SD and RomeBERT on QQP validation split.}
\label{fig:qqp}
\vspace{-0.15cm}
\end{figure}
\begin{figure}[htbp!]
\begin{center}
\includegraphics[width=1.02\linewidth,trim={0cm 0cm 0cm 0cm}]{image/APP-SST-2_9.pdf}
\end{center}
\caption{Exit-layer distributions of DeeBERT, DeeBERT+SD and RomeBERT on SST-2 validation split.}
\label{fig:sst-2}
\vspace{-0.3cm}
\end{figure}
\section{Experiments}
\subsection{Datasets and Experimental Setup}
\label{sec:datasets}
We train all approaches from the BERT-base pre-trained model~\cite{devlin2018bert}, and conduct experiments on the same GLUE benchmark \citep{wang2018glue} that is used by DeeBERT: QQP, MNLI, MRPC, RTE, SST-2, and QNLI. In our experiments, we maintain the same hyperparameters as DeeBERT. Specifically, we set coefficient $\gamma$ to 0.9, self-distillation temperature $T$ to 3.0 and keep them unchanged for all experiments.
Our experiments focus on two aspects of early-exit performance improvements: 1) Group different models with similar performances by changing their adaptive inference entropy values, then compare the expected running time for these models. We follow this setup to compare RomeBERT with DeeBERT and DeeBERT+SD on both validation and test splits. We also visualize the exit-layer distribution for each approach to show the advantage of RomeBERT.
2) Fix the exit layer and calculate the exit performance for all layers. Based on this setting, we compare RomeBERT with DeeBERT and DeeBERT+SD on the validation split, then conduct layerwise ablation study for the two key components of RomeBERT.
To make better comparison, we summarize the core properties of each approach. In terms of training stage, DeeBERT and DeeBERT+SD follow the two-stage training strategy while RomeBERT conducts joint training in only one stage. DeeBERT and DeeBERT+SD both freeze the BERT backbone during the second training stage. In terms of self-distillation, DeeBERT+SD conducts self-distillation in the second stage while RomeBERT performs self-distillation and gradient regularization together within one stage.
\begin{figure*}
\begin{center}
\includegraphics[width=0.99\linewidth,trim={0cm 0cm 0cm 0cm}]{image/NEW-VALID-6.pdf}
\end{center}
\caption{Performance comparison on the \textsc{validation} splits of the six GLUE datasets between DeeBERT and RomeBERT. Ablation study on the two key components of RomeBERT is also included. For three datasets (QQP, MNLI, and QNLI), we enlarge details to better compare the performance of SD only with SD+GR.}
\vspace{-0.3cm}
\label{fig:ablation}
\end{figure*}
\subsection{Performance Comparison and Discussion}
\label{sec:compare}
The performance on test splits of GLUE is shown in Table \ref{tab:main}. Here we regard the expected running time of BERT-base as 100\%, and calculate the relative expected running time percentage for DeeBERT, DeeBERT+SD and RomeBERT in adaptive inference mode. If an input example early exits at layer $i$, its running time is $i/k$ of the situation that exits at the final layer $k$. In Table \ref{tab:main}, we group results from different approaches with similar performances, then compare their expected running time. From the table, we can observe that in most datasets and situations, RomeBERT can achieve better performance than DeeBERT/DeeBERT+SD while requiring less running time.
For small datasets such as RTE, RomeBERT can achieve 69.5\% accuracy, which is 0.1\% better than the BERT-base baseline, and with 10.6\% time saving. In contrast, DeeBERT needs 5.4\% more time with 1.6\% worse performance, DeeBERT+SD requires 1.2\% more time with 1.9\% performance drop. In addition, RomeBERT gets 66.9\% accuracy with a 54.8\% time saving, while DeeBERT needs 33.8\% more time but the performance is 0.8\% worse, DeeBERT+SD requires 25.8\% more time but with 0.6\% performance drop.
For middle-sized datasets such as QNLI, RomeBERT can achieve 88.7\% accuracy which is 2.1\% below BERT-base but with only 34.1\% running time. In contrast, DeeBERT obtains 87.1\% accuracy with 15.2\% more time, DeeBERT+SD gets only 86.6\% accuracy at the cost of 13.8\% more time.
If we constrain the expected running time to 34.1\%, DeeBERT can only achieve 82.4\% accuracy compared with RomeBERT's 88.7\%, and DeeBERT+SD can only obtain 81.7\% accuracy.
For large-sized datasets such as QQP, our RomeBERT obtains 70.8\% $\mathrm{F}_{1}$-score which is only 0.5\% less than BERT-base with a huge 65.2\% time saving. Even when the time cost is further reduced to 15.2\%, RomeBERT only drops 3.6\% $\mathrm{F}_{1}$-score than BERT-base, but DeeBERT needs 20.1\% more time to achieve the same performance. If we change the performance standard to 69.7\%, DeeBERT needs 42.6\% time to achieve this goal while RomeBERT only requires 22.8\%. Besides, in Table~\ref{tab:valid}, we also show the performances of different methods on validation splits of GLUE benchmark for reference.
We illustrate the exit-layer distributions on QNLI, QQP and SST-2 in Figure~\ref{fig:qnli}, Figure~\ref{fig:qqp} and Figure~\ref{fig:sst-2}, respectively. From these figures, we can see that the exit-layer distribution of RomeBERT is more prone to earlier exits than DeeBERT and DeeBERT+SD. For QNLI, the exit layer distribution of DeeBERT/DeeBERT+SD is centered at the 4th layer, while RomeBERT is centered at the 2nd layer. For QQP, the exit layers of DeeBERT/DeeBERT+SD are more uniformly distributed. In contrast, the 1st layer gets the most frequent exits for RomeBERT.
For SST-2, the most frequent exit layer for DeeBERT/DeeBERT+SD is the 2nd layer, but the ratio is at most 40\%, while the 1st layer again gets the most frequent exits for RomeBERT and the ratio is at least 60\%. The observation proves that RomeBERT can really improve the performance and maintain a robust training for early exits.
Moreover, Figure~\ref{fig:curve} shows every-layer performance comparison when the exit layer is fixed for all inputs. We can see that the curves of RomeBERT are above those of DeeBERT and DeeBERT+SD in almost all situations. The performance gaps between RomeBERT and DeeBERT/DeeBERT+SD are especially large for early layers and on large-sized datasets. At the first three layers, for instance, RomeBERT increases nearly 20\% performance over DeeBERT/DeeBERT+SD on both QQP and MNLI. We can also conclude that DeeBERT+SD does not beat DeeBERT in terms of layerwise performance. This implies that freezing the BERT backbone during self-distillation may limit the expressive power of early exits.
\subsection{Ablation Study on RomeBERT}
\label{sec:ablation}
In Figure~\ref{fig:ablation}, we also conduct ablation study on GR and SD. Since GR is built upon SD, we directly compare the performances of RomeBERT with or without GR. Due to the large performance gap in early layers of RomeBERT over DeeBERT, we rescale the curves to better evaluate the function of GR. From the figure, we can conclude that GR is generally helpful to improve the performance upon SD. The degree of improvement depends on the level of gradient conflict. Specifically, GR exhibits its superiority on RTE and QNLI since almost all layers get improved accuracy. In addition, GR improves the performance of most layers on QQP and SST-2, while it is partially effective for certain layers on MRPC and MNLI.
\section{Conclusion}
In this paper, we propose RomeBERT for robust training of multi-exit BERT. We validate the effectiveness and efficiency of RomeBERT on six GLUE classification tasks. Compared with the DeeBERT and FastBERT approaches, RomeBERT, which is driven by self-distillation and gradient regularization to facilitate the early exits, achieves better speed-performance tradeoff on all tasks.
\bibliographystyle{acl_natbib}
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{"url":"https:\/\/proofwiki.org\/wiki\/Distribution_Space_over_Smooth_Functions_is_Unitary_Module","text":"# Distribution Space over Smooth Functions is Unitary Module\n\n## Theorem\n\nThe distribution space over smooth functions is a unitary module.\n\n## Proof\n\nLet $\\phi \\in \\map \\DD {\\R^d}$ be a test function.\n\n### Module Axiom $\\text M 1$: Distributivity over Module Addition\n\n $\\ds \\alpha \\map {\\paren {T_1 + T_2} } \\phi$ $=$ $\\ds \\map {\\paren {T_1 + T_2} } {\\alpha \\phi}$ Definition of Multiplication of Distribution by Smooth Function $\\ds$ $=$ $\\ds \\map {T_1} {\\alpha \\phi} + \\map {T_2} {\\alpha \\phi}$ $\\ds$ $=$ $\\ds \\alpha \\map {T_1} \\phi + \\alpha \\map {T_2} \\phi$ Definition of Multiplication of Distribution by Smooth Function\n\nHence:\n\n$\\alpha \\paren {T_1 + T_2} = \\alpha T_1 + \\alpha T_2$\n\n$\\Box$\n\n### Module Axiom $\\text M 2$: Distributivity over Scalar Addition\n\n $\\ds \\map {\\paren {\\alpha_1 + \\alpha_2} T} \\phi$ $=$ $\\ds \\map T {\\paren {\\alpha_1 + \\alpha_2}\\phi}$ Definition of Multiplication of Distribution by Smooth Function $\\ds$ $=$ $\\ds \\map T {\\alpha_1 \\phi + \\alpha_2 \\phi}$ Real Multiplication Distributes over Addition $\\ds$ $=$ $\\ds \\map T {\\alpha_1 \\phi} + \\map T {\\alpha_2 \\phi}$ Definition of Distribution $\\ds$ $=$ $\\ds \\alpha_1 \\map T \\phi + \\alpha_2 \\map T \\phi$ Definition of Multiplication of Distribution by Smooth Function\n\nHence:\n\n$\\paren {\\alpha_1 + \\alpha_2} T = \\alpha_1 T + \\alpha_2 T$\n\n$\\Box$\n\n### Module Axiom $\\text M 3$: Associativity\n\n $\\ds \\paren {\\alpha \\beta} \\map T \\phi$ $=$ $\\ds \\map T {\\paren {\\alpha \\beta} \\phi}$ Definition of Multiplication of Distribution by Smooth Function $\\ds$ $=$ $\\ds \\map T {\\beta \\paren {\\alpha \\phi} }$ Real Multiplication is Associative, Real Multiplication is Commutative $\\ds$ $=$ $\\ds \\map {\\paren {\\beta T} } {\\alpha \\phi}$ Definition of Multiplication of Distribution by Smooth Function $\\ds$ $=$ $\\ds \\map {\\paren {\\alpha \\paren {\\beta T} } } \\phi$ Definition of Multiplication of Distribution by Smooth Function\n\nHence:\n\n$\\paren {\\alpha \\beta} T = \\alpha \\paren {\\beta T}$\n\n$\\Box$\n\n### Unitary Module Axiom $\\text {UM} 4$: Unity of Scalar Ring\n\nLet $\\mathbf 1 \\in \\map {C^\\infty} {\\R^d}$ be a constant mapping such that:\n\n$\\R^d \\stackrel {\\mathbf 1} {\\mapsto} 1$\n\nThen:\n\n $\\ds \\mathbf 1 \\cdot \\map T \\phi$ $=$ $\\ds \\map T {1 \\cdot \\phi}$ Definition of Multiplication of Distribution by Smooth Function $\\ds$ $=$ $\\ds \\map T \\phi$\n\nHence:\n\n$1 \\cdot T = T$\n\n$\\Box$\n\n$\\blacksquare$","date":"2023-02-01 09:23:12","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 2, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.9925243258476257, \"perplexity\": 601.400240816222}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2023-06\/segments\/1674764499919.70\/warc\/CC-MAIN-20230201081311-20230201111311-00840.warc.gz\"}"}
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\section*{Abstract}
We modeled the dynamics of a soccer match based on a network representation where players are nodes discretely clustered into homogeneous groups. Players were grouped by physical proximity, supported by the intuitive notion that competing and same-team players use relative position as a key tactical tool to contribute to the team's objectives. The model was applied to a set of matches from a major European national football league, with players' coordinates sampled at 10Hz, resulting in $\approx$ 60,000 network samples per match. We took an information theoretic approach to measuring distance between samples and used it as a proxy for the game dynamics. Significant correlations were found between measurements and key match events that are empirically known to result in players jostling for position, such as when striving to get unmarked or to mark. These events increase the information distance, while breaks in game play have the opposite effect. By analyzing the frequency spectrum of players' cluster transitions and their corresponding information distance, it is possible to build a comprehensive view of player's interactions, useful for training and strategy development. This analysis can be drilled down to the level of individual players by quantifying their contribution to cluster breakup and emergence, building an overall multi-level map that provides insights into the game dynamics, from the individual player, to the clusters of interacting players, all the way to the teams and their matches.
\\
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\end{@twocolumnfalse}
]
\section{Introduction}
\label{introduction}
\noindent
Complex systems, with time evolving interactions among its elements, abound in the social, biological and physical domains. In many of these systems,
elements are clustered in groups that also undergo changes with time. A temporal, clustered network can be an appropriate representation of such a system.
In this article we apply this representation to the sport of soccer. Soccer, as many other competitive team sports, can be seen as a social-biological complex system \cite{Ramos2020}. The domain dynamics of these sport modalities are neither fully random nor fully designed. This contributes decisively to their complexity. This is a property shared by many other complex systems that are subject to constrained random chance, therefore we believe the techniques and approaches researched for this article have potential application beyond sports.
We use the term ``clustering'' to mean the set of disjoint non-empty subsets of nodes observed in the network at a given point in time. Some authors call it a ``partition''. These terms represent similar constructs, clustering being semantically associated with an emerging, bottom-up aggregation of nodes, while partition conveys the idea of a top-down driven process. In soccer there is not a single entity controlling group formation \cite{Ribeiro2019b}, at least not directly and in real time, so the former seems more appropriate.
The soccer match is here represented as a succession of network observations where clusters are subsets of players, including the two football goal frames, resulting in a network with a maximum of 24 nodes concurrently active, plus substitutes \cite{Ramos2017}.
While studying a soccer match as an evolving clustered network, we start from the proposition that players' spatial distribution on the pitch is the determining variable for clustering. Intuitively we could think that an optimal assignment of players to clusters would require a physical distance measure, predicating link weights by player relative distance. However, there are complicating factors to the usage of such a precise measurement, as the importance of inter-player distance is not independent of game play \cite{Ramos2018}. It varies with pitch location, ball position, game rules, environmentals (such as playing surfaces or weather), or the relation between time and distance in dynamic game settings. All these contribute to the actual player's instantaneous grasp of his performance environment and perception of opportunity for action \cite{Araujo2016}.
The network representations we are using for the present analysis were built with a different approach. Instead of inter player links weighed by distance, players were clustered into homogeneous and disjoint groups connected by a single link \cite{Ramos2017}, using the formalism of hypergraphs \cite{Berge1973}. A hypergraph is characterized by having multiple nodes connected by a single link in contrast with a traditional graph where links have a maximum of two endpoints. A set of nodes that share a link is called a simplex. The process to identify these sets is non parametric and is explained in \cite{Ramos2017}. It guarantees that no node is closer to a node belonging to a different simplex than to its closest node in the same simplex. In the particular context of the present article, simplices are sets or clusters, and the collection of simplices observed in a single sample, a clustering. In the reminder of this document, we use the terms simplex and cluster interchangeably, all referring to the same construct: a group of players in articulated interaction and proximity. An example of the clustering process is illustrated in figure \ref{fig:7} in the appendix.
\pagestyle{fancy}
\fancyhf{}
\chead{The Soccer Game, bit by bit}
\rfoot{Page \thepage\ of \pageref{LastPage}}
It could be argued that discretization and assignment of nodes to a pairwise disjoint family of sets, would lead to a distorted representation of events on the pitch. After all, players move freely in an Euclidean space and in continuous real time, while in the proposed representation time is discrete and players move on a lattice, understood not as a grid that spans the pitch but as the configuration space of all possible set arrangements \cite{Conway1999, Johnson2010}. Frequent observation, however, mitigates these effects. For example, peripheral players in a simplex will more easily transfer to a different simplex and, if frequently observed, any simplex changes will be quickly captured. Due to the high frequency characteristic of the network (10Hz), errors will smooth out as player simplices form and dissolve, establishing a bridge between the continuous domain of game play and the time sliced network representation employed \cite{Johnson2016}.
This discretization carries with it a significant advantage. We are no longer in a continuous domain, and the toolkit of information theory \cite{Cover2006} becomes available to us. In a discrete domain, information can be quantified for complexity, such as in the Kolmogorov complexity or the Shannon entropy \cite{Kolmogorov1968, C.E.Shannonvol.27pp.JulyOctober1948, Grunwald2008}. Similarly, two pieces of information can be compared for distance. We can determine how far apart or how close they are by the number of units of information that are needed to find one given the other. In this article the pieces of information are the individual clustering samples of the soccer match.
Formally, a clustering is:
\begin{multline}
C = \{c_1, \cdots, c_k\}: \\
(c_i \cap c_j = \varnothing \;\; \forall \;( 1 \leq i, j \leq k\;
\land \; i \neq j)) \land \; \cup _{i=1}^{\,k} \, c_i = V
\label{eq:1}
\end{multline}
where $c$ are the disjoint subsets, $k$ the number of subsets, and $V$ the set of all nodes.
There are several methods to measure the inter-distance between clusterings, with varying properties,
such as the Rand Index \cite{Rand1971}, Adjusted Rand Index \cite{Hubert1985}, the Normalized Mutual Information \cite{Danon2005}, the Van Dongen-Measure \cite{Dongen2000} and others. A thorough discussion of the major methods can be found in \cite{Vinh2010, Wagner2007, Meila2007}.
We chose the Variation of Information $(\mathit{VI})$ \cite{Meila2007} to measure the information distance between samples and thus evaluate the change a clustered network experiences as a function of time.
In a nutshell, $\mathit{VI}$, measures the amount of information gained or lost on every new network observation.
If no changes in the clusters are observed, then there is no variation of information. As clusterings shift from one another, $\mathit{VI}$ increases.
This is easy to visualize when considering the so-called confusion matrix \cite{Stehman1997} between clusterings at successive observations. This matrix describes the node spread, where each element represents the number of nodes moving from one cluster to another. If clusters are unchanged and keep their node affiliation, the confusion matrix will be a monomial matrix, $\mathit{VI}=0$ and we know exactly where each node ends up. But as the number of non-zero entries in the confusion matrix increases and their distribution tends to uniform, the uncertainty about each node destination also increases. Consider as an example a cluster that splits in half versus another that sheds a single node. There is a higher uncertainty about each node final destination in the former than in the latter. In simple terms, $\mathit{VI}$ measures this uncertainty. $\mathit{VI}$ has been applied in multiple contexts, for example to address the problem of clustering news published by online newspapers \cite{Rodrigues2013}. A practical illustration of how to compute $\mathit{VI}$ can be seen in tables \ref{tab:table1} and \ref{tab:table2} in the appendix.
We have selected $\mathit{VI}$ as it is a true metric, respecting the triangle inequality, meaning that no indirect path is shorter than a direct one. This is important in analyzing the rate of change at multiple scales, avoiding the unreasonable possibility of having a greater rate of change for a given time interval, when sampling the network at a lower rate. $\mathit{VI}$ also increases when fragmentation and merges occur in larger clusters, which intuitively relates to playing dynamics, given the rise in degrees of freedom experienced in larger groups of interacting players. Fundamentally, although in this article we consider VI as a proxy for game dynamics, VI itself is not a quantification of informational meaning or semantics, but simply, a quantification of informational variation, or as Shannon puts it "semantic aspects of communication are irrelevant to the engineering problem" \cite[p.1]{C.E.Shannonvol.27pp.JulyOctober1948}.
In this article we consider a split of $\mathit{VI}$ into two terms. A clustering has a signature in the (multi)set of its clusters' sizes. We call it a formation, as it vaguely captures the popular notion of team match formation in soccer, although these concepts do not overlap. A formation, using the previous notation is defined as:
\begin{equation}
\label{eq:2}
F = \{\vert c_1\vert, \cdots, \vert c_k\vert \}: \sum_{i=1}^{k}\vert c_i\vert =\vert V \vert
\end{equation}
Using this construct we split $\mathit{VI}$ into two terms:
\begin{enumerate}
\item $\mathit{VI}_f$, which is the minimum amount of inherent change resulting from the evolving formation as described above, and
\item the compositional $\mathit{VI}_c$ computed as $\mathit{VI}_c = \mathit{VI} - \mathit{VI}_f$, which is the additional information distance accrued on top of the minimum implied by the evolving formation.
\end{enumerate}
To understand these constructs consider that for two consecutive clusterings to show a null $\mathit{VI}$ it is necessary, but not sufficient, that their formations are equal. In fact, the formations can be equal (which implies that $\mathit{VI}_f=0$), but the clusterings' transition can still show a positive $\mathit{VI}$, due to compositional changes (in which case $\mathit{VI}=\mathit{VI}_c>0$). Consider, as illustration, a clustering made up of $n$ clusters. For simplicity, consider they are all of the same size $s$, or formally $C^t = \{c^t_1, \cdots, c^t_{n}\} \land \vert c^t_k \vert = s$. Its formation is $F_{c^t}=\{s^n\}$. Comparing with another clustering $C^{t+\delta}$, also with $F_{c^{t+\delta}}=\{s^n\}$, we have:
\begin{equation*}
\begin{cases}
\textit{VI} = 0 \iff \forall i \in \{1 \cdots n\} \; \exists! \; j \in \{1 \cdots n\} \; \mid c^t_i = c^{t+\delta}_j \\
\textit{VI} > 0, \; \textrm{otherwise}
\end{cases}
\end{equation*}
Another example can be found on figure \ref{fig:7} in the appendix. There we can observe a transition from a formation $\{2^4,3^4,4\}$ in (a) to $\{2^6,3,4,5\}$ in (b). As these formations are not equal, $\mathit{VI}>0$, however it is not the minimum for this transition. We can see that there is additional entropy, for instance in the restructuring of the 4-node simplex from players \{12, 20, 22, 21\} to \{9, 10, 14, 21\}, that the simple changes in formation would not necessarily require. We consider the usefulness of such a split analysis, guided by the intuition that the interplay of strategy, play patterns, set pieces, and individual player initiative \cite{Araujo2016, Ribeiro2019a} may drive differently $\mathit{VI_f}$ and $\mathit{VI_c}$. Depending on the represented system, these two components can have different meanings. This is an open issue that we briefly touch upon but that deserves further research.
While calculating the total $\mathit{VI}$ is computationally trivial if the network partition into clusters is known, finding $\mathit{VI_f}$ is not routinely tractable, as we need to find the minimum node change for the formation transition, an NP-hard problem, meaning that it will be at least as algorithmically complex to solve precisely as any non-deterministic polynomial time algorithm. We employ a heuristic developed previously to approximate it efficiently\cite{Pereira2019a}.
In the reminder of this document, we discuss the correlation of $\mathit{VI}$ and playing dynamics in section \ref{methods}, followed by a section \ref{results} describing the results obtained. We discuss these results in section \ref{discussion} and we conclude with directions for future research in section \ref{conclusion}.
The main research question is whether $(\mathit{VI})$ can be a faithful proxy for game dynamics, and we expect to confirm a strong correlation. We are also interested in how $\mathit{VI_f}$ and $\mathit{VI_c}$ contribute to total $\mathit{VI}$ and how it relates to game tactics and play development.
\section{Methods}
\label{methods}
The proposed approach is applied to the analysis of a set of 9 soccer matches from the 2010-11 season of the English Premier League. Based on an information stream collected from realtime pitch-located raw video feed, each match is modeled as a high-resolution (10Hz) temporal hypernetwork with simplices as clusters\cite{Ramos2017a, Ramos2017}, parsed by player proximity. The whole network is made up of up to 30 nodes (28 players and 2 football goals) of which only a maximum of 24 are present on the pitch at any given moment (11 players from each team and 2 goals). These nodes are clustered into a variable number of simplices, 10 times a second based on the location data. The method used for clustering guarantees that a node and its closest node belong to the same simplex. This implies that the smallest simplex has a minimum of 2 nodes, i.e., there are no isolated nodes. Although there maybe occasions where a player is side-lined, this will be an exception, as the expectation at the top-level of sports performance is that every single player have an active role in-play, in relation to their teammates and their opponents. Although the football goals are obviously fixed on the pitch, there is no fixed frame of reference for the clustering process, and the relation between players and football goals, especially with the goal keeper, are of particular importance, which justifies their inclusion.
On average, considering a match, including extra time, we observed and measured the network $\approx$ 60,000 times. Each of these 60,000 samples is a clustering of the network.
The measure used, $\mathit{VI}$, is a function that takes two clusterings as parameters and returns the information distance between the clusterings. $\mathit{VI}$ is computed as:
\begin{equation}
\label{eq:3}
VI(X;Y) = - \sum_{i=1}^k\sum_{j=1}^lr_{ij}[\log_2(\frac{r_{ij}}{p_i})+\log_2(\frac{r_{ij}}{q_j})]
\end{equation}
where $X=\{x_1,\cdots, x_k\}$ and $Y=\{y_1,\cdots, y_l\}$ are clusterings of a given set $S$, with $n=\vert S \vert$, $k=\vert X \vert$, $l=\vert Y \vert$, $r_{ij}=\frac{\vert x_i \cap y_j \vert}{n}$, $p_i=\frac{\vert x_i \vert}{n}$ and $q_j=\frac{\vert y_i \vert}{n}$. From this equation it is easy to see that when the simplices in $X$ and $Y$ are the same, the result is zero, as $r_{ij}=p_i=q_j$. This result expresses the fact that no information is gained or lost when going from one clustering to the other.
For empty intersections of pairwise simplices, $r_{ij}=0$, and although $\log(0)$ is not defined, applying l'Hopital rule we get a null contribution from these intersections to the overall $\mathit{VI}$. In summary, only pairwise non-disjoint, non-identical clusters contribute to the information distance.
$\mathit{VI}$ works as a distance metric for clusterings of the same set of nodes. In the model used to represent the soccer match, the set of nodes remains constant, except on substitutions and send-offs. However, the number of observations affected by these events are so low, that we have ignored their contribution in the model.
Using base 2 logarithms, $\mathit{VI}$ is measured in bits and describes the balance of information needed to determine one clustering from another. $\mathit{VI}$ is algorithmically simple (it can be computed in $\mathcal{O}(n + k l)$)) and, as mentioned in section \ref{introduction}, it is a true metric \cite{Kraskov2005}, respecting positivity, symmetry, and the triangle inequality.
Using the previous notation, for every individual player $p_{ij} \in \{x_i \cap y_j \}$ his contribution to the overall $\mathit{VI}$ is computed as:
\begin{equation}
\label{eq:4}
\mathit{VI}^{p_{ij}} = -r_{ij}\frac{[\log_2(\frac{r_{ij}}{p_i})+\log_2(\frac{r_{ij}}{q_j})]}{\vert x_i \cap y_j\vert}
\end{equation}
which takes the contribution of pairwise simplices $x_i, y_j$ to the overall $\mathit{VI}$, and divides it in equal parts among all players $\in x_i \cap y_j$. Note that, in the particular case of the network that we built, all nodes/players are present in all observations and are members of one and only one simplex in any one observation. Equation \ref{eq:4} registers the contributions of players involved in their simplices when these change. The only exception is the case of a send-off or substitution, in which case the player no longer contributes to the dynamics of the match.
The $\mathit{VI}$ of two clusterings ($X, Y$) of $S$ can only be zero if $\forall s \in S \mid s \in X \leftrightarrow s \in Y$. If this condition is not met then $\min(\mathit{VI}) \geq \frac{2}{n^*}$ \cite{Meila2007}, where $n^* = \max(k, l)$ still using the same notation. In the soccer match representation proposed in this article the number of nodes is fixed at 24 (barring any red cards), and thus, $n^*=12$ and $\min(\mathit{VI})=\frac{1}{12}$ every time there are any clustering changes. This is also $\min(\mathit{VI_f})$ under those conditions. $\mathit{VI}$ depends on the level of fragmentation on the pitch across observations, which intuitively reflects the situation of players jostling for position, but cannot exceed $\log_2(n)$ \cite{Meila2007}. These extreme values of $\mathit{VI}$ are, however, just boundaries that limit minima and maxima given any set of clusterings. In the present case, we have a minimum of 2 nodes per cluster, which implies a maximum of 12 clusters, resulting in $\max(\mathit{VI})=\log_2(12)=3.585$, which is attained when a clustering with a single cluster splits into 12 clusters with two nodes each, or vice-versa. In practice, the maximum VI registered is substantially lower with typical observed values of $\max{\mathit{VI}} \approx 1.2$, corresponding to the maximum distance between clusterings with $0.1s$ separation, or $\mathit{\dot{VI}} \approx 12$ bps $(\mathit{bits\cdot s^{-1}})$.
As mentioned previously, the data used for this article were captured 10 times a second. A significant amount of sparsity, i.e. a large amount of transitions without clustering changes, is observed at this frequency. This posits the question of the ideal sampling rate \cite{Moura2013}, given the dynamics of a soccer game, the capturing technology and the clustering methodology. The observed sparsity lead us to adopt a set of measures in the results section ahead, to enhance analysis and observability. These included:
\begin{itemize}
\item the usage of differentials and measuring change in bps, denoted as $\mathit{\dot{VI}}$;
\item the use of rolling averages for visualization and compatibility with the rate of change and play of a soccer match. Results shown use 4s sample windows, except when noted;
\item and, finally, we made use of cubic Hermite splines \cite{Neuman1978} to envelope $\mathit{\dot{VI}}$ maxima. Results use an inter pivot distance that dynamically varies up to a maximum of 80s depending on the position of the observed value in the probability density function of $\mathit{\dot{VI}}$ (figure \ref{fig:0}).
\end{itemize}
\begin{figure*}[!ht]
\centering
\includegraphics[scale=0.90, trim= 4 4 4 4]{PdfCdf.png}
\caption{Probability Density Function ($f(\dot{\mathit{VI}})$) and Cumulative Distribution Function ($F(\dot{\mathit{VI}})$) for all nine matches measured on a 4s moving average window. Games color coded. There is a consistency of patterns that likely mirrors energy expenditure and management throughout the game \cite{Osgnach2010}.}
\label{fig:0}
\end{figure*}
\section{Findings}
\label{results}
Given that the space of all clusterings is substantial, corresponding to a lattice of over $4.4\times 10^{17}$ points (Bell number $B_{24}$), the amount of unique clusterings we can observe is just a small fraction of this space, gated by the total of samples collected (average $58283$, $\sigma=1336$). Assuming a random distribution, the probability of observing the same clustering, that is the same sets of simplices, is for all purposes nil when considering the space size. Obviously the real distribution is not random and is heavily condition by its prior state. But, when excluding consecutive observations, a significant level of clustering re-appearances still emerges (average $6.4\%$, $\sigma=0.5\%$), which, intuitively, can be interpreted as the influence of strategic design over match playing patterns \cite{Ramos2020}.
Having analyzed nine soccer matches of the 2010-11 season of the English premier league at 10Hz, on a 40 sample moving average window (4s), we found that the average $\mathit{\dot{VI}}$ and the standard deviation for the whole match is consistent across matches, with a total average of $0.597$ bps, $\sigma=0.0369$. Considering that a typical player spends on average over half of his time standing or walking and only sprints ($ > 8.3 ms^{-1}$) 1.4\% of the time \cite{Ferro2014}, 10Hz is a sampling frequency that often generates no clustering changes in consecutive samples. In fact, in almost 80\% of the network observations clusterings do not change.
The standard deviation per match has an average $\mathit{\dot{VI}}$ of 1.30 bps, with a maximum of 1.37 and a minimum of 1.25 bps across all nine matches. A full report for all matches can be found in table \ref{tab:table3}.
The dispersion of $\mathit{\dot{VI}}$ as measured by the coefficient of variation of all match observations averages $218\%$, reflection of the high activity level of the soccer game.
We found no correlation between the time ordered sets of $\mathit{VI}$ observations between the matches we have analysed. However, a similar $\mathit{\dot{VI}}$ average and dispersion is observed across matches. The probability density functions for all nine matches, which can be seen in figure \ref{fig:0}, are strikingly similar. There is a clear consistency of dynamics as measured by $\mathit{\dot{VI}}$, in which matches exhibit similar probabilities of finding given levels of dynamics. An explanation is player's regulation of exertion during the match to manage fatigue, particularly at the high intensity professional matches are played \cite{Sarmento2018}.
\begin{figure*}[hbtp]
\centering
\includegraphics[scale=0.83, trim= 4 4 4 4]{LinReg.png}
\caption{Linear Regression of $\mathit{\dot{VI}}$ for all nine matches. Games color coded. Only one match (purple line) has an average positive gradient.}
\label{fig:1}
\end{figure*}
In 8 out of the 9 matches we examined, we observe a descending slope when the time ordered $\mathit{\dot{VI}}$ set is linearly regressed as seen in figure \ref{fig:1} ($p=0.0012$, $H_0:$ normal null average distribution, single tailed). It is not a very pronounced slope. Two interpretations for this observation are increased fatigue as the matches progresses on one hand, and adjusted tactics as a result of increased acquaintance with competitor behavior on the other. Similar observations have been previously reported \cite{Rampinini2009}. However, it is important to note that the same team plays in every match. A larger sample of matches, from a wider population, may offer more consistency to this pattern.
At a sampling rate of 10Hz, $\mathit{VI_f}$ is the major contributor to the total $\mathit{VI}$. Typically $\frac{\mathit{VI_f}}{\mathit{VI_c}}\approx 5$. However, decreasing the sampling rate has a dramatic effect on this ratio. For example, sampling every second changes that ratio to $\frac{\mathit{VI_f}}{\mathit{VI_c}}\approx 1.7$.
This could intuitively be expected. Formations and clusterings take time to evolve, but the former has a much more restricted space. The number of possible formations is given by the integer partition function, which is $P_{24}=1575$ reducing to $320$ when considering that formations with isolated players are not allowed, while the space of clusterings, as referred above, is given by the Bell number $B_{24} \approx 4.4\times 10^{17}$, that only reduces to $\approx 4.0 \times 10^{16}$ when excluding clusterings with singleton clusters. In practice we observed an average of $11070, \sigma=678$ unique clusterings, but only an average of $193, \sigma=29$ of full formations per match (i.e. with 22 players on the pitch, red cards impact these results as it reduces the number of players, preventing clusterings from reappearing).
Although $\mathit{VI_f}$ far outweighs $\mathit{VI_c}$ in its contribution to the information distance, the difference in maximum scores is much less dramatic, which points to less frequent contributions but equally impactful at certain moments of game play.
\begin{figure*}[!hbtp]
\centering
\subfloat[][4s moving average window]{
\includegraphics[scale=0.40]{VifVic1.png}
\label{sfig:21}}
\subfloat[][No rolling average]{
\includegraphics[scale=0.4]{VifVic2.png}
\label{sfig:22}}
\caption{On a moving average with sample window of $4s$, $\dot{\mathit{VI}}_{f}$ has a $\approx 5$ times heavier influence on total $\dot{\mathit{VI}}$ than $\dot{\mathit{VI}}_{c}$ when sampled at 10Hz (\ref{sfig:21}). However, when looking at individual sample maxima, that difference almost disappears (\ref{sfig:22}). If we equate $\dot{\mathit{VI}}$ to energy expenditure, we can interpret this is due to energy management by the individual players, being judicious about their marking and unmarking efforts.}
\label{fig:2}
\end{figure*}
This can be seen when comparing the envelope splines for the same match with and without a moving average ($4s$) at $80s$ pivot separation (see figure \ref{fig:2}). This trend can also be seen on the average of the coefficient of variation for $\dot{\mathit{VI}}_{c}$ and $\dot{\mathit{VI}}_{f}$, respectively $547\%$ and $227\%$.
The impact of the sampling rate is sizable and further exploration of the significance of $\mathit{VI_f}$ and $\mathit{VI_c}$ in the context of a soccer match warrants a deeper analysis of the interaction of the sampling rate, the game dynamics and the resulting $\mathit{VI}$.
To validate $\mathit{VI}$ as an indicator of game dynamics, we searched for correlations between known moments of intensive player repositioning and peaks in the information distance. To identify those moments in our datasets we made use of publicly available match commentary, as visual information was not available to us
\begin{figure}[!h]
\begin{center}
\includegraphics[scale=0.50, trim={0, 0.2cm, 0, 0.5cm}]{CornerVI.png}
\end{center}
\caption{Conditional probability of having a peak ($\mathit{\ddot{VI}}=0$) if a corner is taken $P(peak\vert corner)$, with peaks taken from the cubic hermit spline using the inter-pivot distance to control the number of peaks obtained. Analysis performed with $\approx 24 ([23..26])$ peaks per match. Increasing the number of peaks, increases $P(peak \cap corner)$, but $P(peak)$ as well.}
\label{fig:6}
\end{figure}
for most matches. The time accuracy of these commentaries is restricted to a resolution of 60 seconds, leading to a potential error of $\pm 300$ observations, discounting other timing commentary errors. This mismatch between commentary and sampling resolution was addressed as described ahead.
We collected timed tags for goals, redcards, corners and substitutions among others. Out of these, only corners are intuitively associated with quick player re-positioning, which justifies their selection for analysis. It should be noted that there is no special reason to select corners except for the observation that if $\mathit{VI}$, as used in this article, is a good measure for game dynamics, then we should expect peaks when corners are taken, and their time correlation useful for validation of the hypothesis that $\mathit{VI}$ is a good proxy for playing dynamics. In the 9 matches, we observed an average of $10$ corners per match $\sigma=2.5$.
To evaluate the performance of $\dot{\mathit{VI}}$ as a measure of game dynamics, knowing that corners should rate as moments of highly changeable player positioning, we computed the conditional probability $P(peak\mid corner)$ of observing
a peak every time a corner is taken.
As match commentary resolution is 1 minute, $P(peak \cap corner)$ was measured at the real peak $\pm 30s$. This is contrasted to the probability of finding a random peak under the same conditions, see figure \ref{fig:6}.
This analysis is done per match, as this probability is dependent on the number of peaks observed in the match and their time distribution. At $\pm 30s$ overlaps can occur, as successive corners are not infrequent. Peaks were collected from the Hermite splines, with inter pivot distance adjusted to generate $\approx 20$ peaks. With one minute resolution this still covers, assuming no peak overlaps, a little over 20\% of the whole match, which is confirmed by the results obtained for the probability of finding a peak at random.
Using total $\mathit{VI}$, we were able to recognize 72.4\% of all corners. These results shore up the compelling observations recovered from the match $\dot{\mathit{VI}}$ graphs.
$\mathit{VI}$, as used in this study, is clearly a proxy for game dynamics, understood as a rapid pace of
inter-players relative displacement, i.e. without a fixed frame of reference. This is notably obvious during set pieces. Corners and free kicks invariably generate a spike in $\mathit{VI}$, especially supported by $\mathit{VI_f}$, which could indicate the execution of set routines. Conversely, other events, like substitutions or send-offs, generate pauses that are captured by a drop in $\mathit{VI}$.
Examples can be seen in figures \ref{fig:3}, where $\mathit{VI}$ is plotted for a whole match, with vertical bars indicating the type and time of events.
To analyse player contribution to the overall $\mathit{VI}$, we apply equation \ref{eq:4}. We consider the player individual $\mathit{\dot{VI}}$, and his overall activity compared to the average $\mathit{\dot{VI}}$ per player. This may be useful to assess his activity during the match (figure \ref{fig:8}).
\begin{figure*}
\centering
\subfloat[][Match 1, 0-0]{
\includegraphics[scale=0.12]{TypGame1.png}
\label{sfig:31}}
\\
\subfloat[][Match 2, 2-2]{
\includegraphics[scale=0.12]{TypGame2.png}
\label{sfig:32}}
\\
\subfloat{
\includegraphics[scale=0.8]{Legendv2.png}}
\caption{Plots for two matches where orange and purple points are, respectively, observations of $\dot{\mathit{VI}}_{f}$ and $\dot{\mathit{VI}}_{c}$ at each sample transition, and the colored lines the respective peak envelope. $\dot{\mathit{VI}}_{f}$ and $\dot{\mathit{VI}}_{c}$ seem to be heavily correlated with match events, such as corners, where a high level of player repositioning is expected, and player substitutions, usually associated with a trough in $\dot{\mathit{VI}}$. It is also visible at minute 92 in \ref{sfig:31} that the match virtually "stopped" during the send-off of two players from opposing teams.}
\label{fig:3}
\end{figure*}
\begin{figure*}[h]
\centering
\includegraphics[scale=0.10]{player22b.png}
\caption{$\mathit{\dot{VI}}$ for a single player, in a single match, with maxima envelope. His total $\mathit{\dot{VI}}$ is compared against the match average for the whole match on the red bar on right hand side of this plot. In this case, a center forward player is represented, showing a lower than average $\mathit{\dot{VI}}$, which may be expected, because a forward is typically less active than the other players during his team defensive sub-phases of the match.}
\label{fig:8}
\end{figure*}
We also introduce the concept of a simplex transition, a tuple of simplices $(c_i^{t}, c_j^{t+\delta})$ such that $(c_i^t \cap c_j^{t+\delta} \neq \varnothing) \land (c_i^t \neq c_j^{t+\delta})$, that, at successive observations, involves always the same players.
\begin{figure*}
\centering
\includegraphics[scale=0.10]{vi_22.png}
\caption{This chart shows the top ten simplex transitions player 22 of match 1 (figure \ref{sfig:31}) was involved in, as well as their formation. His contribution to the match $\mathit{VI}$ resulting from participating in these simplex transitions, is proportionally encoded in the area of the circle: larger circle signifies higher contributions. Each formation is coded in color and shade, with green and blue representing, respectively, home and visitor players, and the number of shades the number of participating players in the simplex. Each tick signals a transition and the match moment when it occurred, with a full match taking a full circle. The lower and upper semicircles describe, respectively, the formation of the prior (source) and immediately subsequent (destination) simplices, where the player was involved. Finally, simplices are identified by the participating players' numbers, with home players first, followed by visitors.
Player 22 is a visiting forward, and as seen in the picture, is frequently observed alone (the single shade of blue in the semi circles) in a simplex with opposing back player(s), a typical pattern. Transition from formation $3-22$ to $3,12-22$, when home player 12 joins the simplex, has the highest accumulated $\mathit{VI}$ contribution from player 22. It occurs throughout the match but with an emphasis in the first half of the first 45 min. Player 22 is supported by a teammate in only two transitions out of the 10 represented. }
\label{fig:4}
\end{figure*}
We visualize the type of transition, color coded to denote the number of home and visiting players involved. Each simplex transition plot is scaled by overall $\mathit{VI}$ contribution for that set of transitions, and details when those transitions occurred (see figure \ref{fig:9}). Plotted in reference to a single player, the major simplex transitions he was involved in build a full view of the player activity during the match. This is depicted in figure \ref{fig:4}, where the visual representation of this view is detailed. An aggregation of all simplex transition charts provides a full view of a complete match.
\vspace{-2.5mm}
\begin{figure*}[t]
\centering
\includegraphics[scale=0.10]{VI_allplayers.png}
\caption{This chart uses the same symbolic elements as figure \ref{fig:4} but operates at a different level. Each circle represents the overall contribution to the match $\mathit{VI}$ of a whole transition and not just the player's contribution. Here we represent a match top ten transitions. The encoded information in this and in figure \ref{fig:4} can be useful to study and train high frequency transitions that contribute significantly to playing dynamics.}
\label{fig:9}
\end{figure*}
\section{Discussion}
\label{discussion}
In this section we discuss the relevance, principles, relationships and generalizations that can be derived from the results presented above. We cover eight major findings informed by expertise about the soccer game.
\subsection{Information distance time series}
$\mathit{\dot{VI}}$ is highly variable throughout a match. Even with a 4 second moving average sample we found an average $\mathit{\dot{VI}}$ coefficient of variation of $\approx 218\%$ across all nine games.
As expected we found no significant correlation among $\mathit{\dot{VI}}$ time series across matches, as every match is different.
Although these findings confirm empirical expectations from a typical soccer match, it is compounding evidence that $\mathit{\dot{VI}}$ reflects the game dynamics.
\subsection{Information distance variability}
When comparing different matches, we found consistent $\mathit{\dot{VI}}$ averages, with a coefficient of variation of the averages of $\approx 5\%$. The probability density function of a match $\mathit{\dot{VI}}$ measurements is highly consistent across matches as seen on figure \ref{fig:0}. We did not find matches where $\mathit{\dot{VI}}$ is consistently high or consistently low. All matches come from the official English premier league games, usually played at a similar competitive level, so these results are not surprising, if $\mathit{\dot{VI}}$ is indeed a proxy for game dynamics.
\subsection{Information distance match trend}
We observe a general decreasing trend in $\mathit{\dot{VI}}$ as the matches progress. When linearly regressed eight out of nine games exhibit this trend. Player fatigue and inter-team tactical adjustments may be a determining factor, although the evolving match score and significance in the context of each teams general endeavors, may play a role as well.
\subsection{Information distance and event correlation}
There is evidence that the peaks and troughs observed in the values of $\mathit{\dot{VI}}$ correlate with known events, such as corners, free kicks or substitutions that similarly affect the game dynamics.
\subsection{Match sampling frequency}
Sampling at 10Hz generate $\approx 80\%$ of null $\mathit{\dot{VI}}$ measurements. A lower sampling rate may produce similar outcomes, resulting in a more efficient data capture and computing process. However, not all events develop in the same time scale, and further analysis would be required to fine tune the sampling rate to the specific analysis sought.
\subsection{Meso-patterns distribution}
We found that clusterings reappear throughout the matches with a probability ($0.064, \sigma = 0.005\%$) much higher than what would be expected by chance ($1.46^{-12}$). This can be interpreted as player dynamic placement on the pitch according to a game plan design.
\subsection{$\mathit{\dot{VI}}$ components}
We found that, at 10Hz, average $\dot{\mathit{VI}}_{f}$ is the main driver of total $\mathit{\dot{VI}}$, meaning that when clusterings change, players end up in the clusters that frequently minimize the information distance. However if we inspect the maxima of these two components, we find that player repositioning within the clustering, i.e. $\dot{\mathit{VI}}_{c}$, sometimes contribute as much as $\dot{\mathit{VI}}_{f}$ to total $\mathit{\dot{VI}}$. An hypothesis to justify this observation is that players are judicious with their energy expenditure, while individual initiative can heavily impact game dynamics.
\subsection{Multi-layer analysis}
The proposed way of measuring the soccer game enables a multi-layer decomposition of its dynamics from macro level (a full match) to meso (clusters of players, transitions and teams), to micro (individual players), as exemplified by the information presented, respectively, in figures \ref{fig:3}, \ref{fig:9}, and \ref{fig:8}. This enriches the information that can be extracted, helpful to evaluate the dynamics generated by individual players, but also cluster changes experienced during a clustering transition, which can be helpful to understand which sets of players are more prevalent, how they change and how they impact the overall $\mathit{\dot{VI}}$.
\section{Final Remarks}
\label{conclusion}
The presented results endorse the status of $\mathit{\dot{VI}}$ as a measure for game dynamics. The fact that it captures with accuracy and precision well known moments of players jostling for position, such as when corners are taken, supports this interpretation.
With error free and detailed metadata, a more accurate analysis would be possible, especially with concurrent visualization and representation. The present work is based on prior data, captured and clustered independently, that abstract the reality of a soccer match. Based on the promise shown here by the variation of information as an analysis tool, the proposed methods could be valuable to evaluate different approaches to data capture, such as sampling rates, as well as different clustering methods and game representations, such as overlapping, distance weighted networks, non-inertial frames of reference that accommodate ancillary factors, centroid based clustering, among many others.
Although the soccer game was the subject matter of this article, we believe the principles and approaches used extend to other socio-biological systems with structural competing interactions, of which those found in competitive team sports are an example.
This is left for future research.
\section*{Appendix}
\label{appendix}
To illustrate how $\dot{\mathit{VI}}$ is computed, consider the two moments in a fictional match represented in figure \ref{fig:7}.
\begin{figure*}[!h]
\centering
\subfloat[][Clustering at time t]{
\includegraphics[scale=0.45]{Toy1.png}
\label{sfig:71}}
\\
\subfloat[][Clustering at time t+0.9s]{
\includegraphics[scale=0.45]{Toy2.png}
\label{sfig:72}}
\\
\caption{Clustering for two moments of a fictional match separated by 900ms. Cluster 1 (goal and goalkeeper of the red team) and Cluster 9 (goal and goalkeeper of the yellow team), are not visible. The clustering process ensures that a node and its closest neighbor are nodes of the same simplex. Home players are numbered in red circles, visitors in yellow. Blue hexagons identify the simplices. White lines are only used to identify simplex membership. Formation for (a) is $\{2^4,3^4,4\}$ and for (b) is $\{2^6,3,4,5\}$, which correspond to the row and column sums of the matrix in table \ref{tab:table1}.}
\label{fig:7}
\end{figure*}
The corresponding confusion matrix, which describes the transition of nodes between simplices when going from moment t to t+0.9s during the match, is given in table \ref{tab:table1}.
\begin{table*}[!h]
\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|}
\midrule
\multicolumn{1}{|l|}{\textbf{Simplex}} & \textbf{1} & \textbf{2} & \textbf{10} & \textbf{11} & \textbf{12} & \textbf{13} & \textbf{14} & \textbf{15} & \textbf{9} \\
\midrule
\rowcolor[rgb]{ .851, .882, .949} 1 & 2 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
\midrule
2 & 0 & 2 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
\midrule
\rowcolor[rgb]{ .851, .882, .949} 3 & 0 & 0 & 3 & 0 & 0 & 0 & 0 & 0 & 0 \\
\midrule
4 & 0 & 0 & 2 & 0 & 0 & 0 & 0 & 0 & 0 \\
\midrule
\rowcolor[rgb]{ .851, .882, .949} 5 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 3 & 0 \\
\midrule
6 & 0 & 0 & 0 & 2 & 1 & 0 & 0 & 0 & 0 \\
\midrule
\rowcolor[rgb]{ .851, .882, .949} 7 & 0 & 0 & 0 & 0 & 1 & 2 & 0 & 0 & 0 \\
\midrule
8 & 0 & 0 & 0 & 0 & 0 & 0 & 3 & 1 & 0 \\
\midrule
\rowcolor[rgb]{ .851, .882, .949} 9 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 2 \\
\bottomrule
\end{tabular}%
\caption{Confusion matrix going from t to t+0.9s}
\label{tab:table1}%
\end{table*}%
Null matrix elements, as well as unchanged simplices (simplices 1, 2 and 9), do not contribute to informational distance. The contribution of the others is computed according to equation \ref{eq:4}. The result is shown in table \ref{tab:table2}, where the contribution from each simplex transition can be seen.
\begin{table*}[!h]
\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|}
\midrule
\multicolumn{1}{|l|}{\textbf{Simplex}} & \textbf{1} & \textbf{2} & \textbf{10} & \textbf{11} & \textbf{12} & \textbf{13} & \textbf{14} & \textbf{15} & \textbf{9} \\
\midrule
\rowcolor[rgb]{ .851, .882, .949} 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
\midrule
2 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
\midrule
\rowcolor[rgb]{ .851, .882, .949} 3 & 0 & 0 & 0.092121 & 0 & 0 & 0 & 0 & 0 & 0 \\
\midrule
4 & 0 & 0 & 0.110161 & 0 & 0 & 0 & 0 & 0 & 0 \\
\midrule
\rowcolor[rgb]{ .851, .882, .949} 5 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0.05188 & 0 \\
\midrule
6 & 0 & 0 & 0 & 0.048747 & 0.107707 & 0 & 0 & 0 & 0 \\
\midrule
\rowcolor[rgb]{ .851, .882, .949} 7 & 0 & 0 & 0 & 0 & 0.107707 & 0.048747 & 0 & 0 & 0 \\
\midrule
8 & 0 & 0 & 0 & 0 & 0 & 0 & 0.05188 & 0.166667 & 0 \\
\midrule
\rowcolor[rgb]{ .851, .882, .949} 9 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
\bottomrule
\end{tabular}%
\caption{Computing $\mathit{VI}$}
\label{tab:table2}%
\end{table*}%
The end result is $\mathit{VI}=0.785615$ or, given that we are measuring a 0.9s interval, $\dot{\mathit{VI}}=\frac{0.785615}{0.9}=0.872905$ bps.
\begin{table*}[!h]
\begin{tabular}{|c|c|r|r|r|r|r|r|r|r|r|}
\toprule
\multicolumn{2}{|c|}{Match} & \multicolumn{1}{c|}{1} & \multicolumn{1}{c|}{2} & \multicolumn{1}{c|}{3} & \multicolumn{1}{c|}{4} & \multicolumn{1}{c|}{5} & \multicolumn{1}{c|}{6} & \multicolumn{1}{c|}{7} & \multicolumn{1}{c|}{8} & \multicolumn{1}{c|}{9} \\
\midrule
\multicolumn{2}{|c|}{Result} & \multicolumn{1}{c|}{0-0} & \multicolumn{1}{c|}{2-1} & \multicolumn{1}{c|}{2-2} & \multicolumn{1}{c|}{1-0} & \multicolumn{1}{c|}{3-0} & \multicolumn{1}{c|}{1-0} & \multicolumn{1}{c|}{0-1} & \multicolumn{1}{c|}{2-1} & \multicolumn{1}{c|}{1-0} \\
\midrule
\rowcolor[rgb]{ .851, .882, .949} & Avg & 0.544 & 0.591 & 0.631 & 0.665 & 0.622 & 0.573 & 0.568 & 0.599 & 0.581 \\
\rowcolor[rgb]{ .851, .882, .949} & $\sigma$ & 1.255 & 1.278 & 1.346 & 1.369 & 1.330 & 1.276 & 1.273 & 1.292 & 1.282 \\
\rowcolor[rgb]{ .851, .882, .949}\multirow{-2}[2]{*}{$\dot{\mathit{VI}}_t$} & a & -4.6E-4 & -6.0E-4 & -2.9E-4 & -9.9E-4 & 1.4E-4 & -1.2E-3 & -8.7E-4 & -1.3E-3 & -4.7E-4 \\
\midrule
\multirow{3}[2]{*}{$\dot{\mathit{VI}}_h$} & Avg & 0.277 & 0.290 & 0.329 & 0.330 & 0.314 & 0.284 & 0.301 & 0.302 & 0.292 \\
& $\sigma$ & 0.702 & 0.691 & 0.774 & 0.756 & 0.746 & 0.696 & 0.739 & 0.717 & 0.711 \\
& a & -6.2E-5 & -4.2E-4 & 2.4E-4 & -3.6E-4 & -9.4E-5 & -6.2E-4 & 4.4E-4 & -6.3E-4 & -2.9E-4 \\
\midrule
\rowcolor[rgb]{ .851, .882, .949} & Avg & 0.267 & 0.301 & 0.303 & 0.335 & 0.308 & 0.289 & 0.267 & 0.301 & 0.289 \\
\rowcolor[rgb]{ .851, .882, .949} & $\sigma$ & 0.677 & 0.715 & 0.718 & 0.769 & 0.734 & 0.712 & 0.673 & 0.719 & 0.709 \\
\rowcolor[rgb]{ .851, .882, .949} \multirow{-2}[2]{*}{$\dot{\mathit{VI}}_v$} & a & -4.0E-4 & -1.8E-4 & -5.3E-4 & -6.2E-4 & 2.4E-4 & -6.2E-4 & -1.3E-3 & -6.6E-4 & -1.8E-4 \\
\midrule
\multirow{3}[2]{*}{$\dot{\mathit{VI}}_c$} & Avg & 0.083 & 0.102 & 0.102 & 0.112 & 0.105 & 0.095 & 0.095 & 0.104 & 0.097 \\
& $\sigma$ & 0.496 & 0.542 & 0.559 & 0.582 & 0.561 & 0.529 & 0.531 & 0.550 & 0.539 \\
& a & -1.5E-6 & -2.5E-4 & -1.7E-4 & -3.4E-4 & -1.3E-4 & -1.7E-4 & -3.2E-4 & -2.3E-4 & -2.8E-5 \\
\midrule
\rowcolor[rgb]{ .851, .882, .949} & Avg & 0.461 & 0.489 & 0.529 & 0.553 & 0.518 & 0.477 & 0.473 & 0.495 & 0.483 \\
\rowcolor[rgb]{ .851, .882, .949} & $\sigma$ & 1.100 & 1.110 & 1.173 & 1.181 & 1.154 & 1.110 & 1.113 & 1.116 & 1.113 \\
\rowcolor[rgb]{ .851, .882, .949} \multirow{-2}[2]{*}{$\dot{\mathit{VI}}_f$} & a & -4.6E-4 & -3.5E-4 & -1.2E-4 & -6.5E-4 & 2.6E-4 & -1.1E-3 & -5.4E-4 & -1.1E-3 & -4.5E-4 \\
\bottomrule
\end{tabular}%
\caption{Average (avg), standard deviation ($\sigma$), and linear regression slope (a) for $\dot{\mathit{VI}}$ results (Total, Home, Visitor, Compositional and Formation) for the nine matches used in this article}
\label{tab:table3}%
\end{table*}%
\newpage
\section*{Declarations}
\subsection*{Funding}
\begin{samepage}
This project was partly supported by Fundação para a Ciência e Tecnologia through project UID/ Multi/ 04466/ 2019.
R. J. Lopes was partly supported by the Fundação para
a Ciência e Tecnologia, under Grant UID/50008/2020 to Instituto
de Telecomunicações.
D. Araújo was partly funded by Fundação para a Ciência e Tecnologia, grant number UIDB/00447/2020 attributed to CIPER – Centro Interdisciplinar para o Estudo da Performance Humana (unit 447).
\end{samepage}
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La Haie-Traversaine ist eine französische Gemeinde mit Einwohnern (Stand: ) im Département Mayenne in der Region Pays de la Loire; sie gehört zum Arrondissement Mayenne und zum Kanton Lassay-les-Châteaux. Die Einwohner werden Traversainois genannt.
Geographie
La Haie-Traversaine liegt etwa 35 Kilometer nordnordöstlich des Stadtzentrums von Laval am Fluss Mayenne. Umgeben wird La Haie-Traversaine von den Nachbargemeinden Ambrières-les-Vallées im Norden, Saint-Loup-du-Gast im Nordosten, Saint-Fraimbault-de-Prières im Osten und Südosten, Mayenne im Süden, Parigné-sur-Braye im Südwesten sowie Oisseau im Westen.
Bevölkerungsentwicklung
Sehenswürdigkeiten
Kirche Saint-Pierre aus dem 15. Jahrhundert
Kapelle Notre-Dame-de-la-Vallée aus dem 19. Jahrhundert
Schloss Lozé aus dem 18. Jahrhundert
Schloss Le Pont aus dem 18. Jahrhundert
Literatur
Le Patrimoine des Communes de la Mayenne. Flohic Editions, Band 1, Paris 2002, ISBN 2-84234-135-X, S. 56–58.
Weblinks
Ort in Pays de la Loire
Gemeindegründung 1864
Ort an der Mayenne
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I'm A Celebrity fans convinced Shane Richie is keen for EastEnders comeback
I'm A Celebrity viewers reckon Shane Richie is looking to return to EastEnders as Walford legend Alfie Moon.
Tonight, fans were left giggling as Shane taught Mo to become Phil Mitchell - though it was less Walford hardman, more 'Mill Phitchel'.
But eyebrows were also raised as it became the nth time that Shane had slipped back into his alter ego.
Fans took to Twitter to comment, with one writing: "Shane mentions Eastenders everyday. #imaceleb."
(Image: ITV)
While another commented: "As soon as Shane starts talking Eastenders I shut off YOU'RE NOT EVEN IN IT ANYMORE!! #ImACeleb."
A third fumed: "Oh Shane, you're not on EastEnders anymore, f***ing get over it."
Shane first appeared in EastEnders back in 2002 and has appeared on-and-off in the BBC soap for 17 years.
He first left Walford back in 2005 on Christmas Day and returned five years later after wife Kat's return.
Shane then left again in 2016 before briefly returning in May 2018 after Kat's cousin Hayley revealed that she was carrying his baby.
However, Alfie was last seen in 2019 after staging his own death in a bid to get out of his troubling debt.
He had scammed Phil out of £50,000 before leaving Walford and hasn't been seen since.
With Kat's boyfriend Kush's departure imminent, is there room for Alfie to return to the Square?
*I'm A Celebrity airs tomorrow night at 9pm on ITV
Source https://www.mirror.co.uk/tv/tv-news/im-celebrity-fans-convinced-shane-23113126
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Die Malier () waren ein altgriechischer Volksstamm, der in der Mündungsebene des Spercheios in Mittelgriechenland lebte.
Topographie
Das Siedlungsgebiet der Malier erstreckte sich über das Kallidromos-Gebirge, grenzte im Osten an die Thermopylen und wurde im Norden von dem nach ihnen benannten Malischen Golf (Maliakos Kolpos) begrenzt. Im westlichen Spercheiostal grenzte ihr Gebiet an das der Ainianen, die Thermopylen verbanden sie mit Lokrien. Hauptort der Malier war Trachis bei den Trachinischen Felsen.
Geschichte
426 v. Chr. wandten sich die Malier im Krieg gegen die Oitaier um Hilfe an Sparta. Die Spartaner gründeten dann Herakleia Trachis in der Nähe von Trachis. In den folgenden Jahrzehnten waren die Malier vollkommen von Sparta abhängig, bis sie sich im Korinthischen Krieg gegen die Spartaner erhoben. In diesem Krieg verloren sie das Gebiet südlich des Spercheios, Herakleia Trachis fiel an die Oitaier, und die neue Hauptstadt der Malier wurde Lamia weiter im Nordwesten, deren Namen sich wahrscheinlich von Malis ableitete.
Gemeinsam mit den Oitaiern und Ainianen waren die Malier Mitglieder des Korinthischen Bundes und ab ca. 235 v. Chr. gehörten sie zum Aitolischen Bund. 189 v. Chr. wurden sie an Achaia Phthiotis angeschlossen und galten seitdem als Thessalier.
Kult
In der Stadt Anthele auf dem Gebiet der Malier befand sich ein bedeutendes Demeterheiligtum, frühestes Zentrum der pylaiisch-delphischen Amphiktyonie, der auch die Malier angehörten.
Literatur
Historische Ethnie in Griechenland
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_To my family, this book is for you,
Diana, Ralph, Chris, Heidi, and Katherine.
Thank you for encouraging me to chase my dreams,
guiding me spiritually, showing me how to be
of service in the world, and teaching me grace,
patience, and most of all, love._
**CONTENTS**
**PREFACE**
**INTRODUCTION: WHAT DOES IT TAKE TO BE GREAT?**
**CHAPTER 1:** **CREATE A VISION**
**CHAPTER 2:** **TURN ADVERSITY INTO ADVANTAGE**
**CHAPTER 3:** **CULTIVATE A CHAMPION'S MINDSET**
**CHAPTER 4:** **DEVELOP HUSTLE**
**CHAPTER 5:** **MASTER YOUR BODY**
**CHAPTER 6:** **PRACTICE POSITIVE HABITS**
**CHAPTER 7:** **BUILD A WINNING TEAM**
**CHAPTER 8:** **LIVE A LIFE OF SERVICE**
**CONCLUSION**
**ACKNOWLEDGMENTS**
**PREFACE**
_You were born with potential._
_You were born with goodness and trust. You were born with ideals and dreams. You were born with greatness._
_You were born with wings._
_You are not meant for crawling, so don't._
_You have wings._
_Learn to use them and fly._
**—Rumi**
For the last few years, I've felt like the luckiest guy on earth. Every week, my job has been to study at an elite and exclusive—but entirely unofficial—university, a mythical academy where the world's greatest men and women teach, lecture, and pay forward the amazing knowledge they've accumulated on their paths to becoming the best in the world at what they do.
My professors were Olympic gold medalists, award-winning musicians, _New York Times_ best-selling authors, world-changing activists and philanthropists, enormously successful entrepreneurs, and inspiring experts and thinkers. I was fortunate enough to be their student, audit their classes, and learn things from each of them that I will carry with me forever. I consider this education the greatest gift I've ever been given.
Deep down, all of us suspect—we _hope_ —something like this exists somewhere, but we just have no idea where it is or how to get in. Our world is swimming in information and data, unlike at any other point in human history, and for years that has been intoxicating to many of us. We could type anything into the Google search bar and we'd have a million answers in a millionth of a second. We could pick a topic and go down the Wikipedia rabbit hole for hours, if not days. But eventually, information for curiosity's sake wasn't enough. We needed more. We wanted to know how to apply it to the world and to our lives. We wanted knowledge and wisdom, not just 1s and 0s _._ We think that places like the World Economic Forum in Davos are maybe where we can find it. Or Summit Series. Or TED. I've been to a few of those forums and events, and frankly, they're not even close to what I've experienced over these last few years.
The place I am talking about is more like Plato's cave than the red circle on the TED stage. My amazing mentors did not speak to me for 18 minutes and then disappear into the ether; they sat across from me, literally and virtually, and brought me out from the shadows into the light of real knowledge. How did this happen? I'm still not entirely sure, but there is one thing I know beyond any doubt: They fired my passion to sit across from you, through the pages of this book, and share their teachings with you.
I've come to call this place the School of Greatness.
It's not your stereotypical school. There are no classrooms. No homework. No principal or dean enforcing rules or even tracking attendance. Nobody pays tuition (except maybe the price of this book). Some of the "professors" would recoil at being called that. And when we leave to try our hands at the real world once again, there will definitely be no graduation ceremony and certainly no diploma.
Now to be clear, this school is great not because it admits only great students but because the teachers are and the students want to be. Both share big dreams. And as Wilma Rudolph, the Olympic champion who was once the fastest woman in the world, said, "Never underestimate the power of dreams and the influence of the human spirit. We are all the same in this notion: The potential for greatness lives within each of us."
With _The School of Greatness,_ you will learn how to recognize and harness this potential. You will come to understand the importance of dreams and the tools that exist within you to make those dreams reality. _The School of Greatness_ is not a bag of tricks and hacks. It's not a boot camp. It's a way of life, a way of living. When you want to lose weight and keep it off, you don't go on a diet, because diets are about artificial restriction. They're miserable. Instead, you change your lifestyle to match your goals. This is the same thing. _The School of Greatness_ is a lifestyle for a lifetime that you are going to love.
Like the professors and students in _The School of Greatness,_ I've chased big dreams my whole life. Ever since I can remember, I wanted to be an All-American athlete. Growing up in Ohio, and then growing to be 6 foot 4, obviously meant football at the Ohio State University. That was every Ohio boy's dream. Everything I did as I grew up was aimed toward accomplishing that goal. There wasn't a day that went by that I didn't think about it and work on it—and I made it, sort of. I went to a smaller Ohio college after I transferred schools a couple of times for better (and bigger) opportunities, and I even set a number of records along the way. But it wasn't until my fourth year that I finally became an All-American athlete—in the decathlon, of all things: a sport I'd never even trained for. Never in my wildest dreams could I have imagined that happening!
As soon as being an All-American became a reality—first as a decathlete, then the next year, finally, in football—it immediately began to lose its luster, and I had no idea why. I'd accomplished all of my goals, and I went further than most people would have ever expected, but that was little consolation. At a party celebrating my achievements, the moment that should have been my greatest triumph, I was miserable. I couldn't enjoy it because my focus had already shifted to bigger and better things: turning pro. Eventually, I had a tryout in front of a dozen NFL scouts at an indoor training facility at the Ohio State University, my former dream school, along with a number of future NFL players, including an eventual Super Bowl MVP. I performed well, but coming from a smaller school, I had little chance of being drafted. An Arena Football League team—which is technically professional football—did pick me up, but 1 year is all I played as my career ended due to a series of frustrating injuries and recovery setbacks.
Suddenly, those dreams of glory and fame came crashing down to earth. It wasn't pretty. I was 24 years old, washed up, broke, and sleeping on my sister's couch with my arm in a cast and a mountain of credit card debt staring me in the face. My dreams vanished. What I was living through at that point was a nightmare—and I feared that it was something I'd never wake up from. It was the lowest low I've ever experienced.
What I realize now, only in painful hindsight, is that I wasn't chasing the specific dream of being an All-American or playing in the NFL. Those were discrete goals. I was chasing a broader dream: being great. And what was missing from my life, on that couch with a broken wrist and no money to my name, wasn't talent or ability—it was a sense of a greater purpose, a feeling that I was working and striving for something bigger than myself.
I knew I wanted to be better, and I had all this passion and energy, but I had no outlet for it. I had to do something. So I reached out to others: friends of mine, friends of my family, coaches, my siblings. A new mentor suggested I check out LinkedIn, the social media Web site, which back then in 2008 was just starting to get traction among business professionals. I saw all sorts of potential to connect with high-profile business owners and other CEOs whom I never would've encountered otherwise. I began reaching out and connecting like a madman. I reached out specifically to people who worked in the sports business because I had just come from my own athletic experiences. I had a positive message to share, and I enjoyed helping people and relished becoming what Malcolm Gladwell calls a "connector."
I eventually built this presence on LinkedIn into an incredibly lucrative speaking, advising, and teaching business. I had no background in online business, but I had good instincts and was willing to work my butt off, and as I took some advice from mentors, the money started flowing in. After an initial period of figuring it all out, my first year brought in close to $1 million in sales. By year 3, that had more than doubled. Eventually, my business partner bought me out in a deal for seven figures.
There I was, not even 30, with more money than I'd ever seen before, having turned a vision into a lucrative reality and reinvented myself as an entrepreneur in the process. With some help and some hustle, here I was again, on top of the world. It should have been another moment of triumph—I had built a business from scratch and grown it to scale—and yet the call to something larger still haunted me. I knew a piece was missing.
One of my teachers, the author and journalist Steven Kotler, would later define greatness as "waking up every day and saying 'Okay. Today I'm going to move mountains.'" That's what I wanted. That's who I wanted to be.
I started over again, this time with the notion that I would seek out something larger, since it wasn't coming to me through these stereotypical markers of success. In January 2013, I decided that I would start interviewing some of the smartest, most successful, and _greatest_ men and women in the world and ask them every question I could. I wanted to be around only those people who understood what it meant to strive for true greatness, who woke up every morning to move their respective mountains, pay it forward, and help others get to a better place. Part of my motivation was selfish—my own insatiable thirst for understanding how individuals seek and achieve this higher ground—but I also wanted to give readers and listeners access to this wisdom. What good was greatness if I couldn't share it?
The response was overwhelming. My little podcast, _The School of Greatness,_ amassed a large audience with more than five million downloads before the first 2 years and hundreds of thousands of unique visitors every month. In a world with a seemingly infinite supply of available podcasts, _The School of Greatness_ has been featured on the main page section of iTunes more than 10 times and has ranked number one on iTunes' Business and Health list.
Not only were these lessons resonating with listeners and readers but, as I was in the process of conveying them, they were also changing my life. They were the lessons I wish I had been given and understood when I was 16 years old, struggling to make sense of athletic gifts and struggling through a tense and often terrible family life. It's what I wished I could have turned to when, immediately after leaving the All-American podium, I was engulfed by depression and pain. They could have helped me make the most of my opportunity in professional sports—and they could have saved me hundreds of thousands of dollars in costly business mistakes.
Those lessons form the core of this book. The lessons in this book are not _my_ lessons; they are my lecture notes from a unique and wonderful school. I'm simply lucky enough to be the messenger. As I was writing, I learned that there is a long tradition of this kind of book. From Aristotle's _Ethics_ and Epictetus' _Discourses_ more than 2,000 years ago to a more recent book like Peter Thiel's _Zero to One,_ the great thinkers themselves didn't write those books: A student did. What survived was simply the lecture notes from an epic course we were not fortunate enough to have attended in person. Classicists have been kind enough to give author credit to the masters, and I hope you'll see that with this book, too. Although my name is on the cover, the names of my teachers should be as well. I couldn't have written this without them, and it is with the deepest gratitude that I share their wisdom.
**INTRODUCTION**
**What Does It Take to Be Great?**
_Greatness is a spiritual condition worthy to excite love, interest, and admiration; and the outward proof of possessing greatness is that we excite love, interest, and admiration._
**—Matthew Arnold**
I'm a pretty good athlete, but there are legions who are far better than I'll ever be. Olympic gymnast Shawn Johnson accomplished more in sports as a teenager than I will in my entire life. I've done very well in business, but men like Angel Martinez, CEO of the billion-dollar shoe brand Deckers, and fellow lifestyle entrepreneur and angel investor Tim Ferriss aren't looking in their rear-view mirrors for me. So I am not just talking about the kind of greatness that can be measured and assessed by a universal standard; I am talking about the greatness of exploring, reaching, and sustaining your potential—that is, the kind of individual and unique greatness that we are all capable of.
Greatness, as I've come to learn from people like Shawn, is "not just holding a gold medal at the top of a podium." It's about inspiring people, about sharing a message, about believing the truth in that cliché: It's the journey, not the destination to some perceived treasure or moment of adulation. In fact, there are a million ways to be great and a million more things to be great at. Most of them don't come with a medal or a giant check. Consider this list.
Being a parent
Being an artist
Being generous
Being a leader
Being a change maker
Being an advocate
Being healthy
Being an entrepreneur
Being of service
All of these are amazing dreams where greatness is a worthy and attainable goal. Those who have become great at any of them—irrespective of plaques on their walls or trophies on their mantels—are the people we can all learn from. In this book, we're going to learn from people who did stand on podiums—literally and figuratively—but were great at these things as well. They embodied excellence in many facets of their lives, and we can apply their approach to our own.
As Shawn put it to me, "Greatness means having pride in yourself, being happy with yourself, knowing you've worked for something and couldn't have done anything more. That is greatness itself." It is cultivating the character and habits that not only lead to success but also help you overcome any challenge or adversity. It's about lifting yourself up from the depths of despair and using mindfulness, joy, and love to harness your dreams. It is a progression through a series of lessons—eight areas of focus and continual improvement.
**1.** **Create a vision.** Most great athletes describe their ability to visualize the outcome they desire in a competition. They know what they want and where they want to go. It is as much a part of their process as any aspect of training. As the famed acting coach Lee Strasberg put it, "If we cannot see the possibility of greatness, how can we dream it?" Now, what is _your_ dream?
**2.** **Turn adversity into advantage.** It's hard to find the story of someone who has achieved greatness who did not face some sort of significant adversity. When you look more closely, you see that this adversity actually helped them—it put them on the path toward a unique and individual form of greatness. What challenges do you face and how can you use them to develop greatness?
**3.** **Cultivate a champion's mindset.** What does it take to become a champion, and how does a champion see the world that she is trying to conquer? Visualization, meditation, mindfulness, and emotional intelligence are tools that help you understand who you are and where you are at any given moment in your life and allow you to find joy and fulfillment in the moment. This is where greatness takes root. How can you view the world through the eyes of a champion?
**4.** **Develop hustle.** We all face obstacles and seem to have an impossible amount we need to get done. Many get stuck at this wall, but what separates the greats from the rest of us is that they reduce the wall to a barrier and make it into something they can climb over. It's also important to never stop hustling—even after we've accomplished a goal. Where will your hustle and energy come from?
**5.** **Master your body.** No one chooses the body they're born with, but almost everyone has the ability to build and maintain their physical assets far beyond what they imagined. It's all about thinking like a champion, training like a champion, and eating like a champion. Are you taking care of yourself?
**6.** **Practice positive habits.** How many hours _exactly_ does it take to achieve mastery and greatness? It's not about a number, but great things will happen if you practice a certain skill over and over again. Building positive habits is a necessity to achieve your desired goals. And having a deep belief in something that can support those habits, be it religion or community or family, is a key ingredient in the recipe for greatness. What positive habits can you add to your daily life?
**7.** **Build a winning team.** You can't achieve greatness alone, period. Success is a shared process. Finding the right mentor and making the best use of that mentor or coach is a requirement. So is building a team of partners, employees, supporters, and fans. Success is all about developing and cultivating healthy and fruitful relationships—not just with your peers on the field of endeavor but also with those who can truly challenge you—in all aspects of your life. Whom do you need to join forces with?
**8.** **Be of service to others.** Trophies and rings and fat bank accounts have a surprisingly short shelf life when it comes to greatness. Research has shown that the happiest and most thriving people are those who spend their time giving back, helping others, and participating actively in their communities. In fact, the best gifts are the ones you give; they make your own achievements that much more fulfilling. How are you going to contribute and help others?
This book is the distillation of the eight master lessons on greatness that I have discovered on my journey, with help from my network of mentors and coaches, colleagues and teachers. By studying greatness this way, we will learn that it is a process of continuous education and self-realization. It's something we'll follow for the rest of our lives.
If you're like some of my podcast listeners or a lot of people who read books such as this one, you are probably saying to yourself, "This all sounds well and good, but what is this book actually going to help me do?" That's a fair question. I'm not here to waste your time or make false promises.
What _The School of Greatness_ is going to teach you is, first and foremost, what is great and special about you. Most people think greatness or being great is external to themselves, that it's something you acquire or add on. That is not true. Greatness is something that is unearthed and cultivated from within. The lessons and the teachers in _The School of Greatness_ will help you find the greatness in you.
This book will then inspire you to pursue it. It'll show you how to be great—whether you're an athlete, an entrepreneur, a mom, an organizer, a freelancer, or a designer—at whatever passion you harbor deep inside. They say "seeing is believing," but sometimes even that isn't enough. Sometimes people need to be convinced. They need to be inspired to have a vision, let alone pursue it with vigor in the face of countless unseen obstacles. I was fortunate enough to have truly great men and women draw out whatever potential I have inside me, and now you and I and all the other readers are going to work to become the best we can be—together.
**GROUNDING**
Before I do pretty much anything in life, I like to have what I call a "grounding" moment. I originally experienced this process in sports. Before every game, the coach would prepare us for the battle ahead by getting our thoughts together and putting us in the right frame of mind. I call it getting grounded. This is where I commit myself to my vision, get connected to who I am, and focus on what I'm intending to create in that moment. You may already have grounding moments in your daily life and not even realize it. Whether it's meditating in the morning to get ready for the day, taking a moment of silence or saying a prayer before meals, or psyching yourself up mentally and physically before a game or a speech or a sales pitch or any of the other "big" moments we go through in life, it's extremely important to find some head space for whatever your ritual may be.
This grounding process is critical for your success in applying the lessons in this book to your life—and critical for success, period. If you don't give yourself a moment to visualize the clear results you want to create, then you are less likely to achieve what you desire. It's all about setting your intentions for what you want. Getting grounded can be one of the most powerful things you do if you apply this process to your daily life.
Each chapter will begin with my personal grounding statements to let you know what my intention is for you to get out of that chapter and to prepare you for what's to come. When my coaches would ground us before big games, it always gave me that calm confidence I needed to take on some of my most challenging competitors. I want to pass that calm confidence on to you. You have challenges and obstacles that stand in your way on a daily basis, and grounding in the morning and before any big moment is a habit that I know will support you tremendously.
_The School of Greatness,_ in all its parts, is a framework for achieving real, sustainable, repeatable success. This book isn't just about making you feel warm and fuzzy. It's about giving you the tools, knowledge, and actionable resources to take your vision and turn it into a reality.
**Who are you?**
**What do you stand for?**
**What's your dream?**
**What type of legacy do you want to create?**
**How can we become great together?**
**_GET GROUNDED_**
In this chapter on vision, I want you to dream. Allow yourself to clear your mind and look at everything as a possibility—no dream is too big or too crazy. Imagine what you'd want your life to look like if you knew you could never fail. Let go of what someone else wants for you, what you think society wants for you, and what you think you are supposed to do because it's reasonable and "makes sense." You are here to live an extraordinary life. Think about what _you_ want to do in your life and how _you_ want to live.
The lessons in this chapter give you permission to design the life you've always dreamed of while living unapologetically. The exercises at the end will help you practice the lessons and exercises in the seven chapters that follow this one. If you're like I used to be, you might be tempted to skip these exercises because they seem like "work"—but that's the whole point. This can be an uncomfortable process, but it's one that finally shows you what life could be like if you choose to live in a world where "anything is possible."
Get ready, my friend. This is the beginning of a beautiful journey, and I'll be with you every step of the way.
**CREATE A VISION**
_The only thing worse than being blind is having sight but no vision._
**—Helen Keller**
Greatness is my passion, but vision is my obsession. Let me explain. A clear vision can unleash extraordinary, mind-boggling power. I've been known to get more than a little intense on this topic. Let me tell you a story about a guy I met named Steve who reminded me of my younger self and was probably like a lot of you out there. He had been friends with my girlfriend at the time for a number of years, and she wanted us to meet up over dinner. I went through the whole "where are you from, what do you do" small-talk racket that you do when you meet new people, and Steve told me he was in graduate school to be a doctor of physical therapy and was finishing up in the next 6 months. As an athlete who has been through his fair share of injuries, I am familiar with physical therapy, so I found this pretty interesting.
I asked him, "So Steve, what do you want to do after you graduate? What's the dream?"
Like most people who just got blindsided on a first friend date, he said, "I'm not really sure."
"Well, if you could have anything, what would you want? If you could have it all, what would it be?"
Steve started talking about working with the military and doing physical therapy on wounded veterans and enlisted soldiers. The benefits would be good, and he could support his family. There's a big military hospital in Germany, so maybe they could see some of the world that way, too.
"That's really cool," I said. "Has that been what you've always wanted, or is there something else?"
Very quickly, Steve said, "I used to be a football coach. So I'd love to be a physical therapist on a pro sports team and work on these great athletes."
Now he was speaking about something I knew well, and I could tell he meant it. "That's awesome, Steve. So is that what you really want?"
He thought about it and said, "You know, actually, it'll probably be a lot of hours, like 80 hours a week. And I'd have to work my way up. And it'd be a lot of time and energy. So maybe working for a pro team is just one of my options, like plan B or C."
"Okay, so you don't want to work for a pro team?" Now I was confused. "Then what is it you really, really _want_? What's your vision?"
I laugh every time I think back to this dinner conversation, because I feel so bad for Steve. When he ordered his meal, he had no idea it came with a side of interrogation, especially from someone who seemed to be getting frustrated with him. And believe me, I was getting frustrated, because I was asking him to focus in on what he really wanted to do with his life—what he desired _—_ and instead, like so many of us who have not yet recognized the inherent potential for greatness within ourselves, he was listing all the things he could do but probably wouldn't.
I learned about desire—the distinction between what we _can_ do and what we _want_ to do—and how to uncover it from the unstoppable Danielle LaPorte. She's a phenomenal motivational speaker and author who has graced us with her presence on _The School of Greatness_ podcast a couple of times. The first time she came on, she said something that still spins around in my head to this day. She stated, "You need desire to be fully alive and you need vision to fulfill your desires." How amazing is that?!
Together with _The Desire Map: A Guide to Creating Goals with Soul,_ which she published in 2014, Danielle changed my perspective on vision and is mostly responsible for turning it from an interest to an obsession. And now, every time we speak, she hones and clarifies my understanding of vision and desire a little more. The last time, she described her book this way: " _The Desire Map_ is about helping as many people as possible get clear on their core desired feelings."
That was exactly what I was trying to do with Steve: pushing him to get clear on how he felt about life so he could figure out what he truly wanted to do. Finally, he got real: "To have my own practice by the beach. And work like 5 hours a day. And then be able to be there to support my family."
That is a vision—it was practical, it was real, and though he'd been afraid to be direct about it earlier, now you could hear the sincerity in his voice. I was eager to ask him how he felt after saying that out loud, but I didn't want his dinner to get cold, so I let it go until dessert. We all dug into our entrées, and, between bites, Steve added one final thought that sums up the entire reason that holds people back from excelling in the School of Greatness:
"I just don't know if that's possible."
Yes, it is absolutely possible, and it has nothing to do with ability. As the renowned leadership expert John Maxwell says, "Successful and unsuccessful people do not vary greatly in their abilities. They vary in their _desires_ to reach their potential." (emphasis mine) The reason I know this is true and that Steve's dream is possible is because of my time with one of the School of Greatness's greatest teachers: Angel Martinez.
I met Angel Martinez in Goleta, California, at the new headquarters of his company, Deckers Brands, a fast-growing, billion-dollar global footwear company. I'd heard of Deckers from the same mentor who introduced me to the power of LinkedIn, but I had little understanding of the company's size or track record before connecting with Angel, Deckers' CEO. From the looks of the company's beautiful new campus, with its glass walls, intricate woodwork, and gleaming granite floors, it was doing pretty well. It turns out, like millions of other people, I was more familiar with two of their best-selling brands: UGG and Teva. When you think about the uniqueness of those two shoes and then you meet Angel, a guy who looks more like a jazz musician than a CEO, you understand why his motto for Deckers is "We want to inspire the unconventional."
Angel took an unconventional route to greatness. It would be difficult to find another CEO with a similar résumé and worldview. An iconoclast and footwear industry legend, Angel was a founding member of Reebok—its third employee—and the catalyst for the company's explosive growth back in the 1980s. He single-handedly pushed Reebok into the budding aerobics marketplace by combining style with function and designing the world's first aerobic shoe for women. Driven by sales of that shoe (called the Freestyle) and lines of improved tennis, running, and basketball shoes, Reebok became the fastest-growing company in history up to that time and blew past Nike for the dominant position in the US athletic shoe market.
Angel went on to serve as CEO of the Rockport Company, a Reebok subsidiary, before eventually leaving the footwear giant to pursue his own ideas and passions. He later helped found Keen, the popular outdoor footwear brand, and joined Deckers as CEO in 2005, when the company had $200 million in sales. Under Angel's watch, in less than a decade Deckers' revenues have soared to nearly $1.5 billion. Fueled by his entrepreneurial vision, the company has expanded around the world with popular retail outlets, new brands, and record growth. If greatness is built upon insight, acquired wisdom, and a unique vision, Angel is the embodiment of that path to success—a path that begins in prerevolutionary Cuba.
Born in Cuba in 1955, Angel was sent off to live with guardians in New York when he was a toddler, never to return to his native country and never to live with his father or mother again. His mother had left her young family when Angel was born, and because of the revolution in 1959, Angel would not see his father again for 34 years. Raised in a tenement in the South Bronx by his elderly aunt and her disabled husband, Angel always felt like an outsider who never quite fit in.
His first brush with footwear envy came when he was in grade school and yearned for a pair of Converse Chuck Taylor All Star high-top sneakers, the Air Jordans of the day. To be cool, you had to have Cons. At $6.99 a pair, they may as well have cost a million dollars. His aunt offered to pay $1.99 for sneakers—the price of cheap sneakers at Woolworth's—but Angel was determined to get his Cons. He collected bottles that he redeemed at two cents apiece until he earned enough for them. So precious were those shoes to him that he walked the four blocks home from the shoe store on the sides of his feet so as not to get the bottoms of the Cons dirty.
"It was a moment of epiphany, the perfect confluence of attaining something I'd dreamed about for a long time and having it turn out to be just as good if not better than I had hoped for," Angel recalled. "It was my first taste of the power of a product to provide emotional and psychological comfort."
**LESSON #1:
BE SPECIFIC**
This was also Angel's first positive lesson in the power of vision. More important, it was a lesson in the power of a clear, specific vision. He didn't want just any shoes. He didn't ask his aunt for "a cool pair of shoes." He knew exactly what he wanted: the $6.99 top-of-the-line Converse Chuck Taylor All Star sneakers in the iconic black canvas with white laces and toe guard. He dreamed about these shoes so vividly that he could feel them on his feet and would do nearly anything to have them.
As the award-winning Brazilian novelist Paulo Coelho wrote in his bestseller _The Alchemist_ , "People are capable, at any time in their lives, of doing what they dream of." And it's that much easier to accomplish when you know exactly what your dream is. It might seem odd to you that a goal as small as having a pair of nice sneakers of his own would be considered a dream—most of us have never had to struggle so hard for such a small material possession—but for Angel, growing up poor in the Bronx, it put him on the path he followed the rest of his life.
Angel's story blew me away. From my time in the business world after college, I always knew vision was important, but to see the power of a clear vision on one person's life like that was a transformative moment for me. Not only did it guide him toward achieving that first small dream—as a kid, no less—it shaped his entire life. If Angel hadn't obsessed over his Cons to the point that he collected two-cent bottles for months in order to buy his first pair for himself, would he have ended up in the shoe business? Would he have become a founding employee of Reebok or the CEO of Deckers? Probably not. Such is the power of a clear, early vision.
After talking with Angel, I started thinking about my own past. Did I have a big, outsize dream that I was obsessed with while growing up in suburban Ohio? What were my $6.99 Cons? Then it hit me. As I talked with Angel, the entire memory came back to me in a giant flash. I was 6 or 7 years old, sitting on the living room sofa with my dad watching an Ohio State football game. I don't remember who they were playing or who won, but I remember the announcers talking about an Ohio State linebacker named Chris Spielman who'd graduated the year before and been chosen by the Detroit Lions in the second round of the NFL Draft. They said he was a two-time All-American. I had never heard that phrase before.
"Dad, what's an All-American?" I asked.
"They're the best players in all of college," he answered nonchalantly, unaware of the future impact of what he was about to say. "There are only a few of them. They make all the big plays."
_Wow,_ I thought, _one of the guys from my favorite team is one of the best in the entire country?!_
I remember sitting there staring into the television, listening to these announcers talk with energy and passion about Spielman and the other All-Americans on the field that day. _Who are these guys? What makes them so special?_
For those unschooled in the splendor and glory that is Ohio State football, here's a quick lesson. Practically the entire state shuts down on Saturdays in the fall when the Buckeyes play. Their stadium, called the Horseshoe, holds more than 100,000 people, and it's always filled to capacity with screaming fans dressed in scarlet and gray. Many of them are wearing the jerseys of All-American Buckeyes past and present. They're all there, I realized, to see these All-Americans—guys like Chris Spielman—do amazing things and lead their team to victory.
At such a young age, I didn't have the words to describe that feeling, but in that moment, I became obsessed with greatness in sports. I wanted to be like all those All-Americans. I wanted to be _one of the best._ I wanted to be great. Thinking back to that day and then to all the years of practices, workouts, eating regimens, supplement experimentation, games, injuries, and physical therapy sessions, I realized becoming an All-American wasn't just an idea that popped into my head one day. It was the name for the dream I'd had since I was a little kid.
Like Angel's dream for his first pair of shoes, being an All-American can sound a little silly or even a little cute if you don't have the context and you don't know how that singular vision guided decades of our lives. Having a goal that feels attainable but slightly out of reach provides focus and direction. It prevents you from getting distracted or discouraged when things don't go your way. Angel wanted those Cons as soon as humanly possible, but seven dollars' worth of bottles at two cents a pop is a lot of bottles for a little kid. I wanted to be an All-American, but I had no idea how to go about doing it, and neither did anyone I knew. It wasn't as if that kind of greatness was living next door, the way that Steve Jobs lived near the famous Packard's garage or the way it might be for a kid who hopes to succeed his father as CEO of a family business or graduate from the college his parents went to. Our goals felt outsize to those around us, and our timelines were different, but they both were well defined with a clear end point. If you want to be great at anything, you've got to have a clear vision of exactly what you want, why you want it, and when you want it to happen.
All greats do this, including the greats you will hear much more from over the course of the rest of this book. It was an essential component to Shawn Johnson climbing the medal stand in Beijing, Kyle Maynard climbing Mount Kilimanjaro, Rich Roll going from overweight lawyer to world-class ultramarathoner, Scooter Braun building one of the most successful music management firms in the industry, and my brother climbing the ranks of the world's great jazz musicians, to name a few. Now, having a vision isn't all you need to be great, happy, or successful, but it's absolutely true that you can't be those things without one.
**LESSON #2:
LET YOUR VISION BE YOUR IDENTITY**
We focused first on creating a vision because it's the most important step to getting anywhere and achieving anything you want in any area of life. But we also have to be clear about what a vision is. A vision is not just a dream. A powerful vision emerges when we couple our dreams with a set of clear goals. Without both, we are apt to wander in a clueless and purposeless fog, because a dream without goals is just a fantasy. And fantasies are the bad kind of visions—the hallucinogenic kind, not the real kind.
**A powerful vision emerges when we couple our dreams with a set of clear goals.**
Without a real vision, we lack identity. Having a real vision isn't just about clarifying what you want; it's about defining what and who you want to be. My vision was to achieve All-American status when I was younger, but what I really wanted to _be_ was great.
For Angel, the Cons were about being like all the other kids—being equal—at a point in his life when he felt unlike any of them. Most of us can relate to wanting something stylish that our friends have, but few of us can probably understand what it's like to literally and figuratively struggle with identity from such an early age. On Angel's first day of school, his guardian introduced him to the principal as Angelo, even though that wasn't his name. In the 1950s in New York City, it was easier to get by if people thought you were Italian rather than Cuban. It wasn't until he was on his own in college that he could finally convince people to call him what he wanted to be called.
"I just made up my mind," he told me. "'No, that's not my name. Angel is my name. You can call me 'angel' until you figure out how to pronounce my name, but I'll make it easy for you and just give it to you. It's Angel [An-hel]. I'm not even asking you to do it with an accent or anything.'"
But it was about more than people pronouncing his name correctly; it was about making a life. Having his own name was something he needed. He craved becoming someone on his own terms, in line with his vision for who he was (and is to this day), not what some public school administrator said he was on a piece of paper, even if his guardian had the best of intentions. See, what might seem conventional to some of us today—the idea of going to college, getting a good job, having a nice house—was, for someone with Angel's background, not just unconventional but downright crazy when he was growing up. Especially if he insisted on embracing his Cuban immigrant heritage just as the Cold War really started getting chilly.
Listening to Angel talk about his childhood made this distinction clear to me. It revealed a relentless ambition, a life of striving for true accomplishment. To be equal, to be somebody, to be great. But not great in the more traditional, achievement-based way that I was trying to be great. His was greatness in life, in living.
It might seem like Angel had two completely different visions—one to be just like everybody else, the other to be his own man—but actually they are two sides of the same coin. They unify what he wants with who he wants to be. That is the essence of identity. Just as pairing your dreams with your goals is the essence of a real vision, unifying your vision lets you blow past what other people think your limitations are. Beyond those limitations is where greatness lives. If you don't figure out what you want in life and who you want to be, you will most likely feel trapped within those limitations. No path to greatness has ever involved settling for less than what you really want.
Let's go back to the dinner where I met Steve. Steve thought his dream was to be a physical therapist, maybe with the military or a pro sports team. In fact, his dream was to live near the beach and work from home a few hours each day so he could always be there for his family. No wonder he was confused. He wasn't sure it was possible because he didn't realize that being a physical therapist wasn't his dream; it was just a goal on the path and a means to achieving his actual dream. What he was after was control over his life and the luxury of seeing his kids grow up. Once you clarify this, then it becomes possible to develop a real plan for getting there.
"The challenge," Angel told me as we discussed his childhood, "is to be able to project yourself into a future that you have no reference point for. If you grew up in a well-to-do, solidly middle-class family where you got a new car, you lived in a nice house, you took a nice vacation once in a while—I'm not talking about anything exotic, I'm talking about the middle-class American dream—well, for me growing up, that was absolute fantasyland. That was something I saw on TV, on _Leave It to Beaver._ That house on TV was a palace to me, and it was a challenge to convince myself that I belonged there, too."
The famed World War II general and French president Charles de Gaulle is reported to have said, "Greatness is a road leading towards the unknown." And he was right, but only in a particular sense, I think. It's not that you don't know what it looks like; the unknown part is what it's like to _be there._ This is something so many of the students in the School of Greatness—myself included—struggle with when we first get started. Greatness is for those people over there—they've been there and done that. They deserve it for whatever reason. Who am I? What have I done to think I can achieve these great things? I'm just Lewis from Ohio or Steve from LA or Angel from the Bronx.
**LESSON #3:
TURN THE TELESCOPE AROUND**
The key is to understand that the vision creation process doesn't end when you've clearly articulated what your dreams and goals are. There is another part to it—the part where you envision what it's like to have achieved those goals and live that dream. I learned this, too, from Angel Martinez.
"When I was a kid, I came up with this idea while playing with a telescope," he told me. "I realized that you could look through both ends. When you look through the small end, everything is far away. But when you look through the big end, you say, 'Wow, that looks totally different when I turn the telescope around.' I would tell people who doubted themselves, 'You might just be looking at your life through the wrong end of the telescope.'"
Could you have the same problem? That outsize dream that seems so far away is often a lot closer than you think. It just seems distant because we look through the wrong end. Angel's point of view was so absolute and so unusual that it made me reconsider my own story. Then he said something that struck a chord:
"I came to the conclusion that it's easier to come from a place than to go to a place. At Reebok, I thought we were better than Nike," he recalled. "We just hadn't done it yet. I didn't come to Deckers because I wanted to stay in the funky old building we were in before this new one was built. I was already at the other end of the telescope for this company. I saw this as a multibillion-dollar company because of the quality of the people and the products and the brands. I realized, you become what you envision yourself being."
_You become what you envision yourself being._ If Mike Tyson hadn't ruined face tattoos for everyone, I would tattoo that phrase backward on my forehead so I could read it every morning when I got up and I looked in the mirror. Because that is the true power of a vision on the path to greatness. It's not a destination or a specific achievement or an amount of something—it's a state of being that encompasses all of the goals you've set for yourself along the way.
**You become what you envision yourself being.**
One of the amazing things about doing what I do and getting to spend time with these teachers in the School of Greatness is leaving every encounter with far more wisdom than I arrived with. It's a great gift, and sharing it with the world is at the heart of my mission. It's why I've carefully chosen the stories I share with you. For instance, Angel Martinez is one of those rare individuals who could fit into pretty much every category on my list of traits that form the foundation of greatness. But I started the book with his story—a story of true vision in every sense of the word—because he is the kind of inspiring person we can all use as a reference point when we doubt our dreams or ourselves.
Angel has been driven by a vision that has propelled him out of bed every day for more than 50 years, long past the time he's earned enough money to stay in bed as late as he wants. Your job is to create a vision that makes you want to jump out of bed in the morning. If it doesn't, go back to bed until you have a bigger dream.
I have discovered and developed these powerful exercises to help you get crystal clear on what you want, why you want it, and when you want it to happen. To pursue and achieve greatness, you must truly become the author of your own destiny, and the writing starts with these four exercises.
**EXERCISE #1:**
**Your Certificate of Achievement (COA)**
**_Write down your goal. Print it. Frame it. Hang it somewhere you will see it. Every day._**
Writing down your goal is a powerful thing. Declaring your vision and putting a date on it, as though it _will_ happen (or, as Angel would say, like it already did), is even more powerful.
This exercise is about getting total clarity on what you want (like I did with Steve) and why you want it, and then declaring that vision for yourself in the next 6 months or whatever date you have in your head, as long as it's specific. Your goal can be financial, personal, or health or career related. It almost doesn't matter what the vision is. There's only one rule: It should be something hard to achieve. It must be something that terrifies you when you say it out loud to someone you respect. At the same time, it should be something that is possible to achieve in the allotted time frame—provided you put in the work. And then you write yourself a new goal once it is completed.
I am not the first person to come up with the idea to write down goals. Many who have come before me have recommended something similar. But I didn't learn this from them. I came by it honestly, at a fairly early age, watching my coaches. As an athlete, I have played on more teams with more coaches than I can count. We've been good; we've been great; we've been bad; we've been horrible. On most of those teams, the difference between success and failure was razor thin. Rarely could you put your finger on why, and God knows our coaches tried. Over time, though, I noticed one thing that distinguished the good teams from the bad ones or the successful coaches from the unsuccessful. The seasons where coaches had us write out our team vision and our personal goals were the most successful seasons I ever had. That shared vision provided a foundation for the team. Without it, we were athletes playing without greater purpose. Having that purpose and knowing why we were playing enabled the members of those teams to sacrifice for each other in ways the visionless teams never could.
The power of a clear, stated vision struck me so deeply that after my sports career was over, I wanted to see if I could apply this exercise to business and to life. I started with something that had dogged me my whole life: public speaking. I was terrified of speaking in public. I could not get up to talk in front of people to save my life. Whenever I gave speeches in school, I was a sweating, shaking, nervous wreck. I decided I never wanted to feel that way ever again.
A year removed from my professional football career after a number of injury setbacks, I joined Toastmasters International, an educational organization that helps members with their communication and public-speaking skills. I went every week for a year, with the goal of getting over my fear of speaking in public. But that goal wasn't specific enough; the vision wasn't clear enough. "Getting better" was too vague. Toward the middle of the program, excited by my progress but not satisfied with my direction, I wrote down a scary goal: Make $5,000 for a speech. What made it so frightening was the fact that I wasn't able to achieve it in that moment. There was no way anyone was going to pay me to speak at an event, not that version of me. But I knew that stepping toward my fear, that's where the magic is created. I had doubts— _Who is going to listen to a young kid like me? What do I have to offer?_ —but I gave myself a deadline to do it: 9 months.
I wrote it down on a piece of paper. I framed it and hung it on my mirror where I would see it every morning when I woke up. Just like writing down our shared team vision back in my football days, framing and posting my speaking goal (with the date!) gave me a purpose and a destination. It turned my telescope around. Not only did I achieve that goal in the time allotted, but today I am much more comfortable onstage and regularly get offered upwards of $25,000 for speaking opportunities around the world. And it all started with establishing a clear vision and writing down my goals. I've been doing this exercise for more than 15 years now. I started calling it my Certificate of Achievement to make it an official part of the quest for greatness, and it continues to serve me well as both an athlete and an entrepreneur.
Download your Certificate of Achievement at schoolofgreatness.com/resources and you will receive an easy template for completing this exercise in excellence. Once complete, print out your COA, frame it, and place it where you're going to look at it every day. Make it the focal point of your daily routine, always at the top of your mind and on the tip of your tongue as that singular thing you must achieve.
**EXERCISE #2:**
**Perfect Day Itinerary (PDI)**
This may be one of the most powerful exercises you ever do for yourself, so make it count. I've coached many wandering entrepreneurs through this exercise, and most of them have told me it changed their lives. I wasn't surprised—when I did it for the first time years ago, it literally set me up for creating the life I always envisioned and living it every day.
In this exercise, your job is to map out what your perfect day looks like along the path to achieving your vision. There are two parts to this exercise: the macro and the micro. First up is the macro part, where you figure out what your perfect day would look like at a general level. Not every day is going to be exactly the same. Each day will look a little different depending on what happened the day before. It should look a little different; otherwise life would get boring and monotonous. Still, you want to have a broad sense of what each perfect day feels like. This starts with a series of questions.
How do I want every day to look?
How do I want to feel every single day?
What am I creating daily?
Whom am I spending my time with?
What places am I exposing myself to?
What passions am I fulfilling?
Take out a blank piece of paper or open a new document on your computer and fill the first half of the page with the answers, in broad terms, to these questions.
Here was mine from my first time completing the exercise.
**PART 1: MY PERFECT DAY**
In my perfect day, I wake up next to the woman of my dreams and she's crying tears of joy because she's so excited about the life we have together. I'm preparing to compete in the 2016 Olympics with USA Team Handball, so I head to an intense training session with my coach to increase my physical strength and athleticism. Then I'm working on my TV show that's on a major network and supporting my company team with all of my projects that inspire entrepreneurs to follow their own passions and make a living around what they love.
Now, in part 2 (the micro part), write out a detailed itinerary for the next perfect day on the bottom half of the page. This should include everything you want to do and have to do and exactly how and when you want to do it.
Every successful sports season I had included detailed daily itineraries. We received one in the morning and one before practice, and they set us up to win. There was no more wondering what to do, when to do it, or how much time to spend on it. It was all right there, plain as day, laid out in the steps necessary to reach our end goal. This is true for every professional sports team as well. The successful ones have a daily plan designed to lead them to achieve their vision. Theirs are similar, if not in many ways identical, to what I'm asking you to create.
Here is a version of my daily itinerary while I was writing this book.
**PART 2: TOMORROW'S PERFECT DAY**
**7:30 a.m.** Wake up, meditate, and enjoy the views from my balcony.
**8:00 a.m.** Healthy breakfast with green juice or a smoothie.
**9:00 a.m.** CrossFit/kickboxing or private skills training session.
**10:45 a.m.** Check in with my team about projects of the day.
**11:00 a.m.** Complete the top three tasks that were on my list before bed.
**12:00 p.m.** Healthy lunch at home or lunch meeting with someone who inspires me.
**1:30 p.m.** Back to the top three on my to-do list, recording interviews, doing videos, or working with the team.
**3:00 p.m.** Physical therapy to increase flexibility (2 days a week).
**5:00 p.m.** Pickup basketball, hiking with friends, swim in ocean.
**7:30 p.m.** Healthy dinner at home or out with friends.
**9:00 p.m.** Read, movie, events with influencers on the town.
**11:00 p.m.** Make a list of what I'm most grateful for today, create a "completed list" of what I did today. Write the top three list of what I want to create tomorrow.
**11:30 p.m.** Meditate, sleep, dream, recover body.
If you let it, the PDI can be a powerful exercise that will set your year (and many years to come) to contain the best days of your business and life.
It also helps validate your vision and vice versa. If your vision doesn't fit in with your perfect day at either the macro or micro level, you need to either change your vision or be more open, honest, and creative about what it will take at a daily level to reach your vision.
**EXERCISE #3:**
**Personal Principles Declaration (PPD)**
The third vision exercise is the statement of who you will be and what you will stand for in your life, even in the toughest moments. I call it the Personal Principles Declaration (PPD) because that's what it is—a declaration. You're not making a wish list or scribbling down some nice thoughts. You are declaring to yourself and to your world that this list of five principles is what you stand for and live by, no matter what comes your way. When something goes wrong or doesn't happen the way you envisioned, you fall back on these principles instead of falling into a negative spiral or becoming a victim of circumstances. You don't let your bruised ego get the best of you, because your vision is bigger than your ego. You will never achieve what you really want if you let your ego stand in the way of your principles.
Here is my PPD.
**1.** Love myself, everyone, and everything.
**2.** Be in service to support others and the world.
**3.** Always give my best and strive for greatness in everything I do.
**4.**Live in abundance.
**5.** Create a win/win with everything.
Here is Angel Martinez's PPD.
**1.** Tell the truth.
**2.** Be there for your family and friends.
**3.** Respect the opinions of others.
**4.** Know that you don't have all the answers. Ask questions.
**5.** Have humility.
**6.** Persevere.*
Print out your PPD or write it on a card and keep it in your wallet. Read over your principles often. Your ego is strong and very convincing (at least I know mine is), especially when the chips are down, but when you hold fast to your principles, you cannot be deterred on your path to achieving your vision. It doesn't matter what kind of adversity comes your way—and it will come, especially the bigger the vision—your principles are a set of powerful tools that will serve you along the journey.
**EXERCISE #4:**
**Your Personal Statement Plan (PSP)**
This exercise is designed to bring everything about your vision together into a plan of action. We can think and plan and hope and wish, but until we do something about our vision (as you will see in the following chapters), it will only ever be just a dream.
On a blank piece of paper, write the following (to download a sample worksheet, go to schoolofgreatness.com/resources):
Your name.
Today's date.
6 or 12 months from today.
_Answer these questions._
Who am I?
What do I stand for?
What is my vision for myself, my family, and the world?
List your five principles (Personal Principles Declaration)
This is an opportunity to get clear on what you want, but make no mistake—living your vision is a commitment. It demands time and dedication, so don't take it lightly. Pause for a moment, if needed, before you put the vision of your life to paper. But make sure to complete these exercises in the next 24 hours while they're fresh in your mind.
Write out the top three goals you want to either achieve or maintain for the next 6 or 12 months under each of the following categories: family, relationships, business, money, health, recreation, spirituality/inner growth.
Below each goal, write a detailed action plan for how you will achieve that specific goal: Make it so annoyingly step-by-step and spelled out that anyone could read your plan, follow it exactly, and achieve it themselves. Here is a sample of how three categories might look.
**FAMILY**
**GOAL #1 :VISIT PARENTS AND SIBLINGS TWICE A YEAR.**
**Step 1 :**Find time in my schedule every 6 months where I could fly home (in next 3 days).
**Step 2 :**Call Mom, Dad, and siblings to see when they are free (in next 7 days).
**Step 3 :**Save to my calendar the set dates we agree on and book flights (within 2 weeks).
**BUSINESS**
**GOAL #1 :MAKE $10,000 A MONTH IN THE NEXT 6 MONTHS.**
**Step 1 :**Calculate how many customers it will take to reach this (1 day).
**Step 2 :**Break this down into how many sales this will take weekly and daily (1 day).
**Step 3 :**Set up and host one webinar per week to current prospects to generate these sales.
**HEALTH**
**GOAL #1 :LOSE 15 POUNDS IN 60 DAYS.**
**Step 1 :**Find a workout plan I'll be excited about (within 24 hours).
**Step 2 :**Find coach or accountability partner (3 days).
**Step 3 :**Schedule workout days and times of workouts for the next 60 days (3 days).
**Step 4 :**Begin training on this plan in 4 days!
_Write down the type of person you will need to be in order to accomplish this in 6 or 12 months._
**Example:** "I will need to be committed. Most important, I'll need to let go of the pressure or stress and empower others around me to support me instead of doing it all on my own. I'll need to deepen my understanding about business and how the world works for me to be able to flow in it effortlessly."
I will ...
_Now write down the breakthroughs you will create as a result of understanding who you need to be to accomplish your goals._
**Example:** "Letting go of reaction or defensiveness. Peace with myself, and understanding that everything at the end of the day is 'small stuff' and doesn't require me to react in a way that doesn't serve me if things don't go well."
This is your living document that you will adjust over time. Every 6 to 12 months, you should revisit it and make sure you are on track to live your vision.
**_COACHING TIP_**
Your life matters, and so do your dreams. It's time you act like they matter. The best way to start doing that is to visualize and map out how you want your dreams to look on a day-to-day basis. The key to greatness is fulfilling what you want in your life first and being an inspiration to yourself. By creating an inspiring life that works, you inspire others around you to do the same. This ripple effect is powerful. Just imagine if everyone focused on making sure their lives were fulfilling and inspiring. What would the world look like then?! When you complete this homework, show it to a friend or someone you care about and tell them your dreams and what you stand for. Ask them to join you in completing these vision exercises as well, so you have an accountability buddy. Then post it on social media and use #SchoolOfGreatness so others in the community can support you along your journey. You've got this, and I've got your back. It's time to make magic happen, and it starts with you getting clear on exactly what you want in your life and why you want it. Let's go!
* * *
*Of course, Angel added one more principle for good measure. You don't get from where he was to where he is now by doing just enough!
**_GET GROUNDED_**
With everything I've ever wanted in life—from wanting to be a great athlete when I was young yet getting picked last for teams to learning to start my own business from my sister's couch after a career-ending injury with no hope in sight to finding a loving relationship with my ego and insecurities getting in the way—it has always and will continue to come with an equally difficult challenge.
When adversity arises, you have two choices: (1) Do nothing, let it overwhelm you, and fall victim to your circumstances, or (2) embrace the challenge and move toward the adversity, making it part of your success story. Prepare yourself for these moments, because they are going to happen in all areas of your life whether you like it or not. When you understand this and learn to embrace adversity, then you can learn to overcome it and use it to your advantage.
When I face challenges in my life, I think about my friend Kyle Maynard, whom I write about in this chapter, and how he, along with others, shows me how much I have to be grateful for.
**TURN ADVERSITY INTO ADVANTAGE**
_Storms make trees take deeper roots._
**—Dolly Parton**
For most of us, it's difficult to imagine becoming a championship wrestler, a football player, a weight lifter, a mixed martial arts fighter, or a mountain climber. There are so many obstacles that stand in the way of each of those goals: money, opportunity, coaching, talent and ability, confidence. Any one of them could derail these impressive dreams at any time.
Now imagine becoming _all_ those things before you cut the cake on your 30th birthday. A friend of mine did. His name is Kyle Maynard, and he is one of the most inspiring teachers I've ever met. When he was a young man, those physical feats I just listed were only a few of the goals on his bucket list—a bucket that would never go empty and would one day include inspiring others to do great things. Kyle wanted to achieve his goals as badly as any person who aspired to greatness has wanted something. And by the middle of 2012, at the age of 26, he'd accomplished all of them. He played football in middle school. He was a champion wrestler in high school and won 36 varsity wrestling matches during his senior year. He fought a full three-round mixed martial arts (MMA) fight. He climbed the nearly 20,000-foot Mount Kilimanjaro.
On their own, these might not sound like particularly lofty goals. I've met many other people who achieved these same dreams at a much higher level, yet none of them did it the way Kyle did. When they did it, ESPN didn't award them with two ESPYs for their accomplishments, the way the network did in Kyle's case. Why? Kyle's accomplishments stand head and shoulders above those of most other men his age—most other men, period—because Kyle himself stands only 3 feet 8 inches tall. He is a congenital amputee. A birth defect related to something called amniotic band syndrome deprived him of the fully formed arms and legs that most of us take for granted. As he describes it: "Basically, my arms end right where your elbows would be. For each arm, they're both about the same length, and my legs end slightly above where the knee is, and I have two feet. They're just a little bit different."
Amniotic band syndrome occurs when the blood clots in utero and fibrous bands constrict the growth of fetal limbs. Doctors have no idea why it happens or what causes it, but they peg the statistical chances of it happening in an otherwise normal pregnancy at 1 in 10 million. Growing up, Kyle did not just face the typical external obstacles all of us face at one time or another; he dealt with a whole unique set of struggles that were a part of his life from the day he was born. And yet he accomplished each of the things he had envisioned for himself.
**IT'S ALL IN THE DOING**
You should not feel bad for Kyle Maynard. Pity isn't a feeling he's searching for. What I learned from Kyle over the course of our talks brought my understanding of goals and greatness into a kind of focus I'd never had before. Creating a vision is about clearly defining what you want (your goals) and who you want to be (your dreams). But goals and vision are one thing—they are made in our minds. They are only hypotheticals. Anyone can tell themselves they have a vision for what they want to create in the world, but it is our actions that dictate what we create in reality, where anything can (and does) happen. It is in the doing that the goals become real.
To be good at something requires talent, vision, and action. Greatness is what remains when that talent and vision meet adversity—and persist in the face of it. This is what makes Kyle a great teacher, and it's why he can teach us more than just about anyone about overcoming adversity on the path to greatness. When it comes to greatness, he teaches us that there is no room in life for excuses:
"When I was younger, when I was 10 years old, I used to cry myself to sleep some nights because I would just wish that I would wake up and have arms and legs. And no matter how hard I would have focused on that forever, it never would have happened. So when we go and focus on those things that we have no control over, it brings us nothing but unhappiness."
This mindset is unsustainable and unproductive in the face of adversity. It gets us nowhere. How does that old saying go: "Wish in one hand, crap in the other, and see which one fills up first"? That was a reality Kyle was forced to reckon with at an early age. As he said, no amount of focus or wishing was going to change anything. Like many of the breakthrough moments I've had in my life around the issue of adversity, Kyle's aha moment came on the football field. He was 11 years old.
"I made my first tackle in a football game when I was 11," Kyle recalled. "It seems like a relatively simple thing, but my life changed forever in that moment. I stopped having so many concerns over what might happen in the distant future. I stopped being consumed with wondering what I would do with my life. I used to ask questions like 'Would I have to live at home with Mom and Dad forever?' 'Would I ever have a girlfriend or a job someday?' And the interesting part: It wasn't like I was given any answers to any of those questions. I was just playing football."
Kyle wasn't thinking or worrying or wishing, he was _doing._ At 11 years old, no less! It was in the action and the perseverance in the face of tall odds that obstacles started to dissolve and he took his first concrete steps toward greatness. It became almost a philosophy of adversity, one that he lived by from that day forward.
"My life has had its challenges since that tackle," he told me. "But the concerns and fears I had over the future continued to subside until they became relatively nonexistent. I mostly attribute that to putting myself in situations where I'm uncomfortable and staying with it until I become comfortable.
"When I was 19, I gave a speech to several thousand of the world's most successful business owners, sandwiched between then senator Obama and Dr. Steven Covey, best-selling author of _The Seven Habits of Highly Effective People_. Once I gave that talk, it's no wonder every speech since then has been a whole lot easier!"
Amazing! Think about that for a second: In 8 years, Kyle went from crying himself to sleep every night, wondering if he'd ever have a girlfriend or a job or a place of his own, to speaking to a room full of business luminaries between the future president of the United States and the author of one of the most successful self-help business books of all time. And it all started with a tackle on the football field—with one little action.
"We are our greatest ally in terms of our capability to get past adversity. We can be incredibly motivated," Kyle often says. It all lies in how we perceive and engage the adversity we face.
**THE LANGUAGE OF INTERNAL ADVERSITY**
One of the things it took me a long time to learn about adversity, especially in my own life, is that adversity isn't always external or physical. In fact, it usually isn't. I first started to understand this through my work on emotional intelligence with Chris Lee (whom we'll meet next chapter), but it wasn't until I sat down to talk with Nicole Lapin about money that my eyes opened to how broadly adversity can manifest itself in our lives.
Nicole is a finance expert who spent years as a reporter and anchor for networks like CNBC, CNN, and Bloomberg before striking out on her own to write a _New York Times_ best-selling book called _Rich Bitch_ about getting your financial life in order. Her book is fantastic, and—man or woman—if you've always had money or finance issues, you should definitely pick it up and read it cover to cover.
But what struck me about Nicole when we met was the story of her path to financial reporting that began, remarkably, at age 18. It was a journey that was almost over before it began, thanks to a whole different brand of adversity—the internal kind.
A first-generation American, Nicole grew up with immigrant parents who operated a 100 percent cash household. No credit cards, no loans, nothing that typically defined the average American's relationship with money. It was all cash, all the time.
"We didn't have the _Wall Street Journal_ on the kitchen counter, we never talked about stocks or bonds or any of that, and I never learned it in school. So I was pretty clueless growing up," Nicole told me. "I was that awkward girl with no debit card who went out to dinner with girlfriends and either dropped a wad of cash or wrote a check."
The final straw came when she was in college at Northwestern University in Chicago and she needed to buy a last-minute airline ticket. The convenient thing would have been to hop on the computer and buy one online. There was just one problem: She didn't possess a credit card. Instead, she had to go to the bank, withdraw cash, and roll up to the counter at the airport and pay for the ticket with a wad of bills. "I said, 'Enough is enough. This is ridiculous.' I needed to take control of my life and my finances."
Except how do you do that? How do you take control of your financial life and set yourself on a path toward a career in business news when finance is essentially a foreign concept to you? When you can't learn from your parents? When you live in a country where they don't teach you how to master and manage your money—not in elementary school or high school or college, even if you take finance classes?
"That's when I realized, it's just a language, like anything else that's new. It's a very foreign language," Nicole said.
She was totally right! Every single new thing we attempt in our lives is like a new language. The language of MMA and mountain climbing probably scared the crap out of Kyle when he first thought about tackling those feats. The language of LinkedIn and the language of business scared me half to death when I was planted on my sister's couch staring at the end of my career in sports (a language I was very fluent in).
Getting started is always the hardest part of doing anything new. You have to overcome all those fears and anxieties of saying the wrong thing or looking foolish. There can be a lot of shame involved, and shame has stopped more than a few people from doing important things—things they loved. Nicole recognized this and decided to jump in with both feet. She took a job on the floor of the Chicago Mercantile Exchange.
"When you start to speak that language, you feel you're speaking Chinese in your own country," she confessed. "That's what happened to me when I started on the floor of the exchange. I had to learn the language really quickly. When I realized that it was just learning a language and that if I learned it I could join the conversation, I felt so empowered."
I knew exactly what she meant, because I experienced that exact feeling when I was learning how to salsa dance back in 2006. I was living above a jazz club that offered salsa dancing once a week, and I went down there committed to becoming the best tall, goofy, white-guy salsa dancer that I could be. I was petrified, but for 3 months, I trained and studied and had group classes, and I took private lessons, and I watched YouTube videos, and I practiced in front of my mirror by myself like I was dancing with a girl. If you think it's weird when I talk about it, imagine how weird I felt doing it!
But I remember the moment when I finally understood the language of salsa dancing, and believe me when I tell you that when I started, it seemed like a _completely_ foreign language. Nicole nailed it; it was absolutely like speaking Chinese. When it clicked and salsa started to make sense, as though I could speak the language fluently, I felt like I could run up the side of a building. I could do anything I set my mind to no matter what obstacles—physical or mental, internal or external—stood in front of me.
Nicole helped me reframe my outlook on adversity—not just what it is and where it comes from but also how to address and overcome it. It's a lesson I will carry with me into every new challenge, because if there is one thing that is inescapable in life, to say nothing of the path to greatness, it is adversity. We dream, and then reality smacks us in the face. We create a vision for ourselves, and soon enough we learn that the world is, at best, indifferent to it (and us). In some cases, the world seems to want to do everything it can to get in our way. It shows up at nearly every stage along our path: from the early days of figuring out how to walk; learning in school; messing up your first kiss; practicing sports; starting a new business. We experience loads of pain, frustration, and falling down.
No one understands this better than Kyle Maynard. He taught me that not only is no one immune to adversity but that enduring your fair share of it is not an entirely bad thing. When we fail over and over in pursuit of excellence, it actually helps us learn and grow into greatness! Granted, Kyle has endured more than his fair share, compared to someone like me—I don't have a congenital disability, after all—but I still had obstacles to overcome.
**THE HIDDEN ADVANTAGE OF ADVERSITY**
My entire childhood was based around a singular vision: Become an All-American athlete. I thought it would be in football, the sport I'd lived and breathed for so many years. I thought it would happen my sophomore year in college when I set the record for most receiving yards in one game (418 yards) and ended the season with the second most receiving yards in the nation. But my team had barely a .500 winning percentage, and they don't typically award All-American status to players on average teams. Things only got worse from there, on and off the field, as our coaching staff was unable to do what it took to put us in a position to be great. So my senior season, I transferred to another school that offered a real opportunity to achieve my dream. It was a tough decision to leave, especially for someone like me who'd spent his whole life playing with and for the team, but this new school showed a lot of promise, and I couldn't deny the dream that had guided my whole life.
In the second game of the season with my new team, we were playing our crosstown rivals. I was having a good game, making plays, and at one point in the third quarter, I hauled in a slant pass over the middle and took a hard hit to my ribs from one of the linebackers. I felt some soreness at the time, but thanks to adrenaline and competitiveness, I didn't think much of it. Then 2 days later at practice, I went to make a quick cut in warmups, heard a huge pop, and crumpled to the ground in absolute agony. I'd never experienced that kind of pain in my life. It felt like someone was stabbing me in the side, twisting the knife, and then using a sledgehammer to pound on the wound. My teammates thought I was joking because nobody had touched me! Well, it turned out that I'd probably hairline fractured three ribs on my right side in the game, and the quick cut and turn in practice did the rest of the work, breaking them all the way. The cartilage had ripped from the bone and my muscles were twitching at the spot of the tear, chattering my ribs at the place of the breaks. I'd turned my rib cage into a wind chime, and every breath fluttered the chimes even more. Needless to say, I was out the rest of the season.
For a few months, I was in so much pain, I could hardly walk. I couldn't sleep, cough, sneeze, or laugh for at least 2 weeks. I had to have someone lift me out of bed because I couldn't engage my stomach muscles without needing to scream in pain. I had never taken pain medication before, so when I popped the pills the doctors prescribed, my body didn't know how to react to them and I threw them up almost immediately—which was a whole other level of pain to add to the mix.
Yet the physical pain paled in comparison to the emotional agony. I was completely crushed. My dream was slipping away—adversity had smashed my vision to pieces like that linebacker had smashed my ribs. It was one of the lowest points of my life.
Around Christmastime of that year, a few months after the injury occurred, I had recovered enough that I was able to run on a treadmill without pain. I was feeling a little better emotionally, too, but I still couldn't shake the fact that I was nowhere nearer to the goal that meant so much to me. I was a senior, and the football season was over, so becoming an All-American wide receiver was clearly no longer an option. I had to figure something out. There had to be another way.
That's when it occurred to me that I might try my hand at another sport in the months remaining of my NCAA eligibility. Except for my still-healing ribs, I was in good shape, and I was a great track athlete. My freshman year, I jumped 6 feet 6 inches in the high jump and 22 feet in the long jump, and I'd nearly cracked 11 seconds in the 100-meter dash. None of those marks individually would get me within sniffing distance of a medal stand, let alone qualifying for the national championships, but together maybe there was something there. Track and field is a spring sport, so I called my old track coach (who had qualified for the Olympic trials and was a former All-American herself) between Christmas and New Year's and asked her what it would take to become an All-American in the decathlon—the 2-day, 10-event test of strength, agility, and endurance whose winner in the Olympics is often called the "world's greatest athlete." Was it even possible? She said it was, but training would have to start right away, and I would need to do everything she said for the next 6 grueling months. No shortcuts. No excuses.
To use Nicole Lapin's metaphor, it was a new language, but I didn't care—I was in. This new vision gave me the motivation and drive to refocus all of my energy toward doing whatever it took to make that happen. It brought a sense of purpose when before I felt helpless. It gave me that pep in my step that, just a few months prior on the football field, allowed me to distinguish myself as a top-flight wide receiver. I felt like a warrior preparing for battle again. A powerful vision gives us warrior-like strength, which is why it's critically important to find or recalibrate your vision as soon as possible after confronting major adversity.
I immediately began the arduous transfer process back to my previous school (Principia College, where my old track coach was based) and got to work. In the 6 months that followed, I ended up getting into the best shape of my life—probably my peak conditioning as an athlete to date—and not only qualifying for the national championships but making the All-American team. (I'll explain what happened in the next chapter.) Then, if that wasn't enough, I earned a fifth year of eligibility thanks to all the injuries, got back on the football field better than ever thanks to the decathlon training, broke a few receiving records and made big plays in big games, and earned my second All-American honors. This time—finally—in football, my goal all along.
I had unearthed the advantage hidden within my adverse circumstances. What I had dreaded and fought so hard against at first—my injuries—actually got me closer to my dream. In fact, it surpassed the original dream in ways I could have never imagined. How could that be? How could an injury, one that I never anticipated, literally double my chances to be an All-American, which I'd dreamed of since I was a boy?
I didn't realize it then, but it all became clear when I spoke to Ryan Holiday, my friend and author of the book _The Obstacle Is the Way._ Ryan is a best-selling author, the former head of marketing for American Apparel, and the founder of a marketing and strategy firm that allows him to live the life he wants to live. Ryan has faced his own fair share of adversity. He dropped out of college at 19 years old; was virtually disowned by his parents; went to work for a string of high-profile, very difficult, and controversial clients; and spent the better part of the next decade working his butt off to get where he is today.
"It is a timeless truth of history and philosophy," he told me, "that the hardships we face in life can be seen as terrible tragedies or opportunities." The Roman emperor Marcus Aurelius, one of Ryan's great influences, was fond of reminding himself that "the impediment to action advances action. What stands in the way becomes the way."
In fact, you can trace this foundational element of Stoic thought through many of the most revered individuals who ever lived. As young men, both Thomas Jefferson and George Washington read the Stoics—thinkers and leaders like Cato the Younger, Epictetus, and Marcus Aurelius—and it helped them with the adversity they faced during the creation of America. The explorer and writer Robert Louis Stevenson was a longtime admirer of Marcus Aurelius and Stoic thought. So were painters like Eugène Delacroix, writers and thinkers like Adam Smith, and statesmen like Bill Clinton. Tim Ferriss, the investor and entrepreneur and my personal friend, is also a public proponent of this line of ancient philosophy that has relevance for our modern lives.
All these folks faced adversity on their paths to success. Sometimes it was big; sometimes it was quite small. As Ryan writes, there is "one thing that all great men and women have in common. Like oxygen to a fire, obstacles became fuel for that which was their ambition. Nothing could stop them, they were (and continue to be) impossible to discourage or contain. Every impediment served to make the inferno within them burn with greater ferocity."
**YOUR PERSPECTIVE IS YOUR CHOICE**
Kyle Maynard is a Stoic, too, whether he knows it or not. When he says, "Our perspective is always our choice," he is echoing what the philosophers have always claimed—that there is no good or bad but only our perceptions. As he tackled each of his dreams, undaunted, it was the philosopher-statesman Seneca's words that he took most vividly to heart: "It is a rough road that leads to the heights of greatness."
When Kyle started wrestling in high school, he recounted to me, "People would say, 'You'll never be able to win a match.' They wouldn't say it directly to me necessarily, but I'd hear it through the grapevine." A lot of that doubt came from people whose perceptions blinded them. They did not see the hungry dreamer in front of them, only what was missing from him. They saw only what limited him and held him back—not that it might have made him stronger or more determined or that it might have some tactical advantages on the mat!
Some of the doubt and negativity almost certainly came from a place of fear and insecurity that existed in the minds of his potential opponents. What if this armless, legless teenager beat them? How would _that_ look? They were right to be afraid. Kyle not only won 36 matches his senior season but also finished 12th in his weight class at Senior Nationals, beating several state champions and higher-ranked wrestlers along the way.
Kyle used these fearful people's misperceptions and misunderstandings to his advantage. He found fuel in the haters. As Ralph Waldo Emerson asked, "Is it so bad, then, to be misunderstood? Pythagoras was misunderstood, and Socrates, and Jesus, and Luther, and Copernicus, and Galileo, and Newton, and every pure and wise spirit that ever took flesh. To be great is to be misunderstood." Obviously, I'm not trying to say that Kyle is on the same level as Socrates or Jesus or Galileo, but when it comes to guys who fought some uphill battles, you can find worse comparisons. Part of greatness is being doubted and facing difficulty, and it's precisely that struggle that contributes to their greatness.
A year later, Kyle decided he would try his hand at mixed martial arts and began the rigorous training. "MMA actually taught me a lot about myself," he said. "It was the first time that other people really voiced major disapproval with what I was doing." The State of Georgia attempted to ban his first match. The Georgia Athletic Commission refused to issue him a fighter's license—a prerequisite to compete in a sanctioned bout. The nay-saying grapevine from his wrestling days moved online, and they had no problem telling him exactly what they thought. Internet commenters were ruthless and relentless as they wrote about him in all of the major MMA chat rooms and communities online. They threatened him; they called him a legless freak.
"One of my core beliefs is that you have to have things that you're passionate about to go after and live to your potential," Kyle said to me. "I didn't want to be a pro fighter. I had no delusions about that. I just wanted to experience it. Because 99.9 percent of the fans of the sport would never step into the cage, and that's okay, but I didn't want to be afraid. I wanted to go in there and experience it."
The great ones look at every situation this way. They look at adversity as the lesson that moves them toward their goal, not the obstacle that keeps them from it. Fear drove Kyle's opponents and haters to lash out at him. It also drove them off the mat and out of the cage. It drove Kyle to test his limits and pursue his dreams with even more energy and purpose. As the great Lionel Richie put it, "Greatness comes from fear. Fear can either shut us down and we go home, or we fight through it."
This is why adversity is so important and why it is the second lesson in this book. First we have our vision, and then we run into obstacles. The real greats don't worry too much about this—it's inevitable, it's not the end of the world. Instead, this dose of reality is simply used as a challenge. To learn a new language. To channel their energy into their true path. To adjust their vision from fantasy into an actionable, realistic plan.
It occurred to me that this was the common thread in Kyle's life, as he repeatedly said to himself: "Okay, what is it that I should not able to do, and how can I do it? How can I figure out a way to do it?" It applied to tackling a ball carrier in his adolescent years, to speaking among giants in his late teens, and to climbing Kilimanjaro in his twenties. He was born without arms and legs, so he's simply had to modify and adjust and be adaptive to everything, to everyday life.
In this way, we must be grateful for our particular form of adversity, since it is the precise thing that helps us get to where we want to be. _What stands in the way becomes the way._ For instance, I was shocked to hear that not only does Kyle spend a lot of time working with veterans who've lost limbs in war, but when he meets them, he feels a kind of gratitude. Not reluctance or kinship or pity, but gratitude.
"I don't have any idea what it's like to lose my limbs. I was born without my arms and legs, so I have no perspective of that," he said. This is how it's always been for him. He was spared the enormous sense of loss and fear that these veterans feel. He was spared their pain, too, and the lingering effects of injury. Just think about the perspective it takes to live with that kind of attitude—to be grateful for something like being born with a disability because there are worse ways to end up where you are. That perspective and attitude inspire me. Whenever I seem to be having a "bad day," I think about Kyle and realize how much I have to be grateful for as well.
This is something that great men and women understand—that the actual problem, obstacle, or adversity is irrelevant. It's their mindset and response to it that matter. They learn from these obstacles what it is going to take to accomplish what they've set out to do. They learn the importance of persevering toward their vision _despite_ that adversity. They learn the language so they can tell the world what they want to do and who they want to become.
It's funny, when I was speaking with Angel Martinez, this came up almost verbatim. Like me, Angel ultimately became successful in business (way bigger than me, obviously!) through a combination of vision, talent, and perseverance, and he discovered early on that the path to self-esteem was sweaty and intense and competitive—and not where he first expected to find it. I thought I would find it on the receiving end of touchdown passes. It turns out it was at the end of 10 grueling track-and-field events. Angel thought it would be baseball.
"I wanted to play Major League Baseball, like every Cuban kid, but when I was a freshman in high school, I think I was about 5 foot 3 inches and 112 pounds. I couldn't hit or throw the ball out of the infield. I could field well, but that was about it. I could throw to first and second. That was okay when we were playing Little League, but when we got to high school, it was a whole other thing," he told me.
Like Kyle and me, one of Angel's childhood dreams ran smack into the unforgiving reality of physical limitations. And like us, he had to find a way around them. For Angel, it was running.
"What attracted me to running was that I could be as good as I wanted to be," he said. "In distance running, there's no coach who is going to bench you or tell you that you can't play. And the clock never lies. There's no subjectivity. I remember when I started running, the older guys on the team told me, 'We only have one rule. You can't stop. You can go as slow as you need to go, but you cannot stop. You can never drop out.'"
**SLOW AND STEADY WINS A DIFFERENT RACE**
If there is one thing you take from the School of Greatness about pursuing your vision and achieving your dreams, it should be this: You can go as slow as you need to go, but you cannot stop. You can never give up or drop out of giving your best in your life.
Angel unwittingly taught his own son Julian, a cross-country runner at Claremont McKenna College, this lesson. "He had always heard me talk about all this," Angel said of Julian. "Then I went to watch him at one meet, and he was about halfway through the 5 miles when he felt a really sharp pain in his shin area. He started slowing down, and I could see something was wrong. I went out there and said, 'Julian, what's the matter?' He was grimacing but he ignored me, and he finished the race." It turns out, Julian had broken his leg at the 2.5-mile mark. Two hours after the finish, he was in a cast. When Angel asked him why he didn't stop, Julian's answer was simple and obvious: "I don't drop out, Dad." Make no mistake, true greats never drop out.
Of course, you don't want to put yourself through any type of trauma or pain intentionally that will hurt you in the long run (more on the importance of experiencing pain in Chapter 5), but it is the idea and intention behind not giving up or dropping out on giving your best effort at all times. That is what we are talking about here.
"The lesson of running is about what it takes to be successful in life," Angel told me. "It is a metaphor for a lot of things you need to learn. Running, like life, is that constant confrontation of a challenge every day. Some days you don't feel that good; some days you feel great. Some days you're not inspired; other days it's pouring rain and freezing cold but you still have to go and run. As a kid, that's an incredibly important lesson to learn: that it takes commitment and you have to believe in yourself and that you can actually do whatever the hell you want. There's no limit to what you can do."
I discovered the same thing during my decathlon training, and I am reaping the benefits to this day as I train with the United States men's national handball team. There have been many moments when I didn't feel like training, especially after an injury. I've experienced many injuries over the past 4 years as I've trained for this new sport. I pulled my groin three times; I stuck a needle in my elbow multiple times to drain fluid; I've sprained ankles, broken fingers, and even took an elbow to the throat that had me spitting up blood for a week. The list of bumps, breaks, and bruises feels almost endless. But each injury taught me a lesson, and after each recovery, I took the necessary steps to keep moving and (hopefully) learn from them and use them to my advantage going forward. Once you experience the power of this triumph over adversity—over _yourself_ in many ways—it's enough to get you off the couch and back into the game. Kyle Maynard experienced it, too. He has experienced it every day of his life. But it doesn't just get him off the couch, it puts him on the side of mountains in the middle of Africa.
Kyle ascended Tanzania's 19,336-foot Mount Kilimanjaro as part of a nine-man team in early 2012. Unassisted by team members and unaided by prosthetics, he essentially bear-crawled on his elbows for 12½ days—10 days up, 2½ days down. Half a dozen people (with all their limbs) die on that mountain every year. To summit it at all is a serious achievement. To do it like Kyle did it, well, I don't think there is even a word for that except for _greatness_!
Kyle would disagree, obviously, because that is not how he perceives his situation. In fact, the truly striking thing is that the climb wasn't about him at all. Born in a US Army hospital to an Army dad, Kyle has always had a passion for working with veterans. This mission up Kilimanjaro was for them. The goal, he told me, was "just to send a message to some of our troops that have literally sacrificed their limbs for our freedom that 'You may have had this happen to you, but you're still able to go and create the life that you want. It may not include climbing Kilimanjaro, but you have something that you want to do.'"
At some point, adversity happens in everyone's life. It usually comes unannounced, and it doesn't arrive with flowers and candy. It takes different forms and hits each of us differently, but learning to address and overcome it is all about bending but not breaking in the face of the daunting situations it presents. It requires connecting your head and your heart to that deep well of energy within to push you forward in a positive direction.
Kyle had to do it 4 days into his trek up Kilimanjaro as his elbows and feet swelled in incredible pain and nearly broke him. Angel Martinez did it as a runner, struggling to push himself through every mile. The problem he faced, as he tried to run faster and farther, was that the shoes his team wore weren't very good. To get halfway decent running shoes, they'd have to go into Berkeley (he eventually had moved from the Bronx to the Bay Area) and buy shoes that had been imported by a company called Blue Ribbon Sports. The importer? His name was Phil Knight, and he went on to found Nike.
Angel saw these people making a living solving a problem in the sport he loved and thought: _Why not me? Why can't I make a living by connecting my current passion [running] with one of my earliest childhood passions [cool shoes]?_ Eventually, he started working at a small shop and bought half of it from the owner. A few years later, a couple of English guys walked in with a new brand they hoped he would sell. They called it Reebok.
This is what I mean when I say that the obstacle can be the way. If he hadn't been too short, if he hadn't felt like he had something to prove, Angel never would have found himself exposed to the business that changed his life—that became his calling. As Angel puts it, "There's always a challenge if you don't see yourself as a conventional person," so you'd better be prepared and ready for adversity—ready to make the most of it.
Whenever shit would hit the fan for me over the last couple years, I somehow automatically come back to Kyle and Angel and think, _Gosh, how could I possibly have anything to be ungrateful for?_ Sure, like anyone, I have things I can be unhappy about. I am not talking about being a Pollyanna or staring at life through rose-colored glasses. This isn't self-delusion. What I am talking about is looking at things with your eyes open. When I was younger, I would get down on myself if something bad happened or get depressed if I felt things weren't going my way. Now I remember, in a way that is real and meaningful, that I have miraculous advantages that many others have not had. If Kyle can accomplish all that he has, if Angel can go from a Bronx tenement to the corner office of a billion-dollar business, I can pursue my own dreams and strive for my own version of greatness without giving in to a bad attitude when things invariably don't go my way. Whenever I face adversity, I'm always reminded of the examples they set, and I am thankful for our friendship every day because of it.
When you're looking at things with your eyes open, with a different perspective, it is then that you truly see the opportunities at your doorstep and how you can use them to your advantage. At the end of the day, if achieving dreams was easy, then everyone would have done it and no one would suffer from that nagging feeling that either drives or depresses us. What makes achieving your dreams and fulfilling your vision that much more special is the hard work it takes to get there. Proving that adversity is no match for you. That's what this is all about!
**EXERCISE:**
**Embrace the Adversity (Internal and External)**
Adversity is difficulty or misfortune that, for most people, creates an unmanageable amount of stress. Those who learn how to use adversity to their advantage, however, possess the power to turn that adversity into greatness. This is easier said than done, of course, because no one actually _likes_ adversity. When you first experience it and you aren't prepared, what it feels like is failure. Adversity means failure, and failure means you must be bad at something. That's an awful feeling.
In reality, failure is simply feedback. It's not that you are bad or not good enough or incapable. Failure (or feedback) gives you the opportunity to look at what's not working and figure out how to make it work.
Everyone fails. Highly successful people fail many more times than the rest of the world and with much higher stakes at hand. Once we understand this, we can look at failure as something to fall in love with instead of something to shy away from. Thomas Edison endured 10,000 failures before he made the lightbulb, but each "failure" was feedback telling him that he hadn't figured it out yet and that this particular set of choices wasn't the right one for this particular task. His failures weren't evidence of his incompetence—if anything, they highlighted his brilliance and increased the likelihood that the next attempt would be the successful one.
Oftentimes the biggest obstacle we face is ourselves. Negative feelings, self-doubt, self-loathing; they all come from within to sabotage our vision. Adversity of all kinds will remain in your life until you adjust your perspective and embrace the messages failure is trying to send you. Listen to the feedback and apply it to your actions, and before you know it, adversity begins to melt away.
This is an exercise you can and should practice when those negative feelings threaten to overwhelm you. Consider it a daily practice until you fully start shifting and living consistently in a positive way that will support you and your vision instead of bring you down.
**_Step 1: Be Aware of the Adversity_**
Adversity happens to everyone, and though pain is inevitable, despair is optional. Discover precisely what the adversity is and why it is happening. This is your opportunity to take responsibility for every type of adversity that comes your way. Focus on the _why_ —the root of it.
There are two types of adversity.
**1.** **The minor daily adversities that come up from time to time:** Fighting in your relationship, not getting the raise you want at your job, getting parking tickets, receiving poor grades on homework, feeling exhausted and stressed, feeling unsafe in your environment, etc.
**2.** **The major singular adversities that are more rare:** A death in the family, a car crash, injury or illness, a major breakup, losing your job, going bankrupt, etc.
When you become aware that adversity is inevitable, it allows you to prepare for it happening in the future. What adversities do you face right now? What in your life feels like it is standing in the way of fulfilling your vision and achieving greatness?
Write your adversities down. Then identify whether they are chronic, daily obstacles that seem to grind your progress to a halt or big, singular moments of struggle that have thrown you off the path.
How have you been dealing with these issues to this point? How have you dealt with similar issues in the past? Have you overcome any of them? What did you do? There is wisdom and insight to be gleaned from your answers to those questions if not about what to do, then definitely about what _not_ to do.
If you're anything like many of my coaching clients and some of the great teachers you will meet in the coming chapters, the thing you did most often in the face of adversity when you were first starting out was either try to ignore it or avoid it. Sometimes you might even pretend it wasn't there. I know I've been guilty of each of those behaviors in my own past.
Needless to say, this is something you absolutely cannot do. You cannot avoid, ignore, or deny adversity. Be aware of which adversities you are facing and accept the adversity for what it is. Avoid it or resist it and it will only persist.
**_Step 2: Write It Down or Share It_**
Now that you are aware of the adversity, write down how it's making you feel and why you think it's making you feel that way. This helps let go of the stress you are feeling to a certain degree and gets it out of you, where it can be the most toxic and do the most damage. It also allows you to have a written record of what you are feeling over time so you can look for patterns and see areas of growth. Write it down with pen and paper. If you don't have that, put it in your phone or on your computer. Over time, you'll want this all in one place so you can refer to it, so keep that in mind. Get it out! Embrace it.
For example: I'm angry/stressed/frustrated because I had an argument with my girlfriend; upset that I lost my job; still shaking after I got in a car crash, etc.
If you hold this inside, it will only bring more adversity to your life. Remember, what you resist persists.
If you prefer to verbally express yourself, then find a dedicated "adversity friend" whom you can go to anytime you feel frustrated by failure or you're struggling through adversity. Make an agreement with this friend that is reciprocal—you'll always listen to them without judgment so they can purge their emotions, and they will be your sounding board in return.
In the next chapter, you'll read stories and go through exercises that will support you in finding resolution in these breakdowns.
**_Step 3: Acknowledge Yourself_**
Once you let the negative feeling go, replace it by acknowledging yourself for all that you have done that day/week/month/year. You are up to big things! Even if they seem small to you, they are always bigger than where you were earlier in your life. Most of the time, we are comparing ourselves to others in our family or careers, and we do more harm by comparing ourselves rather than giving ourselves credit for where we are along our journey. Acknowledge yourself for reading this—knowledge is power. Your good intention is there.
Examples of things you can acknowledge yourself for: being on time at work, consistently going to the gym or working out, eating clean, being your word, etc.
**_Step 4: Express Your Gratitude_**
It's hard to be upset when you are focusing on what you are grateful for. Verbally tell your significant other, a friend, a family member, or just someone around you three things you are most grateful for in this moment; then ask them what three things they are most grateful for in their lives. Obviously, you don't have to tell the other people that you are beating yourself up on the inside right now, but just be aware in the moment and shift into a conversation of gratitude. When you give, you automatically receive. It's amazing what a compliment to someone opens up.
Examples: I'm grateful for my amazing friends. I'm grateful for my health and that I can walk, see, and feel. I'm grateful for my family and the support they give me. I'm grateful for the bed I get to sleep on.
**_Step 5: Reconnect to Your Vision and Take Action_**
Return your focus to what you want to achieve and why you want to achieve it: your Certificate of Achievement and your Personal Statement Plan from Chapter 1. Then figure out the next step to making your vision happen, and take action toward it. Momentum helps build confidence and positive thoughts and feelings, so it's important to spring into action when you are down on yourself or feeling adversity.
Whenever you are in breakdown or battling adversity in any situation in your life, this five-step process will help you fight off the insidious nature of self-defeating negative thoughts and chart a positive path toward achieving your vision and becoming great.
**_COACHING TIP_**
Learn to fall in love with adversity. Don't fall into a victim mindset and look at it as the thing that is holding you back, but instead find the part of it that can launch you toward achieving your dreams. Remember, no one has ever achieved anything truly great without going through extreme adversity. That doesn't mean you have to suffer through every challenge. Balance out the difficulties that adversity brings by being grateful for what is good in your life and treat yourself with gentle care. Give yourself time to heal, be messy, and experience the painful feelings you are battling. It's okay. You are human. Beating yourself up during adversity is the worst thing you can do, so make sure to love yourself and surround yourself with those who support you and lift you up. Tune back in to your vision, your Certificate of Achievement, and the principles you stand for. Once you are ready, take the next step toward your dreams and living that perfect day. It's within your reach; you are closer and closer to bringing it to reality. Accept and embrace adversity. Failure is simply feedback. Use it and stay committed to your vision through taking action at all times. Don't stop now. Keep moving forward. You've got this, and I've got your back.
**_GET GROUNDED_**
There is a big difference between the person who gets great results and the person who gets average results. And it begins with the conversations in the space between their ears—with how they believe in themselves. When you start to believe in the gifts you have within you, you are already halfway to becoming great. To do this, you must accept where you currently are along your journey and understand that if you are not happy, you have the power to change it. All you have to do is learn the necessary skills and put in the work.
This chapter is about teaching you the skills necessary to develop such a powerful belief in yourself that your mindset won't be shaken even under the most extreme challenges. Take notes and prepare to equip yourself with a powerful inner voice and a deeper understanding of what it takes to become a champion. This isn't just a lesson for sports; it applies equally to life, love, business, and spirit.
**CULTIVATE A CHAMPION'S MINDSET**
_I understand that nothing is easy._
_I say everything happens for a reason._
_I dream of one day the world is in peace._
_I try to see the good in everything,_
_I'm a caring girl who loves to flip._
**—Shawn Johnson, seventh grade**
Michael Jordan, Serena Williams, Michael Phelps, Tom Brady, Janet Evans, Michael Johnson, Mia Hamm, Michael Schumacher (that's a lot of Michaels, but you get the idea). What is it like inside the minds of these champions and champions like them? From a distance, they appear superhuman or super lucky or both. They get all the calls, all the money, all the best parking spots. The ball always seems to bounce their way.
It's like they are living in a different world than the rest of us, and in a way they are. Their world is crystal clear. It isn't foggy and tumultuous and filled with self-doubt, like ours can be if we haven't clarified our vision, battled through adversity, and developed the proper mindset—the champion's mindset.
The champion's mindset is all about focus, flow, belief, and emotional intelligence. It is the complete dedication to your vision of future achievement. The way I have learned to describe it to myself when I do the visualization exercise you will learn at the end of this chapter is as a unique headspace that allows you to focus all your energy on putting yourself in the best position physically, mentally, and emotionally to be successful.
Don't misunderstand when I say the headspace is unique. I don't mean that only some people are capable of having it. I mean that the vision for greatness that defines your mindset and drives your effort is unique to you. I also mean that it is a mindset different than any other you will experience in your life.
I've tasted what it's like inside the mind of a champion. In fact, most of us probably have—we just didn't know it at the time. I didn't realize it the first time it happened to me; I just thought I was doing what needed to be done. I was simply focusing on the task in front of me, completely and totally. It turns out, that is a major component in the mind of a champion, and I learned it on the end of a 15-foot pole and a 40-meter runway.
It was the early summer of my senior year in college. I'd just spent the last 6 months stretching, pushing, pulling, lifting, and willing myself into the best shape of my life in preparation for the NCAA Division III track-and-field national championships in Waverly, Iowa. Held over 2 days, my event, the decathlon, would put all my hard work to the test. After breaking three ribs in the second football game of the season less than a year before, I had come back stronger than ever. I thought the injury had permanently derailed my dream of becoming an All-American, but the decathlon had breathed new life into the dying dream, and if I finished among the top eight competitors, that dream would become a reality.
When the competition began, I was pumped with adrenaline and feeling strong. On the first day of the 2-day event, I did well in some events and not so well in others. I entered the second day of competition right around ninth place, and I knew that I had to excel in the third event of the day, the pole vault, in order to reach the All-American podium.
In the pole vault, each competitor has to clear an opening height to score points. You get three attempts at each height after that, but if you fail to clear the initial height, you get a zero score for that event (which would essentially eliminate you from placing in the top of the competition). On my first attempt at the national championships, I opened at a height I cleared comfortably in practice: 12 feet. I was confident in my approach, ran down the runway, and leaped so high over the bar that I could have cleared 15 feet, but I ended up grazing the bar on the way down and watched it roll off the stands. No worries, though; I still had two attempts left and knew I'd make it on the next one. On my second attempt, I tried to run harder than before and in the process overstretched my footing and missed my mark. I stopped running about 2 feet ahead of my ideal takeoff spot and tried to compensate by lunging forward. I went straight up 15 feet in the air and fell straight back down on the runway, missing the bar completely. Suddenly, the third—and last—attempt took on unexpected weight and pressure. I was only 22 years old, but I felt like my entire life had come down to this moment. Make it and I have a shot at being an All-American. Miss it and my entire 22 years, along with the grueling 6 months of training to prepare for this moment, would be for nothing. That's how I felt. My dream of greatness came down to this.
The pole vault is all about strength, technique, and timing. For a decathlete, it is often a make-or-break event. In 1992, Angel Martinez's old company, Reebok, ran a giant advertising campaign in the lead-up to the Summer Olympics in Barcelona centered around American decathletes Dan O'Brien and Dave Johnson, called "Dan & Dave." They were two of the best decathletes in the world and favored to win medals. There was only one problem: Dan didn't qualify for the Olympics at the Trials. Want to guess why? He no-heighted on the pole vault, missing all three attempts. "Dan & Dave" became "Dave . . . and all those other guys."
My coach looked at me with a calm confidence through her piercing eyes, and strangely, instead of panicking, I began to visualize back to when I was 6 or 7 years old, sitting on the couch with my dad, watching football together and his explaining to me about the All-Americans we were seeing and what it meant to become one of them. The sense of honor and purpose, above the athletic achievements, stuck with me. It cleared away my current confusion and distractions. It lifted the lead weight from my feet. I was aware not only of exactly what I had to do but also of exactly who I was and what I was capable of. That moment put me into intense focus as I sprinted down the track with the pole, hitting my mark and launching myself over the bar with ease. Relief and joy hit me simultaneously. I went on to make a personal best, clearing over 14 feet, that day in the pole vault, and I finished strong in the next two events.
I became an All-American that day.
I have felt versions of that laser focus a handful of times over the past decade in many areas of my life besides sports, including business and relationships. It's addictive. Yet some of us have never felt it—we may not know that it is absent and what feats we're missing out on because of it. Some of us haven't even come close to feeling that state of peak performance and excellence.
I never performed remotely close to my best before that day in the pole vault. That isn't to say I didn't do well other times, but the difference between being good and being fully in the zone—truly in the head space of a champion—is a crucial ingredient in greatness, whether we're talking about sports, business, or life. And it was that day, lying on the vault mat, looking up at the bar still in its blocks 12 feet above my head, that I realized the power of accessing the zone for all areas of your life. I am calling it "laser focus" now, but I didn't fully recognize what I'd been channeling in that moment until I spoke with two amazing people: Steven Kotler and US Olympic gymnast Shawn Johnson—both fully tenured professors of greatness as far as I'm concerned.
Steven Kotler is the author of _The Rise of Superman: Decoding the Science of Ultimate Human Performance_. To say that his book is the one that I had been waiting for my whole life is legitimately an understatement. Growing up a skinny white kid in middle Ohio, all I ever wanted was to figure out what advantages I could get as an athlete to raise my game to the next level and perform at my peak in every sport. I wanted to know how to get in the zone like the All-Americans and world champions I admired—or, as Steven refers to it, the "flow state."
"Flow," Steven told me, "is an optimal state of consciousness, where we perform our best and we feel our best. In flow, we are so focused on the task at hand that everything else vanishes. Time either speeds up, so 5 hours will pass by like 5 minutes, or it slows down, like that freeze-frame effect in a car crash. Your sense of self, your sense of self-consciousness disappear completely, and all aspects of performance, mental and physical, go through the roof."
Yes! That is exactly how I felt as I sprinted down the runway on the track in Waverly, Iowa, drove the pole into the pit, and vaulted myself over the bar and closer to my dream. Talking with Steven, I realized I was wrong about one thing, though: This wasn't my first experience with flow. I'd had a similar experience on the football field as a sophomore 2 years earlier, in a game where I just felt invincible—unstoppable. It was my record-breaking game.
I remember in the first quarter they put one defensive back on me. Before I knew it, there were two on me and then there were three, with the safety shading over. Eventually, it felt like the whole team had been assigned to cover me, but it didn't matter how many people they put on my side of the field, what they did, or what they tried to do. The ball was still coming my way, and I was catching every one of them. I felt like one of the Green Bay Packers wide receivers in the Monday Night Football game against the Oakland Raiders in 2003 when Brett Favre played the day after his father died. They caught everything, no matter where he put the ball. That's what it was like.
The funny thing was, we actually lost the game by a touchdown (42–35), and I remember at the end of the game being more depressed than anything, feeling like I didn't catch enough balls or get enough yards. I had no clue what my stats were or what I had done, yet everyone was coming up to congratulate me as we were taking off our pads in the locker room. "Man, you had an unbelievable game. How many catches do you think you had?" I had no idea. I thought 8, 10 maybe, which was a good game for me or any wide receiver. But I didn't want to think about it. So finally I hit the showers, beating myself up, thinking, _What could I have done better? How could I have been a better teammate?_ I was the last one out of the locker room, just wallowing in my own misery of this loss, and my coach came up to me and said, "I just wanted to say congratulations. You actually broke a world record for the most receiving yards in a single football game: 418 yards."
Four hundred eighteen yards on 17 catches, including four touchdowns, to be exact. Yup. I was in a flow state. The kind that champions live in and greatness results from. To be honest, I was a little in shock at that moment. I was happy to hear the news that I accomplished something that had never happened before in the history of collegiate football (or any level), but I also felt responsible for our loss and was preoccupied with figuring out how I could have done things better. It was a bittersweet moment, but one I'll always remember, not only because of the record but also because I felt like Superman in that flow state, and I knew I wanted to feel that way all of the time, on and off the field.
Fortunately, flow doesn't happen only for athletes, I learned from Steven. The consulting firm McKinsey did a 10-year study of top executives in flow. They found top executives in flow are five times more productive than when out of flow. That's 500 percent more productive. DARPA* did a study with snipers, inducing flow artificially using transcranial direct stimulation and teaching snipers target acquisition skills. The snipers learned the skills 230 percent faster. In a separate nonmilitary study, DARPA also induced flow artificially and cut the time it took to train a novice sniper up to an expert level by 50 percent.
So that's what flow is and what it does, but how do you get it? How do you achieve the kind of flow state that leads to 418-yard receiving games, 230 percent increases in learning, or 500 percent increases in productivity?
"It's twofold," Steven explained. On the one hand, it happens "out of necessity. Meaning the level of performance has gone up so much that in the case of athletes, at least, if you are not in flow when you're performing, you're going to end up in the hospital or dead." I could definitely relate to that. With three guys covering me, if I go over the middle for a pass and I am not in flow, I am on the ground with the wind knocked out of me or with another case of cracked ribs.
The other reason it happens is because you've surrounded yourself with all the necessary flow triggers. True greats have basically created the most high-flow environment they possibly could. Everything in their lives is triggering flow. Psychologists talk about it as the source code of intrinsic motivation. Another way of putting it is that the five neurochemicals you get during flow—norepinephrine, dopamine, anandamide, serotonin, and endorphin—are the most addictive chemicals on earth. They make you quicker, faster, stronger, and more motivated. According to Steven, they do the same thing for your mental output that they do for your physical output.
Talk about an aha moment.
What Steven was saying is that flow is really all about mindset—how you perceive your situation and how you receive information. To be in flow, to sidestep adversity like it is nothing and vault yourself toward your vision, you need to have a champion's mindset.
There's a great quote by Bruce Lee in John Little's documentary _Bruce Lee: A Warrior's Journey_ that explains flow, when he talks about becoming like water: "I said empty your mind. Be formless, shapeless. Like water. You put water into a cup, it becomes the cup. You put water into a bottle, it becomes the bottle. You put it in a teapot, it becomes the teapot. Now water can flow, or it can crash. Be water, my friend. Like that, you see." The champion's mindset, to me, is becoming like water.
Though I'd tasted it in my life and found confirmation of my feelings with Steven, it wasn't until I met my next teacher that I saw these ideas in the living, walking flesh. You'd be hard-pressed to find, pound for pound, someone with a more powerful champion's mindset in the world than Shawn Johnson. At 4 feet 9 inches and 90 pounds and just 16 years old, with hundreds of millions of people watching live and on television, she won an Olympic gold medal in the balance beam and three silver medals in the team, individual all-around, and floor exercise disciplines at the 2008 Beijing Olympic Games. Then, as if to prove her remarkable determination was no fluke, Shawn gave the country a seminar on how to translate the champion's mindset into other areas of life by winning season eight of _Dancing with the Stars_ not long after she returned from Beijing.
From the moment I met Shawn, I knew she was the professor who could teach me how to cultivate the right mindset. I'm 6 foot 4 and she is a shade under 5 feet tall, so naturally we went and did a CrossFit workout together one day to see who could beat out the other in a battle of the fittest. This is my book, so I'm not going to say in print that she whipped my butt, but let's just say that she beat me (and the rest of the class) so badly that it was embarrassing. Not that it should be—this is a woman who has performed and won at the hardest level of sports, in front of billions of people, all before she was old enough to vote. Obviously she is physically gifted, but I think we would both agree that her triumph over me (oh, and the entire gymnastics world) had as much to do with the power of the right mindset as anything else.
"Gymnastics taught me everything—life lessons, responsibility, discipline, and respect," Shawn told me. Imagine the training and discipline she had to embrace at an age when the rest of us were playing video games and hoping for our first kiss. Imagine the focus and the clarity of purpose and the self-awareness it required. This is all part of the champion's mindset. For years, I tried to imagine it, but that part always seemed to be missing from my game. It was the part I could see in the greats and the athletes who practically lived in a flow state and to whom I'd always compared myself (all those Michaels). Yet I struggled with it, and continue to periodically, in life and business, even today.
The reason, I think, is because the champion's mindset is fundamentally about belief. If there's one thing I know about champions, it's that they all have a strong belief in something. Usually they believe they are the greatest thing in the world (like Muhammad Ali) or they believe they have been graced by the guiding hand of a higher power. All you have to do is listen to an athlete being interviewed after a big game to see this in action. The announcer says to them, "Congratulations on the win, you were amazing out there today! How did you do it?" And the player usually responds one of two ways: Either they say, "I want to give thanks to God for giving me these gifts and being by my side, as all the glory goes to him," or they grab the mike, look directly into the camera, and go on and on about how hard they trained and how no one can beat them and how they are the greatest competitor to ever walk this earth in their sport (think Floyd "Money" Mayweather Jr. in boxing). Regardless of the ego involved, it continues to be true that most of the _greatest_ athletes have such a powerful belief in themselves and their desire to accomplish their goals that nothing can stand in their way. Not even failure. It's this 100 percent confidence that they will achieve what they want that is a difference maker on the path to greatness.
I have accomplished a lot of goals since my days in Ohio. I've achieved success, earned a lot of money, but for years it was driven by anger, ego, and resentment. That's what fueled my passion to be successful, and it resulted in a lot of ups and downs. There'd be big moments, and then there would be vast lows of hurt, pain, insecurity, frustration, and loneliness. It was because deep down I didn't believe in myself and wasn't sure if others believed in me, either. I had a clear vision, I had more than my fair share of adversity, but this lack of belief prevented me from creating the kind of champion's mindset that would make flow state more readily accessible and greatness inevitable.
Another amazing person in the School of Greatness, 27-year transformation coach and leadership expert Chris Lee, talked to me in depth about this very issue. "I believe that the most powerful work we can do with ourselves is develop the strategies to uncover, redesign, and reinvent our belief system," he said. "Because the only way you're going to have your business be successful, the only way you're going to have your relationships be successful, the only way you're going to have your life be successful, is by elevating who you are being. You bring that into what you're doing, and that affects what you have. Because if we keep repeating the same thing over and over, we're going to have the same result."
Chris highlighted an issue that many of us face in our pursuit of greatness. We keep doing the same thing, oftentimes blaming external factors for our dissatisfaction, instead of looking within at our beliefs—at our mindset. There is a flip side to a strong belief in self, however, and it is one of the most powerful lessons I learned from my conversations with Shawn Johnson. It was about humility. The champion cannot allow ego and confidence to devolve into self-delusion. Belief in yourself has to be a weapon in your arsenal whose power you respect and revere; it can't be used like impenetrable armor that creates a sense of invincibility or superiority. That distinction can be the difference between achieving your dreams and being blindsided by failure (or getting to the top, then falling quickly once you are there).
Shawn used her belief as a weapon on the balance beam in Beijing. "She takes command of the apparatus," the commentator said as she worked through her routine atop the 4-inch-wide beam 4 feet off the ground. "You can see, she is in charge." She won gold because she was in charge of her belief in herself and therefore everything she encountered. This is not always the case for a lot of people.
"I've seen the type of belief in self that can be destructive," she told me. "Because if you are that person who says, 'I believe so strongly that I'm going to win, and I believe so strongly I've given my all,' you're not opening yourself up to be able to see and respond to what other people are doing in the actual competition. When that happens, it can become a cop-out when you run into adversity."
That is why an equally important part of the champion's mindset is the pursuit of perfection and excellence, independent of external results. This is very different from a drive to "win." Shawn, like many athletes, isn't obsessed with winning so much as she is with doing her absolute best: "I never focused on winning. Especially when I started out and I was in 30-something place out of 39 people. It was never about winning. I couldn't have cared less. I just always wanted to do better. I think the only thing that really made me want to work more and get on top of the podium was the feeling of pride you have when you're successful. It had nothing to do with a medal; that was just extra. It was knowing I had done my best and I was being acknowledged for it. It was about knowing at the end of the day that I worked as hard as I possibly could, and even if a score is worth the very last place, I couldn't be any happier."
Cultivating the mindset of a champion is not an overnight task. Vision, focus, discipline, belief in self, humility, and the pursuit of greatness are all the products of developed emotional intelligence—a fine art that requires a lot of practice. You never "arrive" at this point of knowing and having it all. Greatness is not something that is delivered to you or you are delivered to. It's something you have to work on daily. It takes years of dedication, discipline, and drive that persist in spite of any and all of the constant changes that inevitably occur with your health, business, relationships, and the world around you. If you commit to the process of developing this mindset for yourself, you will blow past every limit you thought was unbreakable.
Steven Kotler has shown us what flow is and why it happens. Shawn Johnson has given us the elements of the champion's mindset that are a prerequisite for flow and for greatness—foremost among them focus, dedication, and a belief in yourself that is tempered by humility. Chris Lee has implored us to reevaluate our personal belief system, the ideas and principles that undergird everything we are trying to do and become. Oftentimes it is those things that are impeding us on our journey toward greatness, not the external factors we love to blame when we run into adversity.
In fact, it wasn't until I had fully absorbed all these lessons that my podcast really started to take off. What most people don't know is that _The School of Greatness_ podcast began as an extension of my online business; it did not start with a grand plan. Fortunately, it gathered a little bit of steam over the following couple of months, thanks to the network I'd built up on social media. Still, it wasn't really going anywhere that I could point to because I hadn't truly articulated a vision for it (I had for myself—I wanted to pick all these great teachers' brains—but that wasn't enough), so it was impossible to develop the kind of focus I needed. As a result, any adversity I faced felt like a mountain instead of a molehill. Beginning with my work with Chris Lee, I started to turn things around and really focus on doing shows that reflected my personal beliefs and helped as many people as possible. Being in a space that I was very comfortable with not only gave me confidence in myself but also tapped into the energy and desire I had previously felt only on the playing field. Then, before I knew it, the podcast started taking off and now here we are.
But you might be asking, "How do you do it? What is the process?" Like Shawn Johnson, thousands of champions have turned inward to develop these positive attributes. Through visualization, meditation, mindfulness, and a focus on cultivating emotional intelligence, they have learned to tap into a powerful belief that they can succeed; that their vision is clear, their obstacles are surmountable, and their path to greatness is a reality.
I've developed a number of great exercises to help you with each step in the process: visualization, meditation, mindfulness, and emotional intelligence. Do these and the building blocks of a champion's mindset will begin to stack themselves.
**EXERCISE #1:**
**Visualization**
The purpose of visualization is to see the results you want to create, before they happen. This is something I did in sports every season (and continue to do in life on a regular basis).
In football, I wanted to be a great wide receiver, and I loved watching Jerry Rice. I'd watch his highlight reel over and over and visualize myself doing the exact thing he was doing.
The night before games, I would see myself on the field. I'd review every play in my head and imagine how I would run the routes perfectly, catch the ball perfectly, and run into the end zone every time.
A few hours before the game, I'd physically walk the field and see myself in position doing what I visualized and experience the feeling of making the big plays and winning the game. This process got me ready for anything and everything that might come my way and put me into position to create with my body what I had already performed in my mind so many times.
I do this every week for my personal life and business as well. This book is a perfect example. For years before writing this book, I would visualize myself walking into bookstores and seeing my book front and center on the big front tables right inside the doors. I would see myself at book signings, speaking in front of thousands of people and spreading these key lessons of greatness to leave a bigger impact on the world. I did this for years before I ever sat down to write one word of this book.
I also practice visualization before I call people on the phone, whether it's personal or for business. I envision what I want to create from the exchange—perhaps a particular result for a business deal, a feeling or experience I want the other person to have at the end, or how I want a controversial situation to resolve. I visualize the whole process.
Each night, I visualize what I want to accomplish the following day. Before giving speeches onstage, doing online webinars, and so on, I visualize what impact I want to have. You could do this before going on a date with someone, preparing a meal you want to create, or anything else you want to do in your life. Visualization is a powerful process. It puts your mind in a place to set you up for success.
**_Your Visualization Process_**
Create a clear space with no distraction. I prefer it to be in nature, which for you might mean at your favorite park or on the beach. Or you can do this in bed before you go sleep and right when you wake up. I've also been known to do visualization in the shower with the water rushing down and imagine myself in a waterfall.
Allow yourself to relax and be calm. Breathe relaxing breaths. Now visualize whatever you want to see as complete. Nothing negative, only positive outcomes.
If your vision is to be a father, visualize yourself holding your newborn baby, what that looks and feels like.
If it's to have a relationship with your soul mate, visualize yourself embracing that person, both of you smiling, and being whole and complete in that moment.
If it's to have a successful business, see yourself making the deals, walking into your office, helping your customers.
In each process, really dive into what it feels like: What does it smell like and taste like? What color is it? What sounds are you hearing?
The key to visualization is to see whatever it is you are envisioning as complete. Then ask yourself how you feel in that moment. What do all of your senses feel?
You can play music in the background if that helps you relax, or the process can just be silent.
I recommend you do this for at least 5 minutes every day, visualizing the outcome you have set out (no vision is too small or too big for this process). I also recommend doing this before attacking any big opportunity in front of you. Take a moment to visualize what you want to create before you enter that moment.
**EXERCISE #2:**
**Meditation—The 15-Second Centering Breath**
If the point of visualization is filling the mind with an image of where we intend to end up, meditation is about clearing the mind of everything else—all the extraneous distractions, obsessions, doubts, and trifling matters that keep us from focusing. It is something we need to do every morning when we wake up and every night before we go to bed (at least I find my days more powerful and intentional when I do it morning and night). You live the day of a champion by beginning as one and ending as one.
The key to meditation is to focus on your breathing and be aware of your breath. You want to unplug and simply breathe. Breathe in joy; breathe out stress. In joy, out stress. Allow yourself to feel connected to the world, to the universe, and, most important, to yourself. Anything that gets you disconnected from business, career, stress, and the rat race is great for you.
My favorite breathing exercise is something I've taken from another of the greats I've had the privilege of learning from, sports psychologist Jim Afremow, PhD. In his book _The Champion's Mind: How Great Athletes Think, Train, and Thrive,_ Jim talks a lot about the importance of breathing to perform like a champion.
"Under perceived pressure, we tend to hold our breath, and then we not only don't have the oxygen to our system that we need but also our muscle tension increases," Jim told me when we talked. "Muscle tension is the number one enemy in sports. If you're a swimmer, you're going to go slower. If you're a pole vaulter, you're not going to jump as high. Deep breathing helps to clear our mind of stress and expectations, and it relaxes our body. I think it's important to have either a meditation practice or, at the very least, to take a deep breath throughout the course of your day and notice whether you're breathing easily and deeply."
**_15 -Second Centering Breath Process_**
**1.** Breathe in through the nose if you can for a count of one, two, three, four, and five, expanding the belly.
**2.** Then hold it for a count of one and two.
**3.** Then breathe out through the mouth for a count of one, two, three, four, five, six, seven, and eight, releasing the air in the belly.
Be prepared, this is a big breath. It's not something you're doing all day. This is just to reboot your breathing. But the key is the exhale. It's a little bit longer than the inhale, and that's where you get the relaxation response.
"When we think about taking a deep breath, most of us just think about the inhale—taking that big inhalation. That's actually the stressful part," Jim made me understand. "Getting all that air out, that's the relaxation part and really helps you to feel your best."
You will be surprised how you feel if you do this before bed or before an important meeting or event. When we focus on our breathing instead of the things that stress us out or that we are afraid of, we don't allow the stress or fears to creep in. Go ahead and try this exercise right now and repeat it for four cycles (1 minute in total). Let me know how you are feeling at the end of it by sending me an e-mail at lewis@schoolofgreatness.com. Anytime you are feeling overwhelmed or stressed, come back to this breathing process for 60 seconds. It will give you the clarity you need to take your next step, wherever you are.
If you want an another free guided meditation from me to get you in the right frame of mind for your day, then check out schoolofgreatness.com/resources for additional resources.
**EXERCISE #3:**
**Mindfulness**
If you don't already have one, I want you to start a gratitude journal. I want you to write down your thoughts and express gratitude. Each night in your gratitude journal, be mindful of what's really working for you and what isn't working. Take the time to jot down everything you are proud of and excited about and to acknowledge yourself for these amazing things you've done. Then write down what you are committed to doing to move those things you are proud of forward.
For example:
_Today I closed the biggest deal of my life. I'm proud of myself, and it's a dream come true._
_Tomorrow I will continue to bring my [product/service/message] to the world to help more people._
Next write down all the things that you reacted to or that weren't effective and failed to get you the results you wanted. Look at what was missing from you in those moments (patience, love, courage, confidence, etc.). What are you committed to creating and who are you going to be moving forward in those kinds of moments?
For example:
_Today I didn't close the sale._
_What was missing was that I didn't have the confidence in my product and I was too pushy about the result of the sale instead of showing my care for the potential customer._
_I wasn't committed to being in a relationship with that customer. I will be connected the next time to understand their needs and wants instead of focusing on the result I want._
We think about these things in our heads constantly, but rarely do we ever speak them out loud or put them down on paper. Verbalizing and writing down these thoughts allow you to be aware and mindful of what you are creating on a daily basis and see what's working and what's not working in your life. Over time, you will create a record of what has worked and what has failed; what you have done to make things better and what you have (or haven't) done that has made things worse. You will spot patterns that will blow your mind. So even if you don't see results right away with this mindfulness exercise, recognize that you are doing the work to make results happen in the near future, when you will be ready to see and accept them.
**EXERCISE #4:**
**Emotional Intelligence—Be Present and Know Thyself**
The first key to greatness is having a vision for your future, but the best way to supercharge that vision is to be emotionally present so that you can give your full attention to the moment.
I love to salsa dance, and not just because it involves beautiful women who know how to move. I love it because it's something that forces me to be totally present and in the moment. If you are worried about how you look, whether you are doing something wrong, not being good enough, or if you're thinking about literally anything else other than that moment in that place, then your partner will be able to tell (and so will everyone watching you). To be good at salsa requires that you be present, that you be connected to what you are expressing in the moment and fully connected to your partner so you can lead them (or be led) to the next step or move during the song.
In that way, life is a lot like salsa dancing. You must be present, connected, and focused on making someone else smile if you want to create something meaningful each day. It's not always easy. Sometimes it can be scary to focus and put yourself out there like this, but it's extremely powerful and can create magical results!
You must learn to be confident with who you are and believe in yourself. All champions, even if they are scared, fall back on their belief in themselves and the work they've put in to get them where they want to be.
Emotional intelligence involves being able to shift in the moment and be aware of your emotions so they don't control you or hold you back; rather, you use them to move you forward. The more you develop emotional intelligence, the better able you will be to handle emotional situations in all areas of your life—with yourself, family, friends, and intimate relationships and in your career.
In short, emotional intelligence is the ability to understand and regulate your emotions and the emotions of others and be able to use that power to guide your thinking and behavior.
One of the key aspects of emotional intelligence is knowing yourself: your strengths and your weaknesses. Feedback is the vehicle you can use to achieve that. Feedback is information about how you are showing up to others and in the world. With that information, you develop greater, more highly tuned awareness of your strengths and weaknesses.
**_Step 1_**
List your five strengths and five weaknesses.
**Some examples of strengths**
Powerful
Passionate
Disciplined
Loving
Committed
**Some examples of weaknesses**
Controlling
Lack of discipline
Overanalytical
Fearful
Judgmental
**_Step 2_**
Contact three people who will be brutally honest with you and give you feedback about what they believe are your top five strengths and five weaknesses. When you have this information completed, put those lists side by side and identify what they have in common. This will let you know what you need to reinforce in your life (your strengths) and what you need to work on moving forward (your weaknesses). Also, it will let you know how calibrated your opinion of yourself is. Do you view yourself more or less the same as others view you, or are you completely delusional in either the positive or negative direction?
If you can be brutally honest with yourself, and you can find good people who will be brutally honest with you as well, this exercise is sure to give you a lot to reflect on.
**Bonus exercise:** Call someone from your past with whom you once had a strong bond but are now no longer in contact (a former partner in an intimate relationship, a friend from your past, or even a family member you lost touch with). Ask them as well to share what they consider your strengths and weaknesses with you. Their responses may surprise you, and I dare you to do it to see what lesson you gain from that conversation.
**_COACHING TIP_**
You have always been great, because you are unique, and _you_ will never happen again in the history of the universe. Most people don't believe in themselves or their abilities because they don't understand how insanely special they are. In fact, we all are special, and only we have the ability to believe in ourselves. Others can be there for us and cheer us on from the sidelines, but even with all the support in the world, some of us still sabotage ourselves. In the game of life, we hold the controls. We are the players who make the plays. Our inner voice—our belief in ourselves—is what determines our mindset. And our way of thinking sets us up for failure or success.
You have a choice. You can think average and get average results or think like a champion and reap remarkable rewards. Which one do you want? It actually takes only a little more effort to believe in yourself than it does to put yourself down. Make the decision to spend that energy on improving your mindset and doing things that give you confidence rather than bring you down. Always come back to understanding how unique and powerful your gifts are in this world. You are the one who needs to understand this first before anyone else can. Now go make it happen!
* * *
*DARPA is the acronym for the Defense Advanced Research Projects Agency. It is essentially the R&D division of the US Department of Defense. Lockheed Martin has its Skunk Works; the Defense Department has DARPA. Most famously, DARPA is responsible for the creation of the Internet.
**_GET GROUNDED_**
If I could attribute one thing to my success, it would be the topic of this next chapter: hustle. It started all the way back in seventh grade with the middle school basketball team. All I wanted was to make that team, to be part of something, and to contribute in a positive way. I wanted to be accepted and valued. I think we all want to feel worthy in the eyes of others, like we matter and that what we do is meaningful. This basketball team was my first opportunity to experience that in an organized fashion. Neither my body nor my skills had developed by that point, but more than anything, I didn't want to get cut (getting picked last was a big fear of mine, as it had happened before), so I ran around like a madman, dove everywhere on the court, and showed that I had all the passion and hustle in the world (a dream quality to any smart coach). I was willing to sacrifice my body unlike any other kid out there. While others didn't want to look stupid or were afraid to get hurt, I had a different vision. My efforts paid off. Not only did I make the team but I worked my way into a starting spot on my first-ever team sport.
It takes more than just hustle to be great, but you can't be great without that burning desire to do what others are unwilling to do. Sacrifice, in some form, will be a necessary part of the process, and whoever is more willing to sacrifice for the hustle will always succeed in the long run. Prepare yourself, as it's time to embrace the underdog within and step into your greatness.
**DEVELOP HUSTLE**
_No one is going to hand me success. I must go out and get it myself. That's why I'm here. To dominate. To conquer. Both the world and myself._
**—Unknown**
In 1991, a college sophomore studying music in the American Midwest made the mistake of selling some drugs to the wrong person. Until then, he hadn't done much more than smoke pot and sell some of it to his friends. Petty vandalism at his high school was as high stakes as his criminal career had been. Then, as these things tend to go when you're just 18 years old, he tried to push the envelope and test his boundaries. He started experimenting with hard drugs like LSD. But he was naive, and the brashness of youth got the best of him. He sold some of that LSD outside his circle—to an undercover policeman. And as if his luck couldn't get worse, like a scene out of a TV movie of the week, the judge, under pressure to make an example out of this young man, sentenced him to 6 to 25 years in prison.
It's a faceless, timeless story that transcends race, class, and region. A young kid makes a mistake that forever changes their lives and their family's lives as well. We are all too familiar with how stories like this usually end: The kid spends their most impressionable years behind bars and comes out worse than when they went in. Life on the outside is too difficult to contend with; habits learned on the inside are too difficult to shed. They reoffend; their crimes escalate. The cycle continues.
This story, however, is a little different. Because this young man didn't go back to jail. In fact, after being released in less than 5 years on good behavior, he went on to become one of the best jazz violinists in the world. He left prison with a fire lit underneath him—to practice, to repent, to humble himself, to hustle, and to do whatever it took to make something of his life. No task was too small, no gig was too tiny, no potential fan was too disinterested for him not to give it everything he had. And he did.
The story is a little different for another reason, too. That young man's name is Christian Howes. He is my older brother.
Chris's journey taught me one of the most important lessons I ever learned about greatness: _how to hustle._ No, not that kind of hustling—selling drugs on the streets. The good kind. The kind that makes you sweat and makes other people nod their heads and marvel at your work ethic. Of course, like most lessons in hustle, it did not start as all silver lining and no black cloud. It was born where necessity met adversity.
Chris went to jail when I was just 8 years old. It was a shock to all of us. I remember sitting in the car outside the courthouse, asking my mom what was happening and her just crying. I remember asking her why it was happening, but my parents wouldn't tell me, not until after he got sentenced. When the news spread and the neighborhood found out—which doesn't take long in a small suburban Ohio town—none of the mothers would let their kids play at my house. I was in second grade, and despite having my parents and my sister still there, I felt alone and helpless.
In retrospect, Chris's situation should not have been a surprise. Despite the musical genius that certified him a child prodigy, he'd been a troubled youth. "I hadn't been motivated," he said. "I didn't have goals. I was just coasting. It was jive." Still, none of what happened to him made any sense to me. It didn't feel real. I thought that only people who killed other people went to jail. Chris hadn't done anything like that. Plus, he didn't look like what I thought prisoners would look like when I was a little kid. He didn't have a smashed nose like a Bugs Bunny gangster. He didn't have a wild beard and crazy tattoos across his back like an outlaw biker. He was just Chris, my big brother, whom I looked up to. He was still a great guy, he just made some dumb decisions. And what's more, when I saw him in person, behind bars, he was still a hero to me.
That didn't alter the fact that this was a stunning and traumatic part of both of our lives. Prison isn't something a family usually comes back from intact. Chris would always be a convicted felon. I would always be the kid from the broken home with the older brother who went away. We'd always be "that family" down the street. If Chris had fallen into the trap that so many others do, he could have absorbed the trauma and spent his years in prison getting angrier and more resentful of the world around him. He could have blamed the cops, the system, or our parents. He could have just given up. The list of places outside of yourself to lay blame is virtually endless if you look hard enough. Instead, he made a clear choice: to overcome the stigma and the setback of his incarceration by resurrecting his life.
He rededicated himself to his musical gift. "When I got in there," he told me later, "I had a purpose. I knew I wanted to be a better person. I wanted to be a man and do something with my life." Music was going to be that something. He persevered against the monotony and put himself in the right mindset, scheduling time with the prison band every week. The only white guy in a group that played gospel, rap, R&B, and soul (Chris grew up playing classical music), he embraced the challenge and earned what would be considered a kind of prison master's degree in music appreciation and the resilience of the human soul. He developed an unrivaled set of skills—both mental and physical—that would set him apart in the world of jazz and spark his unlikely ascent.
To survive in prison, you have to overcome your own mind and protect yourself from everyone around you who is trying to take what's yours (your stuff, your dignity, your sanity, your freedom). You have to be strong, not just physically but also mentally—you can't give in to despair and lethargy. To have a chance on the outside once you're released, the challenge is the opposite—to break through the walls of people who don't want to give you anything you need (respect, opportunities, the benefit of the doubt). When Chris got out, he had to overcome the reality of being a convict and the opinions, biases, and fears of people he encountered as he tried to build his career. He did this with a freakish combination of passion and hustle—both in prison and out.
**SHAMELESS URGENCY**
There's a great quote from Publilius Syrus, a former slave in Roman times, who became famous for his wisdom. "Do not despise the bottom rungs in the ascent to greatness," he said. He was basically saying, you are not too cool for school. That was Chris. When he first got out, he would perform anywhere. He started by playing for free at local restaurants just to put himself out there and build a name for himself. Then he'd do hotel lounges, late-night dive bars, tiny jazz clubs with five people in the audience. He would play whatever time slot they'd give him for however long they needed him to play. He would put 100 percent of his blood, sweat, tears, and soul into each performance to blow the doors off the place. His passion ended up blowing the doors off places that didn't even have doors.
"When I got out, I was not afraid to promote myself," Chris said. "Most people can't get over that fear. In the arts world, you're supposed to stay cool, man. Just do your music, and it will come to you. I said, 'Fuck that. I know what I want to do. I want to be a great jazz violinist, to go onstage with great musicians,' and so I pursued it zealously."
After his final number in every set, Chris would get back up on the mike and promote the hell out of himself. He would thank them all for listening to his music, then grab his stack of CDs and go up to each person at each table in the club trying to sell copies. He was not afraid to put himself out there. Once when I asked why he sold his work so hard, never taking no for an answer (even when the person was saying, "Not a chance!"), he told me: "There's no shame in my game." And he was right. He was shameless but genuinely putting himself out there, and it worked—people bought his music.
Chris was tapping into something that I think 18-time Olympic gold medalist Michael Phelps described best when he talked about his swim training with Piers Morgan on CNN: "If you want to be the best, you have to do things that other people aren't willing to do." I watched with amazement as Chris pulled out all the stops, persuading customers to invest in his recordings and his future. It was about survival for him, about providing for his young family by doing work that he was fortunate enough to be exceptionally passionate about. He was willing to do whatever it took: "You have to chase opportunity whether you are an entrepreneur or an artist—especially for me, because I had to make up for so much lost time."
The irony is, we're all making up for lost time. That is the essence of hustle in the pursuit of greatness—doing whatever it takes and chasing opportunity with great urgency, like your life depends on it. Because it does. Greatness is really the survival of your vision across an extended timeline, based on your willingness to do whatever it takes in the face of adversity and to adopt the mindset to seize opportunity wherever it lives. After all, greatness is not something that comes to you; you go to it, and it's always moving. You slow down, and it moves farther away. You stop, and it disappears over the horizon.
Since those days in tiny jazz clubs and no-name festivals, Chris has toured the world, been on the cover of magazines, played Lincoln Center and Carnegie Hall, and collaborated with greats like Les Paul, Greg Osby, D. D. Jackson, and Spyro Gyra. His list of collaborators and clients is literally as long as my arm. He was a professor at the prestigious Berklee College of Music and set up a highly successful jazz violin camp where professional violinists from all over the world come to learn from him. All of that should have surprised me, but it never did, because he understood the importance of hustle in the pursuit of greatness.
**GET UP AND DUST YOURSELF OFF**
I was not a happy kid during Chris's years in prison. I was never the smartest kid in class. In fact, I was the opposite. I was ugly and awkward (at least until high school). I was lonely. I didn't have friends. I was picked last for everything. I remember telling my teacher a number of times, "I wish I was dead." I got called into the principal's office once in elementary school because I'd been getting into trouble. I said it to him, too, right there in his office: "I don't know what the point is. I probably shouldn't be alive." I didn't feel like I was ever going to matter.
I was 12 years old and smack in the middle of the worst period for most young guys—middle school—when Chris was finally released. It was the best day of my life. He called us on my dad's car phone in a 1988 Oldsmobile. "Order us a couple large pizzas, bro!" he said. "I am coming home!" When he walked in the house, he gave me this huge hug, and it was everything I needed. I had been so filled with all sorts of frustration and painful, confusing feelings. I finally had someone around whom I looked up to, whom I admired, who had also gone through pain and turmoil.
But it wasn't commiserating over our bad luck that was so important—it was his response to the negative circumstances and his ability to lift me out of the hole I'd sunk into. He didn't lie down and cry, like I so often wanted to (and did) as a little kid. He got up and hustled his ass off. He said to me at one point, "I can't go down any farther. I've already been to the bottom. I've embarrassed myself and my family and let everyone down. There's nothing I'm afraid of now, especially looking bad." In those early days, when he was playing at restaurants for free, it's not like he was calling ahead to schedule with a booking agent. He would just show up. He would go door to door until someone said yes. He created something from nothing. He had to. His back was against the wall. He was committed to his vision of being the best jazz violinist he could possibly be, and no amount of adversity was going to stand between him and his ability to make a full-time living at his passion.
Watching him do that—sitting there by his side as he defined his dream, knocked down every obstacle in his path, and then doggedly chased down greatness—was utterly transformational for me, almost more so today, now that I understand how special it was. Chris's passion for music and the hustle he displayed reaching fans and making new ones are what inspired me to get off my sister's couch in Columbus all those years later. For more than a year, I slept on that couch, 6 months of that time in a full-arm cast after a career-ending wrist injury that led to a painful surgery during my first season playing professional football. With no money to pay off my credit card debt and student loans and no college degree, I was left wondering if I had any hope of regrouping and figuring out why I was put on this earth, let alone of defining and achieving the greatness within me. My whole existence had been built on a foundation of becoming a highly successful athlete, and even though I had achieved those early All-American dreams, I was now languishing in self-pity because I'd washed out of professional sports. My vision was dashed; I was depressed and lost.
What Chris's hustle after prison made me realize was that I wasn't depressed because my vision was dead. I was depressed because I hadn't done the work to pick myself up, dust myself off, and figure out what was next. The hustle wasn't over; it was just different and shifted in a new direction.
Soon after that epiphany, I reached out to a number of people for guidance—my father's friends, coaches, my brother (obviously, why not go right to the source?), even the headmaster of my university, a man named Stuart Jenkins. I admired his wisdom and his moral courage. Stuart was hired to make changes and improve the university, and his decisions to cut underperforming members of the faculty were not popular. But his efforts vastly improved the academic standards of the school, and he proved to be an effective leader. He would often say to me, "Is this serving you?" rather than telling me what was right or wrong.
During that period of uncertainty, Stuart suggested I check out LinkedIn.com, the social media Web site, which back then was just starting to get serious traction among business professionals. I saw all sorts of potential to connect with high-profile business owners and other professionals there, and I began connecting with people like a madman. I reached out specifically to people who worked in the sports business because I had just come from my own experiences playing professional football, and I figured that would be a strong connection point to people I'd barely heard of in some cases and, in each case, never met. Lucky for me, I was right and got a high rate of acceptance.
In the first year, I made 10,000 connections! It was crazy but incredibly exciting. I became what Malcolm Gladwell called in his best-selling book _The Tipping Point_ a "connector." It didn't happen overnight—I built these relationships one by one with passion and energy. I would meet people in person, talk to them on the phone, introduce them to others seeking their skills.
It was around this time, with my professional sports career over and my cast off, that I started making a little bit of money by hosting "LinkedIn networking events" around the country. Over the following year, I hosted 20 events in major cities, where 300 to 500 people would attend. They were amazed at how this 24-year-old former pro athlete kid with no degree was able to get so many people to show up at these professional networking events. What they didn't know was that I was literally e-mailing my LinkedIn connections one by one to ask them to come to my events or join one of the groups I'd created to bring everyone together. I adopted the approach Chris took right after he got out of prison—there was nothing I wouldn't do. I'd already reached my bottom, so the only direction was up. E-mailing everyone individually wasn't sustainable at the rate I was growing, obviously, but it kick-started everything I'm doing now and taught me valuable lessons about hustle—first and foremost that you have to be willing to do the work that others are unwilling to do if you want to succeed when starting from a position of disadvantage.
I eventually built this presence on LinkedIn into an incredibly lucrative online business. I had no background in building a business, but I pulled myself up by the bootstraps, went with my gut, took advice from mentors, and worked my ass off. There were no days off, no coffee breaks. I applied Chris's hustle strategies to the launch of the business, adjusting his tested methods to the practical realities of building a different kind of business from the ground up. The end result: The money started flowing in, when only a couple years earlier, I had no clear idea how I would ever make any money.
My inner frustrations and early fears are what drove me to hustle. I didn't want to be a failure. I didn't want to remain unseen. I was going to work my butt off and go through as much pain as I needed to bear. This, in part, is what powers me through a bad meeting or a failure even today. Even more so today, I'm driven by my vision to inspire others to reach their greatness, and it's what keeps my hustle so strong even in my darkest, most difficult days.
**THE CURSE OF DAVID: WORKING HARDER _AND_ SMARTER**
The best hustlers are all underdogs. Even if they're not, they view themselves that way. They have a chip on their shoulder, or they chase something bigger than they are, because it's harder to hustle—to give it your all—when you're in the lead. You have nothing to judge yourself against or chase down besides the finish line. You're always more productive when you're the underdog—when you're David, not Goliath.
Just ask Tom Brady. Brady is arguably the best quarterback in the NFL. He is a no-doubt Hall of Famer; he has four Super Bowl rings, three Super Bowl MVPs, two kids, and one beautiful supermodel wife. Yet he plays with the fiery, junkyard-dog intensity of a Davidian underdog every game because he's got a Goliath-size chip on his shoulder. Not only did he come to the University of Michigan and land _seventh_ on the depth chart (the lowest-ranked quarterback on the team), but once he battled his way into the starting job as a junior, he had to fight off another quarterback, Drew Henson, whom the coach platooned him with the entire first half of his senior season. Then, in the 2000 NFL Draft, despite setting records at Michigan and earning Big Ten all-conference honors, he wasn't drafted until the 199th overall selection in the sixth round—a compensatory pick, no less—by the New England Patriots. Actually, to say that the chip on Tom Brady's shoulder is Goliath-size is an understatement. It is the size of the 198 guys picked before him and the 29 teams who had four or five chances to draft him but chose not to. He works harder than everyone to show all those people what's what. He is a true David in that sense.
My middle name is David, so I've always naturally gravitated to that biblical story and the position of the underdog. In fact, I've felt like an underdog at nearly every point in my life—ever since childhood, when I was picked last for sports teams or, worse, not at all and forced to play by myself alone after school because no one wanted to be my friend. It is part of what has driven me to outtrain anyone and be better than everyone, because I'm not always going to be the biggest, strongest, or smartest. And when that happens, I still have to figure out a way to win no matter the circumstances, whether that means having the most energy, passion, or desire. If I have to, I'll be like a banshee out there. I'm always willing to put in the time and energy because I remember what it was like in elementary school to be picked last for everything and feel like life wasn't worth living.
Hustle isn't about working smarter instead of harder. It's about doing both. Hustlers are better _and_ badder. They take their place in this world, they don't wait or hope or pray for it to come or for someone to hand it to them. And it's that Davidian underdog chip on their shoulder that often gives them the extra push when greatness seems at its most fragile.
In this way, Chris is literally and figuratively my brother-in-arms. But my sister-in-arms is Marie Forleo. Marie is an author, a TV host, and a business coach. She calls herself a "multipassionate entrepreneur," which is another way of saying she's a junkyard dog who attacks everything she does with passion and hustles her butt off, even the stuff she doesn't love to do or she knows isn't going to be what she does for the rest of her life. And she does it for a reason.
"So many opportunities have come from me training myself to show up like a champ wherever I was," she told me. "I got my first job on the floor of a Wall Street trading firm because I did such a good job on this one person's cappuccino at the place I bartended during college. He was like, 'You care so much about what you're doing, what do you want to do after you graduate?' I told him I was a finance major but I couldn't see myself in corporate finance or behind a desk. He said, 'My brother works on the floor; give me your résumé.'"
Part of me couldn't believe that was all it took to get a job on Wall Street, but the other part of me knew from watching my brother, Chris, that you can never underestimate the power of hustle. It can unlock a ridiculous amount of opportunity and potential. Even after Marie left her Wall Street job, she continued to approach her life with the same energy.
"I taught hip-hop at Crunch [a fitness center], and I didn't think I was going to teach hip-hop forever, but I wanted to be the best hip-hop instructor I possibly could be. And because I taught a good class that was always filled, the higher-ups chose me to audition for a new Nike program."
The result? Marie became one of the first four Nike "elite trainers"—a group who got to travel all over the world. She didn't wait around hoping someone would recognize her talent. She shoved it right in their faces and made it impossible for them not to see.
"The opportunities that can come when you do that, you can't even predict," she told me. "When you show up with that attitude of 'I'm going to master this, I'm going to bring my A game,' you feel better. You have more energy, and the results are going to be better."
Once Chris got out of prison, he wasn't waiting for anyone, either. He didn't expect anyone to feel sorry for him or give him the opportunities he always dreamed of—nor could he in his industry—so he went out and hustled to make his vision a reality. Les Paul, the famous guitarist, once remarked, "It used to be you could hardly find a good jazz violinist, but nowadays there are four or five really good players." I think that competition from all these players who hadn't lost 4 years on the inside was what drove my brother to be the best. It's what made him hustle—to try to carve out a space for himself. And if Les Paul is any judge, Chris's work has paid off, because even though there are now four or five really good players, he also said, "There is nobody better than Christian Howes." If there was such a thing as a mike drop in jazz violin, this would be it.
**FALL IN LOVE WITH THE ART AND PAIN OF THE HUSTLE!**
A Japanese proverb says, "Vision without action is a dream. Action without vision is a nightmare." You need both vision and action to achieve great things. Vision guides you; action propels you. But most people settle for the dream, because it is free and easy. It doesn't require action or hustle, which comes at a heavy price sometimes. Most aren't willing to pay that price. This is yet another place where true greats distinguish themselves. Muhammad Ali once said, "I hated every minute of training, but I said, 'Don't quit. Suffer now, and live the rest of your life as a champion.'" Training? Suffering? That is the hustle.
Earlier I joked that if you don't have a vision that gets you out of bed in the morning, go back to sleep until you find one that does. I mean that—it's absolutely critical. At the same time, truer words have never been spoken than by Jonathan Swift when he said, "I never knew a man come to greatness or eminence who lay abed late in the morning." Your vision is what makes you want to get out of bed. Ultimately though, you have to do it _._ And you have to do it over and over and over again with every ounce of energy that you have, even on those days when you hate the suffering the most—especially on those days, in fact.
Do you think during the high school football preseason I enjoyed doing three-a-days in the heat of the summer while other kids were off at the pool flirting with girls? Hell no! It sucked like no other. But I'm a two-sport All-American, I became a pro athlete, and, as a result, I play for my country with USA Team Handball, the men's national handball team. Those guys who were taking it easy at the pool when I was killing myself . . . what are they doing now and what do they have to show for that? I have no idea, and neither does anyone else. And that's the point.
If there is someone who has a right to hate the hustle more than anyone, it's Kyle Maynard. Born with profound physical limitations, every day that he perseveres against the adversity laid before him should be a victory. But not for Kyle. His vision for greatness required not only that he stand up to those who stood in his way but that he put in the work to prove them all wrong and succeed in spite of them. The authorities who didn't want him to fight mixed martial arts and the parents who objected to him as a high school wrestler were no match for someone who was zero percent talk and 100 percent walk. He pushed through day after day and was so earnest in his efforts that he got his shot in both arenas. ESPN didn't just magically hear about Kyle's climb up Mount Kilimanjaro—he didn't wait for good things to come to him. He went out and hustled, promoting it to whoever would listen. He brought attention to his cause with unrivaled passion because he believed in it and wanted his message to get out.
Shawn Johnson talked to me about hustle and passion, too, particularly with respect to talent. So many people think they can skate by on talent to reach their goals and accomplish their dreams. She is firmly in the camp of Team Hustle. Why? "You can be the biggest or the most talented person in the world, but if you don't love what you do, then it's not going to show and it's not going to work. And you don't necessarily have to have the greatest talent, but if you work for it and you love it, then you'll have better results." She is absolutely right.
If Shawn is on Team Hustle, then its captain has to be Angel Martinez. He is pure hustle. He was a great runner not because he was naturally talented but because he was willing to work harder than everyone else. He had grit. It began when he was a grade school kid in the Bronx picking up hundreds of two-cent glass bottles to buy a new seven-dollar pair of Cons. It continued to work for him on the cross-country team in high school as much as it did years later when he was going from meeting to meeting trying to turn Reebok into a global footwear brand.
The difference, I have discovered thanks to so many of these great mentors, between those who achieve greatness and those who cannot get beyond mediocrity is very closely tied to how hard they hustled. My brother showed me the power of hustling to change even the most challenging of circumstances. Chris wasted his natural talent for years, getting distracted by drugs, trying to impress too many losers at school. He went to prison and nearly lost everything. But his passion for music and becoming a better man to make something of his life gave him the direction and the energy that propelled from a prison cell to the practice room every day for 20 years.
I know that's easier said than done. So far, I've only given you the Nike approach to hustle—Just Do It. But hustle is somewhat of a difficult discipline for people to wrap their heads around (most hard things are). It's not something you can learn. It's something you just have to put into action.
The question is, what holds people—what holds you—back from developing it? It's usually not a lack of energy. Everyone is capable of hustling. But we always seem to leave something in the tank; we go at half speed. We don't have that sense of shameless urgency. We won't get up and dust ourselves off. We won't embrace the harder, smarter work of David to the Goliath of our competitors or our haters. We won't just grin and bear it and do the work. Why? In a word: _fear._
**Fear of looking bad:** We don't want people to see us sweat or struggle, and we are afraid of what people think about us.
**Fear of failure:** We must remind ourselves that we will fail 100 percent of the time we don't try.
**Fear of success:** At times we fear our success greater than our failures, because some of us don't want to be put in the spotlight or be required to lead when we succeed.
So how do we step away from these fears in our heads and step into action? Part of the process is understanding, as the 18th-century English writer Samuel Johnson did, that "true greatness consists in being great in little things." Baby steps, essentially. Turning small things into great advantages through hard work by flexing the hustle muscle. It's a skill all the professors in the School of Greatness have mastered at some point along their paths. They understand that you don't just go from starting quarterback of your high school team at 16 years old straight to the Super Bowl, because even if it were allowed, they know you aren't ready for it at that age. You must go through the necessary progression to gain experience, wisdom, and years in college before you are allowed to compete at the NFL level. Then only a small percentage of the best players in college football make it to the NFL. Then only one team a year can win the Super Bowl. It takes years and years of doing the right things to set yourself up for the chance to achieve greatness for something at that level.
All that being said, it's never too late to start. It's never too late to hustle in pursuit of your vision. In 2011, the Jazz Journalists Association nominated my brother, former inmate #260873, for Violinist of the Year. In 2012, he was selected for the prestigious Residency Partner Program from Chamber Music America for his educational outreach work with school music programs. In 2014, the US Embassy in Kiev invited him to tour Ukraine and serve as a cultural ambassador. It wasn't raw talent that got him there; it was his relentless drive to make up for the lost time he'd frittered away as a young man. And that is the lesson that has made all the difference in my life. If I could give one piece of advice to a budding entrepreneur, it would be that—just one word: _hustle._
**EXERCISE #1:**
**What-If Scenarios**
When my students notice their minds falling to any of these fears that hold them back, I give them an exercise to calm their thoughts and get them back to a grounded place of principles and vision that will lead them into action.
With pen and paper or a journal, find a comfortable and quiet place where you won't be interrupted.
Think about your vision and your goals. Imagine the hustle required to make them a reality. Now write down all of the things you are afraid of if you throw yourself headlong into the hustle. Allow yourself to experience the feeling of fear while you write these things down.
What if I look stupid?
What if I mess up?
What if I lose my investment?
What if I go broke?
What if I ruin the relationship?
What if I get fired?
With each what-if, write out all the things that could go wrong, including the worst-case scenario. _What if I get fired . . ._
. . . and my wife leaves me?
. . . and we lose the house?
. . . and we have to live in the car?
. . . and my friends stop talking to me?
. . . and I can't find another job?
Let it all out onto the paper. Experience the fear with each possible outcome. Now redirect each what-if into a potential positive outcome. _What if I get fired . . ._
. . . and it turns into a better job in a few months?
. . . and I can use the severance to take a well-needed family vacation?
. . . and I can spend a month reconnecting with my kids?
Turn every what-if into a positive redirect of "what could" be created instead. Again, your vision won't come to life without your assuming some risk or taking some action. Mistakes will happen no matter what. It's part of the game; it's part of life! Fear is a necessary component of that—it helps you calculate the risk—but you can't let the fear make the decisions for you. You must feel the fear, process it, and do what you need to do to achieve what you've set out for yourself.
A lot of times we don't hustle because we are afraid of the negative potential outcomes. But if we use that fear, process it, and shift our thinking toward the positive potential outcomes, we can turn that fear into faith. When people hustle, it's not because they have no fear—it's because they've harnessed it instead of letting it harness them.
**EXERCISE #2:**
**Working the Hustle Muscle**
There is a popular saying in entrepreneurial circles that goes something like this: "Entrepreneurship is living a few years of your life like most people won't, so that you can spend the rest of your life like most people can't." What they're talking about is hustle. Hustle is about taking consistent action over a period of time in order to build momentum and create the kind of leverage that makes things easier in your life over time. Not surprisingly, this is also the recipe for greatness. It's achieved through consistent action over a long period that begins well before the season begins or opportunities arise.
Everything I've ever been successful at has involved, whether I knew it at the time or not, massive action by being clear about my vision and doing whatever it takes to achieve it. But hustle isn't just about taking consistent, massive action every day toward what you want—it's about taking smart action as well.
There are four smart areas everyone can and should be hustling in:
**1.** Your body
**2.** Your mindset
**3.** Your relationships
**4.** Your skills
Hustle is a muscle. It's something that takes time to develop into a powerful momentum-building machine. To develop your hustle, you must embrace it and fall in love with the process. The daily journey of developing yourself is, in fact, hustle itself, and over time you'll see massive results from it. Here's how I approach it, plus an exercise on how to develop your hustle muscle.
**_1. Your Body_**
Do one thing every day that makes your body healthier and stronger. Something that is painful (the good kind of pain) and requires you to push yourself physically at the gym, on the bike, or during your run. Something that makes you feel uncomfortable, that you'd rather not do. It's this consistent habit of doing something that is painful and uncomfortable that will increase your pain threshold and make you stronger in all areas of your life (in Chapter 5, we cover the steps to mastering your body even more).
**_2. Your Mindset_**
Do something every day to improve your mindset and your way of thinking. The greatest minds question everything. They see the world where anything and everything is possible (even if it sounds absolutely crazy). This process could be:
•Reading a thought-provoking book
•Listening to an inspiring podcast
•Going to a workshop
•Learning from a coach or mentor
•Asking questions about everything (allowing yourself to be curious)
•Understanding that you can learn something from everyone
•Studying meditation and different philosophical ideals
**_3. Your Relationships_**
A leader is someone who understands that relationships are the key to success in business and life. How well you understand people, your compassion, and your ability to flow through others' emotions in stressful situations influence how deep you can go in relationships. But it's also important to know and be known by the influencers in your industry to achieve greatness in your career, business, or brand. If you follow any of the following steps, you'll be setting yourself up to win in the area of relationships.
•Connect with three new people each week in your industry in person, by phone, or online.
•Connect with three influencers each week (any industry).
•Share a meal with three people each week (breakfast, lunch, or dinner), like the great Keith Ferrazzi recommends in his book _Never Eat Alone_.
•Go to one group event every month—a networking event, breakfast meeting, mastermind group, etc. (Mastermind groups have been a key ingredient to my making seven figures in my business, and I dive into how to join and start your own mastermind in Chapter 7.)
•Send video messages online or via phone to your connections. Don't do this just on birthdays but also make it a point to follow up to see how you can support them with anything they are doing, and ask what their biggest challenges are right now. For example, I like to e-mail friends and just let them know how much I appreciate all of the work they are doing in the world, and I talk about something specific I see them doing at that time. Don't ask for anything in return or do it for any reason other than to show how much you care. This will stand out in their minds and deepen the relationship.
•Ask questions and make the conversations about others, not about what you want. When you focus on giving support to those you trust and believe in, they will almost always want to offer support in return.
•Show up at industry conferences, trade shows, and summits.
For many of you, this will come naturally, but for others who are more introverted, this will require stepping out of your comfort zone and developing a stronger mindset (as in Chapter 3). If you are going to events in person and feel uncomfortable at first, simply find a friend whom you can attend with to ease the anxiety, or start with smaller group events and grow from there (more on relationship building in Chapter 7).
**_4. Your Skills_**
Whenever you are in transition or you feel stuck, it's not the time to hunker down, it's the time to hustle and learn new skills. The more skills you have, the more you have to offer in any situation—it's like you've added a new tool on your tool belt to handle any situation in business and life. I'm constantly learning to master new skills and taking on new challenges each year. These are just some of the skills I've picked up over the past decade based on the dreams and passions I have in my life.
•Learning the guitar
•Salsa dancing
•Joining Toastmasters and improving my public speaking
•Picking up a new sport (Team Handball)
•Learning how to write books
•Learning how to build Web sites and grow a following through social media
•Learning to be a coach and workshop facilitator
•Podcasting and editing
•Learning meditation
•Learning acrobatic yoga
•Learning CrossFit, yoga, and different styles of strength and fitness training
•Learning how to make money
•Learning how to invest money and start and launch a business
•Learning how to manage my emotions and let go of my reactive ego
•Learning breathing techniques
•Learning how to hire a powerful team for my business
All of these are things I didn't know how to do when I was growing up or in college. It took time to learn and master these skills, but now because I can pull them off my tool belt at any time and access them in different areas of my life, I'm able to get where I want to be much easier and faster.
Write a list of 10 skills you want to learn. Start with the one that excites you the most and create a game plan for how you will learn it over the next 6 months. It could be a new language, graphic design, a new instrument or hobby. Also think about the skills that will support you in your relationships, your mindset, and your body, as those will be key to supporting you on your path to greatness.
**_COACHING TIP_**
Will Smith once said in a sit-down interview with the great Tavis Smiley, "The guy who is willing to hustle the most is going to be the guy that just gets that loose ball."
Most people get stuck in life because they are obsessed with what could go wrong. I had the opposite experience growing up. Everything was already going wrong. I was made fun of a lot, I was picked last for stuff, I didn't feel accepted. Worrying wasn't an option. I had to take action to improve myself and overcome my fears if I didn't want to feel that insecurity anymore.
When you experience fear, move toward it. When you feel doubt, take the necessary actions to build your confidence. When you are afraid of being wrong or looking bad in front of others, be humble and vulnerable to create real human connection. The hustle takes action. It requires getting over yourself and how you look. It can be a beautiful journey if you give yourself permission to hustle like a maniac because what else are you here to do other than make the most of what you can be?
**_GET GROUNDED_**
Your body is everything. You may think being a little overweight isn't that big of a deal, but on the road to greatness, it affects your overall energy and can be that one thing that holds you back with everything. Each body is different, but we all respond positively to a certain set of guidelines and philosophies. Throughout this chapter, you'll hear about these lessons from some incredible teachers who've studied the body (and the mind) far more than I have in all of my years as an elite athlete. I've been in great shape, and I've been in horrible shape, so I can speak to how much better my entire life is working when I'm on the path of body mastery. Your body is your home; it's time to learn how to keep it clean and free of clutter to fulfill the vision within you!
**MASTER YOUR BODY**
_If the body be feeble, the mind will not be strong._
**—Thomas Jefferson**
Rich Roll was a former NCAA Division I swimmer on some of those amazing Stanford University teams in the 1980s that produced a number of Olympians. After he graduated, he went to Cornell Law School and became a successful entertainment lawyer. He had a beautiful wife, a happy marriage, and a luxurious home near the ocean in Malibu Canyon, California, yet like so many fortunate, accomplished people who appear to have it all, he was not happy. It felt like there was a giant hole in his life from which his spirit and drive and passion steadily leaked out.
_Despair_ is the word a lot of us would use to describe that state, and it can happen whether we have success or not. It's depression. Burnout. Exhaustion. Sick and tired of being sick and tired!
Rich was almost 40 years old and felt stalled out when he should've been at the top of his game. He knew he wasn't living up to his full potential. It's a phase that can hit at nearly any age. Midlife crisis. Quarter-life crisis. Whatever caused it, whenever it happens, it is the opposite of greatness.
"I was just unhappy," he said. "I felt ripped off, cheated. I'd done everything right and should have been celebrating, but instead I was unhappy."
Rich was working 80-hour weeks and bingeing on junk food. It was the only thing he had time for, and at the same time, he was so overworked, the idea of the self-control required to diet seemed laughable. He never had the time to work out and consequently gained 50 pounds. He broke 200 pounds for the first time in his life and kept going. Rich was in denial and rationalizing his deteriorating physical and emotional health.
One day he was climbing a flight of stairs at work, and halfway up, he had to stop. He was out of breath, felt tightness in his chest, and couldn't make it to the top. As a former athlete, this really hit Rich in the stomach—his increasingly flabby stomach.
We've all been there, where having given up on something or run into adversity we can't bear to face, we just pretend. We pretend we don't have a problem and just plain ignore it for so long that it takes an event like this at a moment like this to pierce through our delusions. We sit there paralyzed by grief and confusion: _How did it ever get like this? What happened between then and now that could possibly explain why I can no longer walk up a flight of stairs or play with my kids or sit comfortably in an airplane seat?_
At different times in my life, I've oscillated between exercising like a madman and wanting to just say screw it and be lazy. Being healthy can be a lot of work, and it can be so tempting to procrastinate and kick the can down the road. But if you want to do great things, that is absolutely the wrong attitude. The path to greatness means being responsible to yourself and others.
In that moment, we have a choice. Unfortunately, too many of us choose to do nothing. To continue to pretend.
But Rich did not.
**TACKLING THE IMPOSSIBLE**
"I'm 39," he said to himself right there, "and I had to take a break walking up a simple flight of stairs. Something is really not right. I need to make some changes."
He decided in that moment this would be a new beginning in his life. It was this choice that put Rich _back_ on the path to greatness.
What he did _not_ do was decide to make a small change. A small change or an incremental commitment is too easily forgotten or abandoned. "I'll cut out soda." "I'll eat a salad for lunch." "I'll start Monday." Instead, he started fresh immediately—with a full cleanse to clear his body of the toxins and waste he'd been shoveling into it. He'd been treating his body like a toilet instead of a temple, and now he had to flush it out—and then repair the plumbing. He did this by cutting out all of the junk food and meat and eating a completely plant-based diet.
"The first couple days, I was buckled over, sweating, like I was in rehab," he told me. "It felt like detoxing off heroin or something; it was terrible. By the last couple days of it—and I don't know if you've had this experience—I felt incredible. Better than I'd felt in 20 years or maybe ever. That told me just how resilient the human body is. In a matter of a week, after treating my body so horribly with a terrible diet for so long, I felt better than ever."
The famous English billionaire businessman and adventurer Richard Branson has been asked for his best piece of business advice. His answer is always one word: _exercise._ Why? Because if you don't take care of yourself, you can't take care of your business. A stroll through the Forbes list of the world's billionaires is, with only a couple exceptions, a testament to this idea. Nowhere is the connection between physical health and business wealth more pronounced than with the current generation of entrepreneurs, represented most completely by author, angel investor, and human guinea pig Tim Ferriss.
Tim is best known for the number one _New York Times_ best-selling book _The 4-Hour Workweek,_ but he is just as passionate about human performance as people like Steven Kotler. His second book, in fact, was called _The 4-Hour Body_ and introduced the world to a number of amazing ideas and practices. It shouldn't shock you that physical activity is very important to him, on many levels. "I find sports very helpful as a bookend to close out the day," Tim told me, "to do training at 6:00 p.m., where you are absolutely protecting that time as much as you would protect any other type of conference call or anything else. Not only does it set your body up physically for dinner and the rest of the night, but it also forces you to prioritize your day in order to get all your work done before you head to the gym." The energizing effect of both those things—getting your work done and getting the blood flowing—is a huge asset on the path to greatness.
I think Rich was feeling the truth of all that advice, because he was finally starting to fire on all cylinders again. He loved the way he felt so much that he decided he would stay clean. For him, this meant that he would become a vegan. A significant number of monumentally successful businessmen and leaders have done this over the past 5 or 6 years to get healthier and more productive: Steve Wynn, Bill Clinton, Mort Zuckerman, Al Sharpton, Russell Simmons, Biz Stone, and John Mackey, the CEO of Whole Foods Market. Even Mike Tyson went vegan, and he was an ear-chomping killing machine!
With all the junk out of his diet, Rich made a commitment to exercise again. Not a little bit but a lot. His wife bought him a bike. He started swimming again. He hired a coach, because he was so serious about getting healthy that he wanted to surround himself with experts and good energy. It started off gradual, but at the end, Rich was putting in 25-hour training weeks. It became like a second job, as he had cut back on his law practice significantly to pursue his new lifestyle practice. In a relatively short time, he was an athletic machine nearing the best shape of his life.
And that's when it hit him: He was going to do an ultramarathon—which is essentially any distance-running event beyond a traditional 26.2-mile marathon.
"Two years prior, I couldn't make it up a staircase, and here I was. I had never done an Ironman; it wasn't like I was a seasoned triathlete. I'm a complete newbie. I was very inexperienced at this. I had a level of confidence that I could complete it, but I also had a responsible level of humility about what I was about to do. I wasn't there to win or anything like that. I was there to celebrate the fact that I was sober, that I had lost this weight and changed my life. That was really it."
Despite that humility—or perhaps because of it—Rich didn't just finish the race, he placed 11th. In his very first ultramarathon. You don't need to be an extreme sport enthusiast or an endurance athlete to appreciate the audacity and ridiculousness of Rich's accomplishment. It would be like taking up rock climbing as a New Year's resolution, training on a rock wall for a few months, and then going to Yosemite on the first day of spring and sprinting up the face of El Capitan like a spider monkey.
I found this transformation to be so inspirational and profound. Rich had mastered his body and taken back control of his life along the way. What I love the most about this is that Rich found his calling in life, and a new vision was born in the process. He's built an ultrasuccessful lifestyle business out of his passion. Now a best-selling author, he educates and inspires millions around the world through his books, widely popular podcast, vegan health products, speeches, and more. He turned adversity into advantage and ran with it, literally!
Rich said, "My whole life, I had chased the carrot. Go to the best school. I got in all the Ivy League schools; I studied hard." But where did it get him? Overworked, unhappy, and, worst of all, out of shape. "I was at the point in life where I was supposed to be celebrating everything that I had built," he said. But he couldn't. In his position, who could? Greatness isn't about working a lot or making a lot of money. It's about having purpose and being the best that you can possibly be. And how can you jump for joy when you struggle to walk up a damn flight of stairs?!
**YOUR BRAIN ON JUNK**
All the teachers in this book mastered their bodies in one way or another. I also spent some time learning from Daniel Amen, MD, a leading American psychiatrist, a brain disorder specialist, director of the Amen Clinics, and _New York Times_ best-selling author, which added another layer to my understanding of why mastering the body is so important. It's not just about muscles. Your brain matters, too. Your mind and your body are connected; they are both part of your body. Are you taking care of them? As they say, garbage in, garbage out.
"Your brain is literally involved in everything you do. How you think, how you feel, how you act, how you get along with other people, and when it works right, you work right," he told me. "When it's troubled, though, for whatever reason—toxic exposure, head trauma, drug abuse, lack of oxygen—that's when you start getting sadder, sicker, poorer, less successful."
The problem so many of us have is that we completely ignore the role of our brains in the health of our bodies. "If you never look at the brain," Dr. Amen warned, "you may never know what is going on with you." And when that happens, you can find yourself in a nasty cycle of poor physical health leading to poor emotional health, which in turn leads to worse physical health, and so on and so on.
When I was bummed in my own life and career, I went through a similar bout of lethargy and felt that slow slide toward unhealthiness. What was really tough about it was that it happened so gradually. I steadily gained a pound a month for close to 2 years. To make it more confusing, I also started to become successful (financially and in my business) around that time. That made it harder to see through my own carb-driven haze and question my habits. After a 2-year period of hustling, barely making much each month, I remember making $6,200 on my first webinar and feeling like I was the richest man in the world. I started eating like a rich man, too. After that moment, the money started to roll in, and so did my fat rolls. I was eating 7,000+ calories a day (to be fair, I was working out, too, but it was all out of balance). Worst of all, I had sugar after every meal, which is a huge no-no even if you're interested in only a basic level of health. I just wasn't taking care of my brain or my body. When I look back on it, I know that I wasn't the best I could be. I wasn't thinking or feeling as clearly as I could have.
It turns out, according to Dr. Amen, that when your weight goes up, the size and function of your brain go down. It wasn't until my move to New York to pursue Team Handball and my dream of representing the United States in the Olympics that I finally snapped out of this slump, and it was only because the waistband on my underwear finally snapped back at me. I knew I was getting pretty heavy. My face was so wide my family and friends started to joke about it—they called me "Flewis" . . . _Fat_ Lewis—but when I couldn't wear my underwear anymore without the waistband snapping back and rolling down under my belly like a slap bracelet, that was enough. I stepped on a scale for the first time in a long time, and the digital display shouted "254" back at me in big, red, angry numbers. I decided in that moment to cut out everything bad for the next 30 days (Rich Roll–style).
I didn't have any sugar, gluten, or dairy for 30 days. I'm not saying this is for everyone, nor was it recommended to me by any health expert or doctor; it's simply something I wanted to do to create a new habit for myself, because I understood the power of creating positive habits when something isn't working the way you want it to (more on this in Chapter 6). I lost 28 pounds in the first 28 days and felt better than ever, so I decided to do it for another 30 days and dropped a couple more pounds. I didn't change anything else, and I was still working out the same way . . . it was all from cutting my intake of the stuff that wasn't working for me. I dissolved Flewis by drinking (and falling in love with) green juice every day, eating foods that were organically grown and taken directly from the ground, and eating organic, grass-fed meat. Between choosing the right foods and remaining dedicated to my workouts, I've never since worried about gaining the pounds back.
I now have sugar and sweets from time to time, but my diet is much more balanced, and my weight (and health) is where I want it to be. My life is better every day because of it. And the work I put into mastering my body has made all the other decisions I have to make and the work I have to do that much easier.
But naturally—and my brother, Chris, was an example of this—people put a lot worse stuff in their bodies than sugar: drugs, excessive alcohol, and nasty chemicals. We deprive ourselves of sleep or even have "natural" addictions like gambling and sex. This has a real and tangible effect on your ability to perform. Forget about the kind of flow state that Steven Kotler describes in his books—that's way outside the realm of possibility with these negative influences at play, because they can quickly and easily destroy your body and tap-dance on your brain. So stop abusing yourself!
**SLEEP YOUR WAY TO THE TOP**
Just like Rich Roll, 5 years ago Ameer Rosic, Canadian kettlebell champion and an expert on sleep optimization, was in a bad place. He suffered from deep depression, he dabbled in alcohol and drugs, and his outlook on life was horrendous. "I had no meaning in life at all," he told me. "I felt like there was a dark hole, an abyss, in my heart. Then life hit me on the head with a hammer."
The epiphany came when he woke up and realized that much of his struggle was due to a lack of sleep. He was up into the late hours nearly every night partying, getting very little sleep, thinking he was a superman who could take on anything. His physical and emotional health began to suffer, and with that his life suffered tremendously, too. He knew he had to do something, so he began to learn about circadian rhythms and the importance of getting the proper amount of sleep. "Everybody needs to realize, we are like batteries," he said. "Sleep recharges you. It increases and balances hormones, strengthens your immune system, gives you clarity, gives you focus, and so much more." The more he researched, the more Ameer realized that sleep was the pivotal factor in achieving optimal health, ahead of diet, ahead of exercise, ahead of everything.
And for Ameer, the turnaround could not have been more stark. "I have somehow encapsulated so much passion in my soul, in my being, and it is because of the way I sleep, the way I eat, and the way I treat my body, because when you treat yourself first, everything else follows and everything else is greater," he said.
The impact of proper sleep wasn't just physical either. Ameer raised his IQ, became the Canadian biathalon champion in kettlebells (the national sport of Russia—don't ask, I was as confused as you are), and built a business helping others optimize their health. Ameer put it best when he said, "If you want to run a business and you want to do good in this world, if you want to deliver value in this world, it's all about treating one's self first. When you treat yourself first and you create that perfect vessel, you then have the ability to affect so many more people globally."
It's crazy how important a foundational habit sleep is! As Shawn Stevenson, sleep specialist, author of _Sleep Smarter: 21 Proven Tips to Sleep Your Way to a Better Body, Better Health, and Bigger Success_ , and another great mentor whom I have had the privilege to learn from, put it: "Sleep is something our genes expect of us." He calls it vitamin S, which perfectly explains the additive and restorative role of sleep in our lives. When he talked to me about the information in his book, he could not overstate just how detrimental a lack of sleep can be to every aspect of life.
"We have a thousand things going on in our lives, and sleep is often one of the first things we tend to omit," he warned. "We don't understand that by lacking that high-quality sleep, we're actually _demolishing_ our ability to achieve at a high level in everything else in our lives." (emphasis mine)
This is especially true for entrepreneurs, many of whom wear their marathon coding sessions or back-to-back all-nighters as badges of honor in the race to start-up success. To you folks, Ameer has some shocking news that you need to take to heart: "Around 2013, a study came out that showed people who stay up 48 hours or more, which many people do in these crazy stressed-out days we're living, have the same blood sugar as a diabetic." As a diabetic! "Now can you imagine," he continued, "what happens when this gets compounded? Day in, day out, year after year after year. It's going to end up in something not very beneficial."
I think we can nominate that last sentence from Ameer for the Understatement of the Century. It was definitely a "holy crap" moment for me, I can tell you that.
If you're like a lot of people who are struggling with turning your dreams into reality, with realizing your vision for greatness, right now you are probably saying, "Look, I have a demanding job. I have kids. I can't exercise 25 hours a week like Rich Roll or go to bed at 10:00 every night and sleep 8 to 9 hours like Ameer Rosic. I don't have the time, I have commitments." Well, Rich did, too. "We need to be extremely selfish a few hours a day and take care of ourselves and our bodies," he said. Echoing Ameer's point, he continued, "You can't help someone else if you are not taking care of yourself."
I've learned that it's a lot like when you're on an airplane and they say, "Put your own mask on first, before assisting others." You can't help anyone if your brain is oxygen starved or, worse, you're already dead. The same principle applies to taking care of ourselves so that we might help others. We need to make sure we're really taking care of our bodies, physically, mentally, and emotionally. We need to make sure we're getting all of our needs met, that we're going after all of our wants and desires. Those don't come last, they come first—no matter how selfish that might feel. When they come first, everything else follows quickly after.
Rich said, "I'm a better person when I'm taking care of myself in this way. There's a certain part of me that feels like that's what I'm supposed to be doing. I'm wired for it. I'm happier, I'm more productive, I'm a better husband, and I'm a better father when I am training and taking care of myself in that way."
**WHAT IS POSSIBLE WHEN YOU MASTER YOUR BODY**
Chalene Johnson, a _New York Times_ best-selling author and a world-renowned fitness coach, has trained hundreds of thousands of people and sold millions of copies of her workout videos. She witnesses firsthand what's possible when you take ownership of your health. Her students send thank you messages on a regular basis sharing what they've created in their family lives, careers, and personal relationships due to her training. Some people find it difficult to change their lifestyles with years and years of bad habits; trust me, I get it. But Chalene, now a close friend, said to me, "Anything and everything is possible with a plan. If this [healthy body] is what I'm interested in right now, what am I willing to give up?" If you want to make a change, then something needs to actually be different in order to get better results. Meaning, what vices in your life would you need to remove to improve your health and your body and gain all that is possible with a mindful lifestyle?
For Rich, his relationship with his family improved when he made physical health a priority. He was content. He was happy. Much as Ameer's work with sleep became more than just a curiosity, Rich's success at training and running quickly became more than a hobby. He built an entire lifestyle business out of it, for crying out loud, and he became _great_ in more ways than one to boot.
I know this sounds crazy, but I am convinced that a major reason many people don't achieve greatness or even reach for it is because they just don't have the energy. They aren't taking care of themselves. We all need to do a better job of this, for ourselves and in support of others. Remember, it doesn't matter how great your vision is, you cannot muster the will to overcome adversity or marshal the energy to hustle tirelessly if you're out of breath or stuck on the couch.
Your greatness problem might just be a health problem.
And just because you haven't taken care of yourself in the past doesn't mean you can't and shouldn't start right this second. Rich was 40 when he got serious. We can't turn back time and start over, but we can choose how it will end, and it is never too late to take the first step in the right direction. That's what mastering your body is about. The past is irrelevant—what matters is where you go now. Maybe your road will end on (or include) many miles of high-endurance running. Or maybe it's just getting in better shape so you can play with your kids. Or maybe it's eating right so your head is clear and fresh so that you can think without the fog.
Regardless, mastering your body is a fundamental, foundational part of your journey toward greatness. It is the engine that powers the runaway train of your vision, pushes you over obstacles, clears a path for you to focus, and fuels the hustle that takes your dreams even further than you imagined possible when you first dreamed them. Do not take advantage of your body. Do not take your brain for granted. As Ameer described it to me, "We are like banks, and there's a mechanism in our brain called sleep debt that actually accumulates the seconds, the minutes, the days that we miss out on sleep. And just like with a loan that doesn't get properly serviced, one day the bank will come knocking on your door, saying, 'Hey, Lewis, well, you owe us about 2 to 3 years of catch-up time.'" And just like with real banks, that knock almost always comes at the worst possible time. In the pursuit of greatness, mastering your body is all about not letting your body write checks that your brain can't cash.
The idea of entering a CrossFit gym or training like an elite athlete may be as terrifying to you as giving a speech was to me when I went to Toastmasters the first time. But that doesn't let you off the hook from mastering your body in the School of Greatness. If you want to play a big game in life, you need the energy it requires physically and emotionally to take on every challenge and obstacle that stand between you and your vision. Here are three things you can do to master your own body starting right now!
**EXERCISE #1:**
**Take a Picture of Your Body . . . Naked!**
If you really want to inventory how you view yourself—what you like and don't like—there is one place to start. See yourself naked, literally, and then take a picture.
Accepting (and loving) your body is the first step. Take a picture of yourself naked and evaluate the parts you love and the parts you want to improve on, and write them down. Notice where you're putting your negative energy and focus on accepting those aspects of your body. Only then will you have the positive energy you need to make the improvements you want.
Without your accepting responsibility for your body the way it is at this moment, the unhappiness or negative energy becomes a source of your results. Anything that's based on fear ends up in fear. By accepting and loving my body, I've got the positive energy I need to stay on a workout plan and lifestyle diet that others might struggle with. When you love your body—or maybe more accurately, the person _inside_ your body—it's much easier to stay committed to a vision than to do something out of fear and self-loathing. From this place, you are able to choose to lose weight because it matters to you, not because how you look matters to others.
**EXERCISE #2:**
**Develop a Fitness Lifestyle Plan That You Love**
My goal for this book is to open you up to any and all possibilities. No matter where you are on your fitness journey, each step can be one in the right direction. Know that your body should not hold you back but only move you forward in achieving your vision.
First, carve out the time—write it down in your schedule. This should be a minimum of 5 days a week for at least 30 minutes per day. This will create a routine and reinforce a commitment to physical health as part of your lifestyle. It doesn't matter what time you exercise during the day; at this point, the most important thing is to do it at the same time every day to make it a consistent habit. Pick a time that works well for you and your lifestyle. I prefer mornings because it kick-starts my day and puts me in a positive mental space, since I've completed something before I've really even begun my day. As my mom says, completion is powerful.
Second, start moving and get active. I always incorporate things that I love into my fitness program, because that is the easiest way to get and stay motivated. As an athlete, I play a lot of pickup basketball, go running, do sprints, lift weights, swim in the ocean, and try different boot camp–style workouts because that's what gets me excited when I exercise.
This doesn't mean you need to spend 2 hours crushing your body every single day. The important thing is not to get paralyzed by the overwhelming expanse of the fitness industry. Whether it's jogging in the neighborhood, walking with purpose to the café to get your daily tea, or stretching for a few minutes in the morning, every little bit of movement counts. Remember, this is a journey, not a destination.
Third, find an accountability partner for support. This could be a friend, spouse, trainer, or even pet (yes, make a commitment to keep your dog in shape as well!). You are that much more likely to commit when you have someone else holding you to your word. Many people hate working out, which is why they don't stay with it. If this is where you are, then an accountability partner might be the perfect thing to help you stay committed and make working out more fun.
Last, I've learned to do one painful exercise every day so that I can expand my comfort zone and take my body and mind to new levels. So do something each day that makes you uncomfortable. This doesn't mean you should go and try to pull a muscle because it's painful. You essentially want to do something new and/or difficult that is consistent with what you are striving for with your body. Although I love certain things about my workouts, I never keep to the same routine for too long. Change is good. I always push myself to a level of discomfort that eventually becomes painless and rewarding.
This probably sounds like I'm telling you to search out crazy, exotic exercises that target muscles you didn't know you had. Nothing could be further from the truth. Your goal when it comes to painful exercise is really doing anything that makes you sweat and sends your heart rate up—doing pushups (or any lift or exercise) to failure, repeating hill sprints with minimal rest, or simply working out harder than the previous day. It's simple: _Push yourself!_
I'm personally a big fan of interval training. This includes making your own workout of four to six exercises that you'll do for 45 seconds at a time with a 15-second rest between each exercise for as many rounds as you want.
**Example of an Interval Workout**
45 seconds: pushups
15 seconds: rest
45 seconds: air squats
15 seconds: rest
45 seconds: jumping rope
15 seconds: rest
45 seconds: lunges
15 seconds: rest
45 seconds: situps
15 seconds: rest
Do this for four rounds (or adjust the rounds and time for each exercise to push yourself however you want). You can get as creative as you wish with this simple workout plan and add in any type of exercise, with weights or just your body weight. You can do this at home, at the gym, or wherever is most convenient for you. Make sure to change things up and keep it fresh. Depending on how many rounds you do, the workout will take roughly 30 minutes with light stretching before and after.
The key here is to do something that you enjoy (even though it will be painful) and find someone to make it fun with you. For more workout resources and options, go to schoolofgreatness.com/resources.
**EXERCISE #3:**
**Find Out What's MISSING**
Aubrey Marcus, my good friend, a health expert, and CEO of the nutrition company Onnit, designed this exercise exclusively for you! With his focus on total human optimization, his method for mastering your body begins with finding out what's missing from your health and lifestyle. It's so important that he has turned it into an acronym to guide your progress (MISSING). Figuring out where you are physically and physiologically in each of these seven areas is critical to your health and your ability to effectively pursue your vision on the path to greatness. Use this exercise as a guide to see what's currently missing from your health and adjust each area as needed.
**_M—Mineralization_**
The body is made up of a variety of minerals. Every single system in our bodies requires adequate minerals to function properly. We get these in the foods we eat. Ask yourself where your foods are coming from. Are your fruits and vegetables organic and locally grown? Is your beef grass fed? If the answer is yes, you're on the right track. Trace your food back to the source.
One of the best ways to return minerals to your daily diet is to use Himalayan salt. Regular table salt contains only three minerals: sodium, chloride, and iodine. Himalayan salt has anywhere from 65 to 85 trace minerals. The expression "worth one's salt" comes from Roman times, when soldiers were given an allotment of salt as their _salarium,_ which is where we derive our word _salary._ To function efficiently, it was essential that soldiers replenish the salt lost by their bodies during long marches. Having the right salt could mean the difference between life and death.
**_I—Inflammation_**
A lot of top doctors now are saying that pretty much all disease stems from some type of inflammation. The reason is that the body has to combat inflammation, just like you would combat any other type of pathogen. When the body is using resources to deal with inflammation, it has far fewer resources to deal with immune response and proper function, and thus disease can grab a foothold. Managing inflammation is incredibly vital.
Paying attention to those inflammatory processes is important. Inflammation can even come from poor digestion! One thing that can be valuable in dealing with inflammation is using proteolytic enzymes. Proteolytic enzymes go through the body and start to break down any kind of dead proteins that are lying around the body and stimulating inflammatory responses. Utilizing a good proteolytic enzyme can be a major benefit to mastering your own health. (My personal recommendations for enzymes are at schoolofgreatness.com/resources.)
**_S— Stress_**
As discussed in Chapter 2, stress is a part of the human experience that we need to manage. We don't realize the physical cost of being under chronic stress. Stress releases a hormone called cortisol, which reduces immune function. Stress is fine if temporarily you need to run away from an animal, hit a deadline at work, or do something that requires a short burst of all of your focused energy. If the stress is chronic, however, the body is severely limited in how effectively it can deal with any number of stressors. Stress will eventually burn out your adrenal glands, and through a variety of chemical processes and substitutions, you'll start to produce fewer of other hormones that are essential for optimal living. So managing stress is incredibly important.
Now take time to write down what you do to manage stress. One of the simplest ways to reduce stress goes back to our meditation exercise in Chapter 3. It's been shown scientifically through a number of studies that deep diaphragm breathing will naturally release your stress. So focusing on your breathing is an important way to release stress.
Here are a few examples of what I personally do and don't do to manage stress.
**_S— Sleep_**
Sleep is probably the most important health tonic you can provide your body. It is the time to repair, restore, recover, and rejuvenate. Sleep is the key. There are great books, like _Sleep Smarter_ by Shawn Stevenson, that talk about the different ways to improve your sleep. First and foremost is understanding that the body is designed to sleep during the night and be awake during the day. If you can optimize your schedule to get 7 to 8 hours of sleep during the night so you are fully awake during the day, you've taken the first big step.
Once you've gotten yourself on a better schedule, the next step is to optimize sleep itself. Photosensitive elements of the eye trigger melatonin production—that's the hormone responsible for letting you know that it's time to sleep and for helping the body fall asleep. Additional light in the late-evening hours short-circuits the melatonin process. So minimize artificial light sources like late-night TV and smartphones. No electronics in bed! Track your sleep nightly. Early to bed, early to rise, and get 7 to 8 hours of sleep nightly. It's that simple.
**_I—Inhalation_**
Our meditation exercise should reinforce the importance of breathing. Inhalation is one process that we do constantly throughout the day, and if we stop, we're dead. We don't realize how crucial getting oxygen to our body is. We just take it for granted. But not all breaths are equal.
If you're taking shallow chest breaths, you're not adequately oxygenating your body for optimal health and stress management. So paying attention to your breathing, using that as a rudder to navigate different health modalities, is key. Breath can help you deepen your meditation, it can power you in your workouts and in your training, and it can keep your body more alkalized, which will improve your mineralization. Breath is incredibly important and too often overlooked in the health picture.
If you get the chance when you have an extra minute (maybe while sitting in traffic), simply focus on your breath—those full diaphragm breaths that go deep down into your belly. The benefits to your health can be massive. Are you breathing optimally? Could you use more cardiovascular fitness? It starts here.
**_N—Nutrient Density_**
Nutrition in America has been calorie focused for a long time. What we have learned over the past couple decades, though, is that calories are not as important to health and having a great body as nutrient density. You can get 500 calories from sugar or you can get 500 calories from a grass-fed rib eye; your choice will have a vastly different effect on your body. How many nutrients are you providing your body? How many green vegetables? How many healthy fats, like coconut oil and avocado and olive oil, with their omega-3s and omega-9s? What kind of nutrient density does your food have? What doesn't have nutrient density? Make sure your meals are balanced and rich in nutrients. Water is the most essential nutrient; without it, human life cannot survive. Make sure you are staying hydrated. Are you drinking enough each day?
**_G— Gut Health_**
The gut is the cauldron of health. This is where your digestive system works to convert minerals and nutrients into fuel that will sustain a healthy body. From the very first doctor, Hippocrates, to doctors in the present day, medical practitioners have always been aware of gut health, but it's something that is only now getting its proper respect. Matter cannot be created or destroyed, so how do we grow or change? We grow by assimilating nutrients from our food and building our bodies and regenerating our cells by using those nutrients. Poor digestion can lead to inflammation and what's called leaky gut syndrome, where food particles escape through the gut barrier and trigger an inflammatory response.
Gut health is influenced by the probiotic flora in your gut, also known as the gut biome. These microorganisms are important for digestion. Additionally, many of the neurotransmitters and hormones that are responsible for your mood, your happiness, and everything that makes you feel great are either affected by or originate from the gut. Most of our serotonin production comes from the gut. Our immune cells are produced in the gut. Having a healthy gut biome—one that works symbiotically with the body—is vital for your immune function, for your mood, and for your health.
So when you're looking to master your body, pay attention to what you're MISSING. When you aren't missing anything, only then can you say you've mastered your body. Your goal at that point is to maintain where you are for as long as you can!
For the complete guide to figuring out what's MISSING from your health, along with resources on supplements and products to optimize your body plus my personal fitness plan, go to schoolofgreatness.com/resources.
**_DO_** | **_DON'T DO_**
---|---
Meditation | Smoke
Physical activities | Drink
Listen to music | Binge on TV
Change my environment | Overeat
Dance | Oversleep or lounge for days
**_COACHING TIP_**
Listen, I'm not perfect. My weight goes up and down sometimes. I don't always eat perfectly. Like most people, I love sugar and sweets. But I'm sick and tired of seeing people who have given up on themselves! The only difference between those people and me (and you, I hope!) is that I'm willing to put in the work and experience the pain necessary to keep my body and mind in shape so that I can perform throughout the day on a high level, live the life of my dreams, and pursue my vision come what may.
If you aren't getting what you want in life and you are out of shape, don't think for a second that those two things are unrelated. It's time to say, "Enough is enough." It's time to admit, "I'm sick and tired of feeling sick and tired." It's time to get up and do something every single day that makes you sweat and gets your heart racing. Put yourself through some type of daily discomfort, whether it's for 5 minutes or 50 minutes. Do something that is so uncomfortable that it starts you on the process of getting your body where it needs to be, and then maintain that by falling in love with the feeling of that pain. Yes, your vision and relationships and dreams depend on it, but most important, so does your life. It's time to step up and make your body great!
**_GET GROUNDED_**
Our habits shape who we become and the results we create in the world. In my life, I've cultivated habits that supported me and others that brought me down. We've all been there. Unfortunately, most of us don't know how important our habits actually are. The most successful, fulfilled, and vision-focused individuals in the world have daily rituals and habits to which they attribute a significant amount of their success.
If you want to achieve greatness in your life or your business, then everything you do needs to be done with a purpose and for a reason. It doesn't take long to form a new habit, but it can slip away from you just as quickly. True greatness comes from the intentional act of doing something positive over and over and over again. It's time to take a look at the habits you've been forming and begin forging a new path right now by applying some of the habits of the most successful people in the world.
**PRACTICE POSITIVE HABITS**
_Successful people are simply those with successful habits._
**—Brian Tracy**
Armchair quarterbacks love to yell at athletes who "waste their potential" or "take their gift for granted" or "don't hustle" or "don't act like a good role model." This is usually just empty projection, aimed at great men and women who have accomplished more than the fans can ever dream. But sometimes there is truth to it.
Anyone who has ever tried to make it in sports can tell you that while they were out at practice leaving everything they had on the field, there were other athletes using merely a fraction of their capabilities. Guys like NBA All-Star Allen Iverson (who, during an infamous press conference where he was being judged for missing practice, said, "I'm supposed to be the franchise player, and we're sitting here talking about _practice_?!") and National Football League All-Pro Charles Woodson were notorious for giving the bare minimum to get by until the lights came on. Woodson's ability as an All-American, Heisman-winning, All-Pro NFL cornerback was so freakish, so otherworldly, that he didn't dial up his practice habits until 10 years into his now 18-year professional career, and even then he only did it because he realized he was setting a bad example and creating bad habits in some of the younger players who looked up to him. He didn't do it because he didn't need it to compete at an elite level—a fact that drove his coaches on every team he ever played for stark raving mad.
This is not a story unique to the playing field. Poor practice habits—or preparation problems, as I like to call them—transcend the world of sports and affect us in our jobs and our relationships. Doing the bare minimum at work. Rushing to complete a task at the 11th hour because experience has taught you that you don't need the previous 10 to get it done. Forgetting your partner's birthday and running around the day of for a present that doesn't feel like you forgot. Crash dieting to lose 10 pounds before going on a beach vacation. We do these things because we've gotten away with them in the past. We were fast enough, smart enough, young enough, lucky enough. We lean on experience and ability, not on proper preparation. We have poor habits, and sooner or later our luck is going to run out.
One of my most inspiring teachers let his poor habits get the best of him. He is actually a guy with a story very similar (minus the fame and millions of dollars, of course) to Charles Woodson's. His name is Graham Holmberg, and I played college football with him. Practice after practice, week after week, season after season, I watched him get by purely on his physical prowess and agility, a substantial gift he was bent on wasting. I was glad he was on our team (you don't want to be on the other side of the ball from a guy like Graham), but I was also jealous and angry at the same time. Despite what seemed like unlimited athletic potential, reaching for true greatness didn't seem to be on his agenda. Instead, Graham preferred to party, chew tobacco (on the sidelines during practice even!), stay out late and sleep in late, chase women, and enjoy himself. He had no ambitions beyond being pretty dang good and having fun.
You might be saying to yourself right now, "Wait, that sounds pretty awesome!" And it is, or it can be, at least for a while. Who doesn't like to have fun and tear it up every once in a while? But that's the operative phrase: _every once in a while._ If that's all you do, eventually it gets boring, especially when it doesn't produce anything lasting or when talent can no longer bridge the gap that bad habits create.
Now others of you might be asking a different question: "Well, what if you don't have any talent? What then?" First of all, that's garbage. Every single one of us has talent churning away inside; you either have misdiagnosed yours, denied it, or taken it for granted. But second, talent—at least of the kind I'm talking about with Graham—isn't destiny. Sure, talent can make greatness easier to achieve, but greatness is not the exclusive domain of the talented. Greatness is the result of visionaries who persevere, focus, believe, and _prepare._ It is a habit, not a birthright.
Unfortunately, because he was so supremely talented and so much had been given to him at birth, Graham ignored the power of habits that his parents, teachers, and coaches tried futilely for years to drill into him. Or maybe a better way of saying that is, he let his life be ruled by those bad habits. And as I have come to learn after talking with true greats like Angel, Shawn, Ameer, and my brother, the number one way to waste your talents is to allow bad habits to take over. The consequences of a life led by bad habits are inevitable.
**TREADING WATER**
Now you wouldn't think that Graham would be the teacher we need. He never approached the kind of greatness we all saw in him, and over time he became deeply unhappy. But Graham's story doesn't end there—it gets worse and then better. When he left school, he didn't go pro. He didn't go semipro. He didn't go anywhere! He stayed right where he was, like all those people who peaked in high school, never left, and watched life unspool in front of them. It was almost like Graham was the real-life Al Bundy from the famous 1990s sitcom _Married with Children,_ whose greatest achievement in life was scoring four touchdowns in the 1966 city championships for Polk High. And it was all downhill from there. Like Al, Graham was basically treading water. Treading water is not a growth strategy. It doesn't get you anywhere. There is no progress with treading water. All you're doing is fighting to stay in one place, with enough of your head above water to keep from drowning.
That was exactly where Graham was one day a few years later, when he learned that a close cousin had been killed in a car crash. Something in Graham clicked. It was like he finally woke up from the stupor he'd put himself in, and instead of treading water, he began to kick and paddle with purpose. I've never seen someone turn his life around as quickly as he did, giving up all his vices cold turkey and going to the gym nonstop. On this new path, he developed the workout and lifestyle habits that would eventually turn him into the world champion at the CrossFit Games and earn him the label "the world's fittest man."
But the greatness he achieved in fitness is not what we can learn most from, or at least what I learned most from. Graham's turnaround was rooted in his mind. He became intensely spiritual and devoted to his faith. He became a baseball coach at the high school his beloved cousin had gone to. He opened his own CrossFit gym, where he offered Bible study on the weekends. He married and started a family. He turned the adversity that stopped him cold in his tracks into a new vision where positive habits fueled an amazing transformation that affected all areas of his life.
"It was like, I don't want to be a hypocrite to these kids, and inspire them and coach them up and teach them the right habits, if I'm doing bad stuff as well. I made a decision to just wipe that stuff out of my life and not let it control me anymore," Graham told me.
For Graham, that meant cutting out everything from chewing tobacco and drinking to other less tangible but equally toxic sins: jealousy, anger, ingratitude, ego. That is the tricky secret about habits—they are best built or changed one by one, but eventually, you have to get to all of them if you want to be great. In the quest for greatness, there is no substitute for developing positive habits.
**AN OLD GREEK'S ADVICE**
Aristotle said, "We are what we repeatedly do. Excellence, then, is not an act but a habit." That old Greek understood how important positive habits are to overcoming adversity and enduring the quest to become a champion. I have learned that champions aren't just born; champions can be made when they embrace and commit to life-changing positive habits.
Having known Graham for more than a decade and watching how he made a conscious shift to that new path, I decided to examine my own habits. I saw how quickly positive habits built strength and resulted in a deeper sense of belief—in myself, in my vision, and even spiritually.
This process wasn't easy at first. I never got into any of the obvious things we think of when we talk about bad habits—drugs, drinking, or smoking—because from an early age I saw what they did to my brother and realized I didn't want to make those same mistakes. I wasn't perfect by any stretch (and achieving greatness isn't about being perfect anyway), but my bad habits were less clear to see or less straightforward to understand. Thanks to a lot of introspection and coaching from greats like Chris Lee and Tony Robbins, I finally came to see all the bad habits I'd developed starting as far back as my time on the middle school basketball team.
•Beating myself up
•Being ungrateful
•Failing to acknowledge positive growth
•Being overly judgmental (toward myself and others)
•Disrespecting my parents and family
•Staying in unfulfilling relationships too long
•Eating poorly
•Not exercising regularly
•Keeping a messy living space
•Swearing like a sailor
•Staying up all night
•Sleeping in all morning
•Cheating on homework and tests
•Reacting to situations in a way that upsets others
•Getting by without practicing
It took a lot of time and constant feedback to realize what wasn't working in my life, and it will be an ongoing journey until the day I die. Over the years, I began adding positive habits and noticed a dramatic change in my results and the way I felt internally as well. Some of these include:
•Constantly expressing gratitude
•Smiling at as many people as possible
•Going to bed early
•Getting 7 to 8 hours of committed sleep
•Making my bed in the morning
•Staying organized
•Acknowledging myself and others
•Loving people wherever they are on their personal journey
•Eating clean
•Training my body
•Saving and investing my money wisely
•Meditating
•Visualizing my results and creating a game plan
•Respecting others
•Investing in my personal growth
•Preparing before big moments
•Surrounding myself with inspiring people
Staying consistent with positive habits can be a challenge. I still go back and forth on them. There have been many times where I was working out intensely and in the best shape of my life, and then for whatever reason, I got off track. Before I knew it, 3 or 4 months would go by, and all of a sudden, I'd find myself in the same position as Rich Roll—exhausted halfway up a flight of stairs!
The key to surviving and then thriving after these moments is to not beat yourself up when you do break a habit. Rather, you need to reconnect to your vision to refamiliarize yourself with why it's important to stay true to your positive habits in the first place.
A habit and its results can change fast, so it's crucial to set yourself up to win and do what works for you to stay on track. For some, that's journaling the habits you kept and the habits you broke and creating rewards and consequences for yourself when you do. For others, that's hiring a coach to keep you accountable or finding an accountability buddy or friend with whom you can work on these things together. For still others, it's finding a mastermind group where you are all constantly challenging yourselves to stay on track.
The tricky part about habits is that any one of them (good or bad), when you look at them individually, doesn't seem all that critical. It's when you take them in combination or as a whole that they become incredibly powerful. They can easily and shockingly thwart the same amount of progress that they can create. This is why we admire people with great self-discipline. It's not because they were born great. It's because they learned the power of habits and applied that power to create a lifestyle that supports the best version of themselves.
Almost everyone knows the famous (and mythical) story about Michael Jordan getting cut from his high school basketball team. Not only did he use that as motivation (in reality, he got demoted to JV as a sophomore), but he cultivated an entire regimen of positive training habits that built him into the greatest basketball player to ever play the game—including spending every off-season adding a new move to his repertoire to make himself more unstoppable.
James Altucher, the great entrepreneur and writer, has talked openly for years about hitting rock bottom over and over again. His brilliant book, _Choose Yourself!,_ is all about the positive habits he's developed to pick himself up off the floor and be more successful than he was before—from writing down 10 ideas every day to his now famous "daily practice" in which he works on and calibrates his physical, emotional, mental, and spiritual health. My former teammate Graham Holmberg did the exact same thing to turn his life around.
Now, I don't want you to think this is all about morals. Though morals are important, this is really about human optimization—not avoiding sin. Ironically, it was Eric Thomas, the inspirational speaker and "hip-hop preacher," who made this clear to me when he pointed out a simple bad habit that almost everyone has: getting distracted. Think about how hard it is for us to stay on task these days; from social media to e-mail, there is an endless pull on our time.
So Eric set out to change that tendency in his own work. He told me that he practices a "no interruptions" policy when he is being creative: "When I get started, I don't care if it's my wife, my children, they know that from a certain time frame, I'm going all in. And I can't go all in answering the phone. I can't go all in watching TV. I can't go all in with those kinds of distractions swirling around me." This has helped him craft messages that have reached millions of people around the globe.
Meanwhile, he pushes back at entrepreneurs and artists who can't seem to create work that resonates. "It's because you're not in abstraction," he said to me. "You don't have that moment of your day—I don't care if it's 10 minutes or 4 hours—where you shut the entire world out. No Twitter, no Facebook, no Instagram, nothing. For that time, you're going all in. Once you come out, then we can do Instagram. And I'll be honest. Your content probably would be stronger if you had that time of isolation, of solitude, where you give yourself a chance to think. You give yourself a chance to go in, and when you go in, you go 120 percent. That's my ritual."
Really, it's a habit. An excellent habit. The beauty (and curse) of habits is that once they are formed, they are hard to break. Consciously pursuing great habits consistently will click you into autopilot on the path to greatness.
**MAKE YOUR BED, CHANGE YOUR LIFE**
I'll give you another example just to make it clear how simple and small good habits can be: Make your bed. In 2014, Admiral William McRaven gave an amazing commencement address at the University of Texas at Austin. In the speech, he focused on the critical nature of making and inspecting a sailor's bed each morning. This might seem like some petty, officious quirk of military regulations at first. After all, isn't that what your mother bothered you about every morning? But when you hear it from Admiral McRaven, it becomes the definition of a positive habit. It's a way to start off your day with an accomplishment and encourage you to keep tackling the tasks of your day. And furthermore, as Admiral McRaven said, "Making your bed will also reinforce the fact that little things in life matter. If you can't do the little things right, you will never do the big things right."
Admiral McRaven was not the first person to stumble onto the power of making your bed every day. Gretchen Rubin, the habit expert and number one _New York Times_ best-selling author of _The Happiness Project,_ has talked on her blog about making your bed since way back in 2007! In fact, of her millions of readers who worked on their own "happiness projects," she reported that making the bed had the biggest impact on their happiness. Her explanation for why this was the case, which she wrote about a few months before the release of _The Happiness Project,_ echoes Admiral McRaven's words in many ways.
First, making your bed is a step that's quick and easy, yet makes a big difference. Everything looks neater. It's easier to find your shoes. Your bedroom is a more peaceful environment. For most people, outer order contributes to inner calm.
Second, sticking to any resolution—no matter what it is—brings satisfaction. You've decided to make some change, and you've stuck to it. Because making my bed is one of the first things I do in the morning, I start the day feeling efficient, productive, and disciplined.
I have to be honest, when my first company had its first million dollars in sales, one of the few splurges I made was to hire an assistant. I'm embarrassed to say that one of the things I had that assistant do every morning was make my bed (hey, at least someone was developing the habit!). But as I learned about the importance of positive habits, I stopped this. I realized that by having my assistant do a task like this for me, I was depriving myself of an opportunity to practice a positive habit that could kick-start my day on my own personal path to greatness. And now, every morning when I wake up, I make my bed—starting my day with some satisfaction and discipline.
**HABITS OF HIGHLY SUCCESSFUL PEOPLE**
Here is the thing about positive habits: It isn't that important which habits you practice, as long as they are beneficial and they work for you. What matters is that you commit to them and that you do them every day. Just like developing hustle is really about doing the work, practicing positive habits is about committing to a routine. A routine guaranteed to move you closer to greatness, especially if you develop positive habits related to the other lessons in the book: creating a vision, overcoming adversity, cultivating a champion's mindset, developing hustle, mastering your body, building a team, and being of service.
If you are like I was before I watched my friend Graham turn his life around and propel himself into the highest echelons of CrossFit like a blond-haired kangaroo, you might need help figuring out which positive habits are worth practicing. And to be honest, I still struggle with that at times. That's why, whenever I meet great people, I have a little habit (or I suppose it is a _meta_ habit) I make sure I do. I try to observe them for positive habits to learn what made them great. I often explicitly ask about their habits when they appear on my podcast. The reason? I want to see which habits I should deploy in my own life.
In early 2014, _Entrepreneur_ magazine ran a story about this very subject on their Web site. It featured a cool info graphic that showed the daily habits of the wealthiest people in the world. While making money is only one element of greatness (it is not everything by any means), there is something to be said for how their habits translate over to success in other areas of life.
These are their habits.
**1.** Maintain a to-do list.
**2.** Wake up 3+ hours before work (to set themselves up for the day).
**3.** Listen to audiobooks during commutes (or you can read, if you take public transportation, or listen to my podcast!).
**4.** Network 5+ hours each month.
**5.** Read 30+ minutes each day.
**6.** Exercise 4 days a week (I recommend 5 days myself, with daily movement, of course).
**7.** Eat minimal junk food.
**8.**Watch 1 hour or less of TV a day.
**9.** Teach good daily success habits to their children.
**10.** Make their children volunteer 10+ hours per month (I encourage you to do it with them to set the example).
**11.** Encourage their children to read 2+ books per month (I didn't read much as a kid and wish I would have).
**12.** Write down their goals.
**13.** Focus on accomplishing a specific goal.
**14.** Believe in lifelong educational self-improvement.
**15.** Believe good habits create opportunities.
**16.** Believe bad habits have a negative impact.
Following all of these habits won't guarantee that you'll become rich or that you will immediately achieve whatever form of greatness you are after, but they can't hurt, and they could very well be the springboard you were looking for!
I have incorporated a number of these habits into my life. Here are the daily habits I focus on the most.
**1.** Wake up early and say thank you for being alive another day (not 3 hours early, but it's an ongoing practice!).
**2.** Make my bed!
**3.** Meditate for 10 minutes.
**4.** Drink a green juice at breakfast.
**5.** Stretch and move my body.
**6.** Have a high-intensity training workout.
**7.** Eat organic, home-cooked meals.
**8.**Watch very little TV (for 4 years I didn't even own a set so that I would stay focused).
**9.** Focus on my goals and take action steps toward them.
**10.** Network with a purpose to give to others.
**11.** Acknowledge others and smile in every conversation.
**12.** Express gratitude throughout the day and the last thing before bed.
**13.** Work with a coach and mentors.
**14.** Constantly learn new information and skills.
Here are a handful of other habits I've picked up and adopted from some of the greats I've met along my path.
**Be your word.** I learned this when I was 11 years old from my father when he caught me stealing money one day. I remember lying to him about it and then feeling a tremendous amount of guilt and shame from the consequences of my actions after he found out the truth. He taught me that those emotions that made me feel sick inside were the result of not being your word. This meant simply doing what you say you are going to do when you say you're going to do it. Not lying is part of being your word. A friend of mine once said that as long as we are breathing, we will always be breaking our word. I'm not perfect, but it's something I strive for every day. The easiest way to make a person feel unappreciated or like they don't matter is to break your word to them or fail to follow through without a renegotiation (of what time you'll show up to a meeting, what they can expect from you, etc.). Being dependable to other people makes it easier for you to depend on yourself. Honoring your commitments to other people makes it easier to honor the commitment you have made to yourself when you created your vision for greatness.
**Focus on gratitude.** This is a habit I picked up from Tony Robbins. In his book _Awaken the Giant Within,_ he talks a lot about gratitude and said that even if you do not feel grateful, you can always ask yourself, "What _could_ I be grateful for?" I've found this to be a great mindset habit that works when you're stuck. A few years ago, when I had Ramit Sethi on my podcast, it struck me in the middle of the interview that I wanted to thank this person whom I looked up to and had learned so much from. (His _New York Times_ best-selling book helped me get out of debt from the student loans I had. It was a major game changer in my life when I completed that.)
I don't know why, but saying that was hard. I guess I was worried it might come out weird. People wait their whole life to be acknowledged, and most of the time they only get it when they graduate from school or after it's too late and they are dead (this is the story of at least half of the famous impressionist painters whose priceless works hang in the world's most prestigious galleries). Why wait? I've realized. Every night I recount in my head what I am grateful for. My voice-mail message is about gratitude. And like I did with Ramit, I try to tell people in person how much they've done for me. In fact, you could say that this book is an exercise in gratitude, too!
**Have a morning ritual.** I learned the importance of a morning ritual from Tim Ferriss. He told me, "I think for entrepreneurs, it's very valuable for a week, for instance, to just figure out what your ritual is going to be in the morning or when you wake up. What is the first 60 minutes going to look like, and then script it out so that you do the same thing every day. I think it's a very freeing experience to allocate more thought power to the things that matter as opposed to trying to decide what you should have for breakfast today. I think ritual and routine are extremely important for people who want to be creative."
It doesn't have to be complicated. Here is my morning ritual on most days when I'm not traveling.
•Wake up and express to myself what I'm grateful for.
•Do a guided meditation for 10 minutes and visualize what I want to create in the world that day.
•Perform light stretching and simple yoga poses.
•Make my bed and brush my teeth.
•Work out for 30 to 60 minutes.
•Shower and get dressed.
•Have a green juice with my vitamins and breakfast.
Only then do I get into what I'm creating for the day with my business and vision.
**Let go of reaction.** Building a habit to let go, to not take anything personally, is a great way to reduce stress in your body. So when someone cuts you off on the highway, don't flip them off or curse or react in a negative way; instead, relax your body, take a deep breath, and focus on how safe you are and what you are most grateful for in the moment/day that is bigger than yourself and bigger than someone cutting you off.
**Express your wants and needs.** So many people shy away from expressing and communicating what they want and need (in life, relationships, business deals, and marriage; with their teammates, etc.). They bottle up their feelings and emotions, and it comes back to make them resentful or frustrated later. Of all the people in my life, my mom taught me this most clearly. She has always been big on open communication and being clear on what you want. Ask questions when you aren't sure about something instead of going along with it, and speak up to discuss what is on your mind even if you don't like confrontation.
**Acknowledge others (and yourself).** Similar to how I expressed my gratitude to Ramit, getting in the habit of acknowledging others is a powerful tool because our natural tendency is to deflect attention from the crowd. It's a defense mechanism. By acknowledging others—for their contribution, for their assistance, for their existence—you acknowledge their humanity and, in turn, your own. I saw the immediate impact and power of this habit in talking and working with Chris Lee. I watched him help others acknowledge those around them, and the change was almost instantaneous. This is incredibly important in the pursuit of greatness, because you will never get there alone. You need a team that will be your support system. The only way that team works is if you acknowledge each other for all the great things you do and are.
**Be vulnerable.** I also learned about the importance of being vulnerable and willing to discuss the past from Chris Lee, who showed me how to open up about some of the darkest moments in my childhood. He helped me share things I'd never told anyone before and exposed me to the freedom that resulted from that naked vulnerability. Not only is it a great virtue that helps build self-confidence, but getting in the habit of discussing the past instead of bottling it up is also the only way you will learn from your mistakes and grow as a person. Greatness is about getting better every day—at life, at business, at relationships, at whatever your vision is—and you can't do that if you keep making the same mistakes over and over again.
They say love is about the willingness to be completely vulnerable, but so is success in anything you do. Graham Holmberg doesn't become a CrossFit champion and Shawn Johnson doesn't become an Olympic champion unless they push themselves to the limit of their abilities and the brink of exhaustion—that is physical vulnerability. Angel Martinez doesn't help build Reebok into a footwear juggernaut without taking some serious risks in the early 1980s, just out of a recession, by going all in on an aerobics shoe—that is economic vulnerability.
This was one of the hardest habits for me to learn, because there is a lot from my past that for a long time I was trying to erase or forget or run away from. It's no coincidence that once I turned to face it and allowed myself to be vulnerable enough that I could talk about it openly with people that everything I was working toward started to take off!
I am not going to sit here and tell you that developing and practicing positive habits will be easy or fun all the time. It can be very hard, especially at the beginning. You'll have lapses, and that's okay. You just need to keep your eyes focused on your vision, harness your resolve to persevere against those temporary failures, and bust your butt like the champion you want to become. That is the price of greatness. Like Benjamin Franklin said, "Energy and persistence conquer all things." What I can tell you, however, is that slowly but surely you will begin to make strides and reap the rewards. And when that happens, you will embrace these positive habits with the same energy with which you are pursuing your own greatness.
**EXERCISE #1:**
**The Attitude of Gratitude**
As I mentioned in Chapter 2, by expressing gratitude in all areas of your life, you can fight internal and external adversity. If you concentrate on what you have, you'll always have more. If you concentrate on what you don't have, you'll never have enough. Cultivating positivity takes work. I'm not suggesting you can't ever have a bad day, but life is better if you develop an attitude of gratitude. Your homework for the next 2 weeks is simple and straightforward and, if done right, will begin to shift your entire perspective on how you interact with everyone in your life. For the past year, I have made it a habit to tell whomever I'm with at the end of my day the three things I'm grateful for. It's awesome.
By doing this every day, you'll consciously begin looking for things to be grateful for. You'll feel more alive and receptive to the goodness that comes in your life, and you'll increase your joy of simple moments.
Some things that you might want to express gratitude for:
•Catching up with a friend you haven't spoken to in a while
•The great workout you had this morning
•Landing a new client and booking the gig
•Completing any project you were working on
•The love you received today
No matter how bad your day is, there is so much to be appreciated. The fact that you are alive and have been given another day is a huge gift. We have so much to be grateful for, including the essentials and basics—the food we eat, our environment, our health, our friends.
Share your gratitude and give it away. This is something you should do when things are going well in your life _and_ when everything seems to be against you.
These small things might feel completely irrelevant and trivial in comparison to your goals or your vision, and I understand that, but what you need to understand is that the effects these small things have on your life bleed into all areas—not just one.
**EXERCISE #2:**
**Write Your Habits Manifesto**
This is straight from the Gretchen Rubin playbook of building good habits. She published her own Habits Manifesto in 2014.
**HABITS MANIFESTO**
What we do _every day_ matters more than what we do _once in a while._
Make it easy to do right and hard to go wrong.
Focus on actions, not outcomes.
By giving something up, we may gain.
Things often get harder before they get easier.
When we give more to ourselves, we can ask more from ourselves.
We're not very different from other people, but those differences are _very_ important.
It's easier to change our surroundings than ourselves.
We can't make people change, but when we change, others may change.
We should make sure the things we do to feel _better_ don't make us feel _worse._
We manage what we monitor.
Once we're ready to begin, begin _now._
Contemplate the dozen statements Gretchen makes. Think about each of them as they relate to your life. How do they apply? What would you add or take away or change? Why?
Now look back to here at the lists of positive habits I compiled for myself and the wealthiest people in the world. Make a checklist to see if you are doing any of them or if you are doing the opposite.
Then look for three things on those lists that you can add to your daily routine for the next 2 weeks, and start applying them right now. It almost doesn't matter which three you choose to start. After the 2 weeks, assess where you are in your life, how you are feeling, and if you see the value in these habits.
After those 2 weeks, add three more habits to your routine and adjust the others to support your vision until you are on track to living a life full of positive habits. I'm not perfect and I don't always have my habits in check, so I don't expect you to either. But when you set a foundation of positive habits, the rewards that manifest down the line are almost always far better than you can imagine. And they get you that much closer to achieving your vision and that much farther down the path toward greatness.
**EXERCISE #3:**
**The 28-Day Morning Routine Challenge**
Small changes lead to big shifts. What you do when you wake up sets your pace for the day. And while goal setting, vision casting, and the power of intention are all extremely important, greatness is about taking action toward change.
This month your challenge is a _daily morning_ challenge. This exercise will be like setting the refresh button on how you begin each day. The 28-day challenge is long enough to reset a bad habit and propel you into greatness. Completing this challenge will make you more efficient and focused with your time. Your time is valuable, and I want you to attack this challenge as intentionally as you can with how you spend it.
For the next 4 weeks, you're committing to an action you will be taking on this month to work toward your vision. This challenge is forcing you to break through and commit to the simple (and possibly mundane) tasks that will help you lead a life of greatness.
Choose from one of the following to do every morning before you check your e-mail or phone or do any work.
•Spend 30 minutes writing as soon as you wake up (journaling your goals, free writing from your heart, writing about your vision/struggles/dream).
•Make your bed—this is something I do every morning, as it gives me a sense of completion early in the day.
•Make a to-do list for the day. Create a list of your top priorities or the most important things you need to accomplish that day.
•Work out, stretch, or go on a walk to get up and moving first thing in the morning before distractions get in the way.
•Sit down and eat breakfast. This may seem simple, but instead of grabbing the coffee and bagel to go/in your car and eating mindlessly, set time before you leave in the morning to prepare and enjoy a healthy, balanced breakfast.
The decision of what to do in the morning is your own, but make it something that, even in a small way, supports your bigger vision. Establishing a morning routine sets the tone for the rest of the day—so select one that can propel you forward in achieving your dreams.
**_COACHING TIP_**
It is absolutely critical that you weigh the price and the reward for the decisions you make on a daily basis. And don't kid yourself—everything has a price and a reward. There is a reward for good habits (growth), and there is a reward for bad ones (instant gratification). Unfortunately, the prices for each are way out of whack. And oftentimes, the price can be your ultimate vision. You need to figure out which habits give you the best chance of reaching your goals.
It's time to get connected to your vision, understand its power, and realize that it's not worth the instant gratification that bad habits pay out to you. Because when you put positive habits in place, you set yourself up to win. Period. When you don't have them in place, something almost always falls out of order in your life and you will likely not know why. It's time to step up and get serious with your daily actions, as this is what builds the momentum in your life toward the vision you want to achieve.
**_GET GROUNDED_**
Having played sports my entire life, I know the importance of playing with a powerful team and what kind of team to look for when your goal is greatness. With every season in sports and in life, there will always be a different role that we play or that others around us play. Sometimes we'll be the star, and other times we'll need to take a supportive role. We must learn to flow with the changes as we grow and bring on new opportunities and experiences in life. I used to try to do everything on my own when people would "let me down," and I thought I'd go through life solo proving others wrong. That ended up emotionally draining me and was stressful beyond belief (not to mention very lonely). It wasn't until I began allowing others to support my dreams and me that life started to come to me with ease.
If you've been playing solo in your life, I want you to open up to the possibility of what a team could look like moving forward. That might require you to adjust your attitude and mindset or find a whole new team altogether. Let's dive in here and see what comes up for you with my exercises at the end of this chapter.
**BUILD A WINNING TEAM**
_If you want to go fast, go alone; if you want to go far, go together._
**—African proverb**
Justin Bieber has sold millions of records, toured hundreds of cities, performed in front of thousands of people, and personally made hundreds of millions of dollars in a handful of years. If you sat down and asked him how this could have happened, how he could have gone from uploading little videos of himself singing on YouTube to being one of the biggest stars in the history of music, he would give you a single name: Scooter Braun.
That is the hugely successful talent manager who discovered Bieber from a YouTube video when the megastar was only 14 years old and living in Canada. At just 34 years old—still a kid himself by some people's standards—Scooter emerged as one of the music industry's most influential and intelligent people for one reason: He knew how to build a winning team. It's not just about finding talented individuals (creative, management, or otherwise), he realized. The path to platinum status and personal greatness is about turning those people into a team. It's a lesson understood by leading figures across disciplines; their experience—as well as my own—shows that greatness simply cannot be achieved in a vacuum or through a solitary effort.
Scooter learned this invaluable lesson from an unlikely and unwitting mentor: legendary NBA coach Phil Jackson. As a kid, Scooter wanted to be a basketball player. And like most kids, at some point he realized he wasn't tall enough. It usually happens when you're pretending to be Michael Jordan, down by two, with the clock winding down, and then someone who seems the size of Shaquille O'Neal eats your lunch. When that moment occurs, some kids hang up their kicks while others channel their love of the sport in a different direction. In Scooter's case, he picked up Phil Jackson's classic book, _Sacred Hoops._ By the time he closed the back cover, he had decided he wanted to be a coach. It was there that he fell in love with the idea of creating the perfect winning team.
**CULTIVATE STRONG RELATIONSHIPS**
Scooter built his first real-life team in college as a nightclub promoter. He learned early on that cultivating strong relationships in business and in life is a basic building block for greatness. Which is why today, if you spent some time in the offices of Scooter's company, SB Projects—considered to be one of the most important music firms in the business—you'd see a team made up of his best friends and contacts, some dating back to high school.
Talking to Scooter about the intersection of his personal and professional relationships made me realize just how important my own relationships have been on my journey toward greatness—particularly in business and sports. With sports, I've been on great teams and awful ones. I've also been on great teams that lost and awful teams that won. But it was the ones that were so toxic and disconnected that I literally wanted to quit (and sometimes did) that had the greatest impact.
I remember my freshman year at Southwest Minnesota State playing for a coach whose style of leadership resembled a potent mix of Bobby Knight and the drill sergeant from _Full Metal Jacket._ If you did something wrong, he got up and screamed in your face. If you didn't do something fast enough, he took great pains (and pleasure) in calling you out in front of everyone—humiliating you. There is nothing worse than being on a team with that kind of negative energy. It brings everyone else down. It's not like we wanted to fail. We all wanted to win. We all wanted to succeed and do our best. It was our coach's belief that the best way to do that wasn't to build relationships with his team and create unstoppable winning chemistry but instead to scare us to victory by making us more afraid of losing than excited about winning.
Needless to say, his leadership style didn't work for me nor for many of my teammates. Our team never really gelled. We looked ahead to each game on the schedule not as an opportunity to get better but as 1 week closer to the end of this miserable experience. But that team, miserable though it may have been, taught me one of the most valuable lessons I've learned: You need to get everyone rowing in the same direction, and the only way you do this effectively is by cultivating the kinds of strong relationships where heading in the same direction feels like the only option. And that direction can't be as far away from you as they can possibly get either: At best, you will go nowhere. What's more likely is that their numbers will overwhelm your singular force of will, and you'll head in the wrong direction.
This phenomenon is especially true in dysfunctional workplaces and families. Many of us have suffered in jobs where you are on edge every day, waiting for your boss to yell at you or call out your mistakes in front of everyone, never acknowledging you for the hard work you put in day in and day out. At home, with parents always yelling at each other (or at you), never feeling like your talents are being nurtured or cultivated, all you can do is put your head down and simply do your best to survive without getting punished.
The best companies and families are great teams. The importance of building winning teams and the principles that go into them aren't just about sports, they're about all areas of life, all of the time.
**SURROUND YOURSELF WITH GREATNESS**
Building a powerful team is obviously important, but how do you know the difference between a good team and a bad one? How do you make sure that you have a winning team behind you or, even better, feel like you are just one player on a team that is changing the world together?
These were questions I was not equipped to answer on my own. This was probably the main reason I decided to start (and attend) the School of Greatness, so I could connect a collection of professors and teachers to my own winning team and join them in the great things they were doing.
Don Yaeger is the author of seven best-selling books and is best known for his collaborations with Hall of Fame running back Walter Payton and another famed basketball coach, John Wooden. The most important lesson Coach Wooden ever taught Don was this: You will never outperform your inner circle. If you want to achieve outer success, improve your inner circle.
This is what Don passed on to me in my time with him. Our capacity for success and greatness is embodied by the people we surround ourselves with. If you aspire to greatness, make sure that you have greatness around you. For Don, this was an eye-opening insight that applied not only to basketball and his projects with John and other athletes but also to life in general.
"I find myself, all the time, thinking about my inner circle," Don admitted. "Who's in it? Who should be in it? Whether or not some people maybe need to have a different spot in the circle."
The difficulty lies in the fact that some people who have been in your circle for years, often by default, can't simply be cut off. Don was talking specifically about family members.
"Let's be honest, you can't get rid of a family member, right? So what I realized was rather than the amount of time I was allotting every week to conversation, maybe it's half that. It really is a great challenge, but governing who you put in your circle is one of those places where your decision making will impact you greatly."
Now here's the million-dollar question you need to ask yourself. It's a question Don asked me, and I'm sure Coach Wooden asked him numerous times over their 12 years working together: How is this model for greatness different when we're talking about sports as opposed to business or relationships or life? The answer, of course, is that it's not.
Think about it: A successful book (as I hope this one will be) requires the right editors, the right publisher, the right publicists, the right designers, the right researchers, and the right support staff—all of whom will make you better, none of whom will waste your time. Without excellence in each of those areas, it is impossible to have an excellent and successful book. Don has hit the _New York Times_ nonfiction bestseller list seven times. According to him, there are fewer than 50 individuals to ever accomplish that. Don didn't do this alone; he did it with the help of his team.
As transformative as this insight was for Don—after collaborating with Coach Wooden, Don's focus shifted toward mentorship and greatness and the notion of "paying it forward"—it was equally so for me, if only a little different. I'd heard before how you are the average of the five people you spend the most time with, for better or worse. But that advice was related to happiness and self-improvement. I'd never heard it like this, in relation to teams and to success and greatness. Then Don hit me with another John Wooden quote: "You show me your friends, and I'll show you your future."
That brought it home for me and the entire purpose behind the School of Greatness. Think about Rich Roll and his wife, Julie Piatt, who was the one who bought him the bike that changed his life. She was the catalyst and inspiration for him to get back to working out and change his entire health lifestyle. Or Kyle Maynard and Shawn Johnson, whose parents supported and facilitated their passions—from football and wrestling to ballet and gymnastics. Or Angel Martinez and the elderly relatives who took him in and gave him the opportunity to have and pursue the American dream.
Each of these great men and women had friends and family who pushed them to be greater, who ensured that they would have a world-changing future. Beware of people who instead will drag you down or make you feel bad for having ambition. Sometimes it's hard to be honest with yourself about relationships like that when you're focused on achieving your vision and living your dream. But it's important to take a step back every once in a while and look at your inner circle. Are they pushing you to be great? Are they supporting your dream? Because that's what a winning team does, that's what it looks like, and that's why you need to have one.
**FIND THE RIGHT MENTOR(S)**
Let's say you are one of those people who has to rebuild your inner circle, and you're trying to figure out the first person to add to your winning team. Who is it? It's the coach. Your mentor. Your advisor. Your father/mother figure. Their role on your path to greatness is literally invaluable.
The writer Denis Waitley has an apt analogy that I'd like to borrow and paraphrase here, from an article titled "The Champion Within" from his very popular newsletter.
He uses an example relating new military technology to mentors. A missile system that was introduced during the Gulf War in 1991 was revolutionary because it would self-adjust its trajectory to ensure that it kept its target in range. Likewise, as Denis says, "A highly motivated person, when he or she has targeted a worthwhile goal, uses a coach or mentor the same way a missile uses the new guidance system—to assist you in making adjustments and navigating difficult, uncertain, ever-changing terrain."
Without the right mentor, we're like an unguided missile on the path to greatness. If we're lucky, we'll end up exactly where we need to go. But that's only if everything goes precisely as planned. Life never seems to happen that way, though—especially when we're trying to do something different, something more. What we need is someone who can not only help us set our original course but also constantly correct and guide us through the problems and adversity we will inevitably face.
This brings us back to Scooter. His first mentor was Jermaine Dupri, a successful record producer, songwriter, and rapper, whom he met while promoting parties and eventually ended up working for. Dupri taught him the music business and how to work with artists. But Scooter didn't stop there. "Sometimes people say they have one mentor. I've never had one mentor," he told me. "If I had one mentor, it'd be my father, but I have other really great mentors as well: people like Jeffrey Katzenberg and Lucian Grainge, who's the chairman of Universal Music Group. We're very close, and he's been an incredible mentor and friend. David Geffen has become a mentor to me as well. Those kinds of people I'm eternally grateful to because they allow me to draw from them."
When Scooter reached out to Justin Bieber and sketched out a path for the young singer's career, it was these ideas that he founded it on. Without the right friends, without the right guidance, without the right team (along with all the hard work and talent he had), there was no way that Bieber would break through. We are so heavily influenced by the people we spend the most time with that we can't afford to leave it up to chance. Being selective about mentors, friends, and partners is going to be one of the biggest factors in the journey to greatness.
Point being, it's extremely important—I'd even say absolutely necessary—to find the right coaches for you if you want to achieve greatness in any area of your life. Can you be successful without them? Of course. But the greatest athletes in the world all have coaches even when they are at the peak of their game. In fact, they want coaching and feedback on ways to get better and improve more than anyone. Michael Jordan didn't add all those new moves in the off-season or win all those championships in the postseason without Phil Jackson on the bench. It's important to find coaches who inspire you but also give it to you straight. Ones you can look up to and take their guidance seriously. Ones you can commit to and show that you are willing to take action to achieve your own greatness.
**THE POWER OF POSITIVE ENERGY**
"I've been able to bring some amazing people into my life and surround myself with people, I think, who are skilled in ways that I am not, and we've been able to scale an incredible business because they make things happen," Scooter said. It's something he teaches his artists, too. They can't do it alone. They can't be successful in isolation. But Scooter looks for something else in addition to talent and smarts: positivity.
"I'm a firm believer that it's more important to have positive energy around you than the smartest people. Now, luckily I've been able to have, in my opinion, some of the smartest people around me who are also positive," he told me. I've found this in my own business. I'd rather have someone who has a tremendous amount of heart and hustle over the most talented person who has an energy of entitlement about them and selfish tendencies.
This is the tricky part about talent within a team: It is a delicate balancing act between the positivity of heart and hustle and the negativity that can arise with the natural competitiveness that develops within teams. Smart, talented people want to achieve. They want to realize the potential that so many—including the person who has hired them—have identified in them. The key is to show them, by example, how everyone individually wins when the team wins. If you allow ego to get in the way, the positive energy you could otherwise harness and direct outward at the competition or the marketplace morphs into negative energy and turns inward. You end up with people competing against each other, or worse, against you, and the vision you have built for your business and your life. Defining precisely what success looks like is a big part of turning the natural competitive instincts of smart, talented, ambitious people into positive, supportive energy instead of negative, destructive, selfish energy.
You see this in sports teams as well, where a team of "average" players can beat a team of All-Stars if they work together, are positive, and stick to the game plan. The way they win is by passing the ball and working within the system, not trying to do too much by themselves. Instead, they understand that everyone has their role, and they stick to that role. If everyone does their own job and doesn't try to win the game alone, then they give themselves a chance to win. After all, you can't hit a game-winning grand slam until you have players on base.
"I learned that lesson the hard way," Scooter admitted to me. "I had some negativity in my life before, and you start to question yourself because negativity projects onto you. You start to look in the mirror and say, 'Am I really a good person? Am I doing the right thing?' That isn't you. That's their bullshit feeding on you." You've got to have positive energy to create winning chemistry. It's that simple.
It reminds me of a quote by Edmund Lee, who encouraged people to "surround yourself with the dreamers and the doers, the believers and the thinkers, but most of all, surround yourself with those who seek greatness within you even when you don't see it yourself."
Beyond surrounding yourself with these positive people, it's also important that you build a network of them. Bill Clinton, in his rise from a broken home to the governorship of Arkansas to the presidency, created a network of some 10,000 physical note cards containing the names, addresses, and relationship history of classmates, professors, friends, lawyers, donors, supporters, reporters, and influencers that he could cultivate and call on when needed. He became not just a connector, as Malcolm Gladwell described and I tried to emulate on LinkedIn, but a _superconnector_ —working every room, schmoozing every influencer, charming every guest. Eventually, he digitized this system and continues to use it to this day for his work with the Clinton Foundation. He is living proof that, as my friend and networking expert Porter Gale puts it, "your network is your _net worth._ "
**PUTTING IT ALL TOGETHER**
But not every talented and positive team wins, as we know. There is more to greatness than that. It takes strategy and leadership. This was something I also asked Scooter about. How do you ensure that you get the most out of your team?
"You've got to realize," he told me, "the only way to scale is to delegate and to empower others and to say, 'You know what? They're not going to do it exactly like me, but they're going to do it exactly like them.'" You have to be okay with the fact that some people will be better than you at certain things in the long run. Why should that threaten you? Isn't that why you brought them on in the first place? There is always friction on any team. With a bench player picking up the starting job (which means kicking someone else to the bench), with new hires, as people get raises and increase their "rank" in companies, there will always be competition and egos that come out.
Being transparent in the beginning about the importance of communication and clearing up any misunderstandings with people so no one holds on to frustration is an essential part of a winning team. The "clearing" process, or open communication, will allow the team to have breakthroughs in stressful situations instead of breakdowns and implosion.
Scooter brought the analogy home to me after we played a pickup basketball game together: "That's the same idea as when we play basketball. Sometimes you're going to make a great assist and a guy's going to miss that easy shot, and you're going to be frustrated because that was another assist on your stat line. But at the end of the day, it isn't about our individual stat line, it's about winning the game." The key, even if the missed gimme layup was the difference between victory and defeat, is to communicate with your teammate about what happened. Like we talked about in Chapter 6, you need to let go of reaction and get on the same page about what went wrong and what went right, so you can go back out there tomorrow and do it all over again, together. After all, as Scooter reminded me, "you cannot win the game on your own."
Jack Welch, former CEO and chairman of General Electric, who knows a thing or two about building a winning team, has written things on this subject that very much apply to what Scooter was talking about. In an article for _Newsweek_ a few years ago, he and his wife, Suzy Welch, wrote, "First, the leaders of winning teams always—always—let their people know where they stand. . . Second, winning teams know the game plan." It's your job, as you assemble your team, to let them know what's important and create a plan for them to follow. Not a plan that's all about you. Instead, it's about creating a plan in which everyone has a role and everyone's role is designed for them to thrive in. That's what Scooter has done so well.
**THE TEAM ISN'T JUST ABOUT THE BUSINESS**
There is one final thing I think is worth discussing here, especially as Scooter's most prominent protégé has had no shortage of troubles at various points in his life. Justin Bieber has been arrested for DUI and drag racing in Miami; he's been taken in for egging a neighbor's house in Calabasas, California; he's been charged with hitting a limo driver in Toronto; he tagged a hotel wall in Brazil and ran through customs and passport control in Turkey. Yet Scooter stood by him. Perhaps because he knows that all young people, especially famous young people, do dumb things. But I think there is another reason. Scooter doesn't see what he does as being just business. His clients and his employees are his family. And family is everything.
I realized that when I spotted some writing on Scooter's wrist. It was a tattoo. Just one word: _Family._ When I asked him about his family, he lit up. His grandparents were Holocaust survivors. His brother, Adam, whom you'll meet next chapter, is an amazing person doing incredible things. And his parents? The day I interviewed him for the podcast just happened to be his parents' 35th wedding anniversary.
To have parents who really, truly love each other and are good to each other, and to witness that growing up and to have that love all the time, I always felt full. I always felt safe.
Yet for a period in his late teens and early twenties, Scooter lost sight of that love. He still appreciated it for what it was but not for its role in guiding his life.
"I was lost, and I was chasing the money because I didn't really understand. I was just going for it. What I realized was all I'm doing it for is this," he said as he pointed to the tattoo. Interestingly, he talked about getting that tattoo for a while before going in to get it inked. What finally pushed him to go in and make it real?
The day before, Jay Williams, the former All-American point guard from Duke and the second overall pick in the 2002 NBA Draft by the Chicago Bulls, had gotten into a motorcycle accident that would ultimately end his professional basketball career. "Jay's one of my closest friends," Scooter said. "I had chickened out about getting this tattoo a couple weeks earlier, and when I found out what happened to him, I realized I couldn't take that for granted anymore."
Add to the mix the fact that his mother had fallen ill during that period—she's fine now, thank goodness—and you can see the power and meaning this tattoo carries for Scooter.
"For the rest of my life, people will ask me about this tattoo," he told me, "and I will have to tell this story of why I got it, which is this simple, and it will remind me for the rest of my life what's really important."
But how can work and family be the same? Much like Don Yaeger talked about, you can't fire someone from being related to you. Okay, so it's not a perfect analogy, but it is important. When I first started my company and I hired people, I used to think that they were there to work _for_ me. That almost always ended badly because I set myself and them up to lose. I've since learned that I am actually in service to my team, as well as to everyone else. Just like you are to your family—it's a matter of give and take, mutual respect, and, ultimately, gratitude and love.
What I try to think about after learning about great teams from Scooter and Don Yaeger is this: How can I be of service to every member of my team and set them up to win as best as possible? This doesn't mean I need to hold everyone's hand daily or coddle them; it simply means that I make sure that if anyone ever needs to talk about anything, I'm always there to listen, and that they are set up with what they need to be successful in their position and their role.
Together we win _as a team._ Not just me, not just a paycheck for them, but a winning team, aiming for and achieving greatness.
**EXERCISE #1:**
**Take Inventory of Your Relationships**
It's not always easy to find quality people to be on your team. You might go through some disappointing relationships before you find the right people, but don't compromise. If you let a few difficult experiences convince you to go it alone, you'll hamstring yourself. I look back on my career-ending injury, and I had many mentors during that time, but I specifically attribute my transition into business to one man who I am forever grateful to have met—Chris Hawker. Chris was a successful inventor and could have easily brushed me aside when I so eagerly requested to work with him. Instead, I showed him the value I could bring, so he took me under his wing and shared his wisdom and experience with me. Think about the people you most look up to versus the people you spend the most time with. If those lists are drastically different, fix that. Reach out to your role models and mentors and involve them in your journey. Cut out those people you spend a lot of time with who are not helping you on your path to greatness.
To find out if someone is serving you in your life or holding you back, ask yourself these four questions.
**1.** Do I feel energized or stressed when I'm around or think about this person?
**2.** Does this person inspire me or have a negative mindset around me?
**3.** Does this person pursue greatness in their life, or are they often a victim to circumstances?
**4.** Do they get excited about my success and want to see me succeed, or do they complain about their own life when I achieve my dreams?
If your answers left you on the positive side, then it sounds like this person is still a great team member in your life! If they are on the energy-draining side, however, you may want to have a "clearing conversation" with them and let them know how you feel about your relationship. Come from a loving place when you talk to them about this and don't fault them for anything. Then make your request for how you'd like to be in relationship moving forward and what you can expect from them moving forward.
**EXAMPLES OF CLEARING CONVERSATIONS**
Hi, (friend/colleague). I appreciate the time we share together. I have created a new vision for my life, and I am making a commitment to being more positive. I feel like the conversations we tend to have are negative and not productive, and I take responsibility for this. Are you open to working on this with me?
Hi, (parent/spouse/friend). I love you and appreciate you. I have taken a stand in my life to work on my goals and not fixate on the stress in life. I want to focus my energy on what I'm grateful for and not complain about what I do not have. Do you support me and stand to keep me to my word?
Most relationships don't work because people don't clearly communicate their requests in a loving way; it usually comes in the form of an attack, which rarely solves anything. You don't need to tell them where they are not supporting, but let them choose to support you in the way you need. This is the path of least confrontation. If you are like me, you want to get clear with all your friends, colleagues, and family in the most direct yet least aggressive way possible.
Hi, (parent/colleague/friend). I want to start by saying I appreciate you, and I request of you . . .
Hi, (boyfriend/girlfriend/significant other). I care about your vision, but you seem to be off course and you are also steering me off course by . . . Let's commit ourselves to . . .
If the relationship doesn't shift over a specific period of time that you define with the person you are trying to get clear with, and you continue to need to make that request, then it's another sign that you may want to distance yourself from the person and start surrounding yourself with a more positive inner circle for your team.
Always try to take action together, but if extreme measures need to be taken, that is when the power of _no_ comes into play. It takes strength to remove someone from your life or take a step back from that person's energy. Understand that nothing is more important than your emotional well-being. This drain will undoubtedly hold you back from greatness. This exercise is a game changer.
**EXERCISE #2:**
**Join or Create a Mastermind**
A mastermind is a group of influential individuals who support you to take your business or life to the next level. With the collective mind of the group, you find support, information, and resources to serve you on your path. And you will get there much faster than trying to do it on your own.
I was just starting out in my business when I joined my first mastermind with an online marketing group. It was essentially a 2-day meeting where we sat at a round table with a group of 15 other online marketing business professionals and shared best practices and ideas and supported each other on our specific goals. The power of the mastermind lies with the people in it and the opportunities you can create from that network. In this first meeting, I ended up sitting next to someone who directly helped me make $250,000 over the next 3 months by selling my products as an affiliate partner and referring me to five others who promoted my product as well. This was a huge boost to everything we were doing at the time, accelerating our profits and success much faster than we ever could have without the mastermind.
Masterminds were the key ingredient for me in taking my business from six figures to seven figures so quickly. There is no other way it would have grown that quickly. It's essential to be a part of at least one mastermind (if not more), and I highly recommend being the creator and leader of one yourself at some point, too.
Napoleon Hill, the legendary author of _Think and Grow Rich_ , has a great way to think about masterminds: "the coordination of knowledge and effort of two or more people, who work toward a definite purpose, in the spirit of harmony." This isn't actually his description of mastermind groups—it's really one of his main principles for how to become successful. The fact that those two concepts overlap so fully—masterminds and being successful—is not a coincidence in my mind.
If you're still not sold, or if someone has given you a negative impression of masterminds, let me try to clear things up for you. Here is what masterminds are or can be.
•Teams of influencers in your community connected for a purpose
•A catalyst for business and personal growth
•A space for goals and holding each other accountable
•A peer advisory board
•An education, support, and brainstorming group
•Confidential
•A commitment
•A group of people supporting each other to create the life/business they want
•Supportive of your success
•A group of people who have your best interest in mind
Here is what masterminds are not or should never be.
•Group therapy
Masterminds are meant to help you attain your major purpose in life by borrowing the wisdom and using the education, experience, and influence of other people who are mutually invested in your success. When run right, they allow you to accomplish in the next 6 to 12 months more than you could accomplish without them in your entire life if you depended solely upon yourself.
There are two essential components to every successful mastermind group: the right attitude and the right members. You can have one without the other and get by okay, but we're not interested in that. We're not interested in settling. This book is not called _The School of Average._ It's about greatness, so that's what we're going to strive for: a great mastermind, with a great attitude and great members.
The mastermind attitude looks like this. You are:
•Friendly and cooperative
•Noncompetitive
•Willing to be creative and brainstorm ideas/solutions for others' businesses
•Supportive of each other with total honesty, respect, and compassion
•Not ever, at any point, indifferent
Think of your mastermind as your basketball dream team. It is a group of differently yet equally talented peers who are there to support your success. Thus, selecting members for your own mastermind group should look like this. They should have:
•A strong commitment to the group
•Similar success and experience
•An agreement about the mastermind attitude
•An agreement on written guidelines created by and for the group
•The ability to give and take equally when it comes to advice, support, and resources
Ultimately, your mastermind group should start with 4 to 6 people (up to 15 max) and a simple (no more than one page) mastermind agreement you're all aligned with that includes:
•The group name
•How you're going to connect (in person or via Skype, GoToMeeting, Google Hangouts, or phone)
•How long your meetings will be (1 to 2 hours minimum is recommended, but some could be 2 or 3 days)
•How often you will meet (weekly, monthly, quarterly, etc.)
•When you will meet
•The agenda for your meetings
Understand all this about masterminds and follow this process with purpose and intentionality, and you are on your way to building a winning team for your business and your life. For more information on this and the different masterminds to join, go to schoolofgreatness.com/resources.
**EXERCISE #3:**
**The Three Lists to Freedom**
This exercise I learned from my friend and "Virtual CEO" Chris Ducker. Chris is the author of _Virtual Freedom,_ a book that teaches people how to work with virtual staff in order to have more time for themselves while at the same time being more productive. This was specifically designed for businesspeople but is easily adapted to use in your life. It will fundamentally change how you manage both life and business.
Get a piece of paper and a pen. Create three columns with the following headlines:
•Things you don't like doing
•Things you can't do
•Things you shouldn't do
Now fill in all the things that fit in these categories relating to your business or your lifestyle.
**_The Things You Don't Like Doing_**
These are the things you procrastinate on all day. Things like replying to social media messages, managing e-mail, doing your bookkeeping, etc. Life and business demand that you get these things done, so it's your job to find someone you can pass them off to or develop a system that allows you to be more efficient.
**_The Things You Can't Do_**
Many people, especially entrepreneurs, feel like they have to do a lot of things themselves. The only problem is, there are many things you can't do even if you wanted to. I love design and playing with designs on my computer, but I'm the worst at using design software and designing things myself. After a few hours of intense work, the best I can draw is a bad-looking stick figure of a cat! Just because you have an interest in something or doing it yourself would be cheaper doesn't mean you are qualified to do it at a high level. In fact, your lack of experience and expertise might actually make doing it yourself more costly than hiring a professional, since it would take up more of your valuable time that could otherwise be spent on high-level business and life activities that you're actually good at.
**_The Things You Shouldn't Do_**
In my business, I'm very capable of doing a number of different things that I shouldn't be doing even though I like doing some of them. That's just the natural consequence of earning five-figure consulting and speaking fees for a couple hours of my time. It means I shouldn't be spending 15 minutes figuring out what to post on social media or handling customer support. I may be good at those things or like doing them, but they are literally a waste of my time.
Chris Ducker still prepares these lists every 90 days because, he says, we sometimes slip back into bad habits out of necessity or we just get busy with life. I recommend checking in with this as well to see what tasks you can put in these lists and start letting go of them.
This becomes the road map to working with your team. These lists flag the jobs that aren't the best uses of your time with the skills you have for making a bigger impact and getting closer to your vision. They indicate how to best set up your team or support structure.
When I first started in business, I worked 15-hour days because I did all of these tasks on my own. I wasn't good at a lot of them, which meant they took me even longer. When I switched my mentality and allowed others to support me and join my team, the stress went away, efficiency went up, and I was able to focus on what I loved doing at all times instead of the things I didn't need to do. My life seemed to come together and flow. It's been like living in a dream world ever since, and it's possible for anyone who is committed to making it happen as well!
Keep in mind that this exercise isn't just for entrepreneurs or for businesses generally. It works as well in your personal life. I hate shopping and get tired in about 30 minutes at the mall, I struggle with cooking (I enjoy doing it, but it rarely tastes as good as it should), and I shouldn't be doing yard work or deep cleaning my place. Based on the time I use in my business and toward making money that I charge for speaking, coaching, or consulting, my time is better spent doing what I'm great at and hiring others on my team for support with those lists as well.
Think of all the things in your personal life that you want to add to this. Even if you don't think you can afford to hire or outsource for some of these tasks, put them on the list anyway. There are tools and apps coming online every day designed to solve these problems and offer support on a friendly budget.
**_Don't Like Doing_** | **_Can't Do_** | **_Shouldn't Do_**
---|---|---
Checking e-mail | Graphic design | Updating media social
Managing my calendar | Developing a Web site | Handling customer support
Handling basic inquiries | Editing podcast episodes | Managing company blog
Researching travel | Bookkeeping and accounts | Collecting dry cleaning
**EXERCISE # 4:**
**The Personality Matrix**
The Personality Matrix is a process you can follow to discover not only who you are but also to understand whom you are interacting with on a daily basis. Imagine knowing exactly what to say to someone—a teammate, a family member, a business colleague, a customer—because you know their personality type. Imagine being able to immediately connect with them in a way they understand and relate to. There are a number of personality tests online and different ways of examining them, but I learned about this process from Chris Lee, so it has stuck with me to great success. The Personality Matrix divides people into four main personality styles: promoters, analyzers, controllers, and supporters.
**_The Promoter (Opposite of an Analyzer)_**
The gift of a promoter is the ability to contribute and grow many ideas. Their primary challenge is with completing projects. They are the life of the party and have a lot of passion but, because of this challenge, tend to break their word and become overwhelmed.
If you find yourself in the position of trying to sell something to a promoter or get them excited about an idea of yours, there's one reliable way to do it: Show up excited. Be enthusiastic. Talk about your experience and how great it will make them feel.
Promoters are relationship driven, all about fun and energy.
**_The Analyzer (Opposite of a Promoter)_** The gift of an analyzer is that they are detail oriented, disciplined, systematic, process driven, structured, and organized.
If you're selling to an analyzer, you must know everything about what you're working with down to the smallest details.
Analyzers are their word. When an analyzer says they will do something, you can take it to the bank. They lack passion and spontaneity, and they can show up as if they are hardly alive. Analyzers are visual and logical. They are formal in their dress and their energy.
**_The Controller (Opposite of a Supporter)_**
The gift of a controller is that they can get things done. They are driven, decisive, confident, goal oriented, and focused.
When you're selling to a controller, you better show up powerfully and dressed well. Agree with them and speak in a leading way that implies that they believe your idea was theirs. Stroke their ego. Connect with them at their level.
Controllers appear insensitive, mean, uncaring, and inflexible, and they pay for it in their personal and business relationships. A controller is dominant and formal. You have to present to them in a dominant, formal way.
**_The Supporter (Opposite of a Controller)_**
The gift of a supporter is being a giver focused on emotions, love, acknowledgment, and self-respect.
Selling to a supporter is all about emotion. Discuss the benefits not just to those who would be customers or users but also to everyone around who stands to be better off due to the actions or decisions you're proposing.
Supporters often come off like doormats. They don't stand up for themselves immediately, and it may seem like you're taking advantage of them. The way to avoid that is to provide positive feedback, which they respond to overwhelmingly.
So, which one are you? What is your dominant personality and your secondary personality? Being a leader in relationships requires the ability to access and be flexible with each of these personality types at any given time. If you can match or complement the energy of others around you, you can understand them better, and they will in turn feel more appreciated. Most important, being a successful, productive member of a good team demands that you don't tip too far in any one direction.
Are you an analyzer? Be outrageous!
A controller? Be vulnerable.
A promoter? Keep your word.
A supporter? Tell yourself, "I matter."
**_COACHING TIP_**
We are all in this together, and it's time to start living in a world where you embrace this concept. Life flows when you find a team you gel with, so why not start finding the All-Star players right now? The way you do this is by first becoming an All-Star player yourself. Do the work, improve your attitude, hustle, and sharpen your skills so that everyone else wants to make you a starter on their team! When you become a valuable asset to the world, then the world starts giving you what you dream of. It's that simple.
People matter. And you can't achieve anything great on your own. Letting people know how much they matter and how much you care about them is equally important (if not more). The saying goes that "people don't care about how much you know until they know how much you care." This is true in family, sports, business, and any other situation in life. Continue to surround yourself with positive people who care about you and always find ways to create a win-win in every relationship in your life. Relationships are the key to success, and it's time to start investing in yours.
**_GET GROUNDED_**
For many years, I thought there had to be a winner and a loser in sports, business, and life. I was so attached to the scoreboard and making sure that my team and I had more points than our opponent that I failed for a long time to grasp the meaning of a full life: creating win-win relationships. I never thought about what happens when you do "win." Then what? Are you just supposed to keep winning and gaining momentum and building an empire of success, yet be the loneliest winner in the world? Or is there more to living a great life?
Slowly but surely, moments happened where I witnessed and started to understand the value of giving back and being in service to others. This may be my most important lesson to date. Making money matters, having your needs met matters, achieving your vision matters, and turning your dreams into reality matters. But if you aren't looking for ways to improve the lives of everyone around you—your family, community, environment, and the world—then what's the point of all of it? In this chapter, we dissect the value of giving back. It's not about looking good or doing it because you feel you are supposed to. I want you to really see why giving to others is so important, because it took an army of people to turn you into the person you are today.
**LIVE A LIFE OF SERVICE**
_The best way to find yourself is to lose yourself in the service of others._
**—Mahatma Gandhi**
One family. Two sons. Two different paths toward greatness.
From the first son, Scooter, we learned about how to assemble a winning team. But it was from the second son, Adam, that I learned one of the most important lessons of all.
I met Adam Braun at a Summit Series conference called Summit at Sea, a kind of summer camp for people who want to change the world. When you see Adam for the first time, he seems like just a regular person, not a superhuman athlete or high-rolling entrepreneur like some of the others you've met in this book. He doesn't have the rock star, Hollywood swagger of his brother. He has an Ivy League pedigree, but I don't think anyone would consider him to be an intimidating genius. He's a regular guy with a big heart, whose high-paying job at a major consulting firm left him dissatisfied and unfulfilled. Like Adam, I, too, had made a little money and had what most people would see as the trappings of success. And as I felt after becoming an All-American in the decathlon, he, too, felt he needed to find some greater purpose, some cause or path to follow.
I could deeply relate to his story that day we met, not just the dissatisfaction but also what it was like to have the shadow of a great sibling follow you and shade your decisions. Given how important my own brother has been to my life, it isn't surprising that I have found myself including brothers as champions of these two chapters. So I consider it serendipity that I encountered Adam—at a conference on a boat, no less—embodying the bold decision to make his life all about giving back.
Adam is the founder of Pencils of Promise, a nonprofit group that has built more than 300 schools and changed the lives of hundreds of thousands of children around the world. Actually, wait, he wouldn't like that I said _nonprofit._ He prefers the term _for purpose._ That purpose is helping kids learn and follow their dreams—kids that most of us pretend don't exist. More recently, his _New York Times_ best-selling book, _The Promise of a Pencil,_ has brought Adam into a much brighter spotlight, but for the past several years he has been building one of the most important charitable education organizations in the world.
There were two seminal events in Adam's life that set him on his unique path. The first occurred when he was 17 years old and a promising basketball player on an AAU team. His parents made the decision to take in two young athletes from Mozambique named Sam and Cornelio. Not unlike what Leigh Anne and Sean Tuohy did for Michael Oher in a story made famous by Michael Lewis in his book _The Blind Side,_ Adam's parents wanted to give these kids a chance to fulfill their potential and experience the American dream. For Adam, his parents' choice was a chance to expand his definition of family by adding two incredible people to it.
Sam was a senior when he came to live with the Braun family. He stayed through his senior year, graduated, then went to Brown University. Cornelio was a sophomore and lived in their house for 3 years before getting a full ride to Georgetown and then transferring to American University after freshman year, from where he ultimately graduated. To this day, Adam considers Sam and Cornelio his brothers. One lives in Los Angeles, the other in DC, and they celebrate all their family events together. Their kids are Adam's nieces and nephews.
"Not only did it change the dynamic of our family, but also it entirely changed my personal worldview. I started to realize the path that Sam and Cornelio had taken was the path that people had taken over generations who wanted to strive for a life that was more than the one that they were born into. It opened my eyes up to how many cultures and people exist outside of that small bubble that I had experienced until that point growing up in Fairfield County, Connecticut, really only seeing New England," he told me.
**AN UNLIKELY JOURNEY**
This was the first step in Adam's path toward greatness. A step that led to aspirations for living a very different life than most people would consider the norm. As a sophomore at Brown University, inspired by his family experience and the powerful 1992 documentary _Baraka,_ Adam enrolled to attend Semester at Sea (noticing a boat theme here?), an academic program aboard a large cruise ship that hosts students from all around the country while circumnavigating the globe and visiting numerous countries over the course of about 100 days. Adam had a friend who had been on Semester at Sea, and upon her return, she could not stop raving about her experience. Their stop in India was particularly transformative for her, which in turn was transformative for him, because it just so happened to be a scene in _Baraka_ shot in Varanasi, India, that had enthralled Adam with all the potential the world held outside his bubble.
"So I looked at the Semester at Sea itinerary, and they were going to India. I thought, 'This is it. I'm going to go to India, go to Varanasi, and also get to see all these other incredible places around the world,'" Adam told me. As he spoke, I could hear the purpose in his voice. "Sometimes you just have this inner voice that compels you. It's your future self speaking to your present self, saying, 'Follow me. This is who and what you were meant to be.'"
For a moment, however, it appeared that Adam was meant to be at the bottom of the Pacific Ocean. Eight hundred miles offshore, shortly after leaving port, the Semester at Sea ship was hit by a 60-foot rogue wave that could have easily sunk the boat and taken everyone on board with it. His journey around the world nearly ended before it began. This near-death experience put Adam in a particularly vulnerable and introspective place as they continued their travels from country to country. Here they would come, week after week, working with, meeting, and learning from all these people who didn't have much; yet in nearly every case, they were met with unexpected levels of happiness that, to Adam, seemed so scant in the materialistic culture he'd left just months ago.
I imagine that this is what led to the conversation that completely changed Adam's life: "Everyone on Semester at Sea did this thing where they collect one thing per country—a beer bottle or a funny hat, or they got a T-shirt, or they took a photo of a Beanie Baby in front of a landmark. My thing was asking one kid per country what they would want if they could have anything in the world."
When Adam started telling me this story, the implications for my own life hit me right away. For a college kid to have that kind of awareness of others, that kind of empathy, was inspiring. For all my focus and perseverance and hustle when I was playing sports in high school and college, I was also pretty selfish and egotistical. I thought mostly about myself instead of how I could help the other guys around me, and when I look back on it, I'm pretty sure that held me back from achieving the kind of happiness and success I was looking for. As selfless as Adam's "one thing" was, his worldview was still dominated by his life inside the Connecticut bubble, and he wanted to escape it.
"I expected to get answers from these kids that were similar to what I wanted when I was a kid, which was, like, a big house, a fancy car, and the latest technology," Adam admitted. "But the answers were just so different."
The most powerful one came from a little boy begging on the outskirts of the city of Agra in northern India. Adam asked him, "If you could have anything in the world, what would it be?" His answer was simple: "I want a pencil." That's it. Just a stick of wood with some graphite in it. As you can imagine, he probably wasn't too particular about whether it was a number 2 Dixon Ticonderoga pencil or a fancy mechanical one, he was willing to take anything. Why? This precious little boy wanted to _learn,_ to go to school, and he believed the pencil was the thing that would get him there.
Even hearing this conversation gives me inspired chills. I know what you're thinking. It shook Adam to his core, motivated him to give up all his worldly possessions and dedicate himself to changing the world, right? Wrong. It did indeed leave an indelible mark on the young man—but he had a bigger vision than becoming a martyr.
**MAKING THE VISION A REALITY**
After his semester wrapped up, Adam headed back to America, where he did what many in his position would do: get a job in corporate America where he made tons of money. Seriously. It's almost become a cliché to complain about how students from elite universities head to Wall Street, but that's exactly what Adam did.
He found himself with a job offer from Bain, one of the world's most successful (and some say ruthless) consulting firms. And when you hear Adam's explanation of what he learned, you understand why he made this seemingly superficial decision: "I went to work at Bain & Company on the consulting side and just went through this incredible training work with absolutely brilliant people, saw the inner workings of Fortune 500 companies, had exposure to how the best businesses in the world were run and even improved upon."
Are you seeing now? Yes, that moment in the street in India changed Adam, but he knew besides handing the kid a pencil, there was nothing much he could do for him in the way of real change. Adam went to work in corporate America precisely to learn the skills, build the relationships, and earn the money he needed to effect the change he wanted to see. In other words, unlike so many young people who find themselves with good jobs at places with names like Goldman Sachs, Google, and BP, Adam wasn't doing it for himself or for the money.
"I realized about a year, year and a half in, two things. The first was that the nonprofits I was passionate about weren't run with any of the business acumen that I was used to seeing." There's no question most nonprofits have their hearts in the right place, but according to Adam: "When you're actually inside of the organizations, they're incredibly inefficient. It's because they're usually based on passion. So the language that I spoke, the sense that I had around business, it was kind of weird and frustrating to me that these humanitarian issues weren't being approached with the same commitment to results."
There was another benefit from being around sharks in suits. He realized he didn't want to be one, not for very long anyway. "I got really bored of meeting people at a bar and them asking, 'What do you do?' and my answer being, 'Well, I'm a 23-year-old management consultant.' That's a really boring conversation after about the fifth time. In a year and a half of living in New York as a young, 20-something single male, I was living what I thought was this great life. I had this sick apartment and access to awesome parties and dating different girls and had great friends around, but I wasn't connected to anything that wasn't in service of myself."
That's when it hit him: "I didn't want to be a management consultant. I wanted to be somebody who builds something—specifically, schools internationally for children in rural communities. That's who I wanted to become." But now he had the skills and support to be able to do it.
Bain allows their employees to take what they call "social impact externships" that offer hands-on experience working on important educational and development problems out in the world for 6 to 9 months. Essentially, if you make it through the first 2 years of employment at the firm (what amounts to a probationary training period) and they promote you on to a third year, in that third year they let you leave and follow your passion. You don't get paid, at least not by Bain, but you can work for any approved program or company that will bring you on (and potentially pay you). Adam decided he would do one of these externships. Initially, he thought he might work with an organization called the Cambodian Children's Fund that he had been volunteering for since college as a fund-raising coordinator selling T-shirts, throwing parties, and doing pretty much anything that might help these kids.
Then one night shortly thereafter, he went to the New York Philharmonic for the first time. "I'd never been to a symphony before, and this guy walks out onstage to play a piano concerto and just starts crushing these keys. He was exuding so much passion into this instrument. I was just mesmerized by it."
Not only was Adam mesmerized, he was inspired. The same way that pianist felt about his music, Adam wanted to feel about . . . anything, really. "I just wanted to feel that passion, I wanted to feel alive the way that he must when he connected to that piano. And in that moment is when this name literally just popped into my head: Pencils of Promise. It was the perfect name."
It was sort of his Jerry Maguire moment. "I went home, wrote everything that I could on paper—like an original mission statement, a charter, a manifesto, all these stupid fund-raising ideas, all the people I would contact wherever I would travel who I thought could help me try to build the school, the very first one. I was really committed to building the first school and dedicating it to my grandmother, who was turning 80 that year. She is a Holocaust survivor and has just been through so much so that I could be in the position I was in."
He thought, "Let me live in service of her, in particular, honoring her, carrying forward her legacy, and then ultimately educating children in poverty who don't have access to high-quality education."
A few weeks later, he went to the bank to open an account. He asked the teller what the minimum amount required was—the answer was $25. And with that, he launched Pencils of Promise with a $25 check and never looked back.
**THE RIGHT KIND OF ROI**
The organization he built meshed Adam's for-profit business acumen with his nonprofit idealism, a model that attracted me. For a few years prior to meeting Adam, I knew I wanted to start giving back and serving others outside of my business, but I didn't know how or what to do. After meeting Adam, I decided this was something I could get behind because even though I never felt like I was a smart kid growing up, I was drawn to learning, I yearned for knowledge, and I valued every type of education on my path to success. I got involved with Adam's organization and donated money to build a school in Guatemala.
Part of the mission of Pencils of Promise is to have the local community take ownership of their school. To do that, the community must build the school themselves. The organization supplies the materials and a contractor with know-how, but the mothers and fathers build the school. The result is an enormous level of pride and stewardship. Investing their own sweat equity, they are determined to keep the school maintained and functioning. I love this mission and follow these principles in my own business with my students. I provide the content, oversight, materials, and tools necessary through my podcast, products, and services, but I don't "do the work for them." If I did, I'd be enabling them instead of empowering them to use their own genius and talents to learn the skills by executing. This way, they can reap the rewards and have much more ownership and pride in what they create.
Talking to Adam is uplifting and inspiring. "As much as I'm a passion-driven person, my background helped immensely because I'm now an entrepreneur who filters every decision through the question 'Will this provide long-term ROI?'" he said. "I always wanted to build an organization with the head of a great business and the heart of a humanitarian idealist."
Think about that: He's not referring to a return _for him._ He means, how can the organization best be of service and deliver the most value to the people it's meant to serve?
I heard a similar sentiment from Angel about his philosophy as a CEO at Deckers: "Greatness to me is just about being there for other people; living a life that is others oriented is where you achieve greatness." That's how Angel tries to think and act as a leader of more than 2,300 employees with their own stories, dreams, hopes, and needs. "Deckers is about all the people who work here having the kind of opportunity that I had, to live a life that maybe is outside of your expectations or your practical reality or that you dream about but don't have the vehicle. I say, 'Here is the vehicle.'"
That's what a true leader, a really great individual, does, whether they run a for-profit or a for-purpose organization. It's not all about you; it's not all about what you want and need. If you want to achieve those things, I've learned, you have to actively and regularly help other people with their own wants and needs. Only then, when you've moved away from selfishness, can your winning team truly thrive.
In our self-centered world, it's easy to buy into the "me" mentality. We are constantly told that to get ahead, we need to invest in ourselves, and then once we've "made it," we can give back. But as Adam Braun's story shows, giving back can be the vehicle to "making it" if we align our service with our passion. Without service, achievement is empty.
**A LONGER, RICHER LIFE**
James Clear, the entrepreneur and travel photographer, wrote about this on his blog after reading a 2012 _New York Times_ article about the research on longevity:
The article didn't come out and say it, but what it alluded to was that as people age, they tend to find themselves consuming more and creating less. To put it bluntly: The easiest way to live a short unimportant life is to consume the world around you rather than contribute to it.
Meanwhile, the people who keep on contributing tend to be the ones who keep on living. The message was clear. People who contribute to their community live longer.
If greatness isn't a good enough reason to be of service to others, I think James has given you the biggest reason of all—a longer life. Still, I get why you might be hesitant. _Service_ is such a loaded term. Fortunately, being of service also has many definitions and iterations. It doesn't mean you have to work in a soup kitchen or take a vow of poverty or work for a nonprofit.
One of my favorite TED talks is by a guy named Ron Finley, who is known as the "guerilla gardener." For years, he has been planting vegetable gardens across South Central Los Angeles. Why? For fun, for the beauty, for food, and to make a small contribution to a neighborhood that desperately needs it. I love this because he isn't asking for anything in return, nor does he expect someone to pay for these services. He simply does this as a random act of kindness to give back and make his community that much more colorful and fruitful. He takes pride in his community and adds his gifts to it. It makes me think about creative ways I can add to my community as well.
Kyle Maynard is of service to veterans—even though he isn't one himself and his injuries were biological instead of the result of violence. But by connecting with these service members, by seeking out challenges and bigger goals, he provides an inspirational service.
Shawn Johnson speaks on behalf of the Women's Sports Foundation, which was founded by tennis legend Billie Jean King back in 1974 to boost the lives of girls through sports and physical activity. Shawn's taking everything she learned from her Olympic and dancing success and paying it forward to a generation of young girls who might need the same kind of boost that the little boy in India needed from Adam Braun.
The other side of my buddy Aubrey Marcus, the CEO of Onnit who gave us the exercise on what's MISSING in Chapter 5, is essentially one giant quest to serve humanity by exploring the possibilities of human happiness and consciousness. He wants everyone to transcend everything, and he works exhaustingly and selflessly to that end—through his dedication to researching the optimal ways for total human optimization using the success of his fitness and nutrition business to make it possible.
I get the sense from many of the authors whom I've learned so much from that they would have written their books for free if they had to. They not only felt that some sort of muse had struck them and they owed it to their art to get it out, but they genuinely felt the world needed to hear their message and would be better if they read it.
I don't think traditional charity is the only way to act with purpose or be in service of others. Every day, I wake up and feel excited about my podcast not because of the important people _I_ get to meet but, rather, because I get to serve as a conduit between them and my audience. I get to learn and help others learn, too. That thought has also helped power me through this book.
That's my point: You can be of service by following your passion. As Adam Smith wrote, "It is not from the benevolence of the butcher, the brewer, or the baker that we expect our dinner, but from their regard to their own interest." Following your passion instead of settling, subsuming yourself as part of a larger goal—that is the first step in being of service to others. But I hope you won't stop there. I hope you'll also see how you can apply your gifts to a big cause and give back without any strings.
Like many successful people, I receive requests for lunch meetings or get asked for advice by people just starting out. They want free coaching, introductions, or a perusal of their business plan. I'm busy, my time is valuable, and the temptation is to say, "Look, I'm sorry, but I don't have the time." And who would fault someone for declining a request for free help? The answer to that question is _you._ You and I, if we are to be great, need to practice empathy and help others. We need to think: "I was once in this person's shoes, and someone helped me out." Like Kyle and Shawn and Aubrey and Angel, we should always be paying it forward.
I'm not saying you need to give an hour of your time to everyone who asks for advice, as you may never get anything done in your own life if you are that popular! However, maybe this means taking a few extra minutes to help a new coworker. Maybe it's pointing out something you noticed in a competitor's game that would help them improve. Maybe it's speaking at your kid's career day. Maybe it's writing an article about a sensitive topic that most people are too ashamed to share their experiences about. Maybe it's smiling at a stranger on the street or helping them pick up something they dropped. For me, it was starting _The School of Greatness_ podcast so I could help all those people I couldn't reach or carve out the time for.
It took me a long time to understand how crucial a life of service is to achieving greatness in any discipline. Adam Braun clearly got this early on and parlayed that insight into an amazing career as a social entrepreneur. Nelson Mandela put it best when he said, "There is no passion to be found playing small and settling for a life that is less than the one you are capable of living."
But Adam realized that thinking about yourself, your bank account, or whatever it happens to be is thinking small. As he puts it, "My definition of greatness would be living a life full of purpose, love, and dignity."
I'll add to that: _for yourself and for others._ I know what you're capable of. I know you can be of service in so many ways.
**EXERCISE #1:**
**Choose Your Avenue of Service**
Get involved in giving back, whether it is through your time, talent, or treasure (dollars).
**_Step 1_**
Write down something simple you can do _today_ to give back to your community, family, and friends or a stranger. Your service can start as a random act of kindness. You could open a door for someone, buy flowers for a stranger, give a compliment, fill someone's expired parking meter, help someone in need, or simply smile. Give back in some way with a positive purpose. You will immediately experience the intrinsic reward whether the act is seen or unseen.
Doing this on a consistent basis, you will quickly find yourself living a life in service to others that does not feel like it is taking away from some other part of your life. Instead, it will feel additive and necessary—like eating or breathing. As your daily acts of kindness grow, you can research a charity, a nonprofit, or an organization you would like to get involved with. Here is some food for thought.
•Education in your community
•The arts (dance, music, theater)
•Advocating for human rights
•Mentorship programs
•Cancer research
•Fund-raising
The possibilities are endless. Whatever you are inspired by and speaks to you, that is exactly what you should be doing. If an organization is not working for you, start your own! Anything is possible, so get involved and spread the word. There are tons of opportunities out there. Stop thinking about what people will say or how they will look at you and be proud to take a stand for the service you have chosen.
For specific organizations that I believe in and more suggestions, check out schoolofgreatness.com/resources.
**_Step 2_**
After deciding on your avenue of service, identify how you can best serve it through your time, talent, or treasure.
**Time**
Some of us have more time to give and can volunteer directly. Offer your time to volunteer with the organization of your choice. Be consistent, whether it's weekly, monthly, or yearly, in order to create a positive habit.
**Talent**
You might have a certain talent that organizations need (maybe you're great at graphic design, and an organization needs help with their logo or Web site development). Reach out to these organizations to offer your expertise. Many organizations have a tremendous vision and all the hustle in the world, but they struggle finding a great team. You can be the difference.
**Treasure**
If you do not feel like you have the time or talent to give directly to an organization, financial donations impact growing organizations disproportionately. Sending $1,000 to the Red Cross is great, but giving $500 to your local veterans group or pediatric cancer charity can change their month. This month, commit to a monthly donation to a campaign or a cause.
Now make a decision about how you intend to get involved and write it down. Make it real. One or all of the three _T_ s? Then choose a date that you are going to begin and prepare to take action!
**EXERCISE #2:**
**Do Your First Act**
Short and sweet, you've got to put your money (or time or talent) where your mouth is. This month, go do something with and for your organization of choice. This can be actually volunteering at an event, organizing your own event/fund-raiser, or donating money or goods. As in exercise #1, start small with simple daily acts of kindness and build upon them.
Not only will this get you serious about helping, but you'll also get to feel that amazing high of doing good. Of course, this is worth sharing, so once you've committed to your act, post to your social media channels with a photo and an update to let everyone know what you are doing and how it went (#greatnessbook). This is a great way to encourage and inspire others to get involved. The only thing more contagious than giving is the joy and the emotion that come with it!
**_COACHING TIP_**
When you fully understand why giving is the key to life, then you make it part of your daily mission to serve others in whatever you do. Don't look at this as an extra task you need to take on. If you do that, you've missed the point entirely. Rather, look at this as a part of who you are, who you become, and your way of being in every moment.
It needs to be in your breath, rushing through your blood. Every aspect of your life should have a component of service. It can be as small as smiling at everyone you come across to as big and broad as you want to take it. There is no right or wrong level of giving; the key is just that you give from a place of love instead of guilt. The way I am sure to do that is a little trick I developed after flying all over the country speaking to and meeting with people just like you. I remind myself of that part of the preflight safety announcement that every flight attendant gives:
Put your own mask on first.
When you make sure your needs are met and you are full, then you'll have even more energy to give to others. Go out and live a life of service!
**CONCLUSION**
In 2012, I moved from New York to Los Angeles for a girl, arriving with two big bags, a guitar, and a smile on my face. Later that night, she broke up with me. What made it worse was that my life in New York was on fire before leaving for LA! My business was thriving, my relationships were growing, I was doing cool stuff all the time. I felt invincible. This move out to LA for love was just one more thing I was going to conquer. Instead, it put me right on my ass.
We were in our mid- and late twenties at the time, so of course our breakup wasn't actually final. We got back together, dating off and on for a few months. I committed to being the perfect boyfriend, doing everything I could do to make my girlfriend happy and our relationship healthy, but I knew it wasn't right, it wasn't working. Everything about LA wasn't working, really. I was in a bad head space. Everything that was happening left me frustrated, confused, and uncertain about the future. I would soon learn that, as my friend Kyle Maynard says: We are only as good and as strong as our adversity makes us. Sometimes we don't know what is working against us until we make our biggest mistakes, and I was about to discover that on the journey to greatness, you sometimes have to fall.
One afternoon I was playing pickup basketball at the courts down the street from my condo building when everything came to a head. I had been guarding this one guy all game—he was a little older than I was and definitely a little heavier—and he had been talking trash and throwing dirty elbows the entire time. Now, I'm a relentless competitor and have been in all areas of my life for as long as I can remember. I can take some trash talk and some hard fouls in the spirit of competition. But this guy was starting to get personal, and he was trying to assert himself over me—dominating me, like an alpha dog.
What he didn't know—and neither did I, really—was that this behavior was one of my major triggers. Being disrespected and dehumanized made me see red. We got in each other's faces. There was a lot of shouting and posturing, literally puffing out and beating our chests like a couple of gorillas trying to show dominance. I was beside myself with anger. I couldn't understand why he was doing this to me. Then he took it a step further and head-butted me right in the face. This was no warning love tap, like you see sometimes in NBA games when two alpha dogs square up against each other after a hard foul around the basket. I couldn't believe how hard he slammed his forehead into mine!
If you've never been head-butted, let me tell you, it _hurts!_ It makes you see stars, and it makes your eyes water. And if you're me, it makes you lose your mind a little. I am not proud of what I did next. I pounded on the guy with every ounce of energy I could muster. Eventually, my best friend, Matt, whom I was playing with, grabbed the guy, and his teammate pulled me off to break us up. Unfortunately, it didn't end there. The guy was still talking trash and insulting me, and I was screaming at him, asking why he would do that to me. Why would he head-butt me like that? What was he thinking? Why did he attack me over a meaningless pickup basketball game?
The questions were rhetorical, mostly. I was basically talking to myself, trying to process what the hell was going on. But this guy decided to answer. I don't remember what he said—it was all kind of a blur—but whatever it was, I responded by running up to him and hitting him one last time as hard as I could.
It was one of those moments like out of a movie. The basketball court went dead quiet except for the sound of my yelling and screaming. I was yelling at everyone, telling them that he hit me first, and I was screaming at him for attacking me. I still couldn't understand it. My friend Matt told me I should get out of there before anything else happened, so I ran. No, I _sprinted_ the blocks back to my building, bounded up 11 flights of stairs, burst through my apartment door into my bedroom, and collapsed onto my bed shaking uncontrollably. What the hell just happened? I felt completely out of control and completely terrified of my own behavior.
_That's not me. I'm not a fighter. I aspire to come from a place of total love. Why did I react like that?_
I repeated those words to myself over and over in my head. The feelings I was being forced to wrestle with were almost totally foreign. I hadn't felt like this in nearly 20 years—since the last time I got into a similar fight as a kid. Lying on my bed looking up at the ceiling, I started thinking about that earlier fight. What I realized very quickly was that this fight was practically a carbon copy of that one.
It happened when I was 12 years old, back in Ohio. Three of us were raking leaves and grass along a path on the golf course where we worked during the summer. Two of us were goofing around and roughhousing. We were playing this game where we'd rake up a little bit of grass, then flip the rake over and flick the grass and leaves at the other person, almost like you'd pick up and throw a lacrosse ball. It was a fun little grass fight. We decided to bring the other kid into the fun. He was older than we were (15), so we decided we couldn't ask him—that probably wouldn't be cool—we would just have to tag-team him a little. The two of us scooped up some grass and leaves at the same time and flicked it at him simultaneously.
At the time, we cracked up, thinking he would join in and playfully fight back. We were half right. As we turned back to keep grass-fighting each other, the 15-year-old kid came up behind me and punched me in the back of the head. I was stunned. Then I was confused. Then I was stark raving furious. All within the span of 2 seconds, I whipped around and hit the kid square across the face with my rake handle. The blow sent him to the ground, and I pounced him. I hit him with everything I had, screaming at him the whole time like in that scene from _A Christmas Story_ when Ralphie finally snaps and beats the snot out of Scut Farkus.
Finally, the other kid got behind me and pulled me off in a full nelson. I shook free and sprinted the 500 yards to the clubhouse, where I burst through the employee entrance, ran into the bathroom, and started washing my hands. Like if I washed away the evidence and got home before anyone else saw me, it meant it didn't happen. My knuckles were scraped bloody. Dirt and grass and blood poured into the sink and swirled down the drain. When I finished and stopped shaking, I came out into the office and there was the 15-year-old. He was screaming at me, "Why did you do that, Lewis?! What is wrong with you?!" I barely heard him, because I was sick to my stomach about what had just happened. Seeing what I was capable of when I let my emotions get the best of me, I vowed right then and there to never fight again.
I succeeded in upholding that vow . . . for 17 years. Lying on my bed staring up at the ceiling, a 29-year-old man with bruised and bloodied knuckles, connecting the dots between those two moments and seeing the parallels, scared me to death. I had to do something about this. I had to figure out what was going on inside of me and why. What had happened to me? And most important, why did I allow this to happen?
Two months later, at the suggestion of my friend Quddus, who'd heard about the fight and the troubles I was having, I signed up for Chris Lee's leadership workshop. Little did I know, being an effective leader requires emotional intelligence, and that's a lot of what we covered. We talked about triggers and being open and vulnerable. All the stuff we discussed in Chapter 3: Cultivate a Champion's Mindset. Why did being attacked unfairly like that turn me into the Hulk? Why was perceived disrespect or feeling taken advantage of such a trigger for me?
Chris helped me trace these emotions back through my life, teaching me how to be vulnerable and open to my past. And that's when it clicked. It all went back to the time when I was 5 years old and I was raped by my babysitter's teenage son. I won't dive into specifics, because that is not what this book is about.* What I will say is that after opening up and sharing this story with listeners of my podcast, I was overwhelmed with love and support from all over the world. I also came to realize just how many people have been affected by sexual abuse in their lives. Listener after listener e-mailed me emotional, heartbreaking stories about their childhood traumas. It pains me to see how many people have experienced their own version of what I went through.**
Before attending this workshop, I had never shared that story with anyone. I'd kept it locked inside for almost 25 years, trying to forget it, trying to deny that it ever happened. But I couldn't anymore. It had planted these triggers in my mind that were starting to sabotage every area of my life—my romantic relationship, my friendships, my business partnerships, my overall confidence and happiness.
With Chris's guidance, I stood up in front of the group at his leadership workshop and shared the story publicly for the first time. And it was a revelation. I had been too scared, too hurt, too superficial to look deep down inside myself and face my own past until that moment. We all have traumas. We all have secret pain. We all make mistakes. It's true. I wish it wasn't so, but it is.
That's the bad news. The good news is that we're all _also_ capable of greatness no matter what we've been through. In fact, it's our past that makes us who we are and our adversity has the potential to become our greatest advantage. You see, the breakdown I experienced in my life which exploded on the basketball court earlier that year led to a profound and life-changing breakthrough. I didn't know I was holding onto that kind of rage inside nor that I was capable of being so violent. Going back into my memories and becoming aware of the stories I had told myself about the pain I experienced as a child was one of the keys to moving from reacting to responding in my life. I was truly disappointed in myself after that incident, and I committed to discovering what was holding me back from really being the man I said I was and wanted to be. By clearing and coming clean about my past, I was able to align my actions with my values and learn new ways of showing up in the world that were previously counterintuitive: Things like cultivating a win-win environment in everything I do, seeing the power in vulnerability, acknowledging my emotions, and holding myself accountable to my vision every day.
**THE SCHOOL OPENS FOR BUSINESS**
I began _The School of Greatness_ podcast in the months between my big fight on the basketball court and my time with Chris. My first guest was the brilliant _New York Times_ best-selling author of _The 48 Laws of Power_ , Robert Greene, and we were going to talk about his (then) new book, _Mastery._ Just being in Robert's presence, this man who had not only written several classic, timeless books but had influenced multiplatinum rappers, fashion designers, and world leaders, was inspiring.
As we sat and talked, Robert spoke about how much time and energy and effort it takes to become truly skilled at something. It had taken him decades to get to where he was, and it had taken the greats of history he wrote about just as long, if not longer. He talked about the critical importance of apprenticeship and studying under other masters. That's where I got the idea to craft my own curriculum, to enroll in a new kind of school where I could learn and reach my potential. The title of that first episode with Robert on my newly launched podcast, _The School of Greatness,_ was "How to Master Anything and Achieve Greatness." I wanted to do both those things very badly.
Like anything new on the Internet, the podcast had its ups and downs at first. I was learning as I went, trying new things, figuring out most of it all by myself. I had no idea what I was doing. But I also didn't know what I didn't know, so anything was possible. Shortly after Chris's workshop, _The School of Greatness_ podcast began to take on a new life and renewed energy. Regular listeners noticed a huge change in the way I connected with guests, how open I was, and how my ego had shifted. I'd learned so much from Chris—and the lessons I learned about myself from his workshop had quite literally changed my life.
The goal now was not just to learn from great, interesting people but to finally get serious about the goals and vision I had for myself as a young man. Yes, I'd accomplished some things in life, but I wasn't fully happy. I knew I could do more. I knew I wanted more. So I availed myself of some of the greatest minds, thinkers, and doers in the world. I put myself at their feet and learned everything I could.
The chapters you've just read are the essence of that education. They are my lecture notes, filtered through the experiences and struggles I've gone through in trying to integrate them into my life.
From Angel Martinez I learned the power and importance of creating a clear vision. He taught me that _you become what you envision yourself being._ I will never forget those words.
From Kyle Maynard and Nicole Lapin I learned that there is no room in our lives for excuses, especially if greatness is our goal. Greatness is what happens when your talent and your vision face adversity, and you persist in the face of it to learn the language of the new, the scary, and the unfamiliar.
From Shawn Johnson I learned that greatness is not about making it to the top of the medal stand. It is a mindset that is fundamentally about belief in yourself and your ability to accomplish your goals.
From my brother, Christian, I learned that there is no shame in hustle. If you want to be great, you have to work harder and smarter. When something knocks you down—when someone says no—you have to be able to pick yourself up, dust yourself off, and do it all over again.
From Rich Roll, Chalene Johnson, Aubrey Marcus, and Shawn Stevenson to many other wellness masters I've studied with, I learned the importance of physical health to greatness, no matter what the dream or the vision. You have a choice—to move, to eat well, to sleep right—and that choice, if you don't make it soon enough and completely enough, _will_ stand in your way on the path to greatness, no matter what else you bring to the table.
From my old buddy Graham Holmberg I learned that it's never too late or too insignificant to develop and practice positive habits, no matter how naturally talented you might be. Those habits are the backbone of the routine that will inch you closer every day to greatness.
From Scooter Braun I learned the critical role of building and leading a winning team to the pursuit of any kind of great achievement. Strong relationships with great people who have positive energy are fundamental to that team.
From Adam Braun, I learned the power of being in service to others. I learned that you don't have to wait until you make it to serve the world. In fact, being of service, in any number of different ways, can be the path to making it.
And now that we're near the end of the book, I have another thing to say: This isn't the end of the road. This isn't a typical school. There is no graduation ceremony. There is no cessation of classes or summer break. The School of Greatness is sort of like the Hotel California: You can check out anytime you like, but you can never leave. What I mean is, these lessons will stay with you always—and their application should never end.
I also mean this in the sense that you can't get kicked out either. Lord knows I should have been expelled, banned, or written off for my inexcusable violence. Or I should have been placed on academic probation for the times I slacked off and reverted to old bad habits—despite my professors' having taught me better. But that's not how this works. That's not how _life_ works.
Greatness is a voluntary degree. Its study is self-administered. That means _it's all on you._ And you get out of life what you put into it. I hope you pursue it with everything you've got. I hope we bump into each other learning from the same master. Actually, I hope one day I might even take a course from you, and you a course from me.
We're in this together. It's time to go out there and do something great!
* * *
*If you want to hear the full story about what I learned about this experience and the good that has come from it, my dear friend Jonathan Fields interviewed me in episode 61 of my podcast.
**If you are a male who has experienced sexual abuse in your life, check out 1in6.org for more information and guidance. For general support, check out rainn.org.
**ACKNOWLEDGMENTS**
Thank you to my family. I'm so blessed to have you all in my life and constantly learn from you as your youngest brother and child. To my father, Ralph, who taught me that time was an illusion and that my age and experience level didn't matter in my pursuit of greatness. You supported all of my dreams, taught me they were always possible, and helped me do whatever it took to make them a reality. You are the best dad I could have ever asked for, and I'm so grateful to be your son. To my mother, Diana, I'm the luckiest child in the world, and you've always supported my crazy ideas, even when they scared you. Thanks for letting me finally play football at 15, even when you were scared I would get hurt. I did get some bruises, but I had years of fun and learned many lessons that made me who I am today. To Chris, you are my hero and the brother I've always looked up to. Your hustle taught me how to be the driven human I am now. To Heidi, my spiritual protector and voice of reason, thank you for opening my heart and guiding me toward love. To Katherine, without your support while living on your couch for over a year (rent free), none of this would have been possible. You are the definition of unconditional love.
To every teacher, house parent, and coach I had during my experience at Principia schools, thank you for giving me structure and guidance I needed the most during that time. You exemplified living a life of service. To Brian Morse, Tom Bania, and Ann Pierson—thank you!
Seven years prior to publishing this book, I read the book _The 4-Hour Workweek_ by Tim Ferriss that influenced me to start my journey. Thank you, Tim, for opening my mind to what is possible so I could create the life of my dreams.
To my agent, Stephen Hanselman, thanks for believing in me. You supported my vision to write the book that I've always wanted to publish. Your guidance has been legendary, and this book wouldn't be this great without you. Thanks to Glenn Rifkin for guiding me in the initial development, structure and layout of this book. A huge thanks to Ryan Holiday and Nils Parker at Brass Check for writing this book with me and advising on the message and positioning along the way. And to Heidi Howes and my entire team for helping with the editing to take the book across the finish line. I appreciate and am grateful for all of you!
To Marisa Vigilante, Mary Ann Naples, Gail Gonzales, Yelena Nesbit, Aly Mostel (along with Amy Stanton and team), and the entire family at Rodale, along with Jeffrey Capshew, Melissa Miceli, Holly Smith, Elena Guzman, Nora Flaherty, Patti Hughes, Eve Fitzgerald, and the rest of the powerful army! Thanks for your countless hours and support in getting this out to the world!
To my three main mentors, Stuart Jenkins, Frank Agin, and Chris Hawker, who believed in me when I was broke and broken and had nothing but a dream, you all stepped up when I needed support the most early on. I'll always be grateful for your level of service and for giving so much to me when I could do nothing for you at the time.
To my team that supported me for countless hours during the writing of this book, Matt Cesaratto, Sarah Livingstone, Brittany Rice, Christine Baird, Aja Wiltshire, and Diana Howes—thank you! We are making a powerful impact together!
To Ian Robinson, thank you for guiding me early on with my podcast editing, and to Pat Flynn, Derek Halpern, Ramit Sethi, James Wedmore, and John Lee Dumas, thank you for the inspiration to launch it.
To everyone who has been on _The School of Greatness_ podcast, this wouldn't be possible without your incredible wisdom and lessons that you shared with all of us!
Robert Greene, Bob Harper, Tim Ferriss, Bryan Clay, Graham Holmberg, David Anderson, Grant Cardone, Drew Canole, Rich Roll, Jamie Eason, Alex Day, Lissa Rankin, John Romaniello, Adam Bornstein, Adam Grant, Ben Nemtin, Don Yaeger, Kyle Maynard, James Altucher, Pat Flynn, Shawn Johnson, Jon Acuff, Jeff Spencer, Quddus Philippe, Carl Paoli, Leyla Naghizada, Tony Blauer, Ameer Rosic, Chris Hawker, Travis Brewer, Mignon Fogarty, Nick Onken, Aubrey Marcus, Chris Lee, AJ Jacobs, Marc Ecko, Derek Halpern, Danielle LaPorte, Gary Vaynerchuk, Guy Winch, Daniel Negreanu, Sean Stephenson, Christian Howes, Adam In-Q, Josh Shipp, Simon Sinek, Marc Fitt, Charlie Hoehn, Steven Kotler, Liz Wolfe, Adam Braun, Alison Levine, Chris Ducker, Simone de la Rue, Glennon Melton, Jennifer Paige, Alexis Carra, Ryan Holiday, Bryan Bishop, Noah Kagan, John Jantsch, Joe De Sena, Timothy Sykes, Carmine Gallo, Chris Bailey, Jason SurfrApp, Jordan Harbinger, CJ Baran, Ramit Sethi, Bo Eason, Tucker Max, Branden Hampton, Brendan Schaub, AJ Roberts, Brett McKay, Scott Barry Kaufman, Jim Afremow, Chris Guillebeau, Hunter McIntyre, Chalene Johnson, Dave Asprey, Mike Michalowicz, Tim Larkin, Christine Hassler, Dan Schawbel, Kevin Kelly, Krista Tippett, DJ Irie, Kelly Starrett, Tim Ryan, Daniel Amen, Vanessa Van Edwards, Bill Harris, Ryan Blair, Jairek Robbins, Tony Robbins, Robbie Rogers, Michael Hyatt, Rory Vaden, Jim Kwik, Yuri Elkaim, Scott Harrison, Keith Ferrazzi, Baratunde Thurston, Eric Thomas, Shawn Stevenson, Angel Martinez, Michele Promaulayko, Scooter Braun, Nicole Lapin, Donald Schultz, Mikkel Svane, Vani Hari, Marie Forleo, Peter Bregman, Marc Goodman, Jack Canfield, David Allen, Kabir Sehgal, Julianne Hough, AJ Hawk, Todd Kashdan, Amanda Enayati, Eric Greitens, Abel James, Jeff Goins, Than Merrill, Dorie Clark, Lee Cockerell, Dale Partridge, Amy Wilkinson, Rob Bell, Jay Papasan, Cassey Ho, Sally Hogshead, Arianna Huffington, Kristina Carrillo-Bucaram, Bill Phillips, Jeff Krasno, Gretchen Rubin, Matthew Hussey, Darren Hardy, Kimberly Guilfoyle, Dan Millman, Donovan Green, Suzy Welch, Justine Ezarik, Jacob Lief, Tom Bilyeu, Prince Ea, Nick Symmonds, Rick Hanson, Laird Hamilton, Gabrielle Reece, Jackie Warner, Fabio Viviani, Bryan Johnson, and the future guests that will inspire the world!
To all my friends and supporters, thank you for being there and inspiring me every step of the way!
**ABOUT THE AUTHOR**
Lewis Howes is a lifestyle entrepreneur, high-performance business coach, and keynote speaker. A former professional football player and two-sport All-American, he is a current USA Men's National Handball Team athlete. Howes hosts _The School of Greatness_ podcast, which has received millions of downloads since it launched in 2013. He was recognized by President Obama as one of the top 100 entrepreneurs in the country under 30. Howes is a contributing writer for _Entrepreneur_ and Yahoo.com and has been featured in the _New York Times_ , _Forbes_ , _Men's Health_ , the _Today_ show, and other major media outlets. Learn more at LewisHowes.com. Follow him @LewisHowes on Facebook, Twitter, and Instagram.
Mention of specific companies, organizations, or authorities in this book does not imply endorsement by the author or publisher, nor does mention of specific companies, organizations, or authorities imply that they endorse this book, its author, or the publisher.
Internet addresses and telephone numbers given in this book were accurate at the time it went to press.
© 2015 by Lewis Howes
Simultaneously published as trade hardcover and international paperback by Rodale Inc.
All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any other information storage and retrieval system, without the written permission of the publisher.
Book design by Joanna Williams
Library of Congress Cataloging-in-Publication Data is on file with the publisher.
ISBN-13: 978–1–62336–596–7 hardcover
ISBN-13: 978–1–62336–714–5 paperback
ISBN-13: 978–1–62336–597–4 ebook
We inspire and enable people to improve their lives and the world around them.
RodaleWellness.com
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\section{Introduction}
Taylor-Couette (TC), the flow between two coaxial and independently rotating cylinders, is commonly used as a basic model and paradigmatic system for shear flows in very diverse topics, for example probing the stability of astrophysical flows \cite{ji13} or more direct applications such as bubbly drag reduction \cite{ber05,gil13}. TC is very accessible experimentally, as it is a closed system, it has a high number of symmetries and a simple geometry. Experiments of TC have been conducted up to $Re\sim\mathcal{O}(10^6)$ \cite{lat92,lat92a,gil11a,gil11}. These large $Re$ allow for the study of the ``ultimate'' regime, in which the flow is fully turbulent both in the boundary layers and in the bulk. It is expected that the scaling laws which hold in this regime can be extrapolated to arbitrarily large Reynolds numbers, such as those present in geo- and astro-physics \cite{kra62,gro11}.
The flow is sheared by the angular velocity difference between the two cylinders. The driving of the cylinders can be expressed non-dimensionally with two Reynolds numbers: $Re_i=r_id\omega_i/\nu$ for the inner cylinder and $Re_o=r_od\omega_i/\nu$ for the outer cylinder, where $r_i$ and $r_o$ are the inner and outer cylinder radius, $\omega_i$ and $\omega_o$ the inner and outer cylinder angular velocity, $d$ is the gap width, $d=r_o-r_i$ and $\nu$ the kinematic viscosity of the fluid. The shear driving of the flow can then be expressed as a shear Reynolds number $Re_s = r_i|\omega_i-\omega_o|d/\nu = |Re_i-\eta Re_o|$, where $\eta$ is the radius ratio $\eta=r_i/r_o$.
Direct numerical simulations (DNS) of TC have received increasing level of sophistication in the last years, in an attempt to reach the ultimate regime numerically. The first attempt at high $Re$ was done using ``large'' computational boxes by Dong \cite{don07,don08}. Dong used a periodic aspect ratio of $\Gamma=2\pi$, where $\Gamma=L/d$, with $L$ the axial periodicity length, for $\eta=0.5$, reaching $Re_s=8000$. Ostilla-M\'onico \emph{et al.}\cite{ost13,ost14c} also achieved $Re_s\approx 8000$ for $\eta=0.714$ using large boxes with $\Gamma=2\pi$. A breakthrough was achieved by Brauckmann \& Eckhardt \cite{bra13,bra13b}, who showed that simulation boxes could be heavily reduced in two ways, while still obtaining accurate data for the torque. For simulation boxes with $\Gamma=2\pi$, three Taylor roll pairs fit in the system. However, only one pair of rolls was sufficient to calculate the torque, so $\Gamma$ could be reduced to $\Gamma=2$ ($\approx2\pi/3$). Secondly, simulating the full azimuthal extent of the cylinder is also not necessary to obtain an accurate result for the torque. A cylindrical wedge, with a rotational symmetry can be imposed, and, for $\eta=0.714$, only a \emph{ninth}\cite{bra13} of the cylinder was necessary. The use of these ``small'' boxes reduces the computational requirements by a factor $\sim 30$, or more, and made later DNS deep inside the ultimate regime by Ostilla-M\'{o}nico \emph{et al.} \cite{ost14,ost14e} possible, who achieved $Re_s\sim\mathcal{O}(10^5)$.
The torque at the inner and outer cylinders are a first order, one-point statistic. The finiteness of the computational domain however may play a role for other statistics, both higher order statistics, or two- and many-point statistics. This is the case for example in the channel flow simulations of Lozano-Dur\'{a}n \emph{et al.} \cite{loz14}, where even if the stream-wise mean velocity profile is well reproduced with small boxes, accurate results for velocity and pressure fluctuations (root mean squared) require larger boxes.
Before we continue, it is worth noting that there are two main difference between channels (and pipes) and TC. In TC, a natural constraint on the azimuthal (streamwise) extent of the domain always exists, i.e. the full cylinder, while one could think of channels and pipes extending infinitely. Second, the axial (spanwise) periodicity length in TC fixes the size of the Taylor rolls. The effect of the box-size in the axial direction is not purely numerical, as the wavelength of the Taylor vortex is a \emph{physical} parameter. These rolls survive up to very large Reynolds numbers, having been observed experimentally up to $Re_s\sim\mathcal{O}(10^6)$ by Huisman \emph{et al.}\cite{hui14}, and, in the corresponding parameter regimes all DNS simulations up to now. Taylor rolls have no direct analog in pipes and channel flow between two parallel plates, and can still play a large role in the DNS for various physical quantiites, even though the torque has been shown to become independent of $\Gamma$ in the range $2\leq\Gamma\leq4$ at about $Re_s\sim 3\cdot 10^4$~~\cite{ost14e}.
In this manuscript we attempt to answer the question: how does the size of the computational domain affect other statistics of TC DNSs and in particular higher order moments? To do so, we performed a series of DNSs of TC using a second-order finite difference code, with fractional time-stepping detailed in Verzicco \& Orlandi. \cite{ver96} This code has been used for all previous DNS of TC, and has been extensively validated against experiments. \cite{ost13,ost14,ost14e}
The radius ratio was fixed to $\eta=0.909$, the inner cylinder was rotated at $Re_i=10^5$, while the outer cylinder was kept stationary, i.e. $Re_o=0$. This resulted in a total shear driving of $Re_s=10^5$. With the chosen parameters, the simulations are in the fully turbulent (ultimate) regime, and still have a strong large-scale axial circulation \cite{ost14e}. The flow is fully Rayleigh unstable, i.e. $d|\omega r^2|/dr < 0$ everywhere. For these conditions, four simulations were conducted with computational boxes of varying sizes. Details of the geometry and resolutions used are available in Table~\ref{tbl:final}. The adequacy of the mesh can be further checked in the spectra shown in later sections. After a sufficiently long time to let transient behaviour die out, simulations were run for about 30 large eddy turnover times based on $d/(r_i\omega_i)$.
Throughout this manuscript, the following conventions will be used: $\langle \phi \rangle_{x_i}$ denotes the average of a quantity $\phi$ with respect to the independent variable $x_i$. The torque $T$ is non-dimensionalized as a pseudo-Nusselt number \cite{eck07b} $Nu_\omega=T/T_{pa}$ where $T_{pa}$ is the torque in the purely azimuthal and laminar state. We also define $\tilde{r}$, the normalized radius as $\tilde{r}=(r-r_i)/d$, the normalized height as $\tilde{z}=z/d$, and the normalized azimuthal distance at the mid-gap as $\tilde{x}=(r_o+r_i)\theta/(2d)$.
Normalizations with respect to ``wall'' variables are denoted with a plus superscript, i.e. $\phi^+$. Wall variables are first averaged azimuthally, axially and temporally. Then, the frictional velocity at the corresponding cylinder $u_\tau = \sqrt{\tau_w/\rho}$ is computed, and used as velocity scale, where $\tau_w$ is the mean friction at the corresponding cylinder, and $\rho$ is the fluid density. As length scale to non-dimensionalize the viscous length $\delta_\nu = \nu/u_\tau$ is used as usual. In these wall variables, we denote the distance to the cylinder(s) with $r^+$. For the inner cylinder wall variables, this is defined as $r^+=(r-r_i)/\delta_{\nu,i}$, while for the outer cylinder wall variables $r^+=(r_o-r)/\delta_{\nu,o}$.
\begin{table}[htp]
\begin{center}
\def~{\hphantom{0}}
\begin{tabular}{|c|c|c|c|c|c|c|}
\hline
Case & $n_{sym}$ & $\Gamma$ & $N_\theta\times N_r \times N_z$ & $Nu_\omega$ & $Re_{\tau,i}$ & Line Style \\
\hline
$\Gamma 2\text{N}20$ & $20$ & $2.09$ & $1024 \times 1024 \times 2048$ & $69.5\pm0.2$ & $1410$ & Solid light blue \\
$\Gamma 2\text{N}10$ & $10$ & $2.09$ & $2048 \times 1024 \times 2048$ & $69.4\pm0.4$ & $1410$ & Solid black \\
$\Gamma 3\text{N}20$ & $20$ & $3.00$ & $1024 \times 1024 \times 3072$ & $69.6\pm0.2$ & $1410$ & Dashed dark green \\
$\Gamma 4\text{N}10$ & $10$ & $4.00$ & $2048 \times 1024 \times 4096$ & $69.8\pm1.6$ & $1410$ & Dash-dot dark red \\
\hline
\end{tabular}
\caption{Details of the numerical simulations. The first column is the name with which the simulation will be refereed to in the manuscript. The second column shows $n_{sym}$, the order of the rotational symmetry imposed on the system. The third column gives $\Gamma$, the axial periodicity aspect ratio. The fourth column represents the amount of points in the azimuthal, radial and axial directions used for the simulations. The resolutions used correspond to approximately $r_o\Delta\theta^+\approx9$ and $\Delta z^+\approx3$ in inner cylinder wall units. The fifth column shows the non-dimensional torque $Nu_\omega$. The sixth column displays $Re_{\tau,i}=u_{\tau,i}d/(2\nu)$, the frictional Reynolds number at the inner cylinder. $Re_{\tau,o}$ can be obtained from $Re_{\tau,o}=\eta Re_{\tau,i}$. The last column indicates the line shapes used for Figs. \ref{fig:q1wall}-\ref{fig:spectraslab9}.}
\label{tbl:final}
\end{center}
\end{table}
Table~\ref{tbl:final} also shows that $Nu_\omega$ is the same within the statistical temporal error due to the necessarily limited time averaging for all simulations. This finding, even if expected from previous research, is still remarkable, considering the large-scale flow patterns, i.e. the Taylor rolls, which are still present in the flow. These patterns can be appreciated from Fig.~\ref{fig:stst4cut}. Structures are emitted from the boundary layers. These can be thought of as hairpin vortices, or as plumes when speaking in the language common for thermal convection. Plumes tend to attract each other, and merge together forming regions with large angular velocity transport, i.e. with a strong correlation between $u_\theta$ and $u_r$. These regions have a very large positive or negative angular velocity transport, which can be orders of magnitude larger than the mean \cite{ost14}. ``Neutral''-transport regions, in the core of the Taylor rolls, lie between them, and in these regions $u_r$ and $u_z$ are small. For a more detailed analysis of the dynamics of these regions, see Refs.\cite{ost14},\cite{ost15}.
\begin{figure}
\centering
\includegraphics[trim=4cm 0cm 3cm 0cm,clip=true,height=6cm,angle=-0]{figs/q1inst-eps-converted-to.pdf}
\includegraphics[trim=4cm 0cm 3cm 0cm,clip=true,height=6cm,angle=-0]{figs/q2inst-eps-converted-to.pdf}
\includegraphics[trim=4cm 0cm 3cm 0cm,clip=true,height=6cm,angle=-0]{figs/q3inst-eps-converted-to.pdf}
\caption{ Pseudocolor of the instantaneous azimuthal (left), radial (middle) and axial (right) velocities for an azimuthal cut of $\Gamma2\text{N}20$. The presence of large scale rolls, which make the flow inhomogeneous, is apparent here. }
\label{fig:stst4cut}
\end{figure}
Taylor-rolls are stationary in time. This is displayed by Fig.~\ref{fig:q1me}, which shows a pseudocolour plot of the azimuthally- and temporally- averaged azimuthal velocity $\langle u_\theta\rangle_{\theta,t}$. For all panels, a single vortex pair is present, which fills up the whole computational domain. This large-scale structure has little to no effect on the total angular velocity transport. The simulations were ran for more than $30$ large eddy turnover times (defined as $\tilde{t}=d/r_i\omega_i$), and this did not significantly modify the position of the roll. Remarkably, for the $\Gamma4\text{N}10$ case, only one roll with wavelength $\lambda_{TR}=4$ fills the domain, instead of two ``square'' rolls with $\lambda_{TR}=2$. This is consistent with the findings that the preferred $\lambda_{TR}$ increases with $Re$, and that large $Re$ simulations and experiments tend to find rectangular Taylor rolls with $\lambda_{TR}>2$, which however cannot be sustained at lower drivings\cite{ost14e} (cf. the experiments of Huisman \emph{et al.}\cite{hui14} at $Re\sim\mathcal{O}(10^6)$ who found Taylor rolls with $\lambda_{TR}>3$).
\begin{figure}
\centering
\includegraphics[trim=4cm 0cm 4cm 0cm,clip=true,height=6cm,angle=-0]{figs/q1me_G2-eps-converted-to.pdf}
\includegraphics[trim=4cm 0cm 4cm 0cm,clip=true,height=6cm,angle=-0]{figs/q1me_G3-eps-converted-to.pdf}
\includegraphics[trim=4cm 0cm 4cm 0cm,clip=true,height=6cm,angle=-0]{figs/q1me_G4-eps-converted-to.pdf}
\caption{ Azimuthally- and time- averaged azimuthal velocity $\bar{u}_\theta$ for the cases $\Gamma 2\text{N}20$ (left), $\Gamma 3\text{N}20$ (middle) and $\Gamma 4\text{N}10$ (right). As $\Gamma$ increases, the Taylor roll pair also grows, filling the entire box. In these panels (and also in Figs.~\ref{fig:stst4cut} \& \ref{fig:q1insttheta}) there is a slight preference for blue (low velocity) regions in the plots, because the mean azimuthal velocity in the bulk is slightly below $0.5$ due to the inherent asymmetry between both cylinders. }
\label{fig:q1me}
\end{figure}
Long wavelength patterns, present in the axial direction, can also form in the azimuthal direction. Fig.~\ref{fig:q1insttheta} shows a pseudocolour plot of the instantaneous velocity $u_\theta$ at the mid-gap $\tilde{r}=0.5$ for the $\Gamma 2\text{N}20$ and $\Gamma 2\text{N}10$ cases. The axial signature of the Taylor rolls can be clearly appreciated in the panels. On top of this signature, additional azimuthal patterns can be seen. On the right panel of Fig.~\ref{fig:q1insttheta} structures similar to wavy Taylor vortices can be seen, which we will refer to as ``wavyness'' of the roll. These structures only appear in the $\Gamma 2\text{N}10$ case, but not in the $\Gamma 4\text{N}10$. This could be due to the increased distance between the plume clustering regions in the $\Gamma 4\text{N}10$, as the simulation domain is larger. We note that unlike Taylor rolls, long wavelength azimuthal structures are not stationary in time, as they are convected with the mean flow velocity and do not show up on temporal averages.
\begin{figure}
\centering
\includegraphics[trim=0cm 1.5cm 0cm 2cm,clip=true,height=3cm]{figs/slab9_q1_n20G2-eps-converted-to.pdf}
\includegraphics[trim=0cm 2.5cm 0cm 4cm,clip=true,height=3cm]{figs/slab9_q1_n10G2-eps-converted-to.pdf}
\caption{ Instantaneous azimuthal velocity $u_\theta$ at the mid-gap $\tilde{r}_a$ for the cases $\Gamma 2\text{N}20$ (left) and $\Gamma 2\text{N}10$ (right), as a function of the azimuthal variable $\theta$ . Increasing $n_{sym}$ allows larger wavelength structures to fit in the simulation. These structures azimuthally modulate the Taylor rolls, and allow for more and stronger fluctuations in the Taylor roll cores. }
\label{fig:q1insttheta}
\end{figure}
We will now quantify the effect of these patterns and thus of the computational box size on the flow. We start with one-point statistics, in particular with the mean azimuthal velocity. The left panel of Fig.~\ref{fig:q1wall} shows the azimuthally-, temporally- and axially- averaged azimuthal velocity $\langle u_\theta\rangle_z$ at the inner cylinder in inner cylinder wall units, while the right panel of Fig.~\ref{fig:q1wall} shows the so-called diagnostic function $\Xi^+=du^+/d(\log r^+)$. which is the local slope of a lin-log plot of the profile.
Only little variation between all cases can be seen between these panels. In the right panel, a slight decrease of the intercept of the logarithmic profile is observed for the $\Gamma 3\text{N}20$ and $\Gamma 4\text{N}10$ simulations. This is caused by the remnant axial dependence of $u_\theta$, which increases with increasing $\Gamma$. On the other hand, there are no appreciable differences in the boundary layers between the $\Gamma 2\text{N}20$ and $\Gamma 2\text{N}10$ simulations indicating that the azimuthal extent of the box is enough to capture the mean profiles in the boundary layer.
\begin{figure}
\centering
\includegraphics[width=0.49\textwidth]{figs/q1me_IcWallUnits-eps-converted-to.pdf}
\includegraphics[width=0.49\textwidth]{figs/xime_IcWallUnits-eps-converted-to.pdf}
\caption{ The left panel shows the axially-, azimuthally- and time-averaged azimuthal velocity in inner cylinder wall units. The dashed lines indicate $u^+=r^+$ and $u^+=2.5\log r^+ + 5.2$. The right panel shows the diagnostic function $\Xi^+=du^+/d(\log r^+)$. Very little to no dependence on the box-size can be seen near the boundary layers, while differences can be appreciated from $r^+>500$, i.e. in the bulk. In the bulk, $u_\theta$, has a strong axial dependence, and this is probably causing the discrepancies. For both panels, symbols are as in Table~\ref{tbl:final}. }
\label{fig:q1wall}
\end{figure}
Fig.~\ref{fig:qrms} shows the velocity fluctuation profiles at the inner cylinder. The root mean square (rms) of a field $\phi$ is computed as $\phi^\prime=\langle \langle \phi^2\rangle_{\theta,t}-\langle\phi\rangle^2_{\theta,t}\rangle_z$. Note that the order of the axial average and subtraction operations is crucial, due to the remnant and significant axial dependence in the mean velocity fields, (cf. Fig.~\ref{fig:q1me}). Axially averaging before subtracting results in rms values which are considerably higher, but originate simply from the Taylor rolls and have nothing to do with the underlying statistics.
While the box-size can be seen to play a small effect on the $u_\theta^+$ profile, it is critical for other averages else. In general, increased box sizes lead to increased fluctuations, in line with what is seen in channels \cite{loz14}. The effect of the wavy patterns seen in Fig.\ref{fig:q1insttheta} on the fluctuations can be appreciated by comparing the $\Gamma2\text{N}10$ and the $\Gamma2\text{N}20$ cases. There is a clear increase in the $u_r^+$ and $u_z^+$ fluctuations in the bulk. This is a direct reflection of the increased mobility of the rolls. The axial extent of the domain can also be seen to affect the velocity fluctuation profiles. A larger axial domain, i.e. increasing $\Gamma$, again leads to larger fluctuations in the boundary layer, due to the increased mobility of the plumes, and the increased axial dependence of the velocity.
Finally, the pressure fluctuations become \emph{smaller} for larger domains. This is probably due to the pressure playing a damping role on the velocity fluctuations in the smaller domains. Again, this is in line with what is seen in channels \cite{loz14}. The geometric (computational) constraint on the flow inside the boundary layers is enforced through these pressure fluctuations. The sharp increase of velocity fluctuations in the bulk seen for the $\Gamma2\text{N}10$ case also results in an sharp increase of pressure fluctuations in the bulk.
\begin{figure}
\centering
\includegraphics[width=0.49\textwidth]{figs/uplusprofile-eps-converted-to.pdf}
\includegraphics[width=0.49\textwidth]{figs/vplusprofile-eps-converted-to.pdf}
\includegraphics[width=0.49\textwidth]{figs/wplusprofile-eps-converted-to.pdf}
\includegraphics[width=0.49\textwidth]{figs/pplusprofile-eps-converted-to.pdf}
\caption{ Velocity and pressure fluctuations near the inner cylinder in inner cylinder wall units for all simulations. Symbols are as in Table~\ref{tbl:final}. }
\label{fig:qrms}
\end{figure}
Fig.~\ref{fig:autocorr} shows the two-point autocorrelation function for all velocity fields in both axial and azimuthal direction. Two main effects of the box size can be seen on the flow. While the azimuthal extent of the box plays a negligible role in the decorrelation in all panels (compare $\Gamma2\text{N}10$ to $\Gamma2\text{N}20$ cases), the axial extent plays an important role in \emph{both} axial and azimuthal correlations. As expected, the axial autocorrelations are dominated by the effect of Taylor rolls. This is especially true in the case of the radial velocity autocorrelation $R_{rr}$. The axial velocity autocorrelation $R_{zz}$ remains relatively unaffected, as axial velocities in the mid-gap are very small (cf. Fig~\ref{fig:q1insttheta}). Additionally, increasing $\Gamma$ allows for a faster drop of $R_{\theta\theta}$ in the azimuthal direction, but not for faster drops in $R_{rr}$ and $R_{zz}$. This is due to the larger cores of the Taylor rolls, which result in more mixing. In these regions, the radial and axial velocities are small, so $R_{rr}$ and $R_{zz}$ are dominated by the strongly correlated regions seen in Fig.~\ref{fig:stst4cut}.
We also note that the azimuthal decorrelation lengths are an order of magnitude smaller than those seen in plane Couette flow\cite{bec95}, which have allowed TC simulations to reach higher $Re_\tau$ with heavily reduced computational costs. Current state-of-the art plane Couette simulations ``only'' reach $Re_\tau=550$ while requiring 2.2 billion points \cite{avs14}.
\begin{figure}
\centering
\includegraphics[width=0.49\textwidth]{figs/Ruu_Theta-eps-converted-to.pdf}
\includegraphics[width=0.49\textwidth]{figs/Ruu_Z-eps-converted-to.pdf}
\includegraphics[width=0.49\textwidth]{figs/Rvv_Theta-eps-converted-to.pdf}
\includegraphics[width=0.49\textwidth]{figs/Rvv_Z-eps-converted-to.pdf}
\includegraphics[width=0.49\textwidth]{figs/Rww_Theta-eps-converted-to.pdf}
\includegraphics[width=0.49\textwidth]{figs/Rww_Z-eps-converted-to.pdf}
\caption{ Two-point autocorrelation functions at the mid-gap ($\tilde{r}=0.5$) for all simulations. Panels on the left column are autocorrelations in the azimuthal direction ($\theta$), while those on the right are autocorrelations in the axial directions. The three rows are for each velocity component: azimuthal (top), radial (middle) and axial (bottom). Symbols are as in Table~\ref{tbl:final}. }
\label{fig:autocorr}
\end{figure}
We now turn to the velocity spectra. Fig.~\ref{fig:spectraslab2} shows the premultiplied velocity spectra in the inner cylinder boundary layer ($r^+\approx12$), while Fig.~\ref{fig:spectraslab9} shows the spectra at the mid-gap ($\tilde{r}=0.5$). In both figures, the size of the computational box can be seen to play a negligible role for the spectra at the small scales, while, as seen in Ref.~\cite{ost15}, the large scales contain a very significant amount of energy both deep inside the boundary layer and in the bulk.
Inside the boundary layer there are two main energy containing scales- that of the plumes at high $k$, and that of the Taylor rolls, at low $k$. In the mid-gap, the plumes have merged with each other, and the main energy content can be found only in the large scales. It is apparent from both figures, that the maximum of the spectra is not converged to their very large box-size value. The box is not large enough to contain all large scales which are energetic. Even then, good collapse for the small scales can be seen. The largest scales contain energy from all three velocity components, and not only for the azimuthal and spanwise components, which is the case in channels\cite{hoy06} and plane Couette\cite{avs14}. All mid-gap spectra neither display the clear inertial range Kolmogorov scaling with $-5/3$ scaling, nor the $-1$ scaling for the $E_{\theta\theta}$ in the $\theta$-direction predicted by Perry \& Chong \cite{per86}. This is consistent with the experimental findings of Lewis \& Swinney \cite{lew99} and those of Huisman \emph{et al.}\cite{hui13b}.
Saw-tooth patterns, indicating preferred even or odd modes can be seen for the axial spectra for all cases. Increasing $\Gamma$ shifts the maxima in $k_z$ accordingly, to accommodate for the different size of the Taylor-roll. We note that inside the boundary layer, simulations with larger $\Gamma$ have a smaller energy peak at the Taylor-roll wavelength $k_z$. This means that the Taylor-roll has a larger effect on the plume generation and its aspect ratio is smaller. Using a small domain may artificially strengthen the roll and lead to an increased correlation inside the boundary layer. Further increases in $\Gamma$ will accommodate for more rolls. This was seen to produce a very sharp dropoff in the spectra for $k_z<k_{TR}$ by Dong\cite{don07}.
Remarkably, sawtooth behaviour at low frequencies is also present in the azimuthal direction if the azimuthal extent of the domain is increased- indicating that by using a reduced azimuthal extent the formation of the wavy patterns is not allowed for. Further proof of this can be seen in Fig.~\ref{fig:spectraslab9}d) and \ref{fig:spectraslab9}f), where the energy of the large scales of the radial and axial velocity increases for the $\Gamma2\text{N}10$ case when compared to the $\Gamma2\text{N}20$ and $\Gamma3\text{N}20$ cases. Again, the spectra are not saturated. Extending the azimuthal extent of the simulation seems to be a necessity to fully capture the energy containing scales. This point requires further study, as due to the natural finiteness of the azimuthal extent, it could be the case that the maximum in the spectra is at the longest wavelength if $n_{sym}=1$.
\begin{figure}
\centering
\includegraphics[width=0.49\textwidth]{figs/slab3EttKth-eps-converted-to.pdf}
\includegraphics[width=0.49\textwidth]{figs/slab3EttKz-eps-converted-to.pdf}
\includegraphics[width=0.49\textwidth]{figs/slab3ErrKth-eps-converted-to.pdf}
\includegraphics[width=0.49\textwidth]{figs/slab3ErrKz-eps-converted-to.pdf}
\includegraphics[width=0.49\textwidth]{figs/slab3EzzKth-eps-converted-to.pdf}
\includegraphics[width=0.49\textwidth]{figs/slab3EzzKz-eps-converted-to.pdf}
\caption{ Premultiplied azimuthal (left column) and axial (right column) spectra for the azimuthal (top), radial (middle) and axial (bottom) velocities at $r_i^+\approx12$. Symbols are as in Table~\ref{tbl:final}. }
\label{fig:spectraslab2}
\end{figure}
\begin{figure}
\centering
\includegraphics[width=0.49\textwidth]{figs/slab9EttKth-eps-converted-to.pdf}
\includegraphics[width=0.49\textwidth]{figs/slab9EttKz-eps-converted-to.pdf}
\includegraphics[width=0.49\textwidth]{figs/slab9ErrKth-eps-converted-to.pdf}
\includegraphics[width=0.49\textwidth]{figs/slab9ErrKz-eps-converted-to.pdf}
\includegraphics[width=0.49\textwidth]{figs/slab9EzzKth-eps-converted-to.pdf}
\includegraphics[width=0.49\textwidth]{figs/slab9EzzKz-eps-converted-to.pdf}
\caption{ Premultiplied azimuthal (left column) and axial (right column) spectra for the azimuthal (top), radial (middle) and axial (bottom) velocities at the mid-gap $\tilde{r}=0.5$. Symbols are as in Table~\ref{tbl:final}. No significant effect of the box size is seen for the small wavelength (large $k$) scales, while for the large scales, the azimuthal size of the domain appears to play a role in the axial structure of the rolls. The ``wavy'' modulations seen in Fig.~\ref{fig:q1insttheta} are clearly reflected in the spectra. }
\label{fig:spectraslab9}
\end{figure}
In summary, a systematic study of the effect of the computational box size on TC DNS was performed. From previous studies \cite{bra13}, it was already known that small boxes can obtain accurate results for the non-dimensional torque. Furthermore, similar to what was found by Lozano-Dur\'{a}n \emph{et al.} \cite{loz14} for DNS of channel flow, small boxes also have accurate mean azimuthal (streamwise) velocity profiles in the boundary layers. Larger boxes are needed in order to obtain box-independent results for fluctuation values, two-point autocorrelations and low-wavelength spectra. The artificial truncation of the spectra by using a reduced box does not bring about significant changes in its structure at low wavelengths- even if the most energetic scales are not accounted for. Azimuthally small boxes do not allow for azimuthal wavy patterns in the Taylor rolls, and thus show a reduced level of fluctuations, as well as missing energy in the large scales for the axial and azimuthal spectra.
In the axial direction, things are different. The size of the underlying Taylor roll dominates the autocorrelations, especially for the radial velocity. As we mentioned previously, the effect of a the computational box-size in the axial direction is not purely numerical, the wavelength of the Taylor vortex is a physical parameter. In experimental and natural realizations of TC, the wavelength of the Taylor rolls is determined by the axial constraints, i.e. end plates or periodicity. It appears from recent work \cite{mar14,ost14e} that for larger $\Gamma$ domains, which can accommodate more than a pair of rolls, the preferred wavelength of Taylor rolls increases with increasing $Re$. This effect cannot be captured in small box simulations, but can lead to bifurcations at high Reynolds numbers \cite{hui14}. Future work should consider simulating large $\Gamma\sim\mathcal{O}(10)$ to check the window of coexistence of different states at high $Re$, and how these affect the flow.
In the near future, a study of larger TC boxes seems mandatory, as to determine the minimal box size for accurate statistics of the velocity and pressure fluctuations and higher order moments. It can be the case that the axial extent is too small and thus non-physical, and that the azimuthal extent is not enough to develop wavyness. It is also unclear whether this wavyness is a product of artificial confinement in the axial direction, as they were only shown by the $\Gamma2\text{N}10$ and not by the $\Gamma4\text{N}10$. These increased fluctuations may provide a way for the system to overcome the energy barrier, and to switch between vortical states, i.e.\ from two vortex pairs with $\lambda_{TR}=2$ to one vortex pair with $\lambda_{TR}=4$. Another reason for doubting their physicality comes from the correlations, as the $\Gamma=2$ cases show unusually large decorrelation lengths in the azimuthal direction, and this might cause the formation of said patterns.
We also point out that the size of this minimal box is larger than those required for channels. The largest box in this manuscript, for which it is not clear yet whether its statistics are box-independent, has relative dimensions of $8$ half-gap lengths in the axial (spanwise) direction and $4.2\pi$ in the azimuthal (streamwise) direction, while accurate statistics were obtained for a box of size $\pi$ half-gaps in the spanwise direction and $2\pi$ half-gaps in the streamwise direction in Lozano-Dur\'{a}n \emph{et al.}\cite{loz14}.
\emph{Acknowledgments:} We would like to thank E. P. van der Poel for various stimulating discussions. RO would like to thank J. Jim\'{e}nez for motivating this study, and his group for the discussions during his stay in Madrid. We gratefully acknowledge an ERC Advanced Grant and the PRACE project 2013091966 resource CURIE based in France at Genci/CEA.
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{"url":"https:\/\/economics.stackexchange.com\/questions\/33979\/what-does-r-represent-in-the-total-cost-function","text":"# What does \u201cr\u201d represent in the total cost function?\n\nI know that the total cost function of a firm in the short run is:\n\nTC = wL + rK,\n\nwhere rK is essentially a constant. I understand the variables w, L and K, but I still don't get what r is. I mean, what do I input as \"r\" when I'm trying to draw up a total cost function?\n\nThank you.\n\n\u2022 If w is the wage that you pay per unit of labour hired, then what would r be for capital? \u2013\u00a0Maarten Punt Feb 12 at 8:07\n\u2022 I mean to say, is it rent? Or like if I purchase the capital good is it just the price? \u2013\u00a0Saad Feb 12 at 8:21\n\u2022 Are you purchasing the worker (slavery) or are you renting his labor? The cost function is for a given time period, so you are doing the same with the capital good. \u2013\u00a0Giskard Feb 12 at 8:56\n\u2022 Thank you, but is it possible for you to give me an example to make it slightly easier for me to understand? \u2013\u00a0Saad Feb 12 at 9:13\n\nThe $$r$$ in the total cost function is the interest rate, which at the same time constitutes the price of capital. You can think of it as an explicit cost, e.g. if you rent the capital or pay interest to the bank, or as an implicit (opportunity) cost, e.g. if you own the capital and by using it yourself you give up the opportunity to rent it out.\n\u2022 The language is a bit confusing. The $r$ is often just called the \"price of capital\", as I also did in my answer, whereas what is meant is not a payment for purchasing one unit of the capital, but for renting one unit of capital for one unit of time. So yes, it's the \"rental price of capital\". \u2013\u00a0VARulle Feb 13 at 8:15","date":"2020-06-03 02:57:03","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 1, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.6657612919807434, \"perplexity\": 699.4520486100362}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2020-24\/segments\/1590347428990.62\/warc\/CC-MAIN-20200603015534-20200603045534-00549.warc.gz\"}"}
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Du Plessis released to join Glasgow Warriors
London Irish has announced that Petrus Du Plessis has been released from his contract to join Glasgow Warriors with immediate effect.
The 37-year-old prop joined London Irish from Saracens in 2017 and made 23 appearances in the club's first team, scoring two tries.
Director of rugby Declan Kidney thanked Du Plessis for his contributions to London Irish.
"Petrus has been a good person to have in the squad, both on and off the pitch, and he leaves with our good wishes," he said. "Because we have no A League fixtures the opportunities for game time are limited, which is why we have agreed to release him at this stage of his career.
"We believe we still have enough quality tight-head props in the squad such as Ollie Hoskins, Pat Cilliers, Manasa Saulo and Lovejoy Chawatama, and will be able to give opportunities for younger players, too."
"I've enjoyed my time at London Irish and know that the club is in good hands," said Du Plessis. "I'd like to thank the squad, coaches, staff and supporters for how they made me feel welcome at Hazelwood, and while I'm looking forward to the new challenge at Glasgow I'll remember my time at London Irish as a fantastic experience. I'd like to wish the club all the best for the future."
Seán O'Brien Twitter takeover this Friday!
The London Irish 'Key Workers' XV
Gary Baker RIP
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Q: Untarring a file with limited hierarchy I have created a tar file in terminal. Let's say I am currently in a directory test7. I am creating a tar in my current directory of a file which is inside another directory (test8).
tar -czvf example.tgz ../test8/a/b
output:
example.tgz
Now, I untar this file using the following command :
tar -xzvf example.tgz
I get the result and a directory named as test8 is produced.
$) cd test8
$) ls
-> a
$) cd a
$) ls
-> b
Now I can go inside the directory b and see my files.
I want the output to be only the directory a and inside of which b will be present i.e.
Output after untarring that I want should be of this hierarchy :
a/b
But not: test8/a/b
Can anyone please help me out with this ?
I have been through the man page of tar but couldn't get much help from it.
A: You can use the -C option to effectively change to the target directory
Ex. instead of
$ tar cvf example.tar ../Apple/Banana/Papaya
tar: Removing leading `../' from member names
../Apple/Banana/Papaya/
../Apple/Banana/Papaya/Papaya.md
use
$ tar cvf example.tar -C ../Apple Banana/Papaya
Banana/Papaya/
Banana/Papaya/Papaya.md
Alternatively you can remove leading directories upon extraction using the --strip-components option:
tar --strip-components=1 -xzvf example.tgz
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Q: Declaration of array of objects - null value I have two-dimensional array
protected MyClass[][] myArray;
in constructor I have this
this.myArray= new MyClass[20][20];
Now, without inicialization (aka this.myArray[2][2] = new MyClass(par0, par1);)
the value of this.myArray[2][2] is "null".
Is this guaranteed? And where can I read more about this subject? (for primitive types like int or boolean too)
Thanks
A: Yes, it's guaranteed. Array values are initialized with null (for objects), 0 (for numeric primitives) and false (for boolean primitives), just like fields.
See http://docs.oracle.com/javase/specs/jls/se7/html/jls-10.html#jls-10.6-100:
Space is allocated for a new array of that length. If there is insufficient space to allocate the array, evaluation of the array initializer completes abruptly by throwing an OutOfMemoryError. Otherwise, a one-dimensional array is created of the specified length, and each component of the array is initialized to its default value (§4.12.5).
(emphasis mine)
A: Yes. This behavior is guaranteed. The default value of an Object is null. Therefore the default values for an array of Objects is also null so every element in the array needs to be instantiated. See Default Values in Data Types.
A: Yes, it is guaranteed. Every type has a default initialization value:
*
*numeric primitives = 0
*boolean = false
*all Objects = null
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"redpajama_set_name": "RedPajamaStackExchange"
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\section{Introduction}
Superconductivity in the absence of inversion symmetry has been attracting much attention for its potential exotic superconducting phenomena~\cite{Gorkov2001PRL,Agterberg2007PRB}. In bulk materials, such superconductivity is realized in crystals without inversion centers, namely in the so-called noncentrosymmetric superconductors (NCSCs)~\cite{Bauer2004PRL}. The lack of the inversion symmetry results in two important features. Firstly, the superconducting state cannot be classified either as a pure spin-singlet or a pure spin-triplet pairing any more, but is a singlet-triplet mixed pairing. Then, the superconducting gap function is generally expressed as $\hat{\varDelta}_{\bm{k}}=\{\varDelta_1\psi(\bm{k})+\varDelta_2\bm{d}(\bm{k})\cdot{\hat{\bm{\sigma}}}\}i\hat{\sigma}_y$. Here, $\psi(\bm{k})$ and $\bm{d}(\bm{k})$ are the normalized scalar superconducting gap function for the spin-singlet component and the normalized vector gap function for the spin-triplet component, respectively; $\varDelta_1$ and $\varDelta_2$ are the gap magnitudes, including $\varDelta_2=0$ (spin-singlet state) or $\varDelta_1=0$ (spin-triplet state) as special cases; and $\hat{\sigma}$ is the Pauli matrices.
Secondly, the lack of inversion symmetry results in electronic energy-band splitting due to the antisymmetric spin-orbit interaction (ASOI). The ASOI term in the Hamiltonian is given by the inner product of the dimensionless $g$-vector ${\bm{g}}({\bm{k}})$ and the $\bm{k}$-dependent electron spin ${\bm{\sigma}}({\bm{k}})$: $H_{\rm{ASOI}}=\alpha\Sigma_k{\bm{g}}({\bm{k}})\cdot {\bm{\sigma}}({\bm{k}})$. Here $\alpha$ characterizes the strength of the ASOI. The ASOI leads to an energy shift of $\pm \alpha|{\bm{g}}({\bm{k}})|$, which can be interpreted as an effective $\bm{k}$-dependent Zeeman splitting of the electron spins~\cite{Kaur2005PRL}. It has been revealed that ${\bm{d}}({\bm{k}}) \parallel {\bm{g}}({\bm{k}})$ is energetically favored for $\alpha \gg |\varDelta_{\bm{k}}|$. Furthermore, $\psi(\bm{k})$ and $\bm{d}(\bm{k})$ belong to the same irreducible representation of the crystalline point group, and ${\bm{d}}({\bm{k}})$ is expressed as ${\bm{d}}({\bm{k}})=\psi(\bm{k}){\bm{g}}({\bm{k}})$~\cite{Sigrist2006MMM,Hayashi2006PRB}. This indicates that the superconducting energy gap $\varDelta_{\bm{k} \pm}$ takes the form $\varDelta_{\bm{k} \pm}=\psi(\bm{k})\{\Delta_1 \pm \Delta_2| \bm{g}(\bm{k})|\}$ on each split energy band.
One of the typical and well-studied ASOIs is of the Rashba-type, whose $g$-vector has the form ${\bm{g}}({\bm{k}}) \propto (k_y, -k_x, 0)$~\cite{Agterberg2007PRB}. Because of this simple form, NCSCs having the Rashba-type ASOI are favorable for the investigation of the novel superconducting state. In fact, a number of unusual superconducting phenomena originating from the parity mixing or the ASOI have been proposed: e.g., helical vortex state and novel magneto electric effect~\cite{Kaur2005PRL,Fujimoto2007JPSJ051008}. For observation of any of such phenomena, single crystalline sample is crucially important, because the novel effects are likely to be canceled out in polycrystals.
Naively speaking, the Rashba-type ASOI is expected to be realized in crystals in which inversion symmetry is broken only along one direction.
To our knowledge, only seven Rashba-type NCSCs with single crystals are reported up until today: $R$Pt$_3$Si ($R$=La, Ce)~\cite{Yasuda2004JPSJ,Takeuchi2007JPSJ}, $R$RhSi$_3$ and $R$IrSi$_3$($R$=La, Ce)~\cite{Kimura2005PRL,Okuda2007JPSJ,Settai2008JPSJ}, and CeCoGe$_3$~\cite{Settai2007IJMPB}. The four Ce-based NCSCs indeed exhibit exotic superconducting behavior. However, they also exhibit antiferromagnetic ordering in the vicinity of the superconducting phase. Thus, it is difficult to distinguish effects originating from the ASOI from effects resulting from active $f$-electrons. In contrast, the other three La-based NCSCs exhibit conventional metallic behavior in their normal states and weak-coupling full-gap behavior in their superconducting states. This fact may suggest importance of the active $f$-electrons for realization of the novel phenomena. However, a few NCSCs having different crystal structures indeed exhibit novel superconducting phenomena, even though active $f$-electrons are not present~\cite{Yuan2006PRL,Bauer2010PRB_Mo3Al2C}. Thus, further investigations of non-magnetic, $f$-electron-free Rashba-type NCSCs are important.
Here, we report our success in growing single crystals of the Ca-based NCSC CaIrSi$_3$, which has the same crystal structure as $R$IrSi$_3$ ($R$=La, Ce). CaIrSi$_3$ exhibits superconductivity below the critical temperature $T_{\rm{c}}=3.6$~K~\cite{Oikawa2008JPSmeeting}, which is the highest $T_{\rm{c}}$ among the known Rashba-type NCSCs. We previously reported that CaIrSi$_3$ is a non-magnetic, fully-gapped superconductor based on studies with polycrystalline samples~\cite{Eguchi2011PRB,Eguchi2012JPSJ}. Single crystalline samples allow examinations of various predicted exotic phenomena as well as investigation of basic information of superconductivity, such as the gap anisotropy and the mixing ratio of the singlet and triplet components. In this paper, we describe the synthesis of single crystalline CaIrSi$_3$, and its normal and superconducting properties. We also present the electronic density of states (DOS) near the Fermi energy $E_{\rm{F}}$ revealed by bulk sensitive hard x-ray photoemission spectroscopy (HAXPES), and by relativistic first-principle calculations~\cite{Schwarz2003}. By comparing the results of HAXPES and the band calculations, we revealed existence of strong SOI in this material. The compound can be a model material having strong SOI with 5$d$ orbital characters.
\section{Single crystal growth}
\begin{figure}
\centering
\includegraphics[width=\columnwidth, clip]{fig1_crystal_xrd.eps}
\caption{(Color online) Experimental and simulated powder x-ray diffraction spectra of CaIrSi$_3$. The small impurity peaks indicated by $\times$ marks are attributed to a by-product CaIr$_3$Si$_7$~\cite{Eguchi2011PRB}, whose grains are distinct from CaIrSi$_3$ crystals. The upper-left inset illustrates the crystal structure of CaIrSi$_3$. This schematic was produced by the software VESTA~\cite{Momma2011AC}. A optical microscope picture of a single crystal and its backscattered Laue photograph are also shown in the upper-right inset.}
\label{crystal}
\end{figure}
Single crystalline CaIrSi$_3$ is synthesized by a combination of the arc melting~\cite{Eguchi2011PRB} and self-flux methods. Firstly, polycrystalline CaIrSi$_3$ was obtained by the arc melting of a pellet made of a powder mixture of CaSi (99.9\%), Ir (99.99\%), and Si (99.999\%) with the molar ratio Ca:Ir:Si~=~3:1:4.7. Secondly, small single crystals of CaIrSi$_3$, which were typically less than 0.1~mm in sizes, were isolated from the arc-melted sample by dissolving a by-product CaSi$_x$ into 3\% hydrochloric acid. Thirdly, these small crystals were mixed with a sufficient amount, typically twenty times of the Ir-molar mass of the crystals, of the CaSi, Ir, and Si powders with the molar ratio Ca:Ir:Si~=~3:1:4.7 in Ar atmosphere, then pressed into a pellet. The small single crystals should play a role of seed crystals. The pellet was put into an alumina crucible, which was then capsulated into a stainless steel container in an Ar atmosphere~\cite{Kihou2010JPSJ}. The container was heated up to 1340$^\circ\mathrm{C}$, cooled to 800$^\circ\mathrm{C}$ by 2$^\circ\mathrm{C}$/h, then quenched. Many pieces of single crystalline CaIrSi$_3$ grown up to the size 0.2-1.4~mm are obtained along with a slight amount of by-product CaIr$_3$Si$_7$.
A powder x-ray diffraction spectrum (Bruker AXS D8 ADVANCE) of crushed single crystals is presented in Fig.~\ref{crystal}. The obtained spectrum well agrees with the simulation. An optical microscope picture of a crystal with the typical size of $0.5 \times 0.5 \times 0.5$~mm$^3$ is presented in the upper-right inset. A backscattered Laue photograph of the presented crystal is also shown. This photograph was taken with an apparatus~(RIGAKU RASCO-BLII) in which a charge-coupled-device~(CCD) camera takes the image of a Laue pattern projected onto a fluorescent screen. The clear four-fold symmetry in the Laue picture indicates that the surface shown corresponds to the basal $ab$~plane.
\section{Hard x-ray photoemission spectrum}
A photoemission spectrum around $E_{\rm{F}}$ revealed by the bulk sensitive HAXPES is presented in Fig.~\ref{PES}(a). The measurement was performed at the beamline BL47XU at SPring-8 (Japan)~\cite{Kobayashi2009NIMA}. The setup of the measurement is depicted in the inset: incident photons with an energy of 7.9399~keV have their polarization plane perpendicular to the sample surface. The DOS deduced from the full potential linearize augmented plane wave (FLAPW) calculation performed by WIEN2k package with/without SOI are presented in Fig.~\ref{PES}(b) together with the partial DOS for each atom. Our calculation well reproduces the previous calculations in Refs.~\cite{Bannikov2010,Kaczkowski2011JAC}. The calculated DOS at $E_{\rm{F}}$ per unit cell~(u.c.) is 1.94~states/eV\hspace{1pt}u.c., and the Sommerfeld coefficient $\gamma_0$ evaluated from the DOS is 4.6~mJ/mol-u.c.\hspace{1pt}K$^2$. This value is consistent with the previous reports~\cite{Bannikov2010,Kaczkowski2011JAC}. Note that $\gamma_0$ per formula unit~(f.u.), which is compared with the experimental results later, is 2.3~mJ/mol-f.u.\hspace{1pt}K$^2$, because one unit cell contains two CaIrSi$_3$ formula unit. From the DOS, we simulate the HAXPES spectrum by assuming a Lorentzian-type lifetime broadening with the energy-dependent line width (FWHM=$0.2|E-E_{\rm{F}}|$)~\cite{Wadati2005PRB}, and compared it in Fig.~\ref{PES}(c) with the background-subtracted experimental spectrum. The calculation with the SOI explains the experimental result better than that without the SOI: In particular, the shoulder-like structure at approximately 3~eV for the latter is absent in the experimental spectrum.
The fact indicates that strong SOI indeed affects the electronic state of CaIrSi$_3$.
The calculated band dispersions with/without the SOI are shown in Fig.~\ref{PES}(d). The four-fold degeneracy at the symmetric $\Gamma$ point is split into two by $\sim0.42$~eV due to the SOI. Note that this energy split at the $\Gamma$ point ($\bm{k}=0$) is caused by the symmetric SOI, which can be finite regardless of the crystal symmetry. The value of the $\Gamma$-point splitting is consistent with a previous study~\cite{Kaczkowski2011JAC}. The value is also comparable to that of CeIrSi$_3$: 0.4~eV~\cite{Jeong2010SSC}, in which Ce 4$f$ orbitals dominantly contribute to the electronic conduction. The remaining two-fold spin degeneracy is split by $\sim0.05$-$0.3$~eV at less symmetric $k$ points due to the ASOI. The band splitting results in approximately 10\% DOS difference ($\delta N \sim 0.1$) between the ASOI-split Fermi surfaces. As presented in Figs.~\ref{PES}(b)(c), the Ir-5$d$ orbital contributes by 20-50\% to the total DOS near $E_{\rm{F}}$. Thus, the influence of the strong SOI discussed above is attributed to the Ir orbitals.
\begin{figure}
\centering
\includegraphics[width=\columnwidth, clip]{fig2_PES_band.eps}
\caption{(Color online) (a) Hard x-ray photoemission spectrum of CaIrSi$_3$ near $E_{\rm{F}}$. A schematic of the experimental setup is presented in the inset. (b) Calculated density of states (DOS) per unit cell by the local density approximation (LDA) band calculation with and without spin-orbit interaction (SOI). Partial DOS for each atom is also presented. (c) Comparison between the background-subtracted experimental spectrum and the calculated spectrum with an assumed life-time broadening. The calculation with SOI well describes the experimental result than that without SOI does. Contribution of each atom to the spectrum is also presented based on the calculation with SOI. (d) Band dispersion with/without SOI. Spin-orbit splitting of the two-fold spin degeneracy near $E_{\rm{F}}$ is $0.05\sim0.3$~eV.}
\label{PES
\end{figure}
\section{Normal-state and Superconducting properties}
\begin{figure}
\centering
\includegraphics[width=8cm, clip]{fig3_cp_etc.eps}
\caption{(Color online) (a) Temperature dependence of the resistivity $\rho$ of the single crystalline CaIrSi$_3$. The solid line is a fit by the conventional Bloch-Gr{\"u}neisen model. (b) Low-temperature resistivity and specific heat divided by temperature, $c_p /T$, at 0~T and 1~T ($H \parallel a$). The broken vertical line indicates $T_{\rm{c}}=3.3$~K based on the entropy conservation, and the solid line is a fit by the conventional Debye-Sommerfeld model: $c_p/T=\gamma +\beta T^2$. The inset is a $c_p/T$-vs-$T^2$ plot, indicating that the model well describes the normal-state behavior.}
\label{cp_etc}
\end{figure}
The temperature dependence of the resistivity $\rho$ is presented in Fig.~\ref{cp_etc}(a), while the low temperature $\rho$ and specific heat $c_p$ of the same sample are presented in Fig.~\ref{cp_etc}(b). The measurements were performed with a commercial apparatus~(Quantum Design, PPMS) down to 0.35~K with a $^3$He refrigerator. For the specific heat measurements, three crystals from the same batch were added to achieve sufficient experimental resolution (total: 7.301~mg). Their crystal axes were determined individually by the Laue photography. The onset temperature of the specific-heat jump in zero field is 3.55~K, which is consistent with the results for polycrystalline samples~\cite{Eguchi2011PRB}. The thermodynamic $T_{\rm{c}}$ determined by the entropy conservation criteria, is 3.3~K. The superconductivity is suppressed by a field of 1~T ($H \parallel a$). Both the specific heat and resistivity in the normal state are magnetic-field independent within the experimental resolutions. The residual resistivity $\rho_0$ of the present sample is 68~$\mu\Omega$cm. The residual resistivity ratio $RRR \equiv \rho(300~{\rm{K}})/\rho(5~{\rm{K}})$ is 2.6. Both $\rho_0$ and $RRR$ are comparable to that of polycrystalline samples~\cite{Eguchi2011PRB}. The temperature dependence of $\rho$ is well fitted by the conventional Bloch-Gr{\"u}neisen formula with the transport Debye temperature 307~K. This fact indicates dominance of electron-phonon scatterings. The transport Debye temperature is also consistent with that of polycrystalline samples~\cite{Eguchi2012JPSJ}.
The normal state $c_p$ below 5~K is well described by the conventional Debye-Sommerfeld model: $c_p=\gamma T + \beta T^3$, where $\gamma$ is the electronic specific heat~(Sommerfeld) coefficient and $\beta$ is the phononic specific heat coefficient. We obtain $\gamma=6.6$ mJ/mol-f.u.\hspace{1pt}K$^2$ and $\beta=0.31$~mJ/mol-f.u.\hspace{1pt}K$^4$ from the fitting to the normal state data between 0.35 and 5~K. The Debye temperature $\varTheta_{\rm{D}}$ calculated from $\beta=(12/5)\pi^4N_{\rm{A}}N_{\rm{f.u.}}k_{\rm{B}}/\varTheta_{\rm{D}}^3$ is 314~K. Here, $N_{\rm{A}}$ is the Avogadro number, $N_{\rm{f.u.}}=5$ is the number of atoms per formula unit, and $k_{\rm{B}}$ is the Boltzmann constant. The $\varTheta_{\rm{D}}$ value is consistent with that obtained from the resistivity data. We obtain the electron-phonon coupling constant $\lambda_{\rm{el-ph}}$ as 0.56 from McMillan's formula $T_{\rm{c}}=(\varTheta_{\rm{D}}/1.45){\rm{exp}}[-1.04(1+\lambda_{\rm{el-ph}})/\{\lambda_{\rm{el-ph}}-\mu^*(1+0.62\lambda_{\rm{el-ph}})\}]$~\cite{McMillan1967PR} with $\varTheta_{\rm{D}}=314$~K and the Coulomb pseudo potential $\mu^*=0.13$. The obtained small value of $\lambda_{\rm{el-ph}}$ indicates that a weak-coupling superconductivity is realized in this compound, being consistent with the electronic specific heat results described below. By comparing the experimental $\gamma$ and the calculated $\gamma_0$ values, the electronic mass enhancement $\gamma/\gamma_0$ is estimated to be 2.9. Assuming that this mass enhancement originates from the electron-phonon interaction and electron-electron interaction, i.e., $\gamma/\gamma_0=(1+\lambda_{\rm{el-ph}})(1+\lambda_{\rm{el-el}})$, we obtain the mass enhancement factor due to the electron-electron correlation $\lambda_{\rm{el-el}}=0.84$.
The temperature dependence of the field-cooled dc susceptibility $\chi_{\rm{dc}}=M/H$ down to 2~K in several magnetic fields are presented in Fig.~\ref{dcchi}(a). Here, $M$ is the magnetization measured with a commercial magnetometer~(Quantum Design, MPMS-XL), and $H$ is the external magnetic field. The measurements were performed with many single crystals without alignment of the crystalline direction. The setup is depicted at the top of Fig.~\ref{dcchi}(a). An additional peak around 50~K is attributed to oxygen molecules that remains in the sample space. The temperature dependence of $\chi_{\rm{dc}}$ is explained by the sum of a constant term $\chi_0$ and the temperature-dependent spin paramagnetism. In order to obtain $\chi_0$ as well as to estimate the upper limit of the number of paramagnetic spins $N$, we fitted the data with the formula $\chi_{\rm{dc}}=\chi_0+(N\mu_{\rm{B}}/H){\rm{tanh}}(\mu_{\rm{B}}H/k_{\rm{B}}T)$, by assuming the paramagnetic spin to be 1/2. Here $\mu_{\rm{B}}$ is the Bohr magnetron. We obtain $\chi_0=-1.25\times10^{-4}$~emu/mol-f.u. and $N=3.3\times 10^{-5}$~mol/mol-f.u.. The small $N$ value indicates that the observed spin paramagnetism is not intrinsic, i.e. attributable to impurities. The constant term $\chi_0$ is attributed to the bulk $\chi_{\rm{DC}}$ of CaIrSi$_3$, and the negative $\chi_0$ value indicates that the compound is a diamagnet. Meanwhile, the Pauli paramagnetic susceptibility of CaIrSi$_3$ estimated from the FLAPW calculations is $\chi_{\rm{P}}=0.31\times10^{-4}$~emu/mol-f.u. The observed diamagnetism is attributable to the dominance of the core diamagnetism.
\begin{figure}
\centering
\includegraphics[width=8cm, clip]{fig4_dcchi.eps}
\caption{(Color online) (a) Temperature dependence of the field-cooled dc susceptibility $\chi_{\rm{dc}}$ in several magnetic fields. The increases of $\chi_{\rm{DC}}$ below 80~K, and the small peaks around 50~K are attributed to impurity spin, and oxygen molecules, respectively (see the text). The measurement setup is also depicted. (b) Magnetization $M$ vs. external field $H$ curves at 2~K for $H \parallel a$ axis (filled symbols) and $H \parallel c$ axis (open symbols). The irreversibility field for each field direction is indicated by arrows. The inset is the full $M-H$ curves. The dotted line with a slight negative slope represents the normal state diamagnetism at 2~K. The onset of the magnetic shielding is 0.2~T at 2~K for both field directions. The measurement setups of the samples are also presented.}
\label{dcchi}
\end{figure}
The superconducting $M-H$ curves at 2~K for dc magnetic fields $H \parallel c$ and $H \parallel a$, obtained from separate measurements with a few aligned single crystals, are presented in Fig.~\ref{dcchi}(b). Photos of the experimental setups are presented at the top of Fig.~\ref{dcchi}(b); we arranged the same crystals so that the difference of demagnetization factors between the measurements is small. Indeed, the difference in their superconducting magnetic shielding in the Meissner state is less than 30\%. The inset is the whole $M-H$ loops, indicating that the magnetic shielding occurs below $\pm$0.20~T for both field directions. The loops, exhibiting typical behavior of type-II superconductivity with weak vortex pinning, provide evidence that CaIrSi$_3$ is a type-II superconductor. The type-II superconductivity is also indicated by our previous study with polycrystalline samples~\cite{Eguchi2011PRB}. As presented in the figure, the irreversible field is 0.12~T for $H\parallel a$, and 0.023~T for $H\parallel c$. This anisotropic behavior indicates that vortex pinning for $H\parallel a$ is stronger than that for $H\parallel c$. Such anisotropic pinning was reproducibly observed in other measurements with a single piece of a crystal from the same batch and with several pieces of crystals from another batch. We note that no anisotropy in the normal state susceptibility was observed within our experimental resolution.
\begin{figure}
\centering
\includegraphics[width=\columnwidth, clip]{fig5_cel.eps}
\caption{(Color online) (a) Temperature dependence of the electronic specific heat divided by temperature $c_{\rm{el}}/T$ for $H \parallel a$ (closed symbols) and for $H \parallel c$ (open symbols). We use the relation $c_{\rm{el}}/T=c_p/T-\beta T^2$ to deduce the electronic contribution. The detailed $c_{\rm{el}}/T$ around 0.1~T and 0.4~T are presented in the insets. The horizontal broken line presents the obtained Sommerfeld coefficient $\gamma=6.6$ mJ/mol-f.u.\hspace{1pt}K$^2$. The solid curve is a BCS curve obtained from $\gamma$ and the thermodynamic $T_{\rm{c}}$. (b) The comparison of the normalized $\varDelta c_{\rm{el}}/\gamma T$ vs. $T/T_{\rm{c}}$ for the single crystals and the polycrystals~\cite{Eguchi2011PRB}. For the polycrystalline data, $\gamma$ has been corrected for the residual $c_{\rm{el}}/T$ at 0~T (such $\gamma$ is denoted as $\gamma_{\rm{s}}$ in Fig.~5 of \cite{Eguchi2011PRB}). (c) Magnetic field dependence of $c_{\rm{el}}/T$ extracted from temperature-sweep data.}
\label{cel}
\end{figure}
The temperature dependence of the electronic specific heat divided by temperature $c_{\rm{el}}/T=c_p/T-\beta T^2$ in several fields are presented in Fig.~\ref{cel}(a). The measurements for $H \parallel a$ and $H \parallel c$ were performed using the same crystals. At 0~T, the residual term of $c_{\rm{el}}/T$ for $T\rightarrow 0$ is almost absent, indicating that the superconducting volume fraction is nearly 100\% for these samples. The thermodynamic critical field $\mu_0H_{\rm{c}}(0)$ evaluated from the relation $\mu_0H_{\rm{c}}^2(0)/2=-\gamma T^2_{\rm{c}}/2+\int_0^{T_{\rm{c}}}c_{\rm{el}}(T) dT$ is 0.028~T. The theoretical $c_{\rm{el}}/T$ based on the weak-coupling BCS model~\cite{Muhlschlegel1959ZP} presented in the figure well reproduces the observed temperature dependence below 2.7~K. The agreement indicates that the superconducting gap is finite on the entire Fermi surface. Note that similar full-gap behavior of the specific heat has been reported for isostructural polycrystalline BaPtSi$_3$~\cite{Bauer2009PRB} and LaRhSi$_3$~\cite{PhysRevB.83.064522}. The deviation of the $c_{\rm{el}}/T$ from the BCS curve above 2.7~K seems to be attributed to a $T_{\rm{c}}$ distribution within the samples. However, we will point out two tendencies opposite to the ordinary behavior. As presented in the lower inset of Fig.~\ref{cel}(a), the transition in 0~T is broader than that in 0.1~T. This is observed with another measurement with single crystalline samples from different batch (not shown). In addition, the specific-heat jump for the single crystals in 0~T is broader than that for polycrystals, as shown in the comparison of normalized $\Delta c_{\rm{el}}/\gamma T$ between the single crystal and the polycrystals in the Fig.~\ref{cel}(b). These features will be discussed again in the next section. Note that the sharpening of the specific-heat jump in 0.1~T is not observed in polycrystals, probably due to the presence of the grain boundaries in polycrystals. As presented in the upper inset of Fig.~\ref{cel}(a), The specific heat jump is visible in 0.35~T but not in 0.41~T for both field directions.
The magnetic field dependence of $c_{\rm{el}}/T$ extracted from temperature-sweep data are presented in Fig.~\ref{cel}(c). The linear $H$ dependence of $c_{\rm{el}}/T$ at 0.5~K, guided by the solid line, indicates nearly isotropic superconducting gap~\cite{PhysRevB.70.100503}.
\begin{figure}
\centering
\includegraphics[width=\columnwidth, clip]{fig6_HT.eps}
\caption{(Color online) Superconducting $H$-$T$ phase diagram based on the thermodynamic $T_{\rm{c}}$ for $H\parallel a$ (filled symbols) and $H\parallel c$ (open symbols). The solid curve represents the conventional Werthamer-Helfand-Hohenberg (WHH) curve determined from the $H\parallel a$ data. The thermodynamic $T_{\rm{c}}$ values of the polycrystalline sample~\cite{Eguchi2011PRB} are also presented.}
\label{HT}
\end{figure}
The $H-T$ phase diagram deduced from the thermodynamic $T_{\rm{c}}$ for each field direction is presented in Fig.~\ref{HT}. For comparison, the thermodynamic $T_{\rm{c}}$ of polycrystals evaluated from the data reported in Ref.~\cite{Eguchi2011PRB} are also presented. The conventional Werthamer-Helfand-Hohenberg (WHH) curve for the $H_{\rm{c2}}(T)$ in the dirty limit, giving $\mu_0H_{\rm{c2}}^{\rm{WHH}}(0)=-0.693T_{\rm{c}}[{\rm{d}}(\mu_0H_{\rm{c2}})/{\rm{d}}T]|_{T=T_{\rm{c}}}=0.35$~T, is also presented~\cite{Helfand1966PRpart3}. The WHH curve well agrees with the experimental result for $H\parallel c$ above 2~K. However, the observed $H_{\rm{c2}}$ becomes substantially larger than $\mu_0H_{\rm{c2}}^{\rm{WHH}}(T)$ at lower temperatures for both field directions. In addition, $H_{\rm{c2}}$ for the $c$ direction is higher than that for the $a$ direction. This is also evident in the specific-heat data in Fig.~\ref{cel}(a). The ratio $H_{\rm{c2}}^{\parallel c}$/$H_{\rm{c2}}^{\parallel a}(T)$ is approximately 1.1, which is almost invariant below 3~K. Such small anisotropy indicates a nearly three-dimensional superconducting nature.
The Ginzburg-Landau~(GL) parameter $\kappa_{\rm{GL}}$ estimated from $\mu_0H_{\rm{c2}}^{\parallel a}=0.375$~T at 0.9~K is 10.2, using the relation $\kappa=H_{\rm{c2}}^{\parallel a}/(\sqrt{2}H_{\rm{c}})$ and $\mu_0H_{\rm{c}}=0.026$~T at 0.9~K. The value of $H_{\rm{c}}$ is evaluated from the $c_{\rm{el}}/T$ data in 0~T (see e.g.~\cite{Tinkham2nd}). The obtained $\kappa_{\rm{GL}}$ value indicates type-II superconductivity, which is consistent with the results of $M$-$H$ curves in Fig.~\ref{dcchi}(b).
The lower critical field $\mu_0H_{\rm{c1}}^{\parallel a}=0.0018$~T at 0.9~K is estimated from the relation $H_{\rm{c}}^2=H_{\rm{c1}}^{\parallel a}H_{\rm{c2}}^{\parallel a}$. The GL superconducting coherence lengths $\xi_{a}$ and $\xi_{c}$ are estimated to be $\xi_c=31$~nm and $\xi_a=29$~nm at 0.9~K from the relation $\mu_0H_{\rm{c2}}^{\parallel a}=\Phi_0/2\pi\xi_{a}\xi_{c}$ and $\mu_0H_{\rm{c2}}^{\parallel c}=\Phi_0/2\pi\xi_{a}^2$. Note that the $\mu_0H_{\rm{c2}}^{\parallel c}$ at 0.9~K is 0.40~T. The corresponding penetration depth is readily obtained from $\kappa_{\rm{GL}}=\lambda/\xi$. All of these values are consistent with those of polycrystals~\cite{Eguchi2011PRB}.
\section{Discussion}
According to the group theory, the superconducting gap symmetry of CaIrSi$_3$ belongs to the $C_{\rm{4v}}$ point group, which is the same as that of CePt$_3$Si~\cite{Sigrist2006MMM}. There are five possible superconducting pairing symmetries allowed for this point group. The observed fully-gapped behavior indicates that the most symmetric $A_1$ state with $\Delta_1>\Delta_2$ is realized, because this is the only case having a fully-gapped superconducting energy gap function. The gap function of the $A_1$ state with the Rashba-type ASOI is expressed as $\Delta_{\pm}(\theta_{\bm{k}})=\Delta_1\pm \Delta_2 {\rm{sin}}\theta_{\bm{k}}$ for the pair of ASOI-split bands. Here $\theta_{\bm{k}}$ is the angle between the $c$ axis and $\bm{k}$. Note that the superconductivity becomes multi-gapped if $\Delta_2$ is finite. Although the low-temperature $c_{\rm{el}}/T$ behavior in 0~T is consistent with the simplest BCS curve, a possibility of a weak band dependence of the superconducting gap is not excluded.
As mentioned above, the superconducting transition at 0~T is broader than that at 0.1~T. Furthermore, the observed $H-T$ curves deviate from the conventional WHH curve below 2~K. These feature may well be explained as a result of a distribution in both $T_{\rm{c}}$ and $H_{\rm{c2}}$. In fact, the observed behavior is also reproducible by assuming a two-$T_{\rm{c}}$ BCS model, having one domain with lower $T_{\rm{c}}$ and higher $H_{\rm{c2}}$, and another domain with higher $T_{\rm{c}}$ and lower $H_{\rm{c2}}$. On the other hand, the observed behavior can also be explained as a result of multi-gapped superconductivity with a weak band dependence of the gap. In the present case, there are two possible multi-gapped superconductivity: one originating from multiple Fermi surfaces, or one from a finite $\Delta_2$. The deviation from the simplest BCS approximation is worth investigation, and a high-resolution photoemission spectroscopy or a scanning tunneling spectroscopy would give crucial indications.
Another interesting feature in the observed superconducting behavior is the anisotropic pinning observed in the $M-H$ curves: the irreversible field at 2~K for $H\parallel a$ is approximately five times larger than that for $H\parallel c$. Such anisotropic behavior cannot be explained by a simple pinning model with random defects and impurities. Thus, the anisotropic vortex pinning probably indicate an anisotropic distribution of lattice imperfections. CaIrSi$_3$ can have twin boundaries of crystalline domains with opposite directions of the Rashba field, as discussed in CePt$_3$Si~\cite{Mukuda2009JPSJ}. Such twin boundaries would run both perpendicular to an in-plane axis and perpendicular to the $c$-axis. The anisotropic pinning may be caused by these twin boundaries. Note that novel vortex behavior occurring at the twin boundary, i.e., a fractional vortex, is discussed for CePt$_3$Si for $H \parallel a$, in order to explain the observed extremely slow vortex dynamics~\cite{Iniotakis2008JPSJ}. Such interesting vortex phenomena might be related to the observed anisotropic pinning in CaIrSi$_3$.
It has been theoretically predicted that the helical vortex state, which is unique to NCSCs, can be stable in the presence of finite $\delta N$~\cite{Agterberg2007PRB,Kaur2005PRL}. The helical vortex state has a superconducting gap function $\varDelta(\bm{r})=|\varDelta| e^{i\bm{q}_{\rm{h}}\cdot\bm{r}}$ with $\bm{q}_{\rm{h}} \propto \hat{c} \times \bm{H}$. This is analogous to the Fulde-Ferrell (FF) state~\cite{Fulde1964PR}, which exhibits a spatial phase modulation of $\varDelta(\bm{r})$. Note that the finite $\bm{q}_{\rm{h}}$ originates from the asymmetric distortion of a Fermi surface induced by $H$, while the finite $\bm{q}_{\rm{FF}}$ of the FF state originates from the electron pairing between the Zeeman-split energy bands. For another difference, the helical vortex state can be realized down to near $H=0$ whereas the FF state can be stable only in high fields near the Pauli-limitting field $H_{\rm{P}}$. For the helical vortex state, an enhancement of low-temperature $H_{\rm{c2}}$ associated with the emergence of a spatially modulated superconducting gap amplitude, or modulated vortex states, are discussed near $H_{\rm{P}}$~\cite{Agterberg2007PRB,Matsunaga2008PRB}. However, this is not relevant to the case of CaIrSi$_3$ because $\mu_0H_{\rm{P}}(0)\sim 6$~T is sufficiently larger than the actual $H_{\rm{c2}}$. Here, $\mu_0H_{\rm{P}}(0)$ is estimated from the relation $\mu_0H_{\rm{P}}(0)/T_{\rm{c}}=1.84$~T/K.
Nevertheless, other signatures related to the helical vortex state may be observed in CaIrSi$_3$. For example, the observed $H_{\rm{c2}}$ enhancement in low temperatures is possibly related to properties of the helical vortex state at $H \ll H_{\rm{P}}$. As well as the sample improvement, further investigation especially in the lower temperature region is necessary.
\begin{table}[h]
\caption{Physical properties of CaIrSi$_3$ obtained by this study. Here $\gamma$ is the electronic specific heat coefficient per formula unit, $\varTheta_{\rm{D}}$ is the Debye temperature, $\chi_0$ is the bulk dc susceptibility per formula unit, $T_{\rm{c}}$ is the thermodynamic superconducting transition temperature, $\mu_0H_{\rm{c}}(0)$ is the thermodynamic critical field, $\lambda_{\rm{el-ph}}$ is the electron-phonon coupling constant, $\lambda_{\rm{el-el}}$ is the electronic mass enhancement due to the electron-electron correlation, $\mu_0H_{\rm{c2}}^{\parallel a}$ is the upper critical field at 0.9~K, $\kappa_{\rm{GL}}$ is the Ginzburg-Landau parameter, $E_{\rm{F}}$ is the Fermi energy, $N(E_{\rm{F}})$ is the density of states per unit cell, and $\chi_{\rm{P}}$ is the Pauli paramagnetic susceptibility per formula unit. The latter three values are obtained from the relativistic first principle calculations.}
\begin{ruledtabular}
\begin{tabular}{cc}
$\gamma$ & 6.6~mJ/mol-f.u.\hspace{1pt}K$^2$ \\
$\varTheta_{\rm{D}}$ & 314~K \\
$\chi_0$ & -1.25$\times 10^{-4}$~emu/mol-f.u. \\
$T_{\rm{c}}$ & 3.3~K \\
$\mu_0H_{\rm{c}}(0)$ & 0.028~T \\
$\lambda_{\rm{el-ph}}$ & 0.56 \\
$\lambda_{\rm{el-el}}$ & 0.84 \\
$\mu_0H_{\rm{c2}}^{\parallel a} $(at 0.9~K) & 0.375~T \\
$\kappa_{\rm{GL}}$ (at 0.9~K) & 10.2 \\ \midrule
$E_{\rm{F}}$ & 8.26~eV \\
$N(E_{\rm{F}})$ & 1.94~states/eV\hspace{1pt}u.c. \\
$\chi_{\rm{P}}$ & 0.31 $\times 10^{-4}$~emu/mol-f.u. \\
\end{tabular}
\end{ruledtabular}
\label{t1}
\end{table}
\section{Summary}
We revealed the existence of strong SOI on CaIrSi$_3$ by HAXPES, and the nearly three-dimensional, fully gapped superconducting nature with anisotropic vortex pinning, using single crystalline samples. The physical properties evaluated in this study is summarized in the Table~\ref{t1}. We emphasize that CaIrSi$_3$ is one of the simplest Rashba-type NCSC having strong SOI without active $f$-electrons. It is expected that the single crystalline samples would provide unique oppotunities for investigations of novel superconducting phenomena related to the lack of the inversion symmetry.
\begin{acknowledgements}
We thank Taichi Matsuda, Hiroaki Ikeda, Y. Yanase, S. Fujimoto, D.C. Peets, M. Kriener, F. Kneidinger, and E. Bauer for fruitful discussions. This work is supported by a Grant-in-Aid for the Global COE program ``The Next Generation of Physics, Spun from Universality and Emergence'' from the Ministry of Education, Culture, Sports, Science, and Technology (MEXT) of Japan, and by the ``Topological Quantum Phenomena'' Grant-in Aid for Scientific Research on innovative Areas from MEXT of Japan. It is also supported by the Japan Society for the Promotion of Science (JSPS) through the ``Funding Program for World Leading Innovative R\&D on Science and Technology (FIRST Program)", initiated by the Council for Science and Technology Policy (CSTP). The synchrotron radiation experiments at SPring-8 were performed under the approvals of the Japan Synchrotron Radiation Research Institute (2011B1710 and 2012A1624). G.E. is also supported by JSPS.
\end{acknowledgements}
\bibliographystyle{apsrev4-1_nocomma}
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"redpajama_set_name": "RedPajamaArXiv"
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stories from my red thread life Do you love Etsy?
People lined up around the block and then filled the atrium of Toronto's MaRS Centre yesterday. The attraction?
Etsy, up close and personal.
The paramount online marketplace of handmade and vintage goods has more than 1 million active shops around the world. But while the experience of buying beautiful things online can be fun, even addictive, there's nothing quite like discovering new treasures with your eyes and your hands.
So in an attempt to promote its Canadian sellers, on September 27, Etsy Made in Canada presented a series of pop-up craft shows in 23 locations across Canada featuring Etsy sellers in their home cities.
The charming Francie of Sister Valentine displayed an eclectic collection of handmade goodies, including crocheted fingerless gloves, fabric pouches fashioned like envelopes, fabric dolls, and these wonderful 3-dimensional animal portraits. Every piece she's crafted is utterly charming. You can find more of her work here.
Flora Cheung stood behind her knitted cacti knitting nonchalantly, her warm contagious smile welcoming visitors to her table of treasures. The softest gloves, scarves, booties and accessories beckoned to me with their promises of cosiness. I easily imagined her creations as treasured gifts. I will definitely be treating myself to a pair of her travellers' mitts pronto! If you like, you can peruse her lovely website here.
Printmaking grad Michelle Galletta spent three years working in Italy before returning home to Toronto in 2012 to create Kiriki Press. The attention to detail she puts into her embroidery kits is simply stunning. Not simply craft kits for children, the beauty of these projects (with varying complexity) makes them attractive to grownups, too. You can see Kiriki's kits on her website.
Lest you think (heaven forbid!) that I am strongly biased toward textile art (I am), I wanted to share the work of a paper/collage artist who uses maps and vintage books in surprising ways. A world traveler with a huge collection of vintage maps and ephemera, her work is loaded with humour and adventure. "Up and Down the Thames," a piece that combines an original 1920s map of London with tiny cutouts of Buckingham Palace guards from a 1940s picture book, was attracting loads of attention on Saturday, and it's easy to see why. Apfelstrudel is a popular Etsy shop, and you can find it here.
I would like to leave you with a stuffed toymaker who in my opinion has exceptional taste in fabric and makes lovely little monsters for children. But rather than show you her work, which you can see here in her Etsy shop, I share with you a photo of my 4-year-old nephew Benji holding one of her seasonal pieces, a soft skeleton perfect for Halloween! Please don't be afraid of Benji's very scary face, it is just for the photo.
Thank you for joining me in supporting handmade!
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"redpajama_set_name": "RedPajamaC4"
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Brian already had this IO-390 Lyc from Aerosport that he had purchased for an RV-8 project. We would be the first ones to mount the angled valve engine on the factory QB Patrol kit.
So the original plan was to put it on the Patrol as it would make the plane an amazing performer off the water, let alone what it would be like on wheels. As it weighs 30 Ibs more than a parallel valve engine, I had started to make compensations for it like putting the battery behind the baggage compartment. I knew it was going to be a tight fit for cowling but wouldn't know for sure how much until it went on the plane. I figured the nosebowl was probably not going to fit as well. It is hard to show in the pictures but a few things were going to present a problem. We would need a bigger nosebowl, in width, in frontal area mainly from the splitline down, and also much larger intakes. American Champion was willing to sell us the nosebowl from their new Denali Scout. The side cowls would have to angle out more from the firewall, especially to clear #4 cyl. The cowls would also have to be wider and deeper to clear the exhaust pipes and the straighter running intake pipes of the 390. Then we would have to custom make the rear exhausts as I don't think there is anything available that would fit. We have the exhaust for the RV-8 but the rear pipes hit the engine mount and the front of the tunnel.
So this was going to drastically change the whole look of the Patrol's front end. It would be doable but was going to be allot more work. If we were scratch building the fit would be easier as you could make the firewall wider, but it would still change the shape quite a bit. So we made the decision to scrap the whole plan of the 390. The consensus now, after discussing this with Mark, is that an angled valve engine is not suited to fit the factory QB kits.
We have a new IO-375 M1S (195hp) coming from Aerosport. It is the same dimension and weight as the 360 so now we are back to a known quantity and won't have to worry so much about the W&B of having the 390 up front.
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\section{Introduction}
Many materials solidify into nonequilibrium structures when particle
interactions become strong and if crystallization proceeds too
slowly. Colloidal dispersions provide a number of model systems to
study these still little understood solidification phenomena as
particle potentials can be tailored and detailed experimental
observations are possible. For example colloidal hard spheres have
been studied intensively, where addition of nonadsorbing polymer
induces an attraction, whose strength and range can be controlled
\cite{Poon2002}. The case of short-ranged attractions has turned out
especially rich. Colloidal particles interacting with already
moderately strong short-ranged attractions can form metastable
amorphous solids which exhibit exceedingly long life times.
Depending on the colloidal density and attraction strength different types of
metastable arrested solids can be formed. At high densities glasses
are observed when repulsions hinder and even prevent structural
rearrangements \cite{Pusey1986}. Weak short ranged attractions at first melt these
'repulsion-driven glasses' because they distort and loosen the local
packing. At attraction strengths somewhat higher, yet still of the
order of the thermal energy, physical bonds are formed in dense
systems, which leads to aggregation into 'attraction driven
glasses' \cite{Pham2002,Pham2004,Eckert2002}. At attraction strengths high compared to thermal
fluctuations aggregation phenomena proceed far from equilibrium
at low density, resulting in tenuous solids, i.e. gels. At even lower density, the aggregation process leads to cluster formation and aggregation \cite{Segre2001,Sedgwick2004,Lu2006,Gopalakrishnan2007}.
The connection between repulsion and attraction driven glass transitions at high densities
has been understood within a microscopic theoretical framework, namely mode coupling theory (MCT)
\cite{Fabbian1999,Fabbian1999b,Bergenholtz1999,Bergenholtz2000,Dawson2001}. Yet, the mechanisms of
solidification at intermediate attraction strengths and low to
intermediate densities are still not completely understood \cite{Bergenholtz2003,Ahlstrom2007}.
Especially the interplay of equilibrium phase transitions and
aggregation effects is presently under scrutiny \cite{Verduin1995,Shah2003,Manley2005,Sedgwick2004,Lu2006}.
Another aspect that has been considered at low densities is the existence of weak
long-ranged repulsive interactions ('barriers') between the
particles, that may induce density modulations (or non-percolating clusters at low density),
and thus prevent solidification for some parameter ranges \cite{Stradner2004}.
Small wavevector scattering peaks indicative of mesoscale
correlations have also been observed and employed to characterize
the cluster or gel structures
\cite{Poon1995,Wu2004,Gopalakrishnan2007}. Their observation in
equilibrium systems with long-ranged barriers is expected because
these systems show tendencies to micro-phase separate and to form
interconnected structures of clusters and voids \cite{Sear1999}.
Yet, such long distance correlations and clusters of finite size
were also observed in systems where barriers supposedly are absent
and there presumably have a nonequilibrium origin and arise from
phase separation and/or aggregation and coarsening
\cite{Sciortino1995,Lu2006}. Nonequilibrium origins of the low angle
scattering peaks also were suggested by the observation of their
time evolution \cite{Giglio1992,Poon1995}. Alternatively, to reach
gelation from the fluid, liquid-gas phase separation can be prevented setting a
maximum number of bonds per particle \cite{Zaccarelli2006} or total
number of bonds in the system \cite{Hurtado2007}. In these cases,
gelation is directly connected to percolation, and the low-$q$ modes
facilitate the relaxation of the whole system, due to the lack of
stiffness (only two to four neighbours are allowed on average). At
higher density, such modes are expected to be less important than
collective relaxations, and a general theory should account for both
relaxation mechanisms.
In this contribution we test quantitatively the MCT predictions for
low density attractive glasses or high density gels and study the
role of the cluster or void structure on bond formation at an
intermediate density. The input structure factor needed for the MCT
calculations is taken from simulations, and we compare the
properties of the density correlation functions. Additionally, by
comparing the results of MCT calculations for systems with and
without small wavevector pre-peak in the structure, we highlight the
importance of mesoscopic heterogeneities on attraction driven
dynamic arrest. We consider a system of particles interacting with a
narrow attraction and a weak long-ranged repulsion whose dynamics
has been studied intensely by simulations
\cite{Pham2002,Puertas2002,Puertas2003,Puertas2007b}. At the
considered density of 40\% packing fraction, our system is above
the percolation threshold, and exhibits an equilibrium structural
pre-peak at small wavevectors for parameter ranges where the barrier
suppresses phase-separation. By switching off the repulsive barrier,
the cluster or void structure can be eliminated and the system
becomes homogeneous (below phase separation).
Similar studies, taking the $S_q$ from simulations as input for MCT,
have been performed previously in repulsion driven systems, for
instance Lennard-Jones \cite{Nauroth1997,Flenner2005}, molecular
glasses \cite{Winkler2000}, silica \cite{Sciortino2001} or sodium
silicate melts \cite{Voigtmann2006}. For attraction driven colloidal
glasses, a similar study has recently been performed by Manley et
al. using experimental structure factors \cite{Manley2005}, and we
reach an analogous conclusion concerning the mechanism of dynamic
arrest. Our study goes beyond Ref.~\cite{Manley2005} because the
input to our MCT calculations is taken from simulations of the
system we address without adjustable parameters, while Manley et al.
adjusted the colloid density arbitrarily and assumed a specific
form for the static structure factor at large wavevectors. We find
that it is exactly the structure at large wavevectors that dominates
bond formation. Similar effects in the dynamics related to a prepeak
in $S_q$ have also been observed in sodium silicate melts
\cite{Meyer2004,Voigtmann2006}.
\section{Mode Coupling Theory}
This section aims to give a brief overview of the most important results
within MCT concerning the description of liquid-to-glass nonergodicity
transitions \cite{Goetze1991b,Goetze1992}. We focus on the coherent part
of the density correlation function as it provides most insights into the
physical mechanisms causing glassy arrest.
MCT gives a self-consistent equation of motion of the (normalized)
intermediate scattering function $\Phi_{ q}(t)$, which is the coherent
part of the autocorrelation function of density fluctuations with
wavevector {\bf q} of $N$ particles, defined by
\beq{eq1}
\Phi_{ q}(t) = \frac{1}{N S_q}\sum_{i,j=1}^N \left\langle \exp\{i\,{\bf q}
[{\bf r}_i(t)-{\bf r}_j(0)]\}\right\rangle.
\eeq
The normalization to unity at time $t=0$ is provided by the static
structure factor $S_q=\sum_{i,j=1}^N\langle \exp\{i\,{\bf q} [{\bf
r}_i-{\bf r}_j]\}\rangle/N$, which captures equilibrium density
correlations. The equation of motion for $\Phi_q(t)$ takes the form of a
relaxation equation, where retardation effects with respect to exponential
relaxation on diffusive timescale ${\cal T}_q = \left(D^{\rm s}
q^2/S_q\right)^{-1}$ are contained in a memory kernel $m_q(t)$.
\beqa
{\cal T}_q\dot{\Phi}_q(t)+\Phi_q(t)+\int_0^t dt'
m_q(t-t')\,\dot{\Phi}_q(t')=0\label{eq2}
\eeqa
The initial decay constant ${\cal T}_q$ describes short time diffusive
particle motion, and is set by the short time collective diffusion
coefficient $D^{\rm s}$; it captures instantaneous particle interactions
and will not play an important role at the glass transition.
The central quantity capturing slow structural rearrangements close
to glassy arrest is the memory function $m_q(t)$ which is given in
MCT-approximation:
\beqa m_q(t)={\cal
F}_q[\{\Phi(t)\}]=\frac{1}{2}\sum_{{\bf k p}} V_{\bf q k p}\;
\Phi_k(t)\Phi_p(t)\label{eq3}
\eeqa
The vertices $V_{\bf q k p}$
couple density fluctuations of different wavelengths and thereby
capture a nonlinear feedback mechanism in dense fluids, which is
interpreted as 'cage effect' \cite{Goetze1992}. The memory kernel
can be regarded as a generalized friction kernel, as can easily be
verified after time-Fourier transformation of Eq.~(\ref{eq2}). MCT
is a first principles approach as the vertices are calculated from
the microscopic interactions
\beqa V_{\bf q k p}=S_q S_k S_p
\frac{\varrho^2}{N q^4}[{\bf q\cdot k}\,c_k+{\bf q\cdot p}\, c_p]^2
\delta({\bf q}-{\bf k}-{\bf p})\label{eq4}
\eeqa
The mode coupling
approximation for $m_q$ yields a set of equations that is solved
self-consistently. Hereby the only input to the theory is the static
equilibrium structure factor $S_q$, which enters the memory kernel
$m_q$ directly and via the direct correlation function $c_q
=(1-1/S_q)/\rho$, with $\rho=N/V$ the average density. According to
MCT the dynamics of the dense fluid is therefore completely
determined by equilibrium quantities plus one scale factor to set the time scale. In the following, we will take
$S_q$ directly from simulations.
Solutions of Eqs.~(\ref{eq2}-\ref{eq4}) show a bifurcation scenario
due to the nonlinear nature of the equations. The bifurcation point
is identified with an idealized liquid-to-glass transition. A
quantity of special interest is the long-time limit of the
normalized density correlator, $f_q=\lim_{t\to\infty}\Phi_q(t)$,
often referred to as glass form factor or Edwards-Anderson
nonergodicity parameter. It describes the frozen-in structure of the
glass and obeys
\beq{eq5} \frac{f_q}{1-f_q}={\cal F}_q[f] \,. \eeq
In the fluid regime density fluctuations at different times
decorrelate, so that the long time limit vanishes, $f_q\equiv 0$. On
approaching a critical packing fraction $\phi_{c}$ or a critical
temperature $T_c$, MCT states that strongly coordinated movements
are necessary for structural rearrangements to relax to equilibrium.
MCT identifies two slow structural processes, $\beta$- and
$\alpha$-process, when the glassy structure (described by $f^c_q$)
becomes metastable and takes a long time to relax. In the idealized
picture of MCT, dynamical arrest sets in at the glass transition
with $f_q>0$ when the particles are hindered to escape from their
neighbouring environments.
This also is accompanied by diverging
relaxation times. Glassy states are called nonergodic states in
MCT. The value of the glass form factor at the transition is called
critical nonergodicity parameter $f^c_q$.
Although experiments on molecular glass formers have revealed that
the dynamics very close to the transition point is dominated by thermally
activated hopping processes, which the described (idealized) MCT cannot account for, MCT has been
very successful in describing the approach to glassy arrest. It gives a
quite accurate description of structural relaxation in colloidal dynamics
and there especially of the $\alpha$-process.
For liquid states and
large times the correlator approaches the $\alpha$-scaling law
$\Phi_q(t)\to\tilde{\Phi}_q(\tilde{t})$ and $\tilde{t}=t/\tau$. Here
the scaling functions $\tilde\Phi_q(\tilde t)$ are independent of
temperature or other control parameters.
The $\alpha$-relaxation scale $\tau$
is given in MCT by \beq{eq7} \tau = \tau(\epsilon)=
\tau_0\,/|\epsilon|^{\gamma} \mbox{ with }
\gamma=\frac{1}{2a}+\frac{1}{2b} \eeq and depends only on the
separation $\epsilon=\frac{T_c-T}{T_c}$ from the critical point. The
scaling factor $\tau_0$ needs to be determined from matching the
microscopic dynamics and the $\beta$-scaling regime to the
$\alpha$-scaling regime. The anomalous exponents $a$ and $b$ are
solutions of the equation \beq{eq72}
\Gamma^2(1-x)/\Gamma(1-2x)=\lambda \eeq for $0<x=a<1/2$ and $-1\le
x=-b<0$. The exponent parameter $\lambda$ enters in the second order
of the asymptotic expansion of the right-hand side of
Eqs.~(\ref{eq3},\ref{eq5}) around the critical plateau $f_q^c$.
Therefore it depends on the structure factor $S_q^c$ at the critical
point via the vertex Eq.~(\ref{eq4}).
In the vicinity of the critical point, von Schweidler's power-law
describes the initial $\alpha$-relaxation from the plateau to zero.
It is nothing more than the short--time expansion of the
$\alpha$-master functions, which is up to second order \beq{eq8}
\tilde{\Phi}_q(\tilde{t})=f_q^c-h_q\, \tilde{t}^b (1 + k_q
\tilde{t}^b)+{\cal O}(\tilde{t}^{3b}). \eeq The coefficients $h_q$
are called critical amplitude, the $k_q$ are correction amplitudes
\cite{Franosch1997}. Von Schweidler's law is the origin of
stretching (viz.~ non-exponentiality) in the $\alpha$-process of
MCT.
The final decay
of the structural relaxations in different correlators provides a
definition of the $\alpha$-relaxation times. We use
$\Phi_q(t=\tau_q)=f^c_q/20$. In MCT the increase of the relaxation
times in different correlators is strongly coupled. Their divergence
is inherited directly from the diverging $\alpha$-relaxation scale
$\tau$ of Eq.~(\ref{eq8}). For the $\alpha$-relaxation times of the
density fluctuations in $\Phi_q(t)$ this means a separation into
$\alpha$-scale and a dimensionless factor $\hat{t}_q$ containing the
wavevector dependence. \beq{eq9} \tau_q=\hat{t}_q\,\tau(\epsilon).
\eeq For large wavevectors, $\hat{t}_q\sim q^{-1/b}$ holds in MCT
\cite{Fuchs1994}.
Summarizing this short presentation of MCT, let us note that the
wavevector dependences of the various amplitudes in the asymptotic
MCT predictions will enable us in the following to identify the
physical mechanisms causing glassy arrest. More details about MCT,
the asymptotic expansions and the scaling-laws can be found in
\cite{Goetze1991b,Goetze1992,Franosch1997,Goetze1999}.
\section{Simulation Setup}
Molecular dynamics simulations in the canonical ensemble were
performed considering 1000 quasi-hard particles interacting by a
short range attraction. Because we aim to study the fluid to
non-ergodic transition induced by attractions, equilibrium phase
transitions, i.e.~crystallization and liquid-gas separation, were
suppressed by suitable choices for the interaction potential, which
we introduce in the following.
The short range attraction mimics the interaction between colloidal
particles induced by non-adsorbing polymers in a colloid polymer
mixture. For monodisperse colloids, this attraction is given by the
Asakura-Oosawa interaction \cite{Poon2002}, which is slightly
modified to include polydispersity \cite{Mendez2000}. The attraction
strength is set by the concentration of polymers, $\phi_p$, and the
range by the polymer size, $\xi$ (see below). This potential has
been slightly corrected near contact $r=d_{12}$ to ensure that the
total interaction potential has the minimum at $d_{12}$
($d_{12}=(a_1+a_2)$, with $a_1$ and $a_2$ the radii of the
interacting particles) \cite{Puertas2003}.
\begin{centering}
\begin{figure}[h]
\centerline{\psfig{file=potential.eps,width=8.5cm}}
\caption{Interaction potential for two particles with the average radius.
The polymer fractions are $\phi_p=0.42$ and $\phi_p=0.25$ for the thin
and thick curves, respectively (values close to the glass transition in
the simulation and MCT, respectively). Note that in our units, the thermal energy is
$k_BT=4/3$.}
\label{potential}
\label{fig1}
\end{figure}
\end{centering}
Crystallization is avoided by using a polydisperse system: particle sizes
are distributed according to a flat distribution of width $\delta=0.1 a$,
where $a$ is the mean diameter. The core-core repulsion is given
by $V_{sc}(r)\:=\:k_BT \left(r/d_{12}\right)^{-36}$.
At high polymer fractions, or attraction strength, this system
separates in two fluid phases with different densities, dilute and
dense -- the critical point is at $\phi_p^{\rm cp}\approx 0.29$. To
avoid this transition, which would interfere with the attractive
glass, a repulsive long-range barrier has been added to the total
interaction potential, which extends from $r=d_{12}+2\xi$ to $r=4a$,
and its height is only $1 k_BT$ (equal to the attraction strength at
$\phi_p=0.0625$). The barrier raises the energy of a dense phase, so
that liquid gas separation does not take place. The resulting total
interaction potential, $V_{tot}=V_{sc}+V_{AO}+V_{bar}$, is
analytical everywhere and allows straightforward integration of the
equations of motions. The total interaction potential is presented
in Fig. \ref{potential} for particles with the average radius.
The inclusion of the repulsive barrier in the interaction potential
effectively inhibits liquid-gas separation \cite{Puertas2003}, but causes
holes and tunnels in the system. This is reflected in the structure factor
as a low-$q$ peak, which grows and moves to lower-$q$ values, as the
strength of the attraction (namely, $\phi_p$) increases. The effect of
this barrier on the glass transition is studied below within MCT.
Lengths are measured in units of the average radius, $a$, time in units of
$\sqrt{4a^2/3v^2}$, where the thermal velocity $v$ was set to
$\sqrt{4/3}$. Equations of motion were integrated using the
velocity-Verlet algorithm, in the canonical ensemble (constant NTV), to
mimic the colloidal dynamics. Every $n_t$ time steps, the velocity of the
particles was re-scaled to assure constant temperature. No effect of $n_t$
was observed for well equilibrated samples. The time step was set to
$0.0025$. The range of the attraction, $2\xi$, is set to $2\xi=0.2a$. The
density of colloids is reported as volume fraction, $\phi_c=\frac{4}{3}\pi
a^3 \left(1+\left(\frac{\delta}{a}\right)^2\right) n_c$, with $n_c$ the
colloid number density, and the attraction strength is given by the
polymer volume fraction, $\phi_p$ (with $\xi=0.1$, the minimum of the
attraction for average sized particles, at $r=2a$, is $V_{min}=-16 k_BT
\phi_p$).
The dynamics of this system has been analyzed previously within the
framework of MCT, i.e. using the density correlation functions
\cite{Puertas2003,Puertas2005}. Increasing the attraction strength,
$\phi_p$, at $\phi_c=0.40$ a glass transition is obtained at
$\phi_p^c=0.4265$, which shows the qualitative features of
attractive glasses, as predicted by MCT. The critical parameters
given below for the transition were obtained analysing $\Phi_q(t)$
for the fluid state $\phi_p=0.42$, close enough to the glass to show
the typical two-step decay (see Fig. \ref{fig9}) -- 1500 independent
configurations were used to calculate $\Phi_q(t)$, from 15
independent "quenches" from hard spheres at the same density. The
$\beta$-regime and early $\alpha$-decay were analyzed from $t=2$ to
$t=500$. A wavevector-independent von Schweidler exponent was fitted
using the correlators at all wavevectors, whereas the non-ergodicity
parameter, $f_q^c$ and critical amplitudes $h_q$ and $k_q$ were
actually fitted for every wavevector.
The structure factors needed as inputs to MCT were calculated from
the definition of $S_q$, using only the allowed wavevectors ${\bf
q}=2\pi /L (n_x, n_y, n_z)$, with $L$ the box size and $n_x$, $n_y$
and $n_z$ integers. Starting from $q=2\pi/L$, the next value of the
${\bf q}$ modulus is selected if the $q$-separation is larger than
$0.1a^{-1}$, up to $qa=40$. The structure factors were then
interpolated to have a constant $q$-grid.
\section{Aspects of the numerical MCT solutions}
For the numerical solution of the MCT equations, algorithms
were used that have been developed in the recent years \cite{Fuchs1991b}.
Dynamic and static analyzes were performed by iteratively solving
Eq.~(\ref{eq2}) with the memory functional given by
Eqs.~(\ref{eq3},\ref{eq4}). The results were accepted if a
convergence to $\Phi_q(t)$ with a relative accuracy of $10^{-15}$
was achieved at each $t,q$. To extend the calculation onto
logarithmic time scales without running into inefficient
time-discretization for late times, we used an algorithm for the
convolution in Eq.~(\ref{eq2}) that doubled the initial time step of
$10^{-9} D^2/D^s$ every 256 time steps, where $D=2a$ is the particle
diameter. The critical polymer concentrations were attained by a
bisection method and determined up to a relative accuracy of
$10^{-5}$ in concentration.
The structure factors for the MCT calculation input were taken
directly from the simulation and linearly interpolated without
further smoothing. We used a wave vector grid with $M=400$ grid
points and a cutoff of $qD=80$. From \cite{Sperl2004} it is known
that with these values neither the discretization nor the cutoff
influence the results significantly. For very small wave vectors
$qD\le0.3$ the algorithm does not produce the correct results
because of numerical error propagation.
This can be recognized by the static
results shown in Figs. \ref{fig4}-\ref{fig6} for the nonergodicity
parameter $f_q$, in Fig. \ref{fig7} for the critical amplitudes $h_q$ and
in Fig. \ref{fig8} for the $\alpha$-relaxation times. The plotted
results exhibit a sudden drop down to 0 for $q\to0$, whereas they should
take a finite value. Despite this, the results for larger q are not
invalidated, as was verified by removing the incorrect values from the integrations in \gl{eq3}.
\section{Results and Discussion}
In order to quantitatively describe the results from the simulations
for the polydisperse system of particles interacting with the
potential shown in Fig. \ref{fig1}, three different calculations
within MCT were performed. They differ in the input static structure
factors, all of which were obtained directly from simulations.
Three additional simulation studies were performed solely to
generate the $S_q$ where the pair potentials employed in the
different simulations differed. Thus, we could highlight the
importance of $(i)$ particle polydispersity, and $(ii)$ the
long-ranged repulsive barrier, in the structural relaxation.
For convenience and clarity we name the different MCT calculations
in the following way: System (A) is the {\em monodisperse} model
{\em without repulsive barrier}, whereas we refer with (B) and (C)
to the {\em monodisperse} and {\em polydisperse} systems,
respectively, {\em with repulsive barrier}. While the calculation in
(C) thus uses exactly the $S_q$ of the system whose dynamics we aim
to describe, the MCT we use considers a monodisperse system.
Calculation (C) thus also is only approximative. True multi-species MCT calculations like in Ref.~\cite{Foffi2004} would be required to capture all polydispersity aspects, yet are too demanding in the present case. All elements of the matrix of partial structure factors would be required, and the multiple wavevector integrations over the required large $q$-ranges would crucially slow down the MCT numerics.
In order to stress the approximative character of the MCT calculation (C), we call the simulation, where the dynamics is analyzed, system
(D). Some results of the calculations like critical polymer
concentrations, exponent parameters, exponents, and localization
length (in units of the diameter D) are summarized in table
\ref{tab1}.
\begin{centering}
\begin{table}[h]
\begin{tabular}{|*{7}{c|}}
\hline
& $\delta$ & $V_{bar}$ & $\phi^c_p$ & $\lambda$ & b & $r_l^2$ \\
\hline
\hline
(A) MCT & 0 & No & 0.2356 & 0.752 & 0.555 & 0.00501\\
\hline
(B) MCT & 0 & Yes & 0.2464 & 0.759 & 0.544 & 0.00510\\
\hline
(C) MCT & 0.10 & Yes & 0.3646 & 0.775 & 0.517 & 0.02628\\
\hline
(D) Simulation & 0.10 & Yes & 0.4265 & 0.863 & 0.37 & 0.0158 \\
\hline
\end{tabular}
\caption{Critical polymer concentrations, exponent parameters,
von-Schweidler exponents and localization lengths resulting from the
different MCT computations: (A) monodisperse without barrier, (B)
monodisperse with barrier, (C) polydisperse with barrier. The first
columns give polydispersity $\delta$ and whether a repulsive barrier
exists. Listed under (D) are the corresponding parameters from the
analysis to the polydisperse simulation with barrier of the fluid
state with $\phi_p=0.42$. All states are at colloid packing fraction
$\phi_c=0.40$.} \label{tab1}
\end{table}
\end{centering}
\subsection{Structure factors}
To clarify the influences of the different pair potentials and the
polydispersity on the equilibrium structure we compare on the one
hand structure factors for the same parameters ($\phi_c, \phi_p$)
for the different potentials and on the other hand results at the
MCT-critical points that are obtained for the different potentials.
The $S_q$ in Fig. \ref{fig2} for $\phi_c=0.40$ and $\phi_p=0.25$
show all a primary peak at $qD\approx7.5$ that indicates the local
fluid order. A peculiarity, which is often seen in gels of
intermediate and lower densities, is a low-$q$ peak in the static
structure factor. It appears on the length scale of the voids in the
structure when the sol-gel transition line is reached, increases
towards the transition \cite{Segre2001,Sciortino2004}, and shifts to
slightly lower $q$-values (cf. Fig. \ref{fig3}). A common
interpretation of the low-$q$ peak is that it indicates the onset of
an arrested phase separation at higher attraction strengths. At
lower density, below the percolation threshold, this peak marks the
presence of clusters in the system, although similar internal
structures for gels and independent clusters have been reported
\cite{Gopalakrishnan2007}. The systems (B) and (C) with repulsive
barrier show this low-$q$ peak, whereas it is absent in the model
(A) without repulsive barrier. The latter $S_q$ clearly grows in
the limit $q\to0$ for increasing polymer fractions, indicating the
proximity of the liquid-gas critical point. The $S_q$ with barrier
stay finite as a result of the weak repulsion preventing phase
separation; rather they develop the prepeak which may signal
closeness to microphase separation.
\begin{centering}
\begin{figure}[h]
\centerline{\psfig{file=Sq-040-025.eps,width=8.5cm}} \caption{$S_q$
from MD-simulations at a colloid packing fraction of $\phi_c=0.40$
and a polymer concentration of $\phi_p=0.25$, which is in the gel
close to the critical point in MCT. The repulsive barrier affects
$S_q$ in the region below $qD\le 13$; system (A) without barrier
(dashed-dotted, black) shows neither a prepeak nor a primary
peak which is as high as in systems (B,C) with barrier (full red, dashed black). The
inset demonstrates that polydispersity causes the q-tail
oscillations in $S_q$ to be suppressed for large wavevectors. The
$S_q$ for the polydisperse model (C) falls below the noise level for
$qD\ge45$, whereas the monodisperse systems (A) and (B) virtually
coincide there.} \label{fig2}
\end{figure}
\end{centering}
Besides the long-ranged barrier, polydispersity has important
effects on the equilibrium structure. The inset of Fig. \ref{fig2}
displays $S_q$ from $qD=30-80$ for the different systems. The $S_q$
of the monodisperse systems both with and without barrier virtually
coincide and show distinct oscillations for these wave vectors,
unlike in the polydisperse case. Indeed $S_q$ for (C) starts to
deviate from (B) above $qD\approx12$ and decays to the noise level
above $qD\approx45$. This rapid decay to unity in the $S_q$ of the
polydisperse systems is due to slight differences in the distances
where the (partial) pair correlation functions for differently sized
particles show their contact maxima. This distribution in the
contact distances leads to negative interferences in the oscillatory
large-$q$ pattern in $S_q$, which gets canceled in the averaged
structure factor of the polydisperse system. This effect of the
short-ranged attraction, viz.~ the increased probability of particle
contact, is thus only contained in the $S_q$ of systems (A) and (B).
\begin{centering}
\begin{figure}[h]
\centerline{\psfig{file=Sq-critical.eps,width=8.5cm}}
\caption{Critical $S_q$ at the boundaries of the gel phase: Black dashed-dotted, red full
and black dashed lines mark results from (A), (B) and (C). The red
diamonds indicate $S_q$ at $\phi_p=0.42$, which is close to the
arrested state in the simulation (D). In the simulation, the prepeak at $qD\simeq 2.5$ rises and
shifts to smaller $q$-values with increasing polymer concentration. The
inset gives an enlarged view of the q-tail where systems (A,B) show pronounced oscillations driven by the short-ranged attraction.}
\label{fig3}
\end{figure}
\end{centering}
Fig.~\ref{fig3} shows $S_q$ at the critical points in MCT (see table
\ref{tab1}) and in the simulation ((D), $\phi^c_p\approx 0.4265$).
It was possible to take the structure factors for the MCT input
directly from the monodisperse simulations, because MCT predicts the
states to be nonergodic already at rather low $\phi_p$, while the
actual system only freezes at higher attraction strengths. The
features discussed in respect to Fig.~\ref{fig2} can be recognized
again even though the attraction strenghts vary. While $S_q$ of the
system (A) without barrier differs from the other systems at small
wavevectors, polydispersity forces the averaged $S_q$ of systems
(C,D) to approach unity quickly at large wavevectors.
\subsection{Nonergodicity parameters}
From the equilibrium structure factor input of the different systems
we calculated the critical Edwards-Anderson nonergodicity parameters
$f_q^c$ using Eq.~(\ref{eq5}). The bifurcation occurs for the
colloid packing fractions of $\phi_c=0.40$, which has been used
throughout the analysis, at polymer concentrations $\phi^c_p=0.2356$
(A), $\phi^c_p=0.2464$ (B) and $\phi^c_p=0.3646$ (C) respectively.
Note that the critical polymer concentrations are lower than the
critical $\phi^c_p$ in the simulation, system (D). Luckily, the
transition point in system (A) occurs below the critical point,
which suppresses effects from the liquid-gas separation. For system
(B), crystallization is far too slow to affect the results (although
this state is indeed metastable with respect to crystallization).
The trend of MCT to overestimate the tendency to freeze leads almost
to a factor of 2 in terms of attraction strengths \cite{Sperl2004}.
This discrepancy has also been observed in former comparisons of MCT
with binary Lennard-Jones fluids \cite{Nauroth1997}.
The non-ergodicity parameter, $f_q^c$, basically oscillates in phase
with the $S_q$. The shape of $f_q^c$ serves to identify the leading mechanism for the freezing. A repulsion driven transition creates an
$f_q^c$ with pronounced peaks and lower values for small wave vectors. Characteristically, it decreases quickly to zero for increasing $q$. The width of $f_q$ as function of $q$ can be taken as a measure for the localization length that describes the spatial extent that a single particle can explore within its glass cage. For repulsion driven glass transitions one generally finds a localization length of the order of the Lindemann-length, viz.~ a value around a tenth of the average particle separation \cite{Goetze1992}.
If attraction drives the transition, the critical nonergodicity parameters
have higher values and smaller localization lengths, showing up in much
wider $f_q^c$-distributions than for repulsion driven nonergodic states.
The width of $f_q$ as function of $q$ is now set by the attraction range.
In our analysis $f_q^c$ compares quite well with the simulation results
for those models where an attraction driven
large-q tail is present in $S_q$ (see Fig. \ref{fig4}). The
MCT calculation for the polydispersity-smeared-out $S_q$ gives far
too small $f_q^c$ and too large localization lengths what resembles
more results from repulsion driven systems. We conclude from the
agreement between the $f^c_q$ from simulation and the MCT
calculations with attraction-driven large-$q$ tails in $S_q$, that
the simulations exhibit an attraction driven glass transition or
what could be referred to as a gel. Note that this good agreement is
found despite the overestimate of the critical attraction, i.e. the
transition is wrongly located but its principal property is
correctly predicted.
\begin{centering}
\begin{figure}[h]
\centerline{\psfig{file=fq.eps,width=8.5cm}}
\caption{Critical nonergodicity parameters $f^c_q$ at the transition
in the simulation (D) (red
diamonds), from MCT with monodisperse (A,B) $S_q$ (black dashed-dotted and
red full line) and polydisperse (C) $S_q$ (black dashed line). Serious
differences occur, when the average $S_q$ of a polydisperse system
is used as input to a monodisperse theory; the shape of $f_q$ for (C)
resembles more the one of a repulsive glass.}
\label{fig4}
\end{figure}
\end{centering}
An important point to be checked is the role of the long ranged
repulsive barrier. We have already stated above that there is hardly
any difference between the critical polymer concentrations in the
monodisperse calculations without (A) and with barrier (B).
Fig.~\ref{fig6} highlights the influence of the barrier on the
nonergodicity parameters $f_q^c$. The localization length as well as
the attraction driven character of the glass remain unchanged. A
significant effect could only be observed in the vicinity of the
prepeak and the primary peak, where $S_q$ also changes.
Domains of higher wave vectors stay practically unaffected (see also
Fig.~\ref{fig4}). This indicates that the modes on the low angle
q-peak, which is related to the void structure seen in the
simulations, follow the relaxation of an attraction driven glass
without dominating it. It is dominated solely by large-$q$ modes.
\begin{centering}
\begin{figure}[h]
\centerline{\psfig{file=fqSq-wob-zoomA.eps,width=8.5cm}}
\caption{Enlarged view of the nonergodicity parameters of Fig. \ref{fig4} and structure
factors in the low-$q$-region: Minor differences in $f^c_q$
show up in the region $qD\le10$ only, where also the input $S_q$ differs
considerably. Simulation data ((D) red symbols) agree qualitatively with the model calculation (B) including the barrier.}
\label{fig6}
\end{figure}
\end{centering}
\subsection{Critical Amplitudes and Von-Schweidler-Law}
Asymptotic expansions of Eq.~(\ref{eq5}) around the critical plateau
$f_q^c$ introduce the critical amplitude $h_q$ in linear order of
the so-called $\beta$-process. During the $\beta$-process, the
dynamics on all length scales is strongly coupled. The amplitude
$h_q$ measures the participation of the correlator at wavevector $q$
in this process. The $\beta$-process describes the rate limiting
process of glassy arrest, as here glassy and fluid dynamics start to
deviate. The amplitude $h_q$ thus provides important information on
the physical mechanism causing glassy arrest. It generally exhibits
a minimum as function of $q$ at the maximum of $f_q^c$, which
describes the stucture that gets frozen in at the glass transition.
From simulation data, $h_q$ can be
obtained via von-Schweidler fits to correlators. Table \ref{tab1}
reveals that in the present case these fits require somewhat smaller
critical exponents $b$ compared to all MCT calculations (A-C). This
is consistent with the observation, see below in Sect.~E, that the
relaxation appears to be somewhat more stretched in the simulation
than predicted by MCT.
\begin{centering}
\begin{figure}[h]
\centerline{\psfig{file=hq.eps,width=8.5cm}} \caption{Critical
amplitudes in simulation (D) (red diamonds) and MCT (A,B,C) (black
dashed-dotted, red full, black dashed) close to dynamic arrest.
Because of the different $\alpha$-times in simulation and theory the
MCT-results for (A,B) were scaled on the simulation results.}
\label{fig7}
\end{figure}
\end{centering}
The critical amplitudes in Fig.~\ref{fig7}, which are associated
with the calculations where the attractions dominate (A,B), all
exhibit a very broad peak in q. This shows that very local motion
takes part in the $\beta$-relaxation of an attraction driven glass
transition. The presence (in (B)) or absence (in (A)) of the pre-peak does not influence $h_q$ beyond tiny changes for $qD<10$. MCT thus correctly identifies local bond-formation as
the rate limiting step during the $\beta$-process. MCT
underestimates $h_q$ in the q-range below $qD=30$ and thus
overestimates the stability of the glassy structure on intermediate
and long length scales. Von Schweidler's law, $\Phi_q(t)=f^c_q - h_q
(t/\tau)^b$ from Eq.~(\ref{eq8}), gives a much stronger initial
relaxation of the frozen-in structure for $qD\le30$ in the
simulations than in the MCT calculations. In the simulation the
small-$q$ modes decay with a larger amplitude during the
$\beta$-process. The overestimate of the stability of the incipient
glassy structure on length scales larger than corresponding to the
average particle position indicates that MCT misses some of the
larger-distance relaxation mechanisms. Nevertheless, the possibility
to match a common von Schweidler series Eq.~(\ref{eq8}) to the
correlators at large and small wavevectors \cite{Puertas2003}
supports our conclusion from Sect. B that the structural relaxation
for all $q$ is enslaved to local bond formation.
The underestimate of $h_q$ at low $q$ suggests that MCT
underestimates the contribution of the repulsion driven mechanism of
vitrification in the present system. Apparently, in the simulatated
system attraction driven and repulsion driven glass transition
compete, and both transition lines are close. Our quantitative MCT
calculations (erroneously) position the system too far from the
repulsive transitions. Within MCT, a higher order singularity
appears in the vicinity of the merging of the two glass transition
lines, signalled by $\lambda=1$. Indeed, a larger $\lambda$ exponent
is observed in the simulations compared to the MCT calculations,
which glassify due to bond formation solely.
\subsection{$\alpha$-relaxation times}
\begin{centering}
\begin{figure}[h]
\centerline{\psfig{file=art-tailA.eps,width=8.5cm}}
\caption{$\alpha$-relaxation times $\tau_q$ in MCT for the systems
(A),(B),(C) (black dashed-dotted, red full, black dashed line) and
in the polydisperse simulation ((D) red diamonds). The curves are
normalized to the value of $\tau_q$ at $qD=22.7$. In the inset, the
results for models (A) and (B) and simulation (D) are shown in a
log-log plot. The straight line gives the asymptotic behavior
$\tau_q=q^{-1/b}$ valid for large $q$ with the corresponding von
Schweidler $b=0.37$ obtained previously.} \label{fig8}
\end{figure}
\end{centering}
The criterion for quantitatively defining the $\alpha$-relaxation
times is somewhat arbitrary. We chose the definition \beq{eq11}
\Phi_q(\tau_q)=X\cdot f_q, \eeq for the $\alpha$-relaxation times,
where in the theory $X=0.05$ and in the simulation $X=0.50$. The latter
choice was required because of the limited simulation time, but
incurs larger corrections to the values of $\tau_q$ arising from
faster relaxation processes. The different definitions are reconciled in the following comparison by normalization of the times, $\tau_q/\tau_{qD=22.7}$, which brings out the $q$-dependence. The $\alpha$-relaxation times $\tau_q$
generally vary in phase with the nonergodicity parameter $f_q^c$ and
the structure factor $S_q$, a phenomenon often referred to as
de~Gennes narrowing. Repulsion driven glass transitions display the
largest $\tau_q$ at the principal peak in $S_q$, which indicates
that the cage formed by the particle's next neighbors induces the
dynamical arrest. Here on the contrary, the slowest relaxation takes
place either (i) at the prepeak, when the barrier causes void
formation, or (ii) for $q\to0$ in model (A) without barrier on
approaching the phase separation region.
Figure \ref{fig8}
gives $\alpha$-relaxation times calculated from the above definition
and normalized to their value at $qD=22.7$. In MCT for models with
barrier (B,C) one finds that the
slowest modes are connected with the prepeak. In model (A) $\tau_q$
decreases by more than a factor 2 at this $q$, when the prepeak in
$S_q$ is eliminated. The simulations, however, do not allow to check this difference, but only show that the slowest modes are those with $qD<2$.
Nevertheless, the different dynamics at small $q$ has no further
impact on the dynamics at larger $q$; in the inset of Fig.~\ref{fig8} the $\tau_q$
for all models agree at large $q$, where the power-law $\tau_q\sim
q^{-1/b}$ is also tested. It holds nicely in the simulation data,
with the von Schweidler exponent obtained from the fitting of the
correlation functions: $b=0.37$. MCT explains $\tau_q$ for larger
wave vectors quite well, though small systematic deviations emerge
because of the difference in the von-Schweidler exponents between
simulation and calculations, models (A), (B) and (C). Let us note in passing that the asymptotic behavior $\tau_q\sim q^{-1/b}$ holds earlier in the polydisperse MCT calculation (C) (not shown), then in the monodisperse ones (A) and (B), where deviations are still noticeable in the inset of Fig.~\ref{fig8}. This appears to support the probabilistic interpretation of the Kohlrausch law within MCT \cite{Goetze1992,Fuchs1994}.
We conclude
that the void structure is completely enslaved by the bond formation
on local length scales. Even though the dissolution of the void
structure is the slowest process, there's no evidence for a
significant influence of the voids on the local dynamics. Local bond
formation proceeds identically in systems (B,C,D) with barrier and
void pre-peak in $S_q$, and in system (A) without barrier and
void-correlation peak in $S_q$.
\subsection{Correlation functions}
For an inclusive check of the results beyond asymptotic expansions we compare
MCT-correlators for a finite distance from the critical point obtained as full
solutions to the equations (\ref{eq2}-\ref{eq4}). The fact that in
simulations only finite distances from the transition point are accessible
necessitates this comparison. We used the monodisperse model
(B), because it provides reasonable nonergodicity parameters and contains
the barrier like the simulation (D).
\begin{centering}
\begin{figure}[h]
\centerline{\psfig{file=correlators-new.eps,width=8.5cm}} \caption{
Density correlation functions in simulation ((D) red solid lines)
and MCT calculations in model (B) (black dashed lines): The
horizontal black bars indicate the critical plateau values of
$f_q^c$ in MCT. The wavevectors from bottom to top are $qD=57.1,
45.9, 33.9, 22.7, 12.5 $. The short time diffusion coefficient was
set to $D^s/D^2=0.133$. The theoretical curves correspond to a
polymer concentration of $\phi_p=0.2461$, which means a separation
parameter of about $\epsilon_{MCT}=-0.001$. The simulation results
were obtained for a polymer concentration $\phi_p=0.42$, which
corresponds to a separation parameter of $\epsilon_{simu}=-0.015$. }
\label{fig9}
\end{figure}
\end{centering}
The wave vectors for the
MCT-correlators have been chosen to be as close as possible to the
simulation values ($\Delta qD \pm 0.1$). The separation parameter for the
MCT calculation was adjusted so that the structural relaxation can be compared most succinctly.
The correlators from simulation in
Fig. \ref{fig9} show a two-step relaxation process with the final
$\alpha$-relaxation from the plateau of height $f_q^c$. The
$\beta$-process describes the dynamics close to $f^c_q$ including
some part of the approach to $f^c_q$ from above. The simulation data
exhibit damped vibrational motion on short time scales. This is
neglected in \gl{eq2}, which therefore can describe the dynamics
only at later times. It is only this structural relaxation that MCT
addresses and thus the modelling at short times is done as simply as
possible. We do not attempt to (a) include vibrational motion, (b)
capture the separation of short time and long time dynamics
quantitatively, but (c) only consider the shape of the structural
relaxation in the following comparison.
The results highlight the strong q-dependence of the structural
relaxation. In addition a strong stretching, i.e. non-exponential
$\alpha$-relaxation is also observed. According to different
von-Schweidler exponents of $b=0.37$ in the simulation and $b=0.54$
in MCT the simulation results appear somewhat more stretched.
Nevertheless, the local dynamics, where the bond formation can be
directly seen, is well described by MCT. Amplitude and shape of the
$\alpha$-process are rather well captured, as would become even
clearer if simulations closer to the transition could be performed.
But for the dynamics on larger scales only qualitative statements
can be made .
\section{Conclusions}
Glass transitions within MCT are bifurcation points in the equations
of motion of the structural relaxation. While the equilibrium
structure of the considered glass forming fluid changes smoothly,
the dynamics slows down significantly and a metastable glassy
structure comes into existence. The bifurcation transitions of MCT
contain universal signatures, like von Schweider's law that is the
origin of the non-exponentiality of the (final or $\alpha$-)
structural relaxation. Non-universal amplitudes, like the critical
glass form factor $f^c_q$ or the critical amplitude $h_q$ entering
von Schweidler's law, contain the information in MCT about the
physical mechanisms causing arrest.
We considered the wavector dependence of $f^c_q$, $h_q$, and of the
$\alpha$ relaxation times $\tau_q$ in order to discover the origin
of glassy arrest in colloidal dispersions of particles with short
ranged attractions at intermediate packing fractions. The study was
motivated to gain insight into the connection between attraction
driven glass transitions at higher densities and colloidal gelation
at lower ones. We looked at simulations of a model system where
particles interact additionally with a weak long-range repulsive
barrier.
Structure factors $S_q$ directly taken from simulations were used as the
only input to MCT, in order to study the importance of the mesoscale
gel-like structure indicated by a pre-peak in $S_q$. It arises in
the simulations from the long-ranged repulsive barrier that
suppresses gas-liquid demixing. This mesoscale peak is the slowest
mode in the system, as the void-structure takes the longest time to
dissolve. Yet, we find that the existence of the pre-peak in $S_q$
does not affect MCT calculations for the attraction driven glass
transition. The latter is caused by local bond formation apparent in
all quantities at large wavevectors. We conclude that the mesoscopic
mode is enslaved to the formation of physical bonds, and that this
local process is not affected by the larger-scale heterogeneities of
the system. MCT quantiatively captures local bond formation but
somewhat overestimates the stability of the glass on larger length
scales. Still, the mechanism of arrest in the dispersion at
intermediate density is the attraction driven one discovered in MCT
at higher densities.
The role of polydispersity in MCT calculations was also considered.
Averaged structure factors of polydisperse systems miss the large
$q$-tail indicative of short ranged attractions. This arises from
negative interference of the various contributions from
particle-pairs with different contact distances. While this prevents
the use of averaged $S_q$ from polydisperse systems to capture an
attraction driven glass transition, it does not imply that the
vitrification mechanism in polydisperse systems is different. Rather
the actual polydisperse system exhibits bond formation, and can be
described quantitatively within MCT using the appropriate $S_q$
from, for example, the corresponding monodisperse system.
\begin{acknowledgments}
We thank M. Cates for valuable discussions. This work was supported by 'Acciones Integradas Hispano-Alemanas' of
the DAAD, by the IFPRI-initiative 'Gelling Systems', and by the
DFG grants SFB~513, International Training Group 667, and SP/714-3.
AMP acknowledges financial support from the MEC under project
MAT2006-13646-C03-02, and JB acknowledges financial support by the
IUF.
\end{acknowledgments}
|
{
"redpajama_set_name": "RedPajamaArXiv"
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| 5,351
|
{"url":"https:\/\/answers.ros.org\/answers\/202165\/revisions\/","text":"# Revision history [back]\n\nXacro is just a scriptig mechanism that allows more modularity and code re-use when defining a URDF model. When using it, what is actually uploaded to the parameter servers (per default as the \"robot_description\" parameter) actually is a URDF, as that gets generated from the xacro file in the launch file (by expanding the xacro macros used).\n\nAs an example, say you have a \"robot.urdf.xacro\" file. You can run\n\nrosrun xacro xacro.py robot.urdf.xacro > robot.urdf\n\n\nand that gives you the URDF generated from your xacro file. The same approach is commonly used in launch files when a xacro-based robot_description is uploaded.\n\nXacro is just another way of defining a URDF, not an alternative to it. It makes certain things easier, for instance you can generate a \"wheel\" macro and instantiate that 6 times with different parameters to put 6 wheels on your robot, as opposed to copying and pasting the same code six times manually.\n\nXacro is just a scriptig scripting mechanism that allows more modularity and code re-use when defining a URDF model. When using it, what is actually uploaded to the parameter servers (per default as the \"robot_description\" parameter) actually is a URDF, as that gets generated from the xacro file in the launch file (by expanding the xacro macros used).\n\nAs an example, say you have a \"robot.urdf.xacro\" file. You can run\n\nrosrun xacro xacro.py robot.urdf.xacro > robot.urdf\n\n\nand that gives you the URDF generated from your xacro file. The same approach is commonly used in launch files when a xacro-based robot_description is uploaded.\n\nXacro is just another way of defining a URDF, not an alternative to it. It makes certain things easier, for instance you can generate a \"wheel\" macro and instantiate that 6 times with different parameters to put 6 wheels on your robot, as opposed to copying and pasting the same code six times manually.","date":"2020-04-01 02:11:22","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.6499893665313721, \"perplexity\": 3035.1414450052885}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2020-16\/segments\/1585370505359.23\/warc\/CC-MAIN-20200401003422-20200401033422-00084.warc.gz\"}"}
| null | null |
PostalAnnex+:
Wheaton PostalAnnex+ Hosts Ribbon Cutting Ceremony
By: PostalAnnex+ | 0 Shares 30 Reads
After Six Months in Business, the Owners are Ready to Celebrate
WHEATON, Illinois - May 5, 2013 – After six months in business, Mark and Kim Rosinski, who opened the Wheaton PostalAnnex+ on November 12, 2012, are hosting their ribbon cutting ceremony in collaboration with the Wheaton Chamber of Commerce. On May 23, 2013 at 9:30am, members of the Wheaton community are invited to attend the ribbon cutting ceremony and grand opening celebration.
"We've had a great first six months in business," said Mark, "and we're thrilled to have the opportunity to host a grand opening. We hope everyone can join us to celebrate, indulge in some coffee and pastries, and participate in the raffle."
Those attending the ribbon cutting ceremony have the opportunity to win great prizes like gift cards, a wine gift basket, and a chocolate gift basket. One lucky winner will receive the grand prize, a Samsung Galaxy Android ice cream tablet. To enter the raffle, stop by the Wheaton PostalAnnex+, located at 123 Danada Sq E, and fill out an entry form on or before May 23, 2013. Store hours are 8 a.m. to 7 p.m. Monday through Friday and Saturday from 9 a.m. to 4 p.m.
"We really appreciate the support we have received from the Wheaton community and are grateful for our loyal customers," continued Mark, "We're excited to celebrate with everyone and look forward to many years of serving the community."
The Rosinskis' PostalAnnex+ offers the Wheaton community a one-stop solution for many home office and business service needs; shipping through UPS, FedEx, USPS and DHL, private mailbox rental, packaging and shipping supplies, notary public, printing and copying services, office supplies and more.
About PostalAnnex+
PostalAnnex+ is a member of the Annex Brands franchise network. Its locations offer one-stop support for packaging, shipping and office supply needs. Founded in 1985 in San Diego, Annex Brands has nearly 400 locations operating in 40 states across the U.S. and into Canada. All PostalAnnex+ locations are independently owned and operated by licensed franchisees. For more information on the company's services or for franchise information, visit www.AnnexBrands.com.
About Annex Brands
Annex Brands, Inc., formerly known as Postal Annex, Inc., was founded by Jack and Martha (Marty) Lentz in 1985 and is headquartered in San Diego. There are five brands in the Annex Brands franchise family: PostalAnnex+, AIM Mail Center, Navis Pack & Ship, Handle With Care Packaging Store and Sunshine Pack & Ship. All together, there are nearly 400 locations across 40 states and into Canada. Each location is an individually owned and operated franchise. Its retail locations offer a one-stop support center for packaging, shipping, postal and office supply needs, including the ability to compare shipping rates with UPS, FedEx, DHL and USPS shipping. The commercial locations provide custom packaging and shipping solutions for larger and more valuable items. For more information on the company's history, services and franchise information, visit www.AnnexBrands.com.
SOURCE Annex Brands
Packaging, shipping and office supply.
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 8,596
|
List of missing in California's deadliest wildfire down to 1
The number of people listed as missing from a deadly Northern California wildfire is down to one after deputies found an Oroville woman
ByThe Associated Press
FILE - In this Nov. 16, 2018, file photo, a firefighter searches for human remains in a trailer park destroyed in the Camp Fire in Paradise, Calif. The number of people listed as missing from the deadly Northern California wildfire is down to one after deputies located an Oroville woman. The Butte County Sheriff's Office said Friday, Aug. 2, 2019, that Wendy Carroll was aware she was listed as missing but never contacted authorities because of possible legal issues. The Nov. 8, 2018 Camp Fire killed 85 people. (AP Photo/John Locher, File)
PARADISE, Calif. -- Only one person remains listed as missing from the deadliest wildfire in California history after deputies found an Oroville woman.
The Butte County Sheriff's Office said Friday that 47-year-old Wendy Carroll was aware she was considered missing but never contacted authorities to say she was safe because of possible legal issues.
The only person left unaccounted for from the 2018 Camp Fire is Sara Martinez-Fabila, although it's uncertain if she was in the area at the time of the fire.
The list of missing went well over 1,000 following the Nov. 8 fire, heightening fears of hundreds dead from the fast-moving fire that decimated Paradise. The fire killed 85 people.
Investigators blame the fire on faulty equipment owned by the San Francisco-based utility Pacific Gas & Electric.
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 7,566
|
Q: Unable to load font in Allegro I'm playing around with Allegro 5 in C++ and Visual Studio 2012, but for some reason I can't get a font to load using the sample code from the Allegro wiki:
ALLEGRO_FONT *font = al_load_ttf_font("pirulen.ttf",72,0 );
if (!font){
fprintf(stderr, "Could not load 'pirulen.ttf'.\n");
return false;
}
al_clear_to_color(al_map_rgb(50,10,70));
al_draw_text(font, al_map_rgb(255,255,255), 640/2, (480/4),ALLEGRO_ALIGN_CENTRE, "It worked!");
I've tried placing the font file in about every feasible directory in my Visual Studio project, as well as in the directory the .exe is in (as is suggested by several other threads). I also tried just dropping a copy of it on the C: drive and calling it with the fully qualified path: I tried C:\\pirulen.ttf and C:/pirulen.ttf neither of which worked. I've also tried adding it to the "Resource Files" folder in my project, but that did not work either.
Any advice on what could be going on?
Thanks.
A: Everything that needs to be said is here:
*
*Loading Resources (Troubleshooting)
A: I know this is a yonks old question, but I've just found it and read the docs as suggested by Matthew (which everyone ought to do), so thought I'd add this here for any others looking for an easy answer.
You can handle creating a path for each resource if you wish but it is easier to use al_change_directory to set up your resources directory, then you can find you assets there.
al_init_font_addon(); // initialize the font addon
al_init_ttf_addon();// initialize the ttf (True Type Font) addon
ALLEGRO_PATH *path = al_get_standard_path(ALLEGRO_RESOURCES_PATH);
al_append_path_component(path, "resources");
al_change_directory(al_path_cstr(path, '/'));
al_destroy_path(path);
Then you can reference paths relative to the resource root.
ALLEGRO_FONT* font = al_load_ttf_font("LibreCaslonText-Bold.ttf", 72, 0);
// Check font is loaded
if (!font) {
fprintf(stderr, "failed to load font!\n");
al_destroy_font(font);
return -1;
}
To clarify LibreCaslonText-Bold.ttf exists in project_dir/resources/LibreCaslonText-Bold.ttf
Side note
In my case, I also needed to copy the resources over to my build directory. So I added this to my CMakeLists.txt.
if (NOT ${PROJECT_SOURCE_DIR} STREQUAL ${CMAKE_CURRENT_BINARY_DIR})
file(COPY "${PROJECT_SOURCE_DIR}/resources" DESTINATION ${CMAKE_CURRENT_BINARY_DIR})
endif()
|
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"redpajama_set_name": "RedPajamaStackExchange"
}
| 9,476
|
d3.sankey = function() {
var sankey = {},
minNodeWidth = 16,
maxNodeWidth = 80,
nodePadding = 8,
size = [1, 1],
nodes = [],
links = [];
sankey.minNodeWidth = function(_) {
if (!arguments.length) return minNodeWidth;
minNodeWidth = _;
return sankey;
}
sankey.maxNodeWidth = function(_) {
if (!arguments.length) return maxNodeWidth;
maxNodeWidth = _;
return sankey;
}
sankey.nodePadding = function(_) {
if (!arguments.length) return nodePadding;
nodePadding = +_;
return sankey;
};
sankey.nodes = function(_) {
if (!arguments.length) return nodes;
nodes = _;
return sankey;
};
sankey.links = function(_) {
if (!arguments.length) return links;
links = _;
return sankey;
};
sankey.size = function(_) {
if (!arguments.length) return size;
size = _;
return sankey;
};
sankey.layout = function(iterations) {
computeNodeLinks();
computeNodeValues();
computeNodeBreadths();
computeNodeDepths(iterations);
computeLinkDepths();
centerNodeBreadths();
return sankey;
};
sankey.relayout = function() {
computeLinkDepths();
return sankey;
};
sankey.link = function() {
var curvature = .5;
function link(d) {
var x0 = d.source.x + d.source.dx / 2,
x1 = d.target.x + d.target.dx / 2,
xi = d3.interpolateNumber(x0, x1),
x2 = xi(curvature),
x3 = xi(1 - curvature),
y0 = d.source.y + d.source.dx / 2,
y1 = d.target.y + d.target.dx / 2;
return "M" + x0 + "," + y0 + "C" + x2 + "," + y0 + " " + x3 + "," + y1 + " " + x1 + "," + y1;
}
link.curvature = function(_) {
if (!arguments.length) return curvature;
curvature = +_;
return link;
};
return link;
};
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// Also, if the source and target are not objects, assume they are indices.
function computeNodeLinks() {
nodes.forEach(function(node) {
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links.forEach(function(link) {
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target = link.target;
if (typeof source === "number") source = link.source = nodes[link.source];
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source.sourceLinks.push(link);
target.targetLinks.push(link);
});
}
// Compute the value (size) of each node by summing the associated links.
function computeNodeValues() {
// nothing to do, nodes should already have a value
// var ms, mt, totalLinksValue;
// totalLinksValue = d3.sum(links, value);
// nodes.forEach(function(node) {
// ms = d3.max(node.sourceLinks, value);
// mt = d3.max(node.targetLinks, value);
// ms = isNaN(ms) ? 0 : ms;
// mt = isNaN(mt) ? 0 : mt;
// node.value = maxNodeWidth*Math.max(ms, mt)/totalLinksValue;
// });
}
// Iteratively assign the breadth (x-position) for each node.
// Nodes are assigned the maximum breadth of incoming neighbors plus one;
// nodes with no incoming links are assigned breadth zero, while
// nodes with no outgoing links are assigned the maximum breadth.
function computeNodeBreadths() {
var remainingNodes = nodes,
nextNodes,
actualMaxNodeWidth,
totalLinksValue,
totalNodesValue,
x = 0;
totalLinksValue = Math.max(d3.sum(links, value), 1);
totalNodesValue = Math.max(d3.sum(nodes, value), 1);
while (remainingNodes.length) {
nextNodes = [];
remainingNodes.forEach(function(node) {
var mt, ms;
node.x = x;
ms = d3.max(node.sourceLinks, value);
mt = d3.max(node.targetLinks, value);
mt = isNaN(mt) ? 0 : mt;
ms = isNaN(ms) ? 0 : ms;
node.dx = Math.max(
minNodeWidth + (maxNodeWidth - minNodeWidth) * node.value / totalNodesValue,
minNodeWidth + (maxNodeWidth - minNodeWidth) * Math.max(mt, ms) / totalLinksValue
);
node.sourceLinks.forEach(function(link) {
if (nextNodes.indexOf(link.target) < 0) {
nextNodes.push(link.target);
}
});
});
remainingNodes = nextNodes;
++x;
}
//
moveSinksRight(x);
nodes.forEach(function(node) {
if (!node.targetLinks.length) {
node.x = 0;
}
});
actualMaxNodeWidth = d3.max(nodes, function(d) {
return d.dx
});
scaleNodeBreadths((size[0] - actualMaxNodeWidth) / (x - 1));
}
// function scaleNodeDx(node) {
// var currentMaxNodeWidth = 0,
// kw;
// currentMaxNodeWidth = d3.max(nodes, function(d) { return d.dx; });
// kw = (maxNodeWidth-minNodeWidth)/currentMaxNodeWidth;
// nodes.forEach(function(node) {
// node.dx = minNodeWidth+node.dx*kw;
// });
// }
function moveSourcesRight() {
nodes.forEach(function(node) {
if (!node.targetLinks.length) {
node.x = d3.min(node.sourceLinks, function(d) {
return d.target.x;
}) - 1;
}
});
}
function moveSinksRight(x) {
nodes.forEach(function(node) {
if (!node.sourceLinks.length) {
node.x = x - 1;
}
});
}
function scaleNodeBreadths(kx) {
nodes.forEach(function(node) {
node.x *= kx;
});
}
function computeNodeDepths(iterations) {
var nodesByBreadth = d3.nest()
.key(function(d) {
return d.x;
})
.sortKeys(d3.ascending)
.entries(nodes)
.map(function(d) {
return d.values;
});
//
initializeNodeDepth();
resolveCollisions();
for (var alpha = 1; iterations > 0; --iterations) {
relaxRightToLeft(alpha *= .99);
resolveCollisions();
relaxLeftToRight(alpha);
resolveCollisions();
}
function initializeNodeDepth() {
var ky = d3.min(nodesByBreadth, function(nodes) {
return (size[1] - (nodes.length - 1) * nodePadding) / d3.sum(nodes, function(node) {
return node.dx;
});
});
nodesByBreadth.forEach(function(nodes) {
nodes.forEach(function(node, i) {
node.y = i;
node.dy = node.dx * ky;
});
});
var totalLinksValue = d3.sum(links, value);
links.forEach(function(link) {
link.dy = maxNodeWidth * link.value / totalLinksValue;
});
}
function relaxLeftToRight(alpha) {
nodesByBreadth.forEach(function(nodes, breadth) {
nodes.forEach(function(node) {
if (node.targetLinks.length) {
var y = d3.sum(node.targetLinks, weightedSource) / d3.sum(node.targetLinks, value);
node.y += (y - center(node)) * alpha;
}
});
});
function weightedSource(link) {
return center(link.source) * link.value;
}
}
function relaxRightToLeft(alpha) {
nodesByBreadth.slice().reverse().forEach(function(nodes) {
nodes.forEach(function(node) {
if (node.sourceLinks.length) {
var y = d3.sum(node.sourceLinks, weightedTarget) / d3.sum(node.sourceLinks, value);
node.y += (y - center(node)) * alpha;
}
});
});
function weightedTarget(link) {
return center(link.target) * link.value;
}
}
function resolveCollisions() {
nodesByBreadth.forEach(function(nodes) {
var node,
dy,
y0 = 0,
n = nodes.length,
i;
// Push any overlapping nodes down.
nodes.sort(ascendingDepth);
for (i = 0; i < n; ++i) {
node = nodes[i];
dy = y0 - node.y;
if (dy > 0) node.y += dy;
y0 = node.y + node.dy + nodePadding;
}
// If the bottommost node goes outside the bounds, push it back up.
dy = y0 - nodePadding - size[1];
if (dy > 0) {
y0 = node.y -= dy;
// Push any overlapping nodes back up.
for (i = n - 2; i >= 0; --i) {
node = nodes[i];
dy = node.y + node.dy + nodePadding - y0;
if (dy > 0) node.y -= dy;
y0 = node.y;
}
}
});
}
function ascendingDepth(a, b) {
return a.y - b.y;
}
}
function computeLinkDepths() {
nodes.forEach(function(node) {
node.sourceLinks.sort(ascendingTargetDepth);
node.targetLinks.sort(ascendingSourceDepth);
});
nodes.forEach(function(node) {
var sy = 0,
ty = 0;
node.sourceLinks.forEach(function(link) {
link.sy = sy;
sy += link.dy;
});
node.targetLinks.forEach(function(link) {
link.ty = ty;
ty += link.dy;
});
});
function ascendingSourceDepth(a, b) {
return a.source.y - b.source.y;
}
function ascendingTargetDepth(a, b) {
return a.target.y - b.target.y;
}
}
function centerNodeBreadths() {
var nodesByBreadth = d3.nest()
.key(function(d) {
return d.x;
})
.sortKeys(d3.ascending)
.entries(nodes)
.map(function(d) {
return d.values;
});
var maxNodeBreadthWidth;
nodesByBreadth.forEach(function(nodes) {
maxNodeBreadthWidth = d3.max(nodes, function(d) {
return d.dx;
});
nodes.forEach(function(node, i) {
node.x += (maxNodeBreadthWidth - node.dx) / 2;
});
});
}
function center(node) {
return node.y + node.dy / 2;
}
function value(link) {
return link.value;
}
return sankey;
};
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 7,492
|
Tank farm cleanup gets green light
After heated debates earlier this fall, city council decided to allow temporary quarrying at the tank farm on Monday night.
Meagan Gillmore
Only Coun. Betty Irwin voted against the motion to change the official community plan to allow for the cleanup activities at the contaminated site. Irwin had previously voted against the motion. She wanted to wait for the Yukon Environmental and Socio-Economic Assessment Board's approval before the city voted to change the official community plan.
"I have to stand behind what I said the first time. I object to any bylaw amending the official community plan without having that YESAB report in place," she told council.
Earlier this year, a proposal was put forward to build a neighbourhood on the 57-hectare piece of land between Valleyview and Hillcrest. Before work could begin, the soil needed to be cleaned and trucked off site.
Hillcrest residents worried this work would create a loud racket and cause the smell of dug-up petroleum to waft near their homes. They wanted the city to put off changing the official community plan until the YESAB process was complete.
Doing so would have meant work on the project wouldn't begin for another year.
In September, the four city councillors who were seeking re-election voted to wait until YESAB completed its work before changing the official community plan. Early in October, council reversed that decision.
Council will still need to approve any zoning changes for the project, Mike Gau, director of development services told council Monday night.
Any changes to zoning will be "where the rubber meets the road," said Coun. Kirk Cameron. He voted against changing the plan in September, but supported October's vote. However, he may oppose future zoning changes.
Coun. Dave Stockdale originally voted against the change because he felt the residents had real concerns about the project, he said. He changed his mind after the planning committee told him no zoning changes can happen until YESAB issues its report. And the city can put restrictions on zoning, he said.
Residents know about the process and are happy with it, he said.
"Previously, I had voted against it because they had real concerns. If they don't have real concerns about it, then I'm just fighting a losing battle," he said.
"We'll have the checks and balances, and see how things go," he said, adding he was comfortable the project will be done properly.
Mayor Dan Curtis was enthusiastic in his support for the project.
"I think it's kind of a win-win-win," he said.
The project can only benefit the city, the neighbourhood residents and the developers.
"I think we all need to get this done," he said. "It has to happen."
Yukon's mining future is bright, but needs balance, industry leader says
Elders group threatens to overthrow LFN chief
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 1,111
|
package org.apache.hive.service.cli.operation;
import java.util.ArrayList;
import java.util.Arrays;
import org.apache.hadoop.hive.conf.HiveConf;
import org.apache.hadoop.hive.metastore.TableType;
import org.apache.hadoop.hive.ql.security.authorization.plugin.HiveOperationType;
import org.apache.hive.service.cli.FetchOrientation;
import org.apache.hive.service.cli.HiveSQLException;
import org.apache.hive.service.cli.OperationState;
import org.apache.hive.service.cli.OperationType;
import org.apache.hive.service.cli.RowSet;
import org.apache.hive.service.cli.RowSetFactory;
import org.apache.hive.service.cli.TableSchema;
import org.apache.hive.service.cli.session.HiveSession;
import org.slf4j.Logger;
import org.slf4j.LoggerFactory;
/**
* GetTableTypesOperation.
*
*/
public class GetTableTypesOperation extends MetadataOperation {
private static final Logger LOG = LoggerFactory.getLogger(GetTableTypesOperation.class.getName());
protected static TableSchema RESULT_SET_SCHEMA = new TableSchema()
.addStringColumn("TABLE_TYPE", "Table type name.");
private final RowSet rowSet;
private final TableTypeMapping tableTypeMapping;
protected GetTableTypesOperation(HiveSession parentSession) {
super(parentSession, OperationType.GET_TABLE_TYPES);
String tableMappingStr =
getParentSession().getHiveConf().getVar(HiveConf.ConfVars.HIVE_SERVER2_TABLE_TYPE_MAPPING);
tableTypeMapping = TableTypeMappingFactory.getTableTypeMapping(tableMappingStr);
rowSet = RowSetFactory.create(RESULT_SET_SCHEMA, getProtocolVersion(), false);
LOG.info("Starting GetTableTypesOperation");
}
@Override
public void runInternal() throws HiveSQLException {
setState(OperationState.RUNNING);
LOG.info("Fetching table type metadata");
if (isAuthV2Enabled()) {
authorizeMetaGets(HiveOperationType.GET_TABLETYPES, null);
}
try {
for (TableType type : TableType.values()) {
String tableType = tableTypeMapping.mapToClientType(type.toString());
rowSet.addRow(new String[] {tableType});
if (LOG.isDebugEnabled()) {
String debugMessage = getDebugMessage("table type", RESULT_SET_SCHEMA);
LOG.debug(debugMessage, tableType);
}
}
if (LOG.isDebugEnabled() && rowSet.numRows() == 0) {
LOG.debug("No table type metadata has been returned.");
}
setState(OperationState.FINISHED);
LOG.info("Fetching table type metadata has been successfully finished");
} catch (Exception e) {
setState(OperationState.ERROR);
throw new HiveSQLException(e);
}
}
/* (non-Javadoc)
* @see org.apache.hive.service.cli.Operation#getResultSetSchema()
*/
@Override
public TableSchema getResultSetSchema() throws HiveSQLException {
assertState(new ArrayList<OperationState>(Arrays.asList(OperationState.FINISHED)));
return RESULT_SET_SCHEMA;
}
/* (non-Javadoc)
* @see org.apache.hive.service.cli.Operation#getNextRowSet(org.apache.hive.service.cli.FetchOrientation, long)
*/
@Override
public RowSet getNextRowSet(FetchOrientation orientation, long maxRows) throws HiveSQLException {
assertState(new ArrayList<OperationState>(Arrays.asList(OperationState.FINISHED)));
validateDefaultFetchOrientation(orientation);
if (orientation.equals(FetchOrientation.FETCH_FIRST)) {
rowSet.setStartOffset(0);
}
return rowSet.extractSubset((int)maxRows);
}
}
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 7,452
|
Elias Kachunga (Köln, 1992. április 22. –) német labdarúgó, az SC Paderborn 07 csatára. Származása révén rendelkezik kongói DK állampolgársággal is.
További információk
Elias Kachunga adatlapja a transfemarkt.de oldalon
Cikk a torfabrik.de oldalon
1992-ben született személyek
Kongói DK származású németek
Észak-rajna-vesztfáliaiak
Német labdarúgók
A Borussia Mönchengladbach labdarúgói
A Borussia Mönchengladbach II labdarúgói
A VfL Osnabrück labdarúgói
A Hertha Berlin II labdarúgói
A Hertha Berlin labdarúgói
Az SC Paderborn 07 labdarúgói
Labdarúgócsatárok
Kölniek
Élő személyek
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 5,910
|
//
// HttpUtil.m
// LeLive
//
// Created by 辛乐 on 17/5/21.
// Copyright © 2017年 辛乐. All rights reserved.
//
#import "HttpUtil.h"
#import <AVFoundation/AVAsset.h>
#import <AVFoundation/AVAssetExportSession.h>
#import <AVFoundation/AVMediaFormat.h>
#import "UploadImgModel.h"
@implementation HttpUtil
static HttpUtil * httpUtil = nil;
static AFHTTPSessionManager *manage;
+(instancetype) instance {
static dispatch_once_t onceToken;
dispatch_once(&onceToken, ^{
if(httpUtil == nil) {
httpUtil = [[HttpUtil alloc] init];
}
});
return httpUtil;
}
-(instancetype) init {
if(self = [super init]) {
manage = [AFHTTPSessionManager manager];
manage.requestSerializer.timeoutInterval = 3;
/**设置相应的缓存策略*/
manage.requestSerializer.cachePolicy = NSURLRequestReloadIgnoringLocalCacheData;
/**分别设置请求以及相应的序列化器*/
manage.requestSerializer = [AFHTTPRequestSerializer serializer];
AFJSONResponseSerializer * response = [AFJSONResponseSerializer serializer];
response.removesKeysWithNullValues = YES;
manage.responseSerializer = response;
/**复杂的参数类型 需要使用json传值-设置请求内容的类型*/
[manage.requestSerializer setValue:@"application/json" forHTTPHeaderField:@"Content-Type"];
/**设置接受的类型*/
[manage.responseSerializer setAcceptableContentTypes:[NSSet setWithObjects:@"text/plain",@"application/json",@"text/json",@"text/javascript",@"text/html", nil]];
}
return self;
}
/**
* 网络请求的实例方法
*
* @param urlString 请求的地址
* @param paraments 请求的参数
* @param successBlock 请求成功的回调
* @param failureBlock 请求失败的回调
*/
+(void)Get:(NSString *)urlString withParaments:(id)paraments withSuccessBlock:(requestSuccess)successBlock withFailureBlock:(requestFailure)failureBlock {
[manage GET:urlString parameters:paraments progress:nil success:^(NSURLSessionDataTask * _Nonnull task, id _Nullable responseObject) {
successBlock(responseObject);
} failure:^(NSURLSessionDataTask * _Nullable task, NSError * _Nonnull error) {
failureBlock(error);
}];
}
+(void)Post:(NSString *)urlString withParaments:(id)paraments withSuccessBlock:(requestSuccess)successBlock withFailureBlock:(requestFailure)failureBlock {
AFHTTPSessionManager *mgr = [AFHTTPSessionManager manager];
[mgr POST:urlString parameters:paraments progress:nil success:^(NSURLSessionDataTask * _Nonnull task, id _Nullable responseObject) {
successBlock(responseObject);
} failure:^(NSURLSessionDataTask * _Nullable task, NSError * _Nonnull error) {
failureBlock(error);
}];
}
/**
* 上传图片
*
* @param operations 上传图片等预留参数---视具体情况而定 可移除
* @param imageArray 上传的图片数组
* @param urlString 上传的url---请填写完整的url
* @param successBlock 上传成功的回调
* @param failureBlock 上传失败的回调
* @param progress 上传进度
*
*/
+(void)uploadImageWithOperations:(NSDictionary *)operations withImageArray:(NSArray *)imageArray withUrlString:(NSString *)urlString withSuccessBlock:(requestSuccess)successBlock withFailurBlock:(requestFailure)failureBlock withUpLoadProgress:(uploadProgress)progress {
[manage POST:urlString parameters:operations constructingBodyWithBlock:^(id<AFMultipartFormData> _Nonnull formData) {
for (UploadImgModel * imageModel in imageArray) {
NSData * imgData = UIImageJPEGRepresentation(imageModel.image, imageModel.compressionQuality);
[formData appendPartWithFileData:imgData name:imageModel.propName fileName:[NSString stringWithFormat:@"%@.jpg" , [self getRandomString]] mimeType: [NSString isEmptyString:imageModel.mimeType] ? @"image/jpeg" : imageModel.mimeType];
}
} progress:^(NSProgress * _Nonnull uploadProgress) {
progress(uploadProgress.completedUnitCount / uploadProgress.totalUnitCount);
} success:^(NSURLSessionDataTask * _Nonnull task, NSDictionary * _Nullable responseObject) {
successBlock(responseObject);
} failure:^(NSURLSessionDataTask * _Nullable task, NSError * _Nonnull error) {
failureBlock(error);
}];
}
+(NSString *) getRandomString {
static NSInteger kRandomLength = 10;
static NSString *kRandomAlphabet = @"abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789";
NSMutableString *randomString = [NSMutableString stringWithCapacity:kRandomLength];
for (int i = 0; i < kRandomLength; i++) {
[randomString appendFormat: @"%C", [kRandomAlphabet characterAtIndex:arc4random_uniform((u_int32_t)[kRandomAlphabet length])]];
}
return randomString;
}
/**
* 文件下载
*
* @param operations 文件下载预留参数---视具体情况而定 可移除
* @param savePath 下载文件保存路径
* @param urlString 请求的url
* @param successBlock 下载文件成功的回调
* @param failureBlock 下载文件失败的回调
* @param progress 下载文件的进度显示
*/
+(void)downLoadFileWithOperations:(NSDictionary *)operations withSavaPath:(NSString *)savePath withUrlString:(NSString *)urlString withSuccessBlock:(requestSuccess)successBlock withFailureBlock:(requestFailure)failureBlock withDownLoadProgress:(downloadProgress)progress {
[manage downloadTaskWithRequest:[NSURLRequest requestWithURL:[NSURL URLWithString:urlString]] progress:^(NSProgress * _Nonnull downloadProgress) {
progress(downloadProgress.completedUnitCount / downloadProgress.totalUnitCount);
} destination:^NSURL * _Nonnull(NSURL * _Nonnull targetPath, NSURLResponse * _Nonnull response) {
return [NSURL URLWithString:savePath];
} completionHandler:^(NSURLResponse * _Nonnull response, NSURL * _Nullable filePath, NSError * _Nullable error) {
if (error) {
failureBlock(error);
}
}];
}
+(void)cancelAllRequest {
[manage.operationQueue cancelAllOperations];
}
@end
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 3,288
|
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
<!--NewPage-->
<HTML>
<HEAD>
<TITLE>
org.apache.poi.dev (POI API Documentation)
</TITLE>
<LINK REL ="stylesheet" TYPE="text/css" HREF="../../../../stylesheet.css" TITLE="Style">
</HEAD>
<BODY BGCOLOR="white">
<FONT size="+1" CLASS="FrameTitleFont">
<A HREF="../../../../org/apache/poi/dev/package-summary.html" target="classFrame">org.apache.poi.dev</A></FONT>
<TABLE BORDER="0" WIDTH="100%" SUMMARY="">
<TR>
<TD NOWRAP><FONT size="+1" CLASS="FrameHeadingFont">
Classes</FONT>
<FONT CLASS="FrameItemFont">
<BR>
<A HREF="OOXMLLister.html" title="class in org.apache.poi.dev" target="classFrame">OOXMLLister</A>
<BR>
<A HREF="OOXMLPrettyPrint.html" title="class in org.apache.poi.dev" target="classFrame">OOXMLPrettyPrint</A>
<BR>
<A HREF="RecordGenerator.html" title="class in org.apache.poi.dev" target="classFrame">RecordGenerator</A></FONT></TD>
</TR>
</TABLE>
</BODY>
</HTML>
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 3,282
|
Addona singled to right center (2-1 BSB).
Connell struck out swinging (0-2 FFS).
Schreckengos flied out to lf (1-0 B).
Fitschen singled to right field (2-2 BKBF); Addona advanced to second.
Yeager reached on a fielder's choice to second base (1-1 FB); Fitschen advanced to second; Addona advanced to third, out at home 2b to c.
Worley flied out to cf (0-0).
Graczyk grounded out to 3b (0-1 K).
Jones flied out to lf (1-1 FB).
Jones flied out to lf (0-2 KFF).
Conaway struck out swinging (1-2 BSSS).
Z. Moore struck out swinging (2-2 BBFKS).
Gaona grounded out to ss (0-0).
B. Campbell struck out swinging (2-2 BFBFS).
Ewald popped up to ss (0-0).
Jenkins flied out to lf (0-0).
Addona out at first 1b to p (2-2 KBBK).
Connell flied out to cf (0-1 F).
Reynolds struck out swinging (0-2 FSS).
Washington grounded out to 1b unassisted (3-1 BFBB).
Lushington struck out swinging (3-2 BBBKKS).
Schreckengos doubled to center field (0-1 F).
Fitschen singled to right center, advanced to second on a fielding error by cf, RBI (2-1 BKB); Schreckengos scored.
Yeager reached on a fielder's choice to pitcher (0-0); Fitschen out at second p to ss.
Jones flied out to rf (1-0 B).
Conaway reached on a fielder's choice to second base (2-2 BBFS); Yeager out at second 2b to ss.
Worley grounded out to 3b (0-0).
Graczyk flied out to lf (2-2 FBSBF).
Jones singled up the middle (0-1 F).
Gaona doubled to right center (0-0); Jones advanced to third.
B. Campbell flied out to lf (1-2 FKBF).
Z. Moore struck out looking (0-2 KKK).
Jenkins struck out swinging, out at first c to 1b (1-2 KKBS).
Addona singled to left field (1-0 B).
Connell grounded out to ss (1-2 BFF).
Ewald grounded out to 3b (0-1 K).
Washington grounded out to 2b (3-2 BBBKS); Reynolds advanced to third.
Lushington grounded out to 2b (1-2 FBSF).
Gibeau to p for Lovvorn.
Fitschen reached on a fielder's choice to shortstop (3-2 BBKBK); Schreckengos out at second ss to 2b.
Yeager grounded into double play 3b to 2b to 1b (1-1 FB); Fitschen out on the play.
Worley flied out to cf (2-0 BB).
Graczyk struck out looking (0-2 KFK).
Jones flied out to cf (0-0).
Jones singled through the left side (1-0 B).
Conaway doubled down the lf line (1-0 B); Jones advanced to third.
Z. Moore singled through the right side, out at second c to ss, 2 RBI (3-2 KBSBFB); Conaway scored; Jones scored.
Jenkins grounded out to ss (2-0 BB).
Addona fouled out to c (1-1 BK).
Gaona grounded out to p (0-2 KSF).
B. Campbell flied out to cf (0-0).
Ewald flied out to cf (1-1 BF).
McKee to p for Gibeau.
Connell doubled down the lf line (3-2 BFFBBF).
Schreckengos flied out to lf (1-2 BKF).
Fitschen singled to center field, out at second c to ss, RBI (0-0); Connell scored.
Yeager struck out looking (2-2 SSBBK).
Reynolds reached on a fielding error by 2b (0-0).
Woolfolk pinch hit for Washington.
Woolfolk flied out to rf (0-1 K).
Murphy pinch hit for Lushington.
Murphy doubled to left field (0-0); Reynolds advanced to third.
Worley singled to shortstop, RBI (1-2 KKBF); Reynolds scored, unearned.
Graczyk grounded into double play ss to 2b to 1b (0-1 S); Worley out on the play.
Conaway struck out swinging (0-2 FFS).
Z. Moore grounded out to ss (1-2 KKB).
Gaona walked (3-1 BBKBB); Jones advanced to second.
Whitt to p for Ergle.
B. Campbell walked (3-2 BBBKSB); Gaona advanced to second; Jones advanced to third.
Whitmire pinch ran for B. Campbell.
Ewald popped up to 2b (0-1 F).
Reynolds hit by pitch, RBI (2-2 SBBF); Whitmire advanced to second; Gaona advanced to third; Jones scored.
Smith pinch hit for Woolfolk.
Smith struck out swinging (0-2 KKFS).
Murphy struck out looking (0-2 SSK).
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 7,492
|
FUTURE Cumnock Primary School teachers studying at Ayrshire College are learning how to introduce LGBT education into the classroom.
It comes after Scotland became the first country in the world to embed LGBT+ inclusive education in the schools' curriculum.
Access to Primary Education and Humanities students at the College's Ayr Campus have been piloting recognised training in LGBT+, which was delivered by representatives from East Ayrshire Council, NHS Ayrshire & Arran, and the Terrence Higgins Trust.
The students participated in a workshop which explored language around allowing the students to gain an understanding of stigma and discrimination faced by young people.
They also learned about current activity in schools and how the experiences of young people can be improved through a fully inclusive curriculum.
The hope is that the students will be much more prepared to deliver an inclusive education and better understand the needs of LGBT+ young people, when they enter the classrooms as teachers.
Kerry Jarvis, Health and Wellbeing Officer, East Ayrshire Council, said "I cannot emphasise enough how important this training is for our next generation of teachers.
"Ayrshire College is breaking new ground by ensuring that this training is embedded into this course.
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 2,769
|
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