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Twitter bias & censorship must end
|In American Values Matter
|By Jim Hanson
Twitter has a lot of faults, but the most destructive one is their bias. They operate as a propaganda arm of the Woke Left. They claim otherwise but their actions constantly betray them with blatant discrimination.
Former CEO Jack Dorsey admitted they have a problem.
"We need to constantly show that we are not adding our own bias, which I fully admit is more left-leaning," he added. "And I think it's important to articulate our own bias and to share it with people so that people understand us. But we need to remove our bias from how we act and our policies and our enforcement."
This manifests itself in a number of ways including suppression of topics they dislike, promotion of topics they do like and a Thought Police mentality toward what they allow to be said.
The most recent victim is Rep. Marjorie Taylor-Green who received a permanent ban for sharing and commenting on CDC vaccine data. She ran afoul of the diktat that none shall question the safety of the brand new & barely tested vaccines.
"Maxine Waters can go to the streets and threaten violence on Twitter, Kamala and Ilhan can bail out Black Lives Matter terrorists on Twitter, CNN and the rest of the Democrat Propaganda Media can spread Russia collusion lies, and just yesterday the Chief spokesman for terrorist IRGC can tweet mourning Soleimani, but I get suspended for tweeting VAERS statistics," Greene said. "Twitter is an enemy to America and can't handle the truth."
If a sitting US Congresswoman is not allowed to question policies which affect her constituents and all Americans, we have a problem. The usual answer from the usual suspects is "Twitter is a private company, they can do what they want". And in the vast majority of cases, I would agree.
But Twitter is not a normal company, it is the single most influential social media platform for media, thought leaders, and political leaders. It operates as a monopoly in that space. It would be fair to say it is a commodity vital to communication with the public for any leader in this country.
Twitter's bias leads to unbalanced application of its own convoluted rules. No one is ever really sure what you can or cannot say, but it is readily apparent if you say things that violate woke orthodoxy, you are much more likely to be sanctioned.
They banned President Trump and now Rep. Greene and in the past they used algorithms to limit the reach of a number of other Republican politicians. But the same doesn't happen to leaders on the Left, and that is not surprising since they are in near lockstep with the censors at Twitter.
The question is what should or even can be done about this. It's easy to say just let the free market sort it out. But this leaves a massive disparity in what information Americans on this platform receive. And it pushes the accepted reality further and further Left.
Twitter claims its rules and implementation of them are neutral. If you accept that a woke worldview should be our reality, then that is ostensibly true. They choose what are accepted beliefs, have them validated by fact-checkers who share their ideology and then have decisions on who is a violator adjudicated by their own true believers.
How could that possibly end up producing a biased outcome?
A large part of the problem is around what are facts vs. opinions and who is the decider on that. If all of the deciders share one belief system and that belief system considers disagreement with the established orthodoxy akin to heresy, then you can either accept their version of reality or face the punishment.
Whether or not having a small group of technocrats deciding what is feal and what is healthy for us to talk about is a new and unhealthy development for free speech. But when those zealots have control of most of the public information space, we end up with an increasingly limited ability to argue about what is good or bad for this country. And that is bad if you believe in political and cultural freedom.
It is even more concerning when the social media platforms conspire with their like-minded fellow travelers in government. This is leading to the government essentially outsourcing censorship of ideas they dislike to the tech tyrants. We saw this espoused as official US policy by the Biden White House in the Domestic Extremism plan.
They start with free speech and propose to partner with the tech tyrants to further marginalize or eliminate ideas they dislike or disagree with:
"These efforts speak to a broader priority: enhancing faith in government and addressing the extreme polarization, fueled by a crisis of disinformation and misinformation often channeled through social media platforms, which can tear Americans apart and lead some to violence."
Translation: "Your ideas are dangerous to our ability to aggregate state power, and we are going to shut you down."
This is not only horrifying to contemplate but almost certainly a violation of the rule against government using private companies to do things it is forbidden to do itself. But it also shows how far down the road to using state and private power to shut down dissent we have already gone.
Changing this is properly difficult in a Constitutional framework and capitalist system that offers tremendous freedom to private entities like Twitter. Taking action to limit their ability to run their company requires great provocation, but they have provoked greatly and action is needed.
Twitter opens itself to a number of actions if it fails to enact remedies to these problems.
As a publicly-traded company, Twitter could be subject to actions from its stockholders if it inaccurately characterizes the current state of viewpoint discrimination.
Twitter's Terms of Service claim that do not discriminate based on ideology. If they can be shown to do so, they can be liable to lawsuits based on consumer protection laws.
Government scrutiny could be applied by a number of agencies:
Federal Election Commission– By providing an advantage to one party in election communications, Twitter makes in-kind contribution. This could extend beyond individual races if the advantage is found to have been systemic in nature.
Securities and Exchange Commission– Public statements claiming a content neutral platform, while operating one that is biased in outcome, could be deemed violations.
Federal Trade Commission– Due to the monopoly-like nature of Twitter in the marketplace and the need for its services by almost all public entities, Twitter could face anti-trust scrutiny.
Federal Communications Commission– Twitter could be reclassified as a publisher to remove exemption as an internet provider under the Communications Decency Act.
The best route forward would be for Twitter to decide that its self-appointed role as arbiters of what is "healthy conversation" is misguided. We have seen that it leads to authoritarian abuses of people's ability to dissent from the dictated reality. If Twitter want to do so, there can expand the many avenues already existing for people to self-select what they want or do not want to be exposed to. If Twitter decides to hold firm or press forward with a role as private Thought Police, then we must push back and break their monopoly on free discussion of ideas.
censorship Free Speech social media thought police twitter
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Hence, we all have to be careful with what we are using. To have a dry & brittle hair, extreme roughness, splits, breakage is nothing uncommon, but instead of experimenting different shampoos, we all should pick the correct one and that can only happen, when we know the quality and requirement of our hair.
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"redpajama_set_name": "RedPajamaC4"
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Badhamiopsis cavifera ist eine Schleimpilzart aus der Ordnung der Physarida. Sie ist nur von einem einzigen Fund aus Japan bekannt.
Merkmale
Die 0,3 bis 0,4 Millimeter im Durchmesser messenden, creme-weiß glänzenden Fruchtkörper sind polsterförmige Sporokarpe, an der Oberfläche mit vielen punktartigen Vertiefungen.
Das Peridium ist gelb-braun und mit weißem Kalk besetzt. Das Capillitium besteht aus einfachen, verzweigten oder etwas netzartig ausfallenden, dunkelbraunen Röhren, die an den Verbindungsstellen verdickt und an den Vertiefungen der Oberfläche mit dem Peridium verwachsen sind. Sie sind nur spärlich mit Kalkkörnchen besetzt. Die Sporen sind blass grau, an der Oberfläche dicht mit dunklen, bis zu 0,5 Mikrometern langen Stacheln besetzt und messen 13,5 bis 15 Mikrometer.
Verbreitung
Badhamiopsis cavifera ist nur von einem Einzelfund aus Japan bekannt.
Systematik und Forschungsgeschichte
Die Art wurde 1988 durch Neeltje Elizabeth Nannenga-Bremekamp und Yukinori Yamamoto erstbeschrieben. Sie gilt als der Gattung Diderma nahestehend.
Nachweise
Fußnoten direkt hinter einer Aussage belegen die einzelne Aussage, Fußnoten direkt hinter einem Satzzeichen den gesamten vorangehenden Satz. Fußnoten hinter einer Leerstelle beziehen sich auf den kompletten vorangegangenen Text.
Myxogastrien
Myxogastria
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\section{Introduction}
\label{intro}
Convection in binary miscible fluids like ethanol-water, $^3$He
$-^4$He, or various gas mixtures shows a rich spectrum of
pattern formation behaviour --- see, e.g.,
(\cite[Platten \& Legros 1984]{PL84};
\cite[Cross \& Hohenberg 1993]{CH93};
\cite[L{\"u}cke \etal 1998]{LBBFHJ98})
for a review. The spatiotemporal properties of convection
in mixtures are more complex than those of one-component fluids due to the
influence of Soret sustained concentration gradients.
The structural dynamics of the concentration distribution in mixtures
results from an interplay between three competing mechanisms: nonlinear
advection and mixing, weak solutal diffusion, and the Soret effect. The latter
generates and sustains concentration gradients in (linear) response to
local temperature gradients. Without Soret coupling, i.e., for vanishing
separation ratio $\psi=0$ any concentration fluctuation diffuses away.
For $\psi \neq 0$\,, however, the
externally imposed vertical temperature difference across the fluid layer
sustains via the Soret
effect concentration variations against the action of advective mixing and
diffusive dissipation.
The concentration field changes the advective properties of mixtures via
solutal buoyancy forces that enter into the momentum balance of the fluid.
Thus, a concentration fluctuation directly influences the flow which in turn
changes and mixes the concentration. In binary {\it liquids\/}, this
nonlinear feed back is only weakly damped by diffusive
homogenisation so that the concentration distribution shows
anharmonic and boundary layer structures. Furthermore, it is ultimately this
feed back that causes already right at onset convection patterns that cannot be
seen there in pure fluids. Examples that occur depending on parameters
are traveling waves of roll structures,
standing wave oscillations, and stationary squares. In addition mixtures show
very interesting secondary structures close to onset: spatially
localized traveling wave states, stationary
crossrolls (CRs), and oscillations between squares and rolls or CRs can be seen
for different parameter combinations. Note that all of the
aforementioned patterns are Soret induced by the concentration field --- they
disappear in the pure fluid limit, $\psi \to 0$,
when switching off the Soret coupling to the concentration field.
In this paper we are concerned with the case of a positive Soret effect,
$\psi>0$,
which causes the heavier (lighter) component of the mixture to be driven
towards lower (higher) temperature regions. Therefore, heating a mixture
with $\psi>0$ from
below establishes a stronger density gradient as in a pure fluid. The solutal
contribution to the buoyancy increases the thermal destabilization of the
fluid layer and convection starts at smaller temperature differences compared
to a pure fluid. One commonly denotes the thermal driving regime with Rayleigh
numbers $R$ below the threshold $R_c^0$ of pure fluids as the Soret regime and
the regime above $R_c^0$ as the Rayleigh region
(\cite[Moses \& Steinberg 1991]{MS91}). As a crude rule of thumb
one can say that in the Soret region, $R<R_c^0$, square patterns are often
observed in mixtures, whereas in the Rayleigh region stable rolls are found.
There have been only few theoretical investigations aimed at explaining the
transition scenario between squares at smaller $R$ and rolls at larger $R$
(\cite[Clune \& Knobloch 1992]{ClK92};
\cite[M{\"u}ller \& L{\"u}cke 1988]{ML88}).
Recently we have elucidated this transition for a fixed wavenumber
(\cite[Jung, Huke, \& L{\"u}cke 1998]{JHL98}).
In this paper we compare the properties of square, roll, and CR patterns and we
present a comprehensive linear stability analysis of
rolls and a more restricted one for squares.
We elucidate how the stability boundaries of rolls that have been
determined by Busse and coworkers
(\cite[Busse 1967]{B67};
\cite[Bolton, Clever, \& Busse 1985]{BBC85};
\cite[Clever \& Busse 1990]{CB90}) for
pure fluid convection are modified by taking into account the influence of the
concentration field in mixtures. We present for the first time a full numerical
investigation of the stability behaviour of rolls and squares and present
the stability balloons of these patterns in the $k-r$--plane for a wide range
of fluid parameters.
The paper is organized as follows: In~\S\,\ref{basics} we describe briefly
the basics of convection in binary fluids and we explain the application of
the Galerkin method to this particular system. In~\S\,\ref{struct} we describe
and compare the stationary solutions for rolls, CRs, and squares.
In~\S\,\ref{stabili} the Galerkin method is used for the linear stability
analysis of roll and square patterns.
We conclude in~\S\,\ref{conclude} with a summary of our results.
\section{Mathematical foundations}
\label{basics}
In this paper we investigate
convection in horizontal binary fluid layers confined between perfectly
heat conducting, rigid, impermeable plates.
Since the system and its basic equations are well known
(\cite[Landau \& Lifshitz 1966]{LL66};
\cite[Platten \& Legros 1984]{PL84}),
we summarize in~\S\,\ref{sec21} only the necessary formulas for our
investigation. Then we present relevant details related to the application of
the Galerkin expansion technique to this system.
\subsection{System and basic equations}
\label{sec21}
We consider a horizontal layer of a binary fluid mixture of thickness $d$ in
a homogeneous gravitational field, ${\bf g} = - g \, {\bf e}_z$.
A vertical temperature gradient is imposed by fixing the temperature
\begin{equation}
T = T_0 \pm \frac{\Delta T}{2}
\,\,\, \mbox{at} \,\,\, z = \mp \frac{d}{2} \, ,
\end{equation}
e.g., via highly conducting plates in experiments. Here we consider the
plates to be infinitely extended, rigid, and impermeable.
Convection is described in terms of the fields of velocity ${\bf u} =(u,v,w)$,
temperature $T$, mass concentration $C$ of the lighter component, total mass
density $\rho$, and pressure. In the balance equations connecting
these fields we scale lengths and positions by $d$, time by the
vertical thermal diffusion time $d^2 / \kappa$, temperature by
$\nu \kappa / \alpha g d^3$, concentration by $\nu \kappa / \beta g d^3$,
and pressure by $\rho_0 \kappa^2/d^2$. Here $\rho_0$ is
the mean density, $\kappa$ the thermal diffusivity, $\nu$ the kinematic
viscosity, and $\alpha$ and $\beta$ are thermal and solutal expansion
coefficients, respectively.
Using the Oberbeck-Boussinesq approximation
the balance equations read
(\cite[Platten \& Legros 1984]{PL84};
\cite[Hort, Linz, \& L{\"u}cke 1992]{HLL92})
\begin{subeqnarray}
{\bf \bnabla\cdot u} & = & 0 \slabel{ground21}\\
(\partial_t + {\bf u\cdot\bnabla\,})\,{\bf u} & = & - {\bf\bnabla}\,p +
\sigma\,\left[\,\left(\theta + c\,\right)\,{\rm\bf e}_z +
\bnabla^2\,{\bf u}\,\right]\slabel{ground22}\\
(\partial_t + {\bf u\cdot\bnabla\,})\,\theta & = &
R\,w + \bnabla^2\,\theta\slabel{ground23}\\
(\partial_t + {\bf u\cdot\bnabla\,})\,c & = & R\,\psi\,w +
L\,\left(\,\bnabla^2\,c - \psi\,\bnabla^2\,\theta\,\right)\slabel{ground24} \;\; .
\end{subeqnarray}
Here $\theta, c$, and $p$ are the reduced deviations of temperature,
concentration, and pressure, respectively, from the conductive profiles.
The Lewis number $L$ is the ratio of the
concentration diffusivity $D$ to the thermal diffusivity $\kappa$, therefore
measuring the velocity of concentration diffusion. The Prandtl number
$\sigma$ is the ratio of the momentum diffusivity $\nu$ and $\kappa$:
\begin{equation}
L = \frac{D}{\kappa}\,\,;\,\, \sigma = \frac{\nu}{\kappa}
\label{GdefLsig} \,.
\end{equation}
The Rayleigh number $R$ measures the thermal driving and the separation ratio
$\psi$ measures the strength of the Soret coupling between temperature and
concentration fields
\begin{equation}
R =\frac{ \alpha g d^3 \Delta T}{\nu \kappa}\,\,;
\,\psi = - \frac{\beta}{\alpha} \frac{k_T}{T_0}\, .
\label{GdefR}
\end{equation}
Here $T_0$ is the mean
temperature and $k_T$ is the thermal diffusion ratio
(\cite[Landau \& Lifshitz 1966]{LL66}). The driving forces entering into
the momentum balance equation (\ref{ground22}) are pressure
gradients and the
buoyancy caused by the temperature and concentration dependence of the
density.
The off-diagonal term
$-L\,\psi\,\bnabla^2\,\theta\,$ and the term $R\,\psi\,w$
in the concentration balance equation (\ref{ground24})
describe the action of the Soret effect, i.e., the generation of concentration
currents and concentration gradients by temperature
variations. A Soret coupling $\psi > 0$ implies a positive Soret effect.
In this case the
lighter component of the mixture is driven into the direction of higher
temperature thus increasing the density variations.
The Dufour effect, i.e., the driving
of temperature currents by concentration variations is of interest only in
gas mixtures (\cite[Hort \etal 1992]{HLL92}). But even there
it is often small (\cite[Liu \& Ahlers 1997]{LA97}).
\subsection{Galerkin method}
\label{sec22}
To describe three--dimensional patterns with wavenumbers $k_x$ and $k_y$ each
field $X$ is expanded as
\begin{equation}
X(x,y,z;t) = \sum_{lmn} X_{lmn}(t) \mathrm{e}^{\mathrm{i} l k_x x}
\mathrm{e}^{ \mathrm{i} m k_y y } f_n(z) \;\; .
\label{expansion}
\end{equation}
Here $l$ and $m$ are integers and the $f_n$ form a complete system of
functions that fits the specific boundary condition for the field $X$ at the
plates.
To find suitable sets of functions $f_n$ we introduce some new fields.
First, two scalar fields $\Phi$ and $\Psi$ are defined via
\begin{equation}
{\bf u} = {\bf \bnabla} \times {\bf \bnabla} \times \Phi {\bf e}_z
+ {\bf \bnabla} \times \Psi {\bf e}_z \;\; . \label{22phipsidef}
\end{equation}
The structures we want to discuss do not show a horizontal mean flow for
mirror symmetry reasons. Then, (\ref{22phipsidef})
is the most general expression that fulfills the incompressibility
condition (\ref{ground21}) (\cite[Clever \& Busse 1989]{CB89}).
The analysis of mean flow effects in the perturbations in discussed in
section~\ref{sec24}.
Second, instead of $c$ we use the field
\begin{equation}
\zeta = c - \psi \theta
\end{equation}
that allows in a more convenient way to guarantee the impermeability of
the horizontal boundaries: The diffusive part of the concentration current,
driven by concentration gradients as well as by temperature
gradients is given by $- L {\bf \bnabla} (c - \psi \theta)$.
At the impermeable plates the vertical component of this current vanishes
which requires
\begin{equation}
0 = \partial_z \left(c - \psi \theta \right) =
\partial_z \zeta \hspace{1cm}
\mbox{at } z = \pm 1/2 \;\; .
\end{equation}
The advective concentration current vanishes at the plates because there
${\bf u} = 0$.
The balance equation for $\zeta$ is obtained by combining (\ref{ground23}) and
(\ref{ground24}).
The boundary conditions for the fields $\Phi, \Psi, \theta$, and
$\zeta$ read
\begin{equation}
\Phi = \partial_z \Phi = \Psi = \theta = \partial_z \zeta = 0
\hspace{2cm} \mbox{at } z = \pm 1/2 \;\; .
\end{equation}
To expand the fields
$\Psi$, $\theta, \zeta$, and $\Phi$ vertically we used different
orthonormal sets $f_n(z)$ as follows
\begin{subeqnarray}
\Psi \mbox{\, and \,} \theta \,:\,f_n(z) &=& \,
\left\{ \begin{array}{ll}
\sqrt{2} \cos(n \upi z) & \mbox{\qquad $n$ odd} \\
\sqrt{2} \sin(n \upi z) & \mbox{\qquad $n$ even}
\end{array} \right.
\slabel{csdefinition} \\
\zeta \,:\, f_n(z) &=& \left\{ \begin{array}{ll}
1 & \mbox{\qquad $n = 0$}\\
\sqrt{2} \, \sin(n \upi z) & \mbox{\qquad $n$ odd} \\
\sqrt{2} \, \cos(n \upi z) & \mbox{\qquad $n \neq 0$ even}
\end{array}
\right.
\slabel{scdefinition} \\
\Phi \,:\, f_n(z) &=& \left\{ \begin{array}{ll}
C_{\frac{n+1}{2}}(z) & \mbox{\qquad $n$ odd} \\
S_{\frac{n}{2}}(z) & \mbox{\qquad $n$ even}
\end{array} \right. \;\; .
\slabel{CSdefinition}
\end{subeqnarray}
Here $C_n$ and $S_n$ are Chandrasekhar functions
(\cite[Chandrasekhar 1981]{C81}).
The balance equations for the new fields are
\begin{subeqnarray}
\partial_t \Delta_2 \Psi & = &
\sigma {\bf \nabla}^2 \Delta_2 \Psi +
\left\{{\bf \bnabla} \! \times \left[ \left({\bf u} \cdot \bnabla \right)
{\bf u} \right] \right\}_z \slabel{ground71}\\
\partial_t {\bf \nabla}^2 \Delta_2 \Phi & = &
\sigma \left\{ {\bf \nabla}^4 \Delta_2 \Phi -
\Delta_2 \left[ \left( 1 + \psi \right) \theta + \zeta \right] \right\}
- \left\{{\bf \bnabla} \! \times {\bf \bnabla} \! \times
\left[ \left( {\bf u} \cdot \bnabla \right) {\bf u} \right] \right\}_z
\slabel{ground72} \\
(\partial_t + {\bf u\cdot\bnabla\,})\,\theta & = &
-R\, \Delta_2 \Phi + \nabla^2\,\theta \slabel{ground73} \\
(\partial_t + {\bf u\cdot\bnabla\,})\,\zeta & = &
L \nabla^2 \zeta - \psi \nabla^2 \theta \slabel{ground74}
\;\; .
\end{subeqnarray}
Here $\Delta_2 = \partial_x^2 + \partial_y^2$.
By inserting the ansatz (\ref{expansion}) for each field into the balance
equations and projecting them
onto the basic functions one gets a nonlinear algebraic system of equations of
the form
\begin{equation}
A_{\kappa \mu} \partial_t X_\mu = B_{\kappa \mu} X_\mu +
C_{\kappa \mu \nu} X_\mu X_\nu \;\; . \label{basicslinsyseq}
\end{equation}
For simplicity amplitudes are labelled here by a single Greek
index and the summation convention is implied in (\ref{basicslinsyseq}) with
$A_{\kappa \mu}, B_{\kappa \mu}$, and $C_{\kappa \mu \nu}$ being constant
coefficients.
The number of modes has to be truncated to get a
finite number of equations as discussed later on. For stationary
convection structures the
left hand side of (\ref{basicslinsyseq}) vanishes and the solution can be
found using a multidimensional Newton method.
\subsection{Symmetries}
\label{sec23}
Symmetries of convective structures impose conditions on the fields and/or
imply relations between different
modes of the fields thereby restricting the number of independent modes that
are necessary to describe the patterns. For example, to describe
two--dimensional roll
patterns with $k_x = k$, $k_y = 0$ that do not depend on $y$, all amplitudes
with $m \neq 0$ are set to zero in (\ref{expansion}). On the other hand,
square patterns are
characterized by $k_x = k_y = k$ and $X_{lmn}=\pm X_{mln}$. But we also
investigate three--dimensional CR
patterns with $k_x = k_y = k$ for which, however, $X_{lmn} \neq \pm X_{mln}$.
\subsubsection{Stationary rolls}
To describe these two--dimensional structures one does not need the
$\Psi$--field.
Furthermore, rolls are even in $x$ with an appropriate choice of the plane
$x=0$. As a consequence of this
mirror symmetry one has $X_{l0n} = X_{-l0n}$ so that the lateral
functions $\mathrm{e}^{\pm \mathrm{i} k l x}$ can be replaced by
$\cos (k l x)$. In addition the roll pattern is antisymmetric under reflection
at the plane $z=0$ combined with a translation by half a wavelength in
$x$-direction. This mirror glide symmetry enforces
half of the amplitudes to be zero, e.~g.\ all amplitudes
$\Phi_{l0n}$ where $l+n$ is an odd number.
It is no accident that stationary roll patterns have these symmetries.
That they are
fulfilled at onset can be shown via a linear stability analysis of the
conductive state (\cite[Hollinger \& L{\"u}cke 1995]{HL95}). The subset of
modes that obey these symmetries is closed in the sense that these modes do
not drive others via nonlinear coupling. Thus, the observed roll solution
remains symmetric as long as no symmetry breaking bifurcation occurs on the
stationary roll branch with symmetry breaking modes becoming linearly unstable.
Such instabilities are covered by our stability analysis.
\cite[Moore, Weiss, \& Willkins (1991)]{MWW91} have discussed these symmetry
breaking
perturbations for free--slip and permeable boundary conditions.
\subsubsection{Stationary squares and crossrolls with $k_x = k_y$}
They have the same symmetry plane at $x=0$ as rolls and an
additional mirror plane at $y=0$. Furthermore, the squares and CRs
show also a mirror glide symmetry. Here, however, the symmetry transformation
consists of a reflection at
the plane $z=0$ combined with a translation by half a wavelength in
$x$- {\em and} $y$-direction. To describe these three--dimensional patterns
the $\Psi$--field
cannot be neglected. We also mention that in contrast to the other fields
$\Psi$ is odd in $x$ and $y$ and has
positive parity under the mirror glide operation thereby reflecting the
symmetries of the velocity field.
For square patterns that are invariant under rotation by $90^{\circ}$
in which the $x$- and $y$-directions are indistinguishable
a further reduction of the number of mode occurs: amplitudes like
$\Phi_{lmn}$ and $\Phi_{mln}$ are the same. This is also true for $\theta$
and $\zeta$. Again $\Psi$ is different. Here $\Psi_{lmn}=-\Psi_{mln}$.
\subsection{Stability analysis}
\label{sec24}
To make a full stability analysis one has to check the stability of the
patterns against perturbations with arbitrary wavevector
$d {\bf e}_x + b {\bf e}_y $. To do so one has
to introduce a Floquet term writing out the perturbation as
\begin{equation}
\delta X(x,y,z;t) = \mathrm{e}^{\mathrm{i} d x +
\mathrm{i} b y} \mathrm{e}^{s t}
\sum_{lmn} \delta X_{lmn} \mathrm{e}^{\mathrm{i} l k_x x +
\mathrm{i} m k_y y} f_n(z).
\end{equation}
Such a perturbation is added to the known solution the stability of which is to
be tested and inserted into the
balance equations. After linearising and projecting one gets a linear eigenvalue
problem of the form
\begin{equation}
s A_{\kappa \mu} \delta X_\mu = B_{\kappa \mu} \delta X_\mu \;\; .
\end{equation}
with constant coefficients $A_{\kappa \mu}$ and $B_{\kappa \mu}$.
The aforementioned solution, i.e., the convective structure described by it
is stable if
every eigenvalue $s$ has a negative real part for every $d$ and $b$.
The symmetry of the convective pattern discussed above can under some
circumstances be
used to get separated classes of possible eigenvectors representing the
perturbations. That means the eigenvalue problem can be reduced
to finding the eigenvalues of two matrices of about half of the size. Because
evaluating the eigenvalues of a matrix is a $O(N^3)$-process this always implies
a reduction of the computation time.
\subsubsection{Stationary rolls}
\label{sec241}
To perform the stability analysis of rolls one determines the growth behaviour
of perturbations of the form
\begin{equation}
\delta X(x,y,z;t) = \mathrm{e}^{\mathrm{i} d x + \mathrm{i} b y}
\mathrm{e}^{s t} \sum_{ln} \delta X_{l0n} \mathrm{e}^{\mathrm{i} l k x} f_n(z).
\label{perturbations}
\end{equation}
Contrary to the roll solutions, their perturbations may contain a mean flow
component that is discarded in (\ref{22phipsidef}). However,
our perturbation ansatz (\ref{perturbations}) contains modes like
$\delta \Phi_{001} \mathrm{e}^{\mathrm{i} d x + \mathrm{i} b y} C_1(z)$
describing a mean flow in the limit $b,d \rightarrow 0$, and the equation
of motion for $\delta \Phi_{001}$ reduces to two independent equations
for the mean flow as they are used e.~g. in
(\cite[Clever \& Busse 1991]{CB91}).
If there is a mean
flow in the perturbations, then modes like the $\delta \Phi_{001}$--mode
diverge when $b,d$ goes to zero such that the long wavelength component of
the velocity remains finite.
However, in the parameter range explored here, the perturbations limiting the
stability balloon of rolls have finite $b$ or $d$ and thus no mean flow.
Because of the periodicity of the patterns in $x$ and its mirror symmetry
it suffices to consider $d \in \left[ 0, k/2 \right]$. In
$y$-direction, however, all perturbation wavenumbers, say, $b \ge 0$
have to be investigated.
The linear system of
equations (\ref{perturbations}) always separates into two subsystems of
perturbations $\delta X_\mu$ that belong to modes with amplitudes $X_\mu$ that
are antisymmetric ($G$--perturbations) or symmetric
($\overline{G}$--perturbations) under the mirror glide operation
$(x, y, z) \rightarrow (x + \lambda/2, y + \lambda/2, -z)$.
E.~g.\ all
perturbations with amplitudes $\delta \Phi_{l0n}$ with even $l+n$ are
$G$--perturbations, and the perturbations with odd $l+n$ are
$\overline{G}$--perturbations.
In general the perturbations (\ref{perturbations}) do not have a well
defined symmetry under the
mirror glide operation. This is only the case if $d = n k$. If $n$ is even
(odd) then the perturbations have the same (opposite) parity as the modes they
belong to. Every $G$--perturbation can be written out as a
$\overline{G}$--perturbation (and vice versa) by choosing a new $d' = d - k$.
Thus the distinction between $G$-- and $\overline{G}$--perturbations is well defined
only for fixed $d$.
It is possible to restrict the stability analysis to {\em one} set of
perturbations by extending the investigated $d$-interval to $[0,k]$.
Consider for example a $\overline{G}$--perturbation with
$d \in \left[0, k/2 \right]$. It can as well be written as
a $G$--perturbation with a new $d' = d - k$ or equivalently
$d' = k - d$. Thus one finds all $\overline{G}$--perturbations with
$d \in \left[0, k/2 \right]$ again as $G$--perturbations with
$d' \in \left[k/2, k \right]$. We will therefore restrict ourselves to
the set of perturbations that has negative parity under the mirror glide
operation at $d=0$, i.~e.,\ we investigate the $G$--perturbations in the whole
interval $\left[0, k\right]$.
In special cases the system of equations can be separated even further. For
$d=0$ the perturbations can be divided into those that are symmetric and those
that are antisymmetric under the operation $x \rightarrow -x$. Furthermore,
if $b=0$ then the perturbations contain either no or only
$\delta \Psi$-amplitudes.
\subsubsection{Stationary squares and CRs with $k_x = k_y$}
Because the amount of computational power needed to make a full stability
analysis of these three--dimensional structures is too large, we will discuss
perturbations only for periodic boundary conditions, i.~e.,\
$d=b=0$. Here again a separation of perturbations is possible into those
that change sign or not under the mirror glide operation.
Furthermore, the stability problem is invariant under $x \rightarrow -x$ and
$y \rightarrow -y$. Thus one can distinguish between perturbations that are
even in $x$ and $y$, odd in $x$ and $y$, or even in $x$ and odd in $y$ (or
equivalently odd in $x$ and even in $y$). If the perturbations have the same
symmetry in both directions one can in the case of squares finally make use of
a last symmetry property and separate between perturbations that are symmetric
or antisymmetric under the exchange of the $x$- and $y$-direction. This is not
possible for CR patterns because of their lack of the
$x \leftrightarrow y$ symmetry.
As we will see in section~\ref{sec43}, the destabilising perturbations of
squares fall into the subclass that is even in $x$ and $y$, and therefore do not
drive a mean flow.
\section{Properties of the patterns}
\label{struct}
Squares, CRs, and rolls are realized as stable convection
structures somewhere in parameter space. Furthermore, if $L$ is sufficiently
small these
three patterns appear for fixed $L$, $\sigma$, $\psi$, and $k$ as global
attractors
at different Rayleigh numbers (however, CRs coexist bistably with
oscillations in a small $R$--interval (\cite[Jung \etal 1998]{JHL98})). So it
is easy to enforce their stable
experimental realization successively by increasing the Rayleigh number
beyond the onset of convection.
To understand the
behaviour of the patterns it is useful to consider the driving region near
onset and the Rayleigh region separately.
In the pure fluid the critical point is at a Rayleigh number
$R_c^0 =R_c(\psi=0)=1707.762$ and a wavenumber
$k_c^0 =k_c(\psi=0) = 3.117$ (\cite[Chandrasekhar 1981]{C81}). In binary
mixtures
with positive separation ratios that we are dealing with, the critical Rayleigh
number is smaller, $R_c(\psi>0) < R_c^0$, since the solutal contribution
to the quiescent state's buoyancy force enhances the latter. Thus a smaller
thermal driving, i.e., a smaller Rayleigh number suffices to reach the
critical buoyancy force size for onset of convection.
The critical wavenumber is also somewhat lower: $k_c(\psi>0) < k_c^0$
(\cite[Knobloch \& Moore 1988]{KM88}).
When presenting our results we shall use the reduced
Rayleigh number
\begin{equation}
r = \frac{R}{R_c^0}
\end{equation}
and the reduced distance
\begin{equation}
\epsilon = \frac{R}{R_c} -1 = \frac{r}{r_c}-1.
\end{equation}
from threshold $r_c=\frac{R_c}{R_c^0}$
\subsection{Small-amplitude convection --- amplitude equation}
\label{sec31}
Very close to onset the wavenumber dependent bifurcation behaviour of rolls
and squares can in pure fluids
as well as in binary mixtures be described most simply by
two coupled cubic amplitude equations of the form
\begin{subeqnarray}
\tau_0\partial_t A & = & \epsilon A +
\xi_0^2\left(\partial_x - \frac{i}{2 k_c}\partial_y^2 \right)^2 A - |A|^2 A
-f |B|^2 A \slabel{ampligleich1} \\
\tau_0\partial_t B & = & \epsilon B +
\xi_0^2\left(\partial_y - \frac{i}{2 k_c}\partial_x^2 \right)^2 B - |B|^2 B
-f |A|^2 B \slabel{ampligleich2} \;\; .
\label{ampligleich}
\end{subeqnarray}
Clune and Knobloch used such equations without the spatial derivative term
(\cite[Clune \& Knobloch 1991]{ClK91}). For a review of such amplitude equations
and how they are related to the basic equations see, e.~g.,
(\cite[Cross \& Hohenberg 1993]{CH93}).
The amplitudes $A$ and $B$ of the eigenfunctions of the linearized
hydrodynamic field equations correspond quite well to the leading
amplitudes
\begin{subeqnarray}
w_{101} = k^2 \Phi_{101} &=& k^2 \int
\,\Phi(x,y,z)\,\mathrm{e}^{\mathrm{i}kx}\,
\, C_1(z) \, \mathrm{d}x\mathrm{d}y\mathrm{d}z \\
w_{011} = k^2 \Phi_{011} &=& k^2 \int
\,\Phi(x,y,z)\,\mathrm{e}^{\mathrm{i}ky}\,
\, C_1(z) \, \mathrm{d}x\mathrm{d}y\mathrm{d}z \;\;.
\end{subeqnarray}
of the vertical velocity field or the corresponding amplitudes of the
temperature field.
The two roll solutions of (\ref{ampligleich}) are
$A=|A_R|\mathrm{e}^{\mathrm{i}(k-k_c)x}, B=0$ for rolls with wavevector
${\bf k} = k {\bf e}_x$ and
$A=0, B=|B_R|\mathrm{e}^{\mathrm{i}(k-k_c)y}$ for rolls with wavevector
${\bf k} = k {\bf e}_y$.
Squares are described by the solution
$A=|A_S|\mathrm{e}^{\mathrm{i}(k-k_c)x},
B=|B_S|\mathrm{e}^{\mathrm{i}(k-k_c)y}$ with $A_S=B_S$.
Crossrolls, i.~e.\ solutions with finite $|A| \neq |B|$ do not exist in
(\ref{ampligleich}).
If $f > -1$, the square solution exists besides the roll solution
for $\epsilon$ above the
neutral stability curve
\begin{equation}
\epsilon_{stab}(k) = \xi_0^2 (k - k_c)^2 \;\; .
\end{equation}
We will always consider roll patterns with $B_R = 0$ and $A_R\neq 0$.
For the roll solutions one has
\begin{equation}
|A_R|^2 = \epsilon - \epsilon_{stab}(k) \;\; ,
\end{equation}
and for squares one finds
\begin{equation}
|A_S|^2 = |B_S|^2 = \frac{\epsilon - \epsilon_{stab}(k)}{1+f} \;\;
\end{equation}
so that
\begin{equation}
|A_R|^2 = (1+f)|A_S|^2\;\; .
\label{amplirelation}
\end{equation}
A stability analysis of the roll and square solutions shows that
squares (rolls) are stable (unstable) whenever $|A_R|^2 < 2|A_S|^2$, i.e., for
$-1 < f < 1$ and they are unstable (stable) whenever $|A_R|^2 > 2|A_S|^2$.
\subsection{Full Galerkin expansion}
\label{sec32}
Both square and roll solutions exist for every $r$ above onset $r_c(\psi,L)$
and the mode intensity $|w_{101}|^2$ for rolls is always greater than
for squares. Hence the parameter $f$ in the amplitude
equation has to be greater than $0$ according to (\ref{amplirelation}).
In figure \ref{flow_intensity} we present
a plot of the leading contribution $|w_{101}|^2+|w_{011}|^2$
to the vertical flow intensity $w^2$ versus $r$ as obtained from the
full Galerkin expansion for several parameters.
By comparing our results from the full Galerkin expansion with the
amplitude equation approximation we verified
that the latter works well near onset
$r_c(\psi)$ which in figure \ref{flow_intensity} lies significantly
below 1 -- outside the plot range of figure \ref{flow_intensity}.
However, at larger $r$ when approaching the Rayleigh regime the
amplitude approximation loses its validity:
$|A|^2 + |B|^2$ continues to grow linearly with $r$
with its initial slope at onset whereas
$|w_{101}|^2 + |w_{011}|^2$ strongly curves upwards in the
Rayleigh regime. Furthermore, while
$|w^{R}_{101}|^2 < |w^{S}_{101}|^2 +
|w^{S}_{011}|^2 = 2 |w^{S}_{101}|^2$
holds close to onset --- as required within the amplitude equation
approximation for squares to be stable --- the full solutions at larger
$r$ are such that
$|w^{R}_{101}|^2 > |w^{S}_{101}|^2 + |w^{S}_{011}|^2$
without, however, rolls becoming stable, what happens at even higher $r$.
In the Rayleigh region the
amplitudes become comparable with those of the pure fluid. This is because the
concentration field gets more and more advectively mixed and equilibrated
and loses
therefore its influence on the convection. Pure fluid
convection, $\psi=0$, can be described close to onset $r_c(\psi=0)=1$
by a cubic amplitude equation. However, the initial slope of $w^2$ versus $r$
is much greater than for the binary mixtures shown in figure \ref{flow_intensity}
with $\psi>0$. The transition between Soret and
Rayleigh region is especially sharp at small $L$ -- c.f. the bifurcation
diagram for $L=0.01$ in figure \ref{flow_intensity}(b). We will observe such a
behaviour again when we consider the stability of the patterns.
In the $r$-range investigated in this paper the field amplitudes
$\Phi_{101}$ and $\Phi_{011}$ that are kept in the amplitude equation
approximation are also the leading ones in the full Galerkin expansion.
To describe only the fixed point solutions it would
indeed be sufficient to approximate the velocity field of rolls (squares and
CRs) by one mode (two modes) only. But this restriction does not suffice
when the linear stability is investigated.
Although more than two amplitudes are needed, a good representation is easier to
achieve for the velocity field than for the $\zeta$-- and
$\theta$--fields. For them very many modes are needed if $L$ is small and
$r$ is large. This is a region of the parameter space where the concentration
field shows narrow boundary layer behaviour which has to be resolved properly.
In addition a consistent description of the temperature field requires then
also --- despite the fact that it is rather smooth --- high $\theta$--modes
as discussed by (\cite[Hollinger \& L{\"u}cke 1998]{HL98};
\cite[Hollinger 1996]{H96}).
We followed
(\cite[Clever \& Busse 1989]{CB89}) when defining our truncation
prescription for the Galerkin expansion. We defined a maximal mode index $N$ and
neglected all modes $X_{lmn}$ with $|l|+|m|+n > N$. We took the smooth
behaviour of the velocity field into account by defining two different
indices: $N_1$ for the $\Phi$-- and $\Psi$--fields and
$N_2 = 2 N_1$ for the $\theta$-- and $\zeta$--fields. For the
most anharmonic roll structures at $r \approx 1.5$, $L < 0.01$, and
$\psi = 0.15$ that we have investigated expansions up to $N_2=40$ were needed.
This is much more
than for pure fluids, where truncations with $N \leq 8$ are sufficient to
describe the stability behaviour quantitatively even at large $r$.
Since the structure of squares is somewhat smoother than the one of rolls
(cf.~\S\,\ref{sec34}) and
since they exist stably only at small $r$ in or
near the Soret region, we needed only $N_2 \leq 20$ for squares.
Also the CR structures could be described well with such a
truncation near the first
bifurcation point at small $r$, where they behave square--like. But in order to
resolve the CR structures also close to
the second bifurcation point at larger $r$ where the CR solution
merges into the roll solution (cf.~\S\,\ref{sec33})
more modes would have been necessary.
\subsection{Bifurcation behaviour of rolls, squares, and crossrolls}
\label{sec33}
Figure \ref{bifdiagram} shows a typical bifurcation diagram for a parameter
combination where the three stationary patterns can be found. It
also contains information on the stability of these patterns.
Crossrolls exist only in a finite $r$--interval. The CR solution
branches emerge out of the square branch slightly above $r = 1$.
At $r\simeq 1.36$ the CR solution disappears when, e.g., the
amplitude $w_{011}^{CR}$ (downwards pointing triangles in
figure \ref{bifdiagram}) becomes zero and the CR branch for
$w_{101}^{CR}$ (upwards pointing triangles) ends on the roll solution
branch $w_{101}^{R}$.
On the other hand, roll as well as square solutions exist for all
$r \ge r_c$ of figure \ref{bifdiagram}. Initially at onset the latter are
stable and the former are unstable. For the parameters of figure \ref{bifdiagram}
squares lose their stability in a Hopf bifurcation at $r\simeq 1.11$ to
oscillations
which eventually undergo with increasing $r$ a subharmonic bifurcation
cascade that is terminated when the CR states have become
sufficiently attractive to quench the oscillations. For other parameter
combinations, in particular for larger $L$ there are no oscillations and
the squares transfer their stability directly to CRs
(\cite[Jung \etal 1998]{JHL98}).
\subsection{Structural properties of roll and square fields}
\label{sec34}
In figure \ref{shadowgraph} we show the concentration distribution
of square convection for two parameter combinations that are representative
for liquid and gas mixtures. This plot and the concentration
field structure of
rolls and squares in a vertical cross section shows a characteristic boundary
layer and plume behaviour at small $L$. Such structures occur when
advective mixing is large compared to diffusion in the bulk of the fluid.
Consequently the boundary layers and plumes are more pronounced in rolls than
in squares since $w_R^2 > w_S^2$ as discussed in~\S\,\ref{sec32}.
Thus squares with their broader boundary layers are much smoother structures
than rolls at the same parameters.
The practically harmonic velocity and temperature
fields are not shown. For squares they resemble the fields of a linear
superposition of two perpendicular sets of rolls.
The Nusselt number $N$ is roughly the same for rolls and squares. Close
to onset
\begin{equation}
N-1 \propto |w_{101}|^2 + |w_{011}|^2 \;\; ,
\end{equation}
and the stable structure has the higher Nusselt number there, i.e.,
$N_R<N_S$ in accordance with the inequalities of~\S\,\ref{sec31} predicted
by the amplitude equation.
Further away from onset, however, one has $N_S<N_R$ thus reflecting the
magnitude relations of $w^2$ discussed in~\S\,\ref{sec32}.
In figure \ref{mixparam} we show the mixing parameter
\begin{equation}
\label{M}
M = \frac{\sqrt{ \left< \delta C^2 \right> }}
{\sqrt{ \left< \delta C_{cond}^2 \right> }} \;\; .
\end{equation}
It is defined by the mean square of the deviation,
$\delta C = C - C_0$, of the concentration from the spatial mean,
$C_0=\left< C \right>$, reduced by the concentration variance in the
quiescent conductive state. Note that $M$ is nearly the same
for the very different concentration fields of rolls and squares, if $L$ is not
too large (figure \ref{mixparam}).
\section{Linear stability analysis of rolls and squares}
\label{stabili}
\subsection{Instability mechanisms of rolls}
\label{sec41}
The stability boundaries of roll patterns in pure fluids are known since the
pioneering work of (\cite[Busse 1978]{B78}).
At small Rayleigh numbers there exist five different instability
mechanisms giving rise to five different stability boundaries
that limit the region of stable rolls in the $(R,k,\sigma)$--parameter space.
At small Prandtl numbers the Eckhaus (EC), the skewed varicose (SV), and the
oscillatory mechanism (OS) are the important instabilities
(\cite[Clever \& Busse 1990]{CB90}).
At higher Prandtl numbers the zigzag (ZZ) and the CR mechanisms dominate
(\cite[Busse 1967]{B67}). Properties and symmetries of these perturbations
are discussed in (\cite[Bolton \etal 1985]{BBC85}). All
these five instabilities of roll patterns can also be found in binary mixtures.
In pure fluids and binary mixtures there exist always perturbations
of the form (\ref{perturbations}) with
$b=d=0$ against which a roll pattern is only marginally stable. Such a
perturbation
has no $\Psi$--component and is odd in $x$. It reflects just an infinitesimal
shift of the whole pattern in the $x$--direction. Therefore such a
perturbation has an eigenvalue $s=0$. For later discussion we point out here
that this particular eigenvalue is connected to nearly all instabilities:
the perturbations causing them and the associated eigenvalues evolve
smoothly into the lateral shift when one moves in the $d-b$ plane
from the $d-b$ coordinates that locate the instability to the origin $d=b=0$.
In the remainder of ~\S\,\ref{sec41} we will briefly characterize the
properties of
the aforementioned five perturbations before presenting our results of
the stability analyses for rolls in ~\S\,\ref{sec42} and for squares in
~\S\,\ref{sec43}. We begin with
the three types (EC, ZZ, and CR) that touch the critical point
$\epsilon = 0$, $k = k_c$ and that
exist also within the
two coupled amplitude equations (\ref{ampligleich1} - \ref{ampligleich2}).
\subsubsection{Eckhaus instability}
\label{sec411}
Perturbations of the Eckhaus type are most critical at $b = 0$
and have no $\Psi$--component. Thus they can be described as
purely two--dimensional.
The EC instability tends to establish a new set of rolls with a better
wavenumber in the direction of the wave vector of the unstable roll pattern.
Within the amplitude
equations EC perturbations can be represented as variations of the
$A$--amplitude that depend only on $x$. Instability occurs here for
$\epsilon$ and $k$ such that
$\epsilon_{stab}(k) < \epsilon < \epsilon_{EC}(k)= 3 \, \epsilon_{stab}(k)$.
At $d \rightarrow 0$ the EC perturbations reduce both in the amplitude equation
approximation and in the full hydrodynamic equations to the lateral shift.
For symmetry reasons $s \sim d^2$ near $d = 0$. In the case of EC
instability (stability) there is a minimum (maximum) of $s$ at
$d =0$. It is therefore sufficient to investigate the pattern at a
single point on the $d$--axis near $d = 0$ numerically in order to determine
the stability behaviour
against EC perturbations. But to find the most critical value of $d$ an
evaluation and interpolation of $s$ along the $d$--axis is necessary.
\subsubsection{Zigzag instability}
\label{sec412}
Zigzag perturbations have $d=0$ and fall into the subclass of
perturbations that are odd in $x$. In the amplitude equations they show up
as $y$--dependent perturbations in the $A$--amplitude.
They cause the growth of a new set of rolls that has always a
greater wavenumber than the original set. Consequently they confine the region
of stable rolls on the small--$k$ side. The amplitude
equations predict a ZZ instability for all $k < k_c$. Like EC
perturbations the ZZ instability reduces to the lateral shift when $b
\rightarrow 0$ and the question of stability can be answered at a single point
near $d=b=0$.
\subsubsection{Crossroll instability}
\label{sec413}
It occurs when roll--like perturbations perpendicular
to the existing pattern can grow.
In the amplitude equations (\ref{ampligleich1} - \ref{ampligleich2}) they
are described as perturbations in the amplitude $B$ when $A$ describes the
stationary roll pattern. Rolls are CR-unstable for
$\epsilon_{stab} (k) < \epsilon < \epsilon_{CR} (k)
= f/(f-1) \,\, \epsilon_{stab} (k)$
when $f > 1$. In this case $\epsilon_{CR} (k)$ can be above or below
the Eckhaus boundary
$ \epsilon_{EC} (k) = 3\, \epsilon_{stab} (k)$ depending on whether
$f < 3/2$ or not.
However, if $f < 1$
(which is the case when squares are stable --- c. f. ~\S\,\ref{sec31})
then rolls are $CR$--unstable for all
$\epsilon > \epsilon_{stab} (k)$ within the amplitude
equations approximation (\ref{ampligleich1} - \ref{ampligleich2}).
Note that the case $f < 1$ does not occur in pure fluids but
it can occur in binary mixtures when squares are stable at onset.
In the multi--mode Galerkin expansion the
leading mode in the velocity field of the CR perturbation has the form
\begin{equation}
\delta \Phi_{001} e^{iby} C_1(z) \;\; , \label{CRmode}
\end{equation}
where near the critical point $b \approx k_c$.
This is a mode of the $\overline{G}$ class of perturbations that are
symmetric under the mirror glide operation as discussed in
~\S\,\ref{sec241}. Being a member of the $\overline{G}$ class this perturbation
cannot be connected smoothly in the $d-b$ plane to $EC$ or $ZZ$
perturbations since the latter belong to the $G$ class of
perturbations
that are antisymmetric under the mirror glide operation. Since we decided to
transform all perturbations into the $G$ class by a shift
$d' = d - k$ as explained in ~\S\,\ref{sec241} we have to rewrite the above
$CR$ perturbation (\ref{CRmode}) into the form
\begin{equation}
\delta \Phi_{-101} e^{i(d-k)x + i b y} C_1(z) \; .
\end{equation}
Writing out the CR perturbations in this form one finds again
that the corresponding eigenvalue is connected to the eigenvalue of the
lateral shift, only taken at a different $d = k$.
Since the CR instability does not occur at arbitrarily small $b$
one therefore has to test several values
of $b$ and then apply an interpolation procedure.
\subsubsection{Skewed varicose instability}
\label{sec414}
This instability is not captured by the simple amplitude
equations. The SV boundary confines the
stability balloon on the large-$k$ side. When crossing this boundary the
perturbation tends to replace the original set of rolls
by a new set with smaller wavenumber. The eigenvalue has its maximum at
$d \neq 0$ and $b \neq 0$. The SV instability too reduces to a lateral shift
at $d,b \rightarrow 0$ and can be found at infinitesimal small $b$ and $d$.
To find the SV stability boundary of rolls one has to find the maximum of the
eigenvalue on a line between the $d$-- and $b$--axis near the origin.
\subsubsection{Oscillatory instability}
\label{sec415}
The oscillatory instability is the only instability with complex
eigenvalues at small $r$. The perturbation is most critical at $d = 0$ and
finite $b$. It is even in $x$. The pair of complex
conjugate eigenvalues undergoes near $b = 0$ a collision and generates two
real eigenvalues. One of these stationary perturbations transforms into the
lateral shift. The real eigenvalues are negative (if the pattern is stable
against ZZ perturbations), so the search for the OS instability requires an
evaluation and interpolation along the $b$--axis as for the CR instability.
\subsection{Stability boundaries of rolls}
\label{sec42}
We saw that the EC, ZZ, CR, SV, and one eigenvalue of the OS instability are
connected to the lateral shift at $b=d=0$. Figure~\ref{bdplane} shows an
example of the most dangerous eigenvalue in the $(d,b)$--plane.
Along the $d$--axis the value of $s$ goes down from $s=0$ at the origin. The
pattern is therefore EC stable. The maxima at $d=0$ and $d=k$ show that
it is unstable against ZZ and CR perturbations. An oscillatory instability
does not occur here for these parameters since
the eigenvalue is always real. There is also no SV instability.
The latter would cause a relative maximum between the $d$-- and $b$--axis.
Besides the perturbation at $d = b = 0$ which describes a lateral
shift in all fields there is another important location in
wavenumber space that is of relevance for concentration field
perturbations and which thus is specific to binary mixtures. It lies at
$d = k$, $b = 0$ and describes a change of the mean concentration. This is
most easily understood by transforming this perturbation from the $G$
class into the $\overline{G}$ class where it then occurs at $d = b = 0$.
Here it consists of one single mode $\delta \zeta_{000}$.
This mode is constant in the fluid layer and describes a change
in the average concentration. But since only derivatives of the
$\zeta$--field show up in the
balance equations such a mode has no influence so that $s=0$. The reason why
this mode has to be taken into account is that for $d$, $b \neq 0$ it
describes a long--wavelength perturbation
$\delta \zeta_{000} e^{idx + iby}$
that is indeed of physical importance. Because the average
concentration is fixed, a divergence in
the $\delta \zeta_{000}$--amplitude (as in $\delta \Phi_{001}$ for mean flow)
cannot occur when approaching $b,d = 0$.
While the eigenvalue of the CR perturbation is connected to the above
described zero eigenvalue the
CR instability occurs always at finite $b$. Only far in the unstable region
the CR eigenvalue becomes positive at arbitrary small $b$.
However, we found no roll instability
to occur directly near this point whereas EC, ZZ, and SV instabilities are
realized near the origin $d = b = 0$ as modifications of the lateral shift.
Figure~\ref{CRevolution} shows the CR instability boundaries of rolls
in the full Galerkin model
in a parameter interval where an exchange of stability between rolls and
squares at onset is predicted in (\cite[Clune \& Knobloch 1991]{CC91}). One
sees that the curvature of the CR boundary at the critical point
diverges --- as is also predicted by the amplitude equation
(\ref{ampligleich1} - \ref{ampligleich2}) for $f = 1$ ---
when this exchange occurs. For the parameters $\sigma =10, \psi=0.01$ of
figure ~\ref{CRevolution} the exchange occurs at $L=0.2$. Decreasing
$L$ below this value the neutral stability curve
(dashed line in figure~\ref{CRevolution}) drops further down in $r$
(not shown in figure~\ref{CRevolution}b) while the CR instability boundary
moves up in $r$. The $r$-range between these two curves locates stable squares.
In such a situation where squares are stable at onset the amplitude equations
predict rolls to be CR-unstable everywhere while in the full equations rolls
become stable against CR-perturbations above the solid lines in
figure~\ref{CRevolution}.
The rolls could still be unstable there against other perturbations but we
found the minimum of the CR boundary always to be the minimal Rayleigh number
for stable rolls to exist. To know the location, $r^c_{CR}$, of this minimum of
the CR boundary for
several parameters is therefore of interest. We have determined
$r_{CR}^c$ and the associated wavenumber $k_{CR}^c$
of the most dangerous CR perturbation for $\psi = 0.01$ and $\psi = 0.15$
and presented the results in figures~\ref{crit0.01} and~\ref{crit0.15},
respectively. They show that rolls are CR unstable at onset, $r_c$
(dashed lined in figures~\ref{crit0.01}a and ~\ref{crit0.15}a), for small $L$
and large $\sigma$. However, for larger $L$
being typical for gas mixtures, rolls are stable at the critical point.
At $\psi=0.15$ the minimum $r^c_{CR}$ of the CR boundary and its wavenumber
location $k^c_{CR}$ strongly increase for small $\sigma$ and $L$ --- cf. the
small-$L$ variation of the respective curves at $\sigma=0.2$ in figures
\ref{crit0.15}a,b. $r^c_{CR}$ seems to diverge here, but a detailed inspection
shows that this is not true. The two branches of the CR boundary meet again at
higher $r$ near the apparent divergence. They limit in the $k-r$ plane an
oval region of CR--stable rolls from below and also {\em above}.
(The upper part of this region can be unstable against OS--perturbations,
though.) By reducing $L$ $r^c_{CR}$ remains finite but the oval region gets
smaller until the region of stable rolls vanishes.
The experimental observation of this behaviour might be
difficult because it occurs in a region of the parameter space that is not
accessible by ordinary fluid mixtures.
We did also investigate the behaviour of $b^c_{CR}$, the wavenumber of the
critical perturbation at $(k^c_{CR},r^c_{CR})$.
Only in the Rayleigh region the values of $k^c_{CR}$
and $b^c_{CR}$ are near $k_c = 3.117$. But in general $k^c_{CR} \neq
b^c_{CR}$. The {\em linear} analysis gives thus a hint for the existence of
patterns with $k_x \neq k_y$ in the Soret region.
We have calculated all stability boundaries at small $r$ for different values
of $L$, $\psi$, and $\sigma$. Concerning the stability behaviour of the roll
structures one sees that in the Rayleigh region, $r \gtrsim 1$, where the
concentration field is nearly uniform the
binary mixture behaves like a pure fluid. And the transition between Soret
and Rayleigh region is very sharp at small $L$ and $\psi$. An example for such
a behaviour is given in figure~\ref{exampleballoon}. Here only the EC, CR,
and ZZ boundaries are of importance. In the Rayleigh region $r\gtrsim 1$
of figure~\ref{exampleballoon} the CR, ZZ, and EC boundaries of the mixture
(full lines with circles, triangles, and squares, respectively) are lying close
to the corresponding boundaries of the pure fluid (long-dashed lines). Note
in particular the vase-like form of the EC boundary $r_{EC}(k)$ and the dent
in the ZZ boundary
$r_{ZZ}(k)$: Close to onset ($r_c \simeq 0.6, k_c \simeq 2.6$ in
figure~\ref{exampleballoon}), i.e., in the Soret regime $r_{EC}(k)$ opens up
parabolically and $r_{ZZ}(k)$ comes out of the critical point linearly with
{\em positive} slope. However, in the crossover range $r \sim 1$ between
Soret and Rayleigh regime the curve $r_{EC}(k)$ pinches inwards and develops
a waist such as to follow in the
Rayleigh regime the parabolic shape of the EC curve of the pure fluid that
starts out at $k_c^0 \simeq 3.1, r_c^0=1$. Similarly $r_{ZZ}(k)$ bends in the
crossover range towards small $k$ to follow then the ZZ boundary of the pure
fluid that shows {\em negative} slope.
Figures~\ref{balloon0.1}--\ref{balloon10} show that this sharp
transition between Soret and
Rayleigh region that causes the vase-like structure of the EC boundary and
the sharp bend of the ZZ boundary does not occur when $L$ is greater. For
$L=0.01$ and $\psi \geq 0.08$ the critical point lies at $k = 0$. In this
case the amplitude equations are not applicable. We found the ZZ boundary and
the left EC branch to go to $r = \infty$ at small $k$. But the right EC
branch does still meet the critical point.
At low Prandtl numbers the roll solutions have a finite region of stability but
their basin of the attraction seems to be very small since typically spiral
defect chaos is observed here in experiments (\cite[Liu \& Ahlers 1996]{LA96}).
But it was shown that rolls could also be observed with special experimental
procedures (\cite[Cakmur \etal 1997]{CEPB97}).
We tried to find laws that connect the position of the boundaries and the
fixed point solutions. We found no easy connection between these values for CR,
ZZ and SV. But the OS boundary for fixed $\sigma$ seems to be independent of
$L$ and $\psi$ in the plane of $k$ and the convection amplitude
$w_{101}$ instead of in the $k$--$r$ plane (figure~\ref{OSscale}).
For the EC boundary a more complicated
procedure is needed. We define an effective control parameter by linear
interpolation of the values for the convection amplitudes
\begin{equation}
\frac{\partial w_{101}^2}{ \partial r} \epsilon_{eff}(r) = w_{101}^2 \;\; ,
\label{epsilon_eff}
\end{equation}
and an effective reduced Rayleigh number
\begin{equation}
r_{eff} = \epsilon_{eff} + r^0_{stab}(k)\;\; .
\label{r_eff}
\end{equation}
Within the amplitude equations it is just
$\epsilon_{eff} = \epsilon$. Plotting the EC boundary in the $k - r_{eff}$
plane instead of in the $k - r$ plane shows in the Rayleigh region only a
dependence on $\sigma$ but not on $\psi$ and $L$, c.f. figure~\ref{ECscale}.
However, this procedure does not hold in the Soret region.
\subsection{Stability boundaries of squares}
\label{sec43}
Performing the stability analysis of squares we had to restrict ourselves to the
case $d=b=0$ where the perturbations separate into different symmetry
classes. An analytical investigation of long wavelength perturbations of
squares near the critical point can be found in (\cite[Hoyle 1993]{H93}).
Because both squares and rolls can be described as even in $x$ and
$y$ and as mirror glide antisymmetric, one expects a perturbation that
destabilises the squares and favours the rolls to fulfill these symmetries, too.
However such a perturbation should break the symmetry $x \leftrightarrow y$.
We actually always found the most critical perturbation to fall into this
symmetry class. Other perturbations that break the mirror symmetry in
$x$-- or $y$--direction are less critical.
Figure \ref{squareballoon} shows typical examples for the stability
region of squares. The left and right side of the stability boundaries should
not be taken too serious --- presumably square structures are destabilised
earlier by instabilities with finite $b$ or $d$ that tune the wavenumber and
that are not considered here.
Even if squares are stable at onset they always lose their stability
against a roll pattern at higher $r$. Furthermore, for certain parameters
there does also exist a band of
$r$--values where neither squares nor rolls are stable. Within this band
three--dimensional CRs that break the $x \leftrightarrow y$ symmetry
can be stable. For certain parameters we found stationary CRs only. For others
oscillating CRs structures appeared as well. We have studied these
structures in more detail in (\cite[Jung, Huke \& L{\"u}cke 1998]{JHL98}).
\section{Conclusion}
\label{conclude}
We investigated roll, crossroll, and square convection in binary mixtures
for a wide range of parameter combinations using a multi--mode Galerkin method.
All these patterns are realized as stable convection structures somewhere in
parameter space.
The bifurcation behaviour of rolls and squares can be modelled near onset by
amplitude equations, which, however lose their applicability in the Rayleigh
region. Moreover, the CR solution that connects the roll and the
square branch at Rayleigh numbers $r \approx 1$ is absent in
a simple ansatz of cubic amplitude equations.
We compared the Nusselt number and also the mixing parameter of the full
numerical solutions for rolls and squares. We found these global properties
of the convective states to be approximatively the same for these patterns
despite the qualitatively different structures of
the concentration fields of squares and rolls: Rolls show a strong boundary
layer behaviour at small $L$ and high $r$, so that compared to pure fluids
much more modes are needed to describe them. Squares, on the other hand,
show a less pronounced boundary layer behaviour making it easier to
determine these three--dimensional solutions numerically.
In the main part of the paper
we investigated the linear stability of rolls and squares. To that end we
performed a full and unrestricted stability analysis for rolls using
arbitrary perturbations and in addition a
stability analysis of squares that uses the periodic boundary conditions of
the squares also for the perturbations. The result is that squares are
stable in the Soret region if $L$ is sufficiently small. But they always
lose their stability at higher $r$. Rolls are stable at onset at higher $L$ and
in the Rayleigh region where squares are unstable. Typically, however, there
is a finite interval of $r$--values in between where neither rolls nor squares
are stable. In this interval either stationary or oscillatory CR patterns are
observed.
The analysis of the rolls shows that in the explored parameter range
only the basic mechanisms of instability
occur that are already known from the pure fluid, namely the Eckhaus, zigzag,
crossroll, oscillatory, and skewed varicose mechanism. When the Soret region is
small, the stability balloon of the mixtures resembles the Busse balloon for
the pure fluid. However, at small $L$
when the Soret region is large the situation is different. The fixed point
solutions show a sharp transition between the two regimes. The convection
amplitudes are very small in the Soret regime. But near $r =1$ they increase
strongly and e.~g.\ the Nusselt number becomes comparable to that of the pure
fluid convection. The stability boundaries of roll convection show a similar
transition here. In the Rayleigh region the boundaries are close to the
boundaries of the pure fluid. But upon reducing the Rayleigh number
the boundaries begin to deviate from their pure fluid
counterparts. Near onset they finally agree with the predictions of the
amplitude equations for the mixtures.
The EC boundary gives a typical example for this behaviour. For high $L$ it has
just a normal parabolic shape. But for small $L$ one observes a qualitatively
different behaviour. When approaching $r = 1$ from above the two branches do
not meet near $r=1$ as in the pure fluid but begin to separate again until $r$
gets small enough for the amplitude equations to become valid. A typical
vase--like shape results.
A detailed inspection of the point where the rolls become unstable at onset
shows that the CR boundary is responsible for this loss of stability. As long
as the rolls are stable at onset, the CR boundary touches the critical point,
as predicted by the amplitude equations. At a certain point the
amplitude equations show a global loss of stability against CR perturbations.
In the full Galerkin analysis this loss of stability does not occur. The
CR boundary disconnects from the neutral curve and the rolls
remain stable not at onset but at higher $r$.
Both the amplitude equations and the full Galerkin expansion show that
square structures get stable at onset when roll structures lose stability
there and vice versa. The stability domain of squares lies mainly in the Soret
region and it is separated from the region of stable rolls at higher $r$ by
the region of
CR structures. The fact that square patterns lose their stability already at
relatively small $r$ was another favourable property which delimited the
requirements for a numerical analysis of these patterns.
The perturbations against which square solutions are unstable show those
symmetries that squares, rolls, and CRs have in common. But they
break the $x \leftrightarrow y$ symmetry, which exists only for
squares. The resulting stability boundary delimits the
region of stable squares in the $k$--$r$ plane not only on top but also at
the sides at smaller and larger wave numbers. It should be noted that our
analysis of squares does not cover instabilities that retune the actual
wavenumber of the considered pattern and which might occur earlier than the
wave number preserving instabilities investigated here.
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 3,021
|
Paperman è un cortometraggio animato statunitense del 2012 diretto da John Kahrs e prodotto dai Walt Disney Animation Studios.
È il primo film d'animazione ad essere stato girato con la cosiddetta Nuova Tecnica d'animazione. È stato proiettato per la prima volta in abbinamento al film d'animazione Ralph Spaccatutto. Ha vinto l'Oscar al miglior cortometraggio d'animazione all'85ª edizione dei Premi Oscar. A fine gennaio del 2013 la Disney pubblica integralmente sul web il cortometraggio, ma pochi mesi dopo toglie questa possibilità in concomitanza con la pubblicazione del corto in home video.
Trama
Il cortometraggio ambientato a Manhattan negli anni 40 inizia ad una fermata del treno con protagonisti un ragazzo, George, ed una ragazza, Meg. Al primo sfugge di mano un foglio che viene portato dal vento addosso alla ragazza che lascia, involontariamente, il segno del rossetto su di esso. Mentre il ragazzo è distratto dalla bellezza della sconosciuta e dal segno sul suo foglio, arriva il treno che lo separa da Meg. Poco dopo, arrivato al lavoro, nota dalla sua finestra la ragazza che è in un ufficio nel palazzo di fronte e prova ad attirare la sua attenzione formando con pratiche lavorative degli aeroplanini di carta. Il suo tentativo non va a buon fine e, una volta finiti i fogli, prova a lanciare come ultima speranza quello macchiato di rossetto dal loro primo incontro, ma gli cade di mano per una folata di vento. Anche in questo caso George non viene notato da Meg, lo stesso non si può dire del suo superiore che lo riprende per il comportamento tenuto. La ragazza esce dall'ufficio per tornare a casa e il giovane innamorato si precipita fuori per cercare di raggiungerla, ma la perde di vista; intanto nel tragitto verso casa tutti i suoi aeroplanini si sono raccolti in un vicolo e, con l'arrivo dell'ultimo lanciato per disperazione, i fogli prendono vita. George viene ricoperto di carta e costretto a prendere un treno; Meg a sua volta riconosce il foglio con il suo rossetto e lo segue su un diverso treno, i due si ricongiungono ad una fermata e, durante i titoli finali, vengono mostrati a chiacchierare seduti in un ristorante, lasciando presagire una futura storia d'amore.
Riconoscimenti
2013 – Premio Oscar
Miglior cortometraggio d'animazione
Note
Collegamenti esterni
Premi Oscar al miglior cortometraggio d'animazione
|
{
"redpajama_set_name": "RedPajamaWikipedia"
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| 9,686
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Paul Michael Robinson (ur. 7 kwietnia 1963 w Long Beach) − amerykański aktor filmowy i telewizyjny, producent filmowy, fotograf i model.
Życiorys
Wczesne lata
Urodził się w Long Beach w stanie Kalifornia. Służył w Armii Stanów Zjednoczonych i stacjonował w Fort Stewart, w stanie Georgia. Był w trzecim batalionie, piętnastej piechoty specjalizującej się w komunikacji. Uczestniczył w I wojnie w Zatoce Perskiej. Po służbie wojskowej rozpoczął karierę w branży filmowej.
Kariera
Wystąpił w czterech filmach Freda Olena Raya: Namiętna zemsta (Friend of the Family II, 1996), Maksymalna ochrona (Maximum Revenge, 1997), Prorok (The Prophet, 1999) u boku Dona "The Dragona" Wilsona i Stacja kosmiczna 'Avna''' (Stranded, 2001) z udziałem Michaela Dudikoffa i Ice'a-T, z którym ponownie spotkał się na planie dreszczowca erotycznego Gry łóżkowe (Kept, 2001) z główną rolą Christiana Olivera.
Zagrał kapitana w dramacie erotycznym Emmanuelle w kosmosie (Emmanuelle in Space, 1994) z Kristą Allen.
Filmografia
Filmy fabularne
1995: Justyna: (Justine: Exotic Liaisons) jako Saul
1995: Justyna: Miłostka (Justine: A Private Affair) jako Klauss Heinmann
1996: W liniach (Within the Lines)
1996: Justyna: Powab niewinności (Justine: Seduction of Innocence) jako Alan Pope/Klauss Heinmann/Saul
1996: Justyna: W gorączce pasji (Justine: In the Heat of Passion) jako Klauss Heinmann
1996: Namiętna zemsta (Friend of the Family II) jako Alex Madison
1997: Fight and Revenge jako szeregowy Michael Stahl
1997: Maksymalna ochrona (Maximum Revenge) jako Mace Richter
1999: Tajna broń (Active Stealth) jako porucznik "Hollywood" Andrews
1999: Prorok (The Prophet) jako Łowca
1998: Bejsbolo-kosz (BASEketball) jako Mim
2000: Wietnamski eksperyment (The Chaos Factor) jako patrolujący oficer
2001: Stacja kosmiczna 'Avna' (Stranded)
2001: Utrzymanek (Kept) jako Tony
2005: Drzewa rosną wysoko i potem one spadają (Trees Grow Tall and Then They Fall) jako Roy
2007: Wojownicze żółwie ninja (TMNT) – dubbing
2007: Wampirowo (Revamped) jako detektyw Peters
2007: Szef, serce i piłki... lub dlaczego dałem w górę palący garnek (Head, Heart and Balls... or Why I Gave Up Smoking Pot) jako narrator
Filmy TV
1994: Emmanuelle: Pierwszy kontakt (Emmanuelle: First Contact) jako kapitan Haffron Williams
1994: Emmanuelle, królowa galaktyki (Emmanuelle, Queen of the Galax) jako kapitan Haffron Williams
1994: Emmanuelle: Lekcja miłości (Emmanuelle 3: A Lesson In Love) jako kapitan Haffron Williams
1994: Emmanuelle: Skrywane fantazje (Emmanuelle 4: Concealed Fantasy) jako kapitan Haffron Williams
1994: Emmanuelle: Czas na marzenia (Emmanuelle 5: A Time to Dream) jako kapitan Haffron Williams
1994: Emmanuelle: Ostatnie rozkosze (Emmanuelle 6: One Final Fling) jako kapitan Haffron Williams
1994: Emmanuelle: Czym jest miłość? (Emmanuelle 7: The Meaning of Love) jako kapitan Haffron Williams
Seriale TV
1996: Wina (The Guilt) jako Carl O'Donnell
1997: Sabrina, nastoletnia czarownica (Sabrina, the Teenage Witch'') jako Zak
Przypisy
Linki zewnętrzne
Amerykańscy aktorzy filmowi
Amerykańscy modele
Amerykańscy producenci filmowi
Urodzeni w 1963
Amerykańscy aktorzy telewizyjni
Ludzie urodzeni w Long Beach
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{
"redpajama_set_name": "RedPajamaWikipedia"
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package org.apache.ibatis.cache;
import java.io.Serializable;
import java.lang.reflect.Array;
import java.util.ArrayList;
import java.util.List;
/**
* @author Clinton Begin
*/
public class CacheKey implements Cloneable, Serializable {
private static final long serialVersionUID = 1146682552656046210L;
public static final CacheKey NULL_CACHE_KEY = new NullCacheKey();
private static final int DEFAULT_MULTIPLYER = 37;
private static final int DEFAULT_HASHCODE = 17;
private int multiplier;
private int hashcode;
private long checksum;
private int count;
private List<Object> updateList;
public CacheKey() {
this.hashcode = DEFAULT_HASHCODE;
this.multiplier = DEFAULT_MULTIPLYER;
this.count = 0;
this.updateList = new ArrayList<Object>();
}
public CacheKey(Object[] objects) {
this();
updateAll(objects);
}
public int getUpdateCount() {
return updateList.size();
}
public void update(Object object) {
if (object != null && object.getClass().isArray()) {
int length = Array.getLength(object);
for (int i = 0; i < length; i++) {
Object element = Array.get(object, i);
doUpdate(element);
}
} else {
doUpdate(object);
}
}
private void doUpdate(Object object) {
int baseHashCode = object == null ? 1 : object.hashCode();
count++;
checksum += baseHashCode;
baseHashCode *= count;
hashcode = multiplier * hashcode + baseHashCode;
updateList.add(object);
}
public void updateAll(Object[] objects) {
for (Object o : objects) {
update(o);
}
}
@Override
public boolean equals(Object object) {
if (this == object) {
return true;
}
if (!(object instanceof CacheKey)) {
return false;
}
final CacheKey cacheKey = (CacheKey) object;
if (hashcode != cacheKey.hashcode) {
return false;
}
if (checksum != cacheKey.checksum) {
return false;
}
if (count != cacheKey.count) {
return false;
}
for (int i = 0; i < updateList.size(); i++) {
Object thisObject = updateList.get(i);
Object thatObject = cacheKey.updateList.get(i);
if (thisObject == null) {
if (thatObject != null) {
return false;
}
} else {
if (!thisObject.equals(thatObject)) {
return false;
}
}
}
return true;
}
@Override
public int hashCode() {
return hashcode;
}
@Override
public String toString() {
StringBuilder returnValue = new StringBuilder().append(hashcode).append(':').append(checksum);
for (int i = 0; i < updateList.size(); i++) {
returnValue.append(':').append(updateList.get(i));
}
return returnValue.toString();
}
@Override
public CacheKey clone() throws CloneNotSupportedException {
CacheKey clonedCacheKey = (CacheKey) super.clone();
clonedCacheKey.updateList = new ArrayList<Object>(updateList);
return clonedCacheKey;
}
}
|
{
"redpajama_set_name": "RedPajamaGithub"
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| 3,205
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\section{Introduction}
\subsection{Isothermic surfaces}
In the year 1837 Gabriel Lam\'{e} presented \cite{Lame-isoth}
results of his studies on distribution
of temperature in a homogeneous solid body in thermal equilibrium.
He was interested, in particular, in
description of the \emph{isothermic surfaces}, i.e. surfaces of constant
temperature within the body;
notice that his definition makes sense only for families of surfaces,
and not for a single surface.
Then he found a condition
under which one parameter family of
surfaces in (a subset of) ${\mathbb E}^3$ consists of isothermic surfaces,
and showed (for details see \cite{Lame} or~\cite{DarbouxOS})
that the three families of confocal quadrics, which provide elliptic
coordinates in ${\mathbb E}^3$, meet that criterion.
Subsequently, he proposed to
determine all triply orthogonal systems composed by three isothermic families
(triply isothermic systems).
Such a program was fulfiled by Gaston Darboux~\cite{DarbouxOS} (see also
\cite{Eisenhart-SV}).
Another path of research was initiated by Joseph Bertrand~\cite{Bertrand} who
showed that the surfaces of triply isothermic systems are divided by their lines
of curvature into "infinitesimal squares", or in exact terms, they allow for
conformal curvature parametrization. This definition of isothermic
surfaces (or surfaces of isothermic curvature lines), which can be
applied to a single surface, was commonly accepted
in the second half of the XIX-th century
(see~\cite{Bianchi,DarbouxIV}). We mention that the minimal surfaces
and the constant mean curvature surfaces are particular examples of
the isothermic surfaces.
The theory of
isothermic surfaces was one of the most favorite subjects of study among
prominent geometers of that period. Such surfaces exhibit particular properties, for example
there exists a transformation, described by Gaston Darboux in~\cite{Darboux-transf}, which produces
from a given isothermic surface a family of new surfaces of the same type.
The Gauss-Mainardi-Codazzi equations for isothermic surfaces constitute a
nonlinear system generalizing the $\mathrm{sinh}$-Gordon equation (the latter governs
the constant mean curvature surfaces),
and the Darboux transformation can be interpreted as B\"{a}cklund-type
transformation of the system. Soon after that Luigi Bianchi
showed~\cite{Bianchi-isoth} that two Darboux transforms of a given isothermic surface
determine \emph{in algebraic terms} new isothermic surface being their simultaneous
Darboux transform.
The Bianchi permutability principle can be
considered as a hallmark of integrability (in the sense of soliton theory) of
the above-mentioned system. Indeed, the isothermic surfaces were reinterpreted
by Cie\'{s}li\'{n}ski, Goldstein and Sym \cite{CGS} within the
theory of soliton surfaces~\cite{Sym}.
More information on isothermic surfaces and their history the Reader can find
in the paper
of Klimczewski, Nieszporski and Sym \cite{KNS}, where also a more detailed description
of the relation between the "ancient"
differential geometry and the soliton theory is given, and in books by Rogers and Schief
\cite{RogersSchief} and by Hertrich-Jeromin \cite{UHJ}.
\subsection{Discrete isothermic surfaces and discrete integrable geometry}
In the recent studies of the
relation between geometry and the integrable
systems theory a particular attention is payed to discrete
(difference) integrable
equations and the corresponding discrete surfaces or lattice
submanifolds.
Also here the discrete analogs of
isothermic surfaces played a prominent role in the development of the subject.
Bobenko and Pinkall \cite{BP2} introduced the integrable discrete analogoue
of isothermic surfaces as mappings built of "conformal squares", i.e., maps
${\boldsymbol x}:{\mathbb Z}^2\to{\mathbb E}^3$ with all
elementary quadrilaterals circular, and such that the complex cross-ratios
(with the plane of a
quadrilateral identified with the complex plane ${\mathbb C}$)
\[ q(m,n) = \mathrm{cr}\big({\boldsymbol x}(m,n),{\boldsymbol x}(m+1,n+1);{\boldsymbol x}(m+1,n),{\boldsymbol x}(m,n+1) \big)_{\mathbb C}
\]
are equal to $-1$.
Soon after that it turned out \cite{BP-V} that it is more convenient to allow
for the cross-rations to satisfy the constraint
\begin{equation} \label{eq:isoth-cr}
q(m,n) q(m+1,n+1) = q(m+1,n)q(m,n+1).
\end{equation}
Then the cross-ratio is a ratio of functions of single variables,
which corresponds to allowed re\-pa\-ra\-met\-ri\-za\-tion of the
curvature coordinates
on isothermic surfaces.
After the pioneering work of Bobenko and Pinkall, which was an important
step in building the geometric
approach to integrable discrete equations (see also
\cite{DS-AL,BP1,DCN} and older results of the difference geometry
(\emph{Differenzengeometrie}) summarized in Robert Sauer's books
\cite{Sauer2,Sauer}),
the discrete isothermic surfaces and their Darboux
transformations
were studied in a number of papers \cite{HeHP,Ciesl,Schief-C}. Distinguished
integrable reductions of isothermic lattices are the discrete constant mean
curvature surfaces or the discrete minimal surfaces \cite{BP-V,UHJ}. It should be
mentioned that the complex cross-ratio condition \eqref{eq:isoth-cr} was
extended
to circular lattices of dimension three \cite{BP-V,Ciesl}
placing the Darboux
transformations of the discrete isothermic surfaces on equal footing with the
lattice itself.
In the present-day approach to the relation between
discrete integrable systems and
geometry \cite{DS-EMP,BobSur} the key
role is played by the integrable discrete analogue of conjugate
nets -- multidimensional lattices of planar quadrilaterals
(the quadrilateral lattices) \cite{MQL}. These are
maps $x:{\mathbb Z}^N\to{\mathbb P}^M$ of $N$-dimensional integer lattice
in $M\geq N$-dimensional projective space with all
elementary quadrilaterals planar. Integrability of such lattices (for $N>2$)
is based on
the following elementary geometry fact (see Figure~\ref{fig:TiTjTkx}).
\begin{figure}
\begin{center}
\includegraphics{TiTjTkx.eps}
\end{center}
\caption{The geometric integrability scheme}
\label{fig:TiTjTkx}
\end{figure}
\begin{Lem}[The geometric integrability scheme] \label{lem:gen-hex}
Consider points $x_0$, $x_1$, $x_2$ and $x_3$ in general position in ${\mathbb P}^M$,
$M\geq 3$. On
the plane $\langle x_0, x_i, x_j \rangle$, $1\leq i < j \leq 3$ choose a point
$x_{ij}$ not on the lines $\langle x_0, x_i \rangle$, $\langle x_0,x_j
\rangle$ and $\langle x_i, x_j \rangle$. Then there exists the
unique point $x_{123}$
which belongs simultaneously to the three planes
$\langle x_3, x_{13}, x_{23} \rangle$,
$\langle x_2, x_{12}, x_{23} \rangle$ and
$\langle x_1, x_{12}, x_{13} \rangle$.
\end{Lem}
Various constraints compatible with the
geometric integrability scheme define
integrable reductions of the quadrilateral lattice. It turns out that such
geometric notion of integrability very often associates
integrable reductions of the quadrilateral lattice
with classical theorems of incidence geometry.
We advocate this point of view in the present paper.
Among basic reductions of the
quadrilateral lattice the so called quadratic
reductions \cite{q-red} play a distinguished role.
The lattice vertices are then contained in a
hyperquadric (or in the intersection of several of
them). Such reductions of the
quadrilateral lattice
can be often associated with various subgeometries of the projective geometry,
when the quadric plays the role of the absolute of the geometry
(see also corresponding remarks in \cite{q-red,W-cong}).
In particular, when the hyperquadric is the M\"{o}bius hypersphere
one obtains, after the stereographic projection,
the circular lattices \cite{Bobenko-O,CDS,DMS,KoSchief2}, which are the
integrable discrete analogue of submanifolds of
${\mathbb E}^M$ in curvature line parametrization.
Because of the M\"{o}bius
invariance of
the complex cross-ratio it is also more convenient to consider (discrete)
isothermic surfaces in the M\"{o}bius sphere (both dimensions of the
lattice and of the sphere
can be enlarged) keeping the "cross-ratio definition".
For a person trained in the projective geometry it is more or less
natural to generalize the M\"{o}bius geometry approach to discrete isothermic
surfaces (lattices) in quadrics replacing the M\"{o}bius sphere by a quadric,
and correspondingly,
the complex cross-ratio by the Steiner cross-ratio
of four points of a conic being intersection of the quadric by the plane of
elementary quadrilateral of the quadrilateral lattice.
However the "cross-ratio point of view" doesn't answer the crucial
question about integrability (understood as compatibility of the
constraint with the geometric integrablity scheme) of such
discrete isothermic surfaces in quadrics. Our general methodological principle
in the integrable
discrete geometry, applied successfuly earlier, for example in
\cite{DS-sym,DNS-Bianchi}, which we would like to follow here
is (i) to isolate basic reductions of the quadrilateral
lattice and then (ii) to
incorporate other geometric systems into the theory considering them as
superpositions of the basic
reductions.
In this context we would like to recall
another equivalent
characterization of the classical isothermic
surfaces which can be found in the classical monograph of
Darboux~\cite[vol. 2, p. 267]{DarbouxIV}:
{\it
Les cinq coordonn\'{e}es pentasph\'{e}riques d'un point de toute surface
isothermique consid\'{e}r\'{e}es comme fonctions des param\`{e}tres $\rho$ et
$\rho_1$ des lignes de courbure satisfont \`{a} une \'{e}quation lin\'{e}aire du
second ordre dont les invariants sont \'{e}gaux.
Inversement, si une \'{e}quation de la forme
\begin{equation} \label{eq:Moutard-diff}
\frac{\partial^2\theta}{\partial \rho \partial \rho_1} = \lambda \theta
\end{equation}
ou, plus g\'{e}n\'{e}ralement, une \'{e}quation \`{a} invariants \'{e}gaux,
admet cinq solutions particuli\`{e}res $x_1$, $x_2$, \dots , $x_5$ li\'{e}es
par
l'\'{e}quation
\begin{equation}
\sum_{1}^{5} x_i^2 = 0,
\end{equation}
les quantit\'{e}s $x_i$ sont les coordonn\'{e}es pantasph\'{e}riques qui
d\'{e}finissent une surface isothermique rapport\'{e}e \`{a} ses lignes de
courbure.
}
In literature there are known two (closely related) discrete integrable
versions
(of Nimmo and Schief \cite{NiSchief} and of Nieszporski \cite{Nieszporski-dK})
of the Moutard equation \eqref{eq:Moutard-diff}. It turns out that for our
purposes it suits the discrete Moutard equation proposed in~\cite{NiSchief}.
Its projectively invariant geometric characterization has been
discovered \cite{DGNS} only recently (for geometric meaning
of the adjoint Moutard equation of Nieszporski in terms of the so called
Koenigs lattice see \cite{Dol-Koe}). Indeed, it turns out that
the generalized
isothermic lattices can be obtained by adding to the quadratic
constraint the projective Moutard constraint. Finally, the quadratic reduction
and the Moutard reduction, when applied simultaneously, give
\emph{a posteriori} the cross-ratio condition \eqref{eq:isoth-cr}.
In fact, the direct algebraic discrete counterpart of the above description of
the isothermic surfaces, i.e. existence of the light-cone lift which
satisfies the (discrete) Moutard equation, appeared first in a preprint by
Bobenko and Suris \cite{BobSur}.
However, the pure geometric characterization of the discrete isothermic surfaces
was not given there.
Because integrability of the discrete Moutard equation can be seen
better when one considers a system of such equations for multidimensional
lattices, there was a need to find the projective geometric
characterization of the system. The corresponding reduction of the quadrilateral
lattice was called in \cite{BQL}, because of its connection with the
discrete BKP equation, the B-quadrilateral lattice (BQL).
In fact, research in this direction prevented me
from publication of the above mentioned generalization of discrete isothermic
surfaces, announced however in my talk during the
Workshop "Geometry and Integrable Systems"
(Berlin, 3-7 June 2005). I suggested also there that the discrete
S-isothermic surfaces
of Tim Hoffmann \cite{Hoffmann} (see also \cite{BobSur})
should be considered as an example of the
generalized isothermic lattices where the quadric under consideration is the
Lie quadric.
The final results of my research on generalized
isothermic lattices were presented on the Conference "Symmetries and
Integrability of Difference Equations VII" (Melbourne, 10-14 July 2006).
When my paper was almost ready there appeared the preprint of Bobenko and Suris
\cite{BobSur-gen-isoth} where similar ideas were presented in application to the
sphere (M\"{o}bius, Laguerre and Lie) geometries. I would like also to point
out a recent paper by Wallner and Pottman \cite{WP} devoted, among others, to
discrete isothermic surfaces in the Laguerre geometry.
\subsection{Plan of the paper}
As it often happens, the logical presentation of results of a research goes
in opposite direction to their chronological derivation. In
Section~\ref{sec:BQL+QQL} we collect some geometric
results from the theory of the B-quadrilateral lattices (BQLs)
and of quadrilateral
lattices in quadrics (QQLs). Some new results concerning the relation between
(Steiner's) cross-ratios of vertices of elementary
guadrilaterals of elementary hexahedrons of
the QQLs are given there as well. Then in Section~\ref{sec:gen-isoth-latt}
we define generalized
isothermic lattices and discuss their basic properties. In particular, we give
the synthetic-geometry proof of a basic lemma (the half-hexahedron lemma) which
immediately gives the cross-ratio characterization of the lattices.
We also present some algebraic consequences (some of them known already
\cite{BobSur}) of the system of Moutard equations supplemented by a quadratic
constraint. In Section~\ref{sec:Darboux} we study in more detail the Darboux
transformation of the
generalized isothermic lattices and the corresponding Bianchi
permutability principle. Finally, in Section~\ref{sec:isothermic} we consider
two dimensional generalized isothermic lattices.
In two Appendices we recall necessary information
concerning the cross-ratio of four points on a conic curve and we perform some
auxilliary calculations.
\section{The B-quadrilateral lattices and the quadrilateral lattices in quadrics}
\label{sec:BQL+QQL}
It turns out that compatibility of both BQLs and QQLs with the geometric
integrablity scheme follows from certain classical geometric facts.
We start each section, devoted to a particular lattice, from the corresponding
geometric statement.
\subsection{The B-quadrilateral lattice \cite{BQL}}
\begin{Lem} \label{lem:BKP-hex}
Under hypothesess of Lemma \ref{lem:gen-hex}, assume that the points
$x_0$, $x_{12}$, $x_{13}$, $x_{23}$ are coplanar, then the points
$x_1$, $x_2$, $x_3$, and $x_{123}$ are coplanar as well (see
Figure~\ref{fig:moutard}).
\end{Lem}
\begin{figure}
\begin{center}
\includegraphics{moutard}
\end{center}
\caption{Elementary hexahedron of the B-quadrilateral lattice}
\label{fig:moutard}
\end{figure}
As it was discussed in \cite{BQL} the above fact is equivalent to the
M\"{o}bius theorem (see, for example \cite{Coxeter}) on mutually inscribed
tetrahedra. Another equivalent, but more symmetric,
formulation of Lemma~\ref{lem:BKP-hex} is
provided by the Cox theorem (see \cite{Coxeter}): \emph{Let $\sigma_1$,
$\sigma_2$, $\sigma_3$, $\sigma_4$ be four planes of general position through a
point $S$. Let $S_{ij}$ be an arbitrary point on the line $\langle \sigma_i,
\sigma_j \rangle$. Let $\sigma_{ijk}$ denote the plane $\langle S_{ij}, S_{ik},
S_{jk} \rangle$. Then the four planes $\sigma_{234}$, $\sigma_{134}$,
$\sigma_{124}$, $\sigma_{123}$ all pass through one point $S_{1234}$.}
\begin{Def} \label{def:BQL}
A quadrilateral lattice $x:{\mathbb Z}^N\to{\mathbb P}^M$ is called the \emph{B-quadrilateral
lattice} if for any triple of different indices $i,j,k$
the points $x$, $x_{(ij)}$,
$x_{(jk)}$ and $x_{(ik)}$ are coplanar.
\end{Def}
Here and in all the paper, given a fuction $F$ on
${\mathbb Z}^N$, we denote its shift in the $i$th direction in a standard manner:
$F_{(i)}(n_1,\dots, n_i, \dots , n_N) = F(n_1,\dots, n_i + 1, \dots , n_N)$.
One can show that a quadrilateral lattice $x:{\mathbb Z}^N\to{\mathbb P}^M$ is a
B-quadrilateral lattice if and only if
it allows for a homogoneous representation ${\boldsymbol x}:{\mathbb Z}^N\to{\mathbb R}^{M+1}_{*}$
satisfying the system of discrete Moutard equations (the
discrete BKP linear problem)
\begin{equation} \label{eq:BKP-lin}
{\boldsymbol x}_{(ij)} - {\boldsymbol x} = f^{ij} ({\boldsymbol x}_{(i)} - {\boldsymbol x}_{(j)}) , \quad 1\leq i< j\leq N,
\end{equation}
for suitable functions $f^{ij}:{\mathbb Z}^N\to{\mathbb R}$.
The compatibility condition of the system \eqref{eq:BKP-lin}
implies that the functions $f^{ij}$ can be written
in terms of the potential $\tau:{\mathbb Z}^N\to{\mathbb R}$,
\begin{equation} \label{eq:tau}
f^{ij} = \frac{\tau_{(i)}\tau_{(j)}}{\tau \, \tau_{(ij)}}, \qquad i\ne j ,
\end{equation}
which satisfies Miwa's discrete
BKP equations \cite{Miwa}
\begin{equation} \label{eq:BKP-nlin}
\tau\, \tau_{(ijk)} = \tau_{(ij)}\tau_{(k)} - \tau_{(ik)}\tau_{(j)} +
\tau_{(jk)}\tau_{(i)}, \quad 1\leq i< j < k \leq N.
\end{equation}
\begin{Rem}
The trapezoidal lattice \cite{BobSur} is another reduction of the
quadrilateral lattice being algebraically described by the discrete Moutard
equations \eqref{eq:BKP-lin}. Geometrically, the trapezoidal lattices are
characterized by parallelity of diagonals of the elementary quadrilaterals,
thus they belong to the affine geometry.
Moreover, because the trapezoidal constraint is imposed on the level
of elementary quadrilaterals then,
from the point of view of the geometric
integrability scheme, one has to check its three
dimensional consistency. In contrary, the BQL constraint is imposed on the level
of elementary hexahedrons, and to prove geometrically its integrability
one has to check four dimensional
consistency.
\end{Rem}
\subsection{The quadrilateral lattices in quadrics}
\begin{Lem} \label{lem:qred-hex}
Under hypotheses of Lemma \ref{lem:gen-hex}, assume that the points
$x_0$, $x_1$, $x_2$, $x_3$, $x_{12}$, $x_{13}$, $x_{23}$ belong to a
quadric $\mathcal{Q}$. Then the point $x_{123}$ belongs to
the quadric $\mathcal{Q}$ as well.
\end{Lem}
\begin{Rem}
The above fact is a consequence of the classical
\emph{eight points theorem} (see, for example \cite{Coxeter}) which says that
\emph{seven points in general position determine a unique eighth point, such
that every quadric through the seven passes also through the eighth}. In our
case the point $x_{123}$ is contained in the three (degenerate) quadrics being
pairs of opposite facets of the hexahedron.
\end{Rem}
\begin{Rem}
Lemma \ref{lem:BKP-hex} can be considered as a "reduced" resion of
Lemma~\ref{lem:qred-hex} when the quadric $\mathcal{Q}$
degenerates to a pair of planes.
\end{Rem}
\begin{Def} \label{def:QQL}
A quadrilateral lattice $x:{\mathbb Z}^N\to\mathcal{Q}\subset{\mathbb P}^M$
contained in a hyperquadric $\mathcal{Q}$ is called the
\emph{$\mathcal{Q}$-reduced quadrilateral lattice} (QQL).
\end{Def}
Integrability of the QQLs was pointed out in \cite{q-red}, where also the
corresponding Darboux-type transformation (called in this context the Ribaucour
transformation) was constructed in the vectorial form.
When the quadric is irreducible then generically
it cuts the planes of the hexahedron along
conics.
\begin{Def}
A quadrilateral lattice $x:{\mathbb Z}^N\to\mathcal{Q}\subset{\mathbb P}^M$ in a
hyperquadric $\mathcal{Q}$ such that the intersection of the planes of
elementary quadrilaterals of the latice with the quadric
are irreducible conic curves is called
\emph{locally irreducible}.
\end{Def}
The following result, which will not be used in the sequel and
whose proof can be found in Appendix~\ref{sec:aux-calc},
generalizes
the relation between complex cross-ratios of the opposite quadrilaterals of
elementary hexahedrons of the circular lattices \cite{Bobenko-O}.
\begin{Prop} \label{prop:qred-cr}
Given locally irreducible quadrilateral lattice
$x:{\mathbb Z}^N\to\mathcal{Q}\subset{\mathbb P}^M$ in a
hyperquadric $\mathcal{Q}$, denote by
\begin{equation*}
\lambda^{ij} = \mathrm{cr}(x_{(i)},x_{(j)};x,x_{(ij)}), \qquad 1\leq i<j\leq N,
\end{equation*}
the cross-ratios (defined with respect to
the corresponding conic curves)
of the four vertices of the quadrilaterals.
Then the cross-ratios are related by the following system of equations
\begin{equation} \label{eq:qred-cross-r}
\lambda^{ij}\lambda^{ij}_{(k)}\lambda^{jk}\lambda^{jk}_{(i)} =
\lambda^{ik}\lambda^{ik}_{(j)}, \quad 1\leq i<j<k\leq N.
\end{equation}
\end{Prop}
\begin{Rem}
The system \eqref{eq:qred-cross-r} can be considered as the gauge invariant
integrable difference equation governing QQLs.
\end{Rem}
\section{Generalized isothermic lattices}
\label{sec:gen-isoth-latt}
Because simultaneous application of integrable constraints preserves
integrability we know \emph{a priori} that the following reduction of the
quadrilateral lattice is integrable.
\begin{Def}
A B-quadrilateral lattice in a hyperquadric $x:{\mathbb Z}^N\to\mathcal{Q}\subset{\mathbb P}^M$
satisfying the local irreducibility condition is called a
\emph{generalized isothermic lattice}.
\end{Def}
\subsection{The half hexahedron lemma and its consequences}
We start again from a
geometric result, which leads to the cross-ratio characterization
of the generalized
isothermic lattice.
\begin{Lem}[The half hexahedron lemma] \label{lem:half-hex}
Under hypotheses of Lemmas \ref{lem:BKP-hex} and \ref{lem:qred-hex} and
assuming irreducibility of the conics of the intersection of the
corresponding planes with the quadric
we have
\begin{equation} \label{eq:product-cr}
\mathrm{cr}(x_1,x_3;x_0,x_{13}) = \mathrm{cr}(x_1,x_2;x_0,x_{12}) \,
\mathrm{cr}(x_2,x_3;x_0,x_{23}),
\end{equation}
where the cross-ratios are defined with respect to the corresponding
conics.
\end{Lem}
\begin{proof}
Denote (see
Figure~\ref{fig:hex-lem})
\begin{figure}
\begin{center}
\includegraphics{hex-lem}
\end{center}
\caption{Geometric proof of Lemma \ref{lem:half-hex}}
\label{fig:hex-lem}
\end{figure}the plane $\sigma=\langle x_1, x_2, x_3 \rangle$, and
represent points of the conic
$\mathcal{C}_{ij}={\mathcal Q}\cap\langle x_0, x_i, x_j \rangle$, $1\leq i < j \leq 3$
by points of the
line $\langle x_i, x_j \rangle$, via the corresponding
planar pencil with the base at $x_0$. In this way the projective structure of
the conics conicides with that of the corresponding lines.
By $\ell_{ij}$ denote the
intersection of the tangent line to $\mathcal{C}_{ij}$ at $x_0$ with $\sigma$.
Notice that the points $\ell_{ij}$ belong to
the intersection line of the tangent plane to the quadric at $x_0$
with $\sigma$, and all they represent
$x_0$ but from the point of view of different conics.
Denote
by $d_{ij}$ the intersection point of the line
$\langle x_0, x_{ij} \rangle$ with the plane $\sigma$. Notice that coplanarity
of the points
$x_0$, $x_{12}$, $x_{23}$ and $x_{23}$ is equivalent to collinearity
of $d_{12}$, $d_{23}$ and $d_{13}$. Moreover, by definition of
the cross-ratio on conics, we have
\begin{equation} \label{eq:cr-c-l}
\mathrm{cr}(x_i,x_j;x_0,x_{ij}) = \mathrm{cr}(x_i,x_j;\ell_{ij},d_{ij}).
\end{equation}
To find a relation between the cross-ratios
consider perspectivity between the lines $\langle x_1, x_2 \rangle$ and
$\langle x_1, x_3 \rangle$ with the center $\ell_{23}$. It transforms
$x_2$ into $x_3$, $x_1$ into $x_1$, $d_{12}$ into $\tilde{d}_{12}$ (this is
just definition of $\tilde{d}_{12}$) and $\ell_{12}$ into $\ell_{13}$,
therefore
\begin{equation}
\mathrm{cr}(x_1,x_2;\ell_{12},d_{12}) =
\mathrm{cr}(x_1,x_3;\ell_{13},\tilde{d}_{12}).
\end{equation}
Smilarly, considering perspectivity between the lines
$\langle x_2, x_3 \rangle$ and
$\langle x_1, x_3 \rangle$ with the center $\ell_{12}$ we obtain
\begin{equation}
\mathrm{cr}(x_2,x_3;\ell_{23},d_{23}) =
\mathrm{cr}(x_1,x_3;\ell_{13},\tilde{d}_{23}),
\end{equation}
where again $\tilde{d}_{23}$ is the projection of $d_{23}$.
The comparison of Figures \ref{fig:hex-lem} and \ref{fig:multiplication}
gives
\begin{equation} \label{eq:cr-l-pr}
\mathrm{cr}(x_1,x_3;\ell_{13},\tilde{d}_{12})
\mathrm{cr}(x_1,x_3;\ell_{13},\tilde{d}_{23})=
\mathrm{cr}(x_1,x_3;\ell_{13},d_{13}),
\end{equation}
which because of equations \eqref{eq:cr-c-l}-\eqref{eq:cr-l-pr} implies the
statement.
\end{proof}
\begin{Rem}
For those who do not like synthetic geometry proofs we give the algebraic proof
of the above Lemma in Appendix~\ref{sec:aux-calc}.
\end{Rem}
\begin{Cor}
Equation \eqref{eq:product-cr} can be written in a more symmetric form
\begin{equation} \label{eq:product-cr-symm}
\mathrm{cr}(x_1,x_2;x_0,x_{12}) \,
\mathrm{cr}(x_2,x_3;x_0,x_{23}) \, \mathrm{cr}(x_3,x_1;x_0,x_{13}) = 1.
\end{equation}
\end{Cor}
\begin{Cor}
The cross-ratio of the four (coplanar) points $x_0$, $x_{12}$, $x_{13}$ and
$x_{23}$ can be expressed by the other cross-ratios as
\begin{equation}
\mathrm{cr}(x_0,x_{12};x_{13},x_{23})=\mathrm{cr}(x_0,x_{2};x_{3},x_{23})
\mathrm{cr}(x_1,x_{0};x_{3},x_{13}).
\end{equation}
\end{Cor}
\begin{proof}
Consider the line $\langle d_{13}, d_{23} \rangle$, which is the section of the
planar pencil containing lines $\langle x_0, x_{13} \rangle$ and
$\langle x_0, x_{23} \rangle$ with the plane $\sigma$. Denote by $\ell$ the
intersection point of the line with the line
$\langle \ell_{13}, \ell_{23} \rangle$, then
\begin{equation*}
\mathrm{cr}(x_0,x_{12};x_{13},x_{23}) = \mathrm{cr}(\ell,d_{12};d_{13},d_{23}).
\end{equation*}
After projection from $\ell_{12}$ we have, in notation of
Figure~\ref{fig:hex-lem},
\begin{equation*}
\mathrm{cr}(\ell,d_{12};d_{13},d_{23}) = \mathrm{cr}(\ell_{13},x_1;d_{13},\tilde{d}_{23})=
\mathrm{cr}(1,\infty;\lambda\nu,\nu).
\end{equation*}
Then the standard permutation properties of the cross-ratio give the statement.
\end{proof}
\begin{Cor}[The hexahedron lemma] \label{cor:hex}
Under assumption of Lemma \ref{lem:half-hex} the cross-ratios on opposite
quadrilaterals of the hexahedron are equal, i.e.
\begin{align}
\nonumber
\mathrm{cr}(x_1,x_2;x_0,x_{12}) & = \mathrm{cr}(x_{13},x_{23};x_3,x_{123}) , \\
\label{eq:equalities-cr}
\mathrm{cr}(x_2,x_3;x_0,x_{23}) & = \mathrm{cr}(x_{12},x_{13};x_1,x_{123}) , \\
\nonumber
\mathrm{cr}(x_1,x_3;x_0,x_{13}) & = \mathrm{cr}(x_{12},x_{23};x_2,x_{123}) .
\end{align}
\end{Cor}
\begin{proof}
Equation \eqref{eq:product-cr-symm} written for the three quadrilaterals
meeting in $x_3$ reads
\begin{equation}
\mathrm{cr}(x_0,x_{12};x_3,x_{1}) \,
\mathrm{cr}(x_{13},x_{23};x_3,x_{123}) \, \mathrm{cr}(x_{23},x_0;x_3,x_{2}) = 1,
\end{equation}
which compared with \eqref{eq:product-cr-symm} gives, after using elementary
properties of the cross-ratio, the first equation of
\eqref{eq:equalities-cr}. Others can be obtained similarly.
\end{proof}
\begin{Cor}
By symmetry we have also
\begin{equation}
\mathrm{cr}(x_0,x_{12};x_{13},x_{23}) = \mathrm{cr}(x_{1},x_{2};x_{3},x_{123}).
\end{equation}
\end{Cor}
\begin{Rem}
Notice that two neighbouring facets of the above hexahedron determine the
whole hexahedron via construction visualized on Fig.~\ref{fig:twotothree}.
\end{Rem}
\begin{figure}
\begin{center}
\includegraphics{twotothree}
\end{center}
\caption{Construction of the point $x_{13}$ from points $x_0$, $x_{1}$, $x_{2}$,
$x_{3}$, $x_{12}$ and $x_{23}$. It belongs to the
intersection line of two planes $\langle x_0, x_{1}, x_{3} \rangle$ with the
plane $\langle x_0, x_{12}, x_{23} \rangle$. Because the line intersects the
quadric at $x_0$, it must have also the second intersection point.}
\label{fig:twotothree}
\end{figure}
\begin{Rem}
It is easy to see that, unlike in the case of isothermic lattices,
three vertices of a quadrilateral of trapezoidal lattice in a quadric
\cite{BobSur} determine
the forth vertex.
\end{Rem}
\begin{Prop} \label{prop:cross-ratio-gen}
A quadrilateral lattice in a quadric $x:{\mathbb Z}^N\to\mathcal{Q}\subset{\mathbb P}^M$
satisfying the local irreducibility condition is a generalized isothermic
lattice if and only if
there exist functions $\alpha^{i}:{\mathbb Z}\to{\mathbb R}$ of single arguments $n_i$ such
that the cross-ratios $\lambda^{ij} = \mathrm{cr}(x_{(i)},x_{(j)};x,x_{(ij)})$
can be factorized as follows
\begin{equation} \label{eq:isot-cross-res}
\lambda^{ij} = \frac{\alpha^i}{\alpha^j}, \qquad 1\leq i<j\leq N.
\end{equation}
\end{Prop}
\begin{proof}
Equations \eqref{eq:product-cr} and \eqref{eq:equalities-cr} can be rewritten as
\begin{equation} \label{eq:izot-cross-r-1}
\lambda^{ij}\lambda^{jk} = \lambda^{ik}, \quad 1\leq i<j<k\leq N,
\end{equation}
and
\begin{equation} \label{eq:izot-cross-r-op}
\lambda^{ij}=\lambda^{ij}_{(k)}, \quad \lambda^{jk} = \lambda^{jk}_{(i)}, \quad
\lambda^{ik}=\lambda^{ik}_{(j)}, \quad 1\leq i<j<k\leq N;
\end{equation}
notice their consistency with
the general system \eqref{eq:qred-cross-r}.
Equations \eqref{eq:izot-cross-r-1}-\eqref{eq:izot-cross-r-op} imply that
cross-ratios of two dimensional sub-lattices of the
generalized isothermic lattice satisfy condition of the form
\eqref{eq:isoth-cr}, i.e.,
\begin{equation}
\lambda^{ij}_{(ij)}\lambda^{ij} = \lambda^{ij}_{(i)}\lambda^{ij}_{(j)},
\quad 1\leq i<j\leq N.
\end{equation}
For a fixed pair $i,j$, the above relation can be resolved as in
\eqref{eq:isot-cross-res} (the first equation in \eqref{eq:izot-cross-r-op}
asserts that the functions $\alpha^i$ and $\alpha^j$ are the same for all $i,j$
sublattices). Finally, equations \eqref{eq:izot-cross-r-1} imply the
the functions $\alpha$ can be defined consistently on the whole lattice.
\end{proof}
For convenience of the Reader we present also
the algebraic proof of the above
properties of the generalized isothermic lattice
(see also \cite{BobSur} for analogous results concerning T-nets in a quadric).
\begin{proof}[The algebraic proof]
Assume that solutions of the system of the discrete Moutard equations
\eqref{eq:BKP-lin} satisfy the quadratic constraint
\begin{equation} \label{eq:q-constr}
({\boldsymbol x} | {\boldsymbol x}) = 0,
\end{equation}
where $(\cdot | \cdot ) $ is a symmetric nondegenerate bilinear form. Then the
coefficients of the Moutard equations should be of the form
\begin{equation} \label{eq:f-isoth}
f^{ij} = \frac{({\boldsymbol x} | {\boldsymbol x}_{(i)} - {\boldsymbol x}_{(j)})}{({\boldsymbol x}_{(i)} | {\boldsymbol x}_{(j)})},
\quad 1\leq i<j\leq N.
\end{equation}
Moreover by direct calculations one shows that
\begin{equation}
({\boldsymbol x}_{(i)} | {\boldsymbol x})_{(j)} = ({\boldsymbol x}_{(i)} | {\boldsymbol x}),
\quad 1\leq i<j\leq N,
\end{equation}
which implies that the products
$({\boldsymbol x}_{(i)} | {\boldsymbol x}) $, which we denote by $\alpha_i$,
are functions of single variables $n_i$.
Consider the points
$x, x_{(i)}, x_{(j)}$ as the (projective) basis of
the plane $\langle x, x_{(i)}, x_{(j)} \rangle$.
Then the homogeneous coordinates of points of the plane can be
written as
\begin{equation}
{\boldsymbol y} = t {\boldsymbol x} + t_i {\boldsymbol x}_{(i)} + t_j {\boldsymbol x}_{(j)}, \qquad (t,t_i,t_j) \in {\mathbb R}^3_*,
\end{equation}
modulo the standard common proportionality factor. In particular, the line
$\langle x, x_{(i)} \rangle$ is given by equation $t_j = 0$,
and the line
$\langle x, x_{(j)} \rangle$ is given by equation $t_i = 0$.
Due to the discrete Moutard equation \eqref{eq:BKP-lin}
the line $\langle x, x_{(ij)} \rangle$ is given by equation $t_i + t_j = 0$.
To find the cross-ratio $ \mathrm{cr}(x_{(i)},x_{(j)};x,x_{(ij)})=\lambda^{ij} $ via
lines of the planar pencil with the base point $x$ we need equation of
the tangent
to the conic $({\boldsymbol y} | {\boldsymbol y} ) =0$ at that point.
It is easy to check that the conic is given by
\begin{equation}
t t_i \alpha_{i} + t t_j \alpha_{j} + t_i t_j ({\boldsymbol x}_{(i)} | {\boldsymbol x}_{(j)}) =0.
\end{equation}
The tangent to the conic at $x$ is then given by
\begin{equation}
t_i \alpha_{i} + t_j \alpha_{j} =0,
\end{equation}
which implies equation \eqref{eq:isot-cross-res}.
\end{proof}
\begin{Rem}
It should be mentioned the a similar quadratic
reduction of the discrete Moutard
equation (for $N=2$) appeared in a paper of Wolfgang Schief~\cite{Schief-C}
under the name
of discrete vectorial
Calapso equation, as an integrable discrete vectorial analogue of the
Calapso equation~\cite{Calapso}, which is of the fourth order and describes
isothermic surfaces. It turns out that the discrete Calapso equation
describes also the so called Bianchi reduction of discrete asymptotic
surfaces~\cite{DNS-Bianchi-ass}.
\end{Rem}
\subsection{Isothermic lattices in the M\"{o}bius sphere
and the so called
Clifford configuration}
In \cite{KoSch-Clifford} Konopelchenko and Schief
observed that the "complex cross-ratio
definition" of the discrete isothermic surfaces, when extended to three
dimensional lattices, is related with the so called
Clifford configuration of circles (see Figure~\ref{fig:Clifford}).
\begin{figure}
\begin{center}
\includegraphics[width=8cm]{Clifford.eps}
\end{center}
\caption{The so called
Clifford configuration of circles (the second Miquel configuration)}
\label{fig:Clifford}
\end{figure}
In this Section we would like to explain that fact geometrically.
Our point of view on the Clifford configuration is closely related to the
geometric definition of the isothermic lattice in the M\"{o}bius sphere.
Therefore we start with another, less restrictive,
configuration of circles on the plane, the Miquel configuration
(see Figure~\ref{fig:Miquel}), which
provides geometric explanation of integrability of the circular
lattice~\cite{CDS}. When the quadric in Lemma \ref{lem:qred-hex} is the
standard sphere
then the intersection curves of the planes of the quadrilaterals with
the sphere
are circles. After the stereographic projection from a generic point of the
sphere we obtain the classical Miquel theorem \cite{Miquel}, which can
be stated as follows (given three distinct points $a$, $b$ and $c$,
by $C(a,b,c)$ we denote the unique circle-line passing through them).
\begin{Th}[The Miquel configuration] \label{th:Miquel}
Given four coplanar points $s_0$, $s_i$, $i=1,2,3$. On each circle
$C(s_0,s_i, s_j)$, $1\leq i < j \leq 3$ choose a point, denoted correspondingly
by $s_{ij}$. Then there exists the unique point $s_{123}$ which belongs
simultaneously to the three circles $C(s_1, s_{12}, s_{13})$,
$C(s_2, s_{12}, s_{23})$ and $C(s_3, s_{13}, s_{23})$.
\end{Th}
\begin{figure}
\begin{center}
\includegraphics[width=8cm]{Miquel.eps}
\end{center}
\caption{The (first) Miquel configuration of circles}
\label{fig:Miquel}
\end{figure}
The additional assumption about coplanarity of the points
$x_0$, $x_{12}$, $x_{13}$,
$x_{23}$ on the sphere is then equivalent to the
additional assumption about concircularity of the corresponding points
$s_0$, $s_{12}$, $s_{13}$, $s_{23}$. In view of Lemma \ref{lem:BKP-hex}
we obtain therefore another configuration
of circles, the so called
Clifford configuration, which can be described as follows.
\begin{Th}[The so called Clifford configuration] \label{th:Clifford}
Under hypotheses of Theorem \ref{th:Miquel} assume that the points
$s_0$, $s_{12}$, $s_{13}$, $s_{23}$ are concircular, then the points
$s_1$, $s_{2}$, $s_{3}$ and $s_{123}$ are concircular as well.
\end{Th}
\begin{Rem}
The original Clifford's formulation of the above result was more symmetric. Its
relation to Theorem~\ref{th:Clifford} is analogous to relation of the Cox
theorem to Lemma~\ref{lem:BKP-hex}. We remark that although
the above theorem is usually attributed (see for example \cite{Coxeter})
to Wiliam Clifford \cite{Clifford} it appeared
in much earlier paper \cite{Miquel} of Auguste Miquel, where we read as
\emph{Th\`{e}or\`{e}me II} the following statement:
\emph{Lorsqu'un quadrilat\`{e}re complet curviligne ABCDEF
est form\'{e} par quatre arcs de cercle AB, BC, CD, DA, qui se coupent tous
quatre en un m\^{e}me point P, si l'on circonscrit des circonf\'{e}rences de
cercle \`{a} chacun des quatre triangles curvilignes que forment les
c\^{o}t\'{e}s de ce quadrilat\`{e}re, les circonf\'{e}rences de cercle AFB, EBC,
DCF, DAE ainsi obtenues se couperont toutes quatre en un m\^{e}me point G}.
Points on Figure~\ref{fig:Clifford} are labelled in double way
to visualize simultaneously
the configuration in formulation of Theorem~\ref{th:Clifford} and in Miquel's
formulation.
\end{Rem}
\section{The Darboux transformation of the generalized isotermic lattice}
\label{sec:Darboux}
\subsection{The fundamental, Moutard and Ribaucour transformations}
Usually, on the discrete level there is no essential difference between
integrable lattices and their transformations.
The analogue of the fundamental transformation of Jonas for
quadrilateral lattices is defined as construction of a new level of the lattice
\cite{TQL} keeping the basic property of planarity of elementary quadrilaterals.
Below we recall the relevant definitions of the fundamental transformation and
its important reductions -- the BQL reduction \cite{BQL}
(algebraically equivalent to the Moutard transformation \cite{NiSchief}),
and the QQL reduction \cite{q-red}
called the Ribaucour transformation.
\begin{Def}
\emph{The fundamental transform} of a quadrilateral lattice
$x:{\mathbb Z}^N\to{\mathbb P}^M$ is a new quadrilateral lattice
$\hat{x}:{\mathbb Z}^N\to{\mathbb P}^M$ constructed under assumption that for any point
$x$ of the lattice and any direction $i$, the four points
$x$, $x_{(i)}$, $\hat{x}$ and $\hat{x}_{(i)}$ are coplanar.
\end{Def}
\begin{Def}
The fundamental transformation of a B-quadrilateral lattice
$x:{\mathbb Z}^N\to{\mathbb P}^M$
constructed under additional assumption that for any point
$x$ of the lattice and any pair $i,j$ of different directions, the four points
$x$, $x_{(ij)}$, $\hat{x}_{(i)}$ and $\hat{x}_{(j)}$ are coplanar is called
\emph{the BQL (Moutard) reduction} of the fundamental transformation of $x$.
\end{Def}
Algebraic description of the above transformation is given as follows
\cite{NiSchief}.
Given solution ${\boldsymbol x}$ of the system of discrete Moutard equations
\eqref{eq:BKP-lin} and given its scalar solution $\theta$, then
the solution $\hat{{\boldsymbol x}}$ of the system
\begin{equation} \label{eq:Moutard-transf}
\hat{\boldsymbol x}_{(i)} - {\boldsymbol x} = \frac{\theta}{\theta_{(i)}}\left( \hat{\boldsymbol x} -
{\boldsymbol x}_{(i)}\right),
\end{equation}
satisfies equations \eqref{eq:BKP-lin} with the new potential
\begin{equation}
\hat{f}^{ij} = f^{ij}\frac{\theta_{(i)}\theta_{(j)}}{\theta\theta_{(ij)}},
\qquad i<j,
\end{equation}
and new $\tau$-function
\begin{equation} \label{eq:transf-Mout-tau}
\hat\tau = \theta\tau.
\end{equation}
\begin{Def}
The fundamental transformation of a quadrilateral lattice
$x:{\mathbb Z}^N\to\mathcal{Q}\subset{\mathbb P}^M$ in a quadric,
constructed under additional assumption
that also $\hat{x}$ satifies the same quadratic constraint
is called
\emph{the Riboucour transformation} of $x$.
\end{Def}
\subsection{The Darboux transformation}
\begin{Def}
The fundamental transformation of a generalized isothermic lattice which is
simultaneously the Ribaucour and the Moutard transformation is called
\emph{the Darboux transformation}.
\end{Def}
Notice that there is essentially no difference between
the Darboux transformation and construction of a new
level of the generalized isothermic lattice. Therefore, given points $x$,
$x_{(i)}$, $x_{(j)}$, $x_{(ij)}$, $i\ne j$, of the initial lattice, and
given points $\hat{x}$, $\hat{x}_{(j)}$ of its Darboux transform then the point
$\hat{x}_{(i)}$ is determined by the "half-hexahedron construction" visualized
on Figure~\ref{fig:twotothree}, i.e., $\hat{x}_{(i)}$ is the intersection point
of the line
$\langle x, x_{(i)}, \hat{x} \rangle \cap
\langle x, x_{(ij)}, \hat{x}_{(j)} \rangle$ with the quadric. Moreover,
Lemma~\ref{lem:half-hex} implies
\begin{equation} \label{eq:cr-prod-transf}
\mathrm{cr}(x_{(i)},\hat{x};x,\hat{x}_{(i)}) = \mathrm{cr}(x_{(i)},x_{(j)};x,x_{(ij)})
\mathrm{cr}(x_{(j)},\hat{x};x,\hat{x}_{(j)}),
\end{equation}
while Corollary~\ref{cor:hex} gives
\begin{equation}
\mathrm{cr}(\hat{x}_{(i)},\hat{x}_{(j)};\hat{x},\hat{x}_{(ij)})=
\mathrm{cr}(x_{(i)},x_{(j)};x,x_{(ij)}).
\end{equation}
The algebraic derivation of the above results is given below.
The Darboux
transformations of the discrete isothermic surfaces in the light-cone
description were discussed in a similar spirit in \cite{BobSur}.
\begin{Prop} \label{prop:Darboux-prod}
If $\hat{x}:{\mathbb Z}^N\to\mathcal{Q}\subset{\mathbb P}^M$ is a Darboux transform of the
generalized isothermic lattice $x:{\mathbb Z}^N\to\mathcal{Q}\subset{\mathbb P}^M$ then
the product $(\hat{{\boldsymbol x}}|{\boldsymbol x})$ of their homogeneous coordinates in the gauge
of the linear problem \eqref{eq:BKP-lin} and the corresponding Moutard
transformation \eqref{eq:Moutard-transf}, with respect to the bilinear form
$(\cdot|\cdot)$ defining the quadric $\mathcal{Q}$, is constant.
\end{Prop}
\begin{proof}
The homogeneous coordinates ${\boldsymbol x}$ and $\hat{{\boldsymbol x}}$ in the Moutard
transformation satisfy equation of the form
\begin{equation}
\hat{{\boldsymbol x}}_{(i)} - {\boldsymbol x} = f^i(\hat{{\boldsymbol x}} - {\boldsymbol x}_{(i)}), \qquad 1\leq i \leq N,
\end{equation}
with appropriate functions $f^i:{\mathbb Z}^N\to{\mathbb R}$. The quadratic condition
$(\hat{{\boldsymbol x}}_{(i)}|\hat{{\boldsymbol x}}_{(i)})=0$ together with other quadratic conditions
give
\begin{equation} \label{eq:fi-isoth}
f^i = \frac{({\boldsymbol x}| \hat{{\boldsymbol x}} -{\boldsymbol x}_{(i)})}{(\hat{{\boldsymbol x}}|{\boldsymbol x}_{(i)})},
\end{equation}
which implies $(\hat{{\boldsymbol x}}_{(i)}|{{\boldsymbol x}}_{(i)}) = (\hat{{\boldsymbol x}}|{\boldsymbol x})$.
\end{proof}
Notice the above proof goes along the corresponding reasoning in the first part of
the algebraic proof of Proposition \ref{prop:cross-ratio-gen}. The analogous
reasoning as in its second part gives the following statement.
\begin{Cor}
Under hypothesis of Proposition \ref{prop:Darboux-prod} denote
$\zeta=(\hat{{\boldsymbol x}}|{\boldsymbol x})$ and $\lambda^i = \mathrm{cr}(\hat{x},x_{(i)};x,\hat{x}_{(i)})$
then equations \eqref{eq:isot-cross-res} and \eqref{eq:izot-cross-r-1}
should be replaced by
\begin{equation} \label{eq:cr-lambda-prod}
\lambda^i = \frac{\zeta}{\alpha_i}, \qquad \lambda^i \lambda^{ij} = \lambda^j.
\end{equation}
\end{Cor}
The above reasoning can be reversed giving the algebraic way to find the
Darboux transform of a given generalized isothermic lattice.
\begin{Th} \label{th:Darboux}
Given a solution ${\boldsymbol x} :{\mathbb Z}^N\to {\mathbb R}^{M+1}_*$ of the system of Moutard equations
\eqref{eq:BKP-lin} satisfying the constraint $({\boldsymbol x}|{\boldsymbol x})=0$, considered as
homogeneous coordinates of generalized isothermic lattice
$x:{\mathbb Z}^N\to\mathcal{Q}\subset{\mathbb P}^M$, denote $\alpha_i = ({\boldsymbol x}_{(i)}|{\boldsymbol x})$.
Given a
point $[\hat{{\boldsymbol x}}_0]=\hat{x}_0\in\mathcal{Q}$, denote $\zeta =
(\hat{{\boldsymbol x}}_0|{\boldsymbol x}(0))$. Then there exists unique solution of the linear system
\begin{equation} \label{eq:Darboux}
\hat{{\boldsymbol x}}_{(i)} = {\boldsymbol x} + \frac{\zeta - \alpha_i}{(\hat{{\boldsymbol x}}|{\boldsymbol x}_{(i)})}
(\hat{{\boldsymbol x}} - {\boldsymbol x}_{(i)}), \qquad, \quad 1\leq i \leq N,
\end{equation}
with initial condition $\hat{{\boldsymbol x}}(0) = \hat{{\boldsymbol x}}_0$ which gives the Darboux
transform of the lattice $x$. In particular
\begin{align} \label{eq:cr-zeta-alpha}
\mathrm{cr}(\hat{x},x_{(i)};x,\hat{x}_{(i)}) & = \frac{\zeta}{\alpha_i} \\
\mathrm{cr}(\hat{x}_{(i)},\hat{x}_{(j)};\hat{x},\hat{x}_{(ij)}) & =
\mathrm{cr}(x_{(i)},x_{(j)};x,x_{(ij)}) =
\frac{\alpha^i}{\alpha^j}.
\end{align}
\end{Th}
Before proving the Theorem let us state a Lemma
relating the parameter $\zeta$ of the Darboux transformation with the functional
parameter $\theta$ of the Moutard transformation \eqref{eq:Moutard-transf}.
\begin{Lem} \label{eq:zeta-theta}
Under hypotheses of Theorem \ref{th:Darboux} the solution $\theta$ of the system
\begin{equation}
\theta_{(i)}=\theta\frac{(\hat{{\boldsymbol x}}|{\boldsymbol x}_{(i)})}{\zeta - \alpha_i}, \qquad
\quad 1\leq i \leq N,
\end{equation}
satisfies the system of discrete Moutard equations \eqref{eq:BKP-lin}
with the coefficients given by \eqref{eq:f-isoth}.
\end{Lem}
\begin{proof}[Proof of the Lemma]
By direct verification. Notice that both ways to calculate
$\theta_{(ij)}$, $i\ne j$, from $\theta$ give the same result, and to do that we
do not use compatibility of the system \eqref{eq:Darboux}.
\end{proof}
\begin{proof}[Proof of the Theorem]
By direct calculation one can check that the system \eqref{eq:Darboux}
preserves
the constraints $(\hat{{\boldsymbol x}}|\hat{{\boldsymbol x}}) =0$ and $(\hat{{\boldsymbol x}}|{\boldsymbol x})=\zeta$,
moreover
$(\hat{{\boldsymbol x}}_{(i)}|\hat{{\boldsymbol x}}) =({\boldsymbol x}_{(i)}|{\boldsymbol x})$.
Compatibility of the system \eqref{eq:Darboux} can be checked by direct
calculation, but in fact it is the consequence of
Lemma \ref{eq:zeta-theta} and properties of the Moutard
transformation \eqref{eq:Moutard-transf}.
\end{proof}
\begin{Rem}
Notice that because there is essentially no diffrence between the lattice
directions and the transformation directions, the tranformation equations
\eqref{eq:Darboux} can be guessed by keeping the Moutard-like form supplementing
it by calculation of the coefficient $f^i$ from the quadratic constraint.
We will use this observation in the next Section where we consider the
permutability principle for the Darboux transformations of generalized
isothermic lattices.
\end{Rem}
\subsection{The Bianchi permutability principle}
The original Bianchi superposition principle for the Darboux transformations of
the isothermic surfaces reads as follows \cite{Bianchi-isoth}:
\emph{Se dalla superficie isoterma $S$ si ottengono due nuove superficie
isoterme $S_1$, $S_2$ mediante le trasformazioni di Darboux $D_{m_1}$, $D_{m_2}$ a
costanti $m_1$, $m_2$ differenti, esiste una quarta superficie isoterma
$\overline{S}$, pienamente determinata e costruibile in termini finiti, che
\`{e} legata alla sua volta alle medesime superficie $S_1$, $S_2$ da due
trasformazioni di Darboux $\overline{D}_{m_2}$, $\overline{D}_{m_1}$ colle
costanti invertite $m_2$, $m_1$.}
\begin{figure}
\begin{center}
\includegraphics{bianchi}
\end{center}
\caption{Geometric construction of the superposition of two Darboux
transformations}
\label{fig:bianchi}
\end{figure}
Its version for generalized isothermic lattices can be formulated analogously.
\begin{Prop} \label{prop:superp}
When from given generalized isothermic lattice $x$ there were constructed two
new isothermic lattices $\hat{x}^1$ and $\hat{x}^2$ via the Darboux transformations with
different parameters $\zeta_1$ and $\zeta_2$, then there exists the unique forth
generalized isothermic lattice $\hat{x}^{12}$, determined in algebraic terms from the
three previous ones, which is connected with two intermediate lattices
$\hat{x}^1$ and
$\hat{x}^2$ via two Darboux transformations with reversed parameters $\zeta_2$,
$\zeta_1$.
\end{Prop}
\begin{proof}
The algebraic properties of the B-reduction of the fundamental transformation
(the discrete Moutard transformation) imply that in
the gauge of the linear problem \eqref{eq:BKP-lin} and of the transformation
equations \eqref{eq:Moutard-transf} the superposition of two such
transformations reads
\begin{equation} \label{eq:-transf-sup}
\hat{{\boldsymbol x}}^{12} - {\boldsymbol x} = f (\hat{{\boldsymbol x}}^1 - \hat{{\boldsymbol x}}^2),
\end{equation}
where $f$ is an appropriate function \cite{NiSchief,BQL}. Because of the
additional quadratic constraints the function is given by (compare also equations
\eqref{eq:f-isoth} and \eqref{eq:f-isoth})
\begin{equation} \label{eq:f-isoth-sup}
f = \frac{({\boldsymbol x} | \hat{{\boldsymbol x}}^1 - \hat{{\boldsymbol x}}^2)}{(\hat{{\boldsymbol x}}^1 | \hat{{\boldsymbol x}}^2)}.
\end{equation}
The lattice $\hat{x}^{12}$ with homogeneous coordinates
given by \eqref{eq:-transf-sup} and \eqref{eq:f-isoth-sup} is superposition
of two Darboux transforms. Finally, direct calculation shows that
\begin{equation}
(\hat{{\boldsymbol x}}^{12} | \hat{{\boldsymbol x}}^2) =
(\hat{{\boldsymbol x}}^1 | {\boldsymbol x}) = \zeta_1, \qquad
(\hat{{\boldsymbol x}}^{12} | \hat{{\boldsymbol x}}^1)=
(\hat{{\boldsymbol x}}^2 | {\boldsymbol x})= \zeta_2 .
\end{equation}
\end{proof}
\begin{Cor}
The final algebraic superposition formula reads
\begin{equation}
\hat{{\boldsymbol x}}^{12} - {\boldsymbol x} = \frac{\zeta_1 - \zeta_2}{(\hat{{\boldsymbol x}}^1 | \hat{{\boldsymbol x}}^2)}
(\hat{{\boldsymbol x}}^1 - \hat{{\boldsymbol x}}^2),
\end{equation}
while the cross-ratio of the four corresponding points calculated with respect
to the conic intersection of the plane $\langle x,\hat{x}^1,\hat{x}^2 \rangle$
and the quadric is given by
\begin{equation}\label{eq:cr-zeta-sup}
\mathrm{cr}(\hat{x}^1,\hat{x}^2;x,\hat{x}^{12}) = \frac{\zeta_1}{\zeta_2}.
\end{equation}
\end{Cor}
To find the lattice $\hat{x}^{12}$ geometrically we can use again
the "half-hexahedron construction" in the new context
visualized on Figure~\ref{fig:bianchi}
(compare with Figure~\ref{fig:twotothree}).
Moreover, Lemma~\ref{lem:half-hex} gives
\begin{equation} \label{eq:cr-prod-sup}
\mathrm{cr}(\hat{x}^1,\hat{x}^2;x,\hat{x}^{12}) =
\mathrm{cr}(\hat{x}^1, x_{(i)};x,\hat{x}^1_{(i)}) \,
\mathrm{cr}(x_{(i)}, \hat{x}^2;x,\hat{x}^2_{(i)}),
\end{equation}
which, due to equation \eqref{eq:cr-zeta-alpha}, is in agreement with
\eqref{eq:cr-zeta-sup}.
\section{Two dimensional generalized isothermic lattice}
\label{sec:isothermic}
In the previous Sections we were mainly interested in generalized isothermic
lattices of dimension greater then two. However, simultaneous application of
the B-constraint and the quadratic constraint lowers dimensionality of the
lattice (in the sense of the initial boundary value problem). One can see it
from Figure~\ref{fig:twotothree}, which implies that two intersecting strips
made of planar quadrialterals with vertices in a quadric (see
Figure~\ref{fig:isoth-init}) can be extended to a
two dimensional quadrilateral lattice in the quadric. Because of
Lemma~\ref{lem:half-hex} such lattice satisfies Steiner's
version of the cross-ratio constraint \eqref{eq:isoth-cr}.
\begin{figure}
\begin{center}
\includegraphics{isoth-init}
\end{center}
\caption{Two intersecting initial strips of a two dimensional generalized
isothermic lattice allow to build all the lattice. The additional transverse
quadrilateral allows to build the lattice (together wih its Darboux transform)
in a three dimensional fashion}
\label{fig:isoth-init}
\end{figure}
One can define however geometrically two dimensional generalized isothermic
lattices (generalized discrete isothermic surfaces) without using the
three dimensional construction. An important tool here is the projective
interpretation of the discrete Moutard equation \cite{DGNS} as representing
quadrilateral lattice with additional linear relation between
any of its points $x$ and its four second-order neighbours $x_{(\pm 1 \pm 2)}$.
Geometrically, such five points of a
\emph{two dimensional B-quadrilateral lattice}
are contained in a subspace of dimension three;
for generic two dimensional quadrilateral lattice such points are
contained in a subspace of dimension four. To exclude further degenerations we
assume that no of the four points $x_{\pm 1}$, $x_{\pm 2}$ belongs to that three
dimensional subspace.
\begin{Def}
A two dimensional B-quadrilateral lattice in a hyperquadric
$x:{\mathbb Z}^2\to\mathcal{Q}\subset{\mathbb P}^M$
satisfying the local irreducibility condition is called a
\emph{generalized discrete isothermic surface}.
\end{Def}
\begin{Rem}
Notice that the above Definition gives (the conclusion
was drawn by Alexander Bobenko) a geometric characterization of the
classical discrete isothermic surfaces of Bobenko and Pinkall. Mainly,
the non-trivial intersection of a three dimensional subspace with
the M\"{o}bius sphere
is a two dimensional sphere. After the stereographic projection,
which preserves co-sphericity of points, a discrete isothermic surface in
the M\"{o}bius (hyper)sphere gives \emph{circular two dimensional lattice
$s:{\mathbb Z}^2\to{\mathbb E}^M$ such that for
any of its points $s$ there exists a sphere containig the point
and its four second-order neighbours $s_{(\pm 1 \pm 2)}$}.
\end{Rem}
Notice that, actually, all calculations where we used simultaneously both the
discrete Moutard equation and the quadratic constraint (algebraic proofs of
Proposition~\ref{prop:cross-ratio-gen}, Theorem~\ref{th:Darboux} and
Proposition~\ref{prop:superp}) remain true for $N=2$. Therefore the
corresponding results on the cross-ratio characterization of generalized
discrete isothermic surfaces, their Darboux transformation and the Bianchi
superposition principle are still valid.
To complete this Section let us present the geometric construction of a
generalized discrete isothermic surface (see
Figure~\ref{fig:geom-constr-surf}).
\begin{figure}
\begin{center}
\includegraphics{geom-constr-surf}
\end{center}
\caption{Geometric construction of generalized discrete isothermic surfaces}
\label{fig:geom-constr-surf}
\end{figure}
The basic step of the construction, which allows to build the generalized
discrete isothermic surface from two initial quadrilateral strips in a quadric
in a two dimensional fashion can be discribed as follows. Consider
the four dimensional subspace
$V_4 = \langle x, x_{(1)}, x_{(2)}, x_{(-1)}, x_{(-2)} \rangle$, where
the basic step takes place. Denote by
$V_3 = \langle x, x_{(-1-2)}, x_{(-12)}, x_{(1-2)} \rangle$ its three
dimensional subspace passing through the points $x$, $x_{(-1-2)}$, $x_{(-12)}$
and $x_{(1-2)}$, and by $V_2 = \langle x, x_{(1)}, x_{(2)} \rangle$ the plane of
the elementary quatrilateral whose fourth vertex $x_{12}$ we are going to find.
In the
construction of the two dimensional B-quadrilateral lattice the vertex must
belong to the line $V_1 = V_3 \cap V_2$. In our case it should also belong to
the conic $\mathcal{C}=V_2 \cap \mathcal{Q}$. Because the conic contains
already one
point $x$ of the line $V_1$, the second point is unique. Notice that
although the points
$x_{(-1)}$ and $x_{(-2)}$ do not play any role in the construction, they
can be easily
recovered in a similar way as above.
\section{Conclusions and discussion}
In the paper we defined new integrable reduction of the lattice of planar
quadrilaterals, which contains as a particular example the discrete
isothermic surfaces. We studied, by using geometric and algebraic means, various
aspects of such generalized isothermic lattices. In particular, we defined the
(analogs of the) Darboux transformations for the lattices and we showed the
corresponding permutablity principle.
The theory of integrable systems is deeply connected with results of geometers
of the turn of XIX and XX centuries. The relation of integrability and geometry
is even more visible on the discrete level, where into the game there
enter basic results of the projective geometry. In our presentation of the
generalized isothermic lattices the basic geometric results were a variant of
the M\"{o}bius theorem and the generalization of the Miquel theorem to arbitrary
quadric, which combined together gave the corresponding generalization of the
Clifford theorem (known already to Miquel).
An important tool in our research was also Steiner's description
of conics and the geometric properties of von Staudt's algebra
(see Appendix~\ref{sec:cr}).
\section*{Acknowledgements}
I would like to thank to Jaros{\l}aw Kosiorek and Andrzej Matra\'{s} for discusions
cencerning incidence geometry and related algebraic questions.
The main part of the paper was
prepared during my work at DFG Research Center MATHEON in
Institut f\"{u}r Mathematik of the Technische Universit\"{a}t Berlin.
The paper was supportet also in part by the Polish Ministry of
Science and Higher Education research grant 1~P03B~017~28.
Finally, it is my pleasure to thank the organizers of the SIDE VII Conference
for support.
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 5,379
|
\section{\label{sec: introduction}Introduction}
Stochastic processes where small fragments merge and form larger ones
are quite useful tools to model physical phenomena at scales ranging
from molecular \cite{1943JChPh..11...45S} to astronomical ones \cite{Wetherill1990336}.
The majority of the mathematical literature on such coagulation processes
treats mean field models: The rate at which the fragments (clusters)
merge is governed only by their sizes - neither the physical location
nor their shape affect this rate. See \cite{MR2253162} for a review.
Stockmayer \cite{1943JChPh..11...45S}, introduced a mean field model
for polymerization where small clusters (sol) merge, however, as soon
as a large cluster (gel) forms, it stops growing. In contrast to the
mean field models, we consider a model which takes the geometry of
the space and the shape of the clusters into account. Following van
den Berg, de Lima and Nolin \cite{Berg2012a}, and Aldous \cite{Aldous2000},
we introduce the following adaptation of Stockmayer's model. Let $G=\left(V,E\right)$
be a graph which represents the underlying geometry and $N\in\mathbb{N}.$
For every vertex $v\in V,$ independently from each other, we assign
a random time $\tau_{v}$ which is uniformly distributed on $\left[0,1\right].$
At time $t=0,$ all of the vertices of $G$ are closed. As time increases,
a vertex $v$ tries to become open at time $t=\tau_{v}.$ It succeeds
if and only if all of its neighbours' open clusters (open connected
components) at time $t$ have size less than $N.$ Note that as soon
as the diameter of a cluster reaches $N,$ it stops growing, i.e freezes.
Hence the name $N$-parameter frozen percolation. Note that we can
also consider an edge (bond) version of the model above where edges
turn open from closed. This edge version of the process was introduced
by van den Berg et al \cite{Berg2012a}.
We are particularly interested in the $N$-parameter frozen percolation
models for large $N$ on graphs such as $d$ dimensional lattices,
since they are discrete approximations of the space $\mathbb{R}^{d}.$
Herein we restrict to the case where $d=2.$ We will mainly work on
the triangular lattice. We will see that the behaviour of this model
rich and interesting too, but in a very different way from the model
studied by Aldous \cite{Aldous2000}.
Let us turn to the model introduced and constructed by Aldous \cite{Aldous2000}.
It is the edge version of the model on the binary tree where we replace
the parameter $N$ by $\infty$ in the description above. An edge
$e$ of the binary tree opens at time $\tau_{e}$ as long as the open
clusters of the endpoints of $e$ are finite. In view of this model,
one could also try to construct a similar, so called $\infty$-parameter,
model on the triangular lattice. However Benjamini and Schramm \cite{Benjamini1999}
showed that it is impossible. Exactly this non-existence result motivated
van den Berg, de Lima and Nolin \cite{Berg2012a} to extend the model
of Aldous for finite parameter $N$: in this case, the $N$-parameter
frozen percolation process (both the vertex and the edge version)
is a finite range interacting particle system, hence the general theory
\cite{Liggett2005} gives existence. One could ask if the $N$-parameter
processes for large but finite $N$ provide a reason for the existence
of the $\infty$-parameter frozen bond percolation and the binary
tree and the non-existence of the $\infty$-parameter frozen site
percolation on the triangular lattice. Before we answer this question,
let us specify the two dimensional model which plays a central role
in this paper.
We will work on the triangular lattice $\mathbb{T}=\left(V,E\right)$
with its usual embedding in the plane $\mathbb{R}^{2}.$ That is,
the vertex set $V$ is the lattice generated by the vectors $\underline{e}_{1}=\left(1,0\right)$
and $\underline{e}_{2}=\left(\cos\left(\pi/3\right),\sin\left(\pi/3\right)\right):$
\begin{equation}
V:=\left\{ a\underline{e}_{1}+b\underline{e}_{2}\left|a,b\in\mathbb{Z}\right.\right\} .\label{eq: vertex set}
\end{equation}
The vertices $u$ and $v$ are neighbours, i.e $\left(u,v\right)\in E$
or $u\sim v$ if their $L^{2}$ distance is $1.$ Moreover, we freeze
clusters as soon as they reach $L^{\infty}$ diameter (inherited from
$\mathbb{R}^{2}$) at least $N.$ For the case where the underlying
lattice is $\mathbb{Z}^{2}$ and for different choices for diameters
of clusters see the discussion below Conjecture \ref{conj: scaling limit}.
Van den Berg, Kiss and Nolin \cite{ECP1694} investigated the edge
version of the $N$-parameter process on the binary tree. They found
that as $N\rightarrow\infty,$ the $N$-parameter process on the binary
tree converges to the $\infty$-parameter process in some weak sense.
This result raises the question if there is a limit of the $N$-parameter
frozen percolation processes on the triangular lattice as $N$ goes
to infinity. The non-existence of the $\infty$-parameter process
suggests that the $N$-parameter model may have a remarkable (anomalous)
behaviour in the limit $N\rightarrow\infty.$ It turns out that there
is a limiting process, but this process is, in some sense, trivial:
\begin{thm}
\label{thm: origin do not freeze}As $N\rightarrow\infty$ the probability
that in the $N$-parameter frozen percolation process the open cluster
of the origin freezes goes to $0.$
\end{thm}
To get some intuition for the behaviour of the process, let us for
the moment forget about freezing, and call the resulting process the
percolation process. That is, at time $\tau_{v}$ the vertex $v$
becomes open no matter how big are the open clusters of its neighbours.
Thus at time $t,$ a vertex $v$ is open with probability $t$ independently
from the other vertices. Hence at time $t$ we see ordinary site percolation
with parameter $t.$ Recall from \cite{Russo1981} that the critical
parameter for site percolation on the triangular lattice is $p_{c}=1/2.$
So at each time $t\leq1/2$ there is no open infinite cluster, and
there is a unique infinite open cluster when $t>1/2.$ Moreover, by
\cite{Aizenmann1987} at time $t<1/2,$ the distribution of the size
of the open clusters has an exponential decay. Note that if a site
is open in the $N$-parameter frozen percolation process at time $t,$
then it is also open in the percolation process at time $t.$ Hence
at time $t<1/2$ the $N$-parameter frozen percolation process and
the percolation process does not differ too much when $N$ is large:
even without freezing, for all $K>0$ the probability that there is
an open cluster with diameter at least $N$ in a box with side length
$KN$ goes to $0$ as $N\rightarrow\infty.$ To our knowledge, there
is no simple argument showing that, roughly speaking, freezing does
not take place at times that are essentially bigger than $1/2,$ which
is one of our main results:
\begin{thm}
\label{thm: no supercritical feezing}For all $K>0$ and $t>1/2,$
the probability that after time $t$ a frozen cluster forms which
intersects a given box with side length $KN$ goes to $0$ as $N\rightarrow\infty.$
\end{thm}
Compare Theorem \ref{thm: no supercritical feezing} with \cite{Aldous2000,Berg2012a}
where it was shown that clusters freeze throughout the time horizon
$\left[1/2,1\right]$ for $N\in\mathbb{N}\cup\left\{ \infty\right\} $
in the edge version of the $N$-parameter frozen percolation process
on the binary tree. (Note that the critical parameter is $1/2$ for
site percolation on the binary tree.) As it turns out, our method
provides a much stronger result than Theorem \ref{thm: no supercritical feezing}.
To state it we need some more notation.
Let $\mathbb{P}$ denote the probability measure corresponding to
the percolation process. For a fixed $p\in\left[0,1\right],$ we call
a vertex $v\in V$ $p$-open ($p$-closed), if its $\tau$ value is
less (greater) than $p.$ We denote by $\mathbb{P}_{p}$ the distribution
of $p$-open vertices.
We borrow some of the notation from \cite{Nolin2008}. Recall the
definition of $V$ from (\ref{eq: vertex set}). The $L^{\infty}$
distance of vertices in $\mathbb{T}$ is the $L^{\infty}$ distance
inherited from $\mathbb{R}^{2}.$ That is, for $v,w\in V$ the distance
$d\left(v,w\right)$ between $v=\left(v_{1},v_{2}\right)$ and $w=\left(w_{1},w_{2}\right)$
is
\begin{align*}
d\left(v,w\right) & =\left\Vert v-w\right\Vert _{\infty}\\
& =\max\left\{ \left|v_{1}-w_{1}\right|,\left|v_{2}-w_{2}\right|\right\} .
\end{align*}
For $a,b,c,d\in\mathbb{R},$ with $a<b,c<d$ we define the parallelogram
\[
\left[a,b\right]\boxtimes\left[c,d\right]:=\left\{ k\underline{e}_{1}+l\underline{e}_{2}\,|\, k\in\left[a,b\right]\cap\mathbb{Z},\, l\in\left[c,d\right]\cap\mathbb{Z}\right\} .
\]
We denote the outer boundary of a set of vertices $S\subseteq V$
by
\[
\partial S:=\left\{ v\in V\setminus S\,|\,\exists u\in S:\, u\sim v\right\} .
\]
Let $cl\left(S\right)=S\cup\partial S$ denote the closure of $S.$
For the parallelogram centred around the vertex $v$ with radius $a>0$
we write
\[
B\left(v;a\right):=\left[-a,a\right]\boxtimes\left[-a,a\right]+v.
\]
We denote the annulus centred around $v\in V$ with inner radius $a>0$
and outer radius $b>a$ by
\[
A\left(v;a,b\right):=B\left(v;b\right)\backslash B\left(v;a\right).
\]
We call $B\left(v;a\right)$ the inner, $B\left(v;b\right)$ the outer
parallelogram of $A\left(v;a,b\right).$
We say that there is an open (closed) arm in an annulus $A\left(v;a,b\right)$
if there is an open (closed) path from $\partial B\left(v;a\right)$
to $\partial B\left(v;b\right)$ in $A\left(v;a,b\right).$ We write
$o$ for open and $c$ for closed. A colour sequence of length $k$
is an element of $\left\{ o,c\right\} ^{k}.$ For $\sigma\in\left\{ o,c\right\} ^{k},$
we denote by $\mathcal{A}_{k,\sigma}\left(v;a,b\right)$ the event
that there are $k$ disjoint arms in $A\left(v;a,b\right)$ such that
the vertices of each of the arms are either all open or all closed,
moreover, if we take a counter-clockwise ordering of these arms, then
their colours follow a cyclic permutation of $\sigma.$
In the case where $v=\underline{0}=\left(0,0\right)$ we omit the
first argument in our notation, that is $B\left(a\right)=B\left(\underline{0};a\right)$
etc. For the critical arm probabilities we use the notation
\begin{equation}
\pi_{k,\sigma}\left(a,b\right):=\mathbb{P}_{1/2}\left(\mathcal{A}_{k,\sigma}\left(a,b\right)\right).\label{eq:crit arm prob}
\end{equation}
In the following we use the near critical parameter scale which was
introduced in \cite{Garban2010}. For a positive parameter $N$ and
$\lambda\in\mathbb{R}$ it is defined as
\begin{equation}
p_{\lambda}\left(N\right):=\frac{1}{2}+\lambda\frac{N^{-2}}{\pi_{4,alt}\left(1,N\right)}\label{eq:def p lambda}
\end{equation}
where $alt$ denotes the colour sequence $\left(o,c,o,c\right).$
Before we proceed, let us stop here and let us briefly explain the
formula (\ref{eq:def p lambda}). Suppose that a vertex $v$ is a
closed pivotal vertex, i.e. it is on the boundary of two different
open cluster with diameter at least $N.$ The two open clusters provide
two disjoint open arms starting from neighbouring vertices of $v.$
Since the open clusters are different, they have to be separated by
closed paths, which provide two disjoint closed arms starting from
$v.$ Hence the event $\mathcal{A}_{4,alt}\left(v;1,N\right)$ occurs.
By (\ref{eq:crit arm prob}), we get that the expected number of pivotal
vertices in $B\left(N\right)$ is $O\left(N^{2}\pi_{4,alt}\left(1,N\right)\right).$
Let $\lambda>0$. Let us look at the percolation process in the parallelogram
$B\left(N\right)$ in the time interval $\left[1/2,p_{\lambda}\left(N\right)\right].$
The probability that a vertex opens in this time interval is $p_{\lambda}\left(N\right)-1/2.$
By a combination of (\ref{eq:crit arm prob}) and (\ref{eq:def p lambda})
we see that the expected number of pivotal vertices which open in
this interval is $O\left(1\right).$ Hence the parameter scale in
(\ref{eq:def p lambda}) corresponds to the time scale where open
clusters of diameter $O\left(N\right)$ merge. See \cite{Garban2010,Garban}
for more details.
The considerations above suggest that the parameter scale (\ref{eq:def p lambda})
is indeed useful for investigating the $N$-parameter frozen percolation
process. We write $\mathbb{P}_{N}$ for the probability measure corresponding
to the $N$-parameter frozen percolation process. The following stronger
version of Theorem \ref{thm: no supercritical feezing} is our main
result.
\begin{thm}
\label{thm: main}For any $\varepsilon,K>0$ there exists $\lambda=\lambda\left(\varepsilon,K\right)$
and $N_{0}=N_{0}\left(\varepsilon,K\right)$ such that
\[
\mathbb{P}_{N}\left(\mbox{a cluster intersecting }B\left(KN\right)\mbox{ freezes after time }p_{\lambda}\left(N\right)\right)<\varepsilon
\]
for all $N\geq N_{0}.$
\end{thm}
In \cite{Berg2012a} the authors investigated the diameter of the
open cluster of the origin at time $1.$ Their main result is the
following.
\begin{defn}
\label{def: open cluster}For $t\in\left[0,1\right]$ let $C\left(v;t\right)$
denote the open cluster of $v\in V$ at time $t\in\left[0,1\right].$
We set $C\left(t\right):=C\left(\underline{0};t\right).$\end{defn}
\begin{thm}
[Theorem 1.1 of \cite{Berg2012a}] \label{thm: Rob, Bernardo, Pierre}For
the bond version of the $N$-parameter frozen percolation on the square
lattice we have
\[
\liminf_{N\rightarrow\infty}\mathbb{P}_{N}\left(diam\left(C\left(1\right)\right)\in\left(aN,bN\right)\right)>0
\]
for $a,b\in\left(0,1\right)$ with $a<b.$
\end{thm}
Analogous result holds for the (site version of) $N$-parameter process
on the triangular lattice. In the following corollary we supplement
this result. It is an extension of Theorem \ref{thm: origin do not freeze}.
\begin{cor}
\label{cor: macroscopic clusters}For any $\varepsilon>0$ there exists
$a=a\left(\varepsilon\right),b=b\left(\varepsilon\right)\in\left(0,1\right)$
with $a<b$ and $N_{0}=N_{0}\left(\varepsilon\right)$ such that
\[
\mathbb{P}_{N}\left(diam\left(C\left(1\right)\in\left(aN,bN\right)\right)\right)>1-\varepsilon
\]
for all $N\geq N_{0}.$
\end{cor}
The results above suggest the following intuitive and informal description
of the behaviour of $N$-parameter frozen percolation processes on
the triangular lattice for large $N$: At time $0$ all the vertices
are open. Then they open independently from each other as in the percolation
process till time close to $1/2.$ Then in the scaling window, frozen
clusters form, and by the end of the window, they give a tiling of
$\mathbb{T}$ such that all the holes (non-frozen connected components)
have diameter less than $N$ but, typically, of order $N.$ After
the window, the closed vertices in these holes open as in the percolation
process restricted to these holes. At time $1$ the non-frozen vertices
are all open.
Hence the interesting time scale is (\ref{eq:def p lambda}), moreover
it raises the question if there is some kind of limiting process which
governs the behaviour of the $N$-parameter frozen percolation processes
as $N\rightarrow\infty$ in the scaling window (\ref{eq:def p lambda}).
We have the following conjecture, somewhat informal, conjecture:
\begin{conjecture}
\label{conj: scaling limit}When we scale space by $N$ and time according
to (\ref{eq:def p lambda}), we get a non-trivial scaling limit, which
is measurable with respect to the near critical ensemble of \cite{Garban2010,Garban}.
Moreover, the scaling limit completely describes the frozen clusters
of the $N$-parameter frozen percolation as $N\rightarrow\infty.$
\end{conjecture}
Let us mention some generalizations of our results. We considered
the site version of the $N$-parameter frozen percolation on the triangular
lattice above. Straightforward adaptations of the proofs give the
same results for the bond version of the $N$-parameter frozen percolation
on the square lattice. See Remark \ref{rem: mod to square} for more
details. Our results remain valid when use some different distance
instead of the $L^{\infty}$ distance in the definition of the $N$-parameter
frozen percolation process, as long as the used distance resembles
the $L^{\infty}$ distance. Examples of such distances include the
$L^{p}$ distances for some $p\geq1,$ or when we rotate the lattice
$\mathbb{T}.$ Finally let us mention that when we freeze clusters
when their \emph{volume} (number of its vertices) reach $N,$ then
we get a quite different process.
\medskip
Let us briefly discuss some related results. A version of the $N$-parameter
frozen percolation process on $\mathbb{Z}$ and the binary tree was
investigated in \cite{Brouwer2005}. We already considered \cite{Aldous2000}
where Aldous introduced the $\infty$-parameter frozen percolation
process on the binary tree. However, we did not mention that this
model has an other interesting, so called self organized critical
(SOC), behaviour: For all $t>1/2,$ the distribution of the active
clusters at time $t$ have the same distribution as critical clusters.
Clearly, the $N$-parameter frozen percolation process on the triangular
lattice does not have this property. A mean field version of the frozen
percolation model on the complete graph investigated by R\'{a}th
in \cite{Rath2009}. He showed that this model has similar SOC properties.
Finally, we refer to \cite{Bertoin2010} where a dynamics similar
to frozen percolation was investigated on uniform Cayley trees.
\medskip
The organization of the paper is the following. In Section \ref{sec:notation and preliminary res},
we introduce some more notation, and briefly discuss the results from
percolation theory required to prove our main result: We start with
some classical correlation inequalities in Section \ref{sub: corr ineq}.
In Section \ref{sub: mixed arms} we introduce mixed arm events where
some of the arms can use only the upper half of the annulus, while
others can use the whole annulus. Here we also recall some of their
well-known properties and discuss some new ones. In particular, we
note that the exponent of the arm events increases when we increase
the number of arms which have to stay in the upper half plane. The
proof of this statement is postponed to Section \ref{sub: winding}
of the Appendix. In Section \ref{sub: near crit scale - corr length}
we describe the connection between the correlation length with the
near critical scaling (\ref{eq:def p lambda}). We prove Theorem \ref{thm: main}
and Corollary \ref{cor: macroscopic clusters} in Section \ref{sec: pf main}
assuming two technical results Proposition \ref{prop: active diameter}
and \ref{prop: big then freeze}. In Section \ref{sec: pf prop big then freeze}
we introduce some more notation and the notion of thick paths. There
we prove Proposition \ref{prop: big then freeze}. In this proof a
deterministic (combinatorial/geometric) result, Lemma \ref{lem: det gridpath},
plays an important role. The proof of this lemma is postponed to Section
\ref{sub: there are thick paths} of the Appendix. The most technical
part of the paper is Section \ref{sec: pf of prop active diameter}
where we prove Proposition \ref{sec: pf of prop active diameter}.
In Section \ref{sub: lowest of lowest in parallelograms} and \ref{sub: lowesr of lowest in reular regions}
we investigate the vertical position of the lowest point of the lowest
closed crossing in regions with half open half closed boundary conditions.
We combine these results with the ones in Section \ref{sec:notation and preliminary res}
and conclude the proof of Proposition \ref{prop: active diameter}
in Section \ref{sec: pf prop big then freeze}. This finishes the
proof of the main result.
\section*{Acknowledgement}
The author thanks Jacob van den Berg, Federico Camia, Pierre Nolin
and G\'{a}bor Pete for fruitful discussions. He thanks G\'{a}bor
Pete and Art\"{e}m Sapozhnikov for calling his attention to Lemma
\ref{lem: near critical arms}, which was instrumental in the proof
of the main result. He is grateful to Jacob van den Berg for his numerous
comments on the earlier versions of the paper.
\section{\label{sec:notation and preliminary res}Preliminary results on near
critical percolation}
We recall some classical results from percolation theory in this section.
With suitable modifications, the results of this section also hold
for bond percolation on the square lattice unless it is indicated
otherwise.
\subsection{\label{sub: corr ineq}Correlation inequalities}
We use the following two inequalities throughout the paper. See Section
2.2 and 2.3 of \cite{Grimmett1999} for more details. We refer to
the first theorem as BK, and as FKG for the second.
\begin{thm}
[BK]\label{thm: BK}Let $A,B$ be arbitrary events, then
\[
\mathbb{P}_{p}\left(A\square B\right)\leq\mathbb{P}_{p}\left(A\right)\mathbb{P}_{p}\left(B\right).
\]
\end{thm}
\begin{defn}
\label{def: inc events}Let $A\subset\left\{ o,c\right\} ^{V}$ and
$U\subseteq V.$ We say that an event $A\subset\left\{ o,c\right\} ^{V}$
is increasing (decreasing) in the configuration in $U,$ if for all
$\omega\in A$ we have $\omega'\in A$ where
\[
\omega'\left(v\right)=\begin{cases}
\omega\left(v\right)\mbox{ or }o\mbox{ (}c\mbox{)} & \mbox{for }v\in U\\
\omega\left(v\right) & \mbox{for }v\in V\setminus U.
\end{cases}
\]
That is, turning some closed (open) vertices in $U$ into open (closed)
ones can only help the occurrence of $A.$ In the case where $U=V$
we simply say that $A$ is an increasing (decreasing) event. \end{defn}
\begin{thm}
[FKG] \label{thm: FKG}For any pair of increasing events $A,B$ we
have
\[
\mathbb{P}_{p}\left(A\cap B\right)\geq\mathbb{P}_{p}\left(A\right)\mathbb{P}_{p}\left(B\right).
\]
\end{thm}
\subsection{\label{sub: mixed arms}Mixed arm events, critical arm exponents}
Recall the definition of arm events from the introduction. There the
arms were allowed to use the whole annulus. We introduce the mixed
arm events, where some of the arms lie in the upper half of the annulus,
while others can use the whole annulus:
\begin{defn}
\label{def: full plane mixed arms}Let $l,k\in\mathbb{N}$ with $0\leq l\leq k,$
and a colour sequence $\sigma$ of length $k.$ Let $v\in V$ and
$a,b\in\left(1,\infty\right)$ with $a<b.$ The the full plane $k,l$
mixed arm event with colour sequence $\sigma$ in the annulus $A\left(v;a,b\right)$
is denoted by $\mathcal{A}_{k,l,\sigma}\left(v;a,b\right).$ It is
the normal $k$ arm event $\mathcal{A}_{k,\sigma}\left(v;a,b\right)$
of the Introduction with the extra the condition that there is a counter-clockwise
ordering of the arms such that the colour of the arms follow $\sigma,$
and the first $l$ arms lie in the half annulus $A\left(v;a,b\right)\cap\left(\mathbb{Z}\boxtimes\left[0,\infty\right)+v\right)$.
When $v=0,$ we omit the first argument from these notations.
We extend the definition (\ref{eq:crit arm prob}) for mixed arm events
by defining
\[
\pi_{k,l,\sigma}\left(a,b\right):=\mathbb{P}_{1/2}\left(\mathcal{A}_{k,l,\sigma}\left(a,b\right)\right).
\]
\end{defn}
\begin{rem}
In the case $k=l,$ we get the so called half plane arm events.
\end{rem}
We fix $n_{0}\left(k\right)=10k$ for $k\in\mathbb{N}.$ Note that
the event $\mathcal{A}_{k,l,\sigma}\left(n,N\right)$ is non-empty
whenever $n_{0}\left(k\right)<n<N.$ Let us summarize the known critical
arm exponents for site percolation on the triangular lattice. To our
knowledge, Theorem \ref{thm: arm exponents} in its generality is
not known to hold for bond percolation on $\mathbb{Z}^{2}.$
\begin{thm}
[Theorem 3 and 4 of \cite{Smirnov2001}]\label{thm: arm exponents}
Let $l,k\in\mathbb{N}$ and $\sigma$ be a colour sequence of length
$k.$ We define $a_{k,l}\left(\sigma\right)$
\begin{itemize}
\item for $k=1,\,$$l=0$ and any colour sequence $\sigma$ as
\[
\alpha_{1,0}\left(\sigma\right):=\frac{5}{48},
\]
\item for $k>1$ and $l=0,$ when $\sigma$ contains both colours, as
\[
\alpha_{k,0}\left(\sigma\right):=\frac{k^{2}-1}{12},
\]
\item for $k=l\geq1$ and any colour sequence $\sigma$ as
\[
\alpha_{k,k}\left(\sigma\right):=\frac{k\left(k+1\right)}{6}.
\]
\end{itemize}
In these cases we have
\[
\pi_{k,l,\sigma}\left(n_{0}\left(k\right),N\right)=N^{-\alpha_{k,l}\left(\sigma\right)+o\left(1\right)}
\]
as $N\rightarrow\infty,$
\end{thm}
To our knowledge, for general $k$ and $l,$ neither the value, nor
the existence of the exponents is not known. We expect that the exponents
do exist. We will see in Proposition \ref{prop: gen mixed arm exp},
that if $\alpha_{k,l}\left(\sigma\right)$ and $\alpha_{k,m}\left(\sigma\right)$
exists for some $k,l,m\in\mathbb{N}$ and $\sigma\in\left\{ o,c\right\} ^{k}$
with $m<l$ , then $\alpha_{k,m}\left(\sigma\right)<\alpha_{k,l}.$
Since we do not need such general result, we only prove the following
proposition in detail.
\begin{prop}
\label{prop: mixed arm exp}For any $k\geq1,$ there are positive
constants $c=c\left(k\right),\,\varepsilon=\varepsilon\left(k\right)$
such that
\begin{equation}
\pi_{k,l,\sigma}\left(n_{0}\left(k\right),N\right)\leq cN^{-\varepsilon}\pi_{k,0,\sigma}\left(n_{0}\left(k\right),N\right)\label{eq: mixed arm exp}
\end{equation}
for $l=1,2,\ldots,k$ uniformly in $N$ and in the colour sequence
$\sigma.$\end{prop}
\begin{rem}
\label{rem: arms with exponent 2}(i) We do not need the exact values
of the critical exponents of Theorem \ref{thm: arm exponents}. For
our purposes it is enough to show that certain arm events have exponents
at least $2.$
(ii) Proposition \ref{prop: mixed arm exp} and its generalization
also hold for mixed arm events in bond percolation on the square lattice. \end{rem}
\begin{proof}
[Proof of Proposition \ref{prop: mixed arm exp}] Proposition \ref{prop: mixed arm exp}
is a simple corollary of Proposition \ref{prop: arms do wind} of
the Appendix. Loosely speaking, it states that conditioning on the
event that we have $k$ arms in $A\left(a,b\right),$ these arms wind
around the centre of the annulus $O\left(\log\left(b/a\right)\right)$
many times with probability $1-\left(\frac{b}{a}\right)^{\kappa}$
for some $\kappa>0.$ The proof of Proposition \ref{prop: arms do wind}
can be found in the Appendix.\end{proof}
\begin{rem}
\label{rem: ord big arm exp} Recall that we do not know in general
if the exponents $\alpha_{k,l}\left(\sigma\right)$ exist or not.
Nonetheless, on the triangular lattice, Proposition \ref{prop: mixed arm exp}
and Theorem \ref{thm: arm exponents} and the BK inequality (Theorem
\ref{thm: BK}) give that for any colour sequence $\sigma,$ there
is an upper bound with exponent strictly larger than $2$ for $\pi_{k,l,\sigma}\left(n_{0}\left(k\right),N\right)$
when
\begin{itemize}
\item $k\geq6,$ and $l\geq0,$ or
\item $k\geq5$ and $l\geq1,$ or
\item $k\geq4$ and $l\geq3$.
\end{itemize}
For arm events with exponents larger than $2$ in the case of bond
percolation on the square lattice see Remark \ref{rem: arms in square lattice}
below.
\end{rem}
An other well-known attribute of critical arm events is their quasi-multiplicative
property. For the full plane, respectively for half plane, arm events
this property is shown to hold in Proposition 17 of \cite{Nolin2008},
respectively in Section 1.4.6 of \cite{Nolin2008}. Simple modifications
of these arguments apply to mixed arm events. We introduce the notation
$\asymp$ when the ratio of the two quantities is bounded away from
$0$ and $\infty.$ With this notation we get:
\begin{prop}
\label{prop: quasi-multiplivativity}Let $k\geq1$ and $\sigma\in\left\{ o,c\right\} ^{k}.$
Then
\begin{align*}
\pi_{k,l,\sigma}\left(n_{1},n_{2}\right)\pi_{k,l,\sigma}\left(n_{2},n_{3}\right) & \asymp\pi_{k,l,\sigma}\left(n_{1},n_{3}\right)
\end{align*}
uniformly in $n_{0}\left(k\right)\leq n_{1}\leq n_{2}\leq n_{3}.$
\end{prop}
In the following lemma we consider arm events where the open arms
are $p$-open and the closed arms are $q$-closed where $p,q\in\left[0,1\right]$
with $p$ not necessarily equal to $q.$ When $p$ and $q$ are of
the form (\ref{eq:def p lambda}), then we call these arm events near
critical arm events. In this case the probabilities of these events
are comparable to critical arm event probabilities. The following
lemma is a generalization of Lemma 2.1 of \cite{Garban2008} and Lemma
6.3 of \cite{Damron2009}.
\begin{lem}
\label{lem: near critical arms} Let $v\in V,$ $\lambda_{1},\lambda_{2}\in\mathbb{R}$
and $a,b\in\left(0,1\right)$ with $a<b.$ Let $\mathcal{A}_{k,l,\sigma}^{\lambda_{1},\lambda_{2},N}\left(v;aN,bN\right)$
denote the modification of the event $\mathcal{A}_{k,l,\sigma}\left(v;aN,bN\right)$
where the open arms are $p_{\lambda_{2}}\left(N\right)$-open and
the closed arms are $p_{\lambda_{1}}\left(N\right)$-closed. Then
there are positive constants $c=c\left(\lambda_{1},\lambda_{2},k\right)$
and $N_{0}=N_{0}\left(\lambda_{1},\lambda_{2},a,b,k\right)$ such
that
\[
\mathbb{P}\left(\mathcal{A}_{k,l,\sigma}^{\lambda_{1},\lambda_{2},N}\left(v;aN,bN\right)\right)\leq c\pi_{k,l,\sigma}\left(aN,bN\right)
\]
for $N\geq N_{0}.$\end{lem}
\begin{proof}
[Proof of Lemma \ref{lem: near critical arms}] It follows from
either of the proof of Lemma 2.1 of \cite{Garban2008} or from the
adaptation of the proof of Lemma 6.3 of \cite{Damron2009} to the
triangular lattice.
\end{proof}
In the following events we collect some of the near critical arm events
which have upper bounds with exponents strictly larger than $2.$
These events play a crucial role in our main result.
\begin{defn}
\label{def: NA}Let $a,b\in\left(0,1\right),$ $\lambda_{1},\lambda_{2}\in\mathbb{R},$
$K>0$ and $N\in\mathbb{N}$ with $a<b.$ Let $\mathcal{NA}^{c}\left(a,b,\lambda_{1},\lambda_{2},K,N\right)$
denote the union of the events $\mathcal{A}_{k,l,\sigma}^{\lambda_{1},\lambda_{2},N}\left(v;aN,bN\right)$
for $\left(k,l\right)\in\left\{ \left(4,3\right),\left(5,1\right),\left(6,0\right)\right\} ,$
$\sigma\in\left\{ o,c\right\} ^{k}$ as well as the versions of these
events where the half plane arms can only use the lower, left or right
half of the annulus $A\left(v;aN,bN\right).$ We define $\mathcal{NA}\left(a,b,\lambda_{1},\lambda_{2},K,N\right)$
as the complement of the event above.
\end{defn}
We show that that for fixed $b,K,\lambda_{1}$ and $\lambda_{2},$
we can set $a\in\left(0,1\right)$ so that the probability of $\mathcal{NA}\left(a,b,\lambda_{1},\lambda_{2},K,N\right)$
becomes as small as we require for large $N.$ More precisely, we
prove the following:
\begin{cor}
\label{cor: no many arms}There is $\tilde{\varepsilon}>0$ such that
for all $a,b\in\left(0,1\right),$ with $a<b$ and $\lambda_{1},\lambda_{2}\in\mathbb{R}$
there are positive constants $c=c\left(\lambda_{1},\lambda_{2},K\right)$
and $N_{0}=N_{0}\left(a,b,\lambda_{1},\lambda_{2},K\right)$ such
that
\[
\mathbb{P}\left(\mathcal{NA}\left(a,b,\lambda_{1},\lambda_{2},K,N\right)\right)\geq1-c\frac{a^{\tilde{\varepsilon}}}{b^{2+\tilde{\varepsilon}}}
\]
for $N\geq N_{0}.$\end{cor}
\begin{proof}
[Proof of Corollary \ref{cor: no many arms}] Suppose that one of
the arm events in Definition \ref{def: NA}, for example $\mathcal{A}_{k,l,\sigma}^{\lambda_{1},\lambda_{2},N}\left(v;aN,bN\right)$
for some $v\in B\left(KN\right),$ occurs. Then the event $\mathcal{A}_{k,l,\sigma}^{\lambda_{1},\lambda_{2},N}\left(\left\lfloor 2aN\right\rfloor z;2aN,\frac{b}{2}N\right)$
occurs for some $z\in V$ with $z\in B\left(\left\lceil \frac{a+K}{2a}\right\rceil \right).$
Combination of Remark \ref{rem: ord big arm exp} and Lemma \ref{lem: near critical arms}
gives that there are constants $c'=c'\left(\lambda_{1},\lambda_{2}\right)$
and $N_{0}=N_{0}\left(a,b,\lambda_{1},\lambda_{2}\right),$ and a
universal constant $\tilde{\varepsilon}>0$ such that the probability
of one of these events is at most
\begin{equation}
c'\left(\frac{2a}{b/2}\right)^{2+\varepsilon}\label{eq: pf cor no many arms}
\end{equation}
for $N\geq N_{0}.$ The same argument works for other arm events which
appear in Definition \ref{def: NA}, and provide an upper bound similar
to (\ref{eq: pf cor no many arms}). Hence (\ref{eq: pf cor no many arms})
combined with $\left|B\left(\left\lceil \frac{a+K}{2a}\right\rceil \right)\right|=O\left(a^{-2}\right)$
concludes the proof of Corollary \ref{cor: no many arms}.\end{proof}
\begin{rem}
\label{rem: arms in square lattice}To our knowledge it is not known
if the direct analogue of Corollary \ref{cor: no many arms} holds
on the square lattice. The reason is that the exponent $\alpha_{5,0}\left(\sigma\right)$
and $\alpha_{3,3}\left(\sigma\right)$ is not known for general $\sigma.$
See Remark 26 of \cite{Nolin2008}.
We recall the proof of Theorem 24 and Remark 26 of \cite{Nolin2008},
where it is shown that $\alpha_{5,0}\left(o,c,o,o,c\right)=2$ and
$\alpha_{3,3}\left(c,o,c\right)=2$ on the square lattice. This implies
that a version of Corollary \ref{cor: no many arms} holds for the
square lattice if we modify Definition \ref{def: NA} so that we only
forbid the occurrence of those arm events where the required set of
arms contain
\begin{itemize}
\item three half plane arm events with colour sequence $\left(o,c,o\right)$
or $\left(c,o,c\right),$ or
\item five full plane arms with colour sequence $\left(o,c,o,o,c\right)$
or $\left(c,o,c,c,o\right)$
\end{itemize}
as a subset.
\end{rem}
\subsection{\label{sub: near crit scale - corr length}Near-critical scaling
and correlation length}
Recall that in Section \ref{sec: introduction} we already gave an
explanation for the near critical parameter scale (\ref{eq:def p lambda}).
In this section we give an other interpretation of this parameter
scale, which is connected to the correlation length introduced by
Kesten in \cite{Kesten1987}.
We say that there is an open (closed) horizontal (vertical) crossing
of a parallelogram $B:=\left[a,b\right]\boxtimes\left[c,d\right]$
if there is an open (closed) path connecting $\left\{ \left\lceil a\right\rceil \right\} \boxtimes\left[c,d\right]$
and $\left\{ \left\lfloor b\right\rfloor \right\} \boxtimes\left[c,d\right]$
in$\left[a,b\right]\boxtimes\left[c,d\right].$ For the event that
there is an open (closed) horizontal crossing of $B$ we use the notation
$\mathcal{H}_{o}\left(B\right)$ ($\mathcal{H}_{c}\left(B\right)$).
One can define similar events for vertical crossings, which we denote
by by $\mathcal{V}_{o}\left(B\right)$ and $\mathcal{V}_{c}\left(B\right).$
For $\varepsilon\in\left(0,1/2\right)$ the correlation length is
defined as
\[
L_{\varepsilon}\left(p\right)=\begin{cases}
\min\left\{ n\,|\,\mathbb{P}_{p}\left(\mathcal{H}_{o}\left(B\left(n\right)\right)\right)\leq\varepsilon\right\} & \mbox{when }p<p_{c}\\
\min\left\{ n\,|\,\mathbb{P}_{p}\left(\mathcal{H}_{o}\left(B\left(n\right)\right)\right)\geq1-\varepsilon\right\} & \mbox{when }p>p_{c}.
\end{cases}
\]
\begin{rem}
The particular choice of $\varepsilon$ is not important in this definition.
Indeed, Corollary 37 of \cite{Nolin2008}, or alternatively Corollary
2 of \cite{Kesten1987}, gives that
\[
L_{\varepsilon}\left(p\right)\asymp L_{\varepsilon'}\left(p\right)
\]
for any $\varepsilon,\varepsilon'\in\left(0,1/2\right)$ uniformly
in $p\in\left(0,1\right).$
\end{rem}
\medskip
We show that the control over the near critical parameter $\lambda$
gives a control over the correlation length in Corollary \ref{cor: char length is O(N)}
and \ref{cor: small char length} below. Recall the remark after Lemma
8 of \cite{Kesten1987}:
\begin{prop}
\label{prop: Kesten}For any fixed $\varepsilon\in\left(0,1/2\right),$
we have
\[
\left|p-p_{c}\right|\left(L_{\varepsilon}\left(p\right)\right)^{2}\pi_{4,0,alt}\left(1,L_{\varepsilon}\left(p\right)\right)\asymp1
\]
uniformly for $p\neq1/2.$
\end{prop}
Note that for fixed $\varepsilon>0,$ the correlation length $L_{\varepsilon}\left(p\right)$
is a decreasing (increasing) function of $p$ for $p>p_{c}$ ($p<p_{c}$).
Combination of this and Proposition \ref{prop: quasi-multiplivativity}
we get:
\begin{cor}
\label{cor: char length is O(N)}For all $\lambda\in\mathbb{R}\setminus\left\{ 0\right\} $
and $\varepsilon\in\left(0,1/2\right),$
\begin{equation}
L_{\varepsilon}\left(p_{\lambda}\left(N\right)\right)\asymp N.\label{eq: bd on corr length}
\end{equation}
\end{cor}
\begin{cor}
\label{cor: small char length}For any $C>0$ and $\varepsilon\in\left(0,1/2\right)$
there exits $\lambda_{1}=\lambda_{1}\left(C,\varepsilon\right)>0$
and $N_{1}=N_{1}\left(C,\varepsilon\right)$ such that for any $\lambda\in\mathbb{R}$
with $\left|\lambda\right|\geq\lambda_{1}$ we have
\[
L_{\varepsilon}\left(p_{\lambda}\left(N\right)\right)\leq CN
\]
for $N\geq N_{1}.$ Also, for any $c>0,$ and $\varepsilon\in\left(0,1/2\right)$
there exists $\lambda_{2}\left(c,\varepsilon\right)>0$ and $N_{2}=N_{2}\left(c,\varepsilon\right)$
such that for any $\lambda\in\mathbb{R}\setminus\left\{ 0\right\} $
with $\left|\lambda\right|\leq\lambda_{2}$ we have
\[
L_{\varepsilon}\left(p_{\lambda}\left(N\right)\right)\geq cN
\]
for $N\geq N_{2}.$\end{cor}
\begin{rem}
On the triangular lattice, a ratio limit theorem for $\pi_{4,0,alt},$
Proposition 4.7 of \cite{Garban2010} holds. This combined with the
definition of $L_{\varepsilon}\left(p\right),$ and Proposition \ref{prop: Kesten}
shows that the following stronger statement holds on the triangular
lattice:
\begin{claim*}
For all $\lambda_{1},\lambda_{2}\in\mathbb{R}$ with $\lambda_{1}\leq\lambda_{2},$
$\lambda_{1}\lambda_{2}>0$ and $\varepsilon\in\left(0,1/2\right)$
there are positive constants $c=c\left(\varepsilon\right),C=C\left(\varepsilon\right)$
and $N_{0}=N_{0}\left(\varepsilon,\lambda_{1},\lambda_{2}\right)$
such that
\[
cN\left|\lambda\right|^{-4/3}\leq L_{\varepsilon}\left(p_{\lambda}\left(N\right)\right)\leq CN\left|\lambda\right|^{-4/3}
\]
for all $\lambda\in$$\left[\lambda_{1},\lambda_{2}\right]$ and $N\geq N_{0}.$
\end{claim*}
\end{rem}
Standard Russo-Seymour-Welsh (RSW) techniques and the definition of
the correlation length give that the control over the correlation
length gives a control over the crossing probabilities of parallelograms.
This combined with the two corollaries above show that that the control
over the near critical parameter gives a control over the crossing
probabilities. See Corollary \ref{cor: posprob of crossing} and \ref{cor: set prob of crossing}
below:
\begin{cor}
\label{cor: posprob of crossing}For all $\lambda\in\mathbb{R}$ and
$a,b\in\left(0,\infty\right),$ there are constants $c=c\left(a,b,\lambda\right)\in\left(0,1\right),$
$C=C\left(a,b,\lambda\right)\in\left(0,1\right)$ and $N_{0}=N_{0}\left(a,b,\lambda\right)$
with such that
\begin{align*}
c & <\mathbb{P}_{p_{\lambda}\left(N\right)}\left(\mathcal{H}_{o}\left(\left[0,aN\right]\boxtimes\left[0,bN\right]\right)\right)<C\\
c & <\mathbb{P}_{p_{\lambda}\left(N\right)}\left(\mathcal{H}_{c}\left(\left[0,aN\right]\boxtimes\left[0,bN\right]\right)\right)<C
\end{align*}
for $N\geq N_{0}.$
\end{cor}
\begin{cor}
\label{cor: set prob of crossing}Let $\delta\in\left(0,1\right),$
and $a,b\in\left(0,\infty\right).$ There exists $\lambda_{1}=\lambda_{1}\left(\delta,a,b\right)>0$
and $N_{1}=N_{1}\left(\delta,a,b\right)$ such that for all $\lambda\geq\lambda_{1}$
\[
\mathbb{P}_{p_{\lambda}\left(N\right)}\left(\mathcal{H}_{o}\left(\left[0,aN\right]\boxtimes\left[0,bN\right]\right)\right)>1-\delta
\]
for $N\geq N_{1}.$ Furthermore, there exists $\lambda_{2}=\lambda_{2}\left(\delta,a,b\right)<0$
and $N_{2}=N_{2}\left(\delta,a,b\right)$ such that for all $\lambda\leq\lambda_{2}$
\[
\mathbb{P}_{p_{\lambda}\left(N\right)}\left(\mathcal{H}_{c}\left(\left[0,aN\right]\boxtimes\left[0,bN\right]\right)\right)>1-\delta
\]
for $N\geq N_{2}.$
\end{cor}
Similar RSW techniques show that it is unlikely to have crossing in
a thin and long parallelogram in the hard direction in the critical
window. See Remark 40 \cite{Nolin2008} for more details.
\begin{cor}
\label{cor: thin crossing}Let $\lambda\in\mathbb{R},$ and $a,b\in\left(0,1\right).$
There exists positive constants $c=c\left(\lambda\right),C=C\left(\lambda\right)$
and $N_{0}=N_{0}\left(\lambda,a,b\right)$ such that
\[
\mathbb{P}_{p_{\lambda}\left(N\right)}\left(\mathcal{H}_{o}\left(\left[0,aN\right]\boxtimes\left[0,bN\right]\right)\right)\leq C\exp\left(-c\frac{a}{b}\right)
\]
for $N\geq N_{0}.$
\end{cor}
The following event plays a crucial role in the proof of our main
result.
\begin{defn}
Let $a,b\in\left(0,1\right),$ $\lambda_{1},\lambda_{2}\in\mathbb{R},$
and $N\in\mathbb{N}$ with $a<b.$ Let $\mathcal{NC}\left(a,b,\lambda_{1},\lambda_{2},K,N\right)$
denote the event that for all parallelograms $B=\left[0,aN\right]\boxtimes\left[0,bN\right]+z$
with $z\in B\left(KN\right),$ there is neither a $p_{\lambda_{1}}\left(N\right)$-open
nor a $p_{\lambda_{2}}\left(N\right)$-closed horizontal crossing
in $B.$
\end{defn}
The following Corollary \ref{cor: no thin crossing} follows from
Corollary \ref{cor: thin crossing} by arguments analogous to the
proof of Corollary \ref{cor: no many arms}.
\begin{cor}
\label{cor: no thin crossing}Let $a,b\in\left(0,1\right),$ $\lambda_{1},\lambda_{2}\in\mathbb{R},$
and $N\in\mathbb{N}$ with $a<b.$ There are positive constants $c=c\left(\lambda_{1},\lambda_{2}\right),\, C=C\left(\lambda_{1},\lambda_{2}\right)$
and $N_{0}=N_{0}\left(a,b,\lambda_{1},\lambda_{2}\right)$ such that
\[
\mathbb{P}\left(\mathcal{NC}\left(a,b,\lambda_{1},\lambda_{2},K,N\right)\right)\geq1-Ca^{-2}\exp\left(-c\frac{b}{a}\right)
\]
for $N\geq N_{0}.$
\end{cor}
We finish this section by stating two lemmas which will be used explicitly
in the proof of our main result.
\begin{lem}
\label{lem: not too many small clusters at lambda}For any fixed $\lambda\in\mathbb{R},$
for any $a,b\in\left(0,\infty\right)$ and $\varepsilon>0,$ there
is are positive integer $K=K\left(\lambda,a,b,\varepsilon\right)$
and $N_{0}=N_{0}\left(\lambda,a,b,\varepsilon\right)$ such that
\[
\mathbb{P}_{p_{\lambda}\left(N\right)}\left(\mbox{there are at least }K\mbox{ disjoint closed arms in }A\left(aN,bN\right)\right)<\varepsilon
\]
for $N\geq N_{0}.$\end{lem}
\begin{proof}
[Proof of Lemma \ref{lem: not too many small clusters at lambda}]
This is a consequence of Corollary \ref{cor: posprob of crossing}
and the BK inequality (Theorem \ref{thm: BK}). The proof also also
appears in the proof of Lemma 15 of \cite{Nolin2008}. \end{proof}
\begin{defn}
\label{def: N_c} Let $a,b,c,d,f\in\mathbb{R}$ with $a\leq b,$ $c\leq d$
and $f>0.$ We say that there is an open (closed) $f$-net in $B=\left[a,b\right]\boxtimes\left[c,d\right]$
if there is an open (closed) vertical crossing in the parallelograms
$\left[a+i\left\lfloor f\right\rfloor ,a+\left(i+1\right)\left\lfloor f\right\rfloor -1\right]\boxtimes\left[c,d\right],$
and there is an open (closed) horizontal crossing in the parallelograms
$\left[a,b\right]\boxtimes\left[c+j\left\lfloor f\right\rfloor ,c+\left(j+1\right)\left\lfloor f\right\rfloor -1\right]$
for $i=0,1,\ldots,\left\lfloor \left(b-a\right)/\left\lfloor f\right\rfloor \right\rfloor $
and $j=0,1,\ldots,\left\lfloor \left(d-c\right)/\left\lfloor f\right\rfloor \right\rfloor .$
For $\lambda\in\mathbb{R}$ and $\delta\in\left(0,\infty\right),$
$\mathcal{N}_{c}\left(\lambda,\delta,K,N\right)$ ($\mathcal{N}_{o}\left(\lambda,\delta,K,N\right)$)
denotes the event that there is a $p_{\lambda}\left(N\right)$-closed
($p_{\lambda}\left(N\right)$-open) $\delta N$-net in $B\left(KN\right).$\end{defn}
\begin{lem}
\label{lem: there is a net}Let $\varepsilon,\delta,K>0.$ There exists
$\lambda_{1}=\lambda_{1}\left(\varepsilon,\delta,K\right)\in\mathbb{R}$
and $N_{1}=N_{1}\left(\varepsilon,\delta,K\right)$ such that
\[
\mathbb{P}\left(\mathcal{N}_{o}\left(\lambda_{1},\delta,K,N\right)\right)>1-\varepsilon
\]
for $N\geq N_{1}.$ Moreover there exists $\lambda_{2}=\lambda_{2}\left(\varepsilon,\delta,K\right)\in\mathbb{R}$
and $N_{2}=N_{2}\left(\varepsilon,\delta,K\right)$ such that
\[
\mathbb{P}\left(\mathcal{N}_{c}\left(\lambda_{2},\delta,K,N\right)\right)>1-\varepsilon
\]
for $N\geq N_{2}.$\end{lem}
\begin{proof}
[Proof of Lemma \ref{lem: there is a net}] This is a consequence
of Corollary $\ref{cor: set prob of crossing}$ and Theorem \ref{thm: FKG}.
\end{proof}
\section{\label{sec: pf main}Proof of the main results}
We prove our main results Theorem \ref{thm: main} and Corollary \ref{cor: macroscopic clusters}
in this section assuming Proposition \ref{prop: active diameter}
and \ref{prop: big then freeze}.
\begin{defn}
In the $N$-parameter frozen percolation process we call a vertex
\emph{frozen} at some time $t\in\left[0,1\right]$, if either it or
one of its neighbours have an open cluster with diameter bigger than
$N$ at time $t.$ If a site is not frozen at time $t,$ then we say
it is \emph{active} at time $t.$ Note that both frozen and active
sites can be open or closed. We say that $F$ is a \emph{(open) frozen
cluster} at time $t\in\left[0,1\right]$ if it is a connected component
of the open vertices at time $t$ with $diam\left(F\right)\geq N.$
In the case where $t=1,$ we simply say that $F$ is a frozen cluster.
\end{defn}
Recall Definition \ref{def: N_c}. We observe the following.
\begin{obs} \label{obs: closed grid-> no freezing}Let $K>0$ and
$N\in\mathbb{N}.$ Then in the $N$-parameter frozen percolation process
there is no frozen cluster at time $p_{\lambda}\left(N\right)$ in
$B\left(KN\right)$ on the event $\mathcal{N}_{c}\left(\lambda,1/6,K+2,N\right).$
Hence on $\mathcal{N}_{c}\left(\lambda,1/6,K+2,N\right),$ a vertex
in $B\left(KN\right)$ is open (closed) in the $N$-parameter frozen
percolation process at time $p_{\lambda}\left(N\right)$ if and only
if it is $p_{\lambda}\left(N\right)$-open ($p_{\lambda}\left(N\right)$-closed).
\end{obs}
We show that the number of frozen clusters intersecting $B\left(KN\right)$
in the $N$-parameter frozen percolation process is tight in $N.$
\begin{lem}
\label{lem: few frozen clusters}Let $K>0$ and $N\in\mathbb{N}.$
Let $FC\left(t\right)=FC\left(t,K,N\right)$ denote the number of
frozen clusters intersecting $B\left(KN\right)$ at time $t\in\left[0,1\right]$
in the $N$-parameter frozen percolation process. Then for all $\varepsilon>0$
there exists $L=L\left(\varepsilon,K\right)$ and $N_{0}=N_{0}\left(\varepsilon,K\right)$
such that
\[
\mathbb{P}_{N}\left(FC\left(1\right)>L\right)<\varepsilon
\]
for $N\geq N_{0}.$\end{lem}
\begin{proof}
[Proof of Lemma \ref{lem: few frozen clusters}] By Lemma \ref{lem: there is a net}
we set $\lambda=\lambda\left(\varepsilon,K\right)\in\mathbb{R}$ such
that
\begin{align}
\mathbb{P}_{N}\left(\mathcal{N}_{c}\left(\lambda,1/6,K+4,N\right)\right) & >1-\frac{1}{2}\varepsilon\label{eq: pf few frozen clusters - 1}
\end{align}
for $N\geq N_{1}\left(\varepsilon,K\right).$ Let $F$ be an open
frozen cluster which intersects $B\left(KN\right).$ From Observation
\ref{obs: closed grid-> no freezing} we get the vertices of $\partial F$
are closed at $p_{\lambda}\left(N\right)$ in the $N$-parameter percolation
process on the event $\mathcal{N}_{c}\left(\lambda,1/6,K+4,N\right).$
Let us cover the parallelogram $B\left(KN\right)$ with the annuli
\[
A_{z}=A\left(\left\lfloor N/20\right\rfloor z;\left\lfloor N/20\right\rfloor ,\left\lfloor N/10\right\rfloor \right)\mbox{ with }z\in B\left(\left\lceil 20K\right\rceil \right).
\]
Suppose that there is an open frozen cluster in the $N$-parameter
frozen percolation which has a vertex in $B\left(KN\right).$ The
construction of the annuli above gives that there is $z\in B\left(\left\lceil 20K\right\rceil \right)$
such that $B\left(\left\lfloor N/20\right\rfloor z;\left\lfloor N/20\right\rfloor \right),$
the inner parallelogram of $A_{z},$ contains a vertex of this open
frozen cluster. Since the diameter of $B\left(\left\lfloor N/20\right\rfloor z;\left\lfloor N/10\right\rfloor \right)$
is less than $N,$ this cluster has to cross the annulus $A_{z}.$
Hence for each open frozen cluster intersecting $B\left(KN\right),$
we find at least one open frozen crossing of an annulus $A_{z}$.
Moreover, if there are $k\geq2$ different frozen clusters crossing
some annulus $A_{z},$ then there are at least $k$ disjoint closed
frozen arms which separate the open frozen clusters in $A_{z}$ at
time $1.$ By the arguments above, these arms are $p_{\lambda}\left(N\right)$-closed.
Thus the number of different frozen clusters intersecting $B\left(\left\lfloor N/20\right\rfloor z;\left\lfloor N/20\right\rfloor \right)$
is bounded above by $1\vee l_{z},$ where $l_{z}$ is the number of
disjoint $p_{\lambda}\left(N\right)$-closed arms of $A_{z}.$ Hence
by the translation variance of the $N$-parameter frozen percolation
process we have
\begin{align}
\mathbb{P}_{N}\left(FC\left(1\right)\geq L,\,\mathcal{N}_{c}\left(\lambda,1/24\right)\right) & \leq\mathbb{P}_{p_{\lambda}\left(N\right)}\left(\sum_{z\in B\left(\left\lceil 20K\right\rceil \right)}\left(1\vee l_{z}\right)\geq L\right)\nonumber \\
& \leq\mathbb{P}_{p_{\lambda}\left(N\right)}\left(\exists z\in B\left(\left\lceil 20K\right\rceil \right)\mbox{ such that }l_{z}\geq\left(2\left\lceil 20K\right\rceil +1\right)^{-2}L\right)\nonumber \\
& \leq\left(2\left\lceil 20K\right\rceil +1\right)^{2}\mathbb{P}_{p_{\lambda}\left(N\right)}\left(l_{0}\geq\left(2\left\lceil 20K\right\rceil +1\right)^{-2}L\right)\label{eq: pf few frozen clusters - 2}
\end{align}
By Lemma \ref{lem: not too many small clusters at lambda} we set
$L=L\left(\varepsilon,K\right)\geq\left(2\left\lceil 20K\right\rceil +1\right)^{2}$
and $N_{2}=N_{2}\left(\varepsilon,K\right)$ such that
\[
\mathbb{P}_{p_{\lambda}\left(N\right)}\left(l_{0}\geq L/200^{2}\right)<\frac{1}{2}\left(2\left\lceil 20K\right\rceil +1\right)^{-2}\varepsilon
\]
for $N\geq N_{2}.$ This combined with (\ref{eq: pf few frozen clusters - 2})
gives that
\begin{equation}
\mathbb{P}_{N}\left(FC\left(1\right)\geq L,\,\mathcal{N}_{c}\left(\lambda,1/6,K+4,N\right)\right)<\frac{1}{2}\varepsilon\label{eq: pf few frozen clusters - 3}
\end{equation}
for $N\geq N_{2}.$ We set $N_{0}:=N_{1}\vee N_{2}.$ A combination
of (\ref{eq: pf few frozen clusters - 1}) and (\ref{eq: pf few frozen clusters - 3})
finishes the proof of Lemma \ref{lem: few frozen clusters}.\end{proof}
\begin{defn}
\label{def: C_a} For $v\in V$ and $\lambda\in\mathbb{R}$ let $\mathcal{C}_{a}\left(v;\lambda\right)=\mathcal{C}_{a}\left(v;\lambda,N\right)$
denote the active cluster of $v$ in the $N$-parameter frozen percolation
process at time $p_{\lambda}\left(N\right).$ We omit the first argument
from the notation above when $v=\underline{0}.$
\end{defn}
We state the two propositions below which play a crucial role in the
proof of Theorem \ref{thm: main}. The proof of these propositions
are rather technical, so we postpone them to the next section. The
first proposition shows that for $\alpha>0,$ it is unlikely to have
an active cluster at time $p_{\lambda}\left(N\right)$ which intersects
$B\left(KN\right)$ and has diameter close to $\alpha N.$
\begin{prop}
\label{prop: active diameter}For all $\lambda\in\mathbb{R}$ and
$\varepsilon,K,\alpha>0,$ there exist $\theta=\theta\left(\lambda,\alpha,\varepsilon,K\right)\in\left(0,1/2\right)$
and $N_{0}=N_{0}\left(\lambda,\alpha,\varepsilon,K\right)$ such that
\[
\mathbb{P}_{N}\left(\exists v\in B\left(KN\right)\mbox{ s.t. }diam\left(\mathcal{C}_{a}\left(v;\lambda\right)\right)\in\left(\left(\alpha-\theta\right)N,\left(\alpha+\theta\right)N\right)\right)<\varepsilon
\]
for $N\geq N_{0}.$
\end{prop}
The second proposition claims that if there is a vertex $v$ such
that $diam\left(\mathcal{C}_{a}\left(v;\lambda_{1},N\right)\right)\geq\left(1+\theta\right)N$
then some part of $\mathcal{C}_{a}\left(v;\lambda_{1},N\right)$ freezes
`soon`:
\begin{prop}
\label{prop: big then freeze} Let $\theta\in\left(0,1\right),$ $\varepsilon>0$
and $\lambda_{1}K,\in\mathbb{R}.$ Recall the notation $FC\left(t,K+2,N\right)$
from Lemma \ref{lem: few frozen clusters}. There exists $\lambda_{2}=\lambda_{2}\left(\lambda_{1},\theta,\varepsilon\right)$
and $N_{0}=N_{0}\left(\lambda_{1},\theta,\varepsilon\right)$ such
that the probability of the intersection of the events
\begin{itemize}
\item $\exists v\in B\left(KN\right)$ such that $diam\left(\mathcal{C}_{a}\left(v;\lambda_{1},N\right)\right)\geq\left(1+\theta\right)N,$
and
\item none of the clusters intersecting $B\left(\left(K+2\right)N\right)$
freeze in the time interval $\left(p_{\lambda_{1}}\left(N\right),p_{\lambda_{2}}\left(N\right)\right],$
i.e.
\[
FC\left(p_{\lambda_{1}}\left(N\right),K+2,N\right)=FC\left(p_{\lambda_{2}}\left(N\right),K+2,N\right)
\]
\end{itemize}
is less than $\varepsilon$ for $N\geq N_{0}.$
\end{prop}
Before we turn to the proof of our main results we make a remark on
how to adapt the proofs for the $N$-parameter frozen bond percolation
process on the square lattice.
\begin{rem}
\label{rem: mod to square} The arguments in Section \ref{sec: pf main},
\ref{sec: pf prop big then freeze}, \ref{sec: pf of prop active diameter}
and in the Appendix can be easily adapted to the $N$-parameter frozen
bond percolation on the square lattice. Some care is required when
we use some Corollary \ref{cor: no many arms}: As we already noted
in Remark \ref{rem: arms in square lattice}, the direct analogue
of Corollary \ref{cor: no many arms} does not hold on the square
lattice. However, one can check that the version of Corollary \ref{cor: no many arms}
which was proposed in Remark \ref{rem: arms in square lattice} is
enough for the proofs appearing in Section \ref{sec: pf main}, \ref{sec: pf prop big then freeze},
\ref{sec: pf of prop active diameter}.
\end{rem}
\subsection{\label{sub: pf main}Proof of Theorem \ref{thm: main}}
\begin{proof}
[Proof of Theorem \ref{thm: main}] The proof follows the following
informal strategy. Consider the following procedure. We set $\lambda_{1}=0.$
We look at the $N$-parameter percolation process at time $p_{\lambda_{1}}\left(N\right).$
We have two cases.
In the first case all the active clusters at time $p_{\lambda_{1}}\left(N\right)$
intersecting $B\left(KN\right)$ have diameter less than $N.$ Hence
no cluster intersecting $B\left(KN\right)$ can freeze after $p_{\lambda_{1}}\left(N\right).$
We terminate the procedure.
In the second case there is $v\in B\left(KN\right)$ such that the
active cluster $\mathcal{C}_{a}\left(v;\lambda_{1},N\right)$ has
diameter at least $N.$ Using Proposition \ref{prop: active diameter}
we set $\theta_{1}$ such that the diameter of this cluster is at
least $\left(1+\theta_{1}\right)N$ with probability close to $1.$
If $diam\left(\mathcal{C}_{a}\left(v;\lambda_{1},N\right)\right)\leq\left(1+\theta_{1}\right)N,$
then we stop the procedure. If $diam\left(\mathcal{C}_{a}\left(v;\lambda_{1},N\right)\right)>\left(1+\theta_{1}\right)N,$
then using Proposition \ref{prop: big then freeze} we set $\lambda_{2}\geq\lambda_{1}$
such that some part of $\mathcal{C}_{a}\left(v;\lambda_{1},N\right)\cap B\left(\left(K+2\right)N\right)$
freezes in the time interval $\left[p_{\lambda_{1}}\left(N\right),p_{\lambda_{2}}\left(N\right)\right]$
with probability close to $1.$ If indeed some part of $\mathcal{C}_{a}\left(v;\lambda_{1},N\right)\cap B\left(\left(K+2\right)N\right)$
freezes in the time interval $\left[p_{\lambda_{1}}\left(N\right),p_{\lambda_{2}}\left(N\right)\right],$
then we iterate the procedure starting from time $p_{\lambda_{2}}\left(N\right).$
Otherwise we terminate the procedure.
Using Lemma \ref{lem: few frozen clusters} we set $L$ such that
the event where there are at least $L$ frozen clusters intersecting
$B\left(\left(K+2\right)N\right)$ at time $1$ has probability smaller
than $\varepsilon/2.$ In each step of the procedure either the procedure
stops, or the the number frozen clusters intersecting $B\left(\left(K+2\right)N\right)$
increases by at least $1.$ Hence the event that the procedure runs
for at least $L$ steps has probability at most $\varepsilon/2.$
Moreover, we set the parameters $\lambda_{i},\theta_{i}$ for $i\geq1$
above such that with probability at least $1-\varepsilon/2$ we terminate
the procedure when there are no active clusters intersecting $B\left(KN\right)$
with diameter at least $N.$ Thus with probability at least $1-\varepsilon$
the procedure stops within $L$ steps, and we stop when there are
no active clusters with diameter at least $N$ intersecting $B\left(KN\right).$
Hence $\lambda=\lambda_{L+1}$ satisfies the conditions of Theorem
\ref{thm: main}, which finishes the proof of Theorem \ref{thm: main}.
\medskip
Let us turn to the precise proof. By Lemma \ref{lem: few frozen clusters},
there is $L=L\left(\varepsilon,K\right)$ and $N_{1}'=N_{1}'\left(\varepsilon,K\right)$
such that
\begin{equation}
\mathbb{P}_{N}\left(FC\left(1,K+2,N\right)\geq L\right)\leq\varepsilon/2,\label{eq: pf main - 1}
\end{equation}
where $F\left(t,K+2,N\right)$ counts the number of frozen clusters
intersecting $B\left(\left(K+2\right)N\right)$ at time $t\in\left[0,1\right].$
We define the deterministic sequence $\left(\lambda_{i},N_{i}',\theta_{i},N_{i}''\right)_{i\in\mathbb{N}}$
inductively as follows. We start by setting $\lambda_{1}=0.$
Suppose that we have already defined $\lambda_{i}$ for some $i\in\mathbb{N}.$
We use Proposition \ref{prop: active diameter} to set $\theta_{i}=\theta_{i}\left(\varepsilon\right)$
and $N_{i}''=N_{i}''\left(\varepsilon\right)$ such that
\[
\mathbb{P}_{N}\left(\exists v\in B\left(KN\right)\mbox{ s.t. }diam\left(\mathcal{C}_{a}\left(v,\lambda_{i}\right)\right)\in\left[N,\left(1+\theta_{i}\right)N\right)\right)<\varepsilon2^{-i-2}
\]
for $N\geq N_{i}''.$
Suppose that we have already defined $\theta_{i}$ for some $i\in\mathbb{N}.$
Then by Proposition \ref{prop: big then freeze} we set $\lambda_{i+1}=\lambda_{i+1}\left(\varepsilon\right)$
and $N_{i+1}'=N_{i+1}'\left(\varepsilon\right)$ such that the probability
of the intersection of the events
\begin{itemize}
\item $\exists v\in B\left(KN\right)$ such that $diam\left(\mathcal{C}_{a}\left(v;\lambda_{i}\right)\right)\geq\left(1+\theta_{i}\right)N,$
and
\item $FC\left(p_{\lambda_{i}}\left(N\right),K+2,N\right)=FC\left(p_{\lambda_{i+1}}\left(N\right),K+2,N\right)$
\end{itemize}
is less than $2^{-i-2}\varepsilon$ for $N\geq N_{i+1}'.$ Note that
\begin{align*}
\left\{ \exists v\in B\left(KN\right)\mbox{ s.t. }diam\left(\mathcal{C}_{a}\left(v,\lambda_{i}\right)\right)\geq N\right\} & \supseteq\left\{ \exists v\in B\left(\left(K+2\right)N\right)\mbox{ s.t. }diam\left(\mathcal{C}_{a}\left(v,\lambda_{i}\right)\right)\geq N\right\} \\
& =\left\{ FC\left(p_{\lambda_{i}}\left(N\right),K+2,N\right)<FC\left(1,K+2,N\right)\right\}
\end{align*}
for $i\geq1.$ Hence the event
\[
\left\{ FC\left(p_{\lambda_{i}}\left(N\right),K+2,N\right)=FC\left(p_{\lambda_{i+1}}\left(N\right),K+2,N\right)<FC\left(1,K+2,N\right)\right\}
\]
is a subset of the union of the events appearing in the definition
of $\theta_{i}$ and $\lambda_{i+1}.$ Thus the construction above
gives that
\begin{align}
\mathbb{P}_{N}\left(FC\left(p_{\lambda_{i}}\left(N\right),K+2,N\right)=FC\left(p_{\lambda_{i+1}}\left(N\right),K+2,N\right)<FC\left(1,K+2,N\right)\right) & \leq2^{-i-1}\varepsilon\label{eq: pf main - 2}
\end{align}
for $i\geq1.$
We set $N_{0}=\bigvee_{i=1}^{L+1}\left(N_{i}'\vee N_{i}''\right).$
By (\ref{eq: pf main - 1}) we have
\begin{align*}
\mathbb{P}_{N}( & \left.\mbox{a cluster intersecting }B\left(KN\right)\mbox{ freezes after time }p_{\lambda_{L+1}}\left(N\right)\right)\\
& =\mathbb{P}_{N}\left(FC\left(p_{\lambda_{L+1}}\left(N\right),K,N\right)<FC\left(1,K,N\right)\right)\\
& \leq\mathbb{P}_{N}\left(FC\left(p_{\lambda_{L+1}}\left(N\right),K+2,N\right)\leq L,\, FC\left(p_{\lambda_{L+1}}\left(N\right),K+2,N\right)<FC\left(1,K+2,N\right)\right)+\mathbb{P}_{N}\left(L<F\left(1,K+2,N\right)\right)\\
& \leq\varepsilon/2+\mathbb{P}_{N}\left(\exists i\in\left[1,L+1\right]\cap\mathbb{Z}\mbox{ s.t. }FC\left(p_{\lambda_{i}}\left(N\right),K+2,N\right)=FC\left(p_{\lambda_{i+1}}\left(N,K+2,N\right)\right)<FC\left(1,K+2,N\right)\right)\\
& \leq\varepsilon/2+\sum_{i=1}^{L+1}\mathbb{P}_{N}\left(FC\left(p_{\lambda_{i}}\left(N,K+2,N\right)\right)=FC\left(p_{\lambda_{i+1}}\left(N,K+2,N\right)\right)<FC\left(1,K+2,N\right)\right)\\
& \leq\varepsilon/2+\sum_{i=1}^{L+1}2^{-i-1}\varepsilon<\varepsilon
\end{align*}
for $N\geq N_{0}$ where we applied (\ref{eq: pf main - 2}) in the
last line. This finishes the proof of Theorem \ref{thm: main}.
\end{proof}
\subsection{\label{sub: pf main cor}Proof of Corollary \ref{cor: macroscopic clusters}}
\begin{proof}
[Proof of Corollary \ref{cor: macroscopic clusters} ] For $\lambda\in\mathbb{R}$
and $N\in\mathbb{N}$ let $NF\left(\lambda\right)=NF\left(\lambda,N\right)$
denote the event that no cluster intersecting $B\left(5N\right)$
freezes after time $p_{\lambda}\left(N\right).$ By Theorem \ref{thm: main}
there is $\lambda=\lambda\left(\varepsilon\right)$ and $N_{1}=N_{1}\left(\varepsilon\right)$
such that
\begin{equation}
\mathbb{P}_{N}\left(NF\left(\lambda\right)\right)<\varepsilon/3\label{eq: pf main cor - 1}
\end{equation}
for $N\geq N_{1}.$
First we consider the case where the origin is in an open frozen cluster
at time $1,$ that is $diam\left(C\left(1\right)\right)\geq N.$ Note
that on the event $NF\left(\lambda\right),$ this frozen cluster was
formed before or at $p_{\lambda}\left(N\right).$ Hence on this event
there is a $p_{\lambda}\left(N\right)$-open path from the origin
to distance at least $N/2.$ Hence the event $\mathcal{A}_{1,0,o}^{\lambda,\lambda,N}\left(1,N/2\right)$
defined in Lemma \ref{lem: near critical arms} occurs.
Let us turn to the case where $diam\left(C\left(1\right)\right)<N.$
Recall the notation $\mathcal{C}_{a}\left(\lambda\right)$ from Definition
\ref{def: C_a}. It is easy to check $C\left(1\right)=\mathcal{C}_{a}\left(\lambda\right)$
that on the event$\left\{ diam\left(C\left(1\right)\right)<N\right\} \cap NF\left(\lambda\right).$
If $diam\left(\mathcal{C}_{a}\left(\lambda\right)\right)<aN,$ then
$\partial\mathcal{C}_{a}\left(\lambda\right)\cap B\left(2aN\right)\neq\emptyset$
for large $N.$ Since $v\in\partial\mathcal{C}_{a}\left(\lambda\right)\cap B\left(2aN\right)$
is frozen, it has a neighbour which has an open frozen path to distance
at least $N/2.$ On the event $NF\left(\lambda\right),$ this path
is $p_{\lambda}\left(N\right)$-open. Hence the event $\mathcal{A}_{1,0,o}^{\lambda,\lambda,N}\left(2aN,N/2\right)$
occurs. This combined with the argument above, for $a\in\left(0,1\right)$
and $N>N_{2}=1/a$ we have
\[
\left\{ diam\left(C\left(1\right)\right)\in\left[0,aN\right)\cup\left[N,\infty\right)\right\} \cap NF\left(\lambda\right)\subseteq\mathcal{A}_{1,0,o}^{\lambda,\lambda,N}\left(2aN,N/2\right).
\]
Hence by Lemma \ref{lem: near critical arms} there is $c=c\left(\lambda\right)$
and $N_{3}=N_{3}\left(\lambda\right)$ such that
\begin{align*}
\mathbb{P}_{N}\left(diam\left(C\left(1\right)\right)\in\left[0,aN\right)\cup\left[N,\infty\right),\, NF\left(\lambda\right)\right) & \leq\mathbb{P}\left(\mathcal{A}_{1,0,o}^{\lambda,\lambda,N}\left(2aN,N/2\right)\right)\\
& \leq c\mathbb{P}_{1/2}\left(\mathcal{A}_{1,o}\left(2aN,N/2\right)\right)
\end{align*}
for $N\geq N_{3}.$ Theorem \ref{thm: arm exponents} gives that there
is $a=a\left(\varepsilon\right)$ and $N_{4}=N_{4}\left(\varepsilon\right)$
such that
\begin{equation}
\mathbb{P}_{N}\left(diam\left(C\left(1\right)\right)\in\left[0,aN\right)\cup\left[N,\infty\right),\, NF\left(\lambda\right)\right)\leq c\mathbb{P}_{1/2}\left(\mathcal{A}_{1,o}\left(2aN,N/2\right)\right)<\varepsilon/3.\label{eq: pf main cor - 3}
\end{equation}
for $N\geq N_{4}.$
Finally, Proposition \ref{prop: active diameter} gives $b=b\left(\varepsilon\right)$
and $N_{5}=N_{5}\left(\varepsilon\right)$ such that
\begin{align}
\mathbb{P}_{N}\left(diam\left(\mathcal{C}_{a}\left(\lambda\right)\right)\in\left[bN,N\right),\, NF\left(\lambda\right)\right) & \leq\mathbb{P}_{N}\left(diam\left(\mathcal{C}_{a}\left(\lambda\right)\right)\in\left[bN,N\right)\right)\nonumber \\
& \leq\varepsilon/3\label{eq: pf main cor - 4}
\end{align}
for $N\geq N_{5}.$
Since $C\left(1\right)=\mathcal{C}_{a}\left(\lambda\right)$ on the
event $\left\{ diam\left(C\left(1\right)\right)<N\right\} \cap NF\left(\lambda\right),$
a combination of (\ref{eq: pf main cor - 1}), (\ref{eq: pf main cor - 3})
and (\ref{eq: pf main cor - 4}) finishes the proof of Corollary \ref{cor: macroscopic clusters}.
\end{proof}
\section{\label{sec: pf prop big then freeze}Proof of Proposition \ref{prop: big then freeze}}
\subsection{\label{sub: notation}Notation}
Let us introduce some more notation. For $u=\left(u_{1},u_{2}\right),v=\left(v_{1},v_{2}\right)\in V,$
we say that $u$ is left (right) of $v$ if $u_{1}\leq v_{1}$ ($u_{1}\geq v_{1}$).
Similarly we say that $u$ is below (above) $v$ if $u_{2}\leq v_{2}$
($u_{2}\geq v_{2}$). For a finite set of vertices $W\subseteq V$
we say that $v=\left(v_{1},v_{2}\right)\in W$ is a leftmost (rightmost)
vertex of $W$ if for all $w=\left(w_{1},w_{2}\right)\in W,$ $v_{1}\leq w_{1}$
($v_{1}\geq w_{1}$). We define the lowest and highest vertices of
$W$ in an analogous way.
Recall that $v,w\in V$, $v\sim w$ denotes that $v$ and $w$ are
neighbours in $\mathbb{T}.$ We extend this notation for subsets of
$V:$ For $S,U\subset V,$ $S\sim U$ denotes that $\exists s\in S,\exists u\in U$
such that $s\sim u.$
\begin{defn}
\label{def: path}Let $n\in\mathbb{N}.$ We say that a sequence of
vertices $v^{1},v^{2},\ldots,v^{n},$ denoted by $\rho,$ is a path
if
\begin{itemize}
\item $v^{i}\sim v^{i+1}$ for $i=1,2,\ldots,\left(n-1\right),$ and
\item $v^{i}\neq v^{j}$ when $i\neq j$ for $i,j=1,2,\ldots,n.$
\end{itemize}
We say that $\rho$ is\emph{ }non self touching, if $u,w\in\rho$
with $u\sim w$ then there is some $i\in\mathbb{N}$ with $1\leq i\leq n-1$
such that either $u=v^{i}$ and $w=v^{i+1}$ or $u=v^{i+1}$ and $w=v^{i}.$
We consider our paths to be ordered: $v^{1}$ is the starting point
and $v^{n}$ is the ending point of $\rho.$ For $u,w\in\rho$ we
say that $u$ is after $w$ in $\rho,$ and denote it by $u\prec_{\rho}w$
if $u=v^{i}$ and $w=v^{j}$ for some $i,j\in\mathbb{N}$ with $1\leq j\leq i\leq n.$
For $u,w\in\rho,$ $u\preceq_{\rho}w$ denotes that either $u=w$
or $u\prec_{\rho}w.$ When it is clear from the context which path
we are considering, we omit the subscript $\rho.$ For $u,w,z\in\rho$
we say that $w$ is in between $u$ and $z$ if $u\preceq w\preceq z$
or $u\succeq w\succeq z.$ For $u,z\in\rho$ with $u\preceq z$ let
$\rho_{u,z}$ denote the subpath of $\rho$ consisting of the vertices
between $u$ and $z.$
We say that two paths $\rho_{1},\rho_{2}$ are non-touching, if $\rho_{1}\nsim\rho_{2}.$
\end{defn}
\begin{defn}
\label{def: loop}Let $n\in\mathbb{N}$ and sequence of vertices $v^{1},v^{2},\ldots,v^{n},$
satisfying
\begin{itemize}
\item $v^{i}\sim v^{i+1\mod n}$ for $i=1,2,\ldots,n,$ and
\item $v^{i}\neq v^{j}$ when $i\neq j$ for $i,j=1,2,\ldots,n.$
\end{itemize}
A loop $\nu$ is the equivalence class of the sequence $\left(v^{1},v^{2},\ldots,v^{n}\right)$
under cyclic permutations, i.e $\nu$ is the set of sequences $\left(v^{j},v^{j+1\mod n},\ldots,v^{j+n-1\mod n}\right)$
for $j=1,2,\ldots,n.$ $\nu$ is non-self touching if for all $\left(w^{1},w^{2},\ldots,w^{n}\right)\in\nu,$
the path $\left(w^{1},w^{2},\ldots,w^{n-1}\right)$ is non-self touching.
We say that $\nu$ contains a vertex $v$ and denote it by $v\in\nu$
if $v=v^{i}$ for some $i\in\left\{ 1,2,\ldots,n\right\} .$ Let $v,w\in\nu$
with $v\neq w$ and let $\rho$ denote the unique path which starts
at $v$ and represents $\nu.$ With the notation of Definition \ref{def: path},
let $\nu_{v,w}:=\rho_{v,w}$ denote the arc of $\nu$ starting at
$v$ and ending at $w.$
\end{defn}
\subsection{\label{sub: thick paths}Thick paths}
\begin{defn}
\label{def: gridpath}Let $M\in\mathbb{N}$ be fixed. The $M$-grid
is the set of parallelograms $B\left(\left(2M+1\right)z;M\right)$
for $z\in V.$ Let $\pi$ be a sequence consisting of some parallelograms
of the $M$-grid. We say that $\pi$ is an $M$-gridpath, if for any
two consecutive parallelograms $B,B'$ of $\pi$ share a side, i.e
$\left|\partial B\cap B'\right|\geq2.$
\end{defn}
\begin{defn}
\label{def: (a,b)-nice}Let $C$ be a subgraph of $\mathbb{T},$ $D\subset V$
and $a,b\in\mathbb{N}.$ We say that $C$ is $\left(a,b\right)$-nice
in $D$, if it satisfies the conditions
\begin{enumerate}
\item $C$ is a connected induced subgraph of $\mathbb{T},$
\item $\partial C$ is a disjoint union of non-touching loops, each with
diameter bigger than $2b.$
\item \label{cond nice: 6 arms, then dead end}Let $u,v\in\partial C\cap D$
with $d\left(u,v\right)\leq a.$ Then $u,v$ are contained in the
same loop $\gamma$ of $\partial C,$ and $diam\left(\gamma_{u,v}\right)\wedge diam\left(\gamma_{v,u}\right)\leq b.$
\end{enumerate}
In the case where $B=V,$ we say that $C$ is $\left(a,b\right)$-nice.
\end{defn}
Let $C$ be $\left(a,b\right)$-nice for some $a,b\in\mathbb{N}.$
Condition \ref{cond nice: 6 arms, then dead end} of Definition \ref{def: (a,b)-nice},
roughly speaking, says that if there is a corridor in $C$ with width
less than $a,$ then it connects two parts of $C$ such that one part
has diameter at most $b.$ This suggests that when $b$ is small compared
to $diam\left(C\right),$ when we can move a parallelogram with side
length $O\left(a\right)$ in $C$ between two distant points of $C.$
This intuitive argument leads us to the following lemma.
\begin{lem}
\label{lem: det gridpath}Let $a,b\in\mathbb{N}$ with $a\geq2000.$
Let $C$ be an $\left(a,b\right)$-nice subgraph of $\mathbb{T}.$
Then there is a $\left\lfloor a/200-10\right\rfloor $-gridpath contained
in $C$ with diameter at least $diam\left(C\right)-2b-2a-12.$
\end{lem}
We use the following `local' version of Lemma \ref{lem: det gridpath}:
\begin{lem}
\label{lem: local det gridpath}Let $a,b,c\in\mathbb{N}$ with $a\geq2000.$
Let $C$ be subgraph of $\mathbb{T}$ which is $\left(a,b\right)$-nice
in $B\left(c\right).$ Let $C'$ be a connected component of $C\cap B\left(c\right).$
Then there is a $\left\lfloor a/200-10\right\rfloor $-gridpath contained
in $C'$ with diameter at least $diam\left(C'\right)-2b-2a-12.$\end{lem}
\begin{proof}
[Proof of Lemma \ref{lem: det gridpath} and \ref{lem: local det gridpath}]
The proof of Lemma \ref{lem: det gridpath} and \ref{lem: local det gridpath}
have geometric/topologic nature, hence it is moved to Section \ref{sub: there are thick paths}
of the Appendix.
\end{proof}
We recall and prove Proposition \ref{prop: big then freeze} in the
following.
\begin{namedthm}
[Proposition \ref{prop: big then freeze}] Let $\theta\in\left(0,1\right),$
$\varepsilon>0$ and $\lambda_{1}K,\in\mathbb{R}.$ Recall the notation
$FC\left(t,K+2,N\right)$ from Lemma \ref{lem: few frozen clusters}.
There exists $\lambda_{2}=\lambda_{2}\left(\lambda_{1},\theta,\varepsilon\right)$
and $N_{0}=N_{0}\left(\lambda_{1},\theta,\varepsilon\right)$ such
that the probability of the intersection of the events
\begin{itemize}
\item $\exists v\in B\left(KN\right)$ such that $diam\left(\mathcal{C}_{a}\left(v;\lambda_{1},N\right)\right)\geq\left(1+\theta\right)N,$
and
\item none of the clusters intersecting $B\left(\left(K+2\right)N\right)$
freeze in the time interval $\left(p_{\lambda_{1}}\left(N\right),p_{\lambda_{2}}\left(N\right)\right],$
i.e.
\[
FC\left(p_{\lambda_{1}}\left(N\right),K+2,N\right)=FC\left(p_{\lambda_{2}}\left(N\right),K+2,N\right)
\]
\end{itemize}
\end{namedthm}
is less than $\varepsilon$ for $N\geq N_{0}.$
\begin{proof}
[Proof of Proposition \ref{prop: big then freeze}] By Lemma \ref{lem: there is a net}
we choose $\lambda_{0}=\lambda_{0}\left(\varepsilon,K\right)\leq\lambda_{1}$
and $N_{1}=N_{1}\left(\varepsilon,K\right)$ such that
\begin{equation}
\mathbb{P}\left(\mathcal{N}_{c}\left(\lambda_{0},1/6,K+6,N\right)\right)>1-\varepsilon/3.\label{eq: thich path - 1}
\end{equation}
By Corollary \ref{cor: no many arms} we choose $\eta<\theta/10$
and $N_{2}=N_{2}\left(\eta,\theta,\lambda_{0},\lambda_{1},K\right)$
such that
\begin{equation}
\mathbb{P}\left(\mathcal{NA}\left(2\eta,\theta/10,\lambda_{0},\lambda_{1},K+4,N\right)\right)>1-\varepsilon/3\label{eq: thich path - 2}
\end{equation}
for all $N\geq N_{2}.$ Let
\[
E:=\mathcal{N}_{c}\left(\lambda_{0},1/6,K+6,N\right)\cap\mathcal{NA}\left(2\eta,\theta,\lambda_{0},\lambda_{1},K+4,N\right).
\]
\begin{claim}
\label{calim: pf big then freeze}Let $u\in B\left(KN\right)$ with
$diam\left(\mathcal{C}_{a}\left(u;\lambda_{1},N\right)\right)\geq\left(1+\theta\right)N.$
Then $\mathcal{C}_{a}\left(u;\lambda_{1},N\right)$ is $\left(\eta N,\frac{\theta}{10}N\right)$-nice
in $B\left(u;2N\right)$ on the event $E.$\end{claim}
\begin{proof}
Let us check the conditions of Definition \ref{def: (a,b)-nice}.
The Condition 1 is satisfied by the definition of $\mathcal{C}_{a}\left(u;\lambda_{1},N\right).$
All the holes of $\mathcal{C}_{a}\left(u;\lambda_{1},N\right)$ contain
a frozen cluster, which have diameter at least $N.$ This combined
with $2\frac{\theta}{10}N<N,$ shows that Condition 2 of Definition
\ref{def: (a,b)-nice} holds.
Let $x,y\in\partial\mathcal{C}_{a}\left(u;\lambda_{1},K\right)\cap B\left(u;2N\right)$
with $d\left(x,y\right)\leq\eta N.$ We have two cases.
\emph{Case 1.} $x,y$ lie in different loops of $\partial\mathcal{C}_{a}\left(u;\lambda_{1},N\right).$
For $i=x,y,$ let $\gamma_{i}$ denote the loop containing $i.$ Furthermore,
let $\tilde{\gamma}_{i}$ denote the connected component of $i$ in
$\gamma_{i}\cap B\left(i;2N\right).$ We have $diam\left(\tilde{\gamma}_{i}\right)\geq N.$
Moreover, $\tilde{\gamma}_{i}\subset B\left(i;2N\right)\subset B\left(\left(K+4\right)N\right).$
Observation \ref{obs: closed grid-> no freezing} gives that on the
event $\mathcal{N}_{c}\left(\lambda_{0},1/6,K+6,N\right),$ $\tilde{\gamma}_{i}$
is $p_{\lambda_{0}}\left(N\right)$-closed. Hence each of $\tilde{\gamma}_{x}$
and $\tilde{\gamma}_{y}$ gives two closed $p_{\lambda_{0}}\left(N\right)$-closed
arms in $A\left(x;2\eta N,N/2\right).$ Moreover, the frozen clusters
neighbouring $x$ and $y$ provide two disjoint $p_{\lambda_{1}}\left(N\right)$-open
arms. Hence there are $6$ disjoint arms in $A\left(x;2\eta N,N/2\right),$
thus $\mathcal{NA}^{c}\left(2\eta,\theta/10,\lambda_{0},\lambda_{1},K+4,N\right)$
occurs.
\emph{Case 2. }$x,y$ lie on the same loop of $\partial\mathcal{C}_{a}\left(u;\lambda_{1},N\right).$
This case can be treated similarly Condition 1, with the difference
that if $x,y$ violate Condition \ref{cond nice: 6 arms, then dead end}
of Definition \ref{def: (a,b)-nice} then we get $6$ arms in $A\left(x;2\eta N,\frac{\theta}{10}N\right).$
Hence $\mathcal{NA}^{c}\left(2\eta,\theta/10,\lambda_{0},\lambda_{1},K+4,N\right)$
occurs.
Hence in both cases $E^{c}$ occurs. Thus on the event $E$ all the
conditions of Definition \ref{def: (a,b)-nice} are satisfied for
$\mathcal{C}_{a}\left(u;\lambda_{1},N\right),$ which finishes the
proof of Claim \ref{calim: pf big then freeze}.
\end{proof}
Let us turn back to the proof of Proposition \ref{prop: big then freeze}.
Let $u\in B\left(KN\right)$ with $diam\left(\mathcal{C}_{a}\left(u;\lambda_{1},N\right)\right)\geq\left(1+\theta\right)N.$
Let $\tilde{\mathcal{C}}_{a}\left(u,\lambda_{1},N\right)$ denote
the connected component of $u$ in $\mathcal{C}_{a}\left(u,\lambda_{1},N\right)\cap B\left(2N\right).$
Since $diam\left(\mathcal{C}_{a}\left(u;\lambda_{1},N\right)\right)\geq\left(1+\theta\right)N$
and $\theta<1,$ we have $diam\left(\tilde{\mathcal{C}}_{a}\left(u;\lambda_{1},N\right)\right)\geq\left(1+\theta\right)N.$
By Lemma \ref{lem: local det gridpath} we set $\eta=\eta\left(\theta\right)\in\left(0,\theta/100\right)$
and $N_{3}=N_{3}\left(\theta\right)$ such that on the event $E$
for all $u\in B\left(KN\right),$ with $diam\left(\mathcal{C}_{a}\left(u;\lambda_{1},N\right)\right)\geq\left(1+\theta\right)N$
there is a $\left\lfloor \eta N\right\rfloor $-gridpath $\rho_{u}\subset\tilde{\mathcal{C}}_{a}\left(u;\lambda_{1},N\right)$
with $diam\left(\rho_{u}\right)\geq\left(1+\theta/2\right)N$ for
$N\geq N_{3}.$
Lemma \ref{lem: there is a net} gives that there is $\lambda_{2}=\lambda_{2}\left(\varepsilon,\eta,K\right)$
and $N_{4}=N_{4}\left(\varepsilon,\eta,K\right)$ such that
\begin{equation}
\mathbb{P}\left(\mathcal{N}_{o}\left(\lambda_{2},\eta/2,K+4,N\right)\right)>1-\varepsilon/3\label{eq: thich path - 3}
\end{equation}
for $N\geq N_{4}\left(\varepsilon,\eta,K\right).$ We set $N_{0}:=\bigvee_{i=1}^{4}N_{i}.$
Let
\begin{align*}
G:= & E\cap\mathcal{N}_{o}\left(\lambda_{2},\eta/2,K+4,N\right),\\
M:= & \left\{ \exists v\in B\left(KN\right)\mbox{ s.t. }diam\left(\mathcal{C}_{a}\left(v;\lambda_{1},N\right)\right)\geq\left(1+\theta\right)N\right\} \cap G.
\end{align*}
Combination of (\ref{eq: thich path - 1}), (\ref{eq: thich path - 2})
and (\ref{eq: thich path - 3}) gives that
\begin{equation}
\mathbb{P}\left(G^{c}\right)<\varepsilon\label{eq: thich path - 4}
\end{equation}
for $N\geq N_{0}.$
Recall that for $N\geq N_{0},$ on the event $E$ for $u\in B\left(KN\right),$
with $diam\left(\mathcal{C}_{a}\left(u;\lambda_{1},N\right)\right)\geq\left(1+\theta\right)N$
there is a $\left\lfloor \eta N\right\rfloor $-gridpath $\rho_{u}\subset\tilde{\mathcal{C}}_{a}\left(u;\lambda_{1},N\right)$
with $diam\left(\rho_{u}\right)\geq\left(1+\theta/2\right)N.$ On
the event $\mathcal{N}_{o}\left(\lambda_{2},\eta/2,K+4,N\right),$
this gridpath $\rho_{u}\subseteq B\left(\left(K+2\right)N\right)$
contains a $p_{\lambda_{2}}\left(N\right)$-open component with diameter
at least $N.$ Hence on the event $M,$ at least one cluster intersecting
$B\left(\left(K+2\right)N\right)$ freezes in the time interval $\left(p_{\lambda_{1}}\left(N\right),p_{\lambda_{2}}\left(N\right)\right].$That
is
\[
M\subseteq\left\{ FC\left(p_{\lambda_{1}}\left(N\right),K+2,N\right)<FC\left(p_{\lambda_{2}}\left(N\right),K+2,N\right)\right\} .
\]
Thus
\[
\left\{ \exists v\in B\left(KN\right)\mbox{ s.t. }diam\left(\mathcal{C}_{a}\left(v;\lambda_{1},N\right)\right)\geq\left(1+\theta\right)N\right\} \cap\left\{ FC\left(p_{\lambda_{1}}\left(N\right),K+2,N\right)=FC\left(p_{\lambda_{2}}\left(N\right),K+2,N\right)\right\} \subset G^{c},
\]
which together with (\ref{eq: thich path - 4}) finishes the proof
of Proposition \ref{prop: big then freeze}.
\end{proof}
\section{\label{sec: pf of prop active diameter}Proof of Proposition \ref{prop: active diameter}}
\subsection{\label{sub: lowest of lowest in parallelograms}Lowest point of the
lowest crossing in parallelograms}
The central object of this section is the following. Recall the notation
of Section \ref{sub: notation}.
\begin{defn}
\label{def: cal L}Let $R$ be a connected subgraph of $\mathbb{T}$
and let $r\subset\partial R$. We define $\mathcal{L}\left(R,r\right)$
as the the (random) set of lowest vertices $v\in R$ such that $v$
is closed, and there are two non-touching closed paths in $R$ starting
at a vertex neighbouring to $v$ and ending at $r.$
\end{defn}
Consider the site percolation model on the triangular lattice with
parameter $p\in\left[0,1\right].$ We investigate the distribution
of $\mathcal{L}\left(R,r\right)$ in the case where $p=p_{\lambda}\left(N\right),$
$R=B\left(bN\right)$ and $r=top\left(B\left(bN\right)\right):=\left[-bN,bN\right]\boxtimes\left\{ \left\lfloor bN\right\rfloor +1\right\} $
for $\lambda\in\mathbb{R}$ and $b>0.$
The distribution of $\mathcal{L}\left(R,r\right)$ was examined in
\cite{Berg2003} in the case where $p=1/2,$ $R$ is the upper half
plane and $r=\left[0,n\right]\boxtimes\left\{ 0\right\} $ for some
$n\in\mathbb{N}.$ The results of \cite{Berg2003} do not imply, nor
follow from ours.
\begin{defn}
\label{def; HCr}For a parallelogram $B,$ let $HCr\left(B\right)$
denote set of paths in $B$ which connect the left and the right sides
of $B.$ For $\rho\in HCr\left(B\right),$ let $Be\left(\rho\right)=Be\left(\rho,B\right)$
denote the set of vertices in $B$ which are `under' $\rho.$ It is
the set of vertices $v\in B\setminus\rho$ which are connected to
the bottom side of $B\left(bN\right).$ Furthermore, we define $Ab\left(\rho\right)=Ab\left(\rho,B\right):=B\setminus\left(\rho\cup Be\left(\rho,B\right)\right).$\end{defn}
\begin{lem}
\label{lem: lowest of lowest}Let $a,b\in\left(0,1\right)$ with $5a<b$
and $\lambda\in\mathbb{R}.$ For $k,l,N\in\mathbb{N}$ with $l<k$
we define the event
\[
L_{l,k}=\left\{ \mathcal{L}\left(B\left(bN\right),\, top\left(bN\right)\right)\cap B_{l,k}\neq\emptyset\right\} .
\]
In words this is the event that at least one of the lowest vertices
of $B\left(bN\right)$ with two non-touching closed paths $B\left(bN\right)$
to the top side of $B\left(bN\right)$ is in the parallelogram
\[
B_{l,k}=\left[-aN,aN\right]\boxtimes\left(\left(2\frac{l}{k}-1\right)aN,\left(2\frac{l+1}{k}-1\right)aN\right].
\]
Let $\lambda_{1},\lambda_{2}\in\mathbb{R}.$ Then there exist $C=C\left(a,b,\lambda_{1},\lambda_{2}\right)$
and $N_{0}=N_{0}\left(a,b,\lambda_{1},\lambda_{2},k\right)$ such
that for all $\lambda\in\left[\lambda_{1},\lambda_{2}\right]$ and
$k,l\in\mathbb{N}$ with $l\leq k-1$ we have
\begin{equation}
\mathbb{P}_{p_{\lambda}\left(N\right)}\left(L_{l,k}\right)\leq Ck^{-1}\label{eq: lowest of lowest}
\end{equation}
for $N\geq N_{0}.$\end{lem}
\begin{proof}
[Proof of Lemma \ref{lem: lowest of lowest}] Note that $L_{l,k}\cap L_{m,k}=\emptyset$
when $l\neq m.$ Hence it is enough to show that there is exists $c=c\left(a,b,\lambda_{1},\lambda_{2}\right)>0$
and $N_{0}=N_{0}\left(a,b,\lambda_{1},\lambda_{2}\right)$ such that
for all $l,m\in\left[0,k-1\right]\cap\mathbb{Z}$ we have
\begin{equation}
c\mathbb{P}_{p_{\lambda}\left(N\right)}\left(L_{l,k}\right)\leq\mathbb{P}_{p_{\lambda}\left(N\right)}\left(L_{m,k}\right)\label{eq: pf lowest of lowest - 0}
\end{equation}
for $N\geq N_{0}.$
Let $k,l$ be given. Let $s_{L}$ ($s_{R}$) denote the left (right)
endpoint of $top\left(bN\right).$ We say that a path $\rho\subseteq B\left(bN\right)\cup top\left(bN\right)$
is good, if it
\begin{itemize}
\item starts at $s_{L}$ and ends at $s_{R},$
\item it is non-self touching
\item and one of its lowest points is in $B_{l,k}.$
\end{itemize}
Let $\rho$ be some given good path. Recall Definition \ref{def; HCr}
and let $Be\left(\rho\right)=Be\left(\rho,\left(B\left(bN\right)\right)\right).$
Let $H_{\rho}$ denote the event that there are two open paths in
$Be\left(\rho\right)\cap\left[-bN,bN\right]\boxtimes\left[aN,\frac{b-2a}{2}N\right]$
from the left and right sides of the parallelogram $\left[-bN,bN\right]\boxtimes\left[aN,\frac{b-2a}{2}N\right]$
to $\rho.$ Let $\gamma$ denote the lowest non-self touching path
in $B\left(bN\right)\cup top\left(bN\right)$ which starts at $s_{L}$
and ends at $s_{R},$ and of which all the vertices outside of $top\left(bN\right)$
are closed. On the event $L_{l,k}$ $\gamma$ is good.
\medskip
\emph{Case 1.} First we consider the case where $l<m.$ Recall the
definition of increasing events from Definition \ref{def: inc events}.
For any good path $\rho,$ on the event that all of the vertices of
$\rho\setminus top\left(bN\right)$ are closed, the event $\left\{ \gamma=\rho\right\} $
is increasing in the configuration in $B\left(bN\right)\setminus\rho.$
Let $H_{1}:=\mathcal{H}_{o}\left(\left[-bN,bN\right]\boxtimes\left[-bN,-\left(b-a\right)N\right]\right).$
The events $H_{1}$ and $H_{\rho}$ are increasing. Thus by FKG and
by Lemma \ref{cor: posprob of crossing}, we have\begin{align}
\mathbb{P}_{p_{\lambda}\left(N\right)} &\left(L_{l,k}\cap H_{1}\cap H_{\gamma}\right) \nonumber\\
&=\sum_{\rho\mbox{ good}}\mathbb{P}_{p_{\lambda}\left(N\right)}\left(\left.H_{1}\cap H_{\rho}\cap\left\{ \gamma=\rho\right\} \,\right|\,\rho\setminus top\left(bN\right)\mbox{ is closed }\right)\mathbb{P}_{p_{\lambda}\left(N\right)}\left(\rho\setminus top\left(bN\right)\mbox{ is closed}\right)\nonumber\\ &\geq\sum_{\rho\mbox{ good}}\mathbb{P}_{p_{\lambda}\left(N\right)}\left(\left.\left\{ \gamma=\rho\right\} \,\right|\,\rho\setminus top\left(bN\right)\mbox{ is closed}\right)\mathbb{P}_{p_{\lambda}\left(N\right)}\left(\left.H_{1}\,\right|\,\rho\setminus top\left(bN\right)\mbox{ is closed}\right)\nonumber\\[-4mm]
& \hspace{4cm} \mathbb{P}_{p_{\lambda}\left(N\right)}\left(\left.H_{\rho}\,\right|\,\rho\setminus top\left(bN\right)\mbox{ is closed}\right)\mathbb{P}_{p_{\lambda}\left(N\right)}\left(\rho\setminus top\left(bN\right)\mbox{ is closed}\right) \nonumber\\
& \geq \sum_{\rho\mbox{ good}}c_{1}\mathbb{P}_{p_{\lambda}\left(N\right)}\left(\left.\left\{ \gamma=\rho\right\} \,\right|\,\rho\setminus top\left(bN\right)\mbox{ is closed}\right)\mathbb{P}_{p_{\lambda}\left(N\right)}\left(\rho\setminus top\left(bN\right)\mbox{ is closed}\right)\nonumber\\
& = c_{1}\mathbb{P}_{p_{\lambda}\left(N\right)}\left(L_{l,k}\right)\label{eq: pf lowest of lowest - 1}\end{align}for $c_{1}=c_{1}\left(a,b,\lambda_{1},\lambda_{2}\right)>0$
and for $N\geq N_{1}=N_{1}\left(a,b,\lambda_{1},\lambda_{2}\right).$
There is $N_{2}=N_{2}\left(k\right)$ such that for $N\geq N_{2}$
and for all $l,m\in\left[0,k-1\right]\cap\mathbb{Z}$ with $l<m$
there is a shift $S=S\left(l,m,k\right)$ which moves the parallelogram
$B_{l,k}$ to a subset of $B_{m-1,k}\cup B_{m,k}.$ Let us take a
configuration in $\omega\in\left\{ o,c\right\} ^{V}$ for which the
event $L_{l,k}\cap H_{1}\cap H_{\gamma}$ holds. Then shifted configuration
$S\left(\omega\right)$ satisfies $L_{m-1,k}\cup L_{m,k}.$ Hence
\begin{align}
\mathbb{P}_{p_{\lambda}\left(N\right)}\left(L_{m-1,k}\cup L_{m,k}\right) & \geq\mathbb{P}_{p_{\lambda}\left(N\right)}\left(L_{l,k}\cap H_{1}\cap H_{\gamma}\right),\nonumber \\
& \geq c_{1}\mathbb{P}_{p_{\lambda}\left(N\right)}\left(L_{l,k}\right)\label{eq: pf lowest of lowest - 2}
\end{align}
by (\ref{eq: pf lowest of lowest - 1}) for $N\geq N_{1}\vee N_{2}.$
\medskip
\emph{Case 2.} When $l>m$ we have a similar argument. The difference
is that now we want to shift downwards. To get a configuration in
$L_{m,k}$ after the shift, we have to extend the closed path $\gamma$
see Figure \ref{fig: lowest of lowest} for more details.
Let $\rho$ be a fixed good path. Let $O_{\rho}$ denote the event
that there is path $\nu$ such that
\begin{itemize}
\item $\nu\subseteq B_{0}:=\left[-bN,bN\right]\boxtimes\left[-bN,\frac{b}{4}N\right]$,
\item $\nu$ connects the left and the right sides of the parallelogram
$B_{1}:=\left[-bN,bN\right]\boxtimes\left[aN,\frac{b}{4}N\right],$
\item $\nu$ is a concatenation of some open paths which lie in $Be\left(\rho\right)\cap B_{1},$
and of some subpaths of $\rho.$
\end{itemize}
Clearly, $O_{\rho}$ is an increasing event. On $O_{\rho},$ let $\xi\left(\rho\right)$
denote the lowest path which satisfies the conditions in the definition
of $O_{\rho}.$ Recall the definition of decreasing events from Definition
\ref{def: inc events}, and the definition of $\gamma$ from Case
1. Let us condition on the event that all the vertices of $\rho\setminus top\left(bN\right)$
are closed. Then the event $\left\{ \gamma=\rho\right\} $ is increasing
on the configuration in $B\left(bN\right)\setminus\rho,$ and it only
depends on the configuration in $Be\left(\rho\right).$ Hence a combination
of FKG and Corollary \ref{cor: posprob of crossing} give that
\begin{align}
\mathbb{P}_{p_{\lambda}\left(N\right)} & \left(L_{l,k}\cap O_{\gamma}\right)\nonumber \\
& =\sum_{\rho\mbox{ good}}\mathbb{P}_{p_{\lambda}\left(N\right)}\left(\left.O_{\rho}\cap\left\{ \gamma=\rho\right\} \,\right|\,\rho\setminus top\left(bN\right)\mbox{ is closed}\right)\mathbb{P}_{p_{\lambda}\left(N\right)}\left(\rho\setminus top\left(bN\right)\mbox{ is closed}\right)\nonumber \\
& \geq\sum_{\rho\mbox{ good}}\mathbb{P}_{p_{\lambda}\left(N\right)}\left(\left.\left\{ \gamma=\rho\right\} \,\right|\,\rho\setminus top\left(bN\right)\mbox{ is closed}\right)\mathbb{P}_{p_{\lambda}\left(N\right)}\left(\left.O_{\rho}\,\right|\,\rho\setminus top\left(bN\right)\mbox{ is closed}\right)\mathbb{P}_{p_{\lambda}\left(N\right)}\left(\rho\setminus top\left(bN\right)\mbox{ is closed}\right)\nonumber \\
& \geq\sum_{\rho\mbox{ good}}\mathbb{P}_{p_{\lambda}\left(N\right)}\left(\left.\left\{ \gamma=\rho\right\} \,\right|\,\rho\setminus top\left(bN\right)\mbox{ is closed}\right)\mathbb{P}_{p_{\lambda}\left(N\right)}\left(\mathcal{H}_{o}\left(B_{1}\right)\right)\mathbb{P}_{p_{\lambda}\left(N\right)}\left(\rho\setminus top\left(bN\right)\mbox{ is closed}\right)\nonumber \\
& \geq c_{2}\left(\lambda_{1},\lambda_{2},a,b\right)\mathbb{P}_{p_{\lambda}\left(N\right)}\left(L_{l,k}\right)\label{eq: pf lowest of lowest - 3}
\end{align}
for $c_{2}=c_{2}\left(a,b,\lambda_{1},\lambda_{2}\right)>0$ and for
$N\geq N_{3}=N_{3}\left(a,b,\lambda_{1},\lambda_{2}\right).$
For $W\subseteq V$ and $\omega\in\left\{ o,c\right\} ^{V},$ $\omega_{W}\in\left\{ o,c\right\} ^{W}$
denotes the restriction of $\omega$ to the configuration in $W.$
That is $\omega_{W}\left(v\right)=\omega\left(v\right)$ for $v\in W.$
Recall Definition \ref{def; HCr}. Let $\zeta\in HCr\left(B_{0}\right)$
be arbitrary. It is easy to check that the event $L_{l,k}\cap O_{\gamma}\cap\left\{ \xi\left(\gamma\right)=\zeta\right\} $
is decreasing in the configuration in $Ab\left(\zeta\right).$ Let
us take the parallelograms $B_{2}=\left[-bN,bN\right]\boxtimes\left[\frac{b}{4}N,\frac{b}{2}N\right],$
$B_{3}=\left[-bN,bN\right]\boxtimes\left[\frac{3}{4}bN,bN\right],$
$B_{4}=\left[-bN,-\frac{1}{2}bN\right]\boxtimes\left[\frac{1}{4}bN,\left(b+2a\right)N\right]$
and $B_{5}=\left[\frac{1}{2}bN,bN\right]\boxtimes\left[\frac{1}{4}bN,\left(b+2a\right)N\right].$
Let $\mathcal{D}=\mathcal{H}_{c}\left(B_{2}\right)\cap\mathcal{H}_{c}\left(B_{3}\right)\cap\mathcal{V}_{c}\left(B_{4}\right)\cap\mathcal{V}_{c}\left(B_{5}\right).$
Clearly, $\mathcal{D}$ is a decreasing event. Hence a combination
of FKG and Corollary \ref{cor: posprob of crossing} give that for
$c_{3}=c_{3}\left(a,b,\lambda_{1},\lambda_{2}\right)>0$ and $N\geq N_{4}=N_{4}\left(a,b,\lambda_{1},\lambda_{2}\right)$
we have
\begin{align}
\mathbb{P}_{p_{\lambda}\left(N\right)} & \left(L_{k,l}\cap O_{\gamma}\cap\mathcal{D}\right)\nonumber \\
& =\sum_{\zeta}\sum_{\sigma}\mathbb{P}_{p_{\lambda}\left(N\right)}\left(\left.L_{k,l}\cap O_{\gamma}\cap\left\{ \xi\left(\gamma\right)=\zeta\right\} \cap\mathcal{D}\,\right|\,\omega_{\zeta\cup Be\left(\zeta\right)}=\sigma\right)\mathbb{P}_{p_{\lambda}\left(N\right)}\left(\omega_{\zeta\cup Be\left(\zeta\right)}=\sigma\right)\nonumber \\
& \geq\sum_{\zeta}\sum_{\sigma}\mathbb{P}_{p_{\lambda}\left(N\right)}\left(\left.L_{k,l}\cap O_{\gamma}\cap\left\{ \xi\left(\gamma\right)=\zeta\right\} \,\right|\,\omega_{\zeta\cup Be\left(\zeta\right)}=\sigma\right)\mathbb{P}_{p_{\lambda}\left(N\right)}\left(\left.\mathcal{D}\,\right|\,\omega_{\zeta\cup Be\left(\zeta\right)}=\sigma\right)\mathbb{P}_{p_{\lambda}\left(N\right)}\left(\omega_{\zeta\cup Be\left(\zeta\right)}=\sigma\right)\nonumber \\
& =\sum_{\zeta}\sum_{\sigma}\mathbb{P}_{p_{\lambda}\left(N\right)}\left(\left.L_{k,l}\cap O_{\gamma}\cap\left\{ \xi\left(\gamma\right)=\zeta\right\} \,\right|\,\omega_{\zeta\cup Be\left(\zeta\right)}=\sigma\right)\mathbb{P}_{p_{\lambda}\left(N\right)}\left(\mathcal{D}\right)\mathbb{P}_{p_{\lambda}\left(N\right)}\left(\omega_{\zeta\cup Be\left(\zeta\right)}=\sigma\right)\nonumber \\
& \geq c_{3}\left(a,b,\lambda_{1},\lambda_{2}\right)\sum_{\zeta}\sum_{\sigma}\mathbb{P}_{p_{\lambda}\left(N\right)}\left(\left.L_{k,l}\cap O_{\gamma}\cap\left\{ \xi\left(\gamma\right)=\zeta\right\} \,\right|\,\omega_{\zeta\cup Be\left(\zeta\right)}=\sigma\right)\mathbb{P}_{p_{\lambda}\left(N\right)}\left(\omega_{\zeta\cup Be\left(\zeta\right)}=\sigma\right)\nonumber \\
& =c_{3}\left(a,b,\lambda_{1},\lambda_{2}\right)\mathbb{P}_{p_{\lambda}\left(N\right)}\left(L_{k,l}\cap O_{\gamma}\right)\label{eq: pf lowest of lowest - 4}
\end{align}
where the summation in $\zeta$ is over $HCr\left(B_{0}\right)$ and
the summation in $\sigma$ is over $\left\{ o,c\right\} ^{\zeta\cup Be\left(\zeta\right)}.$
In the third line we used that $\mathcal{D}$ does not depend on the
configuration in $\zeta\cup Be\left(\zeta\right).$
\begin{figure}
\centering{}\includegraphics[scale=0.8]{lemma3p6}\caption{\label{fig: lowest of lowest}The continuous line represents $\gamma.$
The dashed paths are the closed crossings of $\mathcal{D},$ which
allow us to prolong $\gamma.$ The dashed-dotted paths are the open
parts of $\xi\left(\gamma\right).$ They, together with $\gamma,$
prevent the occurrence of closed vertices below the lowest point of
$\gamma$ with two closed arms to the top side after the shift.}
\end{figure}
There is $N_{5}=N_{5}\left(k\right)$ such that for $N\geq N_{5}$
and for all $l,m\in\left[0,k-1\right]\cap\mathbb{Z}$ with $l>m$
there is a shift $S=S\left(l,m,k\right)$ which moves the parallelogram
$B_{l,k}$ to a subset of $B_{m,k}\cup B_{m+1,k}.$ Let us take a
configuration $\omega\in\left\{ o,c\right\} ^{V}$ which satisfies
$L_{k,l}\cap O_{\gamma}\cap\mathcal{D}.$ Then the shifted configuration
$S\left(\omega\right)$ satisfies $L_{m,k}\cup L_{m+1,k},$ see Figure
\ref{fig: lowest of lowest} for more details. Hence for $N\geq N_{3}\vee N_{4}\vee N_{5}$
we have
\begin{align}
\mathbb{P}_{p_{\lambda}\left(N\right)}\left(L_{m,k}\cup L_{m+1,k}\right) & \geq\mathbb{P}_{p_{\lambda}\left(N\right)}\left(L_{k,l}\cap O_{\gamma}\cap\mathcal{D}\right)\nonumber \\
& \geq c_{2}c_{3}\mathbb{P}_{p_{\lambda}\left(N\right)}\left(L_{l,k}\right)\label{eq: pf lowest of lowest - 5}
\end{align}
by a combination of (\ref{eq: pf lowest of lowest - 3}) and (\ref{eq: pf lowest of lowest - 4}).
(\ref{eq: pf lowest of lowest - 2}) together with (\ref{eq: pf lowest of lowest - 5})
implies (\ref{eq: pf lowest of lowest - 0}) and finishes the proof
of Lemma \ref{lem: lowest of lowest}.\end{proof}
\begin{rem}
The proof of the lemma shows that $\mathbb{P}_{p_{\lambda}\left(N\right)}\left(L_{l,k}\right)=O\left(k^{-1}\right):$
Let $a,b,\lambda,\lambda_{1},\lambda_{2}$ be as in Lemma \ref{lem: lowest of lowest}.
Standard RSW techniques give that there is $c'=c'\left(a,b,\lambda_{1},\lambda_{2}\right)>0$
and $N_{0}=N_{0}\left(a,b,\lambda_{1},\lambda_{2}\right)$ such that
\[
\mathbb{P}_{p_{\lambda}\left(N\right)}\left(\mathcal{L}\left(B\left(bN\right),t\left(bN\right)\right)\cap B\left(aN\right)\neq\emptyset\right)\geq c'
\]
for $N\geq N_{0}.$ This combined with the proof of Lemma \ref{lem: lowest of lowest},
we get that some $C'=C'\left(a,b,\lambda_{1},\lambda_{2}\right)>0$
and $N_{1}=N_{1}\left(a,b,\lambda_{1},\lambda_{2},k\right)$ we have
\[
\mathbb{P}_{p_{\lambda}\left(N\right)}\left(L_{l,k}\right)\geq C'k^{-1}
\]
for $N\geq N_{1}.$
\end{rem}
\subsection{\label{sub: lowesr of lowest in reular regions}Lowest point of the
lowest crossing in regular regions}
Recall Definition \ref{def: cal L}. Let $B\subset B'$ be parallelograms,
and let $R$ be a subgraph of $\mathbb{T}$ with $B\subset R\subset B'.$
Furthermore let $r\subset\partial R.$ Our next aim is to compare
the event $\mathcal{L}\left(R,r\right)\cap B\neq\emptyset$ to $\mathcal{L}\left(B',top\left(B'\right)\right)\cap B\neq\emptyset$
in the case where the pair $\left(R,r\right)$ is `regular'. We make
this precise in the following.
We say that an subgraph $H\subseteq\mathbb{T}$ is simply connected,
if it is connected and for all loops $\sigma\subseteq H,$ all of
the finite components of $\mathbb{T}\setminus\sigma$ are contained
in $H.$
\begin{defn}
\label{def: (a,b)-regular}Let $a,b\in\mathbb{N}$ such that $5a<b.$
A pair $\left(R,r\right)$ is $\left(a,b\right)$-regular, if
\begin{enumerate}
\item $R$ is an induced subgraph of $\mathbb{T}$ such that $cl\left(R\right)$
is simply connected,
\item $B\left(a\right)\subseteq R\subseteq B\left(b\right),$
\item $r\subset\partial R,$ such that $\emptyset\neq r\subsetneqq\partial R.$
Furthermore, $r$ and $\partial R\setminus r$ are self-avoiding paths
such that $R$ is on the right hand side, as we walk along them.
\item \label{cond: r is high}$r\subseteq\left[-b,b\right]\boxtimes\left[5a,b\right].$
\end{enumerate}
\end{defn}
\begin{lem}
\label{lem: compare L}Let $a,b\in\left(0,1\right)$ with $5a<b$
and $\lambda\in\mathbb{R}.$ Let $\left(R,r\right)$ be an $\left(aN,bN\right)$-regular
graph. For $k,l,N\in\mathbb{N}$ with $l<k$ we define the events
\begin{align*}
L_{l,k}\left(B\left(2bN\right),top\left(B\left(2bN\right)\right)\right): & =\left\{ \mathcal{L}\left(B\left(2bN\right),\, top\left(2bN\right)\right)\cap B_{l,k}\neq\emptyset\right\} ,\\
L_{l,k}\left(R,r\right): & =\left\{ \mathcal{L}\left(R,r\right)\cap B_{l,k}\neq\emptyset\right\} ,
\end{align*}
where
\[
B_{l,k}:=\left[-aN,aN\right]\boxtimes\left(\left(2\frac{l}{k}-1\right)aN,\left(2\frac{l+1}{k}-1\right)aN\right].
\]
Let $\lambda_{1},\lambda_{2}\in\mathbb{R}.$ Then there exist $C=C\left(a,b,\lambda_{1},\lambda_{2}\right)$
and $N_{0}=N_{0}\left(a,b,\lambda_{1},\lambda_{2},k\right)$ such
that for all $\lambda\in\left[\lambda_{1},\lambda_{2}\right]$ and
$k,l\in\mathbb{N}$ with $l\leq k-1$ we have
\begin{equation}
\mathbb{P}_{p_{\lambda}\left(N\right)}\left(L_{l,k}\left(R,r\right)\right)\leq C\mathbb{P}_{p_{\lambda}\left(N\right)}\left(L_{l,k}\left(B\left(2bN\right),top\left(B\left(2bN\right)\right)\right)\right)\label{eq: compare L}
\end{equation}
for $N\geq N_{0}.$\end{lem}
\begin{proof}
[Proof of Lemma \ref{lem: compare L}] The proof follows the arguments
of Case 2 in the proof of Lemma \ref{lem: lowest of lowest}. Our
aim is to show that, conditioning on $L_{l,k}\left(R,r\right),$ the
open and closed crossings of Figure \ref{fig: lowest of lowest regular region}
occur with probability bounded away from $0$ cf. Figure \ref{fig: lowest of lowest}.
\begin{figure}
\centering{}\includegraphics[scale=0.8]{lemma3p8}\caption{\label{fig: lowest of lowest regular region} The dashed paths are
the closed crossings of the event $\mathcal{D}$ which allow us to
prolong $\gamma.$ The dashed-dotted paths are the open parts of $\xi\left(\gamma\right).$
They, together with $\gamma,$ prevent the occurrence of closed vertices
below the lowest point of $\gamma$ with two closed arms to the top
side of $B\left(2bN\right).$}
\end{figure}
Let $k,l$ be given. Let $s_{L}$ ($s_{R}$) denote the starting (ending)
vertex of $r.$ We say that a path $\rho\subseteq R\cup r$ is good,
if it
\begin{itemize}
\item starts at $s_{L}$ and ends at $s_{R},$
\item it is non-self touching
\item and one of its lowest points is in $B_{l,k}.$
\end{itemize}
Let $\rho$ be a fixed good path. Let $Be\left(\rho,R\right)$ denote
the set of vertices in $R$ `under` $\rho.$ It is the intersection
of $R$ with the connected component of $\partial R\setminus r$ in
$cl\left(R\right)\setminus r.$ Let $Ab\left(\rho,R\right):=R\setminus Be\left(\rho,R\right).$
Recall Definition \ref{def; HCr}.
Let $O_{\rho}$ denote the event that there is path $\nu$ such that
\begin{itemize}
\item $\nu$ is non self-touching,
\item $\nu\subseteq B_{0}:=\left[-2bN,2bN\right]\boxtimes\left[-aN,2aN\right]$,
\item $\nu$ connects the left and the right side of the parallelogram $B_{1}:=\left[-2bN,2bN\right]\boxtimes\left[aN,2aN\right],$
\item $v\setminus R\subset B_{1}$ and the vertices in $\nu\setminus R$
are open,
\item each of the paths of $\nu\cap R$ is a concatenation of some open
paths which lie in $Be\left(\rho,B\left(bN\right)\right)\cap B_{1},$
and of some subpaths of $\rho.$
\end{itemize}
Let $\gamma$ denote the lowest non-self touching path in $R\cup r$
which starts at $s_{L}$ and ends at $s_{R},$ and of which all the
vertices outside of $r$ are closed. Note that on the event $L_{l,k}\left(R,r\right),$
$\gamma$ is good. By simple modifications of the arguments of Case
2 in the proof of Lemma \ref{lem: lowest of lowest} we get that there
are $c_{1}=c_{1}\left(a,b,\lambda_{1},\lambda_{2}\right)>0$ and $N_{1}=N_{1}\left(a,b,\lambda_{1},\lambda_{2}\right)$
such that
\begin{equation}
\mathbb{P}_{p_{\lambda}\left(N\right)}\left(L_{l,k}\left(R,r\right)\cap O_{\gamma}\right)\geq c_{1}\mathbb{P}_{p_{\lambda}\left(N\right)}\left(L_{l,k}\left(R,r\right)\right)\label{eq: pf compare L - 1}
\end{equation}
for $l,k\in\mathbb{N},$ $0\leq l\leq k-1,$ $\lambda\in\left[\lambda_{1},\lambda_{2}\right]$
for $N\geq N_{1}.$
Recall Definition \ref{def; HCr}. Let $\zeta\in HCr\left(B\left(2bN\right)\right).$
On the event $L_{l,k}\left(R,r\right)\cap O_{\gamma}$ we have $R\cap\left(\mathbb{Z}\boxtimes\left[3aN,bN\right]\right)\subset Ab\left(\xi\left(\gamma\right),B\left(2bN\right)\right).$
Hence the event $L_{l,k}\left(R,r\right)\cap O_{\gamma}\cap\left\{ \xi\left(\gamma\right)=\zeta\right\} $
is decreasing on the configuration in $Ab\left(\zeta,B\left(2bN\right)\right).$
Let $B_{2}=\left[-2bN,2bN\right]\boxtimes\left[3aN,4aN\right],$ $B_{3}=\left[-2bN,-bN\right]\boxtimes\left[3aN,2bN\right],$
$B_{4}=\left[bN,2bN\right]\boxtimes\left[3aN,2bN\right]$ and $\mathcal{D}=\mathcal{H}_{c}\left(B_{2}\right)\cap\mathcal{V}_{c}\left(B_{3}\right)\cap\mathcal{V}_{c}\left(B_{4}\right).$
The arguments of Case 2 of Lemma \ref{lem: lowest of lowest} give
that there exist $c_{2}=c_{2}\left(a,b,\lambda_{1},\lambda_{2}\right)>0$
and $N_{2}=N_{2}\left(a,b,\lambda_{1},\lambda_{2},k\right)$ such
that
\begin{equation}
\mathbb{P}_{p_{\lambda}\left(N\right)}\left(L_{l,k}\left(R,r\right)\cap O_{\gamma}\cap\mathcal{D}\right)\geq c_{2}\mathbb{P}_{p_{\lambda}\left(N\right)}\left(L_{l,k}\left(R,r\right)\cap O_{\gamma}\right)\label{eq: pf compare L - 2}
\end{equation}
for $l,k\in\mathbb{N},$ $0\leq l\leq k-1,$ $\lambda\in\left[\lambda_{1},\lambda_{2}\right]$
for $N\geq N_{2}.$ Note that $L_{l,k}\left(R,r\right)\cap O_{\gamma}\cap\mathcal{D}\subset L_{l,k}\left(B\left(2bN\right),top\left(2bN\right)\right).$
See Figure \ref{fig: lowest of lowest regular region} for more details.
This combined with (\ref{eq: pf compare L - 1}) and (\ref{eq: pf compare L - 2})
finishes the proof of Lemma \ref{lem: compare L}.\end{proof}
\begin{rem}
We could prove a version of Lemma \ref{lem: compare L} where we compare
the probability of the events $L_{l,k}\left(R,r\right)$ and $L_{l,k}\left(B\left(bN,top(B\left(bN\right))\right)\right).$
In view of Lemma \ref{lem: lowest of lowest}, these two versions
are equivalent. However, in the proof of this alternative version,
similarly to Case 2 in the proof of Lemma \ref{lem: lowest of lowest},
we would need an extra horizontal crossing to prolong the closed arms
of $\gamma.$ This would complicate Figure \ref{fig: lowest of lowest regular region}.
This is the reason why we chose to prove Lemma \ref{lem: compare L}
in its current form.
\end{rem}
A combination of Lemma \ref{lem: lowest of lowest} and \ref{lem: compare L}
gives the following:
\begin{cor}
\label{cor: lowest of lowest regular regions} Suppose that the conditions
of Lemma \ref{lem: lowest of lowest} hold. Then there exist $c=c\left(a,b,\lambda_{1},\lambda_{2}\right)$
and $N_{0}=N_{0}\left(a,b,\lambda_{1},\lambda_{2},k\right)$ such
that
\[
\mathbb{P}_{p_{\lambda}\left(N\right)}\left(L_{l,k}\left(R,r\right)\right)\leq ck^{-1}
\]
for $l=0,1,\ldots,k-1,$ $\lambda\in\left[\lambda_{1},\lambda_{2}\right]$
and $N\geq N_{0}.$
\end{cor}
\subsection{\label{sub: diam of active clusters}The diameter of the active clusters
close to time $1/2$}
We turn to the $N$-parameter frozen percolation process. In the introduction
we indicated that the $N$-parameter frozen percolation process exists
since it is a finite range interacting particle system. It is also
true that the process is measurable with respect to the $\tau$ values.
The following lemma follows from the arguments in the second lecture
of \cite{springerlink:10.1007/BFb0095747}.
\begin{lem}
\label{lem: measurable w.r.t tau-s}For $N\in\mathbb{N},$ the $N$-parameter
frozen percolation process is adapted to the filtration generated
by the random variables $\tau_{v},v\in V.$
\end{lem}
Recall the notation $\mathcal{C}_{a}\left(v;\lambda\right)$ from
Definition \ref{def: C_a}. We prove the following proposition.
\begin{namedthm}
[Proposition \ref{prop: active diameter}] For all $\lambda\in\mathbb{R}$
and $\varepsilon,K,\alpha>0,$ there exist $\theta=\theta\left(\lambda,\alpha,\varepsilon,K\right)>0$
and $N_{0}=N_{0}\left(\lambda,\alpha,\varepsilon,K\right)$ such that
\[
\mathbb{P}_{N}\left(\exists v\in B\left(KN\right)\mbox{ s.t. }diam\left(\mathcal{C}_{a}\left(v;\lambda\right)\right)\in\left(\left(\alpha-\theta\right)N,\left(\alpha+\theta\right)N\right)\right)<\varepsilon
\]
for $N\geq N_{0}.$\end{namedthm}
\begin{proof}
[Proof of Proposition \ref{prop: active diameter}] Due to the length
of the proof, we first give an outline.
For simplicity, we only give a sketch which shows that we can choose
$\theta\in\left(0,\frac{1\wedge\alpha}{2}\right)$ such that
\begin{equation}
\mathbb{P}_{N}\left(diam\left(\mathcal{C}_{a}\left(\lambda\right)\right)\in\left(\left(\alpha-\theta\right)N,\left(\alpha+\theta\right)N\right)\right)<\varepsilon\label{eq: pf active diameter - 0}
\end{equation}
for large $N.$
Let us denote by $\tilde{x},\tilde{y}$ a pair of sites in the active
cluster of the origin for which $d\left(\tilde{x},\tilde{y}\right)=diam\left(\mathcal{C}_{a}\left(\lambda\right)\right).$
We consider the case where $\tilde{x}$ is one of the lowest and $\tilde{y}$
is one of the highest vertices of the active cluster. The other case
where the diameter is achieved as a distance between a leftmost and
rightmost vertex can be treated in a similar way. Let $x$ ($y$)
denote a vertex which is a neighbour of $\tilde{x}$ ($\tilde{y}$),
and lies below (above) it. Note that $x$ and $y$ are closed frozen
vertices at time $p_{\lambda}\left(N\right).$
In Step 1 we apply Observation \ref{obs: closed grid-> no freezing}
and Lemma \ref{lem: there is a net} to set $\lambda_{0}$ so that
with probability close to $1,$ there are no frozen clusters at time
$p_{\lambda_{0}}\left(N\right)$ in $B\left(\left(\alpha+2\right)N\right).$
Then we investigate the configuration close to $x.$ In Step 2, we
show that with probability close to $1,$ there is a unique frozen
cluster $F$ close to $x.$ By Step 1, we can assume that it froze
at time $p_{\lambda_{F}}\left(N\right)$ for $\lambda_{F}\in\left[\lambda_{0},\lambda\right].$
In Step 4, we show that with probability close to $1,$ there is a
graph $\mathcal{R}\subseteq\mathbb{T}$ such that its boundary consists
of a $p_{\lambda_{F}}\left(N\right)$-closed arc, denoted by $r_{c},$
and a $p_{\lambda_{F}}\left(N\right)$-open arc. In Step 3,5 and 6
we show that with probability close to $1,$ we can impose some extra
conditions on $\mathcal{R}$ and $r_{c}$ and on the configuration
in $\mathcal{R}.$ We get a pair $\left(\mathcal{R},r_{c}\right)$
with the following properties:
\begin{itemize}
\item $\partial\mathcal{R}$ is a certain outermost circuit, which is measurable
with respect to the $\tau$-values in $\mathbb{T\setminus\mathcal{R}},$
(Step 4)
\item $x$ is one of the the lowest vertices of $\mathcal{R}$ with two
non-touching $p_{\lambda_{F}}\left(N\right)$-closed arms in $\mathcal{R}$
to $r_{c},$ (Step 4)
\item no matter how we change the $\tau$ values in $\mathcal{R},$ the
$N$-parameter frozen percolation outside $\mathcal{R}$ does not
change up to time $p_{\lambda}\left(N\right),$ (Step 3)
\item satisfies a technical condition (Step 5)
\item $y\in\mathbb{T\setminus}cl\left(\mathcal{R}\right)$ (Step 4).
\end{itemize}
Let us condition on the $\tau$-values in $\mathbb{T}\setminus\mathcal{R}.$
By the first and second property of $\left(\mathcal{R},r_{c}\right)$
we get that in the $N$-parameter frozen percolation process the distribution
of open and closed sites in $\mathcal{R}$ at time $p_{\lambda_{F}}\left(N\right)$
is the same as the distribution of ordinary site percolation in $\mathcal{R}$
with parameter $p_{\lambda_{F}}\left(N\right).$ This combined with
$y\in\mathbb{T}\setminus\mathcal{R}$ allows us to decouple the locations
of $x$ and $y.$ Since $d\left(\tilde{x},\tilde{y}\right)=diam\left(\mathcal{C}_{a}\left(\lambda\right)\right),$
to prove (\ref{eq: pf active diameter - 0}), it is enough to show
that the first coordinate of $x$ is not concentrated when we condition
on the configuration in $\mathbb{T}\setminus\mathcal{R}.$ We would
like to use Corollary \ref{cor: lowest of lowest regular regions}
for the pair $\left(\mathcal{R},r_{c}\right).$ Unfortunately, this
pair $\left(\mathcal{R},r_{c}\right)$ might not satisfy all the conditions
of Definition \ref{def: (a,b)-regular}. To solve this problem we
use the technical condition of Step 5 and we construct a pair $\left(\tilde{\mathcal{R}},\tilde{r}_{c}\right)$
in Step 6 such that
\begin{itemize}
\item $\tilde{\mathcal{R}}\subset\mathcal{R},$
\item a translated version of $\left(\tilde{\mathcal{R}},\tilde{r}_{c}\right)$
is $\left(\alpha_{3}N,\alpha_{2}N\right)$-regular as of Definition
\ref{def: (a,b)-regular} for some $\alpha_{2},\alpha_{3}>0,$ and
\item $x$ is one of the the lowest vertices of $\tilde{\mathcal{R}}$ with
two non-touching $p_{\lambda_{F}}\left(N\right)$-closed arms in $\tilde{\mathcal{R}}$
to $\tilde{r}_{c}.$
\end{itemize}
We apply Corollary \ref{cor: lowest of lowest regular regions} to
$\left(\tilde{\mathcal{R}},\tilde{r}_{c}\right)$ and get the required
non-concentration result and finish the proof of Proposition \ref{prop: active diameter}.
We make this argument precise in Step 7.
\begin{rem*}
The structure of the proofs in Step 2-6 is an arm event hunting procedure:
we take a some small neighbourhood of $x.$ We deduce that if the
required condition is violated, then we certain mixed near-critical
arm events or crossing events of thin parallelograms occur. These
events have upper bounds with exponents strictly larger than $2.$
Hence as we decrease the size of the neighbourhood, the probability
of the occurrence of any of these events in the parallelogram $B\left(\left(2\alpha+K+2\right)N\right)$
goes to $0.$ We set the size of the neighbourhood such that the probability
of the event where the condition of the step is not satisfied is as
small as required. This finishes the proof of the step.
\end{rem*}
\medskip
Let us turn to the precise proof.
\textbf{Step 1. }\emph{We set $\lambda_{0}$ such that with probability
close to $1,$ at time $p_{\lambda_{0}}\left(N\right),$ none of the
open clusters intersecting $B\left(\left(2\alpha+K+2\right)N\right)$
are frozen.}
By Lemma \ref{lem: there is a net} we choose $\lambda_{0}=\lambda_{0}\left(\alpha,\varepsilon,K\right)$
and $N_{0}=N_{0}\left(\alpha,\varepsilon,K\right)$ such that the
event
\[
E_{0}:=\mathcal{N}_{c}\left(\lambda_{0},1/24,2\alpha+K+4,N\right)
\]
has probability at least $1-\varepsilon/20$ for $N\geq N_{0}.$ Then
by Observation \ref{obs: closed grid-> no freezing} we have that
none of open clusters intersecting $B\left(\left(2\alpha+K\right)N\right)$
are frozen. In particular, if a vertex $v\in B\left(\left(2\alpha+K\right)N\right)$
is closed at time $p_{\lambda}\left(N\right),$ then it is $p_{\lambda_{0}}\left(N\right)$-closed.
Moreover, if $v\in B\left(\left(2\alpha+K+2\right)N\right)$ is open
at time $p_{\lambda}\left(N\right),$ then it is $p_{\lambda}\left(N\right)$-closed.
This finishes Step 1.
\medskip
Let $\theta\in\left(0,\frac{1\wedge\alpha}{2}\right).$ For $i=1,2,$
let $BA^{i}=BA^{i}\left(\theta\right)$ denote the set of vertices
$v\in B\left(KN\right)$ such that there are $\tilde{x}\left(v\right)=\left(\tilde{x}_{1}\left(v\right),\tilde{x}_{2}\left(v\right)\right),\,\tilde{y}\left(v\right)=\left(\tilde{y}_{1}\left(v\right),\tilde{y}_{2}\left(v\right)\right)\in\mathcal{C}_{a}\left(v;\lambda\right)$
such that
\begin{equation}
\tilde{y}_{i}\left(v\right)-\tilde{x}_{i}\left(v\right)=d\left(\tilde{x}\left(v\right),\tilde{y}\left(v\right)\right)=diam\left(\mathcal{C}_{a}\left(v;\lambda\right)\right)\in\left(\left(\alpha-\theta\right)N,\left(\alpha+\theta\right)N\right).\label{eq: pf active dimeter - 1}
\end{equation}
Note that
\begin{equation}
\left\{ \exists v\in B\left(KN\right)\mbox{ s.t. }diam\left(\mathcal{C}_{a}\left(v;\lambda\right)\right)\in\left(\left(\alpha-\theta\right)N,\left(\alpha+\theta\right)N\right)\right\} =\left\{ BA^{1}\cup BA^{2}\neq\emptyset\right\} .\label{eq: pf active diameter - 1.5}
\end{equation}
Let $u\in BA^{2}.$ In the following we define quantities which depend
on the value of $u.$ In notation we indicate the dependence on $u$
in the first appearance of these quantities, or when we want to emphasize
this dependence. For each $u\in BA^{2}$ we fix a pair $\left(\tilde{x},\tilde{y}\right)=\left(\tilde{x},\tilde{y}\right)\left(u\right)$
which satisfies (\ref{eq: pf active dimeter - 1}). It can happen
that there are more than one candidates for $\tilde{x}$ or $\tilde{y}.$
In this case we choose one of them in some deterministic way. (E.g
we can set $\tilde{x}$ ($\tilde{y}$) as the leftmost vertex among
the candidates.) Let $x=x\left(u\right)$ ($y\left(u\right)$) denote
a neighbour of $\tilde{x}$ ($\tilde{y}$) below $\tilde{x}$ (above
$\tilde{y}$). The active cluster $\mathcal{C}_{a}\left(u;\lambda\right)$
lies between the horizontal lines passing through $x$ and $y$ denoted
by $e_{x}$ and $e_{y}.$ Since $\theta<\alpha/2,$ the outer boundary
of $\mathcal{C}_{a}\left(u;\lambda\right)$ provides two non-touching
closed half plane arms in $x+\mathbb{Z}\boxtimes\left[0,\infty\right)$
to distance $\alpha N/2$ starting from $x.$ Since $\partial\mathcal{C}_{a}\left(u;\lambda\right)\subset B\left(\left(2\alpha+K+2\right)N\right),$
by Step 1, on the event $E_{0}$ these arms are $p_{\lambda_{0}}\left(N\right)$-closed.
We denote the one on the left (right) hand side by $c_{L}=c_{L}\left(u\right)$
($c_{R}=c_{r}\left(u\right)$). Apart from their common starting point,
$c_{L}$ and $c_{R}$ do not even touch, since any active path connecting
$\tilde{x}$ to $\tilde{y}$ separates them. Since $x$ is a closed
frozen vertex, there is at least one open frozen neighbour of $x.$
From this vertex there is a $p_{\lambda}\left(N\right)$-open arm
$o_{B}=o_{B}\left(u\right)$ to distance at least $N/2.$ See Figure
\ref{fig: mixed arms} for more details.
\begin{figure}
\centering{}\includegraphics{drawing2}\caption{\label{fig: mixed arms} The closed boundary of $\mathcal{C}_{a}\left(\lambda\right)$
give rise to the closed arms $c_{L}$ and $c_{R}$ from $x$ to $\partial B\left(x;\alpha N/2\right).$
The frozen vertex neighbouring $x$ provides the arm $o_{B}.$ }
\end{figure}
Let $\beta,\beta'\in\left(0,1\right)$ with $\beta<\beta'.$ Recall
the definition of the events $\mathcal{NA}\left(\beta,\beta'\right):=\mathcal{NA}\left(\beta,\beta',\lambda,\lambda_{0},2\alpha+K+2,N\right)$
and $\mathcal{NC}\left(\beta,\beta'\right):=\mathcal{NC}\left(\beta,\beta',\lambda,\lambda_{0},2\alpha+K+2,N\right)$
from Corollary \ref{cor: no many arms} and \ref{cor: thin crossing}.
In the following we introduce the constants $\alpha_{i}>0$ for $i=1,2,3$
such that $\alpha_{i}/\alpha_{i+1}\gg1.$ Let $\alpha_{3}\in\left(0,\frac{\alpha\wedge1}{2}\right).$
Let $z=z\left(u\right)\in V$ such that $x=x\left(u\right)\in\left[-\alpha_{3}N,\alpha_{3}N\right]\boxtimes\left(-\alpha_{3}N,\alpha_{3}N\right].$
Note that $z\in B\left(\left\lceil \frac{2\alpha+K+2}{\alpha_{3}}\right\rceil \right).$
We define $B_{3}=B_{3}\left(u\right):=B\left(\left\lfloor \alpha_{3}N\right\rfloor z;\alpha_{3}N\right).$
\medskip
\textbf{Step 2.} \emph{We show that with probability close to $1,$
there is only one frozen cluster close to $x=x\left(u\right)$ for
all $u\in BA^{2}.$}
Let $\alpha_{1}\in\left(0,\frac{\alpha\wedge1}{2}\right),$ $B_{1}=B_{1}\left(u\right):=B\left(\left\lfloor \alpha_{3}N\right\rfloor z;\alpha_{1}N\right)$
and $A_{1}=A_{1}\left(u\right):=A\left(\left\lfloor \alpha_{3}N\right\rfloor z;\alpha_{1}N,\frac{\alpha\wedge1}{2}N\right).$
Suppose that there are at least two different frozen clusters in $B_{1}.$
On the event $E_{0}$ we find $5,2$ mixed near critical arms in $A_{1}:$
the two $p_{\lambda_{0}}\left(N\right)$-closed arms $c_{L}$ and
$c_{R},$ the two $p_{\lambda}\left(N\right)$-open arms from the
two frozen clusters, and a $p_{\lambda_{0}}\left(N\right)$-closed
arm separating them. Let $E_{1}:=\mathcal{NA}\left(\alpha_{1},\frac{\alpha\wedge1}{2}\right).$
Hence we get:
\begin{claim}
\label{claim: unique F}On the event $E_{0}\cap E_{1},$ $\forall u\in BA^{2},$
there is a unique frozen cluster denoted by $F=F\left(u\right)$ which
intersects $B_{1}\left(u\right).$ Let $\lambda_{F}=\lambda_{F}\left(u\right)\in\left[\lambda_{0},\lambda\right]$
such that $F$ froze at $p_{\lambda_{F}}\left(N\right).$ On $E_{0}\cap E_{1},$
a vertex in $B_{1}\left(u\right)$ is open in the $N$-parameter frozen
percolation process at time $p_{\lambda_{F}}\left(N\right)$ if and
only if it is $p_{\lambda_{F}}\left(N\right)$-open.
\end{claim}
In the following two steps we write open (closed) for $p_{\lambda_{F}}\left(N\right)$-open
($p_{\lambda_{F}}\left(N\right)$-closed) if it is not stated otherwise.
We finish Step 2 by applying Corollary \ref{cor: no many arms} and
we set $\alpha_{1}$ such that
\begin{equation}
\mathbb{P}\left(E_{1}\right)\geq1-\varepsilon/20\label{eq: pf active dimeter - 2}
\end{equation}
for $N\geq N_{1}\left(\varepsilon,\lambda_{0},\lambda,\alpha,K\right).$
\medskip
\textbf{Step 3.} \emph{We say that a circuit is $p_{\lambda_{F}}\left(N\right)$-open-closed,
or simply open-closed, if it consists of a $p_{\lambda_{F}}\left(N\right)$-open
and a $p_{\lambda_{F}}\left(N\right)$-closed arc. Suppose that there
is a $p_{\lambda_{F}}\left(N\right)$-open-closed circuit close to
and around $x$. We show that with probability close to $1,$ no matter
how we change the $\tau$ values inside this circuit, the $N$-parameter
frozen percolation process does not change till time $p_{\lambda}\left(N\right)$
outside of the circuit.}
Let $\alpha_{2}\in\left(0,\alpha_{1}\wedge\frac{1}{4}\right),$ and
$\beta_{2}\in\left(\alpha_{2},\alpha_{1}\right)$ be some intermediate
scale. We define $B_{2}=B_{2}\left(u\right):=B\left(\left\lfloor \alpha_{3}N\right\rfloor z;\alpha_{2}N\right),$
$B_{2}'=B_{2}'\left(u\right):=B\left(\left\lfloor \alpha_{3}N\right\rfloor z;\beta_{2}N\right),$
$A_{2}=A_{2}\left(u\right):=A\left(\left\lfloor \alpha_{3}N\right\rfloor z;\alpha_{2}N,\alpha_{1}N\right)$
and $A_{2}'=A_{2}'\left(u\right):=A\left(\left\lfloor \alpha_{3}N\right\rfloor z;\beta_{2}N,\alpha_{1}N\right).$
Let $BL=BL\left(u\right)$ denote the set of bordering lines of $F\setminus B_{2}',$
that is the top- and bottom-most horizontal, left- and rightmost vertical
lines which intersect $F\setminus B_{2}'.$ We rule out the case where
there is a line in $BL$ which intersects $B_{2}'$ in the following
technical claim.
\begin{claim}
\label{claim: bdary lines of F are far from x}Let
\begin{equation}
E'_{2}=\mathcal{NA}\left(2\beta_{2},\alpha_{1}-2\beta_{2}\right)\cap\mathcal{NC}\left(2\beta_{2},2\alpha_{1}\right).\label{eq: pf active diameter - 2.1}
\end{equation}
Then
\[
E_{0}\cap E_{1}\cap E_{2}'\subset E_{0}\cap E_{1}\cap\left\{ \forall u\in BA^{2},\forall e\in BL\left(u\right)\mbox{ we have }e\cap\left(F\setminus B'_{2}\right)=\emptyset\right\} .
\]
\end{claim}
\begin{proof}
[Proof of Claim \ref{claim: bdary lines of F are far from x}] Let
$u\in BA^{2}.$ When the bottom-most line of $F\setminus B_{2}'$
intersects $B_{2}',$ then $F\subseteq\left(\mathbb{Z}\boxtimes\left[-\beta_{2}N,\infty\right)\right)+\left\lfloor \alpha_{3}N\right\rfloor z.$
We see $4$ half plane arms: $c_{L},c_{R}$ give two closed and $o_{B}$
gives an open arm, a fourth closed half plane arm separates $F$ from
the line $\mathbb{Z}\boxtimes\left\{ \left\lfloor \beta_{2}N\right\rfloor \right\} +\left\lfloor \alpha_{3}N\right\rfloor z$.
Hence $\mathcal{NA}^{c}\left(2\beta_{2},\alpha_{1}-2\beta_{2}\right)$
occurs.
If the topmost line of $F\setminus B_{2}'$ intersects $B_{2}',$
then the closed arms $c_{L}$ and $c_{R}$ stay in the parallelogram
\[
\left[-\alpha_{1}N,\alpha_{1}N\right]\boxtimes\left[-\beta_{2}N,\beta_{2}N\right]+\left\lfloor \alpha_{3}N\right\rfloor z.
\]
Hence we get a closed horizontal crossing of it, that is the event
$\mathcal{NC}^{c}\left(2\beta_{2},2\alpha_{1}\right)$ occurs.
When a leftmost bordering line of $F\setminus B_{2}'$ intersects
$B_{2}',$ then we find that the arms in $A\left(\left\lfloor \alpha_{3}N\right\rfloor z;\beta_{2}N,\alpha_{1}N\right)$
induced by $c_{L},c_{R}$ and $o_{B}$ stay in half plane
\begin{equation}
\left[-2\beta_{2}N,\infty\right)\times\mathbb{R}+\left\lfloor \alpha_{3}N\right\rfloor z.\label{eq: pf claim bdary lines of F are far from x}
\end{equation}
The frozen cluster $F$ is separated from the line $\left\{ -2\beta_{2}N\right\} \times\mathbb{R}+\left\lfloor \alpha_{3}N\right\rfloor z.$
This provides an additional closed arm in the half plane (\ref{eq: pf claim bdary lines of F are far from x}),
which together the arms induced by $c_{L},c_{R}$ and $o_{B}$ give
$4$ half plane arms, hence the event $\mathcal{NA}^{c}\left(\beta_{2},\alpha_{1}-2\beta_{2}\right)$
occurs.
The case when the rightmost bordering line of $F\setminus B_{2}'$
intersects $B_{2}'$ can be treated similarly.
With the notation (\ref{eq: pf active diameter - 2.1}) we get that
on the event $E_{0}\cap E_{1}\cap E'_{2},$ none of the lines of $BL$
intersect $B'_{2},$ which finishes the proof of Claim \ref{claim: bdary lines of F are far from x}.
\end{proof}
Now we proceed with Step 3. Let $u\in BA^{2}.$ Suppose that there
is an open-closed circuit $OC=OC\left(u\right)$ around $x$ in $B_{2}.$
Let $R=R\left(u\right)$ denote the the union of the finite connected
components of $\mathbb{T}\backslash OC.$ Let us change the $\tau$
values of the vertices in $R$ in some arbitrary non-degenerate way
(that is, the new $\tau$ values are all different), but keep the
original values outside $R.$ Let us run the $N$-parameter frozen
percolation dynamics for this modified set of $\tau$ values.
First we consider the case where this new process differs from the
old one outside of $R$ at some time $t\in\left[0,p_{\lambda_{F}}\left(N\right)\right].$
The closed arc of $OC$ stays closed till time $p_{\lambda_{F}}\left(N\right)$
in both processes. Hence it acts as a barrier for the effect of $\tau$
values in $R.$ The open arc of $OC$ is a subset of $F.$ By Claim
\ref{claim: bdary lines of F are far from x} on the event $E_{0}\cap E_{1}\cap E_{2}'$
if these two processes differ outside $R,$ then in the new one a
frozen cluster $F'$ emerged before time $p_{\lambda_{F}}\left(N\right).$
Since the two processes differ outside $R,$ we have $F'\setminus R\neq F\setminus R.$
On the event $E_{0}$ there are no $p_{\lambda_{0}}\left(N\right)$-open
clusters with diameter at least $N/4$ intersecting $B\left(\left(2\alpha+K+2\right)N\right).$
Since $\alpha_{2}<1/4$ we get that $F'$ froze in the new process
at time $p_{\lambda_{F'}}\left(N\right)$ with $\lambda_{F'}\in\left[\lambda_{0},\lambda_{F}\right].$
Let $BL'$ denote the set of bordering lines of $F'\setminus B_{2}'.$
Since $\lambda_{F'}\in\left[\lambda_{0},\lambda_{F}\right],$ the
arguments of the proof of Claim \ref{claim: bdary lines of F are far from x}
applied to the new process give that on the event $E_{0}\cap E_{1}\cap E_{2}'$
none of the lines of $BL'$ intersect $B_{2}'.$ Hence $F'\setminus R$
has two connected components $F'_{1}$ and $F'_{2}$ such that $diam\left(F_{i}'\right)<N$
for $i\in\left\{ 1,2\right\} ,$ but $diam\left(F_{1}'\cup F_{2}'\right)\geq N.$
Since $R\subset B_{2},$ each of $F_{1}',F_{2}'$ contains a $p_{\lambda_{F'}}\left(N\right)$-open
arm in the annulus $A_{2}''=A_{2}''\left(u\right):=A\left(\left\lfloor \alpha_{3}N\right\rfloor z;\alpha_{2}N,\beta_{2}N\right).$
When for some $i\in\left\{ 1,2\right\} $ $F_{i}'$ lies above $c_{L}$
and $c_{R},$ then we get a $4,3$ near critical arm event: the closed
arms induced by $c_{L},c_{R}$ and the open arm induced by $F_{i}'$
stay above $e_{x},$ and $o_{B}$ provides the fourth arm in $A_{2}''.$
Hence $\mathcal{NA}^{c}\left(\alpha_{2},\beta_{2}\right)$ occurs.
If both of $F_{1}',F_{2}'$ lie below $c_{L}$ and $c_{R}$ then we
get a $5,2$ near critical mixed arm event in $A_{2}'':$ $c_{L},c_{R}$
induce closed half plane arms in $A_{2}''.$ $F_{1}',F_{2}'$ induce
two open arms. Since $F_{1}'$ and $F_{2}'$ are different connected
components of $F'\setminus R$, there is a fifth, $p_{\lambda_{F'}}\left(N\right)$-closed,
arm separating $F_{1}'$ and $F_{2}'$ in $A_{2}''.$ Hence $\mathcal{NA}^{c}\left(\alpha_{2},\beta_{2}\right)$
occurs. Let $E_{2}=E_{2}'\cap\mathcal{NA}\left(\alpha_{2},\beta_{2}\right).$
Let us consider the other case where the new and the old process differ
from each other outside of $R$ at some time $t\in\left(p_{\lambda_{F}}\left(N\right),p_{\lambda}\left(N\right)\right],$
but they agree outside of $R$ till time $p_{\lambda_{F}}\left(N\right).$
Since till time $p_{\lambda_{F}}\left(N\right)$ the two processes
coincide outside of $R,$ then a frozen cluster $F'$ is formed at
time $p_{\lambda_{F}}\left(N\right)$ in the new process. Moreover,
$F'\setminus R=F\setminus R.$ However, the two processes differ at
some time $t\in\left(p_{\lambda_{F}}\left(N\right),p_{\lambda}\left(N\right)\right],$
hence an additional frozen cluster $F''$ has to emerge in this time
period using some of the vertices in $R.$ This induces the $5,2$
near critical mixed arm event of Step 1. Hence we proved the following
claim.
\begin{claim}
\label{claim: conf in R is indep from rest}On the event $E_{0}\cap E_{1}\cap E_{2},$
we have that $\forall u\in BA^{2},$ if there is a $p_{\lambda_{F}}\left(N\right)$-open-closed
circuit around $x=x\left(u\right)$ in $B_{2}\left(u\right)$ then
no matter how we change the $\tau$ values inside this circuit, the
frozen percolation process outside it does not change till time $p_{\lambda}\left(N\right).$
\end{claim}
We finish Step 3 by applying Corollary \ref{cor: no many arms} and
\ref{cor: no thin crossing}: we fix the value of $\beta_{2}',\beta_{2}$
and $\alpha_{2}$ such that
\begin{equation}
\mathbb{P}\left(E_{2}\right)\geq1-\varepsilon/20\label{eq: pf active dimeter - 3}
\end{equation}
for $N\geq N_{2}\left(\varepsilon,\lambda_{0},\lambda,\alpha,K\right).$
\medskip
\textbf{Step 4.} \emph{We show that with probability close to $1,$
there is a $p_{\lambda_{F}}\left(N\right)$-open-closed circuit around
$x,$ such that the location where its colour changes in the circuit
is `far` above $x.$ }
Let $u\in BA^{2}.$ Let $\alpha_{3}\in\left(0,\alpha_{2}\right),$
$B_{3}=B_{3}\left(u\right):=B\left(\left\lfloor \alpha_{3}N\right\rfloor z;\alpha_{3}N\right)$
and $A_{3}=A_{3}\left(u\right):=A\left(\left\lfloor \alpha_{3}N\right\rfloor z;\alpha_{3}N,\alpha_{2}N\right).$
Let $\delta_{3}\in\left(\alpha_{3},\alpha_{2}\right)$ be an intermediate
scale. We cut the annulus $A_{3}$ into three subannuli using two
other intermediate scales $\beta_{3},\beta_{3}'$ with $\alpha_{3}<\delta_{3}<\beta_{3}<\beta_{3}'<\alpha_{2}:$
\begin{align*}
A_{3,0}=A_{3,0}\left(u\right) & :=A\left(\left\lfloor \alpha_{3}N\right\rfloor z;\alpha_{3}N,\beta_{3}N\right),\\
A_{3,1}=A_{3,1}\left(u\right) & :=A\left(\left\lfloor \alpha_{3}N\right\rfloor z;\beta_{3}N,\beta_{3}'N\right),\\
A_{3,2}=A_{3,2}\left(u\right) & :=A\left(\left\lfloor \alpha_{3}N\right\rfloor z;\beta_{3}'N,\alpha_{2}N\right).
\end{align*}
Let $\bar{c}_{L}$ ($\bar{c}{}_{R}$) denote the closed arm induced
by $c_{L}$ ($c_{R}$) in $A_{3,1}.$
If $c_{L}$ and $c_{R}$ are not connected by a closed path in $A_{3,0}\cap\mathcal{C}_{a}\left(u;\lambda\right),$
then there is a open arm separating them. Hence we see a near critical
$4,3$ arm event: $c_{L},c_{R}$ and the separating open arm induce
disjoint half plane arms in $A_{3,0},$ and the fourth arm in $A_{3,0}$
is induced by $o_{B}$. Thus the event $\mathcal{NA}^{c}\left(\alpha_{3},\beta_{3}\right)$
occurs.
If $\bar{c}_{L}\subseteq\left[-\beta_{3}'N,-\beta_{3}N\right]\boxtimes\left[-\alpha_{3}N,\delta_{3}N\right]$
or $\bar{c}_{R}\in\left[\beta_{3}N,\beta_{3}'N\right]\boxtimes\left[-\alpha_{3}N,\delta_{3}N\right],$
then we find a closed horizontal crossing in a narrow parallelogram.
Hence the event $\mathcal{NC}^{c}\left(2\delta_{3},\beta_{3}'-\beta_{3}\right)$
occurs.
In the following we assume that both $\bar{c}_{L}$ and $\bar{c}_{R}$
leave the corresponding parallelograms. Let $w_{L}$ ($w_{R}$) be
an open frozen vertex neighbouring a vertex of $\bar{c}_{L}$ ($\bar{c}{}_{R}$)
which is outside of the aforementioned parallelogram.
Suppose that there is no open arc in $A_{3}$ connecting $w_{L}$
to $o_{B}.$ Since $w_{L}$ is open frozen at time $p_{\lambda_{F}}\left(N\right),$
it has a $p_{\lambda_{F}}\left(N\right)$-open path path to distance
$N/2.$ Let $o_{L}$ denote the part of this path till the first time
it exists $A_{3}.$ Note that $o_{L}$ and $o_{B}$ are disjoint,
and they are not connected by open path inside $A_{3}.$ We have two
cases depending on where $o_{B}$ leaves $A_{3}.$
When it leaves $A_{3}$ by exiting its outer parallelogram, than we
get a $5,2$ near critical arm event in $A_{3,2}:$ two half plane
closed arms induced by $c_{L}$ and $c_{R},$ two open arms induced
by $o_{L}$ and $o_{B}$ an extra closed arm separates $o_{L}$ and
$o_{B}$ in $A_{3,2}.$ Hence the event $\mathcal{NA}^{c}\left(\beta_{3}',\alpha_{2}\right)$
occurs. See Figure \ref{fig:4and1/2arms}.
\begin{figure}
\begin{centering}
\includegraphics[scale=0.8]{fourandhalfarm}
\par\end{centering}
\caption{\label{fig:4and1/2arms} The closed arm $c_{LB}$ separates $o_{L}$
and $o_{B}$ in $A_{3,2,x}.$ Hence $c_{L},c_{R},o_{B},c_{LB},o_{L}$
give $5,2$ near critical mixed arms.}
\end{figure}
When $o_{L}$ leaves $A_{3}$ by entering its inner parallelogram,
then we get a similar $5,2$ arm event in $A_{3,0}.$ Thus $\mathcal{NA}^{c}\left(\alpha_{3},\beta_{3}\right)$
happens. In a similar way we can show that when $w_{R}$ is not connected
to $o_{B}$ in $A_{3,x},$ then $\mathcal{NA}^{c}\left(\beta_{3}',\alpha_{2}\right)\cup\mathcal{NA}^{c}\left(\alpha_{3},\beta_{3}\right)$
occurs.
See Figure \ref{fig:OC}. Note that $w_{L},w_{R}\in\left(\mathbb{Z}\boxtimes\left[\delta_{2}N,\alpha_{2}N\right]\right)+\left\lfloor \alpha_{5}N\right\rfloor z.$
With the notation
\[
E_{3}=\mathcal{NC}\left(\alpha_{3}+\delta_{3},\beta_{3}'-\beta_{3}\right)\cap\mathcal{NA}\left(\alpha_{3},\beta_{3}\right)\cap\mathcal{NA}\left(\beta_{3}',\alpha_{2}\right)\cap\mathcal{NA}\left(\alpha_{3},\beta_{3}\right)
\]
we proved the following claim.
\begin{claim}
\label{claim: nice open-closed circuit}We have that on the event
$E_{0}\cap E_{1}\cap E_{2}\cap E_{3},$ $\forall u\in BA^{2}$ there
is a $p_{\lambda_{F}\left(u\right)}\left(N\right)$-open-closed circuit
in $A_{3}\left(u\right)$ such that locations where the colour changes
in the circuit is $\left(\mathbb{Z}\boxtimes\left[\delta_{3}N,\alpha_{2}N\right]\right)+\left\lfloor \alpha_{3}N\right\rfloor z.$
\end{claim}
We finish Step 4 by choosing the values of $\beta_{3},\beta_{3}'$
and $\delta_{3}.$ The probability of $E_{3}$ is an increasing function
of $\alpha_{3}$ for $\beta_{3},\beta_{3}',\delta_{3}$ fixed. By
Corollary \ref{cor: no many arms} and \ref{cor: no thin crossing}
we choose the value of $\beta_{3},\beta_{3}',\delta_{3},\alpha_{3}$
such that the probability of the event $E_{3}$ is at least $1-\varepsilon/20.$
We only fix $\beta_{3},\beta_{3}',\delta_{3}$ and require $\alpha_{3}$
to be small but unspecified so that
\begin{equation}
\mathbb{P}\left(E_{3}\right)\geq1-\varepsilon/20\label{eq: pf active dimeter - 4}
\end{equation}
for $N\geq N_{3}\left(\varepsilon,\alpha_{3},\lambda_{0},\lambda,\alpha,K\right).$
We choose the value of $\alpha_{3}$ in Step 6.
\medskip
\begin{figure}
\centering{}\includegraphics[scale=0.8]{fourandhalfarm2}\caption{\label{fig:OC}The circuit around $B_{3,x}$ consists of the open
arc drawn with continuous line, subpaths of $c_{L}$ and $c_{R}$
and the closed arc in $A_{3,0,x}.$ }
\end{figure}
Before Step 5, let us summarize what we have proved up to now. Let
$u\in BA^{2},$ and suppose that the event $E_{0}\cap E_{1}\cap E_{2}\cap E_{3}\left(\alpha_{3}\right)$
holds. Consider the circuit $OC$ which we constructed in Step 4.
It has a special property: as we walk from the outside of $B_{2}=B\left(\left\lfloor \alpha_{3}N\right\rfloor z;\alpha_{2}N\right)$
on one of the closed arms $c_{L}$ and $c_{R}$ towards $x,$ we hit
the closed part of $OC$ at its endpoints for the first time. See
Figure \ref{fig:OC} for more details. Let $\mathcal{OC}$ denote
the outermost open-closed circuit in $A_{3}$ satisfying the conditions
appearing Claim \ref{claim: nice open-closed circuit} and this special
property. Let $\mathcal{R}$ denote the union of finite connected
components of $\mathbb{T}\setminus\mathcal{OC}.$ Let $r_{o}$ and
$r_{c}$ denote the open and closed parts of $\mathcal{OC}=\partial\mathcal{R}.$
The pair $\left(\mathcal{R},r_{c}\right)$ and the configuration in
$\mathbb{T\setminus}\mathcal{R}$ satisfies the following conditions:
\begin{enumerate}
\item $\mathcal{R}$ is an induced subgraph of $\mathbb{T}$ such that $cl\left(\mathcal{R}\right)$
is connected, (by Claim \ref{claim: nice open-closed circuit})
\item $B\left(\left\lfloor \alpha_{3}N\right\rfloor z;\alpha_{3}N\right)=B_{3}\subseteq\mathcal{R}\subseteq B_{2}=B\left(\left\lfloor \alpha_{3}N\right\rfloor z;\alpha_{2}N\right)$
(by Claim \ref{claim: nice open-closed circuit})
\item \label{cond: conf out R}$\partial\mathcal{R}$ is disjoint union
of non-empty self avoiding paths $r_{c}$ and $r_{o},$ which are
oriented such that $\mathcal{R}$ lies on the right when we walk along
them, (by Claim \ref{claim: nice open-closed circuit})
\item \label{cond: position of r_c }$r_{c}\subseteq\left[-\alpha_{2}N,\alpha_{2}N\right]\boxtimes\left[-\alpha_{3}N,\alpha_{2}N\right]+\left\lfloor \alpha_{5}N\right\rfloor z,$
(by the proof of Claim \ref{claim: nice open-closed circuit})
\item \label{cond: end of r_c}the endpoints of $r_{c}$ denoted by $s_{L}$
and $s_{R}$ lie in the parallelogram $\left[-\alpha_{3}N,\alpha_{3}N\right]\boxtimes\left[\delta_{3}N,\alpha_{3}N\right]+\left\lfloor \alpha_{3}N\right\rfloor z,$
(by Claim \ref{claim: nice open-closed circuit})
\item \label{cond: c_L hits OC at s_L}when we walk along $c_{L}$ ($c_{R}$)
towards $x,$ we hit $\partial\mathcal{R}$ first at vertex $s_{L}$
($s_{R}$), (by the proof of Claim \ref{claim: nice open-closed circuit})
\item \label{cond: open bdry point has closed path}for every vertex $v\in r_{o},$
there is a closed path in $B_{2}\setminus\mathcal{R}$ to $\partial B_{2},$
($\mathcal{OC}$ is outermost)
\item \label{cond: closed bdry point has open path}for every vertex $v\in r_{c},$
there is an open path in $B_{2}\setminus\mathcal{R}$ to $\partial B_{2}$
or to $\left(c_{L}\cup c_{R}\right)\setminus cl\left(\mathcal{R}\right).$
($\mathcal{OC}$ is outermost)
\end{enumerate}
Note that the first three conditions coincide with the first three
conditions for the pair $\left(\mathcal{R}-\left\lfloor \alpha_{3}N\right\rfloor z,r_{c}-\left\lfloor \alpha_{3}N\right\rfloor z\right)$
being $\left(\alpha_{3}N,\alpha_{2}N\right)$-outer-regular of Definition
\ref{def: (a,b)-regular}. We add an extra condition in the next step.
Note that the vertex $x$ has two non-touching closed arms to $r_{c}.$
Moreover, by Condition \ref{cond: c_L hits OC at s_L}, $x$ is one
of the lowest vertices in $\mathcal{R}$ with this property. With
the notation of Definition \ref{def: cal L} we have that $x\in\mathcal{L}\left(\mathcal{R},r_{c}\right)$
in the $N$-parameter frozen percolation process at time $p_{\lambda_{F}}\left(N\right).$
\medskip
\textbf{Step 5.} Let $u\in BA^{2}.$ \emph{Suppose that the event
$E_{0}\cap E_{1}\cap E_{2}\cap E_{3}$ holds.} Let $\mathcal{W}=\mathcal{W}\left(u\right)$
denote the connected components of $\mathcal{R}\cap\left(\mathbb{Z}\boxtimes\left[-\left\lfloor \alpha_{3}N\right\rfloor +1,\left\lfloor 5\alpha_{3}N\right\rfloor -1\right]\right).$\emph{
Let $S_{M}$ denote the unique element of $\mathcal{W}$ which contains
$B_{3}$ as a subset. We show that with probability close to $1,$
$\partial S_{M}\cap r_{c}=\emptyset.$}
We define $e_{T}=e_{T}\left(u\right):=\left(\mathbb{Z}\boxtimes\left\{ \left\lfloor 5\alpha_{3}N\right\rfloor +1\right\} \right)+\left\lfloor \alpha_{3}N\right\rfloor z$
and $e_{B}=e_{B}\left(u\right):=\left(\mathbb{Z}\boxtimes\left\{ -\left\lfloor \alpha_{3}N\right\rfloor -1\right\} \right)+\left\lfloor \alpha_{3}N\right\rfloor z.$
Suppose that $\partial S_{M}\cap r_{c}\neq\emptyset,$ let $w\in\partial S_{M}\cap r_{c}\cap e_{T}.$
Consider the parallelogram $\bar{B}=B\left(s;\delta_{3}N/2\right).$
Let $w_{L}$ and $w_{R}$ denote the vertices of $r_{c}$ where we
exit $\bar{B}$ the first time as we walk on $r_{c}$ starting from
$s$ towards $s_{L}$ and $s_{R}$. The part of $r_{c}$ between $w_{L}$
and $w_{R}$ cuts $\bar{B}$ into two pieces. Let $\bar{B}_{I}$ ($\bar{B}_{E}$)
denote the part which is on the right (left) hand side of $r_{c}$
when we walk from $w_{L}$ to $w_{R}.$ Let $\bar{A}_{I}=\bar{B}_{I}\setminus B\left(s;6\alpha_{3}N\right)$
and $\bar{A}_{E}=\bar{B}_{E}\setminus B\left(s;6\alpha_{3}N\right).$
By Condition \ref{cond: closed bdry point has open path} above $\bar{A}_{E}$
contains an open arm. We claim that $\bar{A}_{I}$ also contains an
open arm. Suppose the contrary. Then there must be a closed non self-touching
arc in $\bar{A}_{I}$ preventing the occurrence of the open arm. Note
that this arc is contained in $\mathcal{R}.$ Then the lowest vertex
of this arc has two disjoint $p_{\lambda_{F}}\left(N\right)$-closed
arms to $r_{c},$ and it lies lower than $x\in B:=B\left(\left\lfloor \alpha_{3}N\right\rfloor z;\alpha_{3}N\right).$
This contradicts $x\in\mathcal{L}\left(\mathcal{R},r_{c}\right)$
which was shown in the lines before Step 4. See Figure \ref{fig: no ugly boundary}.
Hence $\bar{A}_{I}$ has an open arm, which together the open arm
of $\bar{A}_{E}$ and the two closed arms of $w$ provide a $4,3$
near critical mixed arm event.Hence the event $E_{4}^{c}=\mathcal{NA}^{c}\left(6\alpha_{3},\delta_{3}/2\right)$
occurs. Thus we arrive to the following claim which finishes Step
5.
\begin{claim}
\label{claim: S_M has no closed bdary}On the event $E_{0}\cap E_{1}\cap E_{2}\cap E_{3}\cap E_{4},$
we have $\partial S_{M}\cap r_{c}=\emptyset.$
\end{claim}
\begin{figure}
\begin{centering}
\includegraphics[scale=0.8]{uglypic}
\par\end{centering}
\caption{\label{fig: no ugly boundary} The grey area represents $\bar{A}_{I}.$
If there is no open arm in $\bar{A}_{I}$ then we there is a closed
arc in $\bar{A}_{I}.$ This contradicts with $x$ being one of the
lowest vertices of $\mathcal{C}_{a}\left(\lambda\right).$}
\end{figure}
\medskip
\textbf{Step 6.}\emph{ Recall Definition \ref{def: (a,b)-regular}.
We show that with probability close to $1,$ we can cut down some
parts of $\mathcal{R}$ and get a pair $\tilde{\mathcal{R}}$ and
$\tilde{r}_{c}$ such that the pair $\left(\tilde{\mathcal{R}}-\left\lfloor \alpha_{3}N\right\rfloor z,\tilde{r}_{c}-\left\lfloor \alpha_{3}N\right\rfloor z\right)$
is $\left(\alpha_{3}N,\alpha_{2}N\right)$-regular and
\[
\mathcal{L}\left(\mathcal{R},r_{c}\right)\cap B=\mathcal{L}\left(\tilde{\mathcal{R}},\tilde{r}_{c}\right)\cap B.
\]
}
Let $u\in BA^{2}.$ Suppose that the event $E_{0}\cap E_{1}\cap E_{2}\cap E_{3}\cap E_{4}$
occurs. Let $\tilde{\mathcal{R}}=\tilde{\mathcal{R}}\left(u\right)$
be the connected component of $S_{M}$ in $\mathcal{R}\setminus\bigcup_{S\in\mathcal{W}:\,\partial S\cap r_{c}\neq\emptyset}cl\left(S\right)$
and $\tilde{r}_{c}=\partial\tilde{\mathcal{R}}\setminus r_{o}.$ The
conditions before Step 5 and Claim \ref{claim: S_M has no closed bdary}
gives that the pair\emph{ }$\left(\tilde{\mathcal{R}}-\left\lfloor \alpha_{3}N\right\rfloor z,\tilde{r}_{c}-\left\lfloor \alpha_{3}N\right\rfloor z\right)$
is $\left(\alpha_{3}N,\alpha_{2}N\right)$-regular.
For $R\subset\mathbb{T}$ and $r\subset\partial R$ let $\mathcal{TA}\left(R,r\right)$
denote the set of closed vertices $v\in R$ such that $v$ has two
non-touching closed arms in $R$ to $r.$ Let $M$ denote the connected
component of $S_{M}$ in $R\setminus e_{T}.$ We show the following:
\begin{claim}
\label{claim: cut of R} Let
\begin{equation}
E_{5}:=\mathcal{NA}\left(6\alpha_{3},\beta_{4}\right)\cup\mathcal{NA}\left(\beta_{4},\delta_{3}/2\right).\label{eq: pf active diameter - 4.1}
\end{equation}
On the event $\bigcap_{i=0}^{5}E_{i}$ $\forall u\in BA^{1},$ the
pair $\left(\tilde{\mathcal{R}}-\left\lfloor \alpha_{3}N\right\rfloor z,\tilde{r}_{c}-\left\lfloor \alpha_{3}N\right\rfloor z\right)$
is $\left(\alpha_{3}N,\alpha_{2}N\right)$-regular, and
\[
\mathcal{TA}\left(\mathcal{R},r_{c}\right)\cap M=\mathcal{TA}\left(\tilde{\mathcal{R}},\tilde{r}_{c}\right)\cap M.
\]
In particular,
\[
\mathcal{L}\left(\mathcal{R},r_{c}\right)\cap B=\mathcal{L}\left(\tilde{\mathcal{R}},\tilde{r}_{c}\right)\cap B.
\]
\end{claim}
\begin{proof}
[Proof of Claim \ref{claim: cut of R}] From the definition of $\left(\mathcal{\tilde{R}},\tilde{r}_{c}\right)$
it follows that $\left(\mathcal{TA}\left(\mathcal{R},r_{c}\right)\cap M\right)\subset\left(\mathcal{TA}\left(\tilde{\mathcal{R}},\tilde{r}_{c}\right)\cap M\right).$
Suppose that $\exists v\in\left(\mathcal{TA}\left(\mathcal{R},r_{c}\right)\setminus\mathcal{TA}\left(\tilde{\mathcal{R}},\tilde{r}_{c}\right)\right)\cap M.$
Let $c_{v}^{1}$ and $c_{v}^{2}$ denote two non-touching closed arms
starting from $v$ and ending at $v^{1}\in\tilde{r}_{c}$ and $v^{2}\in\tilde{r}_{c}$
respectively. Since $v\in\mathcal{TA}\left(\mathcal{R},r_{c}\right)\setminus\mathcal{TA}\left(\tilde{\mathcal{R}},\tilde{r}_{c}\right),$
we can assume that $c_{v}^{1}$ cannot be extended in such a way that
it connects to $r_{c}$ and this extension is disjoint from and does
not touch $c_{v}^{2}.$ Hence $v^{1}\in\tilde{r}_{c}\setminus r_{c},$
and $v^{1}\in e_{T}.$ Let $S\in\mathcal{W}$ such that $v^{1}\in\partial S.$
Note that $\partial S\cap r_{c}\neq\emptyset.$ Let $s^{1},s^{2}$
denote the endpoints of the connected component of $v^{1}$ in $\partial S\cap e_{T}.$
At least one of $s^{1}$ and $s^{2}$ is in $r_{c}.$ Let $s^{1}\in r_{c}.$
Let $\beta_{4}\in\left(6\alpha_{3},\delta_{3}/2\right)$ be an intermediate
scale. We divide the annulus $A\left(v^{1};6\alpha_{3}N,\delta_{3}N/2\right)$
into the annuli
\begin{align*}
A_{4,0} & =A\left(v^{1};6\alpha_{3}N,\beta_{4}N\right),\\
A_{4,1} & =A\left(v^{1};\beta_{4}N,\delta_{3}N/2\right).
\end{align*}
We have two cases. If \emph{$c_{v}^{2}\cap A_{4,0}\neq\emptyset,$
}then we see $4$ half plane arms in $A_{4,1}:$ $r_{c}$ provides
two closed arms, and each of $c_{v}^{1}$ and $c_{v}^{2}$ gives one
closed arm. Hence the event $\mathcal{NA}^{c}\left(6\alpha_{3},\beta_{4}\right)$
occurs. If $c_{v}^{2}\cap A_{4,0}=\emptyset,$ we have $4$ half plane
arms in $A_{4,0}:$ $r_{c}$ provides two closed arms, $c_{v}^{1}$
an other closed arm, moreover, we get an open arm which separates
$c_{v}^{1}$ from $r_{c}.$ See Figure \ref{fig: cut} more details.
Hence the event $\mathcal{NA}^{c}\left(\beta_{4},\delta_{3}/2\right)$
occurs. By (\ref{eq: pf active diameter - 4.1}) this finishes the
proof of Claim \ref{claim: cut of R}.
\end{proof}
\begin{figure}
\centering{}\includegraphics[scale=0.8]{evenuglierpic}\caption{\label{fig: cut} If $c_{v}^{2}\cap A_{4,0}=\emptyset,$ we see $4$
half plane arms in $A_{4,0}:$ the two closed induced by $r_{c},$
a closed arm $c_{v}^{1},$ and an open arm $o_{v}$ which separates
$c_{v}^{1}$ from $r_{c}.$}
\end{figure}
By Corollary \ref{cor: no many arms} we set $\alpha_{3}$ such that
\begin{equation}
\mathbb{P}\left(E_{4}\cap E_{5}\right)\geq1-\varepsilon/20\label{eq: pf active dimeter - 5}
\end{equation}
for $N\geq N_{5}\left(\varepsilon,\alpha_{3},\lambda_{0},\lambda,\alpha,K\right).$
Let
\[
E=E_{0}\cap E_{1}\cap E_{2}\cap E_{3}\cap E_{4}\cap E_{5}.
\]
The combination of the lines in the beginning of Step 1, (\ref{eq: pf active dimeter - 2}),
(\ref{eq: pf active dimeter - 3}), (\ref{eq: pf active dimeter - 4})
and (\ref{eq: pf active dimeter - 5}) gives that
\begin{equation}
\mathbb{P}\left(E\right)\geq1-\varepsilon/4\label{eq: pf acitve diameter - 6}
\end{equation}
for $N\geq\bigvee_{i=0}^{5}N_{i}.$ This finishes Step 6.
\medskip
\textbf{Step 7.} \emph{We set $\theta>0$ such that $\mathbb{P}_{N}\left(BA^{2}\neq\emptyset\right)<\varepsilon/2$
for large $N,$ and conclude the proof of Proposition \ref{prop: active diameter}.}
For $v\in V,$ let
\[
Z\left(v\right):=\left\{ \exists u\in BA^{2}\mbox{ such that }z\left(u\right)=v\right\} .
\]
Hence
\[
\left\{ BA{}^{2}\neq\emptyset\right\} =\bigcup_{v\in B\left(\left\lceil \frac{2\alpha+K+2}{\alpha_{3}}\right\rceil \right)}Z\left(v\right)
\]
and
\begin{equation}
\mathbb{P}_{N}\left(BA{}^{2}\neq\emptyset,E\right)\leq\sum_{v\in B\left(\left\lceil \frac{2\alpha+K+2}{\alpha_{3}}\right\rceil \right)}\mathbb{P}_{N}\left(Z\left(v\right)\cap E\right)\label{eq: pf active diameter - 7}
\end{equation}
Note that on the event $Z\left(v\right)\cap E,$ Claim \ref{claim: unique F}
and the arguments above give that $\mathcal{C}_{a}\left(u;\lambda\right),F\left(u\right),\lambda_{F}\left(u\right),\mathcal{R}\left(u\right),r_{c}\left(u\right),\tilde{\mathcal{R}}\left(u\right)$
and $\tilde{r}_{c}\left(u\right)$ do not depend on the choice of
$u\in BA^{2}$ as long as $z\left(u\right)=v.$ Except for $\mathcal{C}_{a}\left(u,\lambda\right),$
we omit the argument $u$ from the notation above.
We set $k:=\left\lfloor 1/2\theta\right\rfloor .$ Recall that $d\left(x,y\right)=d\left(\tilde{x},\tilde{y}\right)+\sqrt{3}=diam\left(\mathcal{C}_{a}\left(u;\lambda\right)\right)+\sqrt{3},$
and $diam\left(\mathcal{C}_{a}\left(u;\lambda\right)\right)\in\left(\left(\alpha-\theta\right)N,\left(\alpha+\theta\right)N\right).$
On the event $Z\left(v\right)$ there is a unique $l=l\left(y\right)\in\left[0,k-1\right]\cap\mathbb{Z}$
such that $x\in B_{l,k}$ where
\[
B_{l,k}=B_{l,k}\left(v\right):=\left[-\alpha_{3}N,\alpha_{3}N\right]\boxtimes\left(\left(2\frac{l}{k}-1\right)\alpha_{3}N,\left(2\frac{l+1}{k}-1\right)\alpha_{3}N\right]+\left\lfloor \alpha_{3}N\right\rfloor v.
\]
Recall from the lines above Step 5 we have $x\in\mathcal{L}\left(\mathcal{R},r_{c}\right).$
From Claim \ref{claim: cut of R} we have $\mathcal{L}\left(\mathcal{R},r_{c}\right)\cap B=\mathcal{L}\left(\tilde{\mathcal{R}},\tilde{r}_{c}\right)\cap B$
where $B=B\left(\left\lfloor \alpha_{3}N\right\rfloor v;\alpha_{3}N\right).$
Hence on the event $Z\left(v\right)\cap E,$ we have $\mathcal{L}\left(\tilde{\mathcal{R}},\tilde{r}_{c}\right)\cap B_{l,k}\neq\emptyset.$
Let $\left(R,r\right)$ be a fixed pair. Hence
\begin{align}
\mathbb{P}_{N}\left(Z\left(v\right),E,\left(\mathcal{R},r_{c}\right)=\left(R,r\right)\right) & =\mathbb{P}_{N}\left(Z\left(v\right),E,\left(\mathcal{R},r_{c}\right)=\left(R,r\right),\,\mathcal{L}\left(\tilde{R},\tilde{r}\right)\cap B_{l,k}\neq\emptyset\mbox{ at time }p_{\lambda_{F}}\left(N\right)\right)\label{eq: pf active diameter - 8}
\end{align}
where $\left(\tilde{R},\tilde{r}\right)$ denotes the pair we get
when we cut down some parts of $R$ as in Step 6.
For $t\in\left[0,1\right]$ and $J\subset V$ let
\[
\mathcal{F}_{t}\left(J\right):=\sigma\left(\left\{ \tau_{w}<s\right\} \left|w\in J,\, s\in\left[0,1\right]\right.\right)
\]
denote the $\sigma$-algebra generated by the $\tau$ values of the
vertices in $J$ up to time $t.$
Lemma \ref{lem: measurable w.r.t tau-s} gives that the $N$-parameter
frozen percolation process is adapted to the filtration $\left(\mathcal{F}_{t}\left(V\right)\right)_{t\in\left[0,1\right]}.$
Hence for all $u\in BA^{2},$ $\left\{ \left(\mathcal{R},r_{c}\right)=\left(R,r\right)\right\} ,$
$l$ and $\lambda_{F}$ are measurable with respect to $\mathcal{F}_{p_{\lambda}\left(N\right)}\left(V\right).$
By Claim \ref{claim: conf in R is indep from rest} we have that on
the event $Z\left(v\right)\cap E\cap\left\{ \left(\mathcal{R},r_{c}\right)=\left(R,r\right)\right\} $
the $\tau$-values in $R$ do not influence the frozen percolation
process in $V\setminus R$ up to time $p_{\lambda}\left(N\right).$
Since $\partial\mathcal{R}$ is a certain outermost circuit, the event
$\left\{ \left(\mathcal{R},r_{c}\right)=\left(R,r\right),l=\bar{l},\lambda_{F}=\bar{\lambda}_{F}\right\} $
is measurable with respect to $\mathcal{F}_{p_{\lambda}\left(N\right)}\left(V\setminus R\right)$
on the event $Z\left(v\right)\cap E.$ Hence
\begin{align}
\mathbb{P}_{N} & \left(Z\left(v\right),E,\left(\mathcal{R},r_{c}\right)=\left(R,r\right),l=\bar{l},\lambda_{F}=\bar{\lambda}_{F},\mathcal{L}\left(\tilde{R},\tilde{r}\right)\cap B_{l,k}\neq\emptyset\mbox{ at time }p_{\lambda_{F}}\left(N\right)\left|\mathcal{F}_{p_{\lambda}\left(N\right)}\left(V\setminus R\right)\right.\right)\nonumber \\
& =\mathbf{1}\left\{ \left(\mathcal{R},r_{c}\right)=\left(R,r\right),l=\bar{l},\lambda_{F}=\bar{\lambda}_{F}\right\} \mathbb{P}_{N}\left(Z\left(v\right),E,\mathcal{L}\left(\tilde{R},\tilde{r}\right)\cap B_{\bar{l},k}\neq\emptyset\mbox{ at time }p_{\bar{\lambda}_{F}}\left(N\right)\left|\mathcal{F}_{p_{\lambda}\left(N\right)}\left(V\setminus R\right)\right.\right),\label{eq: pf active diameter - 8.1}
\end{align}
for $\bar{l}\in\left[0,k-1\right]\cap\mathbb{Z}$ and $\bar{\lambda}_{F}\in\left[\lambda_{0},\lambda\right].$
In (\ref{eq: pf active diameter - 8.1}) the definition of $\mathbf{1}\left\{ \left(\mathcal{R},r_{c}\right)=\left(R,r\right),l=\bar{l},\lambda_{F}=\bar{\lambda}_{F}\right\} $
requires some care. We define it as follows. Recall that the $N$-parameter
frozen percolation process is adapted to the filtration $\left(\mathcal{F}_{t}\left(V\right)\right)_{t\in\left[0,1\right]}.$
Hence we can assume that the sample space is $\Omega=\left[0,1\right]^{V}.$
Let $\omega\in\left[0,1\right]^{V\setminus R}.$ We set $\mathbf{1}\left\{ \left(\mathcal{R},r_{c}\right)=\left(R,r\right),l=\bar{l},\lambda_{F}=\bar{\lambda}_{F}\right\} \left(\omega\right)=1$
if and only if there is $\omega'\in\left[0,1\right]^{V}$ such that
\[
\omega'\in Z\left(v\right)\cap E\cap\left\{ \left(\mathcal{R},r_{c}\right)=\left(R,r\right),l=\bar{l},\lambda_{F}=\bar{\lambda}_{F}\right\}
\]
and $\omega\left(v\right)=\omega'\left(v\right)$ for $v\in V\setminus R.$
From Step 6 we have $\tilde{R}\subset R.$ Claim \ref{claim: cut of R}
shows that we can apply Corollary \ref{cor: lowest of lowest regular regions}
in the following. We have
\begin{align}
\mathbb{P}_{N}\left(Z\left(v\right),E,\mathcal{L}\left(\tilde{R},\tilde{r}\right)\cap B_{\bar{l},k}\neq\emptyset\right. & \left.\mbox{at time }p_{\bar{\lambda}_{F}}\left(N\right)\left|\mathcal{F}_{p_{\lambda}\left(N\right)}\left(V\setminus R\right)\right.\right)\nonumber \\
& \leq\mathbb{P}_{N}\left(\mathcal{L}\left(\tilde{R},\tilde{r}\right)\cap B_{\bar{l},k}\neq\emptyset\mbox{ at time }p_{\bar{\lambda}_{F}}\left(N\right)\left|\mathcal{F}_{p_{\lambda}\left(N\right)}\left(V\setminus R\right)\right.\right)\nonumber \\
& =\mathbb{P}_{p_{\bar{\lambda}_{F}}\left(N\right)}\left(\mathcal{L}\left(\tilde{R},\tilde{r}\right)\cap B_{\bar{l},k}\neq\emptyset\right)\nonumber \\
& \leq c_{1}k^{-1}\label{eq: pf active diameter - 9}
\end{align}
for $N\geq N_{6}\left(\lambda_{0},\lambda,\alpha_{3},\alpha_{2},k\right)$
with $c_{1}=c_{1}\left(\lambda_{0},\lambda,\alpha_{3},\alpha_{2}\right)$
of Corollary \ref{cor: lowest of lowest regular regions}. A combination
of (\ref{eq: pf active diameter - 9}) and (\ref{eq: pf active diameter - 8.1})
gives that
\begin{align*}
\mathbb{P}_{N}\left(Z\left(v\right),E,\right. & \!\!\left.\left(\mathcal{R},r_{c}\right)=\left(R,r\right),l=\bar{l},\lambda_{F}=\bar{\lambda}_{F},\mathcal{L}\left(\tilde{R},\tilde{r}\right)\cap B_{l,k}\neq\emptyset\mbox{ at time }p_{\lambda_{F}}\left(N\right)\left|\mathcal{F}_{p_{\lambda}\left(N\right)}\left(V\setminus R\right)\right.\right)\\
& \leq c_{1}k^{-1}\mathbf{1}\left\{ \left(\mathcal{R},r_{c}\right)=\left(R,r\right),l=\bar{l},\lambda_{F}=\bar{\lambda}_{F}\right\}
\end{align*}
for $N\geq N_{6}.$ Hence
\begin{align}
\mathbb{P}_{N}\left(Z\left(v\right)\cap E\right) & \leq c_{1}k^{-1}.\label{eq: pf active diameter - 9.2}
\end{align}
for $N\geq N_{6}.$
(\ref{eq: pf active diameter - 9.2}) combined with (\ref{eq: pf active diameter - 7})
we get that
\begin{align}
\mathbb{P}_{N}\left(BA{}^{2}\neq\emptyset,E\right) & \leq\sum_{v\in B\left(\left\lceil \frac{2\alpha+K+2}{\alpha_{3}}\right\rceil \right)}\mathbb{P}_{N}\left(Z\left(v\right)\cap E\right)\nonumber \\
& \leq c_{2}k^{-1}\label{eq: pf active diameter - 10}
\end{align}
with $c_{2}=c_{2}\left(\lambda_{0},\lambda,\alpha_{3},\alpha_{2},K\right)$
for $N\geq N_{6}.$ We set $\theta$ such that $k=\left\lfloor 1/2\theta\right\rfloor >4c_{2}/\varepsilon.$
A combination of (\ref{eq: pf active diameter - 10}) and (\ref{eq: pf acitve diameter - 6})
gives that
\begin{align}
\mathbb{P}_{N}\left(BA^{2}\neq\emptyset\right) & \leq\mathbb{P}_{N}\left(BA^{2}\neq\emptyset,\, E\right)+\mathbb{P}_{N}\left(E^{c}\right)\nonumber \\
& \leq c_{2}k^{-1}+\varepsilon/4<\varepsilon/2\label{eq: pf active diameter - 11}
\end{align}
for $N\geq N'=\bigvee_{i=0}^{6}N_{i}.$
A proof analogous to that of (\ref{eq: pf active diameter - 11})
gives that there is $N''=N''\left(\alpha,\lambda,K\right)$
\begin{equation}
\mathbb{P}_{N}\left(BA^{1}\neq\emptyset\right)<\varepsilon/2\label{eq: pf active diameter - 12}
\end{equation}
for $N\geq N''.$ A combination of (\ref{eq: pf active diameter - 1.5}),
(\ref{eq: pf active diameter - 11}) and (\ref{eq: pf active diameter - 12})
finishes the proof of Proposition \ref{prop: active diameter}.
|
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Christopher Lee - Families walk together down Main Street, a central hub to Six Flags that's located close to the entrance of the park.
Most public spaces aren't designed with people with autism in mind. Unfortunately, there are few places that this is more evident than amusement parks, cinemas, and theaters — places intended for entertainment and quality time with family.
Picture the entrance to Disney World, or Universal Studios: Bright, colorful, blinking lights surround the entrance sign. Dramatic orchestral music radiates from speakers in every possible direction: building walls, the sky, the ground. Thousands of people swat at one another with sweaty arms for a place in line. It's overwhelming for most people.
Now imagine also dealing with sensory sensitivity — one of the most common symptoms of autism. Noise is louder. Lights are brighter. Touch is more potent. At its worst, it can be like being trapped inside the THX opening. Sensory sensitivity can make a somewhat hectic environment into something physically painful and emotionally overpowering. Children with autism often have trouble putting this feeling into words, meaning that they may shout or cry.
But public spaces don't have to be this way — at least, not all the time. Over the past several years, private schools for children with autism and organizations like Autism Speaks have been organizing inclusive events at theaters and amusement parks that children with autism can enjoy with their families. One of the most notable examples is Autism Day at Six Flags Great Adventure in Jackson, New Jersey, organized by The Gersh Academy. It's not just a New Jersey event: families travel from all across the country to have the experience.
For the most part, Autism Day is precisely like any other day at Six Flags. There are only two crucial differences: at three different areas — beside the water in the "Fantasy Forest," the carousel, and the cafe — there are decompression tents, or "quiet areas." If a child gets upset or just needs a break, these areas are shaded respites from the rest of the park, complete with iPads and small, sensory friendly pools.
But perhaps more importantly, the event includes only children with autism, their families, and teachers trained to help children with autism. Yes, for "Autism Day," this point seems rather obvious. But the distinction is important. It's what makes the event more than a regular day at Six Flag with amenities for children with autism.
The biggest obstacle to people with autism and their families face in public spaces often isn't a lack of amenities: it's cruelty from other people and families. As the older sister of a brother who has autism, it's an experience I understand intimately.
When ignorant strangers see a child with autism scream or cry, some will glare at the family, even the child. Occasionally, a person will approach the parents, berate them, ask why they don't have better control over their child. But instances like this make up a small fraction of a time that a family spends in public. The most frequent and more painful reactions come during normal moments, when the child isn't upset and the family is generally happy. Some people will whisper and stare at families for no apparent reason — as if they don't believe that the family has the right to exist in public space. Thankfully, very few people behave this way. But even one person is too many.
In an ideal world, "Autism Days" would not have to exist. Quiet, relaxing areas would be a common amenity in public and private space. People with and without autism would coexist without hesitation or judgement. But for now, Autism Days are living proof that there are vast networks of people who love and care about children with autism. For parents with carefree, polaroid-tinted memories of the amusements parks from their childhood, it's a chance to share those memories with their own children. And for children with autism, it's just a bright, happy day of summer.
Hear interviews with children, parents, and the founder of The Gersh Academy on The Outline World Dispatch. Listen later on your favorite app or device below.
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"redpajama_set_name": "RedPajamaC4"
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It's the season for diseases. Flu, colds, bronchitis, you name it–it's out there. Those who make it through the season without getting sick are generally those who take care of their bodies in such a way their immune systems remain strong enough to fight off exposure to disease. However, there is another way in which we fight off disease.
The flu shot. The polio vaccine. Inoculation.
While churches don't want to intentionally introduce disease into the system, most have some element of disease in their system all the time. It's the nature of the church. We are human beings with sinful natures in need of transformation, repentance, forgiveness. Even leaders bring disease into the church without recognizing it.
Whether a church Body ultimately finds itself sick or whether proper handling of the disease continues to build the immune system of the church is a matter of proper response. Exposure to disease is part of ministry. Obviously, we're talking about sinful behavior, viral behavior–expressing itself in symptoms like critical spirit, division, apathy, immorality and the like.
Healthy churches understand the importance of health and the importance of inoculation. In ministry inoculation is the recognition of disease and dealing with it in such a way the Body emerges from the experience healthier and more immune to dangerous disease than before.
Acknowledge your church isn't completely healthy. Ever. As long as there are people in the church, sin will be present.
Recognize the behavior, not the person, is the source of disease that threatens the health of the Body. People can change their behavior.
Accept responsibility for the health of the church. One thing we see in the letters to the seven churches from Revelation is not only Jesus' Lordship, but His expectation that churches correct sinful attitudes and behaviors. The good news is Jesus also provides us the spiritual resources to deal with these problems according to His will.
Deal with it early. This doesn't mean you break out a bazooka to kill a horse fly–creating leadership crises over every mildly critical comment. It means you don't let problems grow. When we deal with problems early, the response can be minimal. If it grows, you'll have to deal with it more aggressively–and the problem will escalate.
Deal with it firmly and biblically. Somewhere, freedom of expression became a civil right in the minds of many Christians. That's America, not the Kingdom. In the Kingdom, it's out of the heart the mouth speaks. In the Kingdom, we are told: "As for a person who stirs up division, after warning him once and then twice, have nothing more to do with him, knowing that such a person is warped and sinful; he is self-condemned" Titus 3:10-11. This doesn't mean we should try to control every thought people have. Rather, it means we recognize viral behavior and seek to correct it according to biblical norms.
Choose health over size. You will inevitably lose some people if dealing with conflict in this way is new to your church. If it's chemotherapy and not inoculation that must take place for the Body to be restored to health…expect to lose some people. However, healthy churches will grow. It's the nature of the Kingdom. Nothing, NOTHING will help your church grow over time like perennial health. This doesn't mean every growing church is healthy. However, I am suggesting that Jesus blesses churches committed to keeping His Bride as unblemished as possible in our broken world. He also wants to redeem what is lost. Many churches like to think of themselves as being "pruned" when in reality Christ is moving their lampstand. However, I also know of numerous churches that turned around quickly and permanently after an initial period of decline by removing or correcting unhealthy ministry leaders, small group leaders, elders, and ministers.
By God's grace, stay healthy. If you're sick, by God's grace, get healthy. It makes all the difference. Our congregations aren't in a disease-free world. However, the Body grows stronger and healthier by learning to deal with disease properly.
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extern int send_alert(const GpErrorData * errorData);
extern int send_alert_from_chunks(const PipeProtoChunk *chunk, const PipeProtoChunk * saved_chunks_in);
extern char *get_str_from_chunk(CSVChunkStr *chunkstr, const PipeProtoChunk *saved_chunks);
#endif
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{"url":"http:\/\/en.wikipedia.org\/wiki\/Equation_of_time","text":"# Equation of time\n\nThe equation of time \u2014 above the axis a sundial will appear fast relative to a clock showing local mean time, and below the axis a sundial will appear slow.\nThis graph uses the opposite sign to the one above it. There is no universally followed convention for the sign of the equation of time.\n\nThe equation of time describes the discrepancy between two kinds of solar time. These are apparent solar time, which directly tracks the motion of the sun, and mean solar time, which tracks a fictitious \"mean\" sun with noons 24 hours apart. Apparent (or true) solar time can be obtained by measurement of the current position (hour angle) of the Sun, or indicated (with limited accuracy) by a sundial. Mean solar time, for the same place, would be the time indicated by a steady clock set so that over the year its differences from apparent solar time average to zero.[1]\n\nThe equation of time is the east or west component of the analemma, a curve representing the angular offset of the Sun from its mean position on the celestial sphere as viewed from Earth. The equation of time values for each day of the year, compiled by astronomical observatories, were widely listed in almanacs and ephemerides.[2][3]\n\n## The concept\n\nDuring a year the equation of time varies as shown on the graph; its change from one year to the next is slight. Apparent time, and the sundial, can be ahead (fast) by as much as 16 min 33 s (around 3 November), or behind (slow) by as much as 14 min 6 s (around 12 February). The equation of time has zeros near 15 April, 13 June, 1 September and 25 December. Ignoring very slow changes in the Earth's orbit and rotation, these events are repeated at the same times every tropical year. However, due to the non-integral number of days in a year, these dates can vary by a day or so from year to year.[4][5]\n\nThe graph of the equation of time is closely approximated by the sum of two sine curves, one with a period of a year and one with a period of half a year. The curves reflect two astronomical effects, each causing a different non-uniformity in the apparent daily motion of the Sun relative to the stars:\n\n\u2022 the obliquity of the ecliptic (the plane of the Earth's annual orbital motion around the Sun), which is inclined by about 23.44 degrees relative to the plane of the Earth's equator; and\n\nThe equation of time is constant only for a planet with zero axial tilt and zero orbital eccentricity. On Mars the difference between sundial time and clock time can be as much as 50 minutes, due to the considerably greater eccentricity of its orbit. The planet Uranus, which has an extremely large axial tilt, has an equation of time that makes its days start and finish several hours earlier or later depending on the time of its solar year orbital period.\n\n## Sign of the equation of time\n\nThere is no universally accepted definition of the sign of the equation of time. Some publications show it as positive when a sundial is ahead of a clock, as shown in the upper graph above; others when the clock is ahead of the sundial, as shown in the lower graph. In the English-speaking world, the former usage is the more common, but is not always followed. Anyone who makes use of a published table or graph should first check its sign usage. Often, there is a note or caption which explains it. Otherwise, the sign can be determined by knowing that, during the first three months of each year, the clock is ahead of the sundial. The mnemonic \"NYSS\" (pronounced \"nice\"), for \"New Year, Sundial Slow\", can be useful. Some published tables avoid the ambiguity by not using signs, but by showing phrases such as \"sundial fast\" or \"sundial slow\" instead.[6]\n\nIn this article, and others in English Wikipedia, a positive value of the equation of time implies that a sundial is ahead of a clock.\n\n## History\n\nThe word \"equation\" is here used in a somewhat archaic sense, meaning \"correction\". Prior to the mid-17th century, when pendulum-controlled mechanical clocks were invented, sundials were the only reliable timepieces, and were generally considered to tell the right time.\n\nA description of apparent and mean time was given by Nevil Maskelyne in the Nautical Almanac for 1767: \"Apparent Time is that deduced immediately from the Sun, whether from the Observation of his passing the Meridian, or from his observed Rising or Setting. This Time is different from that shewn by Clocks and Watches well regulated at Land, which is called equated or mean Time.\" (He went on to say that, at sea, the apparent time found from observation of the sun must be corrected by the equation of time, if the observer requires the mean time.)[1]\n\nThe right time was essentially defined as that which was shown by a sundial. When good mechanical clocks were introduced they agreed with sundials only near four dates each year, so the equation of time was used to \"correct\" their readings to obtain sundial time. Some clocks, called equation clocks, included an internal mechanism to perform this \"correction\". Later, as clocks became the dominant good timepieces, uncorrected clock time i.e. \"mean time\" became the accepted standard. The readings of sundials, when they were used, were then, and often still are, corrected with the equation of time, used in the reverse direction from previously, to obtain clock time. Many sundials therefore have tables or graphs of the equation of time engraved on them to allow the user to make this correction.\n\nThe equation of time was used historically to set clocks. Between the invention of accurate clocks in 1656 and the advent of commercial time distribution services around 1900, one of two common land-based ways to set clocks was by observing the sun's transit across the meridian \u2014 the moment the sun passed overhead, the clock was set to noon and offset by the number of minutes given by the equation of time for that date. This calculated the mean time, albeit local to a point of longitude. (The second method did not use the equation of time; instead, it used stellar observations to give sidereal time, exploiting the relationship between sidereal time and solar time.)[7]\n\nOf course, the equation of time can still be used, when required, to obtain solar time from clock time. Devices such as solar trackers, which move to keep pace with the Sun's movements in the sky, frequently do not include sensors to determine the Sun's position. Instead, they are controlled by a clock mechanism, along with a mechanism that incorporates the equation of time to make the device keep pace with the Sun.\n\n### Ancient history \u2014 Babylon and Egypt\n\nThe irregular daily movement of the Sun was known by the Babylonians, and Book III of Ptolemy's Almagest is primarily concerned with the Sun's anomaly. Ptolemy discusses the correction needed to convert the meridian crossing of the Sun to mean solar time and takes into consideration the nonuniform motion of the Sun along the ecliptic and the meridian correction for the Sun's ecliptic longitude. He states the maximum correction is 8\u00a013 time-degrees or 59 of an hour (Book III, chapter 9).[8] However he did not consider the effect to be relevant for most calculations since it was negligible for the slow-moving luminaries and only applied it for the fastest-moving luminary, the Moon.\n\n### Medieval and Renaissance astronomy\n\nG. J. Toomer uses the Medieval term equation from the Latin aequatio [n 1], for Ptolemy's difference between the mean solar time and the true solar time. Kepler's definition of the equation is \"the difference between the number of degrees and minutes of the mean anomaly and the degrees and minutes of the corrected anomaly.\"[9]\n\n### Apparent time versus mean time\n\nUntil the invention of the pendulum and the development of reliable clocks during the 17th century, the equation of time as defined by Ptolemy remained a curiosity, of importance only to astronomers. However, when mechanical clocks started to take over timekeeping from sundials, which had served humanity for centuries, the difference between clock time and solar time became an issue for everyday life. Apparent solar time (or true or real solar time) is the time indicated by the Sun on a sundial (or measured by its transit over a preferred local meridian), while mean solar time is the average as indicated by well-regulated clocks. The first tables to give the equation of time in an essentially correct way were published in 1665 by Christiaan Huygens.[10] Huygens set his values for the equation of time so as to make all values positive throughout the year.[11][n 2]\n\nAnother set of tables was published in 1672\u201373 by John Flamsteed who later became the first Astronomer Royal of the new Greenwich Observatory. These appear to have been the first essentially correct tables that gave today's meaning of Mean Time (rather than mean time based on the latest sunrise of the year as proposed by Huygens). Flamsteed adopted the convention of tabulating and naming the correction in the sense that it was to be applied to the apparent time to give mean time.[12]\n\nThe equation of time, correctly based on the two major components of the Sun's irregularity of apparent motion,[n 3] was not generally adopted until after Flamsteed's tables of 1672\u201373, published with the posthumous edition of the works of Jeremiah Horrocks.[13]\n\nRobert Hooke (1635\u20131703), who mathematically analyzed the universal joint, was the first to note that the geometry and mathematical description of the (non-secular) equation of time and the universal joint were identical, and proposed the use of a universal joint in the construction of a \"mechanical sundial\".[14]\n\n### 18th and early 19th centuries\n\nThe corrections in Flamsteed's tables of 1672\/3 and 1680 gave mean time computed essentially correctly and without need for further offset. But the numerical values in tables of the equation of time have somewhat changed since then, owing to three factors:\n\n\u2022 general improvements in accuracy that came from refinements in astronomical measurement techniques,\n\u2022 slow intrinsic changes in the equation of time, occurring as a result of small long-term changes in the Earth's obliquity and eccentricity (affecting for instance the distance and dates of perihelion), and\n\u2022 the inclusion of small sources of additional variation in the apparent motion of the Sun, unknown in the 17th century, but discovered from the 18th century onwards, including the effects of the Moon[n 4], Venus and Jupiter.[15]\nA sundial made in 1812, by Whitehurst & Son with a circular scale showing the equation of time correction. This is now on display in the Derby Museum.\n\nFrom 1767 to 1833, the British Nautical Almanac and Astronomical Ephemeris tabulated the equation of time in the sense 'mean minus apparent solar time'. Times in the Almanac were in apparent solar time, because time aboard ship was most often determined by observing the Sun. In the unusual case that the mean solar time of an observation was needed, one would apply the equation of time to apparent solar time. In the issues since 1834, all times have been in mean solar time, because by then the time aboard ship was increasingly often determined by marine chronometers. In the unusual case that the apparent solar time of an observation was needed, one would apply the equation of time to mean solar time, requiring all differences in the equation of time to have the opposite sign than before.\n\nAs the apparent daily movement of the Sun is one revolution per day, that is 360\u00b0 every 24 hours, and the Sun itself appears as a disc of about 0.5\u00b0 in the sky, simple sundials can be read to a maximum accuracy of about one minute. Since the equation of time has a range of about 33 minutes, the difference between sundial time and clock time cannot be ignored. In addition to the equation of time, one also has to apply corrections due to one's distance from the local time zone meridian and summer time, if any.\n\nThe tiny increase of the mean solar day itself due to the slowing down of the Earth's rotation, by about 2 ms per day per century, which currently accumulates up to about 1 second every year, is not taken into account in traditional definitions of the equation of time, as it is imperceptible at the accuracy level of sundials.\n\n## Explanations for the major components of the equation of time\n\n### Eccentricity of the Earth's orbit\n\nGraph showing the equation of time (red solid line) along with its two main components plotted separately, the part due to the obliquity of the ecliptic (mauve dashed line) and the part due to the Sun's varying apparent speed along the ecliptic due to the eccentricity of the Earth's orbit (dark blue dash & dot line)\n\nThe Earth revolves around the Sun. As seen from Earth, the Sun appears to revolve once around the Earth through the background stars in one year. If the Earth orbited the Sun with a constant speed, in a circular orbit in a plane perpendicular to the Earth's axis, then the Sun would culminate every day at exactly the same time, and be a perfect time keeper (except for the very small effect of the slowing rotation of the Earth). But the orbit of the Earth is an ellipse not centered on the Sun, and its speed varies between 30.287 and 29.291\u00a0km\/s, according to Kepler's laws of planetary motion, and its angular speed also varies, and thus the Sun appears to move faster (relative to the background stars) at perihelion (currently around 3 January) and slower at aphelion a half year later. At these extreme points this effect varies the real solar day by 7.9 seconds per day from its mean. Consequently the smaller daily differences on other days in speed are cumulative until these points, reflecting how the planet accelerates and decelerates compared to the mean. As a result the eccentricity of the Earth's orbit contributes a sine wave variation with an amplitude of 7.66 minutes and a period of one year to the equation of time. The zero points are reached at perihelion (at the beginning of January) and aphelion (beginning of July); the extreme values are in early April (negative) and early October (positive).\n\n### Obliquity of the ecliptic\n\nSun and planets at solar midday (Ecliptic in red, Sun and Mercury in yellow, Venus in white, Mars in red, Jupiter in yellow with red spot, Saturn in white with rings).\n\nHowever, even if the Earth's orbit were circular, the perceived motion of the Sun along our celestial equator would still not be uniform. This is a consequence of the tilt of the Earth's rotational axis with respect to the plane of its orbit, or equivalently, the tilt of the ecliptic (the path of the Sun seems to take in the celestial sphere) with respect to the celestial equator. The projection of this motion onto our celestial equator, along which \"clock time\" is measured, is a maximum at the solstices, when the yearly movement of the Sun is parallel to the equator (causing amplification of perceived speed) and yields mainly a change in right ascension. It is a minimum at the equinoxes, when the Sun's apparent motion is more sloped and yields more change in declination, leaving less for the component in right ascension, which is the only component that affects the duration of the solar day. A practical illustration of obliquity is that the daily shift of the shadow cast by the Sun in a sundial even on the equator is smaller close to the equinoxes and greater close to the solstices. If this effect operated alone, then days would be up to 24 hours and 20.3 seconds long (measured solar noon to solar noon) near the solstices, and as much as 20.3 seconds shorter than 24 hours near the equinoxes.\n\nIn the figure on the right, we can see the monthly variation of the apparent slope of the plane of the ecliptic at solar midday as seen from Earth. This variation is due to the apparent precession of the rotating Earth through the year, as seen from the Sun at solar midday.\n\nIn terms of the equation of time, the inclination of the ecliptic results in the contribution of a sine wave variation with an amplitude of 9.87 minutes and a period of a half year to the equation of time. The zero points of this sine wave are reached at the equinoxes and solstices, while the extrema are at the beginning of February and August (negative) and the beginning of May and November (positive).\n\n## Secular effects\n\nThe two above mentioned factors have different wavelengths, amplitudes and phases, so their combined contribution is an irregular wave. At epoch 2000 these are the values (in minutes and seconds with UT dates):\n\n minimum \u221214:15 11 February zero 00:00 15 April maximum +03:41 14 May zero 00:00 13 June minimum \u221206:30 26 July zero 00:00 1 September maximum +16:25 3 November zero 00:00 25 December\n\n[citation needed]\n\nE.T. = apparent \u2212 mean. Positive means: Sun runs fast and culminates earlier, or the sundial is ahead of mean time. A slight yearly variation occurs due to presence of leap years, resetting itself every 4 years.\n\nThe exact shape of the equation of time curve and the associated analemma slowly change[16] over the centuries, due to secular variations in both eccentricity and obliquity. At this moment both are slowly decreasing, but they increase and decrease over a timescale of hundreds of thousands of years. If\/when the Earth's orbital eccentricity (now about 0.0167 and slowly decreasing) reaches 0.047, the eccentricity effect may in some circumstances overshadow the obliquity effect, leaving the equation of time curve with only one maximum and minimum per year, as is the case on Mars.[17]\n\nOn shorter timescales (thousands of years) the shifts in the dates of equinox and perihelion will be more important. The former is caused by precession, and shifts the equinox backwards compared to the stars. But it can be ignored in the current discussion as our Gregorian calendar is constructed in such a way as to keep the vernal equinox date at 21 March (at least at sufficient accuracy for our aim here). The shift of the perihelion is forwards, about 1.7 days every century. In 1246 the perihelion occurred on 22 December, the day of the solstice, so the two contributing waves had common zero points and the equation of time curve was symmetrical: in Astronomical Algorithms Meeus gives February and November extrema of 15 min 39 sec and May and July ones of 4 min 58 sec. Before that time the February minimum was larger than the November maximum, and the May maximum larger than the July minimum. In fact, years before \u22121900 or 1900 BCE the May maximum was larger than the November maximum. In the year \u22122000 the May maximum was +12 minutes and a couple seconds while the November maximum was just less than 10 minutes. The secular change is evident when one compares a current graph of the equation of time (see below) with one from 2000 years ago, e.g., one constructed from the data of Ptolemy.[citation needed]\n\n## Graphical representation\n\nAnimation showing Equation of Time and Analemma path over one year.\n\n## Practical use\n\nIf the gnomon (the shadow-casting object) is not an edge but a point (e.g., a hole in a plate), the shadow (or spot of light) will trace out a curve during the course of a day. If the shadow is cast on a plane surface, this curve will be a conic section (usually a hyperbola), since the circle of the Sun's motion together with the gnomon point define a cone. At the spring and fall equinoxes, the cone degenerates into a plane and the hyperbola into a line. With a different hyperbola for each day, hour marks can be put on each hyperbola which include any necessary corrections. Unfortunately, each hyperbola corresponds to two different days, one in each half of the year, and these two days will require different corrections. A convenient compromise is to draw the line for the \"mean time\" and add a curve showing the exact position of the shadow points at noon during the course of the year. This curve will take the form of a figure eight and is known as an analemma. By comparing the analemma to the mean noon line, the amount of correction to be applied generally on that day can be determined.\n\nThe equation of time is used not only in connection with sundials and similar devices, but also for many applications of solar energy. Machines such as solar trackers and heliostats have to move in ways that are influenced by the equation of time.\n\nCivil time is the local mean time for a meridian that often passes near the center of the time zone, and may possibly be further altered by daylight saving time. When the apparent solar time that corresponds to a given civil time is to be found, the difference in longitude between the site of interest and the time zone meridian, daylight saving time, and the equation of time must all be considered.[18]\n\n## Calculating the equation of time\n\nThe equation of time is obtained from a published table, or a graph. For dates in the past such tables are produced from measurements done at the time, or by calculation; for future dates, of course, tables can only be calculated. In devices such as computer-controlled heliostats the computer is often programmed to calculate the equation of time. The calculation can be numerical or analytical. The former are based on numerical integration of the differential equations of motion, including all significant gravitational and relativistic effects. The results are accurate to better than 1 second of time and are the basis for modern almanac data. The latter are based on a solution that includes only the gravitational interaction between the Sun and Earth, simpler than but not as accurate as the former. Its accuracy can be improved by including small corrections.\n\nThe following discussion describes a reasonably accurate (agreeing with Almanac data to within 3 seconds of time over a wide range of years) algorithm for the equation of time that is well known to astronomers.[19] It also shows how to obtain a simple approximate formula (accurate to within 1 minute of time over a large time interval), that can be easily evaluated with a calculator and provides the simple explanation of the phenomenon that was used previously in this article.\n\n### Mathematical description\n\nThe precise definition of the Equation of Time is[20]\n\n$\\mbox{EOT} = \\mbox{GHA} - \\mbox{GMHA}$\n\nThe quantities occurring in this equation are\n\n\u2022 EOT, the time difference between apparent solar time and mean solar time;\n\u2022 GHA, the Greenwich Hour Angle of the apparent (actual) Sun;\n\u2022 GMHA = Universal Time \u2212 Offset, the Greenwich Mean Hour Angle of the mean (fictitious) Sun.\n\nHere time and angle are quantities that are related by factors such as: 2\u03c0 radians = 360\u00b0 = 1 day = 24 hours. The difference, EOT, is measurable since GHA is an angle that can be measured and Universal Time, UT, is a scale for the measurement of time. The Offset by \u03c0 = 180\u00b0 = 12 hours from UT is needed because UT is zero at mean midnight while GMHA = 0 at mean noon.[n 5] Both GHA and GMHA, like all physical angles, have a mathematical, but not a physical discontinuity at their respective (apparent and mean) noon. Despite the mathematical discontinuities of its components, EOT is defined as a continuous function by adding (or subtracting) 24 hours in the small time interval between the discontinuities in GHA and GMHA.\n\nAccording to the definitions of the angles on the celestial sphere GHA = GAST - \u03b1 (see hour angle)\nwhere:\n\n\u2022 GAST is the Greenwich apparent sidereal time (the angle between the apparent vernal equinox and the meridian in the plane of the equator). This is a known function of UT.[21]\n\u2022 \u03b1 is the right ascension of the apparent Sun (the angle between the apparent vernal equinox and the actual Sun in the plane of the equator).\n\nOn substituting into the equation of time, it is\n\n$\\mbox{EOT = GAST}-\\alpha-\\mbox{UT}+\\mbox{Offset}$\n\nLike the formula for GHA above, one can write GMHA = GAST - \u03b1M, where the last term is the right ascension of the mean Sun. The equation is often written in these terms as[22]\n\n$\\mbox{EOT}=\\alpha_M-\\alpha$\n\nwhere \u03b1M = GAST - UT + Offset. In this formulation a measurement or calculation of EOT at a certain value of time depends on a measurement or calculation of \u03b1 at that time. Both \u03b1 and \u03b1M vary from 0 to 24 hours during the course of a year. The former has a discontinuity at a time that depends on the value of UT, while the later has its at a slightly later time. As a consequence, when calculated this way EOT has two, artificial, discontinuities. They can both be removed by subtracting 24 hours from the value of EOT in the small time interval after the discontinuity in \u03b1 and before the one in \u03b1M. The resulting EOT is a continuous function of time.\n\nAnother definition, denoted E to distinguish it from EOT, is\n\n$\\mbox{E = GMST}-\\alpha-\\mbox{UT}+\\mbox{Offset}$\n\nHere GMST = GAST - eqeq, is the Greenwich mean sidereal time (the angle between the mean vernal equinox and the mean Sun in the plane of the equator). Therefore GMST is an approximation to GAST (and E is an approximation to EOT); eqeq is called the equation of the equinoxes and is due to the wobbling, or nutation of the Earth's axis of rotation about its precessional motion. Since the amplitude of the nutational motion is only about 1.2 sec of time (18 arcsec of longitude) the difference between EOT and E can be ignored unless one is interested in subsecond accuracy.\n\nA third definition, denoted \u0394t to distinguish it from EOT and E, and now called the Equation of Ephemeris Time[23] (prior to the distinction that is now made between EOT, E, and \u0394t the latter was known as the Equation of Time) is\n\n$\\Delta t = \\Lambda-\\alpha$\n\nhere \u039b is the ecliptic longitude of the mean Sun (the angle from the mean vernal equinox to the mean Sun in the plane of the ecliptic).\n\nThe difference \u039b - [GMST - UT + Offset] is 1.3 seconds of time from 1960 to 2040. Therefore over this restricted range of years \u0394t is an approximation to EOT whose error is in the range 0.1 to 2.5 sec depending on the longitude correction in the equation of the equinoxes; for many purposes, for example correcting a sundial, this accuracy is more than good enough.\n\n### Right ascension calculation\n\nThe right ascension, and hence the equation of time, can be calculated from Newton's two-body theory of celestial motion, in which the bodies (earth and sun) describe elliptical orbits about their common mass center. Using this theory the equation of time becomes\n\n$\\Delta t=M+\\lambda_p-\\alpha$\n\nwhere the new angles that appear are\n\n\u2022 M = 2\u03c0(t - tp) \/tY, is the mean anomaly, the angle from the periapsis of the elliptical orbit to the mean Sun; its range is from 0 to 2\u03c0 as t increases from tp to tp + tY;\n\u2022 tY = 365.2596358 day is the length of time in an anomalistic year: the time interval between two successive passages of the periapsis;\n\u2022 \u03bbp = \u039b-M, is the ecliptic longitude of the periapsis;\n\u2022 t is dynamical time, the independent variable in the theory. Here it is taken to be identical with the continuous time based on UT (see above), but in more precise calculations (of E or EOT) the small difference between them must be accounted for[24] as well as the distinction between UT1 and UTC.\n\nTo complete the calculation three additional angles are required:\n\n\u2022 E the Sun's eccentric anomaly (note that this is different from E);\n\u2022 \u03bd the Sun's true anomaly;\n\u2022 \u03bb = \u03bd + \u03bbp the Sun's true longitude on the ecliptic.\nThe celestial sphere and the Sun's elliptical orbit as seen by a geocentric observer looking normal to the ecliptic showing the 6 angles (M, \u03bbp, \u03b1, \u03bd, \u03bb, E) needed for the calculation of the equation of time. For the sake of clarity the drawings are not to scale.\n\nAll these angles are shown in the figure on the right, which shows the celestial sphere and the Sun's elliptical orbit seen from the Earth (the same as the Earth's orbit seen from the Sun). In this figure \u03b5 is the obliquity, while e = [1 \u2212 (b\/a)2]1\/2 is the eccentricity of the ellipse.\n\nNow given a value of 0\u2264M\u22642\u03c0, one can calculate \u03b1(M) by means of the following, well known, procedure:[19]\n\nFirst, given M, calculate E from Kepler's equation[25]\n\n$M=E-e\\sin E$\n\nAlthough this equation cannot be solved exactly in closed form, values of E(M) can be obtained from infinite (power or trigonometric) series, graphical, or numerical methods. Alternatively, note that for e = 0, E = M, and by iteration,[26] E ~ M + e sin M. This approximation can be improved, for small e, by iterating again, E ~ M + e sin M + (1\/2) e2 sin 2M, and continued iteration produces successively higher order terms of the power series expansion in e. For small values of e (much less than 1) two or three terms of the series give a good approximation for E; the smaller e, the better the approximation.\n\nNext, knowing E, calculate the true anomaly \u03bd from an elliptical orbit relation[27]\n\n$\\nu=2\\tan^{-1}\\left[\\sqrt{\\frac{1+e}{1-e}}\\tan\\frac{E}{2} \\right]$\n\nThe correct branch of the multiple valued function tan\u22121x to use is the one that makes \u03bd a continuous function of E(M) starting from \u03bd(E=0) = 0. Thus for 0 E < \u03c0 use tan\u22121x = Tan\u22121x, and for \u03c0 < E 2\u03c0 use tan\u22121x = Tan\u22121x + \u03c0. At the specific value E = \u03c0 for which the argument of tan is infinite, use \u03bd = E. Here Tan\u22121x is the principal branch, |Tan\u22121x| < \u03c0\/2; the function that is returned by calculators and computer applications. Alternatively, this function can be expressed in terms of its Taylor series in e, the first three terms of which are, \u03bd ~ E + e sin E + (1\/4) e2 sin 2E. For small e this approximation (or even just the first two terms) is a good one. Combining the approximation for E(M) with this one for \u03bd(E) produces\n\n$\\nu\\sim M+2e\\sin M+(5\/4)e^2\\sin 2M$\n\nThe relation \u03bd(M) is called the Equation of the center; the expression written here is a second order approximation in e. For the small value of e that characterises the Earth's orbit this gives a very good approximation for \u03bd(M).\n\nNext knowing \u03bd calculate \u03bb from its definition above\n\n$\\lambda=\\nu+\\lambda_p$\n\nThe value of \u03bb varies non-linearly with M because the orbit is elliptical and not circular. From the approximation for \u03bd, \u03bb ~ M + \u03bbp + 2e sin M +(5\/4)e2 sin 2M.\n\nFinally, knowing \u03bb calculate \u03b1 from a relation for the right triangle on the celestial sphere shown above[28]\n\n$\\alpha=\\tan^{-1}[\\cos\\varepsilon\\,\\tan\\lambda]$\n\nNote that the quadrant of \u03b1 is the same as that of \u03bb, therefore reduce \u03bb to the range 0 to 2\u03c0 and write \u03b1 = Tan\u22121[cos \u03b5 tan \u03bb] + k\u03c0, where k is 0 if \u03bb is in quadrant 1, it is 1 if \u03bb is in quadrants 2 or 3 and it is 2 if \u03bb is in quadrant 4. For the values at which tan is infinite, \u03b1 = \u03bb.\n\nAlthough approximate values for \u03b1 can be obtained from truncated Taylor series like those for \u03bd,[29] it is more efficatious to use the equation[30]\n\n$\\alpha = \\lambda - \\sin^{-1}[y\\sin(\\alpha + \\lambda)]$\n\nwhere y = tan2(\u03b5\/2). Note that for \u03b5 = y = 0, \u03b1 = \u03bb and iterating twice, \u03b1 ~ \u03bb - y sin 2\u03bb + (1\/2)y2 sin 4\u03bb.\n\n### Equation of time\n\nThe Equation of Time is obtained by substituting the result of the right ascension calculation into an equation of time formula. Here \u0394t(M) = M + \u03bbp - \u03b1[\u03bb(M)] is used; in part because small corrections (of the order of a second of time), that would justify using E, are not included, and in part because the goal is to obtain a simple analytical expression. Using two term approximations for \u03bb(M) and \u03b1(\u03bb), allows \u0394t to be written as an explicit expression of two terms, which is designated \u0394tey because it is a first order approximation in e and in y.\n\n$\\Delta t_{e y}=-2e\\sin M+y\\sin(2M+2\\lambda_p)=[-7.659\\sin M+9.863\\sin(2M+3.5932)]\\mbox{min}$\n\nThis equation was first derived by Milne,[31] who wrote it in terms of \u039b = M + \u03bbp. The numerical values written here result from using the orbital parameter values, e = 0.016709, \u03b5 = 23.4393\u00b0 = 0.409093, and \u03bbp = 282.9381\u00b0 = 4.938201 that correspond to the epoch 1 January 2000 at 12 noon. When evaluating the numerical expression for \u0394tey as given above, a calculator must be in radian mode to obtain correct values because the value of 2\u03bbp - 2\u03c0 in the argument of the second term is written there in radians. Higher order approximations can also be written,[32] but they necessarily have more terms. For example, the second order approximation in both e and y consists of five terms[33]\n\n$\\Delta t_{e^2y^2}=\\Delta t_{ey}-(5\/4)e^2\\sin 2M+ey\\sin M \\cos(2M+2\\lambda_p)-(1\/2)y^2\\sin(4M+4\\lambda_p)$\n\nThis approximation has the potential for high accuracy, however in order to achieve it over a wide range of years, the parameters e, \u03b5, and \u03bbp must be allowed to vary with time.[34] This creates additional calculational complications. Other approximations have been proposed, for example, \u0394te[35] which uses the first order equation of the center but no other approximation to determine \u03b1, and \u0394te2[36] which uses the second order equation of the center.\n\nThe time variable, M, can be written either in terms of, n, the number of days past perihelion, or, D, the number of days past a specific date and time (epoch)\n\n$M=\\frac{2\\pi}{t_Y}n\\mbox{ day}=M_D+\\frac{2\\pi}{t_Y}D\\mbox{ day}=6.24004077+0.01720197 D$\n\nHere MD is the value of M at the chosen date and time. For the values given here, in radians, MD is that measured for the actual Sun at the epoch, 1 January 2000 at 12:00 noon, and D is the number of days past that epoch. At periapsis M = 2\u03c0, so solving gives D = Dp = 2.508109. This puts the periapsis on 4 Jan 2000 at 11 min and 41 seconds past midnight while the actual periapsis is, according to results from the Multiyear Interactive Computer Almanac[37] (abbreviated as MICA), on 3 Jan 2000 at 5 hr, 17 min and 30 seconds past midnight. This large discrepancy happens because the difference between the orbital radius at the two locations is only 1 part in a million; in other words, radius is a very weak function of time near periapsis. As a practical matter this means that one cannot get a highly accurate result for the equation of time by using n and adding the actual periapsis date for a given year. However, high accuracy can be achieved by using the formulation in terms of D.\n\nCurves of \u0394t and \u0394tey along with symbols locating the daily values at noon (at 10 day intervals) obtained from the Multiyear Interactive Computer Almanac vs d for the year 2000.\n\nWhen D > Dp, M is greater than 2\u03c0 and one must subtract a multiple of 2\u03c0 (that depends on the year) from it to bring it into the range 0 to 2\u03c0. Likewise for years prior to 2000 one must add multiples of 2\u03c0. For example, for the year 2010, D varies from 3653 on 1 January at noon to 4017 on 31 December at noon, the corresponding M values are 69.0789468 and 75.3404748 and are reduced to the range 0 to 2\u03c0 by subtracting 10 and 11 times 2\u03c0 respectively. One can always write D = nY + d, where nY is the number of days from the epoch to noon on 1 January of the desired year, and 0\u2264d\u2264 364 (365 if the calculation is for a leap year).\n\nThe result of the computations is usually given as either a set of tabular values, or a graph of the equation of time as a function of d. A comparison of plots of \u0394t, \u0394tey, and results from MICA all for the year 2000 is shown in the figure on the right. The plot of \u0394tey is seen to be close to the results produced by MICA, the absolute error, Err = |\u0394tey \u2212 MICA2000|, is less than 1 minute of time throughout the year; its largest value is 43.2 sec and occurs on day 276 (3 October). The plot of \u0394t is indistinguishable from the results of MICA, the largest absolute error between the two is 2.46 sec on day 324 (20 November).\n\n#### Remark on the continuity of the equation of time\n\nFor the choice of the appropriate branch of the $\\arctan$ relation with respect to function continuity a modified version of the arcustangent function is helpful. It brings in previous knowledge about the expected value by a parameter. The modified arcustangent function is defined as\n\n$\\arctan _\\eta x=\\arctan x + \\pi\\cdot \\rm{round}\\frac{\\eta-\\arctan x}{\\pi} .$\n\nIt produces a value which is as close to $\\eta$ as possible. The function $\\rm{round}$ rounds to the nearest integer.\n\nThe application e. g. to the first equation of this chapter yields\n\n$\\Delta t(M)=M+\\lambda_p - \\arctan_{M+\\lambda p}\\left(\\cos\\varepsilon\\tan\\lambda\\right).$\n\nThe parameter $M+\\lambda_p$ arranges here to set $\\Delta t$ to the zero nearest value which is the desired one.\n\n### Secular effects\n\nThe difference between the MICA and \u0394t results was checked every 5 years over the range from 1960 to 2040. In every instance the maximum absolute error was less than 3 seconds of time, the largest difference, 2.91 seconds occurred on 22 May 1965 (day 141). However, in order to achieve this level of accuracy over this range of years it is necessary to account for the secular change in the orbital parameters with time. The equations that describe this variation are[38]\n\n$e = 1.6709\\cdot 10^{-2}-4.193\\cdot 10^{-5}\\left(\\frac{D}{36525}\\right)-1.26\\cdot 10^{-7}\\left(\\frac{D}{36525}\\right)^2$\n$\\varepsilon = \\left[23.4393-0.013\\left(\\frac{D}{36525}\\right)-2\\cdot 10^{-7}\\left(\\frac{D}{36525}\\right)^2+5\\cdot 10^{-7}\\left(\\frac{D}{36525}\\right)^3\\right]\\mbox{ deg}$\n$\\lambda_p = \\left[282.93807+1.7195\\left(\\frac{D}{36525}\\right)+3.025\\cdot 10^{-4}\\left(\\frac{D}{36525}\\right)^2\\right]\\mbox{ deg}$\n\nAccording to these relations, in 100 years (D = 36525), \u03bbp increases by about 1\/2 percent (1.7 degrees), e decreases by about 1\/4 percent, and \u03b5 decreases by about 1\/20 percent.\n\nAs a result the number of calculations required for any of the higher order approximations of the equation of time requires a computer to complete them, if one wants to achieve their inherent accuracy over a wide range of time. In this event it is no more difficult to evaluate \u0394t using a computer than any of its approximations.\n\nIn all this note that \u0394tey as written above is easy to evaluate, even with a calculator, is accurate enough (better than 1 minute of time over the 80 year range) for correcting sundials, and has the nice physical explanation as the sum of two terms, one due to obliquity and the other to eccentricity that was used previously in the article. This is not true either for \u0394t considered as a function of M or for any of its higher order approximations.\n\n### Alternative calculation\n\nAnother calculation of the equation of time can be done as follows.[39] Angles are in degrees; the conventional order of operations applies.\n\n$W=360\/365.24$\n\nW is the Earth's mean angular orbital velocity in degrees per day.\n\n$A=W\\times (D+10)$\n\nD is the date, in days starting at zero on 1 January (i.e. the days part of the ordinal date \u22121). 10 is the approximate number of days from the December solstice to 1 January. A is the angle the earth would move on its orbit at its average speed from the December solstice to date D.\n\n$B=A+(360\/\\pi)\\times 0.0167\\times \\sin(W\\times (D-2))$\n\nB is the angle the Earth moves from the solstice to date D, including a first-order correction for the Earth's orbital eccentricity, 0.0167. The number 2 is the number of days from January 1 to the date of the Earth's perihelion. This expression for B can be simplified by combining constants to: $B=A+1.914\\times \\sin(W\\times (D-2))$.\n\n$C=(A-\\arctan(\\tan(B)\/\\cos(23.44)))\/180$\n\nC is the difference between the angles moved at mean speed, and at the corrected speed projected onto the equatorial plane, and divided by 180 to get the difference in \"half turns\". The number 23.44 is the obliquity (tilt) of the Earth's axis in degrees. The subtraction gives the conventional sign to the equation of time. For any given value of x, arctan(x) (sometimes written as tan\u22121x) has multiple values, differing from each other by integer numbers of half turns. The value generated by a calculator or computer may not be the appropriate one for this calculation. This may cause C to be wrong by an integer number of half turns. The excess half turns are removed in the next step of the calculation:\n\n$\\text{EoT}=720\\times (C-\\text{nint}(C))$\n\nEoT is the equation of time in minutes. The expression nint(C) means the nearest integer to C. On a computer, it can be programmed, for example, as INT(C+0.5). It is 0, 1, or 2 at different times of the year. Subtracting it leaves a small positive or negative fractional number of half turns, which is multiplied by 720, the number of minutes (12 hours) that the Earth takes to rotate one half turn relative to the Sun, to get the equation of time.\n\nCompared with published values,[40][41] this calculation has a Root Mean Square error of only 3.7 seconds of time. The greatest error is 6.0 seconds. This is much more accurate than the approximation described above, but not as accurate as the elaborate calculation.\n\nThe value of B in the above calculation is an accurate value for the Sun's ecliptic longitude (shifted by 90 degrees), so the solar declination becomes readily available:\n\n$\\text{Declination} = - \\arcsin(\\sin(23.44)\\times \\cos(B))$\n\nwhich is accurate to within a fraction of a degree.\n\n## Notes and Footnotes\n\nNotes\n2. ^ This meant that any clock being set to mean time by Huygens's tables was consistently about 15 minutes slow compared to today's mean time.\n3. ^ See above\n4. ^ See barycentre\n5. ^ Universal Time is discontinuous at mean midnight so another quantity day number N, an integer, is required in order to form the continuous quantity time t: t = (N + UT\/24 hr) day.\nFootnotes\n1. ^ a b Nautical Almanac 1767\n2. ^ Milham 1945, pp. 11\u201315\n3. ^ See for example, British Commission on Longitude 1794, p. 14.\n4. ^ As an example of the inexactness of the dates, according to the U.S. Naval Observatory's Multiyear Interactive Computer Almanac the equation of time was 0 at 2:00 UT1 on 16 April 2011.\n5. ^ Heilbron 1999, p. 277.\n6. ^ Waugh, p. 205\n7. ^ Olmstead 1866, pp.\u00a057\u201358\n8. ^ Toomer 1998, p. 171\n9. ^ Kepler 1995, p. 155\n10. ^ Huygens, 1665\n11. ^ Huygens 1665\n12. ^ Flamsteed 1672\n13. ^ Vince 1814, p. 49\n14. ^ Mills 2007, p. 219\n15. ^ Maskelyne 1764, pp. 163\u2013169\n16. ^ Karney, Kevin. \"Variation in the Equation of Time\".\n17. ^ Telling Time on Mars\n18. ^ \"How to find the exact time of solar noon\" n.d.\n19. ^ a b Duffet-Smith p 89\n20. ^ Hughes et al., p.1529\n21. ^ \"Computing Greenwich Sidereal Time\", Naval Oceanography Portal\n22. ^ Heilbron p 275, Roy p 45}\n23. ^ Hughes, et. al., p 1532\n24. ^ Hughes, et. al., p 1530, \"Computing Greenwich Sidereal Time\", Naval Oceanography Portal\n25. ^ Moulton p 159\n26. ^ Hinch p 2\n27. ^ Moulton p 165\n28. ^ Burington p 22\n29. ^ Whitman p 32\n30. ^ Milne p 374\n31. ^ Milne p 375\n32. ^ Muller Eqs (45) and (46)\n33. ^ Hughes, et. al., p1535\n34. ^ Duffett-Smith, p 86, Hughes, et. al., p 1531,1535\n35. ^ Duffett-Smith, p 86, Williams\n36. ^ \"Approximate Solar Coordinates\", Naval Oceanographic Portal\n37. ^ U.S.Naval Observatory\n38. ^ Duffett-Smith p 86, Hughes, et. al., p 1531,1535\n39. ^ Williams\n40. ^ Waugh, p. 205\n41. ^ Helyar","date":"2014-04-25 09:43:09","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\": 32, \"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\": 0.7096709609031677, \"perplexity\": 1001.4042438552087}, \"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-2014-15\/segments\/1398223211700.16\/warc\/CC-MAIN-20140423032011-00011-ip-10-147-4-33.ec2.internal.warc.gz\"}"}
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{"url":"https:\/\/cuyler36.github.io\/2018\/07\/14\/creating-a-nes-patch-loader.html","text":"Arbitrary code execution in Animal Crossing has been something I\u2019ve been interested in finding for some time now. After James Chambers informed me about the PAT tag for the NES emulator, which could possibly allow for arbitrary writes to RAM, I had to investigate more. James also mentioned that due to certain restrictions, we could only write a portion of RAM rather than all of it. Writes were also limited in size. He theorized the best way to get around these limitations would be by creating a custom loader. With this knowledge in hand, I set out to do just that.\n\nThe basic idea that I had for the loader was simple. Treat the NES ROM as data itself, rather than a ROM. The loader would simply copy the NES ROM Data to a specified location in RAM. The next thing I had to consider were the limitations. Specifically, the ROM loader had to fulfill the following things:\n\n\u2022 It must be written to memory between 0x80000000 and 0x807FFFFF. This is the write address limitation I mentioned earlier.\n\u2022 It must be no larger than 251 bytes in size, as the tag responsible for patching used four bytes for other information.\n\n#### A Deeper Look at the Limitations\n\nLet\u2019s take a break for a moment to breakdown why the limitations mentioned above exist. First, let\u2019s look at the write address limitation. The GameCube\u2019s main RAM is 24 megabytes in size, and starts at 0x80000000. This makes the effective address range 0x80000000 - 0x817FFFFF. So why can the tag only patch to a third of that address? The answer lies in the code responsible for calculating the write address. Let\u2019s take a look at that code:\n\nTaking the above code into account, we can see there are four cases that determine how the write address is calcuated. The first one checks if the PAT type is 3. If so, it will clear the address entirely, resetting any address we had before.\n\nThe second one checks if the type is 2. If so, it\u2019ll take the next two bytes after the PAT type and use that as a 16 bit value to add to the current patch address.\n\nThe third one checks if the type is 9. If so, it takes the next two bytes and shifts it left by four, which is the same as multiplying by 16, and adds that to the current patch address.\n\nThe final case checks if the type is between 0x80 and 0xFF. If so, it adds the type to 0x7F80, and shifts it left by 16, then adds the 16 bit value to that. This is where the write problem stems from. Let\u2019s look at what would happen if we set the PAT type to 0xFF and use 0xFFFF as the 16 bit add value!\n\nThe equation ends up looking like this:\n\n((0x7F80 + 0xFF) \u00ab\u00a016) + 0xFFFF\n\nThat then becomes:\n\n(0x807F \u00ab\u00a016) + 0xFFFF\n\nWhich becomes:\n\n0x807F0000 + 0xFFFF\n\nFinally, that equates to:\n\n0x807FFFFF\n\nThat\u2019s how the maximum address is reached. Great. So we now know for sure we can only write to addressess between 0x80000000 and 0x807FFFFF. What about the write size limitation though? To understand that, we need to take a look at the PAT tag structure:\n\nstruct TagPAT {\nchar Tag[3] = \"PAT\";\nunsigned char Size;\nunsigned char Type;\nunsigned char CopySize;\nunsigned short WriteOffset;\n};\n\n\nLooking at the structure, we can see that there are two bytes responsible for size. The first one, Size, refers to the entire size of the tag data, minus the Tag type that preceeds it. Since it\u2019s a byte, it can be between 0 and 255 (0x00 - 0xFF). The second size value, CopySize, is how many bytes the emulator should copy during patching. Since we know the maximum size the tag can be is 255 bytes, we can just subtract the size of non-patch data in the struct to figure out the maximum copy size. Since the first size isn\u2019t included, we end up with four bytes of data reserved for calculating the write address.\n\n255 - 4 = 251 (0xFF - 0x04 = 0xFB)\n\nSo that\u2019s where the maximum patch size of 251 comes from! Now that we know our limitations in depth, we can pick where we\u2019ll write the loader to!\n\nAs nice as it\u2019d be to just pick 0x80000000 as the patch loader write address, we need to take caution in where we write it to. The lower addresses in RAM contain important game information and code that would likely crash the game if it was overwritten! Knowing this, I fired up Dolphin Emulator in debug mode, and dumped the game\u2019s RAM while it was running. After a short while of searching, I found a large enough section of unused RAM located at 0x80003640.\n\nNow that we\u2019ve got an address to write the loader to, we can finally get to writing it.\n\nSince we have limited space, the best language choice for programming the patch loader is PowerPC Assembly. Now that the language has been decided, a standard header for reading the fake NES ROM data would need to be decided on. Originally, I considered just reading data until the first zero byte was hit and then stopping. I ultimately decided against that, as it was very inflexible. I settled on having the NES ROM have a header structure like so:\n\nstruct NESROMPatchHeader{\nunsigned int PatchSize;\nunsigned int IsExecutable;\n};\n\n\nLet\u2019s break down what each value in the header is for.\n\nWriteAddress is the absolute address in RAM to begin writing to. It can be anywhere in the full RAM range of 0x80000000 to 0x817FFFFF.\n\nPatchSize is the size of the patch data in the fake NES ROM that will be copied starting at WriteAddress.\n\nIsExecutable is treated as a boolean that determines if the patch loader should execute the data it copied. Anything other than 0 for this value will mean it is executable.\n\nThe patch data should follow immediately after the header. An example of a patch I made for enabling Zurumode 2 looks like this:\n\nNow we can finally begin writing the patch!\n\nThis is the original patch I created:\n\n.text\n\/\/ allocate stack frame\nstwu r1, -0x20(r1)\n\n\/\/ store r3\/r4\/r5\/r6\/r7\/r8 registers\nstw r3, 0x1C(r1)\nstw r4, 0x18(r1)\nstw r5, 0x14(r1)\nstw r6, 0x10(r1)\nstw r7, 0x0C(r1)\nstw r8, 0x08(r1)\n\nlwz r3, 0(r3)\n\n\/\/ check if the ROM start address is nullptr\ncmplwi r3, 0\nbeq exit\n\nlwz r4, 0(r3) \/\/ the first int should be the write pointer\ncmplwi r4, 0\nbeq exit\nmr r8, r4 \/\/ copy the copy offset to r8 in case we need to jump there\nlwz r6, 4(r3) \/\/ the second int should be the size to copy (ROM size - 8)\nlwz r7, 8(r3) \/\/ the third int should be \"bool isExecutable\". If anything other than 0, the loader will jump to the address it started writing to\n\n\/\/ start patching\npatchLoop:\ncmpwi r6, 0\nble exit\nlbz r3, 0(r5)\nstb r3, 0(r4)\nb patchLoop\n\nexit:\ncmplwi r7, 0\nbeq cleanup\nmflr r0 \/\/ copy the current return address as an argument for the executing function to handle\nmtlr r8 \/\/ store the beginning write address as the return address\n\ncleanup: \/\/ restore registers and clear stack frame\nlwz r3, 0x1C(r1)\nlwz r4, 0x18(r1)\nlwz r5, 0x14(r1)\nlwz r6, 0x10(r1)\nlwz r7, 0x0C(r1)\nlwz r8, 0x08(r1)\n\n\/\/ THIS PART CAN BE CHANGED, it's just doing what the instruction it overwrote did\nlis r6, 8\n\n\/\/ return\nblr\n\n.data\n\n\nLooking at it, there are several problems. The first is that the Gekko CPU in the GameCube has an instruction and data cache. If we don\u2019t clear these, any data we overwrite that happens to be cached won\u2019t actually be updated. This causes it to usually fail as the game doesn\u2019t acknowledge we\u2019ve changed the code. The second is overall it\u2019s just bulky and inefficient.\n\nJames Chambers took a look at my code and found that we could overwrite a stored function pointer in my_malloc to avoid overwriting code itself. Ultimately I discovered it was better to overwrite the pointer to my_free instead, as it is always called when the emulator ends. I also implemented instruction and data cache invalidations for the addresses the loader writes to. Here\u2019s the final version of the patch loader:\n\n.text\n\/\/ allocate stack frame\nstwu r1, -0x30(r1)\n\n\/\/ save LR through r0\nmflr r0\n\n\/\/ store r0\/r3\/r4\/r5\/r6 registers\nstw r0, 0x20(r1)\nstw r3, 0x1C(r1)\nstw r4, 0x18(r1)\nstw r5, 0x14(r1)\nstw r6, 0x10(r1)\n\nlwz r3, 0(r3)\n\n\/\/ check if the ROM start address is nullptr\ncmplwi r3, 0\nbeq exit\n\nlwz r4, 0(r3)\ncmplwi r4, 0\nbeq exit\nstw r4, 0x28(r1) \/\/ save jump offset\nlwz r6, 0x08(r3) \/\/ the third int should be \"bool isExecutable\". If anything other than 0, the loader will jump to the address it\nstw r6, 0x24(r1)\/\/ save executable flag\nlwz r6, 0x04(r3) \/\/ the second int should be the size to copy (ROM size - 8)\nstw r6, 0x2C(r1) \/\/ save size for invalidation operation later\n\n\/\/ start patching\npatchLoop:\ncmpwi r6, 0\nble exitPatchLoop\nlbz r3, 0(r5)\nstb r3, 0(r4)\nb patchLoop\n\nexitPatchLoop:\n\/\/ invalidate instruction and data caches\nlwz r4, 0x2C(r1) \/\/ load size\nclrlwi. r0, r4, 27\nbeq align\n\nalign:\nsrwi r4, r4, 5\nmtctr r4\n\ninvalidationLoop:\nicbi r0, r3\ndcbi r0, r3\nbdnz invalidationLoop\n\n\/\/ sync invalidaitons\nflushCache:\nsync\nisync\n\n\/\/ restore register for arguments to my_zelda_free\nlwz r3, 0x1C(r1)\n\n\/\/ restore the original pointer to my_zelda_free and branch to it\nlis r5, MY_ZELDA_FREE@h\nori r5, r5, MY_ZELDA_FREE@l\nlis r6, MY_FREE_PTR@h\nori r6, r6, MY_FREE_PTR@l\nstw r5, 0x0(r6)\nmtctr r5\nbctrl\n\n\/\/ check if the patch is executable\nlwz r4, 0x24(r1)\ncmplwi r4, 0\nbeq restoreLR\n\/\/ restore offset and jump\nlwz r4, 0x28(r1)\nlwz r0, 0x20(r1) \/\/ set previous function LR in r0\nmtlr r4\nb cleanup\n\nrestoreLR:\n\/\/ restore LR\nlwz r0, 0x20(r1)\nmtlr r0\n\ncleanup:\n\/\/ restore rest of registers and clear stack frame\nlwz r4, 0x18(r1)\nlwz r5, 0x14(r1)\nlwz r6, 0x10(r1)\nblr\n\n.data\nMY_ZELDA_FREE = 0x8062D4CC;\nMY_FREE_PTR = 0x806D4B9C;\n\n\nIt\u2019s a lot more concise, and works like a charm! Another thing I should mention is that if the patch is marked as executable, r0 will contain the return address of the function who called the patch loader in it. This allows patch creators to return control back to the game by moving it into the LR register!\n\n### Final Thoughts\n\nThis knowledge has already been used to do some incredible things. You can check out my video showcasing the first mod I created for it called Letter2Item.\n\nFIX94 also created a homebrew launcher using the exploit, which you can find here.\n\nYou can find my ACNESCreator program which can create NES ROM files or the Patch files here.\n\nYou can also find a command line version created by James Chambers here.\n\nI\u2019m excited to see what kinds of things people create with these discoveries and programs.","date":"2019-05-19 21:27:12","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\": 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\": 0.22462785243988037, \"perplexity\": 4141.207724041261}, \"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-2019-22\/segments\/1558232255165.2\/warc\/CC-MAIN-20190519201521-20190519223521-00215.warc.gz\"}"}
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Ovan Babylon är en svensk dokumentärfilm som hade premiär i Sverige den 15 november 2019. Folke Rydén har regisserat och skrivit manus, även producerat filmen för FRP AB.
Handling
Filmen handlar om Murtada Al-Hachami som återvänder till Irak efter flytt till Storbritannien under Saddam Husseins styre. Tillsammans med Folke Rydén vill Murtada visa en annan bild av Irak än den gängse bild som västerländsk media visar upp.
Referenser
Externa länkar
Svenska filmer 2019
Svenska dokumentärfilmer
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
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{"url":"https:\/\/my.spscc.edu\/portal\/schedule\/C014\/course\/CNA251","text":"# Class Schedule\n\n## Primary tabs\n\n### CNA251\n\nCovers the architecture, components, and operations of routers and switches in larger and more complex networks. Includes configuration of routers and switches for advanced functionality. Prerequisite: Eligible for MATH 092 and ENGL 090, CNA 150.\n\n7431\n20 Seats\nNot Open\nCNA251.NHY Details\nTitle Course Credits Location Days Times Instructor Additionally Meets In\n\n### Cisco III\n\nCNA251.NHY 5 034 0202 TTh 5:30p - 6:50p Staff\nThere are additional Class Fees: $75.00 COMPUTER NETWORKING ADMINISTRATION ($75.00 per quarter)\nThese classes have planned times for attendance, which are indicated in the schedule. Depending on COVID-19 circumstances, real-time instruction will be either on online or on campus. The instructor will inform students of the arrangements prior to the start of the quarter.\nThis is a Evening\/Night Class\nThis class is at our Olympia Campus.\nSeptember 29, 2020, 7:00 pm\nJavascript must be enabled to retrieve current messages.","date":"2020-09-30 02:02:47","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\": 0.204214408993721, \"perplexity\": 14967.60321748}, \"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-2020-40\/segments\/1600402101163.62\/warc\/CC-MAIN-20200930013009-20200930043009-00549.warc.gz\"}"}
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\section{Introduction}\label{sec:intro}
Graphs have been found in many emerging applications, including transaction networks, communication networks and social networks. The dense subgraph problem is first studied in~\cite{goldberg1984finding} and is effective for link spam identification~\cite{gibson2005discovering,beutel2013copycatch}, community detection~\cite{dourisboure2007extraction,chen2010dense} and fraud detection~\cite{hooi2016fraudar,chekuri2022densest,shin2016corescope}. Standard peeling algorithms~\cite{tsourakakis2015k,hooi2016fraudar,bahmani2012densest,chekuri2022densest,boob2020flowless} iteratively peel the vertex that has the smallest connectivity (\emph{e.g.,}\xspace vertex degree or sum of the weights of the adjacent edges) to the graph. Peeling algorithms are widely used because of their efficiency, robustness, and theoretical worst-case guarantee. However, existing peeling algorithms~\cite{hooi2016fraudar,tsourakakis2015k,charikar2000greedy} assume a static graph without considering the fact that social and transaction graphs in online marketplaces are rapidly evolving in recent years. One possible solution for fraud detection on evolving graphs is to perform peeling algorithms periodically. We take $\mathsf{Grab}$'s fraud detection pipeline as an example.
\eat{There have been quite a lot of techniques \emph{e.g.,}\xspace \cite{hooi2016fraudar,beutel2013copycatch,shin2016corescope,kumar1999trawling,ren2021ensemfdet,khuller2009finding, tsourakakis2013denser,ma2020efficient} proposed for detecting dense subgraphs.}
\begin{figure}[tb]
\includegraphics[width=0.7\linewidth]{figures/pipeline.eps}
\caption{$\mathsf{\mathbf{Grab}}$'s data pipeline for fraud detection}\label{fig:pipeline}
\end{figure}
\begin{figure}[tb]
\includegraphics[width=0.8\linewidth]{figures/intro.eps}
\caption{An example of fraud detection on evolving graphs}\label{fig:intro}
\end{figure}
\eat{However, existing works~\cite{hooi2016fraudar,tsourakakis2015k,charikar2000greedy} are proposed for static graphs. When graphs change, we have to detect dense subgraphs from scratch, which cannot meet the real-time requirement.}
\eat{Our experiments show that hundreds of new transactions are generated each second on average in 2021.}
\eat{
\stitle{Evolving graphs}. Although peeling algorithms are efficient, identifying the dense subgraph still takes several minutes. Therefore, given graph updates, the detection of dense subgraphs from scratch cannot meet the real-time requirement.
}
\stitle{Fraud detection pipeline in $\mathsf{Grab}$ (Figure~\ref{fig:pipeline})}. $\mathsf{Grab}$ is one of the largest technology companies in Southeast Asia and offers digital payments and food delivery services. On the $\mathsf{Grab}$'s e-commerce platform, 1) the transactions form a transaction graph $G$. 2) $\mathsf{Grab}$ updates the transaction graphs periodically $G = G\oplus \Delta G$. Our experiments show that it takes $28$s to carry out $\mathsf{Fraudar}$ ($\mathsf{FD}{}$)~\cite{hooi2016fraudar} on a transaction graph with $6$M vertices and $25$M edges. Therefore, we can execute fraud detection every $30$ seconds. 3) The dense subgraph detection algorithm and its variants are used to detect fraudulent communities. 4) After identifying the fraudsters, the moderators ban or freeze their accounts to avoid further economic loss. A classic fraud example is customer-merchant collusion. Assume that $\mathsf{Grab}$ provides promotions to new customers and merchants. However, fraudsters create a set of fake accounts and do fictitious trading to use the opportunity of promotion activities to earn the bonus. Such fake accounts (vertices) and the transactions among them (edges) form a dense subgraph.
\setlist{nolistsep}
\begin{example}
Consider the transaction graph in Figure~\ref{fig:intro}, where a vertex is a user or a store, and an edge represents a transaction. Suppose a fraudulent community is identified at time $T_0$ and a normal user becomes a fraudster and participates in suspicious activities at $T_1$. Applying peeling algorithms at $T_1$, the new fraudster is detected at $T_2$. However, many new suspicious activities have occurred during the time period $[T_1,T_2]$ that could cause huge economic losses.
\end{example}
As reported in recent studies~\cite{dailyreport,ye2021gpu}, $21.4\%$ of the traffic to e-commerce portals are malicious bots in 2018. Fraud detection is challenging since many fraudulent activities occur in a very short timespan. Hence, identifying fraudsters and reducing response latency to fraudulent transactions are key tasks in real-time fraud detection.
\begin{table}[tb]
\caption{Comparison of $\mathsf{Spade}${} and previous algorithms}\label{table:comparison}
\centering
\begin{scriptsize}
\begin{tabular}{|c|c|c|c|c|c|}
\hline
& $\mathsf{DG}$~\cite{charikar2000greedy} & $\mathsf{DW}$~\cite{gudapati2021search} & $\mathsf{FD}$~\cite{hooi2016fraudar} & $\mathsf{Spade}$ \\
\hline
Dense subgraph detection & \checkmark & \checkmark & \checkmark & \checkmark \\
\hline
Accuracy guarantees & \checkmark & \checkmark & \checkmark & \checkmark \\
\hline
Weighted graph & \ding{55} & \checkmark & \checkmark & \checkmark \\
\hline
Incremental updates & \ding{55} & \ding{55} & \ding{55} & \checkmark \\
\hline
Edge reordering & \ding{55} & \ding{55} & \ding{55} & \checkmark\\
\hline
\end{tabular}
\end{scriptsize}
\end{table}
To address real-time fraud detection on evolving graphs, a better solution would be to incrementally maintain dense subgraphs. There are two main challenges of incremental maintenance. First, \eat{real-time fraud detection is necessary as fraud detection is an essential path to respond to customer's requests.} operational demands require that fraudsters should be identified in $100$ milliseconds in industry. Maintaining the dense subgraph incrementally in such a short timespan is challenging. Second, fraud semantics continue to evolve and it is not trivial to incrementalize each of them. Implementing a correct and efficient incremental algorithm is, in general, a challenge. It is impractical to train all developers with the knowledge of incremental graph evaluation. To the best of our knowledge, there are no generic approaches to minimize the cost of incremental peeling algorithms. Motivated by the challenges, we design a real-time fraud detection framework, named $\mathsf{Spade}${} to detect fraudulent communities by incrementally maintaining dense subgraphs. The comparison between $\mathsf{Spade}${} and the previous algorithms (\jiaxin{dense subgraphs ($\mathsf{DG}$)~\cite{charikar2000greedy}, dense weighted subgraph ($\mathsf{DW}$)~\cite{gudapati2021search} and $\mathsf{Fraudar}$ ($\mathsf{FD}$)~\cite{hooi2016fraudar}}) is summarized in Table~\ref{table:comparison}.
\stitle{Contributions.} In this paper, we focus on incremental peeling algorithms. In summary, this paper makes the following contributions.
\begin{enumerate}
\item We build three fundamental incremental techniques for peeling algorithms to avoid detecting fraudulent communities from scratch. $\mathsf{Spade}${} inspects the subgraph that is affected by graph updates and reorders the peeling sequence incrementally, which theoretically guarantees the accuracy of the worst case.
\item $\mathsf{Spade}${} enables developers to design their fraud semantics to detect fraudulent communities by providing the suspiciousness functions of edges and vertices. We show that a variety of peeling algorithms can be incrementalized in $\mathsf{Spade}${} (Section~\ref{sec:framework}) including $\mathsf{DG}$, $\mathsf{DW}$ and $\mathsf{FD}$.
\item We conduct extensive experiments on $\mathsf{Spade}${} with datasets from industry. The results show that $\mathsf{Spade}${} speeds up fraud detection up to $6$ orders of magnitude since $\mathsf{Spade}${} minimizes the cost of incremental maintenance by inspecting the affected area. Furthermore, the latency of the response to fraud activities can be significantly reduced. Lastly, once a user is spotted as a fraudster, we identify the related transactions as potential fraud transactions and pass them to system moderators. Up to $88.34\%$ potential fraud transactions can be prevented.
\end{enumerate}
\stitle{Organization.} The rest of this paper is organized as follows: Section~\ref{sec:background} presents the background and the problem statement. We introduce the framework of $\mathsf{Spade}${} in Section~\ref{sec:framework} and three incremental peeling algorithms in Section~\ref{sec:Spade}. Section~\ref{sec:exp} reports on the experimental evaluation. After reviewing related work in Section~\ref{sec:related}, we conclude in Section~\ref{sec:conclusion}.
\section{Background}\label{sec:background}
\subsection{Preliminary}
\eat{
We next introduce some basic notations. Some frequently used notations are summarized in Table~\ref{tab-notations}.
}
\input{notations.tex}
\stitle{Graph $G$.} We consider a directed and weighted graph $G=(V,E)$, where $V$ is a set of vertices and $E$ $\subseteq (V\times V)$ is a set of edges. Each edge $(u_i,u_j)\in E$ has a \textbf{nonnegative} weight, denoted by $c_{ij}$. We use $N(u)$ to denote the neighbors of $u$.
\stitle{Induced subgraph.} Given a subset $S$ of $V$, we denote the induced subgraph by $G[S] = (S, E[S])$, where $E[S]=\{(u,v) | (u,v) \in E \wedge u,v\in S\}$. We denote the size of $S$ by $|S|$.
\stitle{Density metrics $g$.} We adopt the class of metrics $g$ in previous studies~\cite{hooi2016fraudar,gudapati2021search,charikar2000greedy}, $g(S) = \frac{f(S)}{|S|}$, where $f$ is the total weight of $G[S]$, \emph{i.e.,}\xspace the sum of the weight of $S$ and $E[S]$:
\begin{equation}\label{eq:density}
f(S)=\sum_{u_i\in S} a_i + \sum_{u_i,u_j\in S \bigwedge (u_i,u_j)\in E} c_{ij}
\end{equation}
The weight of a vertex $u_i$ measures the suspiciousness of user $u_i$, denoted by $a_i$ ($a_i\geq 0$). The weight of the edge $(u_i,u_j)$ measures the suspiciousness of transaction $(u_i,u_j)$, denoted by $c_{ij} > 0$. Intuitively, $g(S)$ is the density of the induced subgraph $G[S]$. The larger $g(S)$ is, the denser $G[S]$ is.
\stitle{Graph updates $\Delta G$.} We denote the set of updates to $G$ by $\Delta G = (\Delta V, \Delta E)$. We denote the graph obtained by updating $\Delta G$ to $G$ as $G\oplus \Delta G$. Since transaction graphs continue to evolve, we consider edge insertion rather than edge deletion. Therefore, $G\oplus \Delta G = (V\cup \Delta V, E\cup \Delta E)$. Specifically, we consider two types of updates, edge insertion (\emph{i.e.,}\xspace $|\Delta E| = 1$) and edge insertion in batch (\emph{i.e.,}\xspace $|\Delta E| > 1$).
\subsection{Peeling algorithms}
\begin{algorithm}[tb]
\caption{Execution paradigm of peeling algorithms}\label{algo:peeling}
\footnotesize
\SetKwProg{Fn}{Function}{}{}
\KwIn{A graph $G = (V, E)$ and a density metric $g(S)$}
\KwOut{The peeling sequence order $O = Q(G)$ and the fraudulent community}
$S_0 = V$ \label{algo:peeling:init} \\
\For{$i=1,\ldots, |V|$}{
select the vertex $u\in S_{i-1}$ such that $g(S_{i-1}\setminus \{u\})$ is maximized \label{algo:peeling:maximize}\\
$S_{i} = S_{i-1}\setminus \{u\}$ \label{algo:peeling:maximize2} \\
$O.\mathsf{add}$($u$)
}
\Return{$O$ \textnormal{and} $\arg\max_{S_i}g(S_i)$}
\end{algorithm}
Peeling algorithms ($Q$) are widely used in dense subgraph mining~\cite{hooi2016fraudar,tsourakakis2015k,charikar2000greedy}. They follow the execution paradigm in Algorithm~\ref{algo:peeling} and differ mainly in density metrics. They are categorized to three categories: unweighted~\cite{charikar2000greedy}, edge-weighted~\cite{gudapati2021search} and hybrid-weighted~\cite{hooi2016fraudar}.
\stitle{Peeling weight.} Specifically, we use $w_{u_i}(S)$ to indicate the decrease in the value of $f$ when the vertex $u_i$ is removed from a vertex set $S$, \emph{i.e.,}\xspace the peeling weight. Previous work~\cite{hooi2016fraudar} formalizes $w_{u_i}(S)$ as follows:
\begin{equation}
w_{u_i}(S) = a_i + \sum_{(u_j\in S) \bigwedge ((u_i,u_j)\in E)} c_{ij} + \sum_{(u_j\in S) \bigwedge ((u_j,u_i)\in E)} c_{ji}
\end{equation}
\eat{where $c_{ij}$ is the weight of the edge $(u_i,u_j)$ indicating its suspiciousness, $a_i$ is the weight of the vertex $u_i$ indicating the suspiciousness of $u_i$, and $u_j\in N(u_i)$.}
\stitle{Peeling sequence}. We use $S_i$ to denote the vertex set after $i$-th peeling step. Initially, the peeling algorithms set $S_0 = V$. They iteratively remove a vertex $u_i$ from $S_{i-1}$, such that $g(S_{i-1}\setminus \{u_i\})$ is maximized (Line~\ref{algo:peeling:maximize}$\sim$\ref{algo:peeling:maximize2}). The process repeats recursively until there are no vertices left. This leads to a series of sets over $V$, denoted by $S_0, \ldots, S_{|V|}$ of sizes $|V|, \ldots, 0$. Then $S_i$ ($i\in [0, |V|]$), which maximizes the density metric $g(S_i)$, is returned, denoted by $S^P$. For simplicity, we denote $\Delta_i = w_{u_i}(S_i)$. Instead of maintaining the series $S_0,\ldots, S_{|V|}$, we record the peeling sequence $O = [u_1,\ldots u_{|V|}]$ such that $\{u_i\} = S_{i-1}\setminus S_{i}$.
\begin{example}
Consider the graph $G$ in Figure~\ref{fig:peel}. $u_1$ is peeled since its peeling weight is the smallest among all vertices. Similarly, $u_3,u_2,u_4,u_5$ will be peeled accordingly. Therefore, the peeling sequence is $O = [u_1,u_3,u_2,u_4,u_5]$.
\end{example}
\stitle{Complexity and accuracy guarantee.} In Algorithm~\ref{algo:peeling}, Min-Heap is used to maintain the peeling weights, the insertion cost is $O(\log |V|)$. There are at most $|E|$ insertions. Therefore, the complexity of Algorithm~\ref{algo:peeling} is $O(|E|\log |V|)$. We denote the vertex set that maximizes $g$ by $S^*$. Previous studies~\cite{khuller2009finding,hooi2016fraudar,charikar2000greedy} conclude that:
\eat{, we extend the proof of the accuracy guarantee to general graphs as follows.}
\begin{lemma}\label{lemma:2ppr}
Let $S^P$ be the vertex set returned by the peeling algorithms and $S^*$ be the optimal vertex set, $g(S^P) \geq \frac{1}{2} g(S^*)$.
\end{lemma}
\eat{
\begin{proof}
As visualized in Figure~\ref{fig:proof}, we assume that $u_i\in S^P$ is the first vertex in $S^*$ removed by the peeling algorithm. Since $u_i$ is the smallest of the decrease in the value of $f(S')$, we have
\begin{equation}\label{eq:proof}
\footnotesize
g(S') = \frac{f(S')}{|S'|} \geq \frac{\sum\limits_{u_j\in S'} w_{u_j}(S')}{2\times |S'|} \geq \frac{w_{u_i}(S') |S'|}{2\times |S'|} = \frac{w_{u_i}(S')}{2}
\end{equation}
Due to the definition of $S^P$, $g(S^P) \geq g(S')$. Combining Equation~\ref{eq:proof}, we have the following proof.
\begin{equation}
\footnotesize
g(S^P) \geq g(S') = \frac{f(S')}{|S'|} \geq \frac{w_{u_i}(S')}{2} \geq \frac{w_{u_i}(S^*)}{2} \geq \frac{g(S^*)}{2}
\end{equation}
\end{proof}
}
Although peeling algorithms are scalable and robust, we remark that these algorithms are proposed for static graphs, which takes several minutes on million-scale graphs. For evolving graphs, computing from scratch is still time-consuming, which cannot meet the real-time requirement. Moreover, it is not trivial to design incremental algorithms for peeling algorithms. In this paper, we investigate an auto-incrementalization framework for peeling algorithms.
\stitle{Problem definition.} Given a graph $G=(V,E)$, a peeling algorithm $Q$, and the peeling result of $Q$ on $G$, $S^P=Q(G)$, our problem is to efficiently identify the result of $Q$ on $G\oplus \Delta G$, ${S}^{P'}=Q(G\oplus \Delta G)$, where $\Delta G$ is the graph updates.
\begin{figure}
\includegraphics[width=0.65\linewidth]{figures/eg-gdy-fraudar-consistent.eps}
\caption{Example of peeling algorithms}\label{fig:peel}
\end{figure}
\eat{
\begin{figure}
\includegraphics[width=0.65\linewidth]{figures/eg-fraudar.eps}
\caption{Illustration of key notations in peeling algorithms}\label{fig:proof}
\end{figure}
}
\section{The $\mathsf{Spade}${} Framework}\label{sec:framework}
In this section, we present an overview of our proposed framework $\mathsf{Spade}${} and sample APIs. Subsequently, we demonstrate some examples on how to implement different peeling algorithms with $\mathsf{Spade}$.
\begin{figure}
\begin{minipage}[t]{.3\textwidth}
\includegraphics[width=\linewidth]{figures/inc-fraudar-architecture.eps}
\subcaption[]{Architecture}
\end{minipage}
\hfill
\begin{minipage}[t]{.13\textwidth}
\includegraphics[width=\textwidth]{figures/API.eps}
\subcaption[]{Edge insertion
}
\end{minipage}
\caption{Architecture of $\mathsf{Spade}${} and workflow of an edge insertion}\label{fig:architecture}
\end{figure}
\subsection{Overview of $\mathsf{Spade}${} and APIs}
\eat{
\begin{table*}[tb]
\caption{Sample User-defined APIs in $\mathsf{Spade}$}\label{table:api}
\vspace{-1em}
\centering
\begin{scriptsize}
\begin{tabular}{|l|l|}
\hline
\textbf{APIs/Parameters} & \textbf{Descriptions} \\ \hline
$\mathsf{VSusp}$(Function $\mathsf{Score}$(Vertex $u$)) & Given a suspiciousness score function $\mathsf{Score}$, $\mathsf{Spade}${} plugins it in and computes the suspiciousness score for each vertex $u$\\
\hline
$\mathsf{ESusp}$(Function $\mathsf{Score}$(Edge $e$) & Given a suspiciousness score function $\mathsf{Score}$, $\mathsf{Spade}${} plugs it in and computes the suspiciousness for each edge $e$ \\
\hline
$\mathsf{InsertEdge}$(Edge $e$) & Given a new edge $e$, $\mathsf{Spade}${} reorders the peeling sequence with the edge update \\
\hline
$\mathsf{InsertBatchEdges}$(Edge* \textit{e\_arr}) & Given a set of new transactions and the suspiciousness, $\mathsf{Spade}${} reorders the peeling sequence with the batch updates \\
\hline
\end{tabular}
\end{scriptsize}
\end{table*}
}
We follow two design goals to satisfy operational demands.
\begin{itemize}
\item \etitle{Programmability.} We provide a set of user-defined APIs for developers to develop their dense subgraph-based semantics to detect fraudsters. Moreover, $\mathsf{Spade}${} can auto-incrementalize their semantics without recasting the algorithms.
\item \etitle{Efficiency.} $\mathsf{Spade}${} allow efficient and scalable fraud detection on evolving graphs in real-time.
\end{itemize}
\stitle{Architecture of $\mathsf{Spade}$.} Figure~\ref{fig:architecture} shows the architecture of $\mathsf{Spade}${} and the workflow of an edge insertion. $\mathsf{Spade}${} automatically incrementalizes peeling algorithms with the user-defined suspiciousness functions. To avoid computing from scratch on evolving graphs, the engine of $\mathsf{Spade}${} maintains the fraudulent community incrementally with an edge update (Section~\ref{sec:edgebyedge}). Batch execution is developed to improve the efficiency of handling edge updates in batch (Section~\ref{sec:batch}). The updated fraudulent community is identified in real time and returned to the moderators for further analysis. Given an edge insertion, the workflow of $\mathsf{Spade}${} contains the following components:
\begin{itemize}
\item \underline{$\mathsf{VSusp}$ and $\mathsf{ESusp}$.} Given a new vertex/edge, these components are responsible for deciding the suspiciousness of the endpoint of the edge or the edge with a user-defined strategy.
\item \underline{$\mathsf{IsBenign}$.} This component is responsible for deciding whether a new edge is benign (Section~\ref{sec:urgent}). If the edge is benign, it is inserted into an edge vector pending reordering; otherwise, peeling sequence reordering is triggered immediately for the edge buffer with this new edge.
\item \underline{$\mathsf{ReorderSeq}$.} This component is responsible for incrementally maintaining the peeling sequence and deciding the new fraudulent community with the graph updates detailed in Section~\ref{sec:Spade}.
\end{itemize}
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\lstset{language=C++,
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\stitle{APIs and data structure (Listing~\ref{lst:listing-cpp}).} We provide APIs for developers to customize and deploy their peeling algorithms for different application requirements. Developers can customize $\mathsf{VSusp}$ and $\mathsf{ESusp}$ to develop their fraud detection semantics. We design two APIs for edge insertion, namely $\mathsf{InsertEdge}$ and $\mathsf{InsertBatchEdges}$. The $\mathsf{Detect}$ function spots the fraudulent community on the current graph. $\mathsf{IsBenign}$ and $\mathsf{ReorderSeq}$ are two built-in APIs which are transparent to developers. They are activated when new edges are inserted. $\mathsf{Spade}${} uses the adjacency list to store the graph. Two vectors $\textit{_seq}$ and $\textit{_weight}$ are used to store the peeling sequence and the peeling weights.
\begin{center}
\scriptsize
\lstinputlisting[caption=Overview of $\mathsf{Spade}$, label={lst:listing-cpp}, language=C++]{spade.cpp}\label{apis}
\end{center}
\jiaxin{\stitle{Characteristic of density metrics.} We next formalize the sufficient condition of the density metrics that can be supported by $\mathsf{Spade}${}.}
\begin{property}
If 1) $g(S)$ is an arithmetic density, \emph{i.e.,}\xspace $g=\frac{|f(S)|}{|S|}$, 2) $a_i\geq 0$, and 3) $c_{ij} > 0$, then $g(S)$ is supported by $\mathsf{Spade}${}.
\end{property}
\jiaxin{The correctness is satisfied since $\mathsf{Spade}${} correctly returns the peeling sequence order (detailed in Section~\ref{sec:Spade}). We also characterize the properties of these popular density metrics in Appendix~\ref{sec:axioms} of \cite{techreport}.}
\eat{
\noindent\jiaxin{$\mathsf{Spade}${} focuses on the arithmetic density in the form of $g(S) = \frac{|f(S)|}{|S|}$ as introduced in Section~\ref{sec:background}. There are only two simple conditions of $f(S)$ (detailed in Equation~\ref{eq:density}) required by $\mathsf{Spade}${}: i) for any $a_i$, the suspiciousness of $u_i$, is non-negative; and ii) for any $c_{ij}$, the suspiciousness of $(u_i,u_j)$ is positive.}
}
\tr{
\subsection{Instances of $\mathsf{Spade}${}}
}
\stitle{Instances.} We show that popular peeling algorithms are easily implemented and supported by $\mathsf{Spade}${}, \emph{e.g.,}\xspace $\mathsf{DG}$~\cite{charikar2000greedy}, $\mathsf{DW}{}$~\cite{gudapati2021search} and $\mathsf{FD}{}$~\cite{hooi2016fraudar}. \jiaxin{We take $\mathsf{FD}{}$ as an example and leave the discussion of the other instances in the Appendix~\ref{sec:instances} of~\cite{techreport}.} To resist the camouflage of fraudsters, Hooi et al. ~\cite{hooi2016fraudar} proposed $\mathsf{FD}{}$ to weight edges and set the prior suspiciousness of each vertex with side information. Let $S\subseteq V$. The density metric of $\mathsf{FD}$ is defined as follows:
\tr{
\etitle{Instance 1. Dense subgraphs ($\mathsf{DG}{}$)~\cite{charikar2000greedy}.} $\mathsf{DG}{}$ is designed to quantify the connectivity of substructures. It is widely used to detect fake comments~\cite{kumar2018community} and fraudulent activities~\cite{ban2018badlink} on social graphs. Let $S\subseteq V$. The density metric of $\mathsf{DG}{}$ is defined by $g(S) = \frac{|E[S]|}{|S|}$. To implement $\mathsf{DG}$ on $\mathsf{Spade}${}, developers only need to design and plug in the suspiciousness function $\mathsf{esusp}$ by calling $\mathsf{ESusp}$. Specifically, $\mathsf{esusp}$ is a constant function for edges, \emph{i.e.,}\xspace $\mathsf{esusp}(u_i,u_j) = 1$.
}
\tr{
\etitle{Instance 2. Dense weighted subgraphs ($\mathsf{DW}$)~\cite{gudapati2021search}.} On transaction graphs, there are weights on the edges in usual, such as the transaction amount. The density metric of $\mathsf{DW}{}$ is defined by $g(S) = \frac{\sum_{(u_i,u_j)\in E[S]}c_{ij}}{|S|}$, where $c_{ij}$ is the weight of the edge $(u_i,u_j)\in E$. To implement $\mathsf{DW}{}$, users only need to plug in the suspiciousness function $\mathsf{esusp}$, \emph{i.e.,}\xspace given an edge, $\mathsf{esusp}(u_i,u_j) = c_{ij}$.
}
\begin{equation}
g(S) = \frac{f(S)}{|S|} = \frac{\sum_{u_i\in S} a_i + \sum_{u_i,u_j\in S \bigwedge (u_i,u_j)\in E} c_{i,j}}{|S|}
\end{equation}
\tr{
\begin{center}
\scriptsize
\lstinputlisting[caption=Implementation of $\mathsf{FD}{}$ on $\mathsf{Spade}$, label={lst:listing-fd}, language=C++]{fd.cpp}
\end{center}
}
To implement $\mathsf{FD}$ on $\mathsf{Spade}${}, users only need to plug in the suspiciousness function $\mathsf{vsusp}$ for the vertices by calling $\mathsf{VSusp}$ and the suspiciousness function $\mathsf{esusp}$ for the edges by calling $\mathsf{ESusp}$. Specifically, 1) $\mathsf{vsusp}$ is a constant function, \emph{i.e.,}\xspace given a vertex $u$, $\mathsf{vsusp}(u) = a_i$ and 2) $\mathsf{esusp}$ is a logarithmic function such that given an edge $(u_i,u_j)$, $\mathsf{esusp}(u_i,u_j) = \frac{1}{\log (x+c)}$, where $x$ is the degree of the object vertex between $u_i$ and $u_j$, and $c$ is a small positive constant ~\cite{hooi2016fraudar}.
Developers can easily implement customized peeling algorithms with $\mathsf{Spade}${}, which significantly reduces the engineering effort. For example, users write only about $20$ lines of code (compared to about $100$ lines in the original $\mathsf{FD}$~\cite{hooi2016fraudar}) to implement $\mathsf{FD}$.
\section{Incremental peeling algorithms}\label{sec:Spade}
\eat{Given a set of updates to the graph, computing from scratch is costly. On the other hand, large suspicious transactions occur in a very short timeslot. Consequently, fraud cannot be identified and prevented at an early stage. Therefore, i}
In this section, we propose several techniques to incrementally identify fraudsters by reordering the peeling sequence $O$ with graph updates, \emph{i.e.,}\xspace the peeling sequence on $G\oplus \Delta G$, denoted by $O'$.
\tr{In Section~\ref{sec:edgebyedge}, we introduce how to reorder the peeling sequence with edge insertion. In Section~\ref{sec:batch}, we elaborate on how to reorder the peeling sequence in batch. In Section~\ref{sec:urgent}, we show how to distinguish potential fraudulent transactions from benign transactions. $\mathsf{Spade}${} groups the benign transaction insertion to reduce the latency of response to potential fraudulent transactions.}
\subsection{Peeling sequence reordering with edge insertion}\label{sec:edgebyedge}
Given a graph $G=(V,E)$, the peeling sequence $O$ on $G$ and the graph updates $\Delta G=(\Delta V, \Delta E)$, where $|\Delta E| = 1$, $\mathsf{Spade}${} returns the peeling sequence $O'$ on $G\oplus \Delta G$.
\eat{
\begin{lemma}
Given two vertices $u_i$ and $u_j$ where $i\leq j$, $w_{u_i}(S_i) \leq w_{u_j}(S_i)$.
\end{lemma}
\begin{proof}
Since $i\leq j$, $S_i \subseteq S_j$. Hence $w_{u_i}(S_j)$
\end{proof}
}
\stitle{Vertex insertion.} Given a new vertex $u$, we insert it into the head of the peeling sequence and initialize its peeling weight by $\Delta_0 = 0$.
\stitle{Insertion of an edge $(u_i,u_j)$.} Without loss of generality, we assume $i < j$ and denote the weight of $(u_i,u_j)$ by $\Delta = c_{ij}$. \jiaxin{Given an edge insertion $(u_i,u_j)$, we observe that a part of the peeling sequence will not be changed. We formalize the finding as follows.}
\begin{lemma}\label{lemma:seq}
$O'[1:i-1] = O[1:i-1]$.
\end{lemma}
\jiaxin{Due to space limitations, all the proofs in this section are presented in Appendix~\ref{sec:proof} of \cite{techreport}.}
\stitle{Affected area ($G_{\mathcal{T}}$) and pending queue ($T$).} Given updates $\Delta G$ to graph $G$ and an incremental algorithm $\mathcal{T}$, we denote by $G_{\mathcal{T}}${}$=(V_{\mathcal{T}},E_{\mathcal{T}})$ the subgraph inspected by $\mathcal{T}${} in $G$ that indicates the necessary cost of incrementalization. Moreover, we construct a priority queue $T$ for the vertices pending reordering in ascending order of the peeling weights.
\stitle{Incremental algorithm ($\mathcal{T}$).} $\mathcal{T}${} initializes an empty vector for the updated peeling sequence $O'$ and append $O[1:i-1]$ to $O'$ due to the Lemma~\ref{lemma:seq}. We iteratively compare 1) the head of $T$, denoted by $u_{\min}$ and 2) the vertex $u_k$ in the peeling sequence $O$, where $k > i$. The corresponding peeling weights are denoted by $\Delta_{\min}$ and $\Delta_k$. We consider the following three cases:
\stitle{Case 1.} If $\Delta_{\min} < \Delta_k $, we pop the $u_{\min}$ from $T$ and insert it to $O'$. Then we update the priorities in $T$ for the neighbors of $u_{\min}$, $N(u_{\min})$.
\stitle{Case 2.} If $\Delta_{\min} \geq \Delta_{k}$ and $\exists u_{T}\in T, (u_{T},u_{k})\in E$ or $(u_{k},u_{T})\in E$, we insert $u_k$ into $T$. The peeling weight is $w_{u_k}(T\cup S_k)$ $ = \Delta_k $ $ + $ $\sum_{(u_T\in T) \bigwedge ((u_T,u_k)\in E)}$ $ c_{Tk} + $ $\sum_{(u_T\in T) \bigwedge ((u_k,u_T)\in E)} c_{kT}$, $k=k+1$.
\stitle{Case 3.} If $\Delta_{\min} \geq \Delta_{k}$ and $\forall u_{T}\in T, (u_{T},u_{k})\not\in E$ and $(u_{k},u_{T})\not\in E$, we insert $u_{k}$ to $O'$, $k=k+1$.
\setlist{nolistsep}
\eat{
\begin{itemize}[leftmargin=*]
\item \stitle{Case 1.} If $\Delta_{\min} < \Delta_k $, we pop the $u_{\min}$ from $T$ and insert it to $O'$. Then we update the priorities in $T$ for the neighbors of $u_{\min}$, $N(u_{\min})$.
\item \stitle{Case 2.} If $\Delta_{\min} \geq \Delta_{k}$ and $\exists u_{T}\in T, (u_{T},u_{k})\in E$ or $(u_{k},u_{T})\in E$, we insert $u_k$ into $T$. The peeling weight is $w_{u_k}(T\cup S_k)$ $ = \Delta_k $ $ + $ $\sum_{(u_T\in T) \bigwedge ((u_T,u_k)\in E)}$ $ c_{Tk} + $ $\sum_{(u_T\in T) \bigwedge ((u_k,u_T)\in E)} c_{kT}$, $k=k+1$.
\item \stitle{Case 3.} If $\Delta_{\min} \geq \Delta_{k}$ and $\forall u_{T}\in T, (u_{T},u_{k})\not\in E$ and $(u_{k},u_{T})\not\in E$, we insert $u_{k}$ to $O'$, $k=k+1$.
\end{itemize}
}
We repeat the above iteration until $T$ is empty.
\begin{figure*}[tb]
\includegraphics[width=0.95\linewidth]{figures/reordered2.eps}
\vspace{-1.4em}
\caption{\jiaxin{Peeling sequence reordering with edge insertion (A running example)} }\label{fig:reorder}
\end{figure*}
\begin{example}
Consider the graph $G$ in Figure~\ref{fig:peel} and its peeling sequence $O = [u_1, u_3, u_2, u_4, u_5]$. Suppose that a new edge $(u_1,u_5)$ is inserted into $G$ and its weight is $4$ as shown in the LHS of Figure~\ref{fig:reorder}. The reordering procedure is presented in the RHS of Figure~\ref{fig:reorder}. $u_1$ is pushed to the pending queue $T$. Since the peeling weight of the next vertex in $O$, $u_3$, is the smallest, it will be inserted directly into $O'$. Since $u_2\in N(u_1)$, we recover its peeling weight and push it into $T$. Since the peeling weights of $u_2$ and $u_1$ are smaller than those of $u_4$, they will pop out of $T$ and insert into $O'$. Once $T$ is empty, the rest of the vertices, $u_4$ and $u_5$, in $O$ are appended to $O'$ directly. Therefore, the reordered peeling sequence is $O'=[u_3,u_2,u_1,u_4,u_5]$.
\end{example}
\eat{
\begin{lemma}\label{lemma:subset}
If $S_i \subseteq S_j$ and $u_k\in S_i$, $w_{u_k}(S_j) \geq w_{u_k}(S_i)$.
\end{lemma}
}
\eat{
\begin{proof}
By definition, we have the following.
\begin{equation}
\footnotesize
\begin{split}
w_{u_k}(S_j) & = a_k + \sum_{(u_j\in S_j) \bigwedge ((u_k,u_j)\in E)} c_{kj} + \sum_{(u_j\in S_j) \bigwedge ((u_j,u_k)\in E)} c_{jk} \\
& = w_{u_k}(S_i) + \sum_{(u_j\in S_j\setminus S_i) \bigwedge ((u_k,u_j)\in E)} c_{kj} + \sum_{(u_j\in S_j\setminus S_i) \bigwedge ((u_j,u_k)\in E)} c_{jk}
\end{split}
\end{equation}
Since the weights on the edges are nonnegative, $w_{u_k}(S_j) > w_{u_k}(S_i)$.
\end{proof}
}
\noindent\jiaxin{\stitle{Remarks.} If the peeling weight of $u_k$ is greater than that of the head of $T$ (\emph{i.e.,}\xspace $u_{\min}$), then $u_{\min}$ has the smallest peeling weight among $T\cup S_k$. We formalize this remark as follows.}
\begin{lemma}\label{lemma:peel}
If $\Delta_k > \Delta_{\min}$, $u_{\min} = \mathop{\arg\min}\limits_{u\in T\cup S_k}w_{u}(T\cup S_k)$.
\end{lemma}
\eat{
\begin{proof}
\jiaxin{Due to space limitations, the proof is presented in Appendix~\ref{sec:proof} of \cite{techreport}.}
\end{proof}
}
\eat{
\begin{proof}
Consider a vertex $u'\in T\cup S_k$, where $u'\not =u_k$ or $u'\not = u_{\min}$. 1) If $u'\in S_k$, due to Lemma~\ref{lemma:subset}, $w_{u'}(T\cup S_k) > w_{u'}(S_k) > w_{u_k}(S_k) \geq w_{u_k}(T\cup S_k) = \Delta_k >\Delta_{\min}$. 2) If $u'\in T$, $w_{u'}(T\cup S_k) > w_{u_{\min}}(T\cup S_k) = \Delta_{\min}$. Hence, $u'$ is not the vertex that has the smallest peeling weight. Therefore, $u_{\min}$ has the smallest peeling weight.
\end{proof}
}
\stitle{Correctness and accuracy guarantee.} In \textbf{Case 1} of $\mathcal{T}${}, if $\Delta_k > \Delta_{\min}$, $u_{\min}$ is chosen to insert to $O'$ since it has the smallest peeling weight due to Lemma~\ref{lemma:peel}. In \textbf{Case 3} of $\mathcal{T}${}, $\Delta_k$ is the smallest peeling weight and $u_k$ is chosen to insert to $O'$. The peeling sequence is identical to that of $G\oplus \Delta G$, since in each iteration the vertex with the smallest peeling weight is chosen. The accuracy of the worst-case is preserved due to Lemma~\ref{lemma:2ppr}.
\stitle{Time complexity.} The complexity of the incremental maintenance is $O(|E_{\mathcal{T}}|+|E_{\mathcal{T}}|\log|V_{\mathcal{T}}|)$. The complexity is bounded by $O(|E|\log |V|)$ and is small in practice.
\subsection{Peeling sequence reordering in batch} \label{sec:batch}
\begin{figure}
\includegraphics[width=0.9\linewidth]{figures/inc-fraudar.eps}
\caption{\jiaxin{Peeling sequence reordering in batch}}\label{fig:batch}
\end{figure}
Since the peeling sequence reordering by early edge insertions could be reversed by later ones, some reorderings are stale and duplicate. Suppose that the insertion is a subgraph $\Delta G = (\Delta V, \Delta E)$. A direct way to reorder the peeling sequence is to insert the edges one by one. The complexity is $O(|\Delta E| (|E_{\mathcal{T}}|\log|V_{\mathcal{T}}|))$ which is time consuming. To reduce the amount of stale computation, we propose a peeling sequence reordering algorithm in batch.
\begin{figure}
\includegraphics[width=0.65\linewidth]{figures/eg-fraudar-stale.eps}
\caption{Illustration of stale incremental maintenance}\label{fig:stale}
\end{figure}
\begin{example}\label{eg:stale}
Consider a fraudulent community, $S^P$, identified by the peeling algorithm in Figure~\ref{fig:stale}. $u_i$ and $u_j$ are two normal users. Suppose that they have the same peeling weight and that $u_i$ is peeled before $u_j$. When a new transaction \textcircled{\raisebox{-0.9pt}{1}} is generated, we should reorder $u_i$ and $u_j$ by exchanging their positions. When \textcircled{\raisebox{-0.9pt}{2}} and \textcircled{\raisebox{-0.9pt}{3}} are inserted, positions of $u_i$ and $u_j$ will be re-exchanged. However, if we reorder the sequence in batch with the last transaction \textcircled{\raisebox{-0.9pt}{4}}, we are not required to change the positions of $u_i$ and $u_j$.
\end{example}
\begin{algorithm}[tb]
\caption{Peeling sequence reordering in batch}\label{algo:batch}
\footnotesize
\SetKwProg{Fn}{Function}{}{}
\KwIn{Graph $G = (V, E)$, $O$, density metric $g(S)$, $\Delta G = (\Delta V, \Delta E)$}
\KwOut{Peeling sequence order $O' = Q(G\oplus \Delta G)$ and fraudulent community}
sort $\Delta V$ in the ascending order of indices in $O$ and color $\Delta V$ black \\
init a priority pending queue $T$ in the ascending order of peeling weights \\ \label{algo:batch:init}
init an empty vector $O'$ \\
\For{$u_i = O[i] \in \Delta V$}{
add $u_i$ into $T$ \\\label{algo:batch:add1}
color its neighbors $O[j]$ ($j>i$) gray\\\label{algo:batch:add2}
$k = i + 1$ \\
\While{$T$ is not empty}{
\eIf(\jiaxin{\tcp*[h]{\textbf{Case 1}}}){\label{algo:batch:case1b}
$\Delta_{\min} < \Delta_k$}{
pop $u_{\min}$ from $T$ and insert it to $O'$ \\
update the priorities of $N(u_{\min})$ in $T$ \\\label{algo:batch:case1e}
}{\label{algo:batch:case2ab}
\eIf(\jiaxin{\tcp*[h]{\textbf{Case 2(a)}}}){$u_k$ is black or gray}{
add $u_k$ into $T$ and recover its peeling weight\\
color its neighbors $N(u_{k})$ gray \\ \label{algo:batch:case2ae}
}(\jiaxin{\tcp*[h]{\textbf{Case 2(b)}}: $u_k$ is white}){\label{algo:batch:case2bb}
insert $u_k$ to $O'$\\
}
$k = k + 1$ \\\label{algo:batch:case2be}
}
}
append $O[k:i'-1]$ to $O'$, where $u_{i'}=O[i']$ is the next black vertex \\
}
\Return{$O'$ \textnormal{and} $\arg\max_{S_i}g(S_i)$}
\end{algorithm}
\stitle{Peeling weight recovery.} Given a vertex $u_j = O[j]$ and a set of vertex $S_i$ ($i < j$, \emph{i.e.,}\xspace $S_j\subseteq S_i$), the peeling weight $w_{u_j}(S_i)$ can be calculated by $w_{u_j}(S_i) = \Delta_j + \sum_{(i \leq k < j) \bigwedge ((u_j,u_k)\in E)} c_{jk} + \sum_{(i \leq k < j) \bigwedge ((u_k,u_j)\in E)} c_{kj}$.
\stitle{Vertex sorting.} Intuitively, the increase in peeling weight of $u_i$ does not change the subsequence of $O[1:i-1]$ due to Lemma~\ref{lemma:seq}. We sort the vertices in $\Delta V$ by the indices in the peeling sequence. Then we reorder the vertices in ascending order of the indices in $O$. For simplicity, we color the vertices in $\Delta V$ black, affected vertices (\emph{i.e.,}\xspace vertices pending reordering) gray and unaffected vertices white.
\stitle{Incremental maintenance in batch \jiaxin{(Algorithm~\ref{algo:batch} and Figure~\ref{fig:batch})}.} We initialize a pending queue $T$ to maintain the vertices pending reordering (Line~\ref{algo:batch:init}). Iteratively, we add the vertex $O[i]\in \Delta V$ to $T$ and color its neighbors $O[j]$ gray (Line~\ref{algo:batch:add1}-\ref{algo:batch:add2}). If $T$ is not empty, we compare the peeling weight $\Delta_k$ of the vertex $u_k = O[k]$ ($k > i$) with the peeling weight $\Delta_{\min}$ of the head of $T$, $u_{\min}$. We consider the following \jiaxin{two cases as shown in Figure~\ref{fig:batch}}. \textbf{Case 1:} If $\Delta_{\min} < \Delta_k$, we pop $u_{\min}$ from $T$, insert it to $O'$ and update the priorities of its neighbors in $T$ \jiaxin{(Line~\ref{algo:batch:case1b}-\ref{algo:batch:case1e})}; \textbf{Case 2(a):} if $\Delta_{\min} \geq \Delta_k$ and $u_k$ is gray or black, we recover its peeling weight in $S_k\cup T$ and insert it to $T$. Then we color the vertices in $N(u_k)$ gray \jiaxin{(Line~\ref{algo:batch:case2ab}-\ref{algo:batch:case2ae})}; otherwise \textbf{Case 2(b):} if $\Delta_{\min} \geq \Delta_k$ and $u_k$ is white, we insert $u_k$ to $O'$ directly \jiaxin{(Line~\ref{algo:batch:case2bb}-\ref{algo:batch:case2be})}. We repeat the above procedure until the pending queue $T$ is empty. Then we append $O[k:i'-1]$ to $O'$, where $u_{i'}$ is the next vertex in $\Delta V$. We insert $u_{i'}$ into $T$ and repeat the reordering until there is no black vertex. \jiaxin{The correctness and accuracy guarantee are similar to those of peeling sequence reordering with edge insertion. Due to space limitations, we present them in Appendix~\ref{sec:correctness} of ~\cite{techreport}.}
\stitle{Complexity.} The time complexity of Algorithm~\ref{algo:batch} is $O(|E_{\mathcal{T}}|+|E_{\mathcal{T}}| $ $\log|V_{\mathcal{T}}|)$ which is bounded by $O(|E|\log|V|)$.
\subsection{Peeling sequence reordering with edge grouping}~\label{sec:urgent}
\stitle{Update steam $\Delta G^{\tau}$.} In a transaction system, the edge updates are coming in a stream manner (\emph{i.e.,}\xspace a timestamp on each edge) which is denoted by $\Delta G^{\tau}$. Formally, we denote it by $\Delta G^{\tau} = [(e_0,\tau_0),\ldots (e_n, \tau_n)]$ where $\tau_i$ is the timestamp on the edge $e_i=(u_i,v_i)$.
\stitle{Latency of activities $\mathcal{L}(\Delta G^{\tau})$.} Suppose that $e_i=(u_i,v_i)$ is a labeled fraudulent activity which is generated at $\tau_i$ and is responded/inserted at $\tau_i^r$. The latency of $e_i$ is $\tau_i^r - \tau_i$. Given an update stream $\Delta G^{\tau}$, the latency of fraudulent activities is defined as follows.
\begin{equation}\label{eq:latency}
\mathcal{L}(\Delta G^{\tau}) = \sum_{(e_i,\tau_i)\in \Delta G^{\tau}}{\tau_i^r - \tau_i}
\end{equation}
\stitle{Prevention ratio $\mathcal{R}$.} If a fraudster is identified, we ban the following related transactions to prevent economic loss. We denote the ratio of suspicious transactions prevented to all suspicious transactions by $\mathcal{R}$.
\jiaxin{
\begin{example}
Consider an update steam in Figure~\ref{fig:effectivepara}. $e_i$ ($i\in [1,6]$) are a set of labeled fraudulent transactions and $\tau_i$ ($i\in [1,6]$) are their timestamps. Regarding the reordering in batch, the new transactions are queueing until the size of the queue is equal to the batch size. The reordering is triggered at $\tau_s$ and finished at $\tau_f$. Therefore, they are inserted at $\tau_i^r = \tau_f$ The queueing time for each edge is $\tau_s - \tau_i$ while the latency is $\tau_f - \tau_i$. Suppose the fraudster is identified at $\tau_f$, the prevention ratio is $\mathcal{R} = \frac{|\{e_i|\tau_i > \tau_f\}|}{|\{e_i\}|}$.
\end{example}
}
$\mathsf{Spade}${} aims to reduce $\mathcal{L}$ and increase $\mathcal{R}$ as much as possible. \jiaxin{In Figure~\ref{fig:effectivepara}, if the reordering is triggered at $\tau_s=\tau_2$ and responded at $\tau_f=\tau_3$, the following fraudulent activities can be prevented.}
Intuitively, some transactions are generated by normal users (benign edges), while others are generated by potential fraudsters (urgent edges). $\mathsf{Spade}${} groups the benign edges and reorders the peeling sequence in batch. It can both improve the performance of reordering and reduce the latency of the response to potential fraudulent transactions. We define the benign and urgent edges as follows.
\begin{definition}
Given an edge $e=(u_i, u_j)$ and its weight $c_{ij}$, if $w_{u_i}(S_0) + c_{ij} \geq g(S^P)$ or $w_{u_j}(S_0) + c_{ij} \geq g(S^P)$, $e$ is an urgent edge; otherwise $e$ is a benign edge.
\end{definition}
\noindent\jiaxin{Given a benign edge insertion $(u_i,u_j)$, neither $u_i$ nor $u_j$ belongs to the densest subgraph (Lemma~\ref{lemma:optimalset}). And the insertion cannot produce a denser fraudulent community by peeling algorithms (Lemma~\ref{lemma:benign}).}
\eat{
\begin{lemma}\label{lemma:opt}
If $\exists u\in S$, such that $w_{u}(S) < g(S^*)$, then $S\not = S^{*}$.
\end{lemma}
}
\eat{
\begin{proof}
\end{proof}
}
\begin{lemma}\label{lemma:optimalset}
Given an edge $e = (u_i,u_j)$, if $e$ is a benign edge, after the insertion of $e$, $u_i\not \in S^{*}$ and $u_j\not \in S^{*}$.
\end{lemma}
\eat{
\begin{proof}
We prove this lemma in contradiction by assuming that $u_i\in S^{*}$. $w_{u_i}(S^*) \leq w_{u_i}(S_0) + c_{ij} < g(S^P) \leq g(S^*)$. We have $S^*\not = S^*$ due to Lemma~\ref{lemma:opt}. We can conclude that $u_i\not\in S^*$. Similarly, $u_j\not \in S^*$.
\end{proof}
}
\eat{
\begin{lemma}\label{lemma:opt2}
If $\exists u\in S_i$, $w_{u}(S_i) < g(S_i)$, then $S_i\not = S^{P}$.
\end{lemma}
}
\eat{
\begin{proof}
We prove this in contradiction by assuming that $S_i= S^P$. Suppose that $u_i$ is peeled from $S_i$. Hence, $w_{u_i}(S^P) \leq w_{u}(S^P)$ due to the peeling definition. The proof can be obtained as follows:
\begin{equation}
\footnotesize
\begin{split}
g(S^P \setminus \{u_i\}) & = \frac{f(S^{P}) - w_{u_i}(S^{P})}{|S^{P}|-1} > \frac{f(S^P) - w_{u}(S^P)}{|S^P|-1} > g(S^P)
\end{split}
\end{equation}
This contradicts the fact that $S^P$ has the highest density. We can conclude that $S_i \not = S^{P}$.
\end{proof}
}
We denote the vertex subset returned after reordering by $S^{P'}$.
\begin{lemma}\label{lemma:benign}
Given a benign edge $e = (u_i,u_j)$ insertion, at least one of the following two conditions is established: 1) $u_i\not \in S^{P'}$ and $u_j\not \in S^{P'}$; and 2) $g(S^{P'}) < g(S^P)$.
\end{lemma}
Therefore, we postpone the incremental maintenance of the peeling sequence for benign edges which provide two benefits. First, we can perform a batch update that avoids stale computation. Second, an urgent edge insertion, which is caused by a potential fraudster, triggers incremental maintenance immediately. These fraudsters are identified and reported to the moderators in real time.
\begin{figure}[tb]
\includegraphics[width=0.75\linewidth]{figures/metricdemo.eps}
\caption{\small \jiaxin{Metrics for a set of fraudulent transactions made by a fraudster (latency: $\tau_f-\tau_i$, queueing time: $\tau_s-\tau_i$, prevention ratio: $\mathcal{R} = \frac{|\{e_i|\tau_i > \tau_f\}|}{|\{e_i\}|}$)}}\label{fig:effectivepara}
\end{figure}
\stitle{Edge grouping.} We next present the paradigm of peeling sequence reordering by edge grouping. We first initialize an empty buffer $\Delta G$ for the updates (Line~\ref{algo:urgent:init}). When an edge $e_i$ enters, we insert it into $\Delta G$. If $e_i$ is an urgent edge, we incrementally maintain the peeling sequence by Algorithm~\ref{algo:batch} and clear the buffer (Line~\ref{algo:urgent:begin}-\ref{algo:urgent:end}).
\begin{algorithm}[tb]
\caption{Paradigm of edge grouping}\label{algo:urgent}
\footnotesize
\SetKwProg{Fn}{Function}{}{}
\KwIn{A graph $G = (V, E)$, $O$, a density metric $g(S)$, $\Delta G^T$}
\KwOut{Peeling sequence order $O' = Q(G\oplus \Delta G^T)$ and fraudulent community}
init an empty buffer $\Delta G$ for updates \\ \label{algo:urgent:init}
\For{$i=1,\ldots, m$}{
$\Delta G.\mathsf{add}$($e_i$) \\
\If{$e_i$ is an urgent edge}{\label{algo:urgent:begin}
$O' = Q(G\oplus \Delta G)$ by Algorithm~\ref{algo:batch} \\
clear $\Delta G$ \label{algo:urgent:end}
}
}
\Return{$O'$ \textnormal{and} $\arg\max_{S_i}g(S_i)$}
\end{algorithm}
\eat{
\stitle{\ref{sec:Spade}.2 Approximation ratio perserving}
Another approach is that we maintain the same approximation ratio of $\mathsf{FD}$ rather than reorder the sequence $\mathsf{FD}$.
\idea{\cite{tsourakakis2015k} -- peeling algorithms in batch?}
}
\section{Experimental Evaluation}\label{sec:exp}
\eat{Evaluations are classified into two groups: the overall improvement in performance of $\mathsf{Spade}${} (Section~\ref{sec:efficiency}) and the effectiveness of $\mathsf{Spade}${} in preventing fraudulent transactions (Section~\ref{sec:effectiveness}).}
Our experiments are run on a machine that has an X5650 CPU, $16$ GB RAM. The implementation is made memory-resident and implemented in C++. All codes are compiled by GCC-9.3.0 with -$O3$.
\input{exp-datasets}
\input{tab-batchsize.tex}
\input{tab-latency}
\stitle{Datasets.} We conduct the experiments on seven datasets (Table~\ref{table:Statistics}). Four industrial datasets are from $\mathsf{Grab}$ (Grab1-Grab4). \jiaxin{Given a set of transactions, each transaction is represented as an edge. We replay the edges in the \jiaxin{increasing} order of their timestamp. If a user $u_i$ purchases from a store $u_j$, we add an edge $(u_i,u_j)$ to $E$.} Specifically, we construct the graph $G$ as initialization \jiaxin{($V$ and $90\%$ of $E$ as the initial graph), and the remaining $10\%$ of $E$ as increments for testing.} The increments are decomposed into a set of graph updates $\Delta G$ in the increasing order of their timestamp with different batch sizes $|\Delta E|$. We also use three popular open datasets including Amazon~\cite{mcauley2013hidden}, Wiki-vote~\cite{leskovec2010signed} and Epinion~\cite{leskovec2010signed}. Since there are no timestamps on these three datasets, we randomly select $10\%$ edges from $E$ as increments for evaluation.
\stitle{Competitors.} We choose three common peeling algorithms ($\mathsf{DG}$, $\mathsf{DW}$ and $\mathsf{FD}$) as a baseline. \jiaxin{Given an edge insertion, these algorithms identify the fraudulent community on the entire graph from scratch.} We demonstrate the performance improvement of our proposal ($\mathsf{IncDG}${}, $\mathsf{IncDW}${} and $\mathsf{IncFD}${}) implemented in $\mathsf{Spade}${}. We denote batch updates by $\mathsf{IncDG}${}-$x$, $\mathsf{IncDW}${}-$x$ and $\mathsf{IncFD}${}-$x$, where $x =|\Delta E|$ is the batch size. We also denote the reordering of the peeling sequence with edge grouping by $\mathsf{IncDGG}${}, $\mathsf{IncDWG}${} and $\mathsf{IncFDG}${}.
\subsection{Efficiency of $\mathsf{Spade}${}}\label{sec:efficiency}
\begin{figure}[tb]
\subcaptionbox{\jiaxin{Prevention ratio vs. latency\label{fig:prevent}}}{\includegraphics[width=0.41\linewidth]{figures/exp/prevent.eps}}
\subcaptionbox{Graph degree distribution\label{fig:distribution}}{\includegraphics[width=0.41\linewidth]{figures/exp/distribution.eps}}
\caption{Graph characteristic}\label{fig:characteristic}
\end{figure}
\begin{figure}[tb]
\includegraphics[width=0.5\linewidth]{figures/exp/runtime.eps}
\caption{Efficiency comparison between peeling algorithms and corresponding incremental versions on $\mathsf{Spade}${} ($|\Delta E| = 1$)}\label{fig:runtime}
\end{figure}
\stitle{Improvement of incremental peeling algorithms.} We first investigate the efficiency of $\mathsf{Spade}${} by comparing the performance between incremental peeling algorithms and peeling algorithms. In Figure~\ref{fig:runtime}, our experiments show that $\mathsf{IncDG}${} (resp. $\mathsf{IncDW}${} and $\mathsf{IncFD}$) is up to $4.17\times 10^3$ (resp. $1.63\times 10^3$ and $1.96\times 10^6$) times faster than $\mathsf{DG}{}$ (resp. $\mathsf{DW}{}$ and $\mathsf{FD}$) with an edge insertion. The reason \jiaxin{for such a significant speedup} is that only a small part of the peeling sequence is affected for most edge insertions. This is also consistent with the time complexity comparison of those algorithms. In fact, our algorithm on average processes only $3.5\times 10^{-4}$, $7.2\times 10^{-4}$ and $2.5\times 10^{-7}$ of edges compared with DG, DW and FD (on the entire graph), respectively. $\mathsf{Spade}${} identifies and maintains the affected peeling subsequence rather than recomputes the peeling sequence from scratch. \jiaxin{Thus, $\mathsf{Spade}${} significantly outperforms existing algorithms.}
\stitle{Impact of batch sizes $|\Delta E|$.} We evaluate the efficiency of batch updates by varying batch sizes $|\Delta E|$ from $1$ to $100$K. As shown in Table~\ref{tab:batchsize}, $\mathsf{IncDG}$-$100$K (resp. $\mathsf{IncDW}${}-$100$K and $\mathsf{IncFD}$-$100$K) is up to $1211$ (resp. $3448$ and $4.47$) times faster than $\mathsf{IncDG}${} (resp. $\mathsf{IncDW}${} and $\mathsf{IncFD}${}). When the batch size increases, the average elapsed time for an edge insertion keeps decreasing. \jiaxin{As indicated in Example~\ref{eg:stale}, the reordering of the peeling sequence by early edge insertions could be reversed by later ones. Reordering the peeling sequence in batch avoids such stale incremental maintenance by reducing the reversal. \tr{With batch updates, $\mathsf{IncDG}$-$100$K (resp. $\mathsf{IncDW}${}-$100$K and $\mathsf{IncFD}$-$100$K) is up to $2.86\times 10^6$ (resp. $3.21\times 10^6$ and $8.8\times 10^6$) times faster than $\mathsf{DG}$ (resp. $\mathsf{DW}$ and $\mathsf{FD}$).}}
\stitle{Impact of edge grouping.} As shown in Table~\ref{tab:urgent}, $\mathsf{IncDGG}${} (resp. $\mathsf{IncDWG}${} and $\mathsf{IncFDG}${}) is up to $7.1$ (resp. $9.7$ and $1.25$) times faster than $\mathsf{IncDG}${}-$1$K (resp. $\mathsf{IncDW}${}-$1$K and $\mathsf{IncFD}${}-$1$K) since the edge grouping technique generally accumulates more than $1$K edges. Another evidence is that the graph follows the power law, as shown in Figure~\ref{fig:distribution}. Most edge insertions are benign and are processed in batch.
\stitle{Scalability.} We next evaluate the scalability of $\mathsf{Spade}${} on $\mathsf{Grab}$' s datasets \jiaxin{(Grab1-Grab4)} of different sizes which is controlled by the number of edges $|E|$. We vary $|E|$ from $10$M to $25$M \jiaxin{as shown in Table~\ref{table:Statistics}} and report the results in Table~\ref{tab:batchsize}. All peeling algorithms scale reasonably well with the increase of $|E|$. With $|E|$ increasing by $2.5$ times, the running time of $\mathsf{Spade}${} increases by up to $2$ (resp. $2$ and $3$) times for $\mathsf{DG}{}$ (resp. $\mathsf{DW}{}$ and $\mathsf{FD}$).
We also compare the efficiency of $\mathsf{DG}$, $\mathsf{DW}$ and $\mathsf{FD}$. As shown in Columns $2\sim 4$ of Table~\ref{tab:batchsize}, the peeling algorithms have a similar performance. However, $\mathsf{IncFD}${} is much faster than $\mathsf{IncDG}${} and $\mathsf{IncDW}${} since the affected peeling subsequence is smaller due to the suspiciousness function of $\mathsf{FD}$~\cite{hooi2016fraudar}.
\begin{figure}[tb]
\begin{minipage}[t]{.14\textwidth}
\subcaptionbox{$\mathsf{IncDG}$}{\includegraphics[width=1.2\linewidth]{figures/exp/elapsedtime-dg.eps}}
\end{minipage}
\hfill\hfill
\begin{minipage}[t]{.14\textwidth}
\subcaptionbox{$\mathsf{IncDW}${}}{\includegraphics[width=1.2\linewidth]{figures/exp/elapsedtime-dw.eps}}
\end{minipage}
\hfill\hfill
\begin{minipage}[t]{.14\textwidth}
\subcaptionbox{$\mathsf{IncFD}$}{\includegraphics[width=1.2\linewidth]{figures/exp/elapsedtime-fd.eps}}
\end{minipage}
\begin{minipage}[t]{.14\textwidth}
\subcaptionbox{$\mathsf{IncDG}$}{\includegraphics[width=1.2\linewidth]{figures/exp/latency-dg.eps}}
\end{minipage}
\hfill\hfill
\begin{minipage}[t]{.14\textwidth}
\subcaptionbox{$\mathsf{IncDW}${}}{\includegraphics[width=1.2\linewidth]{figures/exp/latency-dw.eps}}
\end{minipage}
\hfill\hfill
\begin{minipage}[t]{.14\textwidth}
\subcaptionbox{$\mathsf{IncFD}$}{\includegraphics[width=1.2\linewidth]{figures/exp/latency-fd.eps}}
\end{minipage}
\caption{\jiaxin{Elapsed time and latency by varying batch sizes}}\label{fig:tplatency}
\end{figure}
\subsection{Effectiveness of $\mathsf{Spade}${}}\label{sec:effectiveness}
\eat{Next, we demonstrate two metrics to measure the effectiveness of $\mathsf{Spade}${}. First, fraudsters should be detected as soon as possible to avoid economic loss, \emph{i.e.,}\xspace the latency $\mathcal{L}$ of response to fraudulent activities should be reduced (defined by Equation~\ref{eq:latency}). Second, once we identify a fraudster, we ban his/her following transactions to prevent economic loss. We use $\mathcal{R}$ to denote the ratio of suspicious transactions that are prevented to all suspicious transactions.}
\stitle{Latency.} Our experiment reveals that when the batch size increases, the latency of the batch peeling sequence increases (shown in Figure~\ref{fig:tplatency}). For example, the latency of $\mathsf{IncDG}${} (resp. $\mathsf{IncDW}${} and $\mathsf{IncFD}${}) is $0.76$ (resp. $0.74$ and $0.76$). We remarked that $99.99\%$ of the latency of $\mathsf{IncDG}${}, $\mathsf{IncDW}${} and $\mathsf{IncFD}${} is the queueing time, \emph{i.e.,}\xspace $\mathsf{Spade}${} accumulates enough transactions and processes them together. Furthermore, the latency in Grab1 is higher than that in Grab4. For example, the latency of $\mathsf{IncFD}${} in Grab1 (resp. Grab4) is $2.93$ (resp. $0.76$). This is because the queueing time on Grab1 is longer than that on Grab4.
\stitle{Prevention ratio.} As shown in Figure~\ref{fig:prevent}, the prevention ratio continues to decrease as latency increases on $\mathsf{Grab}$'s datasets. Our results show that $\mathsf{IncDGG}${} (resp. $\mathsf{IncDWG}${} and $\mathsf{IncFDG}${}) can prevent $88.34\%$ (resp. $86.53\%$ and $92.47\%$) of fraudulent activities. $\mathsf{IncDG}$-$1K$ (resp. $\mathsf{IncDW}$-$1K$ and $\mathsf{IncFD}$-$1K$) can prevent $28.6\%$ (resp. $41.18\%$ and $92.47\%$) of fraudulent activities by excluding queueing time.
\stitle{Case studies.} We next present the effectiveness of $\mathsf{Spade}${} in discovering meaningful fraud through case studies in the datasets of $\mathsf{Grab}$. There are three popular fraud patterns as shown in Figure~\ref{fig:casestudy}. First, \textit{customer-merchant collusion} is the customer and the merchant performing fictitious transactions to use the opportunity of promotion activities to earn the bonus (Figure~\ref{fig:casestudy}(a)). Second, there is a group of users who take advantage of promotions or merchant bugs, called \textit{deal-hunter} (Figure~\ref{fig:casestudy}(b)). Third, some merchants recruit fraudsters to create false prosperity by performing fictitious transactions, called \textit{click-farming} (Figure~\ref{fig:casestudy}(c)). All three cases form a dense subgraph in a short period of time.
We investigate the details of the customer-mercant collusion in Figure~\ref{fig:casestudy}(d). $\mathsf{IncDG}${} and $\mathsf{DG}$ start both at $T_0$. Under the semantic of $\mathsf{DG}$, the user becomes a fraudster at $T_1$ (one second after $T_0$). $\mathsf{IncDG}${} spots the fraudster at $T_1$ with negligible delay. However, $\mathsf{DG}$ cannot detect this fraud at $T_1$, as it is still evaluating the graph snapshot at $T_0$. By $\mathsf{DG}$, this fraudster will be detected after the second round detection of $\mathsf{DG}$ at $T_2$ (about 60 seconds after $T_0$). During the time period $[T_1,T_2]$, there are $720$ potential fraudulent transactions generated. Similar observations are made in the other two cases. \jiaxin{Due to space limitations, they are presented in Appendix~\ref{sec:casestudy} of \cite{techreport}.}
\begin{figure}[tb]
\includegraphics[width=0.9\linewidth]{figures/casestudy2.eps}
\caption{Case study: three fraud patterns}\label{fig:casestudy}
\end{figure}
\section{Related work}\label{sec:related}
\stitle{Dense subgraph mining.} A series of studies have utilized dense subgraph mining to detect fraud, spam, or communities on social networks and review networks~\cite{hooi2016fraudar,shin2016corescope,ren2021ensemfdet}. However, they are proposed for static graphs. Some variants \cite{bahmani2012densest,epasto2015efficient} are designed to detect dense subgraphs in dynamic graphs. \cite{shin2017densealert} is proposed to spot generally dense subtensors created in a short period of time. Unlike these studies, $\mathsf{Spade}${} detects the fraudsters on both weighted and unweighted graphs in real time. Moreover, we propose an edge grouping technique which distinguishes potential fraudulent transactions from benign transactions and enables incremental maintenance in batch.
\stitle{Graph clustering.} A common practice is to employ graph clustering that divides a large graph into smaller partitions for fraud detection. DBSCAN~\cite{gan2015dbscan,ester1996density} and its variant hdbscan ~\cite{mcinnes2017hdbscan} use local search heuristics to detect dense clusters. K-Means~\cite{duda1973pattern} is a clustering method of vector quantization. \cite{yamanishi2004line} detects medical insurance fraud by recognizing outliers. Unlike these studies, $\mathsf{Spade}${} is robust with worst-case guarantees in search results. Moreover, $\mathsf{Spade}${} provides simple but expressive APIs for developers, which allows their peeling algorithms to be incremental in nature on evolving graphs.
\stitle{Fraud detection using graph techniques.} COPYCATCH~\cite{beutel2013copycatch} and GETTHESCOOP~\cite{jiang2014inferring} use local search heuristics to detect dense subgraphs on bipartite graphs. Label propagation~\cite{wang2015community} is an efficient and effective method of detecting community. ~\cite{cortes2003computational} explores link analysis to detect fraud. \cite{wang2021deep} and \cite{dou2020enhancing} explore the GNN to detect fraud on the graph. Unlike these studies, $\mathsf{Spade}${} detects fraud in real-time and supports evolving graphs.
\section{Conclusion}\label{sec:conclusion}
In this paper, we propose a real-time fraud detection framework called $\mathsf{Spade}$. We propose three fundamental peeling sequence reordering techniques to avoid detecting fraudulent communities from scratch. $\mathsf{Spade}${} enables popular peeling algorithms to be incremental in nature and improves their efficiency. Our experiments show that $\mathsf{Spade}${} speeds up fraud detection up to $6$ orders of magnitude and up to $88.34\%$ fraud activities can be prevented.
The results and case studies demonstrate that our algorithm is helpful to address the challenges in real-time fraud detection for the real problems in $\mathsf{Grab}$ but also goes beyond for other graph applications as shown in our datasets.
\begin{acks}
This work was funded by the Grab-NUS AI Lab, a joint collaboration between GrabTaxi Holdings Pte. Ltd. and National University of Singapore. We thank the reviewers for their valuable feedback.
\end{acks}
\section{Proofs of lemmas}\label{sec:proof}
In this section, we provide all the formal proofs in Section~\ref{sec:Spade} of the main paper.
\begin{manuallemma}{\ref{lemma:seq}}
$O'[1:i-1] = O[1:i-1]$.
\end{manuallemma}
\begin{proof}
$\forall k\in [1,i-1]$, $w_{u_i}(S_k)$ and $w_{u_j}(S_k)$ increase by $\Delta$. Therefore, $w_{u_k}(S_k)$ is still the smallest among $S_k$. Hence, $u_k$ will be removed at $k$-th iteration. By induction, $O'[1:i-1] = O[1:i-1]$.
\end{proof}
\begin{lemma}\label{lemma:subset}
If $S_i \subseteq S_j$ and $u_k\in S_i$, $w_{u_k}(S_j) \geq w_{u_k}(S_i)$.
\end{lemma}
\begin{proof}
By definition, we have the following.
\begin{equation}
\footnotesize
\begin{split}
w_{u_k}(S_j) & = a_k + \sum_{(u_j\in S_j) \bigwedge ((u_k,u_j)\in E)} c_{kj} + \sum_{(u_j\in S_j) \bigwedge ((u_j,u_k)\in E)} c_{jk} \\
& = w_{u_k}(S_i) + \sum_{(u_j\in S_j\setminus S_i) \bigwedge ((u_k,u_j)\in E)} c_{kj} + \sum_{(u_j\in S_j\setminus S_i) \bigwedge ((u_j,u_k)\in E)} c_{jk}
\end{split}
\end{equation}
Since the weights on the edges are nonnegative, $w_{u_k}(S_j) > w_{u_k}(S_i)$.
\end{proof}
\begin{manuallemma}{\ref{lemma:peel}}
If $\Delta_k > \Delta_{\min}$, $u_{\min} = \mathop{\arg\min}\limits_{u\in T\cup S_k}w_{u}(T\cup S_k)$.
\end{manuallemma}
\begin{proof}
Consider a vertex $u'\in T\cup S_k$, where $u'\not =u_k$ or $u'\not = u_{\min}$. 1) If $u'\in S_k$, due to Lemma~\ref{lemma:subset}, $w_{u'}(T\cup S_k) > w_{u'}(S_k) > w_{u_k}(S_k) \geq w_{u_k}(T\cup S_k) = \Delta_k >\Delta_{\min}$. 2) If $u'\in T$, $w_{u'}(T\cup S_k) > w_{u_{\min}}(T\cup S_k) = \Delta_{\min}$. Hence, $u'$ is not the vertex that has the smallest peeling weight. Therefore, $u_{\min}$ has the smallest peeling weight.
\end{proof}
\begin{lemma}\label{lemma:opt}
If $\exists u\in S$, such that $w_{u}(S) < g(S^*)$, then $S\not = S^{*}$.
\end{lemma}
\begin{proof}
We prove it in contradiction by assuming that $S = S^{*}$. By peeling $u$ from $S$, we have the following.
\begin{equation}
\footnotesize
\begin{split}
g(S^{*}\setminus \{u\}) & = \frac{f(S^{*}) - w_{u}(S^{*})}{|S^{*}|-1} > \frac{f(S^{*}) - g(S)}{|S^{*}|-1} \\
& = \frac{f(S^{*}) - g(S^*)}{|S^{*}|-1} = \frac{f(S^{*}) - \frac{f(S^{*})}{|S^{*}|}}{|S^{*}|-1} = g(S^*)
\end{split}
\end{equation}
A better solution can be obtained by peeling $u_i$ from $S^*$. This contradicts the notion that $S^*$ is the optimal solution. Hence, $S_i\not = S^{*}$.
\end{proof}
\begin{manuallemma}{\ref{lemma:optimalset}}
Given an edge $e = (u_i,u_j)$, if $e$ is a benign edge, after the insertion of $e$, $u_i\not \in S^{*}$ and $u_j\not \in S^{*}$.
\end{manuallemma}
\begin{proof}
We prove this lemma in contradiction by assuming that $u_i\in S^{*}$. $w_{u_i}(S^*) \leq w_{u_i}(S_0) + c_{ij} < g(S^P) \leq g(S^*)$. We have $S^*\not = S^*$ due to Lemma~\ref{lemma:opt}. We can conclude that $u_i\not\in S^*$. Similarly, $u_j\not \in S^*$.
\end{proof}
\begin{lemma}\label{lemma:opt2}
If $\exists u\in S_i$, $w_{u}(S_i) < g(S_i)$, then $S_i\not = S^{P}$.
\end{lemma}
\begin{proof}
We prove this in contradiction by assuming that $S_i= S^P$. Suppose that $u_i$ is peeled from $S_i$. Hence, $w_{u_i}(S^P) \leq w_{u}(S^P)$ due to the peeling definition. The proof can be obtained as follows:
\begin{equation}
\footnotesize
\begin{split}
g(S^P \setminus \{u_i\}) & = \frac{f(S^{P}) - w_{u_i}(S^{P})}{|S^{P}|-1} > \frac{f(S^P) - w_{u}(S^P)}{|S^P|-1} > g(S^P)
\end{split}
\end{equation}
This contradicts the fact that $S^P$ has the highest density. We can conclude that $S_i \not = S^{P}$.
\end{proof}
\begin{manuallemma}{\ref{lemma:benign}}
Given a benign edge $e = (u_i,u_j)$ insertion, at least one of the following two conditions is established: 1) $u_i\not \in S^{P'}$ and $u_j\not \in S^{P'}$; and 2) $g(S^{P'}) < g(S^P)$.
\end{manuallemma}
\begin{proof}
Without loss of generality, we assume $i\leq j$. We prove this in contradiction by assuming $g(S^{P'}) \geq g(S^P)$ and $u_i\in S^{P'}$ or $u_j\in S^{P'}$ after inserting the edge $e$.
Due to Lemma~\ref{lemma:subset} and $S^{P'} \subseteq S_0$, we have
\begin{equation}\label{eq:subset}
w_{u_i}(S^{P'}) \leq w_{u_i}(S_0) < w_{u_i}(S_0) + c_{ij} < g(S^P) < g(S^{P'})
\end{equation}
Therefore, $S^{P'}$ is not the result returned by peeling algorithms due to Lemma~\ref{lemma:opt2} which contradicts that $S^{P'}$ maximizes $g$.
\end{proof}
\section{More case studies}\label{sec:casestudy}
\begin{figure}[tb]
\includegraphics[width=\linewidth]{figures/caseAppendix.eps}
\caption{Case study: three fraud patterns}\label{fig:casestudyappendix}
\end{figure}
We next present the effectiveness of $\mathsf{Spade}${} in discovering meaningful fraud through case studies in the datasets of $\mathsf{Grab}$. There are three popular fraud patterns as shown in Figure~\ref{fig:casestudyappendix}. First, \textit{customer-merchant collusion} is the customer and the merchant performing fictitious transactions to use the opportunity of promotion activities to earn the bonus (Figure~\ref{fig:casestudyappendix}(a)). Second, there is a group of users who take advantage of promotions or merchant bugs, called \textit{deal-hunter} (Figure~\ref{fig:casestudyappendix}(b)). Third, some merchants recruit fraudsters to create false prosperity by performing fictitious transactions, called \textit{click-farming} (Figure~\ref{fig:casestudyappendix}(c)). All three cases form a dense subgraph in a short period of time.
\etitle{Customer-merchant collusion.} We detail the customer-mercant collusion in Figure~\ref{fig:casestudyappendix}(d). $\mathsf{IncDG}${} and $\mathsf{DG}$ start both at $T_0$. Under the semantic of $\mathsf{DG}$, the user becomes a fraudster at $T_1$ (one second after $T_0$). $\mathsf{IncDG}${} spots the fraudster at $T_1$ with negligible delay. However, $\mathsf{DG}$ cannot detect this fraud at $T_1$, as it is still evaluating the graph snapshot at $T_0$. By $\mathsf{DG}$, this fraudster will be detected after the second round detection of $\mathsf{DG}$ at $T_2$ (about 60 seconds after $T_0$). During the time period $[T_1,T_2]$, there are $720$ potential fraudulent transactions generated.
\etitle{Deal-hunter.} We investigate the details of customer-merchant collusion in Figure~\ref{fig:casestudyappendix}(e). $\mathsf{IncDW}${} and $\mathsf{DW}$ start both at $T_0$. Under the semantic of $\mathsf{DW}$, the user becomes a fraudster at $T_1$ ($0.7$ second after $T_0$). $\mathsf{IncDW}${} identifies the fraudster at $T_1$ with negligible delay. However, $\mathsf{DW}$ cannot detect this fraud at $T_1$, as it is still evaluating the graph snapshot at $T_0$. By $\mathsf{DW}$, this fraudster will be detected after the second round detection of $\mathsf{DW}$ at $T_2$ (about 60 seconds after $T_0$). During the time period $[T_1,T_2]$, there are $71$ potential fraudulent transactions generated.
\etitle{Click-farming.} Last but not least, we present the details of click-farming in Figure~\ref{fig:casestudyappendix}(f). $\mathsf{IncFD}${} and $\mathsf{FD}$ start both at $T_0$. Under the semantic of $\mathsf{FD}$, the group of users becomes fraudsters at $T_1$ ($1.6$ second after $T_0$). $\mathsf{IncFD}${} spots the fraudsters at $T_1$ with negligible delay. However, $\mathsf{FD}$ cannot detect this fraud at $T_1$, as it is still evaluating the graph snapshot at $T_0$. By $\mathsf{FD}$, these fraudsters will be detected after the second round detection of $\mathsf{FD}$ at $T_2$ (about 60 seconds after $T_0$). During the time period $[T_1,T_2]$, there are $1853$ potential fraudulent transactions generated.
\begin{figure}[tb]
\includegraphics[width=0.65\linewidth]{figures/dense.eps}
\caption{Multiple fraud instances}\label{fig:dense}
\end{figure}
\begin{figure*}[tb]
\includegraphics[width=1\linewidth]{figures/casestudy_normalize.eps}
\caption{\jiaxin{$\mathsf{Spade}${} spots and enumerates the new fraudsters. The appearances of dense subgraphs indicates various types frauds including customer-merchant collusion, deal-hunter and click-farming. We show that fraudulent instances are identified in a week. Each bar represents the number of fraudulent instances are detected in the corresponding timespan. The numbers are normalized to the number of fraudulent instances during the first timespan.}}\label{fig:spot}
\end{figure*}
\noindent\jiaxin{Consider a dense subgraph $G$, it could consists of multiple fraud instances as shown in Figure~\ref{fig:dense}. $G$ consists of $G_{s_1}$, $G_{s_2}$ and $G_{s_3}$ and all of their densities are equal to $3$. Therefore, all will be returned, since they commonly form a dense subgraph $G$. We enumerate these instances once new fraudsters are identified.}
\noindent\jiaxin{\stitle{Fraud enumeration.} Figure~\ref{fig:spot} depicts the new fraudsters identified by $\mathsf{Spade}${} in $28$ timespans. Once new fraudsters are detected, $\mathsf{Spade}${} enumerates them and reports them to the moderators. In Figure~\ref{fig:spot}, each bar represents the number of fraudulent instances are detected in the corresponding timespan. We investigated the detected fraudsters and found that most of their transactions corresponded to actual fraud, including customer-merchant collusion, deal-hunter and click-farming.}
\eat{, $\mathsf{M}70980$ is highly connected to several fraudsters, such as $\mathsf{U}30592$, $\mathsf{U}7036$, $\mathsf{U}90618$, etc. With $\mathsf{Spade}${}, $\mathsf{IncFD}${} detects $\mathsf{M}70980$ in the $46$th transaction, while $\mathsf{FD}$ detects him/her in the $1899$th transaction.}
\section{Future extensions}\label{sec:extension}
We discuss a few possible extensions of our current system, including edge deletion, enumeration and fraud detection within a given period of time.
\subsection{Peeling sequence reordering with edge deletion}\label{sec:extension:deletion}
The company will delete some outdated transactions since they are not of much value for fraud detection in some operational demands, \emph{e.g.,}\xspace some transactions generated several years ago. Given such an operational demand, we consider the extension of incremental maintenance with edge deletion of $(u_i,u_j)$ (without loss of generality, we assume $i < j$). A straightforward solution is also to reorder the peeling sequence. We summarize the key steps as follows and leave the extension details of $\mathsf{Spade}${} in future work.
\stitle{Incremental algorithm ($\mathcal{T}^d$).} $\mathcal{T}^d${} initializes an empty vector for the updated peeling sequence $O'$. $\mathsf{Spade}${} maintains a pending queue $T$ to store the vertices pending reordering. We iteratively compare 1) the head of $T$, denoted by $u_{\min}$ and 2) the vertex $u_k$ in the peeling sequence $O$, where $k < i$. The corresponding peeling weights are denoted by $\Delta_{\min}$ and $\Delta_k$. We consider the following two cases.
\stitle{Case 1.} If the peeling weight $w_{u_k}(S_0) > \Delta_{\min}$, we insert $u_k$ into $T$ and update the priorities in $T$ for the neighbors of $u_k$, $N(u_{\max})$, $k=k-1$.
\stitle{Case 2.} If the peeling weight $w_{u_k}(S_0) \leq \Delta_{\min}$, we append $O[1:k]$ to $O'[1:k]$.
\begin{figure*}[tb]
\includegraphics[width=0.85\linewidth]{figures/reordered-deleted.eps}
\caption{Peeling sequence reordering with edge deletion (A running example)}\label{fig:run:deleted}
\end{figure*}
While $T$ is non-empty, we iteratively compare 1) the head of $T$ and 2) the vertex $u_k$ in the peeling sequence $O$, where $k \geq i + 1$. The incremental maintenance is identical to that of edge insertion in Section~\ref{sec:edgebyedge}. Specifically, we consider the following three cases:
\stitle{Case 1.} If $\Delta_{\min} < \Delta_k $, we pop the $u_{\min}$ from $T$ and insert it to $O'$. Then we update the priorities in $T$ for the neighbors of $u_{\min}$, $N(u_{\min})$.
\stitle{Case 2.} If $\Delta_{\min} \geq \Delta_{k}$ and $\exists u_{T}\in T, (u_{T},u_{k})\in E$ or $(u_{k},u_{T})\in E$, we insert $u_k$ into $T$. The peeling weight is $w_{u_k}(T\cup S_k)$ $ = \Delta_k $ $ + $ $\sum_{(u_T\in T) \bigwedge ((u_T,u_k)\in E)}$ $ c_{Tk} + $ $\sum_{(u_T\in T) \bigwedge ((u_k,u_T)\in E)} c_{kT}$, $k=k+1$.
\stitle{Case 3.} If $\Delta_{\min} \geq \Delta_{k}$ and $\forall u_{T}\in T, (u_{T},u_{k})\not\in E$ and $(u_{k},u_{T})\not\in E$, we insert $u_{k}$ to $O'$, $k=k+1$.
\setlist{nolistsep}
\eat{
\begin{itemize}[leftmargin=*]
\item \stitle{Case 1.} If $\Delta_{\min} < \Delta_k $, we pop the $u_{\min}$ from $T$ and insert it to $O'$. Then we update the priorities in $T$ for the neighbors of $u_{\min}$, $N(u_{\min})$.
\item \stitle{Case 2.} If $\Delta_{\min} \geq \Delta_{k}$ and $\exists u_{T}\in T, (u_{T},u_{k})\in E$ or $(u_{k},u_{T})\in E$, we insert $u_k$ into $T$. The peeling weight is $w_{u_k}(T\cup S_k)$ $ = \Delta_k $ $ + $ $\sum_{(u_T\in T) \bigwedge ((u_T,u_k)\in E)}$ $ c_{Tk} + $ $\sum_{(u_T\in T) \bigwedge ((u_k,u_T)\in E)} c_{kT}$, $k=k+1$.
\item \stitle{Case 3.} If $\Delta_{\min} \geq \Delta_{k}$ and $\forall u_{T}\in T, (u_{T},u_{k})\not\in E$ and $(u_{k},u_{T})\not\in E$, we insert $u_{k}$ to $O'$, $k=k+1$.
\end{itemize}
}
We repeat the above iteration until $T$ is empty.
\begin{example}
Consider the graph $G$ in Figure~\ref{fig:run:deleted} and its peeling sequence $O = [u_3, u_2, u_1, u_4, u_5]$. Suppose that an outdated edge $(u_1,u_5)$ is deleted from $G$ as shown in the LHS of Figure~\ref{fig:run:deleted}. The reordering procedure is presented in the RHS of Figure~\ref{fig:run:deleted}. $u_1$ is pushed to the pending queue $T$. Since the peeling weights $w_{u_2}(S_0)$ and $w_{u_3}(S_0)$ are larger than the peeling weight of $u_1$. $u_2$ and $u_3$ are inserted into $T$. Since the peeling weight of $u_1$ is less than that of $u_4$, it will be appended to $O'$. Similarly $u_3$ and $u_2$ are appended to $O'$ accordingly. Once $T$ is empty, the rest of the vertices, $u_4$ and $u_5$, in $O$ are appended to $O'$ directly. Therefore, the reordered peeling sequence is $O'=[u_1,u_3,u_2,u_4,u_5]$.
\end{example}
\subsection{Dense subgraph enumeration}
In case of the enumeration of dense subgraphs due to some operational demands, we consider both static graphs and dynamic graphs.
\stitle{Static graphs.} Given a graph $G=(V,E)$, peeling algorithm $Q$ returns $S^P$. To enumerate dense subgraphs, we can perform the peeling algorithm $Q$ by removing $S^P$ from $G$, denoted by $G'=(V', E')$. Specifically, $V' = V\setminus S^P$ and $E' = E\setminus E^P$, where $\forall (u_i,u_j) \in E^P, u_i\in S^P$ or $u_j\in S^P$. Therefore, ${S^P}'$ will be returned as the second densest subgraph. We can perform the peeling algorithm $Q$ recursively to enumerate all dense subgraphs.
It is remarkable that we do not have to compute ${S^P}'$ from scratch. Instead, we can perform the incremental maintenance of edge deletion as introduced in Section~\ref{sec:extension:deletion}.
\stitle{Dynamic graphs.} Given a graph $G$ and graph updates $\Delta G = (\Delta V, \Delta E)$, a straightforward solution is to reorder the peeling sequence by Algorithm~\ref{algo:batch} first. For the enumeration, we can think of this dynamic graph $G \oplus \Delta G$ as a static graph.
\subsection{Fraud detection during some time period}
Given a graph $G=(V,E)$ generated during a timespan $[\tau_s, \tau_e]$ ($\tau_s < \tau_e$) and the peeling sequence $O = Q(G)$. Taking a new graph $G'=(V',E')$ generated during a timespan $[\tau_{s'},\tau_{e'}]$, we would like to identify the peeling sequence on $G'$, \emph{i.e.,}\xspace $O' = Q(G')$. To simply our discussion, we denote a set of edges generated during timespan $[\tau_s, \tau_e]$ by $E_{[s,e]}$
\stitle{Case 1.} If $\tau_{e'} < \tau_s$ or $\tau_e < \tau_{s'}$, $G$ and $G'$ do not overlap. Therefore, we directly apply the peeling algorithm $Q$ on $G'$.
\stitle{Case 2.} If $\tau_{s'} < \tau_s$ and $\tau_e < \tau_{e'}$, we perform Algorithm~\ref{algo:batch} by inserting two sets of edges, $E_{[s',s]}$ and $E_{[e,e']}$ to $G$. Then we can identify the peeling sequence $O'$ on $G'$.
\stitle{Case 3.} If $\tau_s < \tau_{s'}$ and $\tau_{e'} < \tau_e$, we perform incremental maintenance in Section~\ref{sec:extension:deletion} by deleting two sets of edges, $E_{[s,s']}$ and $E_{[e',e]}$ from $G$. Then we can identify the peeling sequence $O'$ on $G'$.
\stitle{Case 4.} If $\tau_{s'} < \tau_{s} < \tau_{e'} < \tau_e$, we perform Algorithm~\ref{algo:batch} by inserting a set of edges, $E_{[s',s]}$ to $G$ and perform incremental maintenance in Section~\ref{sec:extension:deletion} by deleting a set of edges $E_{[e',e]}$ from $G$.
\stitle{Case 5.} If $\tau_{s} < \tau_{s'} < \tau_{e} < \tau_{e'}$, we perform Algorithm~\ref{algo:batch} by inserting a set of edges, $E_{[e,e']}$ to $G$ and perform incremental maintenance in Section~\ref{sec:extension:deletion} by deleting a set of edges $E_{[s,s']}$ from $G$.
\begin{figure}[tb]
\includegraphics[width=0.95\linewidth]{figures/timeperiod.eps}
\caption{Fraud detection during some time period}\label{fig:timeperiod}
\end{figure}
\section{Accuracy guarantee of Algorithm~\ref{algo:batch}}\label{sec:correctness}
\stitle{Correctness and accuracy guarantee.} In \textbf{Case 1}, if $\Delta_k > \Delta_{\min}$, $u_{\min}$ is chosen to insert to $O'$ since it has the smallest peeling weight due to Lemma~\ref{lemma:peel}. In \textbf{Case 2(b)}, $\Delta_k$ is the smallest peeling weight and $u_k$ is chosen to insert to $O'$. The peeling sequence is identical to that of $G\oplus \Delta G$, since in each iteration the vertex with the smallest peeling weight is chosen. The accuracy of the worst-case is preserved due to Lemma~\ref{lemma:2ppr}.
\section{Properties of density metrics}\label{sec:axioms}
\newtheorem{axiom}{Axiom}
\stitle{Density metrics $g$.} We adopt the class of metrics $g$ in previous studies~\cite{hooi2016fraudar,gudapati2021search,charikar2000greedy}, $g(S) = \frac{f(S)}{|S|}$, where $f$ is the total weight of $G[S]$, \emph{i.e.,}\xspace the sum of the weight of $S$ and $E[S]$:
\begin{equation}\label{eq:density}
f(S)=\sum_{u_i\in S} a_i + \sum_{u_i,u_j\in S \bigwedge (u_i,u_j)\in E} c_{ij}
\end{equation}
We use $f_E(S)$ to denote the total suspiciousness of the edges $E[S]$ and $f_V(S)$ to denote the total suspiciousness of $S$, \emph{i.e.,}\xspace
\begin{equation}
f_V(S)= \sum_{u_i\in S} a_i
\end{equation}
and
\begin{equation}
f_E(S)= \sum_{u_i,u_j\in S \bigwedge (u_i,u_j)\in E} c_{ij}
\end{equation}
The density metric defined in Equation~\ref{eq:density} satisfies Axiom~\ref{ax:first}-\ref{ax:fourth}. We adapted these basic properties from \cite{jiang2015general}.
\begin{axiom}
\label{ax:first}
\stitle{[Vertex suspiciousness]} If 1) $|S| = |S'|$, 2) $f_E(S) = f_E(S')$, and 3) $f_V(S) > f_V(S')$, then $g(S) > g(S')$.
\end{axiom}
\begin{proof}
\begin{equation}
g(S) = \frac{f_V(S) + f_E(S)}{|S|} > \frac{f_V(S') + f_E(S')}{|S'|} = g(S')
\end{equation}
\end{proof}
With slight abuse of definition, we use $g(S(V,E))$ to denote the total suspiciousness of $S$ on the graph $G=(V,E)$.
\begin{axiom}
\label{ax:second}
\stitle{[Edge suspiciousness]} If $e=(u_i,u_j)\not\in E$, then $g(S(V,E\cup \{e\})) > g(S(V,E))$.
\end{axiom}
\begin{proof}
\begin{equation}
g(S(V,E\cup \{e\})) = \frac{f_V(S) + f_E(S) + c_{ij}}{|S|} > \frac{f_V(S) + f_E(S)}{|S|} = g(S)
\end{equation}
\end{proof}
\begin{axiom}
\label{ax:fourth}
\stitle{[Concentration]} If $|S| < |S'|$ and $f(S) = f(S')$, then $g(S)>g(S')$.
\end{axiom}
\begin{proof}
\begin{equation}
g(S) = \frac{f(S)}{|S|} > \frac{f(S')}{|S'|} = g(S')
\end{equation}
\end{proof}
\section{Instances of $\mathsf{Spade}${}}\label{sec:instances}
We show that the popular peeling algorithms can be easily implemented and supported by $\mathsf{Spade}${}, \emph{e.g.,}\xspace $\mathsf{DG}$~\cite{charikar2000greedy}, $\mathsf{DW}{}$~\cite{gudapati2021search} and $\mathsf{FD}{}$~\cite{hooi2016fraudar}.
\etitle{Instance 1. Dense subgraphs ($\mathsf{DG}{}$)~\cite{charikar2000greedy}.} $\mathsf{DG}{}$ is designed to quantify the connectivity of substructures. It is widely used to detect fake comments~\cite{kumar2018community} and fraudulent activities~\cite{ban2018badlink} on social graphs. Let $S\subseteq V$. The density metric of $\mathsf{DG}{}$ is defined by $g(S) = \frac{|E[S]|}{|S|}$. To implement $\mathsf{DG}$ on $\mathsf{Spade}${}, developers only need to design and plug in the suspiciousness function $\mathsf{esusp}$ by calling $\mathsf{ESusp}$. Specifically, $\mathsf{esusp}$ is a constant function for edges, \emph{i.e.,}\xspace $\mathsf{esusp}(u_i,u_j) = 1$.
\etitle{Instance 2. Dense weighted subgraphs ($\mathsf{DW}$)~\cite{gudapati2021search}.} On transaction graphs, there are weights on the edges in usual, such as the transaction amount. The density metric of $\mathsf{DW}{}$ is defined by $g(S) = \frac{\sum_{(u_i,u_j)\in E[S]}c_{ij}}{|S|}$, where $c_{ij}$ is the weight of the edge $(u_i,u_j)\in E$. To implement $\mathsf{DW}{}$, users only need to plug in the suspiciousness function $\mathsf{esusp}$, \emph{i.e.,}\xspace given an edge, $\mathsf{esusp}(u_i,u_j) = c_{ij}$.
\etitle{Instance 3. Fraudar ($\mathsf{FD}{}$)~\cite{hooi2016fraudar}.} To resist the camouflage of fraudsters, Hooi et al. ~\cite{hooi2016fraudar} proposed $\mathsf{FD}{}$ to weight edges and set the prior suspiciousness of each vertex with side information. Let $S\subseteq V$. The density metric of $\mathsf{FD}$ is defined as follows:
\begin{equation}
g(S) = \frac{f(S)}{|S|} = \frac{\sum_{u_i\in S} a_i + \sum_{u_i,u_j\in S \bigwedge (u_i,u_j)\in E} c_{i,j}}{|S|}
\end{equation}
\begin{center}
\scriptsize
\lstinputlisting[caption=Implementation of $\mathsf{FD}{}$ on $\mathsf{Spade}$, label={lst:listing-fd}, language=C++]{fd.cpp}
\end{center}
To implement $\mathsf{FD}$ on $\mathsf{Spade}${}, users only need to plug in the suspiciousness function $\mathsf{vsusp}$ for the vertices by calling $\mathsf{VSusp}$ and the suspiciousness function $\mathsf{esusp}$ for the edges by calling $\mathsf{ESusp}$. Specifically, 1) $\mathsf{vsusp}$ is a constant function, \emph{i.e.,}\xspace given a vertex $u$, $\mathsf{vsusp}(u) = a_i$ and 2) $\mathsf{esusp}$ is a logarithmic function such that given an edge $(u_i,u_j)$, $\mathsf{esusp}(u_i,u_j) = \frac{1}{\log (x+c)}$, where $x$ is the degree of the object vertex between $u_i$ and $u_j$, and $c$ is a small positive constant ~\cite{hooi2016fraudar}.
Developers can easily implement customized peeling algorithms with $\mathsf{Spade}${}, which significantly reduces the engineering effort. For example, users write only about $20$ lines of code (compared to about $100$ lines in the original $\mathsf{FD}$~\cite{hooi2016fraudar}) to implement $\mathsf{FD}$ as shown in List~\ref{lst:listing-fd}. $\mathsf{Spade}${} enables $\mathsf{FD}{}$ to be incrmental by nature. Similar observations are made in $\mathsf{DG}$ and $\mathsf{DW}$.
\section{Background}
\label{sec-pre}
\vspace{-0.3ex}
\begin{table}[tb!]
\caption{Representative random walk}
\label{tab:mf}
\begin{scriptsize}
\begin{center}
\vspace{-5mm}
\setlength{\tabcolsep}{0.5em}
\begin{tabular}{|c|c|c|c|c|}
\hline
\multirow{2}{*}{} & \multirow{2}{*}{xxxx} & \multirow{2}{*}{xxx} & \multicolumn{2}{c|}{xxx} \\ \cline{4-5}
& & & Exact index & Approximate index \\ \hline
XXX & 11 & 12 \cite{} & 13\cite{} & 14\cite{}\\ \hline
XXX & \cite{} & \cite{} & \cite{} & $-$ \\ \hline
XXX & \cite{} & \cite{} & \cite{} & \cite{} \\ \hline
\end{tabular}
\end{center}
\end{scriptsize}
\end{table}
This section presents the background for the technical discussions and then the problem statement. Some frequently used notations are summarized in Tab~\ref{tab-notations}.
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 6,270
|
<?php
namespace Scalr\Upgrade\Updates;
use Scalr\Upgrade\SequenceInterface;
use Scalr\Upgrade\AbstractUpdate;
class Update20140204143602 extends AbstractUpdate implements SequenceInterface
{
protected $uuid = '698c5619-cea3-45fd-811f-2468a00aa1c0';
protected $depends = array('0f65a2c9-7592-4517-86d8-6789405ffaa2');
protected $description = 'Refactor scripts table. Add new fields env_id, created_by, changed ... Add foreign key.';
protected $accountsCache = array();
protected $ignoreChanges = true;
/**
* {@inheritdoc}
* @see Scalr\Upgrade.SequenceInterface::getNumberStages()
*/
public function getNumberStages()
{
return 5;
}
protected function isApplied1($stage)
{
return !$this->hasTableColumn('scripts', 'origin');
}
protected function validateBefore1($stage)
{
return $this->hasTable('scripts');
}
protected function run1($stage)
{
$this->db->Execute('ALTER TABLE scripts DROP origin');
}
protected function isApplied2($stage)
{
return !$this->hasTableColumn('scripts', 'approval_state');
}
protected function validateBefore2($stage)
{
return $this->hasTable('scripts');
}
protected function run2($stage)
{
$this->db->Execute('ALTER TABLE scripts DROP approval_state');
}
protected function isApplied3($stage)
{
return !$this->hasTable('script_revisions') || !$this->hasTableColumn('script_revisions', 'approval_state');
}
protected function validateBefore3($stage)
{
return $this->hasTable('script_revisions');
}
protected function run3($stage)
{
$this->db->Execute('ALTER TABLE script_revisions DROP approval_state');
}
protected function isApplied4($stage)
{
return $this->hasTableColumn('scripts', 'created_by_id');
}
protected function validateBefore4($stage)
{
return $this->hasTable('scripts');
}
protected function getUserInfoByAccountId($accountId)
{
if (! isset($this->accountsCache[$accountId])) {
if ($accountId) {
try {
$acc = new \Scalr_Account();
$acc->loadById($accountId);
$this->accountsCache[$accountId] = array(
'id' => $acc->getOwner()->id,
'email' => $acc->getOwner()->getEmail()
);
} catch (\Exception $e) {
$this->console->error($e->getMessage());
return array('id' => 0, 'email' => '');
}
} else {
$user = new \Scalr_Account_User();
$user->loadByEmail('admin', 0);
$this->accountsCache[$accountId] = array(
'id' => $user->id,
'email' => $user->getEmail()
);
}
}
return $this->accountsCache[$accountId];
}
protected function run4($stage)
{
$this->console->out('Creating fields');
$this->db->Execute('ALTER TABLE scripts ADD `dtchanged` datetime DEFAULT NULL AFTER dtadded, ADD `created_by_id` int(11) DEFAULT NULL, ADD `created_by_email` varchar(250) DEFAULT NULL');
$this->db->Execute('ALTER TABLE script_revisions ADD `changed_by_id` int(11) DEFAULT NULL, ADD `changed_by_email` varchar(250) DEFAULT NULL');
$this->db->Execute('UPDATE scripts SET `dtchanged` = `dtadded`');
$this->console->out('Look for old scripts');
$ids = $this->db->GetCol('SELECT scripts.id FROM scripts LEFT JOIN clients ON scripts.clientid = clients.id WHERE clientid != 0 AND ISNULL(clients.id)');
if (count($ids)) {
$this->db->Execute('DELETE FROM scripts WHERE id IN (' . implode(',', $ids) . ')');
$this->console->out('Clean ' . count($ids) . ' old scripts');
}
$ids = $this->db->GetCol('SELECT script_revisions.id FROM script_revisions LEFT JOIN scripts ON scripts.id = script_revisions.scriptid WHERE ISNULL(scripts.id)');
if (count($ids)) {
$this->db->Execute('DELETE FROM script_revisions WHERE id IN (' . implode(',', $ids) . ')');
$this->console->out('Clean ' . count($ids) . ' old script revisions');
}
$this->console->out('Add foreign key for script_revisions');
$this->db->Execute('ALTER TABLE `script_revisions` ADD CONSTRAINT `fk_script_revisions_scripts_id` FOREIGN KEY (`scriptid`) REFERENCES `scripts` (`id`) ON DELETE CASCADE');
$this->console->out('Adding creator info');
$scripts = $this->db->Execute('SELECT * FROM scripts');
while ($script = $scripts->FetchRow()) {
$info = $this->getUserInfoByAccountId($script['clientid']);
$dtChanged = $this->db->GetOne('SELECT MAX(dtcreated) FROM script_revisions WHERE scriptid = ?', array($script['id']));
$this->db->Execute('UPDATE scripts SET created_by_id = ?, created_by_email = ?, dtchanged = ? WHERE id = ?', array($info['id'], $info['email'], $dtChanged, $script['id']));
$this->db->Execute('UPDATE script_revisions SET changed_by_id = ?, changed_by_email = ? WHERE scriptid = ?', array($info['id'], $info['email'], $script['id']));
}
}
protected function isApplied5($stage)
{
return $this->hasTableColumn('scripts', 'env_id');
}
protected function validateBefore5($stage)
{
return $this->hasTable('scripts');
}
protected function run5($stage)
{
$this->db->Execute("ALTER TABLE scripts ADD `env_id` int(11) DEFAULT '0' AFTER clientid, ADD INDEX `clientid` (`clientid`), ADD INDEX `env_id` (`env_id`)");
}
}
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 7,459
|
\section{INTRODUCTION}
Discovery of the top quark -- one of the basic components of the Standard
Model -- is one of the most important goals of present and future
high-energy colliders. At present, indirect evidence from electroweak
radiative corrections suggests a top quark mass between 100 and 200 GeV
(see for example reference \cite{LEPTOP}), and null results from searches
at the Fermilab $p \bar p $ collider yield a $95\%$~c.l. lower limit of
108~GeV and 103~GeV from the CDF \cite{CDFTOP} and D0 \cite{D0TOP}
collaborations, respectively. Optimistically, the top quark will be
discovered at the Fermilab $p \bar p $ collider in the next few years.
The two most important properties of the top quark, which can be measured
once its existence is established, are the mass $m_t$ and the decay width
$\Gamma_t$. The first of these is a fundamental parameter of the theory,
while the second provides an opportunity to check the existence of any
non-Standard Model decay channels. However, obtaining precise
measurements of these parameters at a hadron collider is a far from easy
task. In particular, a detailed knowledge of the structure of the final
state is necessary. For example, gluon radiation from the initial state,
from the produced top quarks, and from the top quark decay products can
influence the reconstruction of the top mass from its decay products. Soft
gluon radiation, in particular the interference between radiation before
and after top decay, also depends sensitively on the decay width
\cite{KOS,JIKIA}.
In this paper we study the \lq antenna pattern' of soft gluon radiation in
$t \bar t$ production in high energy hadron-hadron collisions. In
particular, we are interested in (a) the process dependence ($q \bar q \to
t \bar t$ {\it vs.} $ gg \to t \bar t$ ) of this radiation and (b) the
effect of the top quark instability on the radiation pattern. The former
depends on the colour topology of the different processes, while the latter
induces dependence on $\Gamma_t$ and on the orientation of the top decay
products. Our study builds on earlier work. In reference \cite{KOS}, for
example, the colour-singlet production process $e^+e^-\to t\bar t \to b W^+
\bar b W^-$ was analyzed in detail, and a gauge-invariant approach for
identifying and calculating the various production and decay contributions
to the radiation pattern was presented. It is the extension of these ideas
to the more complicated processes $q \bar q , gg\to t\bar t \to b W^+ \bar
b W^-$ which constitutes the main goal of the present study. The radiation
pattern for {\it stable} top production $q \bar q , gg\to t\bar t$ has been
analyzed in detail in reference \cite{KELLIS,MW} (see also \cite{BOOK}).
Again, our purpose here is to extend this analysis to the experimentally
more relevant $b W^+ \bar b W^-$ final state.
Note that in our analysis the soft gluons are sufficiently energetic
so that a
perturbative treatment is valid.
Non-perturbative effects, including possible long distance
interactions
with the spectator partons, have been discussed in Ref.~\cite{ORR}.
Our aim, then, is to give a complete and systematic account of soft gluon
radiation in hadronic $t \bar t$ production, accounting for colour topology
of the different processes, decay product kinematics, and finite top width
effects. In the next section, we describe a method for writing down the
antenna pattern for {\it any} $\;t \bar t$ production process of the form
$A B \to t\bar t \to b W^+ \bar b W^-$. Although our main interest here is
in the strong interaction processes $q \bar q, gg \to t \bar t$, we also
present results for $q \bar q \to Z^* \to t \bar t$ and $gg \to H \to t
\bar t$. These processes, with their unique colour structure, are useful
for comparison. In Section III we present some numerical results. In
particular, we consider final states with particular (and experimentally
typical) orientations of the final state $b$ quarks and $W$ bosons. We
study the soft gluon antenna patterns, focusing on the process and top
width dependence. Our objective is not to emulate a Monte Carlo
analysis including realistic detector acceptances, but rather to emphasize
the most important features of the soft gluon radiation accompanying $ t
\bar t $ production and decay which should be taken into account in more
realistic studies. Finally, in Section IV we summarize our main
results.
\section{FORMALISM}
In the soft gluon limit, the radiation pattern for {\it any} elementary
$2\to 2$ hard scattering process $f$ can be written as \cite{BOOK}
\begin{eqnarray}
\overline{\sum} |{\cal M}^{(f)} |^2 =
\sum_{ij} \; \widehat{ij} \; A^{(f)}_{ij} \; ,
\end{eqnarray}
where the sum $i,j$ is over the external particles.
The `antenna' $\widehat{ij}$ is defined by
\begin{eqnarray}
\widehat{ij} \; \equiv \; {p_i\cdot p_j \over p_i\cdot k \ p_j\cdot k} \; ,
\end{eqnarray}
where $p_i$ and $p_j$ are the four-momentum vectors of particles $i$ and
$j$ and $k$ is the gluon four-momentum vector. The coefficients
$A^{(f)}_{ij}$ are functions of the kinematic invariants of the $2\to 2$
process. The simplest example is the process $e^+e^- \to q \bar q (g)$
where, for massless quarks, there is only one such antenna and
$\overline{\sum} |{\cal M}|^2 \propto \widehat{q \bar q}$.
In the present context we are interested in the following $t\bar t$
production processes:
\begin{mathletters}
\begin{eqnarray}
&&e^- e^+ \to t \bar t \>, \\
&&q \bar q \to Z^* \to t \bar t \>, \\
&&gg \to H \to t \bar t \>, \\
&&q \bar q \to t \bar t \>, \\
&&gg \to t \bar t \>.
\label{EQ:TT}
\end{eqnarray}
\end{mathletters}
(Note that the soft gluon radiation pattern for the process $\gamma \gamma
\to t \bar t$ is identical to the pattern for the $e^- e^+ \to t \bar t$
process.) Labeling the initial and final state momenta by
\begin{eqnarray}
A(k_1) + B(k_2) \to t(q_1) + \bar{t}(q_2) \to
b(p_1) + W^+ + \bar{b}(p_2) + W^- \>,
\end{eqnarray}
the general form of the differential distribution for soft
gluon radiation $(k^\mu)$ is \cite{KOS}
\begin{eqnarray}
{1\over d\sigma_0}\ {d\sigma\over d\omega_g\> d\cos\theta_g \> d\phi_g}\ = \
{\alpha_s\over 4 \pi^2} \ \omega_g \ {\cal F} \; ,
\label{EQ:dN}
\end{eqnarray}
where $d\sigma_0$ is the differential cross section for the lowest order
process ({\it i.e.}, with no gluon radiation), $\omega_g$ is the energy of
the soft gluon, and $\alpha_s$ is the strong coupling. For the case of
{\it stable} top quarks and massless initial state particles, the
distribution function ${\cal F}$ has the general form
\begin{eqnarray}
{\cal F}_0 = c_1 \widehat{k_1 k_2} + c_2 \widehat{k_1 q_1}
+ c_3 \widehat{k_1 q_2} + c_4 \widehat{k_2 q_1}
+ c_5 \widehat{k_2 q_2} + c_6 \widehat{q_1 q_2} + c_7 \widehat{q_1 q_1}
+ c_8 \widehat{q_2 q_2} \>,
\label{EQ:GENERAL}
\end{eqnarray}
where the antennae are defined as before by
\begin{eqnarray}
\widehat{pq} \> \equiv \> {p\cdot q \over p\cdot k \ q\cdot k} \; .
\end{eqnarray}
The coefficients $c_i$ are given in Table~\ref{TAB:COLOUR} for the five
$t\bar t$ production processes listed in Eq.~(3). The functions $X$ and $Y$
appearing in the $gg\to t \bar t$ process are discussed later.
The general method for treating {\it unstable} heavy particles such as the
top quark has been presented in Ref.~\cite{KOS}. The top quark {\it decay}
is included by letting ${\cal F}_0 \to {\cal F}$, with ${\cal F}$ given by
Eq.~(\ref{EQ:GENERAL}) with the replacements:
\begin{eqnarray}
\widehat{k_1 k_2} &\to& \widehat{k_1 k_2} \>, \nonumber \\
\widehat{k_1 q_1} &\to& \widehat{k_1 q_1}
+ \chi_1\; [ \widehat{k_1 p_1} -\widehat{k_1 q_1} ] \>, \nonumber \\
\widehat{k_1 q_2} &\to& \widehat{k_1 q_2}
+ \chi_2\; [ \widehat{k_1 p_2} -\widehat{k_1 q_2} ] \>, \nonumber \\
\widehat{k_2 q_1} &\to& \widehat{k_2 q_1}
+ \chi_1\; [ \widehat{k_2 p_1} -\widehat{k_2 q_1} ] \>, \nonumber \\
\widehat{k_2 q_2} &\to& \widehat{k_2 q_2}
+ \chi_2\; [ \widehat{k_2 p_2} -\widehat{k_2 q_2} ] \>,
\label{EQ:REPS} \\
\widehat{q_1 q_2} &\to& \widehat{q_1 q_2}
+ \chi_2\; [ \widehat{q_1 p_2} -\widehat{q_1 q_2} ]
+ \chi_1 \; [ \widehat{q_2 p_1} -\widehat{q_1 q_2} ] \nonumber \\
& & \ + \ \chi_{12} \; [ \widehat{p_1 p_2} - \widehat{q_1 p_2}
- \widehat{q_2 p_1} + \widehat{q_1 q_2} ] \>,
\nonumber \\
\widehat{q_1 q_1} & \to & 2 \widehat{q_1 q_1} + \widehat{p_1 p_1}
-2\widehat{q_1 p_1} + 2 \chi_1 \; [ \widehat{q_1 p_1}
- \widehat{q_1 q_1} ] \>, \nonumber \\
\widehat{q_2 q_2} &\to& 2 \widehat{q_2 q_2} + \widehat{p_2 p_2}
- 2\widehat{q_2 p_2}
+ 2 \chi_2\; [ \widehat{q_2 p_2} -\widehat{q_2 q_2} ] \> .
\nonumber
\end{eqnarray}
We make the following comments concerning the above results.
\begin{itemize}
\item[{(i)}] For unstable top quarks, we see that there are additional
contributions from antennae involving the daughter $b$~quarks,
corresponding to gluon emission both before {\it and} after the $t$~quarks
decay. The profile functions $\chi$, which depend on the top width
$\Gamma_t$ and determine the size of the interference effects, are given by
\cite{KOS}
\begin{eqnarray}
\chi_i & = & {m_t^2\Gamma_t^2 \over (q_i\cdot k)^2 + m_t^2 \Gamma_t^2 } \>,
\label{EQ:CHII} \\
\noalign{\vskip 5pt}
\chi_{12} & = & {m_t^2\Gamma_t^2\; (q_1\cdot k\; q_2\cdot k + m_t^2\Gamma_t^2)
\over \Bigl[ (q_1\cdot k)^2 + m_t^2 \Gamma_t^2 \Bigr]
\; \Bigl[ (q_2\cdot k)^2 + m_t^2 \Gamma_t^2 \Bigr] } \; .
\label{EQ:CHI}
\end{eqnarray}
These functions have the (formal) property that $\chi_i, \chi_{12} \to 0$
as $\Gamma_t \to 0$, and $\chi_i, \chi_{12} \to 1$
as $\Gamma_t \to \infty$. In the former limit, we have
\begin{eqnarray}
{\cal F} \to {\cal F}_0 + c_7 \bigl[ \widehat{q_1 q_1}
+ \widehat{p_1 p_1} -2\widehat{q_1 p_1} \bigr]
+ c_8 \bigr[ \widehat{q_2 q_2}+ \widehat{p_2 p_2}
- 2\widehat{q_2 p_2} \bigr] \; ,
\end{eqnarray}
which is the stable top result together with additional $\widehat{t\, b}$
and $\widehat{\bar{t}\, \bar{b}}$ antennae \cite{KOS}. In the other
extreme, $\chi_i, \chi_{12} \to 1$, the top quarks decay immediately after
production and the radiation pattern is identical to that for the process
\begin{eqnarray}
A(k_1) + B(k_2) \to b(p_1) + \bar{b}(p_2)
\end{eqnarray}
at reduced invariant squared energy $W^2 = (p_1 + p_2 )^2$ in the final
state.
\item[{(ii)}] The functions $X$ and $Y$ appearing in the coefficients
for the $gg \to t \bar t$ process are given by
\begin{eqnarray}
X & = & {N^2\over 4C_F}\; \left[ (1+2\mu)\left( {1\over U} - {1\over T}\right)
- \mu^2 \left( {1\over U^2} - {1\over T^2}\right) + 2(U-T) \right] \nonumber
\\
& & \times \; \left[ {1\over UT} - {N\over C_F} \right]^{-1}
\; \left[ T^2+U^2 + 2 \mu -{\mu^2\over UT} \right]^{-1} \; ,
\end{eqnarray}
and
\begin{eqnarray}
Y & = & {1\over 4C_F}\; \left[{1\over N^2UT} + 2 \right]
\; \left[ {1\over UT} - {N\over C_F} \right]^{-1}\; ,
\end{eqnarray}
where
\begin{eqnarray}
T= {k_1\cdot q_1 \over k_1\cdot k_2}, \qquad
U= {k_1\cdot q_2 \over k_1\cdot k_2}, \qquad
\mu= {m_t^2 \over k_1\cdot k_2} \; .
\end{eqnarray}
(The $X$ and $Y$ functions here are closely related to those given in Ellis
and Sexton \cite{KELLIS}; here we have normalized $X$ and $Y$ by dividing
them by the $gg \to t \bar t$ squared amplitude.) Figure~\ref{FIG:XYFUN}
shows the functions $X$ and $Y$ plotted versus the $t$ quark scattering
angle (in the $gg$ centre-of-mass frame) for three different beam energies.
Note that at threshold $T=U=\mu=1/2$ and
\begin{eqnarray}
X = 0,\qquad Y = {1\over 2N^2} \; {2+N^2\over 4C_F - N} =
{11 \over 42} \quad (N=3) \>.
\end{eqnarray}
The numerically small values of $Y$ [$Y/X \sim {\cal O}(1/N^2)$], together
with the fact that collinear singularities are absent from the
corresponding combination of antennae, leads to a negligible contribution
from this piece in practice \cite{KELLIS,MW}. The contributions from the
$t\bar t$ antenna are not suppressed by $1/N^2$ in processes 3a, b, and c,
where the $t\bar t$ pair is produced in a colour singlet state. In
processes 3d and e, the azimuthal asymmetry of emission off $t$-quarks is
violated even in the large $N$ limit, because of the presence of the
$\widehat{k_i q_j}$ antennae.
\item[{(iii)}] Although the bulk of the coefficients in
Table~\ref{TAB:COLOUR} are simply colour factors, independent of the
subprocess invariants, the cross section for soft gluon radiation does {\it
not} in general factorize into an eikonal factor times the lowest-order
cross section. This lack of factorization is the origin of the $X$ and $Y$
terms appearing in Table~\ref{TAB:COLOUR} for the $gg \to t \bar t$
process. The reason can be traced to the colour structure of the $2\to 2 $
process \cite{MW,BOOK}. For all but the $gg\to t \bar t$ process, the
colour flow at the amplitude level can be uniquely represented by
continuous lines (\lq strings') linking the external particles. Thus
Figs.~\ref{FIG:COLOR}(a) and (b) show the colour flow for $e^-e^+\to t \bar
t$ and $q \bar q \to t \bar t$, respectively. Note that in the leading
$1/N$ limit (the planar limit) there is a one-to-one correspondence between
the colour flow lines and the non-zero antenna coefficients. In contrast,
the $gg\to t \bar t$ process has two possible colour flows at the
amplitude level as shown in Figs.~\ref{FIG:COLOR}(c) and (d). It is the
interference between these two contributions that spoils the identification
of the colour flows in the planar limit. However, this interference is
suppressed in the large $N$ limit, where we find
\begin{eqnarray}
{\cal F} &\to&
{1\over 4}\; (N-2X)\; \left[ 2 \widehat{k_1 q_1} + 2 \widehat{k_2 q_2}
+ 2\widehat{k_1 k_2}
- \widehat{q_1 q_1} - \widehat{q_2 q_2} \right] \nonumber \\
&+&
{1\over 4}\; (N+2X)\; \left[ 2 \widehat{k_1 q_2} + 2 \widehat{k_2 q_1}
+ 2 \widehat{k_1 k_2}
- \widehat{q_1 q_1} - \widehat{q_2 q_2} \right] \; ,
\end{eqnarray}
which is the separation into two positive-definite colour structures
discussed in Ref.~\cite{MW}.
\item[{(iv)}]In the large $N$ limit, the $\widehat{tb}$ and $\widehat{\bar t
\bar b}$ antennae can interfere only in the case of the first three
processes in Eq.~(3). For processes 3d and 3e, in this limit, the decays are
uncorrelated in colour and the interference is absent.
\end{itemize}
\section{NUMERICAL RESULTS}
In the previous section we have seen how the different colour structure of
the various processes leads to different weightings of the antennae
contributions. In this section we study the implications of this for the
actual gluon distribution. Our purpose is not to give a comprehensive
treatment of all the possibilities, but rather to consider some simple
configurations which illustrate the underlying physics.
In studying the way in which the various antennae contribute, it is
instructive to consider all five processes listed in Eq.~(3). Since we
may neglect the soft gluon in the kinematics, the $t$- and $\bar
t$-momenta are back-to-back in the centre-of-mass frame of the collision.
The $b$- and $\bar b$-momenta are also taken to be back-to-back. This is
for simplicity only -- the qualitative features are unchanged as long as
the $b \bar b$ angle is not chosen particularly small.
Distributions of the soft gluon radiation in the polar and azimuthal angles
(relative to the beam direction) are presented for a soft gluon with
energy $\omega_g = 5$~GeV. Again, this value is not critical: what matters
as far as the interference contributions are concerned is the relative size
of $\omega_g$ and $\Gamma_t$. Our results should be interpreted as
referring to the distribution of a soft hadronic jet accompanying the
significantly more energetic $b W^+ \bar b W^-$ particles. The
distributions are calculated at the parton level and are plotted in the
parton subprocess centre-of-mass frame. Unless otherwise stated, we assume
a parton beam energy of $E_{\rm beam} = 2 m_t$, motivated by the fact that at
hadron colliders the average subprocess centre-of-mass energy is several
times the threshold energy for $t \bar t$ production. A realistic study of
soft gluon radiation in hadronic $t\bar t$ production would of course
require a convolution of the parton-level cross sections with parton
distribution functions. Such a convolution would smear the results
illustrated here, although one could in principle reconstruct this frame
directly if all the top quark decay products were measured.
The following short-hand notation will be used to denote the polar
($\theta_g$) and azimuthal angle ($\phi_g$) distributions:
\begin{eqnarray}
{dN \over d\cos \theta_g} &\equiv& \omega_g \, {1\over d\sigma_0} \,
{d\sigma \over d\omega_g d\cos \theta_g d\phi_g}
\Biggl|_{\phi_g = 0^{\circ} \phantom{{\rm GeV}} \atop \omega_g = 5\; {\rm GeV}}
= {\alpha_s \over 4 \pi^2} \, \omega_g^2 \, {\cal F}(\theta_g) \>, \\
\noalign{ \hbox{\rm and} }
{dN \over d\phi_g} &\equiv& \omega_g \, {1\over d\sigma_0} \,
{d\sigma \over d\omega_g d\cos \theta_g d\phi_g}
\biggl|_{\theta_g = 90^{\circ} \phantom{{\rm GeV}}
\atop \omega_g = 5\;{\rm GeV}}
= {\alpha_s \over 4 \pi^2} \, \omega_g^2 \, {\cal F}(\phi_g) \>.
\end{eqnarray}
Recall that in the soft gluon approximation, the gluon energy distribution
falls as $1/\omega_g$. Thus an extra factor of $\omega_g$ has been included
in the above definitions to make the distributions dimensionless
quantities. The numerical results presented here have been generated
using the following input parameters: $m_t = 140$~GeV, $m_b = 5$~GeV,
$M_W^{} = 80$~GeV, and $\alpha_s = 0.1$. For all the distributions, the
coordinate system is chosen such that the three-momenta of the incoming
partons are along the $\pm \hat z$ directions. Furthermore, the
three-momenta of the outgoing $t$ and $\bar t$ are chosen to be in the
$+\hat x$ and $-\hat x$ directions, respectively. For the
$dN/d\cos\theta_g$ distributions, the three-momenta of the $b$ and $\bar b$
quarks are chosen to be back-to-back in the $xz$-plane, with the $b$-quark
three-momentum vector $45^{\circ}$ away from the $t$-quark three-momentum
vector as illustrated in Fig.~\ref{FIG:XYZPLANE}(a). The soft gluon
three-momentum is also taken to be in the $xz$-plane, and thus the
three-momenta of all the partons lie in the $xz$-plane as depicted in
Fig.~\ref{FIG:XYZPLANE}(a). For the $dN/d\phi_g$ distributions, the
three-momenta of all the final state partons are taken to be in the
$xy$-plane, which is transverse to the momenta of the incoming partons; see
Fig.~\ref{FIG:XYZPLANE}(b).
We begin by presenting results for the polar angle distribution of the soft
gluon. Figure~\ref{FIG:A} shows $dN/d\cos\theta_g$ versus $\theta_g$ for
incoming partons with energy $E_{\rm beam} = 2m_t = 280$~GeV, where $m_t =
140$~GeV is the top quark mass. The Standard Model Born value $\Gamma_t =
\Gamma_{\rm sm}^{(0)} = 0.67$~GeV for $m_t=140$~GeV, has been used for the
top quark width. The soft gluon radiation patterns for the five processes
listed in Eq.~(3) are shown in the figure. The angles of the incoming and
outgoing partons are indicated at the top of the figure. The divergence
in the radiation pattern at $\theta_g = 0^\circ$ and $180^\circ$ (and
$360^\circ$) for the hadronic production processes is the initial state
collinear singularity, {\it i.e.}, $ q \to q+g$, $g \to g+g$. The strength
of the singularity simply reflects the colour charge of the incoming
particles. For example, the radiation pattern in the region $\theta_g
\approx 0^\circ$ is dominated by the antennae containing a factor of
$k_1$. If $k$ is almost parallel to $k_1$ then
\begin{eqnarray}
\widehat{k_1 a} \approx {2\over \omega_g^2}\;{1\over \theta_g^2} \>,
\label{EQ:COL}
\end{eqnarray}
independent of the other momentum ($a^\mu$) in the antenna. There are
three such terms on the right-hand-side of Eq.~(\ref{EQ:GENERAL}), and
hence
\begin{eqnarray}
{\cal F} \approx {2\over \omega_g^2}\;
{c_1+c_2+c_3\over \theta_g^2} \>.
\end{eqnarray}
From Table~\ref{TAB:COLOUR}, we see that $c_1+c_2+c_3 = 2C_F\ (2N)$ for
the $q \bar q\ (gg)$ initiated processes, respectively. Thus near $\theta_g
= 0^\circ$ and $180^\circ$ the curves for the $gg$ initiated processes are
larger than those for the $q \bar q$ initiated processes, while the
non-singular $e^-e^+$ distribution is very small.
In the same way, all of the processes exhibit a sharp dip in the radiation
pattern in the direction of the $b$ and $\bar b$ quarks when $m_b/E_b \ll 1$.
These dips are the well known heavy-quark dead cones \cite{DEAD}.
For example, close to the $b$-quark direction we have [{\it cf.},
Eq.~(\ref{EQ:COL})]
\begin{eqnarray}
\widehat{p_1 a} \approx {2\over \omega_g^2}\;{\tilde\theta_g^2\over
\bigl[ \tilde\theta_g^2 + (m_b/E_b)^2 \bigr]^2} \; ,
\label{EQ:COLB}
\end{eqnarray}
where now $\tilde\theta_g$ is the angle between the gluon and $b$-quark
directions. The angular width of these dead cones is proportional to
$m_b/E_b$. Again, it is straightforward to check that the dead-cone
behavior near the $b$-quark directions is the same for all processes. This
follows from the fact that $c_2+c_4+c_6 =-2 c_7 = 2C_F$ (see
Table~\ref{TAB:COLOUR}).
The corresponding dead cones about the $t$ and $\bar t$ quark directions
are much broader due to the larger top quark mass. The minimum of the $t
\> (\bar t)$ quark dead cone does not coincide with the $t \> (\bar t)$
quark direction, instead, the minimum is shifted to a slightly larger
angle. This is because the $\widehat{q_1 p_1}$ and $\widehat{q_2 p_2}$
terms in Eq.~(\ref{EQ:REPS}) give a contribution which is a decreasing
function of $\theta_g$ in the neighborhood around the $t \> (\bar t)$ quark
direction, whereas the contribution from the other terms has a minimum in
the $t \> (\bar t)$ quark direction. The resulting sum thus has a
minimum at a value of $\theta_g$ that is slightly larger than the
direction of the $t \> (\bar t)$ quark. The other interesting feature to
note in Figure~\ref{FIG:A} is the difference between the distributions for
the $q \bar q \to Z^* \to t \bar t $ and $q \bar q \to t \bar t $
processes. The presence of the $\widehat{k_1 q_1}$ and $\widehat{k_2 q_2}$
antenna for the latter {\it increases} the radiation between the $q$ and
$b$ quarks, and {\it decreases} that between the $b$ and $\bar q$ quarks,
relative to the former process. The effect is clearly seen in the dips on
either side of the $b$-quark dead cone in Figure~\ref{FIG:A}.
Figure~\ref{FIG:C} shows $dN/d\cos\theta_g$ versus $\theta_g$ for incoming
partons with energy $E_{\rm beam} = 2m_t = 280$~GeV as in
Fig.~~\ref{FIG:A}, but now with the top quark width taken to the formal
limit $\Gamma_t \to \infty$. In this limit, the interference factors
$\chi_1, \chi_2$, and $\chi_{12}$ in Eqs.~(\ref{EQ:CHII}) and
(\ref{EQ:CHI}) all go to 1. This limit corresponds to the top quark
decaying instantly, thus the resulting radiation pattern is equivalent to
the radiation pattern for $b \bar b$ production. In particular, the
radiation pattern is independent of the $t \> (\bar t)$ direction.
Comparing the case of $\Gamma_t = \Gamma_{\rm sm}^{(0)}$ in
Fig.~\ref{FIG:A} with the present case of $\Gamma_t = \infty$, we see that
with the exception of the $e^-e^+$ process, the radiation is again not
symmetric around the $b \> (\bar b)$ dead cone. However, the maximum now
appears on the side of the cone closest to the incoming beam direction.
For the reasons noted above, the asymmetry is particularly strong for the
$q \bar q \to t \bar t$ process. We also see that in the regions where
the $t \> (\bar t)$ dead cones were previously located ($\theta_g \approx
100^\circ$ and $280^\circ$), the $e^- e^+ \to t\bar t$ and $q\bar q \to t
\bar t$ curves have changed considerably, whereas the $gg \to H \to t\bar
t$ and $gg \to t \bar t$ curves have changed little. For these latter
processes, the radiation pattern receives a larger contribution from
radiation off the initial-state $gg$, which is of course independent of
$\Gamma_t$. On the other hand, the radiation patterns for the $e^- e^+ \to
t \bar t$ and $q\bar q \to t \bar t$ processes are more sensitive to the
radiation from the final state quarks, which is very different for the two
cases of $b\bar b$ production versus $t \bar t$ production and decay.
The variation of the radiation pattern with the top quark width is
illustrated in Fig.~\ref{FIG:E} for the process $gg \to t \bar t$. As
before, the distribution $dN/d\cos\theta_g$ is plotted versus $\theta_g$
for incoming partons with energy $E_{\rm beam} = 2m_t = 280$~GeV. Curves
are shown for four values of the top quark width: $\Gamma_t = \infty$,
5~GeV, 0.67~GeV (the Standard Model Born value), and 0. The radiation
pattern for the Standard Model Born top quark width is very close to the
radiation pattern for $\Gamma_t = 0$. Between the incoming $g(k_1)$ and the
$b$-quark, the $\widehat{k_1 p_1}$ antenna causes the radiation to increase
as $\Gamma_t$ (and hence $\chi_1$) increases. On the other side of the
$b$-quark dead-cone, the effect of emission from the top quark is seen to
decrease as $\Gamma_t$ increases. On the whole, however, the curves show
that the $gg \to t\bar t$ process is not very sensitive to the top quark
width. The $q\bar q \to t\bar t$ process on the other hand is much more
sensitive to the top quark width (see Figs.~\ref{FIG:A} and \ref{FIG:C}).
A more graphic representation of the effects described above can be
obtained by considering the radiation pattern in polar coordinates. Thus
Fig.~\ref{FIG:G} shows $dN/d\cos\theta_g$ versus $\theta_g$, with the
distance from the origin proportional to the magnitude of the
distribution. As before, all particles lie in the $xz$-plane; their
directions are indicated by arrows on the figure. The radiation pattern
for the process $gg \to t\bar t$ is shown for two values of the top quark
width: the Standard Model Born value and the $\Gamma_t \to \infty$ limit
which is equivalent to $b \bar b$ production. (Note that this is simply a
different representation of the same two curves in the previous figure.)
The collinear singularities along the $\pm \hat z$ directions are clearly
evident, as are the dead cones about the $b \> (\bar b)$ and $t \> (\bar
t)$ quark directions. Notice again that the asymmetry of the lobes about
the $b$-quark direction is different for the two cases, for the reasons
discussed earlier.
The polar angle distributions presented above emphasize the contributions
involving radiation from the incoming particles, {\it i.e.}, the antennae
involving $k_1$ and $k_2$. To focus on the radiation from the final state
particles it is useful to consider the azimuthal angle distribution of the
soft gluon radiation. The three-momenta of the final state partons are now
fixed to lie in the plane transverse to the incoming partons. In this
configuration, the effects of the initial state radiation are minimized.
We might therefore expect the $dN/d\phi_g$ distributions to be more
similar than the $dN/d\cos \theta_g$ distributions for the five processes
listed in Eq.~(3). Figure~\ref{FIG:H} shows the azimuthal distribution
of soft gluon radiation when all the outgoing partons are in the
transverse plane. Distributions are again shown for the five processes
listed in Eq.~(3). The directions of the three-momenta of the outgoing
heavy quarks are indicated at the top of the figure. The momenta of the $t$
and $\bar t$ quarks are at $0^\circ$ and $180^\circ$, respectively, while
the $b$ and $\bar b$ momenta are at $90^\circ$ and $270^\circ$,
respectively. The dead cones in the directions of the $t$ and $b$ ($\bar
t$ and $\bar b$) quarks are clearly evident in this figure. The width of
the dead cones is proportional to $m_Q/E_Q$, and thus the $t$ ($\bar t$)
quark dead cone is much wider than the $b \> (\bar b)$ quark dead cone.
The minimum in the $t \> (\bar t)$ dead cone does not coincide with the $t
\> (\bar t)$ direction, instead, the minimum is shifted to a slightly
smaller angle. The reason for this shift is the same as discussed for the
$dN/d\cos \theta_g$ distribution in Fig.~\ref{FIG:A}, except that now the
$\widehat{q_1 p_1}$ and $\widehat{q_2 p_2}$ terms in Eq.~(\ref{EQ:REPS})
give a contribution which is an increasing function of $\phi_g$ in the
neighborhood around the direction of the $t \> (\bar t)$ quark. The
contribution from the other terms has a minimum in the $t \> (\bar t)$
direction and is symmetric about this direction. The resulting sum now has
a minimum at a value of $\phi_g$ that is slightly smaller than the $t \>
(\bar t)$ quark direction. The $\widehat{tb}$ antennae, {\it i.e.}, the
$\widehat{q_1 p_1}$ and $\widehat{q_2 p_2}$ terms in Eq.~(\ref{EQ:REPS}),
are also responsible for the lack of symmetry in the radiation pattern
about the $t$ and $b$ quark directions. Note that the ordering of the
different processes is preserved over the complete $\phi_g$ range, with
the effects of the initial radiation providing an approximately constant
background to the dominant contributions involving the $t$ and $b$
quarks. The ordering reflects the colour charges of the initial particles,
$gg > q \bar q > e^-e^+$. Note, however, that the hadronic production
processes are suppressed relative to the corresponding $s-$channel colour
singlet processes, {\it e.g.}, $(q \bar q \to Z^* \to t \bar t) \; > \: (q
\bar q \to t\bar t)$. The reason, evident in Table~\ref{TAB:COLOUR}, is the
suppression of the $\widehat{t \bar t}$ antenna (the coefficient $c_6$) for
the hadronic production processes.
Figure~\ref{FIG:I} is the same as Fig.~\ref{FIG:H}, except that now the
$b$ and $\bar b$ momenta have been fixed at $45^\circ$ and $235^\circ$,
respectively. The $b \> (\bar b)$ quark is now closer to the $t \> (\bar
t)$ direction, consequently, the $b \> (\bar b)$ quark is now moving
faster, and thus the $b \> (\bar b)$ quark dead cone is now narrower than
in the previous figure. If the trend of moving the $b \> (\bar b)$ quark
closer to the $t \> (\bar t)$ quark direction continues, the $b \> (\bar
b)$ quark continues to move faster and its dead cone continues to narrow.
In the limiting case of the $t$ and $b$ ($\bar t$ and $\bar b$) quarks
parallel, the dead cone is very narrow and the radiation pattern is
symmetric about the $t\, b$ and $\bar t \, \bar b$ directions.
Figure~\ref{FIG:L} is the same as Fig.~\ref{FIG:H}, but with the top quark
width set to infinity. This corresponds to the top quark decaying
instantly, and so the radiation pattern is equivalent to that of $b\bar b$
production. The major difference between this figure and Fig.~\ref{FIG:H}
is the lack of the top quark dead cones in the present figure. The
radiation pattern is now symmetric about the $b$ and $\bar b$ directions.
(The $t$ and $\bar t$ directions are irrelevant since the $t$ and $\bar t$
decay instantly). Notice that the magnitude of the $q \bar q \to t \bar t$
curve is now less than the $e^- e^+ \to t \bar t$ curve. The reason for
this is that in the limit $\Gamma_t \to \infty$ ($\chi_{12} \to 1$) the
$\widehat{p_1 p_2}$ antenna (negative) contribution is enhanced.
The colour suppression
of this contribution in the $q \bar q \to t \bar t$ case is no longer
compensated by the background initial state radiation.
The variation of the azimuthal radiation pattern with the top quark width
is illustrated in Fig.~\ref{FIG:N} for the process $gg\to t\bar t$. The
distribution $dN/d\phi_g$ is plotted versus $\phi_g$ for incoming partons
with energy $E_{\rm beam} = 2m_t = 280$~GeV. The radiation pattern is
shown for four values of the top quark width: $\Gamma_t = \infty$, 5~GeV,
0.67~GeV (the Standard Model Born value), and 0. The radiation pattern for
the Standard Model Born top quark width is almost identical to the
$\Gamma_t = 0$ pattern. The dead cone about the $t \> (\bar t)$ quark is
obscured already for $\Gamma_t = 5$~GeV.
In Fig.~\ref{FIG:P} we plot $dN/d\phi_g$ versus $\phi_g$ in polar
coordinates. The radiation pattern for the process $gg \to t\bar t$ is
shown for $\Gamma_t = \Gamma_{\rm sm}^{(0)}$ (solid line) and $\Gamma_t =
\infty$ (dashed line). The angle between the momenta vectors of the $t$ and
$b$ quarks is $0^\circ, 45^\circ, 90^\circ, 135^\circ$, and $180^\circ$,
for parts (a), (b), (c), (d), and (e), respectively. The radiation
patterns are quite different for the two cases. The $b\bar b$ radiation
pattern (dashed line) is always symmetric about the $b \bar b$ direction.
(The $t\bar t$ direction is irrelevant in this case.) For the Standard
Model width (solid line), the radiation is always largest in the angular
sector between the $t$ and $b$ ($\bar t$ and $\bar b$) directions. For
example, in part (c), the radiation in the first and third quadrants is
much larger than in the second or fourth quadrants. This is a consequence
of the colour antenna connecting the $t$ and $b$ ($\bar t$ and $\bar b$)
quarks. As the angle between the $t$ and $b$ quarks increases, the
velocity of the $b$ quark decreases, the $b$ quark dead cone becomes wider,
the magnitude of the radiation decreases, and the radiation pattern becomes
more isotropic.
\section{SUMMARY}
In this paper we have calculated the soft gluon distribution in $t \bar t$
production, taking the decay of the top quarks fully into account. Although
our primary interest is in hadronic $t \bar t$ production, we have also
considered several other processes with different colour structures. This
allows us to quantify the contributions from the different antennae which
determine the radiation patterns.
We have seen how, in general, the radiation pattern depends on the colour
flow in the $2\to 2$ process, the orientation of the final state particles
with respect to the beam and to each other, and on the top decay width. The
latter controls the interference between radiation before and after the top
decay and between radiation in two decays. When the decay width is large,
the $b$ and $\bar b$ appear almost instantaneously and they can radiate
coherently, as though produced directly.
We have focussed in particular on two types of distributions. The
distribution in polar angle of the gluon with respect to the beam is
sensitive to radiation off the initial state particles, and also to the
presence of antennae linking the initial and final state particles (which
are absent in $s$-channel colour-singlet exchange processes). When all the
final state particles are in the transverse plane, the distribution in the
gluon azimuthal angle is more sensitive to the radiation off the final
state particles, in particular to the dead cones of the $t$ and $b$ quarks.
The study of soft gluon radiation in $t \bar t$ events is important not
only for theoretical reasons. The effects we have calculated are
responsible for the distribution of soft hadrons and jets accompanying the
final state $b$'s and $W$'s. These in turn could play an important role in
the determination of the top mass from the reconstructed invariant mass
of its decay products. For example, the interference between emission {\it
before} and {\it after} top decay constitutes an irreducible uncertainty
in such a procedure. It is important that Monte Carlos used to correct for
these effects in the data contain all the relevant underlying physics.
\acknowledgements
This work was supported in part by the UK Science and Engineering Research
Council. We are grateful to Yuri~Dokshitzer and Lynne~Orr
for useful discussions.
\newpage
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 532
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Али́са Пле́зенс Ли́дделл (; 4 мая 1852, Вестминстер, Лондон, Великобритания — 16 ноября 1934, Вестерхам, Кент, Великобритания) — прототип персонажа Алисы из книги Льюиса Кэрролла «Алиса в Стране чудес» (а также один из прототипов героини в книге «Алиса в Зазеркалье»).
Биография
Алиса Лидделл была четвёртым ребёнком Генри Лидделла (6 февраля 1811 — 18 января 1898) — филолога-классика, декана одного из колледжей в Оксфорде и соавтора знаменитого греческого словаря «Лидделл-Скотт», — и его жены Лорины Ханны Лидделл (урождённой Рив) (3 марта 1826 — 25 июня 1910). Родители долго выбирали имя для малышки. Вариантов было два: Алиса или Марина. Родители посчитали первый из этих вариантов более подходящим.
У Алисы были два старших брата — Эдвард Гарри (6 сентября 1847 — 14 июня 1911) и Джеймс Артур Чарльз (28 декабря 1850 — 27 ноября 1853, умер от скарлатины), — и старшая сестра Лорина Шарлотта (11 мая 1849 — 29 октября 1930). После Алисы у Генри и Лорины Ханны родилось ещё шесть детей:
Эдит Мэри (1854 — 26 июня 1876);
Рода Каролина Энн (1859 — 19 мая 1949);
Альберт Эдвард Артур (1863 — 28 мая 1863);
Вайолет Констанция (10 марта 1864 — 9 декабря 1927);
Фрэдерик Фрэнсис (7 июня 1865 — 19 марта 1950);
Лайонел Чарльз (22 мая 1868 — 21 марта 1942).
Алиса была очень близка с Эдит и Фредериком. После рождения Алисы её отец, который до этого был директором Школы Уэстминстер, был назначен на пост декана колледжа Крайст-черч, и в 1856 году семейство Лидделл переехало в Оксфорд. Вскоре Алиса встретила Чарльза Латуиджа Доджсона, который столкнулся с её семьёй 25 апреля 1856 года, когда фотографировал собор. Он стал близким другом семьи в последующие годы.
Алиса росла в основном в обществе Лорины и Эдит. По праздникам вместе со всей семьёй они отдыхали на западном побережье северного Уэльса в загородном доме «Пенморфа» (ныне - отель «Гогарт-Эбби») на Западном Побережье Лландидно в Северном Уэльсе.
У отца Алисы учились многие замечательные художники, он был другом королевской семьи. Отрочество и юность Алисы совпали с расцветом творчества прерафаэлитов (предшественников модерна). Она занималась рисованием, а уроки живописи ей давал Джон Рёскин, знаменитый художник и наиболее влиятельный английский художественный критик XIX века. Рёскин находил у неё большие способности, она сделала несколько копий его картин, а также картин его друга Уильяма Тёрнера, великого английского живописца. Позже Алиса позировала Джулии Маргарет Камерон — фотохудожнику, тоже близкой к прерафаэлитам, чьё творчество относят к золотому веку английской фотографии.
По некоторым данным, мистер Доджсон обращался к родителям Алисы с просьбой позволить ему просить её руки, когда она повзрослеет. Однако точных данных об этом нет. Вполне возможно, что это часть «мифа Льюиса Кэрролла и Алисы», возникшего позднее.
Известен также другой «миф»: в юношеских годах Алиса вместе с сёстрами отправилась путешествовать по Европе и в этой поездке они встретились с принцем Леопольдом, младшим сыном королевы Виктории, когда он жил в Крайст-Чёрч. Согласно «мифу», Леопольд влюбился в Алису, но доказательства этого факта маловесомы. Факт, что сёстры Лидделл с ним встречались — реален, но современные биографы Леопольда считают, что есть большая вероятность того, что он был увлечён её сестрой Эдит (хотя свою первую дочь Леопольд назвал Алисой). Во всяком случае, Леопольд был в числе носильщиков гроба с телом Эдит на её похоронах 30 июня 1876 года (она умерла 26 июня — по разным сведениям, от кори или перитонита).
15 сентября 1880 года в Вестминстерском аббатстве Алиса вышла замуж за крикетиста Реджинальда Харгривса (13 октября 1852 — 13 февраля 1926), который был учеником доктора Доджсона. От него она родила трёх сыновей — Алана Ниветона Харгривса (25 октября 1881 — 9 мая 1915), Леопольда Реджинальда «Рекса» Харгривса (январь 1883 — 25 сентября 1916) и Кэрила Лидделла Харгривса (1887 — 26 ноября 1955 года) (ходит версия, что его назвали в честь Кэрролла, однако Лидделлы это отрицали). Алан и Леопольд погибли в Первой мировой войне во время боёв во Франции: Алан погиб на поле боя и был похоронен во Флербе, Реджинальд умер от ранений и был похоронен в Жильмоне. В замужестве Алиса была обычной домохозяйкой и стала первым президентом Женского института при деревне Эмери-Дон.
Последний раз она встретилась с Чарльзом Доджсоном в 1891 году, когда вместе с сёстрами навестила его в Оксфорде.
После смерти тело Алисы было кремировано в крематории Голдерс-Грин и прах был захоронен на кладбище у церкви Собора Святого Михаила и Всех ангелов в Линдхёрсте в Гэмпшире.
Создание «Алисы в Стране чудес»
4 июля 1862 года на лодочной прогулке Алиса Лидделл попросила своего друга Чарльза Доджсона сочинить историю для неё и её сестёр Эдит и Лорины. Доджсон, которому и раньше приходилось рассказывать детям Лидделла сказки, придумывая события и персонажей на ходу, с готовностью согласился. На этот раз он поведал сёстрам о приключениях маленькой девочки в Подземной Стране, куда она попала, провалившись в нору Белого Кролика. Главная героиня очень напоминала Алису (и не только именем), а некоторые второстепенные персонажи — её сестёр Лорину и Эдит. История так понравилась Алисе Лидделл, что она попросила рассказчика записать её. Доджсон обещал, но все равно напоминать пришлось несколько раз. Наконец он выполнил просьбу Алисы и подарил ей манускрипт, который назывался «Приключения Алисы под землёй». Позже автор решил переписать книгу. Для этого весной 1863 года он отправил её на рецензию своему другу Джорджу Макдональду. Также в книгу были добавлены новые детали и иллюстрации Джона Тениела (John Tenniel). Новую версию книги Доджсон преподнёс своей любимице на Рождество 1863 года. В 1865 году Доджсон опубликовал книгу «Приключения Алисы в Стране чудес» под псевдонимом Льюис Кэрролл. Вторая книга — «Алиса в Зазеркалье» — вышла шестью годами позже, в 1871 году. Обе сказки, которым уже значительно больше ста лет, популярны и поныне.
После смерти её мужа в 1926 году Алиса, чтобы оплатить коммунальные счета своего дома, выставила на аукцион подаренный ей Доджсоном рукописный экземпляр «Приключений Алисы под землёй» (изначальное название сказки). Аукцион «Сотбис» оценил её стоимость в 15 400 фунтов и в конечном итоге на столетие со дня рождения Доджсона в Колумбийском университете она была продана одному из основателей фирмы по производству грампластинок Victor Talking Machine Company Элдриджу Р. Джонсону (восьмидесятилетняя Алиса лично присутствовала на этой церемонии). После смерти Джонсона книга была куплена консорциумом американских библиофилов. Сегодня рукопись хранится в Британской библиотеке.
См. также
Александра Рода Китчин — другая подруга () Льюиса Кэрролла и его любимая фотомодель.
Алиса Лидделл в образе нищенки, фотография 1858 года
Поликсени Папапетру — австралийская фотограф, известная пересъёмкой фотографий Кэрролла, где роль Алисы Лидделл играла её дочь Олимпия Нельсон.
«Восстаньте из праха» — роман американского писателя-фантаста Филиппа Фармера, где Алиса Лидделл фигурирует в качестве одного из основных персонажей.
Примечания
Ссылки
Прототипы литературных персонажей
Алиса в Стране чудес
Женщины Викторианской эпохи
Алиса Лидделл
Почётные доктора Колумбийского университета
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{
"redpajama_set_name": "RedPajamaWikipedia"
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| 4,453
|
import os, sublime, sublime_plugin, subprocess
# Array of Git repositories
repositories = [
]
def conf_error(me):
sublime.sublime.error_message("[%s] No repository specified" % me)
def git_error(me):
import sys, webbrowser
if sublime.ok_cancel_dialog("Some package dependencies could not be installed automatically. Please refer to the installation guide to resolve this problem.\n\nDo you want to open the website for this package?", "Open website"):
webbrowser.open("https://packagecontrol.io/packages/"+me)
sys.exit()
def plugin_loaded():
from package_control import events
from subprocess import check_call
# Get name of package
me = os.path.basename(os.path.dirname(os.path.realpath(__file__)))
if events.install(me) or events.post_upgrade(me):
# Get absolute package path
package_path = sublime.packages_path() + '/' + me
# Install packages specified in the array
if len(repositories) > 0:
for repository in repositories:
if repository:
try:
os.chdir(package_path)
repository_dir = os.path.basename(repository)
# git-pull if directory exists
if os.path.isdir(repository_dir):
os.chdir(repository_dir)
sublime.status_message("[%s] git pull" % me)
check_call(['git', 'pull', repository])
# git-clone
else:
sublime.status_message("[%s] git clone" % me)
check_call(['git', 'clone', repository])
except subprocess.CalledProcessError:
git_error(me)
sublime.status_message("[%s] Completed" % me)
else:
conf_error(me)
else:
conf_error(me)
|
{
"redpajama_set_name": "RedPajamaGithub"
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| 9,384
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{"url":"https:\/\/math.stackexchange.com\/questions\/405234\/prove-that-2n-s-can-be-written-as-the-sum-of-perfect-squares-where-s-is","text":"Prove that $2^{n} s$ can be written as the sum of perfect squares, where $s$ is the sum of perfect squares\n\nI need require assistance in proving that $$2^{n} s$$ can be written as the sum of two perfect squares, where $$s$$ is a sum of two perfect squares. My teacher has told me I'm not allowed to use induction and I'm not really sure how to go about it.\n\nIf anyone could nudge me in the night direction, I'd be appreciative.\n\n\u2022 Hint: Think about the case when n is even and the case when n is odd \u2013\u00a0Amr May 28 '13 at 23:54\n\u2022 Relevant question (possible duplicate): math.stackexchange.com\/q\/100506\/264 \u2013\u00a0Zev Chonoles May 28 '13 at 23:55\n\u2022 I've thought about that...but I get that it can be expressed as the sum of 2 perfect squares when 'n' is odd and it can't when 'n' is even but I'm required to show it works for all natural n :( \u2013\u00a0user78416 May 28 '13 at 23:55\n\u2022 As a nuclear overkill, you can use Fermat's classification of numbers which can be written as the sum of 2 squares. But please just follow Amr's hint. \u2013\u00a0Calvin Lin May 28 '13 at 23:56\n\u2022 Because you say you have trouble when $n$ is even, I thought it might help to remind you that $0$ is a perfect square. E.g., $2^2=2^2+0^2$. \u2013\u00a0Jonas Meyer May 28 '13 at 23:57\n\nIn the case that $n$ is odd, let $s = k^2$ and $n = 2m + 1$. Hence $$2^{2m + 1}k^2 = \\left(2^m k\\right)^2 + \\left(2^mk\\right)^2$$ Otherwise, $n = 2m$ and we have that $$2^{2m}k^2 = \\left(2^m k \\right)^2 + 0^2$$ No induction needed here. $m$ and $k$ are both in $\\mathbb{N} \\cup \\{0\\}$.\n\nYou might think the zero is \"cheating\" but it is definitely necessary in some cases such as $2^n s = 16$.\n\n\u2022 There is a problem when n is odd \u2013\u00a0Amr May 29 '13 at 0:03\n\u2022 Thank you. I have fixed it. \u2013\u00a0Jon Claus May 29 '13 at 0:06\n\u2022 I'm sorry, I had a typo in the original problem :( s is not a perfect square, it is the sum of two perfect squares, sorry :( \u2013\u00a0user78416 May 29 '13 at 0:43\n\nHint: If the numbers $x$ and $y$ can each be written as the sum of 2 perfect squares, then so can the number $xy$. This is known as the Brahmagupta-Fibonacci Identity.\n\nYou can either prove this statement yourself, or click on the Wikipedia link.\n\n\u2022 So that covers the case of even n! Thanks very much! :D \u2013\u00a0user78416 May 29 '13 at 1:55","date":"2019-06-25 02:16:10","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\": 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\": 0.8161871433258057, \"perplexity\": 218.5462871570128}, \"config\": {\"markdown_headings\": false, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.3, \"absolute_threshold\": 20, \"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-2019-26\/segments\/1560627999783.49\/warc\/CC-MAIN-20190625011649-20190625033649-00239.warc.gz\"}"}
| null | null |
Elsie Jane Van Name (1890-4 de noviembre de 1934) fue una guionista y actriz estadounidense activa durante la época del cine mudo de Hollywood.
Biografía
Fue la segunda esposa del actor y director Francis Ford, a quien conoció cuando coprotagonizaron juntos una obra de teatro. La pareja se casó en Nueva York en 1909. Trabajaron juntos en varios proyectos, aunque su relación parece haber sido difícil.
Se separaron al principio del matrimonio (Ford siguió temporalmente con la actriz Grace Cunard), pero volvieron a casarse en Los Ángeles en 1916. La pareja fundó Fordart Films en 1917, y estrenó la película Berlin Via America bajo esta enseña.
En 1919, mientras Ford estaba de viaje en un rodaje, Elsie lo dejó brevemente por su gerente de negocios y vendió el estudio. Murió en Los Ángeles el 4 de noviembre de 1934, y le sobrevivieron Ford (con quien aún estaba casada) y sus dos hijos.
Filmografía seleccionada
Como guionista:
Storm Girl (1922)
The Great Reward (1921) (serial)
Crimson Shoals (1919)
The Mystery of 13 (1919)
The Silent Mystery (1918) (serial)
Berlin Via America (1918)
The Mystery Ship (1918) (serial)
Como actriz:
The Mystery of 13 (1919)
The Silent Mystery (1918) (serial)
The Mystery Ship (1918) (serial)
John Ermine of Yellowstone (1917)
Referencias
Enlaces externos
Actrices de la ciudad de Nueva York
Actrices de cine mudo de Estados Unidos
Actrices de Estados Unidos del siglo XX
|
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| 5,459
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package com.nisoft.inspectortools.ui.base;
import android.app.Activity;
import android.app.DialogFragment;
import android.content.ContentUris;
import android.content.Intent;
import android.database.Cursor;
import android.net.Uri;
import android.os.Build;
import android.os.Bundle;
import android.provider.DocumentsContract;
import android.provider.MediaStore;
import android.support.annotation.Nullable;
import android.support.v4.content.FileProvider;
import android.util.Log;
import android.view.LayoutInflater;
import android.view.View;
import android.view.ViewGroup;
import android.widget.Button;
import android.widget.LinearLayout;
import com.nisoft.inspectortools.R;
import com.nisoft.inspectortools.ui.typeinspect.WorkingFragment;
import com.nisoft.inspectortools.utils.FileUtil;
import java.io.File;
import java.io.IOException;
import java.util.UUID;
/**
* Created by NewIdeaSoft on 2017/5/3.
*/
public class UpdatePhotoMenuFragment extends DialogFragment {
public static final int TAKE_PHOTO = 2;
public static final int CHOOSE_PHOTO = 3;
public static String IMAGE_POSITION = "image_position";
public static String IMAGE_ROOTPATH = "image_rootpath";
public static String DELETE_BUTTON_VARIABLE = "delete_button_variable";
private Button mMakePhoto;
private Button mChoosePhoto;
private Button mDeleteButton;
private String path;
private int position;
public static UpdatePhotoMenuFragment newInstance(int position, String rootPath, boolean deleteButtonVariable) {
Bundle args = new Bundle();
args.putInt(IMAGE_POSITION, position);
args.putString(IMAGE_ROOTPATH, rootPath);
args.putBoolean(DELETE_BUTTON_VARIABLE, deleteButtonVariable);
UpdatePhotoMenuFragment fragment = new UpdatePhotoMenuFragment();
fragment.setArguments(args);
fragment.setStyle(DialogFragment.STYLE_NO_TITLE, 0);
return fragment;
}
@Nullable
@Override
public View onCreateView(LayoutInflater inflater,
@Nullable ViewGroup container, Bundle savedInstanceState) {
View view = inflater.inflate(R.layout.fragment_dialog, container);
position = getArguments().getInt(IMAGE_POSITION);
boolean canDelete = getArguments().getBoolean(DELETE_BUTTON_VARIABLE);
mMakePhoto = (Button) view.findViewById(R.id.make_picture);
mChoosePhoto = (Button) view.findViewById(R.id.choose_picture);
if (canDelete) {
mDeleteButton = new Button(getActivity());
mDeleteButton.setText("删除照片");
mDeleteButton.setLayoutParams(
new ViewGroup.LayoutParams(ViewGroup.LayoutParams.MATCH_PARENT,
ViewGroup.LayoutParams.WRAP_CONTENT));
mDeleteButton.setOnClickListener(new View.OnClickListener() {
@Override
public void onClick(View v) {
deletePicture();
UpdatePhotoMenuFragment.this.dismiss();
}
});
((LinearLayout) view).addView(mDeleteButton);
}
mMakePhoto.setOnClickListener(new View.OnClickListener() {
@Override
public void onClick(View v) {
openCamera();
}
});
mChoosePhoto.setOnClickListener(new View.OnClickListener() {
@Override
public void onClick(View v) {
openAlbum();
}
});
return view;
}
private void deletePicture() {
if (getTargetFragment() instanceof WorkingFragment) {
((WorkingFragment) getTargetFragment()).removeSelectedPic(position);
}
}
private void openCamera() {
//调用系统相机拍摄照片
//照片文件存储路径
Uri uri = null;
File dir = new File(getArguments().getString(IMAGE_ROOTPATH));
if (!dir.exists()) {
dir.mkdirs();
}
File outputImage = new File(dir, UUID.randomUUID().toString() + ".jpg");
path = null;
if (outputImage.exists()) {
outputImage.delete();
}
try {
outputImage.createNewFile();
path = outputImage.getAbsolutePath();
Log.d("PhotoPath", path);
} catch (IOException e) {
e.printStackTrace();
}
if (Build.VERSION.SDK_INT >= 24) {
uri = FileProvider.getUriForFile(getActivity(), "com.nisoft.inspectortools.fileprovider", outputImage);
} else {
uri = Uri.fromFile(outputImage);
}
Intent intent = new Intent("android.media.action.IMAGE_CAPTURE");
intent.putExtra(MediaStore.EXTRA_OUTPUT, uri);
startActivityForResult(intent, TAKE_PHOTO);
}
/**
* 打开相册
*/
private void openAlbum() {
Intent intent = new Intent("android.intent.action.GET_CONTENT");
intent.setType("image/*");
startActivityForResult(intent, CHOOSE_PHOTO);
}
@Override
public void onActivityResult(int requestCode, int resultCode, Intent data) {
if (resultCode != Activity.RESULT_OK) {
return;
}
if (getTargetFragment() == null) {
return;
}
String photoPath = null;
String targetPhotoPath = null;
switch (requestCode) {
case TAKE_PHOTO:
targetPhotoPath = path;
break;
case CHOOSE_PHOTO:
Uri uri = data.getData();
if (DocumentsContract.isDocumentUri(getActivity(), uri)) {
String docId = DocumentsContract.getDocumentId(uri);
if ("com.android.providers.media.documents".equals(uri.getAuthority())) {
String id = docId.split(":")[1];
String selection = MediaStore.Images.Media._ID + "=" + id;
photoPath = getImagePath(MediaStore.Images.Media.EXTERNAL_CONTENT_URI, selection);
} else if ("com.android.providers.downloads.documents".equals(uri.getAuthority())) {
Uri contentUri = ContentUris.withAppendedId(Uri.parse("content://downloads/public_downloads"), Long.valueOf(docId));
photoPath = getImagePath(contentUri, null);
}
} else if ("content".equalsIgnoreCase(uri.getScheme())) {
photoPath = getImagePath(uri, null);
} else if ("file".equalsIgnoreCase(uri.getScheme())) {
photoPath = uri.getPath();
}
File dir = new File(getArguments().getString(IMAGE_ROOTPATH));
if (!dir.exists()) {
dir.mkdirs();
}
targetPhotoPath = getArguments().getString(IMAGE_ROOTPATH) + UUID.randomUUID().toString() + ".jpg";
// targetPhotoPath = getArguments().getString(IMAGE_ROOTPATH) + position + ".jpg";
FileUtil.moveFile(photoPath, targetPhotoPath);
photoPath = targetPhotoPath;
}
Intent i = new Intent();
if (new File(targetPhotoPath).exists()) {
i.putExtra("PhotoPath", targetPhotoPath);
i.putExtra("resourcePhotoPath", photoPath);
}
i.putExtra("position", position);
getTargetFragment().onActivityResult(getTargetRequestCode(), resultCode, i);
this.dismiss();
}
private String getImagePath(Uri uri, String selection) {
String path = null;
Cursor cursor = getActivity().getContentResolver().query(uri, null, selection, null, null);
if (cursor != null) {
if (cursor.moveToFirst()) {
path = cursor.getString(cursor.getColumnIndex(MediaStore.Images.Media.DATA));
}
cursor.close();
}
return path;
}
}
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 7,249
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{"url":"https:\/\/www.ncatlab.org\/nlab\/show\/semilattice","text":"Contents\n\n(0,1)-category\n\n(0,1)-topos\n\n# Contents\n\n## Definition\n\nA join-semilattice is a poset which admits all finite joins, or equivalently which admits a bottom element $\\bot$ and binary joins $a\\vee b$. If we think of a poset as a category, a join-semilattice is the same as a poset with finite colimits, or equivalently, a poset with finite coproducts.\n\nIn a join-semilattice the binary join $\\vee$ is commutative, associative, has $\\bot$ as a unit, and is idempotent: $a\\vee a =a$. And in fact, given any commutative and idempotent monoid $(A,\\vee,\\bot)$, we can define $a\\le b$ to mean $a \\vee b = b$ to make it into a poset with finite joins; thus we have an equivalent algebraic definition of a join-semilattice.\n\nDually, a meet-semilattice is a poset which admits all finite meets, including a top element $\\top$ and binary meets $\\wedge$. Once again $\\wedge$ is commutative, associative, unital for $\\top$, and idempotent. Once again we can recover the order from it, but this time defining $a\\le b$ to mean $a \\wedge b = a$. If we think of a poset as a category, a meet-semilattice is the same as a poset with finite limits, or equivalently, a poset with finite products.\n\nIf we treat join- and meet-semilattices purely algebraically there is no difference: they are both just idempotent commutative monoids. The difference comes in how we define the order starting the commutative monoid structure, or in the notation we use (just as we distinguish additive and multiplicative groups notationally).\n\nSince the opposite of a join-semilattice is a meet-semilattice, it would be possible to take one as standard and call the other a cosemilattice (compare directed and codirected sets), but this may not have ever been done.\n\nIf a poset is both a join- and a meet-semilattice, then we call it a lattice.\n\n## Bounded semilattices and semipseudolattices\n\nTraditionally, a semilattice need have only finite inhabited meets\/joins; that is, it need not have a top\/bottom element. Algebraically, this means that a semilattice need not be a monoid, but is any commutative idempotent semigroup.\n\nOne might call a semilattice that does have a top\/bottom element a bounded semilattice; the problem with this is that a bounded poset already means a poset that has both top and bottom elements, whereas here we really only want to require one.\n\nAnother approach is to define a semilattice, as above, to require a top\/bottom element and then use the term pseudosemilattice or semipseudolattice to allow for the possibility that it might not.\n\nSee lattice for more discussion of this issue.\n\n## Semilattice homomorphisms\n\nA homomorphism of join-semilattices $f: A \\to B$ is a function that preserves finite joins, or equivalently:\n\n$f(x \\vee y) = f(x) \\vee f(y),\\; f(\\bot) = \\bot .$\n\nNote that such a homomorphism is necessarily a monotone function, but the converse fails. Thus, a semilattice is a poset with property-like structure.\n\nA homomorphism of meet-semilattices is defined in an analogous (i.e., dual) way. In what follows we take join-semilattices as the default, but all results apply to meet-semilattices with slight modifications.\n\n## The category of semilattices\n\nSemilattices and semilattice homomorphims form a concrete category SemiLat. By the remarks above, this is equivalent to the category of commutative idempotent monoids. Since these are algebras of a Lawvere theory, or equivalently a finitary monad on $Set$, the category $Semi Lat$ has all the properties that finitary monadic categories enjoy.\n\nThe poset $\\{F,T\\}$ where $F \\le T$ becomes a commutative rig with $\\vee$ and meet $\\wedge$ as addition and multiplication, respectively; let us call this rig $Bool$. We can define a module of a rig much as we define a module of a ring, but with the module\u2019s underlying abelian group generalized to be a commutative monoid (thus eliminating the need for negatives). The underlying commutative monoid of a $Bool$-module is idempotent because, writing addition in this monoid as $+$, we have $a + a = (T \\vee T)a = T a = a$. Conversely, any idempotent commutative monoid becomes a $Bool$-module in a unique way. Thus, the category $Semi Lat$ is equivalent to the category of $Bool$-modules.\n\n## The free join-semilattice on a poset\n\nThere a forgetful functor\n\n$U \\colon SemiLat \\to Poset$\n\nThis has a left adjoint\n\n$F \\colon Poset \\to SemiLat$\n\nwhere for any poset $P$, the join-semilattice $F(P)$ is the poset of finitely generated downsets of $P$, ordered by inclusion. Here a downset of a poset $P$ is a subset $S \\subseteq P$ such that\n\n$s \\in S, s' \\le s \\quad \\implies \\quad s' \\in S.$\n\nThis set of all downsets in $P$, say $\\hat{P}$, is ordered by inclusion, and it\u2019s a suplattice: any union of downsets is a downset. There\u2019s an embedding of $P$ in $\\hat{P}$ that sends each $p \\in P$ to its principal downset $\\{s \\in P : \\; s \\le p \\}$. A downset is finitely generated if it is the union of finitely many principal downsets. (To give a finitely generated downset is to give a finite antichain, and so the free join-semilattice is sometimes described equivalently as the set of finite antichains in $P$ equipped with a certain partial order.)\n\nTo understand this description of the free join-semilattice on a poset, some enriched category theory is useful. A preorder is the same as a $Bool$-enriched category, where now $Bool$ stands for the monoidal category with two objects $F$, $T$ and one nontrivial morphism $F \\implies T$, its monoidal structure being \u201cand\u201d. The downsets of a poset $P$ correspond in a one-to-one way with order-preserving maps $f \\colon P^{op} \\to Bool$, but in terms of enriched category theory these are precisely the $Bool$-enriched functors $f \\colon P^{op} \\to Bool$, just as presheaves on a category $C$ are functors $f \\colon C^{op} \\to Set$. Thus, the embedding $y \\colon P \\to \\hat{P}$ that sends each $p \\in P$ to its principal downset is the $Bool$-enriched version of the Yoneda embedding. So, just as the category of presheaves on a category $C$ is the free cocomplete category on $C$, $\\hat{P}$ is the free cocomplete $Bool$-enriched category on $P$. But a cocomplete $Bool$-enriched category that happens to be a poset (instead of a mere preorder) is the same as a suplattice. Thus, the free suplattice on $P$ is $\\hat{P}$.\n\nSimilarly, the free join-semilattice on a poset $P$ is the $Bool$-enriched analogue of the free finitely cocomplete category on a category $C$, since objects in this category are presheaves that are finite colimits of representables.\n\n## Examples\n\nLast revised on October 5, 2019 at 20:56:51. See the history of this page for a list of all contributions to it.","date":"2020-04-04 02:16:08","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 70, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"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\": 0.8861647248268127, \"perplexity\": 377.6036495812593}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.3, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": false}, \"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\/1585370519111.47\/warc\/CC-MAIN-20200404011558-20200404041558-00539.warc.gz\"}"}
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Die Geschichte von der Wunderbaren Kartoffel (Eventyret om den vidunderlige kartoffel) ist ein 1985 gedrehter dänischer Zeichentrickfilm von Anders Sørensen. Er wurde vom Dänischen Institut für Film herausgegeben und behandelt die Herkunft der Kartoffel und deren Einführung in Europa während der Neuzeit.
Inhalt
Der Film behandelt die Verbreitung der Kartoffel in Südamerika, später in Europa. Dabei geht er auf die sozialen Zustände im Europa der frühen Neuzeit ein, erklärt die Bedeutung der Kartoffel als Nahrungsquelle und schließt mit der Kartoffelpest in Irland.
Produktion und Veröffentlichung
Der Film wurde 1985 nach einem Drehbuch und unter der Regie von Anders Sørensen produziert. Die Musik komponierte Anders Koppel, die Erzählstimme sprach Kai Løvring. Für die Kamera war Jette Michaelsen verantwortlich, für die Hintergründe Claus Deleuran.
Rezeption
Video Education Australasia empfiehlt den Film für den Unterricht im 5. bis 8. Schuljahr.
Einzelnachweise
Weblinks
Zeichentrickfilm
Dokumentarfilm
Filmtitel 1985
Dänischer Film
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{
"redpajama_set_name": "RedPajamaWikipedia"
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It was a fantastic March for Manchester United and we have the list of goals for the March with some stunning strikes.
The Belgium international was in unstoppable form at the start of the month, scoring a couple of beauties in the dramatic 3-2 victory over Southampton. The winner was the first time he has found the net from outside the box since joining the Reds. He followed it up with a double in Paris that proved vital in overturning the two-goal deficit from the first leg. Lukaku was unable to add to a tally of six in three games when drawing a blank at Arsenal, when he was only denied by the bar and a fine save by keeper Bernd Leno, and he has not seen any action since due to a foot injury.
The Academy product continues to go from strength to strength and, like Lukaku, he was instrumental in the glorious win at PSG. An ambitious shot led to Romelu's second goal on the night, when Gianluigi Buffon spilled the effort, and he then stepped up to the plate when required to nervelessly drill the late penalty past the World Cup winner and prove his character for the biggest of occasions. The 21-year-old plundered a late consolation in the Emirates FA Cup defeat at Wolves and opened the scoring against Watford last weekend to register double figures in terms of Premier League strikes for the first time in his burgeoning career. All of this has been achieved while nursing an ankle knock sustained in February's draw with Liverpool.
|
{
"redpajama_set_name": "RedPajamaC4"
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Back in 2010 one of my capelet designs were featured in Vogue Knitting/Designer Knitting. So many of my fans have asked for the pattern over the last year and it is a pleasure for med to tell you that it is now available in Vogue Knitting's pattern store!
It costs $6.00, and if you keep an eye out Vogue Knitting sometimes have great pattern sales.
The capelet on the model is knitted in Tilli Tomas Symphony Lace (mohair/silk/nylon/wool with beads and glitter) in goldenrod.
I have knitted the capelet in many different yarns, including mohair and chunky wool, with good results! Check out how they turned out on Ravelry.
In this video you can see how it looks in real life!
That's gorgeous! I've always wanted to learn how to knit and crochet.
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{
"redpajama_set_name": "RedPajamaC4"
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{"url":"http:\/\/www.reddit.com\/r\/LaTeX\/comments\/y1jif\/splitting_a_large_document_into_separate_files\/","text":"[\u2013] 3 points4 points\n\nsorry, this has been archived and can no longer be voted on\n\nYou want the standalone package.\n\n\\usepackage{standalone}\n\n\nI'm using it for my thesis, as compiling the thesis itself just to see the change in one chapter is a pain as it's fairly slow due to the size of the thesis.\n\nEach chapter has a the normal LaTeX preamble included and compiles as it's own document. The thesis document then includes each chapter using the \\include code but with the standalone package in the thesis preamble - this then compiles all the chapters, ignoring each preamable except the one in the thesis document.\n\n[\u2013] 1 point2 points\n\nsorry, this has been archived and can no longer be voted on\n\nSounds like you are spending your time arguing with your setup. :-(\n\nAs to splitting LaTeX, the standard way is \\include and \\includeonly.\n\n[\u2013] 0 points1 point\n\nsorry, this has been archived and can no longer be voted on\n\nYou can do the following. In the main file put (before you include the files):\n\n\\newif\\ifsubsidiary\n\\subsidiarytrue\n\n\nAnd then in the other files use\n\n\\newif\\ifsubsidiary\n\\ifsubsidiary\n\\else\n\\documentclass[12pt]{report}\n...\n\\begin{document}\n\\fi\n...\n\\ifsubsidiary\n\\else\n\\end{document}\n\\fi\n\n\nHopefully it's fairly self explanatory.\n\nThat said, there should be a way to tell Gummi about your project. I haven't used Gummi though, so I can't help you.","date":"2014-07-22 13:43:00","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\": 0.8808344602584839, \"perplexity\": 1924.9487919878763}, \"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\/1405997858892.28\/warc\/CC-MAIN-20140722025738-00109-ip-10-33-131-23.ec2.internal.warc.gz\"}"}
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\section{Introduction}
Video moment retrieval (VMR) is a task to find a temporal moment in untrimmed video specified by a text description as illustrated in Figure \ref{fig:task}. With the rising number of videos along with the need for a more detailed and refined search capability that demand a better understanding of the video, the task of Video Moment Retrieval is drawing appreciable attention.
A number of fully-supervised methods that learn from a set of videos with ground-truth time stamps corresponding to a given query have been proposed \cite{TALL,MCN,EFRC,MAN}.
For these methods, a large-scale video dataset that requires the laborious burden of temporally annotating the boundaries corresponding to each query is a sine qua non.
In general, the performance of a fully-supervised method hinges on the quality of the dataset; however, for VMR, temporal boundaries are often ambiguous to annotate and may act as noise in the learning process.
Recently, weakly-supervised VMR (wVMR) \cite{that,SCN} that does not require the temporal boundary annotation for each query has been studied.
To leverage the weak supervision, contrastive learning is applied such that higher scores are predicted for the correct video-query pairs than for incorrect pairs.
This learning process improves the accuracy of the attention mechanism which plays a vital role in wVMR.
Inspired by recent methods \cite{that,SCN}, this paper addresses two critical challenges: (1) generating appropriate multi-scale video candidate proposals, and (2) learning the latent alignment between the text query and the retrieved video segment.
\begin{figure}[t]
\centering
\includegraphics[width=11cm,height=5.55cm]{./images/task_3}
\caption{Illustration of video moment retrieval task. The goal is to search the temporal boundary of the video moment that is most relevant to the given natural language query.}
\label{fig:task}
\end{figure}
The first challenge is that the video segment proposals should be adequate in number to give high recall without excessive computational load, and the video segment should be of appropriate length to have high intersection-of-union (IoU) with ground truth.
Previous methods \cite{TALL,MCN,that,SCN} greedily generated video candidate proposals using a pre-defined set of multi-scale sliding windows.
As a consequence, these methods generally produce large number of multi-scale proposals which increase the chance of achieving high recall at the expense of high computational cost.
When an attention mechanism is used thereafter to weigh the proposals, the attention becomes blurry as there are too many proposals to attend.
The second challenge is to learn a similarity measure between video segment and text query without ground truth annotation.
In \cite{that}, a text-to-video attention mechanism is incorporated to learn the joint embedding space of video and text query.
More accurate multi-modal similarity could be attained with a text query representation that is more effective in interacting with video frame feature.
Representing the text query as the last hidden feature of the Gated Recurrent Unit (GRU), as used in some previous methods \cite{that,SCN}, is overly simplistic .
In addition, applying one-way attention from query to video is not sufficient to bring out the most prominent feature in the video and query.
Recent studies in Visual Question Answering \cite{MCAN,InterIntra,SMAN} have explored the possibility of applying multi-directional attention flows that include both inter- and intra-modality attention.
This paper devises an analogous idea for the problem of wVMR, and validate its effectiveness in retrieving the moment using the weak labels.
To rise to the challenge, this paper proposes a Video-Language Alignment Network (VLANet) for weakly-supervised video moment retrieval.
As a first step, the word-level query representation is obtained by stacking all intermediate hidden features of GRU.
Video is divided into overlapping multi-scale segment groups where the segments within each group share a common starting time.
Then, the Surrogate Proposal Selection module selects one surrogate from each group which reduces the number of effective proposals for more accurate attention.
To consider the multi-directional interactions between each surrogate proposal and query, the Cascaded Cross-modal Attention (CCA) module performs both intra- and inter-modality attention.
The CCA module performs self-attention on each modality: video to video (V2V) and query to query (Q2Q), which considers the intra-modal relationships.
Thereafter, the CCA module performs cross-modal attention from query to video (Q2V), video to query (V2Q) and finally attended query to attended video (Q2V).
This cross-modal attention considers the inter-modal relationships that is critical in learning the multi-modal alignment.
To leverage the weak labels of video-query pairs, VLANet is trained in an end-to-end manner using contrastive loss that enforces semantically similar videos and queries to cluster in the joint embedding space.
The experiment results show that the VLANet achieves state-of-the-art performance on Charades-STA and DiDeMo datasets.
Extensive ablation study and qualitative analyses validate the effectiveness of the proposed method and provide interpretability.
\section{Related Work}
\subsection{Temporal Action Detection}
The goal of temporal action detection is to predict the temporal boundary and category for each action instance in untrimmed videos.
Existing works are divided into two groups: the fully-supervised and weakly-supervised.
Zhao \textit{et al.} \cite{SSN} proposed a structured segment network that models the temporal structure of each action instance by a structured temporal pyramid.
Gao \textit{et al.} \cite{CBR} proposed Cascaded Boundary Regression which uses temporal coordinate regression to refine the temporal boundaries of the sliding windows.
Lin \textit{et al.} \cite{BSN} proposed Boundary Sensitive Network that first classifies each frame as the start, middle, or end, then directly combines these boundaries as proposals.
In the weakly-supervised settings, however, only the coarse video-level labels are available instead of the exact temporal boundaries.
Wang \textit{et al.} \cite{UntrimmedNet} proposed UntrimmedNet that couples two components, the classification module, and the selection module, to learn the action models and reason about the temporal duration of action instances, respectively.
Nguyen \textit{et al.} \cite{STPN} proposed a Sparse Temporal Pooling Network that identifies a sparse subset of key segments associated with the target actions in a video using an attention module and fuse the key segments using adaptive temporal pooling.
Shou \textit{et al.} \cite{AutoLoc} proposed AutoLoc that uses Outer-Inner-Contrastive loss to automatically discover the required segment-level supervision to train a boundary predictor.
Liu \textit{et al.} \cite{CleanNet} proposed CleanNet that leverages an additional temporal contrast constraint so that the high-evaluation-score action proposals have a higher probability to overlap with the ground truth action instances.
\subsection{Video Moment Retrieval}
The VMR task is focused on localizing the temporal moment that is semantically aligned with the given natural language query.
For this task, various supervised methods have been proposed \cite{TALL,MCN,EFRC,MAN}.
In Gao \textit{et al.} \cite{TALL} and Hendricks \textit{et al.} \cite{MCN}, candidate moments are sampled using sliding windows of various lengths, and multi-modal fusion is performed to estimate the correlation between the queries and video moments.
Xu \textit{et al.} \cite{EFRC} proposed a model that integrates vision and language features using attention mechanisms and leverages video captioning as an auxiliary task.
Zhang \textit{et al.} \cite{MAN} proposed Moment Alignment Network (MAN) that considers the relationships between proposals as a structured graph, and devised an iterative algorithm to train a revised graph convolution network.
Recently, the task was studied under the weakly-supervised setting \cite{Duan,that,SCN}.
Duan \textit{et al.} \cite{Duan} proposed to decompose weakly-supervised dense event captioning in videos (WS-DEC) into a pair of dual problems: event captioning and sentence localization.
They proposed a cycle system to train the model based on the assumption that each caption describes only one temporal segment.
Mithun \textit{et al.} \cite{that} proposed Text-Guided-Attention (TGA) model that learns a joint representation between video and sentence.
The attention weight is used to retrieve the relevant moment at test time.
Lin \textit{et al.} \cite{SCN} proposed Semantic Completion Network (SCN) that selects the top-K proposals considering exploration and exploitation, and measures the semantic similarity between the video and query.
As an auxiliary task, SCN takes the masked sentence as input and predicts the masked words from visual representations.
\section{Method}
\begin{figure}[t]
\centering
\includegraphics[width=\textwidth]{./images/architecture}
\caption{Illustration of VLANet architecture. The Surrogate Proposal Selection module prunes out irrelevant proposals based on the similarity metric. Cascaded Cross-modal Attention considers various attention flows to learn multi-modal alignment. The network is trained end-to-end using contrastive loss.}
\label{fig:method}
\end{figure}
\subsection{Method Overview}
\label{ssec:method_overview}
Figure \ref{fig:method} illustrates the overall VLANet architecture.
The input text query is embedded using GloVe \cite{GloVe} after which each embedded representation is fed into a GRU \cite{GRU}. In the meanwhile, the video is embedded based on C3D \cite{C3D}.
Video is divided into overlapping multi-scale segment groups where the proposals within each group share a common starting time.
Given the video and query representations $V$ and $Q$, the similarity $c$ between video and query is evaluated by the Cascaded Cross-modal Attention (CCA) module.
The learned attention weights by CCA are used to localize the relevant moment at test time.
A video-query pair $(V,Q)$ is positive if it is in the training data; otherwise, it is negative.
The network is trained in an end-to-end manner using contrastive loss to enforce the scores of the positive pairs to be higher than those of the negative pairs.
In practice, the negative pairs are randomly sampled in a batch.
\subsection{Input representation}
\subsubsection{Query representation}
Gated Recurrent Unit (GRU) \cite{GRU} is used for encoding the sentences.
Each word of the query is embedded using GloVe and sequentially fed into a GRU.
Prior methods \cite{that} use only the final hidden feature of GRU to represent the whole sentence, which leads to the loss of information by excluding the interactions between frame- and word-level features of video and query.
Motivated by recent works in visual question answering \cite{InterIntra,MCAN}, this paper uses all intermediate hidden features of the GRU.
The query $Q$ is represented as:
\begin{eqnarray}
Q = \left[ {\bf w}_1 \ {\bf w}_2 \ \cdots \ {\bf w}_M \right]
\end{eqnarray}
where ${\bf w}_m \in \mathbb{R}^D$ denotes the $m$-th GRU hidden feature, and $D$ is the dimension of the hidden feature.
Each ${\bf w}_m$ is L2 normalized to output a unit vector.
\subsubsection{Video representation}
Video is encoded using a C3D \cite{C3D} model pre-trained on Sports-1M dataset \cite{Sports1M} as in \cite{TALL}.
The feature was extracted at every 16 frames for Charades-STA.
The VGG16 model \cite{VGG} is used for frame-level feature extraction for DiDeMo dataset following \cite{MCN}.
Both C3D and VGG16 features were extracted from the penultimate fully-connected layer, which results in the feature dimension of 4096.
\subsubsection{Video proposal generation}
\begin{figure}[t]
\centering
\begin{subfigure}[t]{0.45\textwidth}
\includegraphics[width=\linewidth, height=10em]{images/prop_a.png}
\caption{Multi-scale proposal generation}
\end{subfigure}
\begin{subfigure}[t]{0.45\textwidth}
\includegraphics[width=\linewidth, height=10em]{images/prop_b.png}
\caption{Surrogate Proposal Selection}
\end{subfigure}
\caption{Comparison between the previous and the proposed proposal generation method. (a) generates large number of proposals of various lengths. (b) groups the proposals, and selects the surrogate proposals based on the proximity to the query. }
\label{fig:proposal}
\end{figure}
As depicted in image Figure \ref{fig:proposal}(a) previous methods \cite{that,SCN} generated proposals using multi-scale sliding windows.
Meanwhile, as in Figure \ref{fig:proposal}(b), VLANet organizes the multi-scale windows in segment groups such that within a group, all windows start at the same time instance.
Each group will have the same number of windows of fixed scales.
The interval between the starting times of each segment group is regular.
With $K$ segment groups and $L$ multi-scale proposals, the total number of proposals is $K \cdot L$.
Then, the video $V$ is represented by:
\begin{eqnarray}
V = \begin{bmatrix}
{\bf p}_{11} & {\bf p}_{12} & \cdots & {\bf p}_{1K} \\
{\bf p}_{21} & {\bf p}_{22} & \cdots & {\bf p}_{2K} \\
\vdots & & \cdots & \\
{\bf p}_{L1} & {\bf p}_{L2} & \cdots & {\bf p}_{LK}
\end{bmatrix}
\end{eqnarray}
where each ${\bf p}_{lk} \in \mathbb{R}^{D}$ denotes the proposal feature of the $l$-th scale in the $k$-th segment group, which is the average of the C3D features of the frames participating in the proposal.
Fully-connected layers are used to resize the feature dimension of $Q$ and $V$ to $D$.
L2 normalization is performed to make each ${\bf p}_{lk}$ a unit vector.
\subsection{Surrogate Proposal Selection module}
To reduce the large number of proposals, \cite{SCN} proposed a sampling-based selection algorithm to prune out irrelevant proposals considering the exploration and exploitation.
However, the method is trained using policy gradient algorithm \cite{PG} which suffers from high variance.
Instead, as depicted in Figure \ref{fig:proposal}(b), the Surrogate Proposal Selection module selects the best-matched proposals from each segment group based on the cosine similarity to the final hidden feature of the query.
A surrogate proposal of the $k$-th segment group is defined as the proposal that has the largest cosine similarity to the final hidden feature of the query.
The cosine similarity between each proposal and query is given by
\begin{eqnarray}
\begin{bmatrix}
{\bf p}_{11} \cdot {\bf w}_M & {\bf p}_{12} \cdot {\bf w}_M & \cdots & {\bf p}_{1K} \cdot {\bf w}_M \\
{\bf p}_{21} \cdot {\bf w}_M & {\bf p}_{22} \cdot {\bf w}_M & \cdots & {\bf p}_{2K} \cdot {\bf w}_M \\
\vdots & & \cdots & \\
{\bf p}_{L1} \cdot {\bf w}_M & {\bf p}_{L2} \cdot {\bf w}_M & \cdots & {\bf p}_{LK} \cdot {\bf w}_M
\end{bmatrix}
\end{eqnarray}
where ${\bf w}_M$ is the final hidden feature of the query.
It is empirically determined that the final hidden query feature is sufficient in pruning out irrelevant proposals at a low computational cost.
The Surrogate Proposal Selection module pick the $l^{\prime}$-th scale from each $k$-th segment group which is given by,
\begin{eqnarray}
& l^{\prime} = \mbox{argmax}\left[ {\bf p}_{1k} \cdot {\bf w}_M \ {\bf p}_{2k} \cdot {\bf w}_M \ \cdots \ {\bf p}_{Lk} \cdot {\bf w}_M \right], \\
& {\bf s}_{k} = {\bf p}_{l^{\prime}k}
\end{eqnarray}
where ${\bf s}_k$ is the surrogate proposal feature of the $k$-th segment group.
In backpropagation, only the surrogate proposals ${\bf s}_{k}$'s contribute to the weight update which allows end-to-end learning.
Then the video is represented by $K$ surrogate proposal features:
\begin{eqnarray}
\mathcal{V} = \left[ {\bf s}_1 \ {\bf s}_2 \ \cdots \ {\bf s}_K \right]
\end{eqnarray}
where $\mathcal{V}$ is the updated video representation composed of the surrogate proposals.
\subsection{Cascaded Cross-modal Attention module}
Cascaded Cross-modal Attention (CCA) module takes the video and query representations as inputs, and outputs a compact attended video representation. Compared to text-guided attention (TGA) \cite{that}, CCA module considers more diverse multi-modal feature interactions including V2V, Q2Q, V2Q, and Q2V where each has its own advantages as described below.
\subsubsection{Dense Attention}
\label{sssec:dense_attention}
The basic attention unit of CCA module is referred to as Dense Attention which calculates the attention between two multi-element features.
Given $Y=[{\bf y}_1 \ldots {\bf y}_M]^T\in \mathbb{R}^{M \times D}$ and $X=[{\bf x}_1 \ldots {\bf x}_N]^T \in \mathbb{R}^{N \times D}$, the Dense Attention $A(X,Y) : \mathbb{R}^{N \times D} \times \mathbb{R}^{M \times D} \rightarrow \mathbb{R}^{N \times D} $ attends $X$ using $Y$ and is defined as follows:
\begin{eqnarray}
& \mathcal{E}({\bf x}_n,Y) = \sum_{m=1}^{M} \mbox{tanh}(W_1 {\bf x}_n \cdot W_2 {\bf y}_m), \\
& A(X,Y) = \mbox{Softmax}(\left[ \mathcal{E}({\bf x}_1,Y) \ \mathcal{E}({\bf x}_2,Y) \ \cdots \ \mathcal{E}({\bf x}_N,Y)\right]) X,
\end{eqnarray}
where $W_1, W_2$ are learnable parameters. Here, $\mathcal{E}: \mathbb{R}^D \times \mathbb{R}^{M \times D} \rightarrow \mathbb{R}$ is referred to as the Video-Language Alignment (VLA) function that performs the multi-modal alignment.
\subsubsection{Self-attention}
Based on the Dense Attention defined above, the CCA module initially performs a type of self-attention that attends $\mathcal{V}$ and $Q$ using $\mathcal{V}$ and $Q$ respectively as given below,
\begin{eqnarray}
\mathcal{V} \leftarrow A(\mathcal{V},\mathcal{V}), \\
Q \leftarrow A(Q,Q).
\end{eqnarray}
The intra-attention allows each element of itself to be attended by its global contextual information.
The attention from $\mathcal{V}$ to $\mathcal{V}$ is capable of highlighting the salient proposals by considering the innate temporal relationships.
The attention from $Q$ to $Q$ updates the each word-level feature by considering the context of the whole sentence.
\subsubsection{Cross modal attention}
Following self-attention defined above, the CCA module is used to cross-attend $\mathcal{V}$ and $Q$ using $Q$ and $\mathcal{V}$ respectively such that cross-modal attention is defined as follows:
\begin{eqnarray}
\mathcal{V} \leftarrow A(\mathcal{V},Q), \\
Q \leftarrow A(Q,\mathcal{V}).
\end{eqnarray}
The above attention is critical in learning the latent multi-modal alignment.
It has been empirically observed that cross-modal attention applied in series several times until near-saturation can be conducive in producing better performance.
Finally, a compact attended video representation ${\bf v}_{comp}$ is obtained by taking the sum of all elements of $\mathcal{V}$, and video-level similarity $c$ is obtained by the VLA function between ${\bf v}_{comp}$ and $Q$ as given below:
\begin{eqnarray}
c = \mathcal{E}({\bf v}_{comp},Q).
\end{eqnarray}
The network is trained using the following contrastive loss:
\begin{eqnarray}
\mathcal{L}_{contrastive} = max[0, \Delta - \mathcal{E}({\bf v}_{comp},Q^+) + \mathcal{E}({\bf v}_{comp},Q^-)]
\end{eqnarray}
where $\mathcal{E}$ is the VLA function defined above in section \ref{sssec:dense_attention} and $\Delta$ is the margin. $Q^+$ and $Q^-$ is positive and negative query features.
\section{Experiment}
\subsection{Datasets}
\subsubsection{Charades-STA}
The Charades dataset was originally introduced in \cite{Charades}.
It contains temporal activity annotation and multiple video-level descriptions for each video.
Gao \textit{et al.} \cite{TALL} generated temporal boundary annotations for sentences using a semi-automatic way and released the Charades-STA dataset that is for video moment retrieval.
The dataset includes 12,408 video-sentence pairs with temporal boundary annotations for training and 3,720 for testing.
The average length of the query is 8.6 words, and the average duration of the video is 29.8 seconds.
\subsubsection{DiDeMo}
The Distinct Describable Moments (DiDeMo) dataset \cite{MCN} consists of over 10,000 unedited, personal videos in diverse visual settings with pairs of localized video segments and referring expressions.
The videos are collected from Flickr and each video is trimmed to a maximum of 30 seconds.
The dataset includes 8,395, 1,065 and 1,004 videos for train, validation, and test, respectively.
The videos are divided into 5-second segments to reduce the complexity of annotation, which results in 21 possible moments per video.
The dataset contains a total of 26,892 moments with over 40,000 text descriptions.
The descriptions in the DiDeMo dataset are natural language sentences that contain activities, camera movement, and temporal transition indicators.
Moreover, the descriptions in DiDeMo are verified to refer to a single moment.
\subsubsection{Evaluation Metric}
For Charades-STA, the evaluation metric proposed by \cite{TALL} is adopted to compute "R@n, IoU=m".
For the test set predictions, the recall R@n calculates the percentage of samples for which the correct result resides in the top-n retrievals to the query.
If the IoU between the prediction and the ground truth is greater than or equal to $m$, the prediction is correct.
The overall performance is the average recall on the whole test set.
For DiDeMo, the evaluation metric proposed by \cite{MCN} is adopted.
The evaluation metric is also R@n with different criteria for correct prediction.
If the ground truth moment is in the top-n predictions, the prediction for the sample is counted as correct.
The mIoU metric is computed by taking the average of the IoU between the predicted moment and the ground truth moment.
\begin{table}[t]
\centering
\caption{Performance comparison of VLANet to the related methods on Charades-STA}\smallskip
\begin{tabular}{c|l||c c c | c c c}
\Xhline{3\arrayrulewidth}
\multirow{2}{*}{Type} & \multirow{2}{*}{Method} & & R@1 & & & R@5 & \\ & & IoU=0.3 & IoU=0.5 & IoU=0.7 & IoU=0.3 & IoU=0.5 & IoU=0.7 \\ \Xhline{3\arrayrulewidth}
Baseline & Random & 19.78 & 11.96 & 4.81 & 73.62 & 52.79 & 21.53 \\ \hline
\multirow{5}{*}{Fully}
& VSA-RNN \cite{TALL} & - & 10.50 & 4.32 & - & 48.43 & 20.21 \\
& VSA-STV \cite{TALL} & - & 16.91 & 5.81 & - & 53.89 & 23.58 \\
& CTRL \cite{TALL} & - & 23.63 & 8.89 & - & 58.92 & 29.52 \\
& EFRC \cite{EFRC} & 53.00 & 33.80 & 15.00 & 94.60 & 77.30 & 43.90 \\
& MAN \cite{MAN} & - & 46.53 & 22.72 & - & 86.23 & 53.72
\\ \hline
\multirow{3}{*}{Weakly}
& TGA \cite{that} & 32.14 & 19.94 & 8.84 & 86.58 & 65.52 & 33.51 \\
& SCN \cite{SCN} & 42.96 & 23.58 & 9.97 & 95.56 & 71.80 & {\bf 38.87} \\
& \bf{VLANet (ours)} & \bf{45.24} & \bf{31.83} & \bf{14.17} & \bf{95.70} & \bf{82.85} & 33.09 \\
\Xhline{3\arrayrulewidth}
\end{tabular}
\label{tab:quantitative_1}
\end{table}
\begin{table}[t]
\centering
\caption{Performance comparison of VLANet to the related methods on DiDeMo}\smallskip
\begin{tabular}{c|l||c c c}
\Xhline{3\arrayrulewidth}
Type & Method & R@1 & R@5 & mIoU \\
\Xhline{3\arrayrulewidth}
\multirow{3}{*}{Baseline}
& Upper Bound & 74.75 & 100 & 96.05 \\
& Random & 3.75 & 22.50 & 22.64 \\
& LSTM-RGB-Local \cite{MCN} & 13.10 & 44.82 & 25.13 \\ \hline
\multirow{5}{*}{Fully}
& Txt-Obj-Retrieval \cite{TOR} & 16.20 & 43.94 & 27.18 \\
& EFRC \cite{EFRC} & 13.23 & 46.98 & 27.57 \\
& CCA \cite{CCA} & 18.11 & 52.11 & 37.82 \\
& MCN \cite{MCN} & 28.10 & 78.21 & 41.08 \\
& MAN \cite{MAN} & 27.02 & 81.70 & 41.16 \\ \hline
\multirow{2}{*}{Weakly}
& TGA \cite{that} & 12.19 & 39.74 & 24.92 \\
& {\bf VLANet (ours)}& {\bf 19.32} & {\bf 65.68} & {\bf 25.33} \\ \hline
\Xhline{3\arrayrulewidth}
\end{tabular}
\label{tab:quantitative_2}
\end{table}
\subsection{Quantitative result}
Table \ref{tab:quantitative_1} shows the performance comparison between VLANet and the related methods on Charades-STA.
The first section indicates random baseline, the second section indicates fully-supervised methods, and the third section indicates weakly-supervised methods.
VLANet achieves state-of-the-art performance on Charades-STA among weakly-supervised methods.
It outperforms the random baseline, VSA-RNN, and VSA-STV by a large margin.
Compared to the other fully-supervised methods such as CTRL and EFRC, its performance is comparable.
Besides, compared to the other weakly-supervised methods TGA and SCN, VLANet outperforms others by a large margin.
Table \ref{tab:quantitative_2} shows the performance comparison on DiDeMo.
The first section contains the baselines, the second section contains fully-supervised methods, and the third section contains weakly-supervised methods.
VLANet achieves state-of-the-art performance among the weakly-supervised methods.
In the R@5 based test, especially, its performance is 25.94 higher than the runner-up model TGA.
It is comparable to some fully-supervised methods such as CCA \footnote{Here, CCA refers to a previous method \cite{CCA}, but not Cascaded Cross-modal Attention proposed in this paper.} and Txt-Obj-Retrieval.
These indicate that even without the full annotations of temporal boundary, VLANet has the potential to learn latent multi-modal alignment between video and query, and to localizing semantically relevant moments.
\begin{table}[t]
\centering
\caption{Performance of model variants and ablation study of VLANet on Charades-STA. The unit of stride and window size is frame. }\smallskip
\begin{tabular}{l||c c c | c c c}
\Xhline{3\arrayrulewidth}
\multirow{2}{*}{Method} & & R@1 & & & R@5 & \\ & IoU=0.3 & IoU=0.5 & IoU=0.7 & IoU=0.3 & IoU=0.5 & IoU=0.7 \\ \Xhline{3\arrayrulewidth}
stride 4, window(176, 208, 240) & 44.76 & 31.53 & 14.78 & 77.04 & 63.17 & 31.80 \\
stride 6, window(176, 208, 240) & 42.17 & 28.60 & 12.98 & 88.76 & 74.91 & {\bf 34.70} \\
stride 8, window(176, 208, 240) & 45.03 & 31.82 & 14.19 & 95.72 & 82.82 & 33.33 \\
stride 6, window(128, 256) & 42.39 & 28.03 & 13.09 & 94.70 & 73.06 & 30.69 \\
stride 6, window(176, 240) & 42.92 & 30.24 & 13.57 & 95.72 & 82.80 & 33.46 \\ \hline
w/o cross-attn & 43.41 & 30.08 & 13.23 & 95.72 & 82.41 & 33.06 \\
w/o self-attn & 42.31 & 30.81 & 15.38 & 95.38 & 80.02 & 33.76 \\
w/o surrogate & 35.81 & 25.30 & 12.26 & 80.61 & 64.57 & 31.31 \\ \hline
\bf{full model} & \bf{45.03} & \bf{31.82} & \bf{14.19} & \bf{95.72} & \bf{82.82} & 33.33 \\
\Xhline{3\arrayrulewidth}
\end{tabular}
\label{tab:ablation}
\end{table}
\subsection{Model variants and ablation study}
Table \ref{tab:ablation} summarizes the performance of model variants and the ablation study conducted on VLANet.
The first section shows the performance variation by varying stride and window sizes, and the second section shows the performance drop without core components.
The strides and the sizes of the windows were determined by considering the average video length.
The first three rows show that the network performs best with the stride of 8.
While the proposals with stride 4 have finer granularity, the large number of proposals decreases the performance.
The networks with three multi-scale proposals tend to achieve higher performance than the networks with two multi-scale proposals.
This shows the importance of stride and the number of scales.
After finding the best hyper-parameters of `stride 8, window(176, 208, 240)'\, these values were fixed for the subsequent experiments and analyses.
The network without cross-attention, self-attention show a decrease in performance, demonstrating the importance of the attention mechanisms.
We generally notice a drop in performance with an increasing IoU metric. The drop is more drastic without cross-attention than without self-attention. This observation indicates that cross-modal attention has a larger influence on performance than self-attention.
The performance of w/o surrogate is decreased significantly across all metrics. This indicates that selecting probable proposals in the early stage is critical to the performance.
\subsection{Analysis of multi-modal similarity}
Figure \ref{fig:separation} shows similarity predicted by the network on the whole test set of Charades-STA while training.
The x-axis indicates the epoch of training, and the y-axis indicates the similarity.
It is observed that the similarity scores of the positive pairs (blue) increase and reach a high plateau of about 0.9, while those of the negative pairs (red) keep a low value of about 0.15.
These demonstrate that contrastive learning was successfully conducted.
\begin{figure}[t]
\centering
\includegraphics[width=7cm]{./images/EpochSim_13font_legend.png}
\caption{The multi-modal similarity prediction by VLANet on the positive and negative pairs while training. The similarity gap increases as epoch increases. }
\label{fig:separation}
\end{figure}
\begin{figure}[t]
\centering
\includegraphics[width=\textwidth]{./images/Q2_2print.PNG}
\caption{Visualization of Cascaded Cross-modal Attention. The attention map is calculated by the outer-product of video and query features that are obtained after the Cascaded Cross-modal Attention module and before the
pooling layer. }
\label{fig:attention}
\end{figure}
\subsection{Visualization of attention map}
Figure \ref{fig:attention} visualizes the attention map of the proposed Cascaded Cross-modal Attention.
The x-axis indicates the words in the query and the y-axis indicates the time.
In the left example, the attention weight of the ``put the sandwich down" is high when the person is putting the sandwich down.
Similarly in the right example, important words such as action or object have high attention weight with the related moment of the video.
The high attention weights are biased on the right side in Figure \ref{fig:attention} as the final GRU feature has the context information about the whole sentence.
The above example demonstrates that VLANet can learn the latent multi-modal alignment.
\begin{figure}[t]
\centering
\includegraphics[width=11cm]{./images/inference8}
\caption{At inference time, VLANet successfully retrieves the moment described by the query. Due to the limited space, only some proposals are visualized. The color indicates the attention strength. The top-2 predicted moments are visualized with the temporal boundaries. }
\label{fig:inference}
\end{figure}
\subsection{Visualization of inference}
Figure \ref{fig:inference} provides a visualization of the inference of VLANet.
Only a subset of total proposals were depicted whose color indicates the attention strength.
In the first example, both top-1 and top-2 predictions by VLANet have high overlaps with the ground truth moment.
In the second example, the network localizes the moment when the person actually \textit{opens} the refrigerator.
Similarly in the third example, the network localizes the moment when person \textit{puts} the pillow.
This shows that the network successfully captures the moment when a certain action is taken or an event occurs.
The inference visualization demonstrates the moment retrieval ability of VLANet and suggests its applicability to real-world scenarios.
\section{Conclusions}
This paper considers Video-Language Alignment Network (VLANet) for weakly-supervised video moment retrieval.
VLANet is able to select appropriate candidate proposals using a more detailed query representation that include intermediate hidden features of the GRU.
The Surrogate Proposal Selection module reduces the number of candidate proposals based on the similarity between each proposal and the query. The ablation study reveals that it has the largest influence on performance.
The Cascaded Cross-modal Attention module performs a modified self-attention followed by a cascade of cross-attention based on the Dense Attention defined. It also has a significant influence on performance.
VLANet is trained in an end-to-end manner using contrastive loss which enforces semantically similar videos and queries to cluster in the joint embedding space.
The experiments shows that VLANet achieves state-of-the-art performance on Charades-STA and DiDeMo datasets.
\section*{Acknowledgement}
This work was partly supported by Institute for Information \& communications Technology Planning \& Evaluation(IITP) grant funded by the Korea government(MSIT) (2017-0-01780, The technology development for event recognition/relational reasoning and learning knowledge based system for video understanding) and partly supported by Institute for Information \& communications Technology Planning \& Evaluation(IITP) grant funded by the Korea government(MSIT) (No. 2019-0-01396, Development of framework for analyzing, detecting, mitigating of bias in AI model and training data)
\clearpage
\bibliographystyle{splncs04}
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Todd County Funeral Home
Send Flowers for Alpha
Alpha Kay Jenkins
November 9, 1935 ~ December 16, 2021 (age 86)
Alpha Kay Jenkins, age 86 of Elkton, passed away on Thursday, December 16th at the Hospice House of Southern Kentucky in Bowling Green of natural causes.
She was born November 9, 1935 in Butler County, Kentucky the daughter of the late Avery and Elsie Christie Jenkins.
She was a member of the Collier Springs Baptist Church. She loved her family, animals, bird watching and playing Bingo.
In addition to her parents, she was preceded in death by a brother, James Jenkins and two sisters, Lucy Mae Bauduin and Lorraine Board. She is survived by a sister, Omega Richmond of Elkton.
Visitation with the family will be on Sunday, December 19th from 12:00 until funeral service time at 2:00 in the Rose Chapel of the Todd County Funeral Home with Shane Hessey officiating. Interment will follow at the Pleasant Hill Cemetery in Claymour.
In lieu of flowers, the family request that donations be made to the Hospice House of Southern Kentucky.
To send flowers to the family or plant a tree in memory of Alpha Kay Jenkins, please visit our floral store.
Visitation Before Funeral
Todd County Funeral Home & Cremation Services
Elkton, KY 42220
Pleasant Hill Church Cemetery
120 Pleasant Hill Church Road
© 2022 Todd County Funeral Home. All Rights Reserved. Funeral Home website by CFS & TA | Terms of Use | Privacy Policy
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\section{Introduction}\label{Sec:Introduction}
In this paper, we consider mixed integer linear programs with two
equality constraints, two free integer variables and any number of
nonnegative continuous variables. We assume that the two integer
variables are expressed in terms of the remaining variables as
follows.
\begin{equation} \label{SI}
\begin{array}{rrcl}
& x & = & f + \sum_{j=1}^{k} r^j s_j \\
& x & \in & \mathbb{Z}^2 \\
& s & \in & \mathbb{R}_+^k .
\end{array}
\end{equation}
This model was introduced by Andersen, Louveaux, Weismantel and Wolsey \cite{alww}. It is a natural relaxation of a general mixed integer linear
program (MILP) and therefore it can be used to generate cutting
planes for MILP. Currently, MILP solvers rely on cuts that
can be generated from a single equation (such as Gomory mixed integer cuts
\cite{go}, MIR cuts \cite{mw}, lift-and-project cuts \cite{bcc},
lifted cover inequalities \cite{cjp}). Model (\ref{SI}) has attracted
attention recently as a way of generating new families of cuts from two
equations instead of just a single one \cite{alww,cm,dw,esp, go07}.
We assume $f \in \mathbb{Q}^2 \setminus \mathbb{Z}^2$, $k \ge 1$,
and $r^j \in \mathbb{Q}^2 \setminus \left\{ 0 \right\}$. So $s=0$ is
not a solution of (\ref{SI}). Let $R_f(r^1,\ldots,r^k)$ be the
convex hull of all vectors $s \in \mathbb{R}_+^k$ such that $f +
\sum_{j=1}^{k} r^j s_j$ is integral. A classical theorem of Meyer
\cite{meyer} implies that $R_f(r^1,\ldots,r^k)$ is a polyhedron.
Andersen, Louveaux, Weismantel and Wolsey \cite{alww} showed that
the facets of $R_f(r^1,\ldots,r^k)$ are $s \geq 0$ (called {\it
trivial inequalities}), split inequalities \cite{COOK} and
intersection cuts (Balas \cite{bal}) arising from triangles or
quadrilaterals in $\mathbb{R}^2$. Borozan and Cornu\'ejols \cite{bc}
investigated a relaxation of (\ref{SI}) where the vector $(s_1,
\ldots, s_k) \in \mathbb{R}_+^k$ is extended to infinite dimensions
by defining it for all directions $r^j \in \mathbb{Q}^2$ instead of
just $r^1, \ldots , r^k$. Namely let $R_f$ be the convex hull of all
infinite-dimensional vectors $s$ with finite support that satisfy
\begin{equation} \label{SIinfinite}
\begin{array}{rrcl}
& x & = & f + \sum_{r \in \mathbb{Q}^2} r s_r \\
& x & \in & \mathbb{Z}^2 \\
& s & \geq & 0.
\end{array}
\end{equation}
Theorem~\ref{THM:minfunc} below shows that there is a one-to-one
correspondance between minimal valid inequalities for $R_f$ and
maximal lattice-free convex sets that contain $f$ in their interior.
By {\em lattice-free convex set} we mean a convex set with
no integral point in its interior. However integral points are
allowed on the boundary. These maximal lattice-free convex sets
are splits, triangles, and quadrilaterals
as proved in the following theorem of Lov\'asz \cite{lovasz}.
\begin{theorem} \label{THM:maxconv}
{\em (Lov\'asz \cite{lovasz})}
In the plane,
a maximal lattice-free convex set with nonempty interior
is one of the following:
\begin{itemize}
\item[(i)] A split $c \le a x_1 + b x_2 \le c+1$ where $a$ and $b$ are coprime
integers and $c$ is an integer;
\item[(ii)] A triangle with an integral point in the interior of each of its edges;
\item[(iii)] A quadrilateral containing exactly four integral points,
with exactly one of them in the interior of each of its edges;
Moreover, these four integral points are vertices of a parallelogram
of area 1.
\end{itemize}
\end{theorem}
$R_f(r^1,\ldots,r^k)$ is a polyhedron of blocking type, i.e.
$R_f(r^1,\ldots,r^k) \subseteq \mathbb{R}^k_+$ and if $x \in
R_f(r^1,\ldots,r^k)$, then $y \geq x$ implies $y \in
R_f(r^1,\ldots,r^k)$. Similarly $R_f$ is a convex set of blocking
type. Any nontrivial valid linear inequality for $R_f$ is of the
form
\begin{equation} \label{valid:infinite}
\sum_{r \in \mathbb{Q}^2} \psi(r) s_r \geq 1
\end{equation}
where $\psi: \mathbb{Q}^2 \rightarrow \mathbb{R}$. The nontrivial
valid linear inequalities for $R_f(r^1,\ldots,r^k)$ are the
restrictions of (\ref{valid:infinite}) to $r^1, \ldots , r^k$
\cite{cm}:
\begin{equation} \label{valid}
\sum_{j=1}^k \psi(r^j) s_j \geq 1.
\end{equation}
A nontrivial valid linear inequality for $R_f$ is {\em minimal} if
there is no other nontrivial valid inequality $\sum_{r \in
\mathbb{Q}^2} \psi'(r) s_r \geq 1$ such that $\psi'(r) \leq \psi(r)$
for all $r \in \mathbb{Q}^2$.
\begin{theorem} \label{THM:minfunc}
{\em (Borozan and Cornu\'ejols \cite{bc})} Minimal nontrivial valid
linear inequalities for $R_f$ are associated with functions $\psi$
that are nonnegative positively homogeneous piecewise linear and
convex. Furthermore, the closure of the set
\begin{equation} \label{Bpsi}
B_{\psi} := \{ x \in \mathbb{Q}^2: \; \psi(x-f) \leq 1 \}
\end{equation}
is a maximal lattice-free convex set containing $f$ in its interior.
\end{theorem}
Conversely, any maximal lattice-free convex set $B$ with $f$ in its
interior defines a function $\psi_B: \mathbb{R}^2 \rightarrow
\mathbb{R}_+$ that can be used to generate a minimal nontrivial
valid linear inequality. Indeed, define $\psi_B(0) = 0$ and
$\psi_B(x-f)=1$ for all points $x$ on the boundary of $B$. Then, the
positive homogeneity of $\psi_B$ implies the value of $\psi_B(r)$
for any vector $r \in \mathbb{R}^2 \setminus \{ 0 \}$: If there is a
positive scalar $\lambda$ such that the point $f + \lambda r$ is on
the boundary of $B$, we get that $\psi_B(r) = 1/\lambda$. Otherwise,
if there is no such $\lambda$, $r$ is an unbounded direction of $B$
and $\psi_B(r) = 0$.
Note that the above construction of $\psi_B$ is nothing but the derivation of the intersection cut as introduced by Balas \cite{bal}.
Following Dey and Wolsey \cite{dw}, the maximal lattice-free
triangles can be partitioned into three types (see Figure
\ref{The4cases}):
\begin{itemize}
\item {\it Type 1 triangles}: triangles with integral vertices
and exactly one integral point in the relative interior of each edge;
\item {\it Type 2 triangles}: triangles with at least one fractional
vertex $v$, exactly one integral point in the relative interior
of the two edges incident to $v$ and at least two integral points
on the third edge;
\item {\it Type 3 triangles}: triangles with exactly three integral
points on the boundary, one in the relative interior
of each edge.
\end{itemize}
Figure \ref{The4cases} shows these three types of triangles as well as
a maximal lattice-free quadrilateral and a split satisfying the properties of
Theorem \ref{THM:maxconv}.
\begin{figure}[htbp]
\centering \scalebox{0.6}{ \epsfig{file=lattice_free_sets.eps} }
\caption{Maximal lattice-free convex sets with nonempty interior in
$\mathbb{R}^2$} \label{The4cases}
\end{figure}
In this paper we will need conditions guaranteeing that a split,
triangle or quadrilateral actually defines a facet of
$R_f(r^1,\ldots,r^k)$. Such conditions were obtained by Cornu\'ejols
and Margot \cite{cm} and will be stated in Theorem
\ref{THM:mainRfk}.
\subsection{Motivation}
\label{SUB:MOTIVATION}
An unbounded maximal lattice-free convex set is called a
{\it split}. It has two parallel edges whose direction is called the
{\it direction} of the split. Split inequalities for (\ref{SI}) are
valid inequalities that can be derived by combining the two
equations in (\ref{SI}) and by using the integrality of $\pi_1 x_1 +
\pi_2 x_2$, where $\pi \in \mathbb{Z}^2$ is normal to the
direction of the split. Similarly, for general MILPs, the
equations can be combined into a single equality from which a split
inequality is derived. Split inequalities are equivalent to Gomory
mixed integer cuts \cite{nw}. Empirical evidence shows that split
inequalities can be effective for strengthening the linear
programming relaxation of MILPs \cite{balsax,dgl}. Interestingly,
triangle and quadrilateral inequalities cannot be derived from a
single equation \cite{alww}. They can only be derived from (\ref{SI}) without
aggregating the two equations. Recent computational experiments by
Espinoza \cite{esp} indicate that quadrilaterals also induce
effective cutting planes in the context of solving general MILPs. In
this paper, we consider the relative strength of split, triangle and
quadrilateral inequalities from a theoretical point of view. We use
an approach for measuring strength initiated by Goemans
\cite{goemans}, based on the following definition and results.
Let $Q \subseteq \mathbb{R}_+^n \setminus \{ 0 \}$ be a polyhedron
of the form $Q = \{ x: \; a^i x \geq b_i \mbox{ for } i=1, \ldots ,
m \}$ where $a^i \geq 0$ and $b_i \geq 0$ for $i = 1 , \ldots , m$
and let $\alpha > 0$ be a scalar. We define the polyhedron $\alpha
Q$ as $\{ x: \; \alpha a^i x \geq b_i \mbox{ for } i=1, \ldots , m
\}$. Note that $\alpha Q$ contains $Q$ when $\alpha \geq 1$. It will
be convenient to define $\alpha Q$ to be $\mathbb{R}_+^n$ when
$\alpha = + \infty$.
We need the following generalization of a theorem of Goemans \cite{goemans}.
\begin{theorem} \label{THM:goemans}
Suppose $Q \subseteq \mathbb{R}_+^n \setminus \{ 0 \}$ is defined as
above. If convex set $P \subseteq \mathbb{R}^n_+$ is a relaxation of
$Q$ (i.e. $Q \subseteq P$), then the smallest value of $\alpha \ge 1$
such that $P \subseteq \alpha Q$ is
$$\max_{i=1, \ldots, m} \left\{\frac{b_i}{\inf\{ a^i x \ : \ \ x \in P\}} \ :
\ b_i > 0\ \right\}.$$ Here, we define $\frac{b_i}{\inf\{ a^i x \ :
\ \ x \in P\}}$ to be $+\infty$ if $\inf\{ a^i x \ : \ \ x \in P\} =
0$.
\end{theorem}
In other words, the only directions that need to be considered to
compute $\alpha$ are those defined by the nontrivial facets of $Q$.
Goemans' paper assumes that both $P$ and $Q$ are polyhedra, but one
can easily verify that only the polyhedrality of $Q$ is needed in
the proof. We give the proof of Theorem \ref{THM:goemans} in Section
\ref{SEC:goemans_proof}, for completeness.
\subsection{Results}\label{SEC:Results}
Let the {\it split closure} $S_f(r^1,\ldots,r^k)$ be the
intersection of all split inequalities, let the {\it triangle
closure} $T_f(r^1,\ldots,r^k)$ be the intersection of all
inequalities arising from maximal lattice-free triangles, and let
the {\it quadrilateral closure} $Q_f(r^1,\ldots,r^k)$ be the
intersection of all inequalities arising from maximal lattice-free
quadrilaterals. In the remainder of the paper, to simplify notation,
we refer to $R_f(r^1,\ldots,r^k)$, $S_f(r^1,\ldots,r^k)$,
$T_f(r^1,\ldots,r^k)$ and $Q_f(r^1,\ldots,r^k)$ as $R_f^k, S_f^k,
T_f^k$ and $Q_f^k$ respectively, whenever the rays $r^1,\ldots,r^k$
are obvious from the context.
Since all the facets of $R_f^k$ are induced by these three families
of maximal lattice-free convex sets, we have
$$R_f^k=S_f^k \cap T_f^k \cap Q_f^k.$$
It is known that the split closure is a polyhedron (Cook, Kannan and
Schrijver \cite{COOK}) but such a result is not known for the
triangle closure and the quadrilateral closure.
In this paper we show the following results.
\begin{theorem} \label{THM:inclusion}
$T_f^k \subseteq S_f^k$ and $Q_f^k \subseteq S_f^k.$
\end{theorem}
This theorem may seem counter-intuitive because some split
inequalities are facets of $R_f^k$. However, we show that any split
inequality can be obtained as the limit of an infinite collection of
triangle inequalities. What we will show is that, if a point is cut
off by a split inequality, then it is also cut off by some triangle
inequality. Consequently, the intersection of \emph{all} triangle
inequalities is contained in the split closure. The same is true of
the quadrilateral closure.
\begin{example}
\label{TfEx} As an illustration, consider the simple example in
Figure \ref{FIG:TfEx}. The split inequality is $s_1 \ge 1$ and the
split closure is given by $S_f^2 = \{(s_1, s_2) \ | \ s_1 \ge 1, s_2
\ge 0\}$. All triangle inequalities are of the form $a s_1 + b s_2
\ge 1$ with $a \ge 1$ and $b > 0$. The depicted triangle inequality
is of the form $s_1 + 2 s_2 \ge 1$ and by moving the corner $v$
closer to the boundary of the split, one can get a triangle
inequality of the form $s_1 + b s_2 \ge 1$ with $b$ tending to 0,
but remaining positive. Note that the split inequality can not be
obtained as a positive combination of triangle inequalities, but any
point cut by the split inequality is cut by one of the triangle
inequalities. As a result, the triangle closure is $T_f^2 = \{(s_1,
s_2) \ | \ s_1 + b s_2 \ge 1, \mbox{\ for \ all \ } b > 0, s_1 \ge
0, s_2 \ge 0\} = S_f^2$. \flushright\qed
\end{example}
\begin{figure}[htbp]
\centering \scalebox{0.45}{\epsfig{file=TfEx.eps}}
\caption{Illustration for Example \ref{TfEx}} \label{FIG:TfEx}
\end{figure}
We further study the strength of the triangle closure and
quadrilateral closure in the sense defined in Section
\ref{SUB:MOTIVATION}. We first compute the strength of a single Type
1 triangle facet as $f$ varies in the interior of the triangle,
relative to the entire split closure.
\begin{theorem}
\label{THM:T1split} Let $T$ be a Type 1 triangle as depicted in
Figure \ref{FIG:T1split}. Let $f$ be in its interior and assume that
the set of rays $\{r^1,\ldots ,r^k\}$ contains rays pointing to the
three corners of $T$. Let $\sum_{i=1}^{k} \psi(r^i) s_i\ge 1$ be the
inequality generated by $T$. The value
$$
\min\left\{ \sum_{i=1}^k \psi(r^i)s_i \ : \; s \in S_f^k \right\}
$$
is a piecewise linear function of $f$ for which some level curves
are depicted in Figure \ref{FIG:T1split}. This function varies from
a minimum of $\frac{1}{2}$ in the center of $T$ to a maximum of
$\frac{2}{3}$ at its corners.
\end{theorem}
\begin{figure}[htbp]
\centering \scalebox{0.7}{\epsfig{file=Type1_triangle.eps}}
\caption{Illustration for Theorem
\ref{THM:T1split}}\label{FIG:T1split}
\end{figure}
Next we show that both the triangle closure and the quadrilateral
closure are good approximations of the integer hull $R_f^k$ in the
sense that
\begin{theorem} \label{THM:T&Q} $\;$
$R_f^k \subseteq T_f^k \subseteq 2 R_f^k$ and
$R_f^k \subseteq Q_f^k \subseteq 2 R_f^k.$
\end{theorem}
Finally we show that the split closure may not be a good
approximation of the integer hull.
\begin{theorem} \label{THM:T&Q_2} For any $\alpha > 1$, there is a
choice of $f$, $r^1, \ldots , r^k$ such that
$S_f^k \not\subseteq \alpha R_f^k.$
\end{theorem}
These results provide additional support for the recent interest in
cuts derived from two or more rows of an integer program
\cite{alww,bc,cm,dw,esp, go07}.
\section{Proof of Theorem
\ref{THM:goemans}}\label{SEC:goemans_proof}
\begin{proof}
Let
$$\alpha = \max_{i=1, \ldots, m} \left\{\frac{b_i}{\inf\{ a^i x \ : \ \ x \in P\}} \ :
\ b_i > 0\ \right\}.$$
We first show that $P \subseteq \alpha Q$. This holds when $\alpha =
+ \infty$ by definition of $\alpha Q$. Therefore we may assume $1 \le
\alpha < + \infty$. Consider any point $p\in P$. The inequalities
of $\alpha Q$ are of the form $\alpha a^i x \geq b_i$ with $a^i \geq 0$
and $b_i \geq 0$. If $b_i = 0$, then since $p \in P \subseteq
\mathbb{R}^n_+$, $a^i p \geq 0$ and hence this inequality is
satisfied. If $b_i > 0$, then we know from the definition of
$\alpha$ that
\[
\frac{b_i}{\inf\{ a^i x \ : \ \ x \in P\}} \leq \alpha .
\]
This implies
\[
b_i \leq \alpha \inf\{ a^i x \ : \ \ x \in P\} \leq \alpha a^i p .
\]
Therefore, $p$ satisfies this inequality.
We next show that for any $1 \le \alpha' < \alpha$, $P \not\subseteq
\alpha' Q$. Say $\alpha = \frac{b_j}{\inf\{ a^j x \ : \ \ x \in
P\}}$ (i.e. the maximum, possibly $+ \infty$, is reached for index
$j$). Let $\delta = \frac{b_j}{\alpha'} - \frac{b_j}{\alpha}$. We
have $\delta > 0$. From the definition of $\alpha$ we know that
$\inf\{ a^j x \ : \ \ x \in P\} = \frac{b_j}{\alpha}$. Therefore,
there exists $p \in P$ such that $a^j p < \frac{b_j}{\alpha} +
\delta = \frac{b_j}{\alpha'}$. So $\alpha' a^j p < b_j$ and hence $p
\not\in \alpha' Q$.
\end{proof}
\section{Split closure vs. triangle and quadrilateral
closures}
In this section, we present the proof of
Theorem~\ref{THM:inclusion}.
\begin{proof} (Theorem \ref{THM:inclusion}).
We show that if any point $\bar{s}$ is cut off by a split
inequality, then it is also cut off by some triangle inequality.
This will prove the theorem.
Consider any split inequality $\sum_{i=1}^k \psi_S(r^i)s_{i} \ge 1$
(see Figure~\ref{fig:split_with triangle}) and denote by $L_1$ and
$L_2$ its two boundary lines. Point $f$ lies in some parallelogram
of area 1 whose vertices $y^1, y^2, y^3, \textrm{and }y^4$ are
lattice points on the boundary of the split.
Assume without loss of generality that $y^1$ and $y^2$ are on $L_1$.
Consider the family $\mathcal{T}$ of triangles whose edges are
supported by $L_2$ and by two lines passing through $y^1$ and $y^2$
and whose interior contains the segment $y^1y^2$. See
Figure~\ref{fig:split_with triangle}. Note that all triangles in
$\mathcal{T}$ are of Type $2$. For $T \in \mathcal{T}$ we will
denote by $\psi_T$ the minimal function associated with $T$.
\begin{figure}[htbp]
\begin{center}
\scalebox{.5}{\epsfig{file=split_with_triangle.eps}}
\caption{Approximating a split inequality with a triangle
inequality. The triangle is formed by $L_2$ and the two dashed lines}
\label{fig:split_with triangle}
\end{center}
\end{figure}
By assumption, $\sum_{i=1}^{k} \psi_S(r^i)\bar{s}_i < 1$. Let
$\epsilon = 1 - \sum_{i=1}^{k} \psi_S(r^i)\bar{s}_i$.
We now make the following simple observation. Given a finite set $X$
of points that lie in the interior of the split $S$, we can find a
triangle $T \in \mathcal{T}$ as defined above, such that all points
in $X$ are in the interior of $T$. To see this, consider the convex
hull $\mathcal{C}(X)$ of $X$. Since all points in $X$ are in the
interior of $S$, so is $\mathcal{C}(X)$. This implies that the
tangent lines from $y^1$ and $y^2$ to $\mathcal{C}(X)$ are not
parallel to $L_1$. Two of these four tangent lines along with $L_2$
of $S$ form a triangle in $\mathcal{T}$ with $X$ in its interior.
Let $s_{max} = \max \{\bar{s}_i \ : \ i = 1 \ldots, k\}$ and define
$\delta = \frac{\epsilon}{2 \cdot k \cdot s_{max}} > 0$. For every
ray $r^i$ define $c(r^i) = \psi_S(r^i) + \delta$. Therefore, by
definition $p^i = f + \frac{1}{c(r^i)} \cdot r^i$ is a point
strictly in the interior of $S$. Using the observation stated above,
there exists a triangle $T\in \mathcal{T}$ which contains all the
points $p^i$. It follows that the coefficient $\psi_T(r^i)$ for any
ray $r^i$ is less than or equal to $c(r^i)$.
We claim that for this triangle $T$ we have $\sum_{i=1}^{k}
\psi_T(r^i)\bar{s}_i < 1$. Indeed,
\begin{eqnarray*}
\sum_{i=1}^{k} \psi_T(r^i)\bar{s}_i & \leq & \sum_{i=1}^k c(r^i)\bar{s}_i \\
& = & \sum_{i=1}^k(\psi_S(r^i) + \delta) \bar{s}_i
= \sum_{i=1}^k\psi_S(r^i)\bar{s}_i + \sum_{i=1}^k\frac{\epsilon}{2 \cdot k \cdot s_{max}}\bar{s}_i\\
& \leq & \sum_{i=1}^k\psi_S(r^i)\bar{s}_i + \frac{\epsilon}{2} =
1 - \frac{\epsilon}{2} < 1
\end{eqnarray*}
The first inequality follows from the definition of $c(r^i)$ and the
last equality follows from the fact that
$\sum_{i=1}^k\psi_S(r^i)\bar{s}_i = 1 - \epsilon$.
This shows that $T_f^k \subseteq S_f^k$. For the quadrilateral
closure, we also use two lines passing through $y^3$ and $y^4$ on
$L_2$ and argue similarly.
\end{proof}
Note that even though there can be a zero coefficient in a split
inequality for some ray $r$, in the proof above we exhibit a
sequence of triangle inequalities with arbitrarily small
coefficients for ray $r$. Any point cut off by the split inequality
is also cut off by a cut in the sequence.
\section{Tools}
\label{SEC:PRELIM}
\subsection{Conditions under which a maximal lattice-free convex set gives rise to a facet}
Andersen, Louveaux, Weismantel and Wolsey \cite{alww}
characterized the facets of $R_f^k$ as arising from
splits, triangles and quadrilaterals.
Cornu\'ejols and Margot \cite{cm} gave a converse.
We give this characterization in Theorem \ref{THM:mainRfk}. Roughly speaking, for a maximal lattice-free triangle or quadrilateral to give rise to a facet,
it has to have its corner points on half-lines $f+\lambda r^j$ for some $j =
1, \ldots , k$ and $\lambda > 0$; or to
satisfy a certain technical condition called the ray condition.
Although the ray condition is not central to this paper (it is only used once
in the proof of Theorem \ref{thm:7.2}), we need to include it for technical completeness.
Let $B_\psi$ be a maximal lattice-free split,
triangle or quadrilateral with
$f$ in its interior. For any $j=1, \ldots, k$ such that $\psi(r^j) > 0$,
let $p^j$ be the intersection of the half-line
$f + \lambda r^j$, $\lambda \geq 0$, with the boundary of $B_\psi$.
The point $p^j$ is called the {\it boundary point} for $r^j$. Let
$P$ be a set of boundary points. We say that a point $p \in P$ is
{\it active} if it can have a positive coefficient in a convex
combination of points in $P$ generating an integral point. Note that
$p \in P$ is active if and only if $p$ is integral or there exists
$q \in P$ such that the segment $pq$ contains an integral point in
its interior. We say that an active point $p \in P$ is {\it uniquely
active} if it has a positive coefficient in {\it exactly one} convex
combination of points in $P$ generating an integral point.
Apply the following {\it Reduction Algorithm}:
\begin{itemize}
\item[0.)]
Let $P = \{ p^1, \ldots , p^k \}$.
\item[1.)]
While there exists $p \in P$ such that $p$ is active and $p$
is a convex combination of
other points in $P$, remove $p$ from $P$.
At the end of this step, $P$ contains at
most two active points on each edge of $B_\psi$ and all points of $P$ are distinct.
\item[2.)]
While there exists a uniquely active $p \in P$, remove $p$ from $P$.
\item[3.)]
If $P$ contains exactly two active points $p$ and $q$
(and possibly inactive points), remove both $p$ and $q$ from $P$.
\end{itemize}
\medskip
{\em The ray condition holds for a triangle or a quadrilateral}
if $P = \emptyset$ at termination of the Reduction Algorithm.
{\em The ray condition holds for a
split} if, at termination of the Reduction Algorithm, either $P =
\emptyset$, or $P= \{p_1, q_1, p_2, q_2\}$ with $p_1, q_1$ on one of
the boundary lines and $p_2, q_2$ on the other and both line
segments $p_1q_1$ and $p_2q_2$ contain at least two integral points.
\begin{theorem} \label{THM:mainRfk}
{\em (Cornu\'ejols and Margot \cite{cm})} The facets of $R_f^k$ are
\begin{itemize}
\item[(i)] split inequalities where the unbounded direction of $B_\psi$ is
$r^j$ for some $j = 1, \ldots , k$ and the line $f+\lambda r^j$
contains no integral point; or where $B_\psi$ satisfies the
ray condition,
\item[(ii)] triangle inequalities where the triangle $B_\psi$ has
its corner points on three half-lines $f+\lambda r^j$ for some $j =
1, \ldots , k$ and $\lambda > 0$; or where the triangle $B_\psi$
satisfies the ray condition,
\item[(iii)] quadrilateral inequalities where the corners of $B_\psi$ are
on four half-lines $f+\lambda r^j$ for some $j = 1, \ldots , k$ and
$\lambda > 0$, and $B_\psi$ satisfies a certain ratio condition (the ratio
condition will not be needed in this paper; the interested reader is referred
to \cite{cm} for details).
\end{itemize}
\end{theorem}
Note that the same facet may arise from different convex sets. For
example quadrilaterals for which the ray condition holds define
facets, but there is always also a triangle that defines the same
facet, which is the reason why there is no mention of the ray
condition in (iii) of Theorem \ref{THM:mainRfk}.
\subsection{Reducing the number of rays in the analysis}
The following technical theorem will be used in the proofs of
Theorems~\ref{THM:T1split}, \ref{THM:T&Q} and \ref{THM:T&Q_2}, where
we will be applying Theorem~\ref{THM:goemans}.
\begin{theorem}
\label{THM:corner} Let $B_1, \ldots, B_m$ be lattice-free convex
sets with $f$ in the interior of $B_p$, $p=1,\ldots,m$. Let $R_c
\subseteq \{1,\ldots,k\}$ be a subset of the ray indices such that
for every ray $r^j$ with $j\not\in R_c$, $r^j$ is the convex
combination of some two rays in $R_c$. Define
\[
\begin{array}{rlcl}
z_1 = \;\; \min &
\displaystyle
\sum_{i=1}^k s_i \\[0.1in]
& \displaystyle \sum_{i=1}^k \psi_{B_p}(r^i) s_i & \geq 1 &
\mbox{ for \ } p = 1, \ldots, m \\[0.1in]
& s \geq 0
\end{array}
\]
and
\[
\begin{array}{rlcl}
z_c = \;\; \min &
\displaystyle \sum_{i \in R_c} s_i \\[0.1in]
& \displaystyle \sum_{i \in R_c} \psi_{B_p}(r^i) s_i & \geq 1 &
\mbox{ for \ } p = 1,\ldots,m \\[0.1in]
& s \geq 0 \ .
\end{array}
\]
Then $z_1 = z_c$.
\end{theorem}
\begin{proof}
Assume there exists $j \not \in R_c$ and $r^1, r^2$ are the rays in
$R_c$ such that $r^j = \lambda r^1 + (1-\lambda)r^2$ for some $0 <
\lambda <1$. Let $K = \{1, \ldots, k\} - j$ and define
\[
\begin{array}{rlcl}
z_2 = \;\; \min & \displaystyle \sum_{i \in K} s_i \\[0.1in]
& \displaystyle \sum_{i\in K} \psi_{B_p}(r^i) s_i & \geq 1 &
\mbox{ for \ }p = 1, \ldots, m \\[0.1in]
& s \geq 0 \ .
\end{array}
\]
We first show that $z_1 = z_2$. Applying the same reasoning
repeatedly to all the indices not in $R_c$ yields the proof of the
theorem.
Any optimal solution for the LP defining $z_2$ yields a feasible
solution for the one defining $z_1$ by setting $s_j = 0$, implying
$z_1 \leq z_2$. It remains to show that $z_1 \geq z_2$.
Consider any point $\hat{s}$ satisfying $\sum_{i=1}^k
\psi_{B_p}(r^i)\hat{s}_i \geq 1$ for every $p \in \{1,\ldots,m\}$.
Consider the following values $\bar{s}$ for the variables
corresponding to the indices $t \in K$.
\[
\bar{s}_t = \left\{\begin{array}{ll} \hat{s}_t & \mbox{if \ }
t \not \in \{1, 2, j\} \\
\hat{s}_{1} + \lambda\hat{s}_{j} & \mbox{if \ } t = 1\\
\hat{s}_{2} + (1-\lambda)\hat{s}_{j} & \mbox{if \ } t = 2
\end{array}\right.
\]
One can check that
\[
\sum_{i \in K} \bar{s}_i = \hat{s}_j + \sum_{i \in K} \hat{s}_{i} \
.
\]
By Theorem~\ref{THM:minfunc} $\psi_{B_p}$ is convex, thus
$\psi_{B_p}(r^j) \leq \lambda\psi_{B_p}(r^1) +
(1-\lambda)\psi_{B_p}(r^2)$ for $p = 1, \ldots, m$. It follows that
$\sum_{i\in K}\psi_{B_p}(r^i)\bar{s}_{i} \geq
\psi_{B_p}(r^j)\hat{s}_j + \sum_{i \in K}\psi_{B_p}(r^i)\hat{s}_{i}
= \sum_{i=1}^k \psi_{B_p}(r^i)\hat{s}_i \geq 1$ for $p = 1, \ldots,
m$. Hence $\bar{s}$ satisfies all the inequalities restricted to
indices in $K$ and has the same objective value as $\hat{s}$. It
follows that $z_1 \geq z_2$.
\end{proof}
\section{Proof sketch for Theorems~\ref{THM:T1split}
and~\ref{THM:T&Q}}\label{SEC:proof_sketch}
In this section, we give a brief outline of the proofs of
Theorems~\ref{THM:T1split} and~\ref{THM:T&Q}.
A complete proof will be given in Sections \ref{SEC:T1split} and \ref{Section7} respectively.
In Theorem~\ref{THM:T1split}, we need to analyze the optimization problem
\begin{equation}\label{eq:Type1_over_Sf}
\min\left\{ \sum_{i=1}^k \psi(r^i) s_i \ : \; s \in S_f^k\right\} \
,
\end{equation}
\noindent
where $\psi$ is the minimal function derived from the Type 1 triangle.
For Theorem~\ref{THM:T&Q}, recall that all nontrivial facet defining
inequalities for $R_f^k$ are of the form $a^i s \geq 1$ with $a^i
\geq 0$. Therefore, Theorem \ref{THM:goemans} shows that to prove
Theorem~\ref{THM:T&Q}, we need to consider all nontrivial facet
defining inequalities and optimize in the direction $a^i$ over the
triangle closure $T_f^k$ and the quadrilateral closure $Q_f^k$. This
task is made easier since all the nontrivial facets of $R_f^k$ are
characterized in Theorem~\ref{THM:mainRfk}. Moreover,
Theorem~\ref{THM:inclusion} shows that every split inequality
$\sum_{i=1}^k \psi(r^i)s_i \geq 1$ is valid for $T_f^k$. Therefore,
if we optimize over $T_f^k$ in the direction $\sum_{i=1}^k
\psi(r^i)s_i$, we get a value of at least one.
Theorem~\ref{THM:inclusion} shows that this also holds for $Q_f^k$.
Thus, we can ignore the facets defined by split inequalities.
Formally, consider a maximal lattice-free triangle or quadrilateral
$B$ with associated minimal function $\psi$ that gives rise to a
facet $\sum_{j=1}^{k} \psi(r^j) s_j \ge 1$ of $R_f^k$. We want to
investigate the following optimization problems:
\begin{equation}\label{eq:facet_over_Tf}
\displaystyle \inf \left\{ \sum_{j=1}^{k} \psi(r^j) s_j : \; s \in
T_f^k \right\}
\end{equation}
and
\begin{equation}\label{eq:facet_over_Qf}
\displaystyle \inf \left\{ \sum_{j=1}^{k} \psi(r^j) s_j : \; s \in
Q_f^k \right\} .
\end{equation}
We first observe that, without loss of generality, we can make the
following simplifying assumptions for problems
(\ref{eq:Type1_over_Sf}), (\ref{eq:facet_over_Tf}) and
(\ref{eq:facet_over_Qf}).
\begin{assumption}\label{ass:scaling}
Consider the objective function $\psi$ in problems
(\ref{eq:Type1_over_Sf}), (\ref{eq:facet_over_Tf}) and
(\ref{eq:facet_over_Qf}). For every $j$ such that $\psi(r^j)
> 0$, the ray $r^j$ is such that the point $f+r^j$ is on the
boundary of the lattice-free set $B$ generating $\psi$.
\end{assumption}
Indeed, this amounts to scaling the coefficient for the ray $r^j$ by
a constant factor in every inequality derived from all maximal
lattice-free sets, including $B$. Therefore, this corresponds to a
simultaneous scaling of variable $s_j$ and corresponding
coefficients in problems (\ref{eq:Type1_over_Sf}),
(\ref{eq:facet_over_Tf}) and (\ref{eq:facet_over_Qf}). This does not
change the optimal values of these problems. Moreover, Cornu\'ejols
and Margot \cite{cm} show that the equations of all edges of
triangles of Type 1, 2, or 3, of quadrilaterals and the direction of
all splits generating facets of $R_f^k$ are rational. This implies
that the scaling factor for ray $r^j$ is a rational number and that
the scaled ray is rational too.
As a consequence, we can assume that the objective function of
problems (\ref{eq:Type1_over_Sf}), (\ref{eq:facet_over_Tf}) or
(\ref{eq:facet_over_Qf}) is $\sum_{j=1}^k s_j$.
When $B_{\psi}$ is a triangle or quadrilateral and $f$ is in its
interior, define a {\it corner ray} to be a ray $r$ such that $f+
\lambda r$ is a corner of $B_{\psi}$ for some $\lambda > 0$.
\begin{remark}\label{rem:simplify}
If $\{r^1, \ldots, r^k\}$ contains the corner rays of the convex set
defining the objective functions of
(\ref{eq:Type1_over_Sf}), (\ref{eq:facet_over_Tf}) or
(\ref{eq:facet_over_Qf}), then Assumption~\ref{ass:scaling} implies
that the hypotheses of Theorem~\ref{THM:corner} are satisfied.
Therefore, when analyzing
(\ref{eq:Type1_over_Sf}), (\ref{eq:facet_over_Tf}) or
(\ref{eq:facet_over_Qf}), we can assume that $\{r^1, \ldots, r^k\}$ is exactly
the set of corner rays.
\end{remark}
\section{Type 1 triangle and the split closure}
\label{SEC:T1split}
In this section, we present the proof of Theorem \ref{THM:T1split}.
Consider any Type $1$ triangle $T$ with integral vertices $x^j$, for
$j=1, 2, 3$, and one integral point $y^j$ for $j = 1, 2, 3$ in the
interior of each edge. We want to study the optimization problem
(\ref{eq:Type1_over_Sf}). Recall that Remark~\ref{rem:simplify} says
that we only need to consider the case with three corner rays $r^1$,
$r^2$ and $r^3$.
We compute the exact value of
\begin{equation} \label{Split3}
\begin{array}{rlcl}
z_{SPLIT} = \;\; \min & \displaystyle \sum_{j=1}^3 s_j \\[0.1in]
& \displaystyle \sum_{j=1}^{3} \psi(r^j) s_j & \geq 1 &
\mbox{ for all splits } B_\psi \\[0.1in]
& s \in \mathbb{R}_+^3 .
\end{array}
\end{equation}
Observe that, using a unimodular transformation, $T$ can be made to
have one horizontal edge $x^1x^2$ and one vertical edge $x^1x^3$, as
shown in Figure \ref{FIG:T1split}. Without loss of generality, we
place the origin at point $x^1$.
We distinguish two cases depending on the position of $f$ in the
interior of triangle $T$: $f$ is in the inner triangle $T_I$ with
vertices $y^1 = (1,1)$, $y^2 = (0,1)$ and $y^3 = (1,0)$; and $f \in
int(T) \setminus T_I$. We show that $z_{SPLIT} = \frac{1}{2}$ when
$f$ is in the inner triangle $T_I$ and that $z_{SPLIT}$ increases
linearly from $\frac{1}{2}$ when $f$ is at the boundary of $T_I$ to
$\frac{2}{3}$ at the corners of the triangle $T$ when $f \in int(T)
\setminus T_I$. See the right part of Figure \ref{FIG:T1split} for some
level curves of $z_{SPLIT}$ as a function of the position of $f$ in
$T$. By a symmetry argument, it is sufficient to consider the inner
triangle $T_I$ and the corner triangle $T_C$ defined by $f_1+f_2
\leq 1$, $f_1,f_2 \geq 0$.
\begin{theorem} \label{THM:TrIntVer}
Let $T$ be a Type 1 triangle with integral vertices, say $(0,0)$,
$(0,2)$ and $(2,0)$. Then
\begin{itemize}
\item[(i)]
$z_{SPLIT} = \frac{1}{2}$ when $f$ is interior to the triangle with
vertices $(1,0)$, $(0,1)$ and $(1,1)$.
\item[(ii)]
$z_{SPLIT} = 1-\frac{1}{3-f_1-f_2}$ when $f=(f_1,f_2)$ is interior
to the corner triangle $f_1+f_2 \leq 1$, $f_1,f_2 \geq 0$. The value
of $z_{SPLIT}$ when $f$ is in the other corner triangles follows by
symmetry.
\end{itemize}
\end{theorem}
To prove this theorem, we show that the split closure is completely
defined by only three split inequalities. In other words, all other
split inequalities are dominated by these three split inequalities.
Define $S_1$ as the convex set $1 \le x_1+x_2 \leq 2$,
$S_2$ as the convex set $0 \le x_1 \leq 1$ and $S_3$
as the convex set $0 \le x_2 \leq 1$. Define {\it Split 1} (resp.
{\it Split 2}, {\it Split3}) to be the inequality obtained from $S_1$
(resp. $S_2$, $S_3$).
Let $S$ be a split $c \leq a x_1 + b a_2 \leq c+1$ with $f$ in the interior of $S$. The {\it shores} of $S$
are the two half-planes $a x_1 + b a_2 \leq c$ and $a x_1 + b a_2 \geq c+1$.
\begin{remark} \label{LEM:OppSides}
Let $A$, $B$, and $C$ be three points on a line, with $B$ between
$A$ and $C$ and let $S$ be a split.
If $A$ and $C$ are not in the interior of $S$ but $B$ is, then $A$ and $C$ are
on opposite shores of $S$.
\end{remark}
\begin{figure}[htbp]
\centering \scalebox{0.5}{\epsfig{file=Splits123_1.eps}}
\caption{Illustration for the proof of Lemma \ref{Splits123}}
\label{FIG:Splits123}
\end{figure}
\begin{lemma} \label{Splits123}
If $f$ is in the interior of the triangle $T_I$ with vertices
$(0,1)$, $(1,0)$ and $(1,1)$, then the split closure is defined by
Split 1, Split 2 and Split 3.
\end{lemma}
\begin{proof}
Let $S$ be a split defining an inequality that is not dominated by either of
Split 1, Split 2, or Split 3.
For $i = 1, 2, 3$, let $z^i$ (resp. $w^i$)
be the boundary point for $r^i$ on the boundary of $T_I$ (resp. $S$)
(see Figure \ref{FIG:Splits123}). (Note that since $x^i = f + r^i$
is integer, these points exist.) Observe that if
$z^1$ is not in the interior of $S$, then the inequality obtained from $S$ is
dominated by Split 1, since the three boundary points $w_1, w_2, w_3$
are closer to $f$ than the corresponding three boundary points $z^1,
x^2, x^3$ for the three rays on the boundary of $S_1$.
A similar observation holds for $z^2$ and Split 2
and for $z^3$ and Split 3, yielding that $z^2$ and $z^3$ are also in
the interior of $S$.
Since the points $y^1, y^2$ and $y^3$ are integer, they are not
in the interior of $S$.
Applying Remark \ref{LEM:OppSides} to $y^1, z^3, y^2$, we must have that $y^1$ and $y^2$ are on opposite shores of
$S$. Now, $y^3$ is in one of the two shores of $S$. Assume without
loss of generality that it is on the same shore as $y^1$.
Applying Remark \ref{LEM:OppSides} to $y^1, z^2, y^3$, we have that $y^1$ and $y^3$ are on opposite shores of
$S$, a contradiction.
\end{proof}
\begin{lemma}
If $f$ is in the interior of the triangle $T_I$ with vertices
$(0,1)$, $(1,0)$ and $(1,1)$, then $z_{SPLIT} = \frac{1}{2}$.
\end{lemma}
\begin{proof} By Lemma \ref{Splits123}, $z_{SPLIT}$ is given by
\begin{equation}
\begin{array}{rlcl}
z_{SPLIT} = \;\; \min & \displaystyle \sum_{j=1}^3 s_j \\[0.1in]
&\displaystyle \sum_{j=1}^{3} \psi_i(r^j) s_j & \geq 1 &
\mbox{ for } i=1,2,3 \\[0.1in]
& s \in \mathbb{R}_+^3
\end{array}
\end{equation}
\noindent where $\psi_i(r^j)$ is the coefficient of $s_j$ in Split
$i$, for $i = 1, 2, 3$. Let $f=(f_1, f_2)$. The coefficient of $s^j$
in the split inequality can be computed from the boundary point for
$r^j$ with the corresponding split. For example, the boundary points
for $r^2$ and $r^3$ with $S_1$ are the integer points $x^2$ and
$x^3$. This implies that $\psi_1(r^2)=\psi_1(r^3)=1$. On the other
hand, the boundary point for $r^1$ is the point $t=
\left(\frac{f_1}{f_1+f_2}, \frac{f_2}{f_1+f_2} \right)$. The length
of $r^1$ divided by the length of the segment $ft$ determines the
coefficient $\psi_1(r^1)$ of $s_1$ (This follows from the
homogeneity of $\psi_1$ and the fact that $\psi_1(t - f)=1$ since
$t$ is on the boundary of $S_1$). We get
$\psi_1(r^1)=\frac{f_1+f_2}{f_1+f_2-1}$. Repeating this for $S_2$
and $S_3$, we get that $z_{SPLIT}$ is the optimal value of the
following linear program.
\begin{equation} \label{Split123}
\begin{array}{rrrrl}
z_{SPLIT} = \;\; \min & s_1 & + s_2 & + s_3 \\
& \frac{f_1+f_2}{f_1+f_2-1} s_1 & + s_2 & + s_3 & \geq 1 \\
& s_1 & + \frac{2-f_1}{1-f_1} s_2 & + s_3 & \geq 1 \\
& s_1 & + s_2 & + \frac{2-f_2}{1-f_2} s_3 & \geq 1 \\
& & s \geq 0.
\end{array}
\end{equation}
Its optimal solution $s^*$ is $s^*_1 = \frac{f_1+f_2-1}{2}$, $s^*_2 =
\frac{1-f_1}{2}$, $s^*_3 = \frac{1-f_2}{2}$ with value $z_{SPLIT} =
s^*_1 + s^*_2 + s^*_3 = \frac{1}{2}$. Indeed,
note that all three inequalities in (\ref{Split123}) are satisfied
at equality and that the dual of (\ref{Split123}) is feasible (for example,
$(0,0,0)$ is a solution).
Therefore the complementary slackness conditions hold for $s^*$ with any
feasible solution of the dual.
\end{proof}
Now we prove the second part of the theorem, when $f$ is interior to
the corner triangle with vertices $(0,0)$, $(1,0)$ and $(0,1)$ or an
inner point on the segment $y^2y^3$.
\begin{lemma} \label{Splits23}
If $f$ is in the interior of the triangle with vertices $(0,0)$,
$(0,1)$ and $(1,0)$, or an inner point on the segment joining
$(0,1)$ to $(1,0)$, then the split closure is defined by Split 2 and
Split 3.
\end{lemma}
\begin{proof}
Let $S$ be a split defining a split inequality that is not dominated
by either of Split 2, or Split 3. Let $z^2$ be the intersection point of $r^2$
with $y^1y^3$ and let $z^3$ be the intersection point of $r^3$ with
$y^1y^2$. For $i = 1, 2, 3$, let $w^i$ be the intersection point of $r^i$
with either $L_1$ or $L_2$. (Note that since $x^i$ is integer, $r^i$
has to intersect one of the two lines.) Observe that if $z^2$ is not
in the interior of $S$, then the inequality obtained from $S$ is
dominated by Split 2, since the three intersection points $w_1, w_2, w_3$
are closer to $f$ than the corresponding three intersection points $x^1,
z^2, x^3$ for $S_2$. A similar observation holds for $z^3$ and
$S_3$, yielding that $z^3$ is also in the interior of $S$.
Since the points $y^1, y^2$ and $y^3$ are integer, they are not
in the interior of $S$. Applying Remark \ref{LEM:OppSides} to $y^1, z^3, y^2$, we have that $y^1$ and $y^2$ are on opposite shores of $S$.
Applying Remark \ref{LEM:OppSides} to $y^1, z^2, y^3$, we have that $y^1$ and $y^3$ are on opposite shores of $S$. It
follows that $y^2$ and $y^3$ are on the same shore $W$ of $S$ and
thus the whole segment $y^2y^3$ is in $W$. This is a contradiction
with the fact that both $f$ and $z^3$ are in the interior of $S$, as
the two segments $y^2y^3$ and $fz^3$ intersect.
\end{proof}
\begin{lemma}
If $f = (f_1,f_2)$ is in the interior of the triangle with vertices
$(0,0)$, $(0,1)$ and $(1,0)$, or an inner point on the segment
joining $(0,1)$ to $(1,0)$, then $z_{SPLIT} = 1-
\frac{1}{3-f_1-f_2}$.
\end{lemma}
\begin{proof}
The optimal solution of the LP
\begin{equation} \label{Split12}
\begin{array}{rrrrl}
z_{SPLIT} = & \min s_1 & + s_2 & + s_3 \\
& s_1 & + \frac{2-f_1}{1-f_1} s_2 & + s_3 & \geq 1 \\
& s_1 & + s_2 & + \frac{2-f_2}{1-f_2} s_3 & \geq 1 \\
& & s \geq 0.
\end{array}
\end{equation}
\noindent is $s_1=0$, $s_2 = \frac{1-f_1}{3-f_1-f_2}$, $s_3 =
\frac{1-f_2}{3-f_1-f_2}$.
\end{proof}
This completes the proof of Theorem \ref{THM:TrIntVer}.
This theorem in conjunction with Theorem~\ref{THM:goemans} implies
that including all Type 1 triangle facets can
improve upon the split closure only by a factor of 2.
\begin{corollary}
Let $\mathcal{F}$ be the family of all facet defining inequalities
arising from Type 1 triangles. Define
$$
\bar S_f = S_f^k\cap \left\{\sum_{i=1}^{k} \psi(r^i)s_i \geq 1 \ : \
\psi \in \mathcal{F} \right\}\ .
$$
Then $\bar S_f \subseteq S_f^k \subseteq 2 \bar S_f$.
\end{corollary}
\section{Integer hull vs. triangle and quadrilateral closures}
\label{Section7}
In this section we present the proof of Theorem~\ref{THM:T&Q}. We
show that the triangle closure $T_f^k$ and the quadrilateral closure
$Q_f^k$ both approximate the integer hull $R_f^k$ to within a factor
of two. As outlined in Section~\ref{SEC:proof_sketch}, we can show
this by taking a facet of $R_f^k$, and optimizing in that direction
over $T_f^k$ or $Q_f^k$. As noted in that section, we need to
analyze the optimization problems (\ref{eq:facet_over_Tf}) and
(\ref{eq:facet_over_Qf}), where the objective function comes from a
maximal lattice-free triangle or quadrilateral.
\subsection{Approximating the integer hull by the triangle
closure}
\label{sub:IHbyT}
We only need to consider facets of $R_f^k$ derived from
quadrilaterals to obtain the objective function of problem
(\ref{eq:facet_over_Tf}). We prove the following result.
\begin{theorem}
Let $Q$ be a maximal lattice-free quadrilateral with corresponding
minimal function $\psi$ and generating a facet $\displaystyle
\sum_{i=1}^k \psi(r^i) s_i \geq 1$ of $R_f^k$. Then
$$
\inf\left\{ \displaystyle \sum_{i=1}^k \psi(r^i) s_i \ : \; s \in
T_f^k\right\} \geq \frac{1}{2} \ .
$$
\end{theorem}
\begin{proof}
The theorem holds if the facet defining inequality can also be
obtained as a triangle inequality. Therefore by
Theorem~\ref{THM:mainRfk}, we may assume that rays $r^1, \ldots r^4$
are the corners rays of $Q$ (see Figure~\ref{fig:quad_with
triangle}). We remind the reader of Remark~\ref{rem:simplify},
showing that we can assume that $k = 4$ and that the four rays are
exactly the corner rays of $Q$.
By a unimodular transformation, we may further assume that the four
integral points on the boundary of $Q$ are $(0,0), (1,0), (1,1),
(0,1)$. Moreover, by symmetry, we may assume that the fractional
point $f$ satisfies $f_1\leq \frac{1}{2}$ and $f_2\leq \frac{1}{2}$
as rotating this region about $(\frac{1}{2},\frac{1}{2})$ by
multiples of $\frac{\pi}{2}$ covers the entire quadrilateral. Note
that $f_1 < 0$ and $f_2 < 0$ are possible.
We relax Problem (\ref{eq:facet_over_Tf}) by keeping only two of
the triangle inequalities, defined by triangles $T_1$ and $T_2$.
$T_1$ has corner $f+r^4$ and edges supported by the two
edges of $Q$ incident with that corner and by the line $x=1$. $T_2$
has corner $f+r^1$ and edges supported by the two edges
of $Q$ incident with that corner and by the line $y=1$. The two
triangles are depicted in dashed lines in Figure~\ref{fig:quad_with
triangle}.
\begin{figure}[htbp]
\begin{center}
\scalebox{.5}{\epsfig{file=quad_with_triangle.eps}}
\caption{Approximating a quadrilateral inequality with triangle inequalities}
\label{fig:quad_with triangle}
\end{center}
\end{figure}
Thus, Problem (\ref{eq:facet_over_Tf}) can be relaxed to the LP
\begin{equation}\label{LP7}
\begin{array}{rlcl}
\;\; \min & s_1 + s_2 + s_3 + s_4 \\
& \displaystyle \sum_{i=1}^4 \psi_{T_1}(r^i)s_i & \geq 1 &
(\textrm{Triangle }T_1) \\[0.1in]
& \displaystyle \sum_{i=1}^4 \psi_{T_2}(r^i)s_i & \geq 1 &
(\textrm{Triangle }T_2) \\[0.1in]
& s \in \mathbb{R}_+^4 .
\end{array}
\end{equation}
Let $(\alpha, \beta) = f + r^2$ and $(\gamma, \delta) = f + r^3$.
Computing the coefficients $\psi_{T_1}(r^2)$ and $\psi_{T_2}(r^3)$,
LP (\ref{LP7}) becomes
\begin{equation}\label{LP8}
\begin{array}{rlcl}
\;\; \min & s_1 + s_2 + s_3 + s_4 \\
& s_1 + \displaystyle \frac{\alpha-f_1}{1-f_1}s_2 + s_3 + s_4 & \geq 1 &
(T_1) \\[0.1in]
& s_1 + s_2 + \displaystyle \frac{\delta-f_2}{1-f_2}s_3 + s_4 & \geq 1 &
(T_2) \\[0.1in]
& s \in \mathbb{R}_+^4 .
\end{array}
\end{equation}
Using the equation of the edge of $Q$ connecting
$f + r^2$ and $f + r^3$, we can find bounds on
$\psi_{T_1}(r^2)$ and $\psi_{T_2}(r^3)$. The edge has equation $x_1 \frac{1}{t}
+ \frac{t-1}{t} x_2 = 1$ for some $1 < t < \infty$.
Therefore $\alpha \leq t$ and $\delta \leq \frac{t}{t-1}$.
Using these two inequalities together with $f_1 \leq \frac{1}{2}$ and $f_2 \leq \frac{1}{2}$
we get
\[
\frac{\alpha-f_1}{1-f_1} = \frac{\alpha - 1}{1-f_1} + 1 \leq 2(t-1)
+ 1 = 2t -1
\hspace{1cm} \mbox{and} \hspace{1cm}
\frac{\delta-f_2}{1-f_2} \leq 2\frac{t}{t-1} - 1 \ .
\]
Using these bounds, we obtain the relaxation of LP (\ref{LP8})
\begin{equation}
\begin{array}{rlcl}
\;\; \min & s_1 + s_2 + s_3 + s_4 \\[0.1in]
& s_1 + (2t-1)s_2 + s_3 + s_4 & \geq 1 &
(T_1) \\[0.1in]
& s_1 + s_2 + \displaystyle (2\frac{t}{t-1} - 1)s_3 + s_4 & \geq 1 &
(T_2) \\[0.1in]
& s \in \mathbb{R}_+^4 .
\end{array}
\end{equation}
Set $\lambda = 2t - 1$ and $\mu = 2\frac{t}{t-1} - 1$. Then $t > 1$
implies $\lambda >1$ and $\mu > 1$. The optimal solution of the
above LP is $s_1 = s_4 = 0$, $s_2 = \frac{\mu - 1}{\lambda\mu - 1}$
and $s_3 = \frac{\lambda - 1}{\lambda\mu - 1}$ with value
\[
s_1 + s_2 + s_3 + s_4 = \frac{\lambda + \mu - 2}{\lambda\mu - 1} = \frac{t^2 - 2t
+ 2}{t^2} \ .
\]
To find the minimum of this expression for $t >1$, we set its derivative to 0,
and get the solution $t=2$. Thus the minimum value of
$s_1 + s_2 + s_3 + s_4$ is equal to $\frac{1}{2}$.
\end{proof}
\subsection{Approximating the integer hull by the quadrilateral
closure}
\label{sub:IHbyQuad}
In this section, we study Problem (\ref{eq:facet_over_Qf}).
We can approximate the
facets derived from Type $1$ and Type $2$ triangles using
quadrilaterals in a similar manner as the splits were approximated
by triangles and quadrilaterals. See Figure~\ref{fig:triangle_with
quad}. We again define the set $X$ of points which lie strictly
inside the Type $1$ or Type $2$ triangle, similar to the proof
of Theorem~\ref{THM:inclusion}. Then we can find quadrilaterals as shown in
Figure~\ref{fig:triangle_with quad} that contain the set $X$. The
proof goes through in exactly the same manner.
However triangles of Type $3$ pose a problem. They
cannot be approximated to any desired precision by a
sequence of quadrilaterals.
\begin{figure}[htbp]
\begin{center}
\scalebox{.5}{\epsfig{file=triangle_with_quad.eps}}
\caption{Approximating a triangle inequality with a
quadrilateral inequality} \label{fig:triangle_with quad}
\end{center}
\end{figure}
In this section, we work under Assumption \ref{ass:scaling}.
By Theorem \ref{THM:mainRfk}, a Type $3$ triangle $T$ defines a facet
if and only if either the ray condition holds, or
all three corner rays are present. First we consider the case where the ray condition holds.
\begin{theorem} \label{thm:7.2}
Let $T$ be a triangle of Type 3 with corresponding minimal function
$\psi_T$ defining a facet of $R_f^k$. If the ray condition holds for
$T$ then Problem (\ref{eq:facet_over_Qf}) has optimal value 1.
\end{theorem}
\begin{proof}
We first prove that if the ray condition holds the points
$p^j = f + r^j$ are integral points on the boundary of $T$,
for $j = 1, \ldots, k$.
For $i=1, 2, 3$, let $P_i$ be the set of points left at the end of Step $i$
of the Reduction Algorithm given in Section \ref{SEC:PRELIM}.
Each $p^j \in P_1$ with $p^j$
integral is uniquely active and is removed during Step 2 of
the Reduction Algorithm. Hence, all points in $P_2$ are non-integral.
Observe that Step 3 can only remove boundary points $p$ and $q$
when the segment
$pq$ contains at least two integral points in its relative interior.
Therefore this step does not remove anything in a Type 3 triangle
and $P_3 = P_2$.
Since the ray condition holds, we have $P_3 = P_2 = \emptyset$ and
$P_1$ contains only integral points. But then $P_1 = P$,
showing that all boundary points
at the beginning of the Reduction Algorithm are integral.
It is then straightforward to construct a maximal lattice-free
quadrilateral $Q$ with $p^j$, $j = 1, \ldots, k$ on its boundary,
and containing $f$ in its interior.
It follows that
the value of Problem (\ref{eq:facet_over_Qf}) is equal to 1.
\end{proof}
We now consider the case where $T$ is a Type $3$ triangle with the
three corner rays present. In this case, we can approximate the
facet obtained from $T$ to within a factor of two by using
inequalities derived from triangles of Type $2$. Define another
relaxation $\bar{T}_f^k$ as the convex set defined by the
intersection of the inequalities derived only from Type $1$ and Type
$2$ triangles. By definition, $T_f^k\subseteq \bar{T}_f^k$. From the
discussion at the beginning of this section, we also know
$Q_f^k\subseteq \bar{T}_f^k$. Hence (\ref{eq:facet_over_Qf}) can be
relaxed to
\begin{equation}\label{eq:facet_over_barTf}
\inf\left\{ \displaystyle \sum_{i=1}^k \psi(r^i) s_i: \; s \in
\bar{T}_f^k\right\} \ .
\end{equation}
\begin{theorem}\label{thm:type3_with_type2}
Let $T$ be a triangle of Type 3 with corresponding minimal function
$\psi$ and generating a facet $\displaystyle \sum_{i=1}^{k}
\psi(r^i) s_i \geq 1$ of $R_f^k$. Then,
$$\inf\left\{ \sum_{i=1}^k \psi(r^i) s_i \ : \; s \in
\bar{T}_f^k\right\} \geq \frac{1}{2} \ .
$$
\end{theorem}
This theorem implies directly the following corollary.
\begin{corollary}
$Q_f^k \subseteq 2R_f^k$.
\end{corollary}
\begin{proof}[Proof of Theorem~\ref{thm:type3_with_type2}]
We first make an affine transformation to simplify computations.
Let $y^1, y^2, y^3$ be the three lattice points on the
sides of $T$. We choose the transformation such that the two following
properties are satisfied.
\begin{itemize}
\item[(i)] The standard lattice is mapped to the lattice
generated by the vectors $v^1 = (1,0)$ and
$v^2 = (\frac{1}{2}, \frac{\sqrt{3}}{2})$, i.e. all points of the form
$z_1 v^1 + z_2 v^2$, where $z_1, z_2$ are integers.
\item[(ii)]
$y^1, y^2, y^3$ are respectively mapped to $(0,0),(1,0),(0,1)$ in the above
lattice.
\end{itemize}
We use the basis $v^1, v^2$ for
$\mathbb{R}^2$ for all calculations and equations in the remainder of the
proof. See Figure~\ref{fig:triangle_with triangle}.
\begin{figure}[htbp]
\begin{center}
\scalebox{.5}{\epsfig{file=triangle_with_triangle.eps}}
\caption{Approximating a Type $3$ triangle inequality with Type $2$ triangle
inequalities. The Type 3 triangle is in solid lines. The basis vectors are
$v^1 = (1, 0)$ and $v^2 = (\frac{1}{2}, \frac{\sqrt{3}}{2})$
}
\label{fig:triangle_with triangle}
\end{center}
\end{figure}
With this transformation, we can get a simple characterization for
the Type $3$ triangles. See Figure~\ref{fig:triangle_with triangle}
for an example. We make the following claim about the relative
orientations of the three sides of the Type $3$ triangle.
\begin{lemma} \label{LEM:type_3_triangle}
Let $\mathcal{F}$ be the family of triangles formed by three lines
given by:
\[
\begin{array}{rcc}
\textrm{Line }1 :
& \displaystyle -\frac{x_1}{t_1} + x_2 = 1 & \mbox{with \ }
0 < t_1 < \infty \ ; \\[0.1in]
\textrm{Line }2 :
& t_2 \ x_1 + x_2 = 0 & \mbox{with \ } 0< t_2 < 1 \ ; \\[0.1in]
\textrm{Line }3 :
& x_1 + \displaystyle \frac{x_2}{t_3} = 1 & \mbox{with \ }
1 < t_3 < \infty \ .
\end{array}
\]
Any Type $3$ triangle is either a triangle from $\mathcal{F}$
or a reflection of a triangle from $\mathcal{F}$ about the
line $x_1 = x_2$.
\end{lemma}
\begin{proof}
Take any Type $3$ triangle $T$. Consider the edge passing through
$(1,0)$. Since it cannot go through the interior of the equilateral
triangle $(0,0), (0,1), (1,0)$, there are only two choices for its
orientation : a) It can go through the segment $(0,1),(1,1)$, or b)
It can go through the segment $(0,0),(1,-1)$.
In the first case its equation is that of $\textrm{Line }3$. This
now forces the edge of $T$ passing through $(0,0)$ to have the
equation for $\textrm{Line }2$. This is because the only other
possibility for this edge would be for the line to pass through the
segment $(-1,1),(0,1)$. But then the lattice point $(1,-1)$ is
included in the interior of the triangle. Similarly, the third edge
must now have $\textrm{Line }1$'s equation, because $(-1,1)$ needs
to be excluded from the interior.
Case b) can be mapped to Case a) by a reflection about the line $x_1 = x_2$.
\end{proof}
\begin{remark}
We can choose any values for $t_1, t_2, t_3$ independently in
the prescribed ranges, and we get a lattice free triangle. This
observation shows that the family $\mathcal{F}$ defined above is
exactly the family of all Type $3$ triangles modulo an affine
transformation.
\end{remark}
We now show how to bound Problem (\ref{eq:facet_over_barTf}) and
hence prove Theorem~\ref{THM:T&Q_2}.
Consider any Type $3$ triangle $T$. It
is sufficient to consider the case where the lines supporting the edges
of $T$ have equations as stated in the Lemma \ref{LEM:type_3_triangle}.
We consider two cases for the position of the fractional point
$f = (f_1,f_2)$.
\begin{enumerate}
\item[(i)] $f_1\leq\frac{1}{2}$, $f_2\leq\frac{1}{2}$;
\item[(ii)] $f_1 \leq 0$, $f_1+f_2\leq \frac{1}{2}$.
\end{enumerate}
The union of the two regions described above when rotated by
$2\pi/3$ and $4\pi/3$ about the point $(\frac{1}{3},\frac{1}{3})$
(the centroid of the triangle formed by (0,0),(0,1) and (1,0)),
cover all of $\mathbb{R}^2$. Hence they cover all of $T$ and by
rotational symmetry, investigating these two cases is enough.
For the first case, we relax Problem (\ref{eq:facet_over_barTf}) by
using only two inequalities from $\bar{T}_f^k$. These are derived
from Type $2$ triangles $T_1$ and $T_2$ (see
Figure~\ref{fig:triangle_with triangle}), which are defined as
follows. $T_1$ has $\textrm{Line }1$ and $\textrm{Line }2$
supporting two of its edges and $x_1 = 1$ supporting the third one
(with more than one integral point). $T_2$ has $\textrm{Line }2$ and
$\textrm{Line }3$ supporting two of its edges and $x_2 = 1$
supporting the third one (with more than one integral point). Let
$\psi_{T_1}$ and $\psi_{T_2}$ be the corresponding minimal functions
derived from $T_1$ and $T_2$.
The following LP is a relaxation of Problem
(\ref{eq:facet_over_barTf}).
\begin{equation}\label{LP9}
\begin{array}{rlcl}
\;\; \min & \displaystyle \sum_{i=1}^k s_i \\[0.1in]
& \displaystyle \sum_{i=1}^k \psi_{T_1}(r^i)s_i & \geq 1 &
(\textrm{Triangle }T_1) \\[0.1in]
& \displaystyle \sum_{i=1}^k \psi_{T_2}(r^i)s_i & \geq 1 &
(\textrm{Triangle }T_2) \\[0.1in]
& s \in \mathbb{R}_+^k .
\end{array}
\end{equation}
Theorem~\ref{THM:corner} and Remark~\ref{rem:simplify} imply that
LP (\ref{LP9}) is equivalent to
\begin{equation}\label{LP1}
\begin{array}{rlcl}
\;\; \min & s_1 + s_2 + s_3 \\
& \psi_{T_1}(r^1)s_1 + \psi_{T_1}(r^2)s_2 + \psi_{T_1}(r^3)s_3 & \geq 1 &
(\textrm{Triangle }T_1) \\
& \psi_{T_2}(r^1)s_1 + \psi_{T_2}(r^2)s_2 + \psi_{T_2}(r^3)s_3 & \geq 1 & (\textrm{Triangle }T_2) \\
& s \in \mathbb{R}_+^3 .
\end{array}
\end{equation}
where $r^1$, $r^2$ and $r^3$ are the three corner rays (see
Figure~\ref{fig:triangle_with triangle}).
We now show that this LP has an optimal value of at least $\frac{1}{2}$.
Note that $\psi_{T_1}(r^2) = \psi_{T_1}(r^3) = 1$. $\psi_{T_1}(r^1)$
needs to be computed. First we compute $r^1$ and $r^2$ in terms of
$t_1, t_2, t_3, f_1$ and $f_2$.
The intersection of $\textrm{Line }2$ and $\textrm{Line }3$ is given
by
$$
\left(\frac{t_3}{t_3 - t_2}, \frac{-t_2t_3}{t_3 - t_2}\right)
\hspace{0.4in} \mbox{and \ thus} \hspace{0.4in}
r^1 = \left(\frac{t_3}{t_3 - t_2}, \frac{-t_2t_3}{t_3 - t_2}\right) - (f_1,f_2) \ .
$$
As $\psi_{T_1}(r^1)=\frac{1}{\gamma}$ where $\gamma$ is such that
$(f_1,f_2) + \gamma r^1$ lies on the line $x_1=1$, we get
$$
\psi_{T_1}(r^1) = \frac{\frac{t_3}{t_3 - t_2} - f_1}{1-f_1} \ .
$$
Similarly, we only need $\psi_{T_2}(r^2)$ as $\psi_{T_2}(r^1) =
\psi_{T_2}(r^3) = 1$. The intersection of $\textrm{Line }1$ and
$\textrm{Line }3$ is
$$
\left(\frac{t_1(t_3 - 1)}{1 + t_1t_3}, \frac{t_3(t_1+ 1)}{1 +
t_1t_3}\right) \hspace{0.4in} \mbox{and \ thus} \hspace{0.4in} r^2 =
\left(\frac{t_1(t_3 - 1)}{1 + t_1t_3}, \frac{t_3(t_1 + 1)}{1 +
t_1t_3}\right)-(f_1,f_2) \ .
$$
Computing the
coefficient like before, we get
$$
\psi_{T_2}(r^2) = \frac{\frac{t_3(t_1 + 1)}{1 + t_1t_3} - f_2}{1 - f_2} \ .
$$
Hence LP (\ref{LP1}) becomes
\begin{equation}\label{LP2}
\begin{array}{rlcl}
\;\; \min & s_1 + s_2 + s_3 \\
& \displaystyle
\frac{\frac{t_3}{t_3 - t_2} - f_1}{1-f_1}s_1 + s_2 +s_3 & \geq 1 &
(\textrm{Triangle }T_1) \\[0.1in]
& s_1 +
\displaystyle
\frac{\frac{t_3(t_1 + 1)}{1 + t_1t_3} - f_2}{1 - f_2}s_2 + s_3 &
\geq 1 & (\textrm{Triangle }T_2) \\
& s \in \mathbb{R}_+^3 .
\end{array}
\end{equation}
As
$$\frac{\frac{t_3}{t_3 - t_2} - f_1}{1-f_1} =
\frac{\frac{t_3}{t_3 - t_2} - 1}{1-f_1} + 1 \ ,
$$
the assumptions
$f_1\leq \frac{1}{2}$ and $t_2 < 1$ yield
$$
\frac{\frac{t_3}{t_3 - t_2} - 1}{1-f_1} + 1
\leq 2\frac{t_3}{t_3 - 1} - 1 \ .
$$
Similarly,
$$
\frac{\frac{t_3(t_1 + 1)}{1 + t_1t_3} - f_2}{1 - f_2} =
\frac{\frac{t_3(t_1 + 1)}{1 + t_1t_3} - 1}{1 - f_2} + 1
$$
and the assumption $f_2\leq \frac{1}{2}$ gives
$$
\frac{\frac{t_3(t_1 + 1)}{1 + t_1t_3} - 1}{1 - f_2} + 1 \leq
2\frac{t_3(t_1 + 1)}{1 + t_1t_3} - 1 = 2\frac{t_3 - 1}{1 + t_1t_3} + 1 \ .
$$
Under the assumption $t_1 > 0$, we obtain
$2\frac{t_3 - 1}{1 + t_1t_3} + 1 \leq 2t_3 - 1$.
To get a lower bound on (\ref{LP2}), we thus can relax its constraints to
\begin{equation}\label{LP3}
\begin{array}{rlcl}
\;\; \min & s_1 + s_2 + s_3 \\[0.1in]
& (2 \displaystyle \frac{t_3}{t_3 - 1} - 1)s_1 + s_2 +s_3 & \geq 1 &
(\textrm{Triangle }T_1) \\[0.1in]
& s_1 + (2t_3 - 1)s_2 + s_3 & \geq 1 & (\textrm{Triangle }T_2) \\[0.1in]
& s \in \mathbb{R}_+^3 .
\end{array}\end{equation}
Set $\lambda = 2t_3 - 1$ and $\mu = 2\frac{t_3}{t_3-1} - 1$. Then
$t_3 > 1$ implies $\lambda >1$ and $\mu > 1$.
The optimal solution of LP (\ref{LP3}) is
$s_1 = \frac{\lambda - 1}{\lambda\mu - 1}$,
$s_2 = \frac{\mu - 1}{\lambda\mu - 1}$ and
$s_3 = 0$
with value
\[
s_1 + s_2 + s_3 = \frac{\lambda + \mu - 2}{\lambda\mu - 1} = \frac{t_3^2 -
2t_3 + 2}{t_3^2} \ .
\]
To find the minimum over all $t_3 >1$, we set the derivative to 0,
which gives the solution $t_3=2$. Thus the minimum value of
$s_1 + s_2 + s_3$ is $\frac{1}{2}$.
\bigskip
Next we consider $f_1 \leq 0$ and $f_1+f_2 \leq \frac{1}{2}$, the
shaded region in Figure~\ref{fig:triangle_with triangle_2}. We relax
Problem (\ref{eq:facet_over_barTf}) using only two inequalities.
We take $T_1$ as before, but $T_2$ is the triangle formed by the
following three lines : $\textrm{Line }2$ from
Lemma~\ref{LEM:type_3_triangle}, line parallel to $\textrm{Line }1$
from Lemma~\ref{LEM:type_3_triangle} but passing through $(-1,1)$
and the line passing through $(1,0),(0,1)$.
\begin{figure}[htbp]
\begin{center}
\scalebox{.5}{\epsfig{file=triangle_with_triangle_2.eps}}
\caption{Approximating a Type $3$ triangle inequality with Type $2$
triangles inequalities - Case 2} \label{fig:triangle_with triangle_2}
\end{center}
\end{figure}
As in the previous case, we formulate the relaxation as an LP with
constraints corresponding to $T_1$ and $T_2$. The only difference from
LP (\ref{LP1}) is the coefficient $\psi_{T_2}(r^2)$. This time the
point $(f_1,f_2) + \gamma r^2$ lies on the line $x_1 + x_2 = 1$ (recall
that $\psi_{T_2}(r^2) = \frac{1}{\gamma}$). This gives us
$$
\psi_{T_2}(r^2) = \frac{\frac{2t_1t_3 + t_3 - t_1}{1 + t_1t_3} -f_1-f_2}
{1-f_1-f_2} \ .
$$
We then have the following LP.
\begin{equation}\label{LP4}
\begin{array}{rlcl}
\;\; \min & s_1 + s_2 + s_3 \\
& \displaystyle
\frac{\frac{t_3}{t_3 - t_2} - f_1}{1-f_1}s_1 + s_2 +s_3 & \geq 1 &
(\textrm{Triangle }T_1) \\[0.2in]
& s_1 + \displaystyle
\frac{\frac{2t_1t_3 + t_3 - t_1}{1 + t_1t_3} -f_1-f_2}{1-f_1-f_2}s_2 + s_3 & \geq 1 & (\textrm{Triangle }T_2) \\[0.2in]
& s \in \mathbb{R}_+^3 .
\end{array}
\end{equation}
We simplify the coefficients as earlier :
$$
\frac{\frac{t_3}{t_3 - t_2} - f_1}{1-f_1} =
1 + \frac{\frac{t_3}{t_3 - t_2} - 1}{1-f_1}
\hspace{0.4in} \mbox{and} \hspace{0.4in}
\frac{\frac{2t_1t_3 + t_3 - t_1}{1 + t_1t_3}
-f_1-f_2}{1-f_1-f_2} =
1 + \frac{\frac{2t_1t_3 + t_3 - t_1}{1 + t_1t_3} - 1}{1-f_1-f_2} \ .
$$
Using the assumptions $f_1\leq 0, f_1+f_2\leq\frac{1}{2}$, we
get that
$$
1 + \frac{\frac{t_3}{t_3 - t_2} - 1}{1-f_1} \leq
\frac{t_3}{t_3 - t_2}
\hspace{0.4in} \mbox{and} \hspace{0.4in}
1 + \frac{\frac{2t_1t_3 + t_3 - t_1}{1 + t_1t_3} - 1}{1-f_1-f_2}
\leq 2 (\frac{2t_1t_3 + t_3 - t_1}{1 + t_1t_3}) - 1 \ .
$$
We also have the conditions $t_2 < 1$ and $t_1 > 0$.
$t_2 < 1$ implies $\frac{t_3}{t_3 - t_2} \leq \frac{t_3}{t_3 -
1}$. Moreover
$$
2\left(\frac{2t_1t_3 + t_3 - t_1}{1 + t_1t_3}\right) - 1 =
2\left(2 + \frac{t_3-t_1 -2}{1 + t_1t_3}\right)-1
$$
decreases in value as $t_1$ increases. Its maximum value is less
than the value for $t_1 = 0$, because of the condition $t_1 > 0$.
It follows that $2(\frac{2t_1t_3 + t_3 -
t_1}{1 + t_1t_3}) - 1 \leq 2t_3 - 1$. After putting these
relaxations into the constraints of LP (\ref{LP4}), we get
\begin{equation}\label{LP5}
\begin{array}{rlcl}
\;\; \min & s_1 + s_2 + s_3 \\[0.1in]
& \displaystyle \frac{t_3}{t_3 - 1}s_1 + s_2 +s_3 & \geq 1 &
(\textrm{Triangle }T_1) \\[0.1in]
& s_1 + (2t_3 - 1)s_2 + s_3 & \geq 1 & (\textrm{Triangle }T_2) \\
& s \in \mathbb{R}_+^3 .
\end{array}
\end{equation}
The optimal solution of LP (\ref{LP5}) is
$$
s_3 = 0, \hspace{0.1in}
s_1 = \frac{2(t_3-1)^2}{2t_3^2 - 2t_3 + 1}, \hspace{0.1in}
s_2 = \frac{1}{2t_3^2 - 2t_3 + 1}, \hspace{0.1in}
\mbox{and} \hspace{0.1in}
s_1 + s_2 + s_3 = \frac{2t_3^2 -4t_3 + 3}{2t_3^2-2t_3+1} \ .
$$
Under the condition $t_3>1$, the minimum value of $s_1 + s_2 + s_3$
is achieved for $t_3=1 + \sqrt{\frac{1}{2}}$ with value $\frac{1}{1
+ \sqrt{\frac{1}{2}}}
> \frac{1}{2}$.
\end{proof}
\section{Split closure vs. a single triangle or quadrilateral
inequality}
In this section, we prove Theorem \ref{THM:T&Q_2}.
This is done by showing that there exist examples of integer
programs (\ref{SI}) where the optimal value for optimizing in the
direction of a triangle (or quadrilateral) inequality over the split
closure $S_f^k$ can be arbitrarily small. We give such examples for
facets derived from triangles of Type $2$ and Type $3$, and from
quadrilaterals.
These examples have the property that the point $f$ lies in the relative
interior of a segment joining two integral points at distance 1.
Furthermore, in these examples, the
rays end on the boundary of the triangle or quadrilateral and hence
the facet corresponding to it is of the form $\sum_{j=1}^k s_j \geq
1$. We show that the following LP has optimal value much less
than 1.
\begin{equation} \label{Split}
\begin{array}{rlcl}
z_{SPLIT} = \;\; \min & \displaystyle \sum_{j=1}^k s_j \\[0.1in]
& \displaystyle \sum_{j=1}^{k} \psi(r^j) s_j & \geq 1 &
\mbox{ for all splits } B_\psi \\[0.1in]
& s \in \mathbb{R}_+^k .
\end{array}
\end{equation}
Theorem~\ref{THM:goemans} then implies
Theorem~\ref{THM:T&Q_2}.
A key step in the proof is a method for constructing a polyhedron
contained in the split closure (Lemma \ref{lem:conv_comb}).
The resulting LP implies an upper bound on $z_{SPLIT}$.
We then give a family of examples showing that this upper bound can be
arbitrarily close to 0.
We start the proof with an easy lemma.
\subsection{An easy lemma}
Refer to Figure
\ref{FIG:LConv} for an illustration of the following lemma.
\begin{figure}[htbp]
\centering
\scalebox{.5}{\epsfig{file=LConv.eps}}
\caption{Illustration for Lemma \ref{LEM:LConv}} \label{FIG:LConv}
\end{figure}
\begin{lemma}
\label{LEM:LConv} Let $r^1$ and $r^2$ be two rays that are not
multiples of each others and let $H_1$ and $H_2$ be the half-lines
generated by nonnegative multiples of $r^1$ and $r^2$ respectively.
Let $p := k_1 \ r^1 + k_2 \ r^2$ with $k_1, k_2 > 0$. Let $L_1,
L_2$, and $L_3$ be three distinct lines going through $p$ such that
each of the lines intersects both $H_1$ and $H_2$ at points other
than the origin. Let $d_{ij}$ be the distance from the origin to the
intersection of line $L_i$ with the half-line $H_j$ for $i= 1, 2, 3$
and $j = 1, 2$. Assume that $d_{11} < d_{21} < d_{31}$. Then there
exists $0 < \lambda < 1$ such that
\begin{eqnarray*}
\frac{1}{d_{21}} = \lambda \ \frac{1}{d_{11}} + (1-\lambda) \
\frac{1}{d_{31}} \hspace{1cm} \mbox{and} \hspace{1cm}
\frac{1}{d_{22}} = \lambda \ \frac{1}{d_{12}} + (1-\lambda) \
\frac{1}{d_{32}}.
\end{eqnarray*}
\end{lemma}
\begin{proof}
Let $u^i$ be a unit vector in the direction of $r^i$ for $i=1, 2$.
Using $\{u^1, u^2\}$ as a
base of $\mathbb{R}^2$, for $i=1, 2, 3$, $L_i$
has equation
$$
\frac{1}{d_{i1}} x_1 + \frac{1}{d_{i2}} x_2 = 1
$$
As $L_2$ is a convex combination of $L_1$ and $L_3$, there exists $0
< \lambda < 1$ such that $\lambda L_1 + (1-\lambda) L_3 = L_2$. The
result follows.
\end{proof}
\begin{corollary}\label{COR:LConv}
In the situation of Lemma \ref{LEM:LConv}, let
$L_4$ be a line parallel to $r^1$ going through $p$. Let $d_{42}$ be
the distance between the origin and the intersection of $H_2$ with
$L_4$. Then there exists $0 < \lambda < 1$ such that
\begin{eqnarray*}
\frac{1}{d_{21}} = \lambda \ \frac{1}{d_{11}} \hspace{1cm}
\mbox{and} \hspace{1cm} \frac{1}{d_{22}} = \lambda \
\frac{1}{d_{12}} + (1-\lambda) \ \frac{1}{d_{42}}.
\end{eqnarray*}
\end{corollary}
\begin{proof}
Similar to the proof of Lemma \ref{LEM:LConv}.
\end{proof}
\begin{figure}[htbp]
\begin{center}
\scalebox{.5}{\epsfig{file=split_closure.eps}}
\caption{Dominating the Split closure with pseudo-splits}
\label{fig:split_closure}
\end{center}
\end{figure}
\subsection{A polyhedron contained in the split closure}
\label{Subsec:on_segment}
Our examples for proving Theorem~\ref{THM:T&Q_2} have the property that
the point $f$ lies in the relative interior of a segment joining two
integral points $y^1$, $y^2$ at distance 1.
To obtain an upper bound on the value $z_{SPLIT}$ of the split
closure, we define some inequalities which dominate the split
closure (\ref{Split}). A \emph{pseudo-split} is the convex set
between two distinct parallel lines passing through $y^1$ and $y^2$
respectively. The direction of the lines, called {\it direction} of
the pseudo-split, is a parameter. Figure~\ref{fig:split_closure}
illustrates three pseudo-splits in the directions of three rays. The
\emph{pseudo-split inequality} is derived from a pseudo-split
exactly in the same way as from any maximal lattice-free convex set.
Note that pseudo-splits are in general not lattice-free and hence do
not generate valid inequalities for $R_f^k$. However, we can
dominate any split inequality cutting $f$ by an inequality derived
from these convex sets. Indeed, consider any split $S$ containing
the fractional point $f$ in its interior. Since $f$ lies on the
segment $y^1y^2$, both boundary lines of $S$ pass through the
segment $y^1y^2$. The pseudo-split with direction identical to the
direction of $S$ generates an inequality that dominates the split
inequality derived from $S$, as the coefficient for any ray is
smaller in the pseudo-split inequality.
The next lemma states that we can dominate the split closure by
using only the inequalities generated by the pseudo-splits with
direction parallel to the rays $r^1, \ldots , r^k$ under mild assumptions
on the rays.
\begin{lemma}\label{lem:conv_comb}
Assume that none of the rays $r^1, \ldots, r^k$ has a zero first
component and that $f = (0, f_2)$ with $0 < f_2 < 1$. Let
$y^1 = (0, 1)$ and $y^2 = (0, 0)$, these two points being used to
construct pseudo-splits. Let $S_1, \ldots ,S_k$ be the pseudo-splits
in the directions of rays $r^1, \ldots, r^k$ and denote the
corresponding minimal functions by $\psi_{S_1},\ldots,\psi_{S_k}$.
Let $S$ be any split with $f$ in its interior and let $S'$ be the
corresponding pseudo-split. Then the inequality $\sum_{j=1}^k
\psi_{S'}(r^j) s_j \geq 1$ corresponding to $S'$ is dominated by a
convex combination of the inequalities $\sum_{j=1}^k
\psi_{S_i}(r^j)s_j \geq 1$, $i=1,\ldots, k$. Therefore, the split
inequality corresponding to $S$ is dominated by a convex combination
of the inequalities corresponding to $\psi_{S_1},\ldots,\psi_{S_k}$.
\end{lemma}
\begin{proof}
As a convention, the direction
of a pseudo-split forms an angle with the $x_1$-axis in the range of
$]-\frac{\pi}{2},\frac{\pi}{2}[$. Without loss of generality, assume
that the slope of the directions of the pseudo-splits corresponding to
the rays $r^1, \ldots r^k$ are monotonically non increasing.
We can assume that the direction of $S'$ is different than the direction of
any of the rays in $\{r^1, \ldots, r^k\}$ as otherwise the result
trivially holds.
\begin{figure}[htbp]
\begin{center}
\scalebox{.55}{\epsfig{file=split_closure_3.eps}} \caption{Bounding
the split closure with a finite number of pseudo-splits}
\label{fig:split_closure_3}
\end{center}
\end{figure}
First note that, if $S'$ has a direction with slope greater
than the slope of $r^1$, then the inequality
generated by $S'$ is dominated by the one generated by $S_1$.
Indeed, any ray $r^j$ having a slope smaller than $r^1$ has its boundary
point for $S'$ closer to $f$ than the one for $S_1$.
It follows that $\psi_{S'}(r^j) \geq \psi_{S_1}(r^j)$. See
Figure~\ref{fig:split_closure_3}. A similar reasoning holds for the
case where $S'$ has a direction with slope smaller
than the slope of $r^k$.
Thus we only have to consider the case where the slope of the direction of
$S'$ is strictly between the
slopes of the directions of $S_i$ and $S_{i+1}$, for some $1 \le i \le k-1$.
We claim the following.
\begin{observation}\label{obs:conv_comb}
There exists a $0< \lambda <1$ such that $\psi_{S'}(r) =
\lambda\psi_{S_i}(r) + (1-\lambda)\psi_{S_{i+1}}(r)$ for every ray
$r \in \{r^1, \ldots, r^k\}$.
\end{observation}
\begin{proof}
For each pseudo-split $S \in \{S', S_i, S_{i+1}\}$, we denote by
$L^S_1$ its boundary line passing though $(0,1)$ and by $L^S_2$
its boundary line passing through $(0,0)$.
Consider first any ray $r^j$ with $j < i$ and let
$L^{r^j}$ be the half-line $f + \mu r^j$, $\mu \ge 0$.
We have that $L^{r^j}$ has a slope greater than the slope of the
direction of $S_i$ and thus $L^{r^j}$ intersects the boundaries of $S', S_i$
and $S_{i+1}$ on $L^{S'}_1$, $L^{S_{i+1}}_1$ and $L^{S_i}_1$.
By Lemma~\ref{LEM:LConv},
there exists a $0 < \lambda_1 < 1$ such
that, for all $r \in \{r^1, \ldots, r^{i-1}\}$
\begin{equation}\label{eq:conv_comb1}
\psi_{S'}(r) = \lambda_1\psi_{S_i}(r) + (1-\lambda_1)\psi_{S_{i+1}}(r) \ .
\end{equation}
By Corollary~\ref{COR:LConv}, equation (\ref{eq:conv_comb1}) also holds
for $r = r^i$.
Using a similar reasoning for the rays $\{r^{i+1}, \ldots, r^k\}$
and the boundary lines $L^{S'}_2$, $L^{S_{i+1}}_2$ and $L^{S_i}_2$,
there exists a $0 < \lambda_2 < 1$ such that, for all
$r \in \{r^{i+1}, \ldots, r^{k}\}$
\begin{equation}\label{eq:conv_comb2}
\psi_{S'}(r) = \lambda_2\psi_{S_i}(r) + (1-\lambda_2)\psi_{S_{i+1}}(r) \ .
\end{equation}
It remains to show that $\lambda_1 = \lambda_2$. Consider any line $L$
through $f$ that is not collinear with $r^i$ or $r^{i+1}$ and not going
through $y^1$ and $y^2$. For each $S \in
\{S', S_i, S_{i+1}\}$, let $z^S_1$ (resp. $z^S_2$) be the
intersection of $L$ with $L^{S}_1$ (resp. $L^S_2$) and let $d^S_{1}$
(resp. $d^S_{2}$) be the distance from $f$ to $z^S_1$ (resp.
$z^S_2$). See Figure~\ref{fig:split_closure_3}. By
Lemma~\ref{LEM:LConv}
\begin{eqnarray}\label{eq:equalLambdas}
\frac{1}{d^{S'}_{1}} = \lambda_1 \ \frac{1}{d^{S_i}_{1}} + (1-\lambda_1) \
\frac{1}{d^{S_{i+1}}_{1}} \hspace{1cm} \mbox{and} \hspace{1cm}
\frac{1}{d^{S'}_{2}} = \lambda_2 \ \frac{1}{d^{S_i}_{2}} + (1-\lambda_2) \
\frac{1}{d^{S_{i+1}}_{2}}.
\end{eqnarray}
The length of segments $fy^1, fz^S_1, fy^2$ and $fz^S_2$ are
respectively $1-f_2, d^S_1, f_2$ and $d^S_2$.
Observe that the triangles $fz^S_1y^1$ and $fz^S_2y^2$
are homothetic with homothetic ratio $t = \frac{1-f_2}{f_2}$.
It follows that
$\frac{d^S_1}{d^S_2} = t$.
Substituting $d^S_1$ by $t \cdot d^S_2$ in (\ref{eq:equalLambdas})
yields $\lambda_1 = \lambda_2$.
\end{proof}
This observation proves the lemma.
\end{proof}
Using the above lemma, we can bound the split closure for three
rays. We assume that none of the rays has a zero first component
and that the three rays generate $\mathbb{R}^2$.
Without loss of generality, we make the
following assumptions. The rays are $r^1 = \mu_1(-1, t_1)$, $r^2 =
\mu_2(1,t_2)$ and $r^3 = \mu_3(-1, t_3)$, where $t_i$'s are rational
numbers in the range $]-\infty,\infty[$, with $t_1 > t_3$ and
$\mu_i$'s are scaling factors with $\mu_i > 0$. Any configuration of
three rays satisfying the above assumptions either fits this
description or is a reflection of it about the segment
$(0,0),(0,1)$. In addition, we must have $-t_1 < t_2 < -t_3$. See
Figure~\ref{fig:split_closure} for an illustration.
\begin{theorem}
Assume that $f = (0, f_2)$ with $0 < f_2 < 1$.
Consider rays $r^1 = \mu_1(-1, t_1)$, $r^2 = \mu_2(1,t_2)$ and $r^3 =
\mu_3(-1, t_3)$, where $t_i$'s are rational numbers with
$-t_1 < t_2 < -t_3$ and $\mu_i > 0$. Then
$$
z_{SPLIT} \leq
\frac{1}{t_1 - t_3}\left(\frac{1-f_2}{\mu_1}+\frac{f_2}{\mu_3}\right) \ .
$$
\end{theorem}
\begin{proof}
Let $y^1 = (0, 1)$ and $y^2 = (0, 0)$, these two points being used to
construct pseudo-splits.
By Lemma~\ref{lem:conv_comb}, we know that the three pseudo-splits
$S_1, S_2, S_3$ corresponding to the directions of $r^1, r^2, r^3$
dominate the entire split closure. More formally, the following LP
is a strengthening of (\ref{Split}) in this example of three rays.
\begin{equation}\label{eq:split_closure}
\begin{array}{rlcl}
\min & s_1 + s_2 + s_3 & &\\
&\psi_{S_1}(r^1)s_1 + \psi_{S_1}(r^2)s_2 + \psi_{S_1}(r^3)s_3 & \geq 1 & \\
&\psi_{S_2}(r^1)s_1 + \psi_{S_2}(r^2)s_2 + \psi_{S_2}(r^3)s_3 & \geq 1 & \\
&\psi_{S_3}(r^1)s_1 + \psi_{S_3}(r^2)s_2 + \psi_{S_3}(r^3)s_3 & \geq 1 & \\
& s \in \mathbb{R}_+^3 .
\end{array}
\end{equation}
It is fairly straightforward to compute the coefficients in the above
inequalities. We give the calculations for $S_1$; the coefficients for
the other two follow along similar lines.
$\psi_{S_1}(r^1)$ is $0$, since $r^1$ is parallel to the direction of $S_1$.
Consider $r^2$ and let its boundary point $p$ for $S_1$ be
$(0,f_2) + \gamma \mu_2(1,t_2)$, for some $\gamma \geq 0$. Then
$\psi_{S_1}(r^2)$ is $\frac{1}{\gamma}$. To compute $\gamma$, we
observe that $p$ is on boundary $1$ of $S_1$, by assumption of
$t_2 > -t_1$. Hence, the slope of the line connecting $p$ and $(0,1)$ is
$-{t_1}$. Therefore,
\[
\frac{f_2 + \gamma\mu_2 t_2 - 1}{0 + \gamma\mu_2} = -{t_1}
\]
which yields $\gamma = \frac{1-f_2}{\mu_2(t_1 + t_2)}$. Hence
$\psi_{S_1}(r^2) = \frac{\mu_2(t_1 + t_2)}{1-f_2}$.
Now consider $r^3$. As before, let its boundary point $p'$ for $S_1$
be $(0,f_2) + \gamma' \mu_3(-1,t_3)$, for some $\gamma' \geq 0$.
This time note that the ray intersects boundary $2$ (by the assumption
$t_3 < t_1$). Equating slopes, we get
\[
\frac{f_2 + \gamma' \mu_3t_3}{0 - \gamma'\mu_3} = -{t_1}
\]
which yields $\gamma' = \frac{f_2}{\mu_3(t_1 - t_3)}$. Hence
$\psi_{S_1}(r^3) = \frac{\mu_3(t_1 - t_3)}{f_2}$.
So we have that the inequality corresponding to $S_1$ is
\[
0\cdot s_1 + \frac{\mu_2(t_1 + t_2)}{1-f_2}s_2 + \frac{\mu_3(t_1 -
t_3)}{f_2}s_3 \geq 1 \ .
\]
By very similar calculations, we can get the inequalities corresponding to
$\psi_{S_2}$ and
$\psi_{S_3}$. LP (\ref{eq:split_closure}) becomes
\begin{equation}\label{eq:split_closure2}
\begin{array}{rlcl}
\min & s_1 + s_2 + s_3 & &\\
& 0\cdot s_1 + \displaystyle
\frac{\mu_2(t_1 + t_2)}{1-f_2}s_2 + \frac{\mu_3(t_1 - t_3)}{f_2}s_3 &
\geq 1 & \\[0.1in]
& \displaystyle \frac{\mu_1(t_1 + t_2)}{1-f_2}s_1 + 0\cdot s_2 +
\frac{\mu_3(-t_3 - t_2)}{f_2}s_3 & \geq 1 & \\[0.1in]
& \displaystyle \frac{\mu_1(t_1 -t_3)}{1-f_2}s_1 +
\frac{\mu_2(-t_3 - t_2)}{f_2}s_2 + 0 \cdot s_3 & \geq 1 & \\[0.1in]
& s \in \mathbb{R}_+^3 .
\end{array}
\end{equation}
As a sanity check, note that the assumption $-t_1 < t_2 < -t_3$
implies that all the coefficients are nonnegative.
The following solution is feasible for LP (\ref{eq:split_closure2}):
$$
s_1 = \frac{1-f_2}{\mu_1(t_1 - t_3)}, \hspace{0.1in}
s_2 = 0, \hspace{0.1in}
s_3 = \frac{f_2}{\mu_3(t_1 -t_3)} \hspace{0.1in}
\hspace{0.1in} \mbox{and} \hspace{0.1in}
s_1 + s_2 + s_3 =
\frac{1}{t_1 - t_3}\left(\frac{1-f_2}{\mu_1}+\frac{f_2}{\mu_3}\right) \ .
$$
Since the above LP was a strengthening of (\ref{Split}),
we obtain
$$
z_{SPLIT} \leq s_1 + s_2 + s_3 =
\frac{1}{t_1 - t_3}\left(\frac{1-f_2}{\mu_1}+\frac{f_2}{\mu_3}\right) \ .
$$
\end{proof}
If the rays are such that $\mu_1 = \mu_3 = 1$, then the above
expression is $\frac{1}{t_1 - t_3}$. This implies that in this case
if we have rays such that $(t_1 - t_3)$ tends to infinity, then
$z_{SPLIT}$ tends to $0$.
\subsection{Type $2$ triangles that do much better than the split closure}
\label{sec:type2}
In Section \ref{Subsec:on_segment}, we showed that we can bound the
value of the split closure under mild conditions on $f$ and the
rays. In particular, we showed that as $t_1 - t_3$ increases in
value, the split closure does arbitrarily bad. In this section, we
consider an infinite family of Type $2$ triangles with rays pointing
to its corners which satisfy these conditions.
Consider the same situation as in Section \ref{Subsec:on_segment}
and consider the Type $2$ triangle $T$ with the following three
edges. The line parallel to the $x_2$-axis and passing through
$(-1,0)$ supports one of the edges, and the other two edges are
supported by lines passing through $(0,1)$ and $(0,0)$ respectively.
See left part of Figure~\ref{fig:type2_triangle}. Note that in this
example, the rays are of the form $r^1 = (-1,t_1), r^2 = \mu(1,t_2),
r^3 = (-1,t_3)$. In the notation of Section~\ref{Subsec:on_segment},
$\mu_1 = \mu_3 = 1$.
\begin{figure}[htbp]
\begin{center}
\scalebox{.5}{\epsfig{file=type2_triangle.eps}}
\caption{Facets from Type 2 triangles with large gap versus the
split closure}
\label{fig:type2_triangle}
\end{center}
\end{figure}
\begin{theorem}
Given any $\alpha > 1$, there exists a Type 2
triangle $T$ as shown in Figure~\ref{fig:type2_triangle}
such that for any point $f$ in the relative interior of the
segment joining $(0,0)$ to $(0,1)$, LP
(\ref{Split}) has value $z_{SPLIT} \leq \frac{1}{\alpha}$.
\end{theorem}
\begin{proof}
Let $M = \lceil\alpha\rceil$.
When the fractional point $f$ is on the segment connecting
$(0,0)$ and $(0,1)$, consider the triangle $T$ with $M$ integral points in the
interior of the vertical edge (the triangle on the left in
Figure~\ref{fig:type2_triangle}). This implies $t_1 - t_3 \geq M$.
Therefore, from the result of Section~\ref{Subsec:on_segment},
$\mu_1 = \mu_3 = 1$ implies that $z_{SPLIT}\leq \frac{1}{t_1 - t_3}
\leq \frac{1}{\alpha}$.
\old{
When the fractional point is not on the
segment connecting $(0,0),(0,1)$ but is in the interior of triangle $\Delta$
with vertices $(0,0)$, $(0,1)$ and the vertex $x^2$ of $T$ with
positive first coordinate (on the right in
Figure~\ref{fig:type2_triangle}), consider a triangle $T$ with $2M$
integral points on the vertical edge. Thus, $t_1 - t_3 \geq 2M$.
From Section~\ref{Subsec:off_segment}, $\mu_1 = \mu_3 = 1$ implies
that $z_{SPLIT}\leq \frac{2}{t_1 + t_3} \leq \frac{1}{M} \leq
\frac{1}{\alpha}$.
}
\end{proof}
In this example, for any large constant $\alpha$, optimizing
over the split closure in the direction of the facet defined by
these Type $2$ triangles yields at most $\frac{1}{\alpha}$. This
implies Theorem~\ref{THM:T&Q_2}.
\subsection{More bad examples}
The examples of Section \ref{sec:type2} can be modified in various ways while keeping the property that the split closure is arbitrarily bad. The proofs are similar to that of Theorem~\ref{THM:T&Q_2}.
\subsubsection{Type 2 triangles when $f$ is not on the segment
joining $(0,0)$ to $(0,1)$}
The example of Section \ref{sec:type2} can be generalized to the case
where $f$ is not on the segment connecting the points $(0,0)$ and $(0,1)$
as follows. Let $T$ be a Type 2 triangle as shown on the right part of
Figure~\ref{fig:type2_triangle}. Let $\Delta$ be the triangle
with vertices $(0,0)$, $(0,1)$ and the vertex $x^2$ of $T$ with
positive first coordinate.
When the fractional point $f$ is in the interior of triangle $\Delta$,
and triangle $T$ has $2M$ integral points on its vertical edge, one can show that $z_{SPLIT}\leq \frac{1}{M}$.
However, such bad examples cannot be constructed for any position of
point $f$ in the triangle $T$. In particular, define the triangle
$\Delta '$ obtained from $\Delta$ by a homothetic transformation
with center $x^2$ and factor 2 (so one vertex of $\Delta '$
is $x^2$ and points $(0,0)$ and $(0,1)$ become the middle points of the
two edges of $\Delta '$ with endpoint $x^2$).
When $f$ is an interior point of $T$ outside $\Delta '$, it is easy
to see that the split inequality obtained from the split parallel
to the $x_2$-axis $-1 \leq x_1 \leq 0$ approximates the triangle
inequality defined by $T$ to within a factor at most 2. Indeed the
linear program is
\begin{equation}
\begin{array}{rlcl}
\min & s_1 + s_2 + s_3 & &\\[0.1in]
& \displaystyle
s_1 + \frac{f_1 - u}{f_1}s_2 + s_3 & \geq 1 & \\[0.1in]
& s \in \mathbb{R}_+^3 ,
\end{array}
\end{equation}
\noindent where $u$ is the first coordinate of $x^2$. The optimal
solution is $s_1 = 0$, $s_2=\frac{f_1}{f_1-u}$, $s_3=0$. Thus
$s_1+s_2+s_3= \frac{f_1}{f_1-u} \geq \frac{1}{2}$ since $f_1 \leq
-u$ for any $f \in T \setminus \Delta '$. This implies that the
split inequality approximates the triangle inequality by a factor at
most 2 when $f$ is outside $\Delta '$.
\begin{figure}[htbp]
\begin{center}
\scalebox{.5}{\epsfig{file=type3_and_quad.eps}} \caption{Facets from
Type 3 triangles and quadrilaterals on which the split closure does
poorly} \label{fig:type2_and_quad}
\end{center}
\end{figure}
\subsubsection{Triangles of Type 3 and quadrilaterals}
We now show how to modify the construction of Section
\ref{sec:type2} to get examples of Type $3$ triangles and
quadrilaterals that do arbitrarily better than the split closure.
To get a Type 3 triangle, we tilt the vertical edge of the triangle in
Figure~\ref{fig:type2_triangle} around its integral point with minimum
$x_2$-value. See Figure \ref{fig:type2_and_quad}. The same bound on
$z_{SPLIT}$ is then achieved.
Similarly, quadrilaterals can be constructed by breaking the
vertical edge in Figure~\ref{fig:type2_triangle} into two edges of
the quadrilateral. See Figure \ref{fig:type2_and_quad}. By very
similar arguments as in the previous section, we can show that
$z_{SPLIT}$ tends to $0$.
\bigskip
{\bf Acknowledgements:} We thank the referees for their very helpful comments.
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 9,686
|
package org.auraframework.modules.impl.source;
import org.auraframework.adapter.ComponentLocationAdapter;
import org.auraframework.annotations.Annotations.ServiceComponent;
import org.auraframework.def.DefDescriptor.DefType;
import org.springframework.context.annotation.Lazy;
/**
* Provides location of components for aura-modules
*/
@Lazy
@ServiceComponent
public class AuraModulesModulesLocationAdapter extends ComponentLocationAdapter.Impl {
public AuraModulesModulesLocationAdapter() {
super(AuraModulesFiles.MODULES_DIR.asFile(), null, "modules_aura_modules");
}
/**
* Distinguish between Aura component and modules locations.
* Module require separate registry that handles its own def type to allow
* coexistence of components and modules of the same name.
*
* Overrides default with MODULE
*
* @return DefType.MODULE for module
*/
@Override
public DefType type() {
return DefType.MODULE;
}
}
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 965
|
Produced by Al Haines
LONDON
IN MODERN TIMES;
Or, Sketches of
THE ENGLISH METROPOLIS
DURING THE
SEVENTEENTH AND EIGHTEENTH CENTURIES.
New York
PUBLISHED BY CARLTON & PORTER,
SUNDAY-SCHOOL UNION, 200 MULBERRY-STREET.
1851
CONTENTS.
Chap.
INTRODUCTION
I.--LONDON UNDER THE FIRST TWO MONARCHS OF THE STUART DYNASTY
II.--LONDON DURING THE CIVIL WARS
III.--THE PLAGUE YEAR IN LONDON
IV.--THE FIRE OF LONDON
V.--FROM THE RESTORATION OF THE CITY TO THE CLOSE OF THE CENTURY
VI.--LONDON DURING THE FIRST HALF OF THE EIGHTEENTH CENTURY
VII.--LONDON DURING THE LATTER HALF OF THE EIGHTEENTH CENTURY
LONDON
IN MODERN TIMES.
INTRODUCTION.
This history of an old city opens many views into the realms of the
past, crowded with the picturesque, the romantic, and the
religious--with what is beautiful in intellect, sublime in feeling,
noble in character--and with much, too, the reverse of all this.
Buildings dingy and dilapidated, or tastelessly modernized, in which
great geniuses were born, or lived, or died, become, in connection with
the event, transformed into poetic bowers; and narrow dirty streets,
where they are known often to have walked, change into green alleys,
resounding with richer notes than ever trilled from bird on brake.
Tales of valor and suffering, of heroism and patience, of virtue and
piety, of the patriot's life and the martyr's death, crowd thickly on
the memory. Nor do opposite reminiscences, revealing the footprints of
vice and crime, of evil passions and false principles, fail to arise,
fraught with salutary warnings and cautions. The broad thoroughfare is
a channel, within whose banks there has been rolling for centuries a
river of human life, now tranquil as the sky, now troubled as the
clouds, gliding on in peace, or lashed into storms.
These dwelling-places of man are proofs and expressions of his
ingenuity, skill, and toil, of his social instincts and habits. Their
varied architecture and style, the different circumstances under which
they were built, the various motives and diversified purposes which led
to their erection, are symbols and illustrations of the innumerable
forms, the many hues, the strange gradations of men's
condition, character, habits, tastes, and feelings. Each house has its
own history--a history which in some cases has been running on since an
era when civilization wore a different aspect from what it does now.
What changeful scenes has many a dwelling witnessed!--families have
come and gone, people have been born and have died, obedient to the
great law--"the fashion of this world passeth away." Those rooms have
witnessed the birth and departure of many, the death of the guilty
sinner or pardoned believer, the gay wedding and the gloomy funeral,
the welcome meeting of Christmas groups around the bright fireside, and
the sad parting of loved ones called to separate into widely divergent
paths. Striking contrasts abound between the outward material aspect
and the inward moral scenery of those habitations. In this house,
perhaps, which catches the passenger's eye by its splendor, through
whose windows there flashes the gorgeous light of patrician luxury, at
whose door lines of proud equipages drive up, on whose steps are
marshaled obsequious footmen in gilded liveries, there are hearts
pining away with ambition, envy, jealousy, fear, remorse, and agony.
In that humble cottage-like abode, on the other hand, contentment,
which with godliness is great gain, and piety, better than gold or
rubies, have taken up their home, and transformed it into a terrestrial
heaven.
All this applies to London, and gives interest to our survey of it as
we pass through its numerous streets; it clothes it with a poetic
character in the eyes of all gifted with creative fancy. The poetry of
the city has its own charms as well as the poetry of the country. The
history of London supplies abundant materials of the character now
described; indeed, they are so numerous and diversified that it is
difficult to deal with them. The memorials of the mother city are so
intimately connected with the records of the empire, that to do justice
to the former would be to sketch the outline, and to exhibit most of
the stirring scenes and incidents of the latter. London, too, is
associated closely with many of the distinguished individuals that
England has produced, with the progress of arts, of commerce and
literature, politics and law, religion and civilization; so that, as we
walk about it, we tread on classic ground, rich in a thousand
associations. Its history is the history of our architecture, both
ecclesiastical and civil. The old names and descriptions of its
streets, houses, churches, and other public edifices, aided by the few
vestiges of ancient buildings which have escaped the ravages of fire,
time, and ever-advancing alterations, bring before us a series of
views, exhibiting each order of design, from the Norman to the Tudor
era. In the streets of London, too, may be traced the progress of
domestic building, from the plain single-storied house of the time of
Fitzstephen, to the lofty and many-floored mansion of the fifteenth
century, with its picturesque gables, ornamented front, and twisted
chimneys. Then these melt away before other forms of taste and art.
In the days of Elizabeth, churches and dwellings become Italianized.
The architects under the Stuart dynasty make fresh innovation, till,
during the last century, skill and genius in this department reached
their culminating point. Since that period a recurrence to the study
of old models has gradually been raising London to distinction, with
regard to the elegance and beauty of its architectural appearance.
The history of London is the history of our commerce. Here is seen
gushing up, in very early times, that stream of industry, activity, and
enterprise, which from a rill has swelled into a river, and has borne
upon its bosom our wealth and our greatness, our civilization, and very
much of our liberty.
The London guilds and companies; the London merchant princes; the
London marts and markets; the London granaries for corn; the public
exchanges, built for the accommodation of money-brokers and traders
long before Gresham's time; the London port, wharfs, and docks, crowded
with ships of all countries, laden with treasures from all climes; the
London streets, many of which still bear the names of the trades to
which they were allotted, and the mercantile purposes for which they
were employed:--all these, which form so large a part of the materials,
and supply so great a portion of the scenes of London history, are
essentially commercial, and bring before us the progress of that
industrial spirit, which, with all its failings and faults, has
contributed so largely to the welfare and happiness of modern society.
The history of London is a history of English literature. Time would
fail to tell of all the memorials of genius with which London abounds;
memorials of poets, philosophers, historians, and divines, who have
there been born, and lived, and studied, and toiled, and suffered, and
died. No spot in the world, perhaps, is so rich in associations
connected with the history of great minds. There is scarcely one of
the old streets through which you ramble, or one of the old churches
which you enter, but forthwith there come crowding over the mind of the
well-informed, recollections of departed genius, greatness, or
excellence.
The history of London is the history of the British constitution and
laws. There thicken round it most of the great political conflicts
between kings and barons, and lords and commons; between feudalism and
modern liberty; between the love of ancient institutions and the spirit
of progress, from which, under God, have sprung our civil government
and social order.
The history of London is the history of our religion, both in its
corrupted and in its purified forms. Early was it a grand seat of
Romish worship; numerous were its religious foundations in the latter
part of the mediaeval age. Here councils have been held, convocations
have assembled, controversies were waged, and truth exalted or
depressed. Smithfield and St. Paul's Churchyard are inseparably
associated with the Reformation. The principles proclaimed from the
stone pulpit of the one could not be destroyed by the fires that blazed
round the stakes of the other. The history of the Protestant
Establishment ever since is involved in that of our city; places
connected with its grand events, its advocates, and its ornaments, are
dear to the hearts of its attached children; while other spots in
London, little known to fame, are linked to the memory of the Puritans,
and while reverently traced out by those who love them, are regarded as
hallowed ground.
In London, too, have flourished many of the excellent of the earth; men
who, amidst the engrossing cares and distracting tumults of a large
metropolis, have, like Enoch, walked with God, and leavened, by virtue
of their piety and prayers, the masses around them. Here also have
flourished, and still flourish, those great religious institutions,
which have made known to the remotest parts of the earth the glad
tidings of the gospel, that "God so loved the world, that he gave his
only begotten Son, that whosoever believeth in him should not perish,
but have everlasting life"--truths more precious than the merchandise
of silver, and the gain whereof is greater than pure gold.
Some of the early chapters of London history we have already
written;[1] we have given some sketches of its scenes and fortunes,
from the time when it was founded by the Romans to what are called,
with more of fiction's coloring than history's faithfulness, "the
golden days of good queen Bess." We now resume the story, and proceed
to give some account of London during the seventeenth and eighteenth
centuries.
[1] See "London in the Olden Time," No. 492 Youth's Library.
CHAPTER I.
LONDON UNDER THE FIRST TWO MONARCHS OF THE STUART DYNASTY.
London was hugely growing and swelling on all sides when Elizabeth was
on the throne, as may be seen from John Stow, from royal orders and
municipal regulations. Desperately frightened were our fathers lest
the population should increase beyond the means of support, lest it
should breed pestilence or cause famine. But their efforts to repress
the size of the then infant leviathan, so far as they took effect, only
kept crowded together, within far too narrow limits, the
ever-increasing number of the inhabitants of the city, thus promoting
disease, one of the greatest evils they wished to check. In spite of
all restrictions, however, the growth of population, together with the
impulses of industry and enterprize, would have their own way, and
building went on in the outskirts in all directions. James imitated
Elizabeth in her prohibitions, and the people imitated their
predecessors in the disregard of them. The king was soon obliged to
give way, so far as to extend the liberties of the city; and in the
fifth year of his reign he granted a new charter, embracing within the
municipal circuit and jurisdiction the extra-mural parishes of Trinity,
near Aldgate-street, St. Bartholomew, Little St. Bartholomew,
Blackfriars, Whitefriars, and Cold Harbor, Thames-street. These grants
were confirmed by Charles I., whose charter also enclosed within the
city boundaries both Moorfields and Smithfield. These places rapidly
lost more and more of their rural appearance, and became covered in the
immediate vicinity of the old walls with a network of streets. But
London as it appears on the map of that day, was still a little affair,
compared with its subsequent enormous bulk. Pancras, Holloway,
Islington, Kentish Town, Hampstead, St. John's Wood, Paddington,
Kilburn, and Tottenham Court, were widely separated from town by rural
walks; these "ways over the country," as a poet of the day describes
them, not being always safe for travelers to cross. St. Giles's was
still "in the fields," and Charing Cross looked towards the west, upon
the fair open parks of the royal domain. But the Strand was becoming a
place of increasing traffic, and the houses on both sides were
multiplying fast. So valuable did sites become, even in the beginning
of the seventeenth century, that earls and bishops parted with portions
of their domains in that locality for the erection of houses, and
Durham Place changed its stables into an Exchange in 1608.
Of the architecture which came into fashion in the reign of James I.,
three noble specimens remain in London and the neighborhood.
Northumberland House, which stands on the spot once occupied by the
hospital of St. Mary, finally dissolved at the Reformation, was erected
by Henry Howard, earl of Northampton, son of the poet Surrey, and
originally called from him Southampton House; he died in 1614. It
afterwards took the name of Suffolk House, from its coming into the
possession of the earl of Suffolk; its present name was given on the
marriage of the daughter of Suffolk with Algernon Percy, tenth earl of
Northumberland. It was built with three sides, forming with the river,
which washed its court and garden, a magnificent quadrangle. Jansen is
the reputed architect, but the original front is considered to have
been designed by Christmas, who rebuilt Aldersgate about the same time.
The fourth side was afterwards built by the earl of Northumberland,
from a design by Inigo Jones. Holland House, at Kensington, now
occupied by Lord Holland, belongs to the same period, being erected in
1607 by Sir Walter Cope, and enlarged afterwards by the Earl of
Holland, from plans prepared by the illustrious architect just named.
These structures are worthy of examination. They evince some lingering
traits of the Tudor Gothic, which flourished in the middle of the
former age, but exhibit the predominance of that Italian taste which
had been introduced in the reign of Elizabeth, and which continued to
prevail till it ended in the corrupt and debased style of the last
century. The Banqueting House at Whitehall is a more imposing and
splendid relic, and presents an instance of the complete triumph of the
Italian school of architecture over its predecessors. It was designed
by Inigo Jones in the maturity of his genius, and forms only a small
part of a vast regal palace, of which the plans are still preserved.
The exterior buildings were to have measured eight hundred and
seventy-four feet on the east and west sides, and one thousand one
hundred and fifty-two on the north and south. The Banqueting House was
finished in 1619, and cost L17,000. It is curious to learn, that the
great "architect's commission" amounted to no more than 8_s._ 1_d._ a
day as surveyor, and L46 a year for house-rent, a clerk, and other
expenses. It may be added, that further specimens of this architecture
and sculpture of that period can be seen in some parts of the Charter
House.
Generally, it may be observed, London retained much of its ancient
architectural appearance till it was destroyed by the fire. Old public
buildings were still in existence; Gothic churches lifted up their gray
towers and spires, and vast numbers of the houses of the nobility and
rich merchants of a former age displayed their picturesque fronts, and
opened their capacious hospitable halls; while the new habitations of
common citizens were usually built in the slightly modified style of
previous times, with stories projecting one above another, adorned with
oak carvings or plastic decorations. Royal injunctions were repeatedly
issued to discontinue this sort of building, and to erect houses of
stone or brick. A writer of the day affords many peeps into the state
of London at the time we now refer to. He describes ladies passing
through the Strand in their coaches to the china houses or the
Exchange. He tells of 'a rare motion, or puppet-show,' to be seen in
Fleet-street, and of one representing 'Nineveh, with Jonah and the
whale,' at Fleet-bridge. Indeed, this was the thoroughfare or the
grand place for the quaint exhibitions of the age. Cold Harbor is
described as a resort for spendthrifts, Lothbury abounded with
coppersmiths, Bridge-row was rich in rabbit-skins, and Panyer's-alley
in tripe. So nearly did the houses on opposite sides of the way
approach together, that people could hold a _tete a tete_ in a low
whisper from each other's windows across the street. From another
source we learn that dealers in fish betook themselves to the Strand,
and there blocked up the highway. "For divers years of late certain
fishmongers have erected and set up fish-stalls in the middle of the
street in the Strand, almost over against Denmark House, all which were
broken down by special commission this month of May, 1630--lest, in
short space, they might grow from stalls to sheds, and then to
dwelling-houses, as the like was in former times in Old Fish-street,
and in St. Nicholas's shambles, and other places."[1]
It may be added, that it was still, at this period, the custom for
persons of a similar trade to occupy the same locality. "Then," says
Maitland, in his History of London, "it was beautiful to behold the
glorious appearances of goldsmiths' shops on the south row of
Cheapside, which in a continued course reached from Old Change to
Bucklersbury, exclusive of four shops only of other trades in all that
space." This "unseemliness and deformity," as his majesty was pleased
to call it in an order of council in 1629, greatly provoked the royal
displeasure; yet in spite of efforts to the contrary from that high
quarter, not only did the four obnoxious tradesmen keep their ground,
but a few years after the king had to complain of greater
irregularities. Four and twenty houses, he affirmed, were inhabited by
divers tradesmen, to the beclouding of the glory of the goldsmiths, and
the disturbance of his majesty's love of order and uniformity. He went
so far as to threaten the imprisonment of the alderman of the ward, if
he would not see to this matter, and remove the offenders. It is said
of Charles V., that after he resigned his crown, he amused himself by
trying to make several clocks keep the same time, and on the failure of
his experiment observed, that if he could not accomplish that, no
wonder he had not succeeded in bringing his numerous subjects into a
state of ecclesiastical conformity. Charles I. might, from his
inability to make men of the same trade live together in one row, have
learned a similar lesson. This trifling conflict exhibits no unapt
similitude of one of the aspects of the great evil conflict, the edge
of which he was then approaching. Other street irregularities were
loudly complained of by the lord mayor. Notwithstanding the numerous
laws made to restrain them from so doing, bakers, butchers, poulterers,
and others, would persist in encumbering the public thoroughfares with
their stalls and vendibles.
London, during the reign of the first James and Charles, was a sphere
of commercial activity. Monopolies and patents did, it is true,
greatly <DW36> the movements of trade. Nothing scarcely could be done
without royal permission, for which large sums of money had to be paid.
It was complained of, that "every poor man that taketh in but a horse
on a market-day, is presently sent up for to Westminster and sued,
unless he compound with the patentees (of inns) and all ancient
innkeepers; if they will not compound, they are presently sued at
Westminster for enlargement of their house, if they but set up a post,
or a little hovel, more than of ancient was there." Yet the very
patents sought and granted for exclusive trades and manufactures,
though tending to diminish commerce by fettering it, are proofs of
demand and consumption, and of the industrial energy of the age. These
monopolies were bestowed on courtiers and noblemen, but still, no
doubt, some of the citizens of London were employed in their
management. Of the wealth yielded by commerce, in spite of these
restrictions, ample proof was given in the supplies yielded repeatedly
to the exorbitant demands of the crown. Both James and Charles knew
what it was to have an empty exchequer, and in their emergencies they
usually repaired to the good city of London as to a perfect California.
Loan on loan was obtained. These demands, like leeches, sucked till
one would have supposed they had drained the body municipal; but soon
its veins appear to have refilled, and the circulation of wealth went
briskly on. One of the most remarkable enterprises in the reign of
James I. was that of Sir Hugh Myddelton, who in 1608 began, and in 1613
finished his project of providing London with water, by means of the
canal commonly called the New River. The importance of this laborious
and expensive achievement, which reflects great honor on its
originator, can be estimated sufficiently only after remembering how
difficult, if not impossible almost, it was before to obtain a large
supply of the indispensible element in a state at all approaching
purity. The opening of the river and the filling of the basin formed a
very splendid gala scene, the laborers being clothed in goodly apparel,
with green caps, and at a given signal opening the sluices, with the
sound of drums and trumpets, and the acclamations of the people; the
lord mayor and corporation being present to behold the ceremony.
In the train of wealth came indulgence and luxury. Sad lamentations
were expressed on account of the extravagance of the upper classes, who
spent their money in the city on "excess of apparel, provided from
foreign parts to the enriching of other nations, and the unnecessary
consumption of the treasures of the realm, and on other vain delights
and expenses, even to the wasting of their estates." London, during
the sitting of the law courts, seems to have been deluged with people,
who came up from the country, and vied with each other in their
expensive mode of living; so that, at the Christmas of 1622, the
monarch, with a very paternal care of his subjects, ordered the country
nobility and gentry forthwith to leave the metropolis, and go home and
keep hospitality in the several counties. St. Paul's Cathedral was
desecrated at this time, by its middle walk being made a lounging and
loitering place for the exhibition of extravagant fashions, and for
indulgence in all kinds of pursuits. There the wealthy went to exhibit
their riches, and the needy to make money, the dissolute to enjoy their
pleasures, the mere idler to while away his time. Bishop Earle, in his
Microcosmographic, published in 1628, gives the following description
of the place, and thereby throws light on the habits of the Londoners:
"It is the land's epitome, or you may call it the lesser isle of Great
Britain. It is more than this; the world's map, which you may here
discern in its perfectest motion justling and turning. It is a heap of
stones, and men with a vast confusion of languages; and, were the
steeple not sanctified, nothing liker Babel. The noise in it is like
that of bees, a strange humming or buz mixed of walking, tongues, and
feet. It is a kind of still roar or loud whisper. It is the great
exchange of all discourse, and no business whatsoever but is here
stirring and a-foot. It is the synod of all pates politic, jointed and
laid together in the most serious posture, and they are not half so
busy at the parliament. It is the market of young lecturers, whom you
may cheapen here at all rates and sizes. It is the general mint of all
famous lies, which are here, like the legends of popery, first coined
and stamped in the church. All inventions are emptied here, and not
few pockets. The best sign of a temple in it is, that it is the
thieves' sanctuary, which rob more safely in a crowd than a wilderness,
while every searcher is a bush to hide them. The visitants are all men
without exception, but the principal inhabitants and possessors are
state knights and captains out of service--men of long rapiers and
breeches, which after all turn merchants here and traffic for news.
Some make it a preface to their dinner, and travel for a stomach; but
thrifty men make it their ordinary, and board here very cheap."
Riding about in coaches, as well as walking in smart array about St.
Paul's, was a method of display which those who could afford it were
very fond of. Hackney coaches made their appearance in 1625, and so
greatly did they multiply, that the king, the queen, and the nobility,
could hardly get along; while, to add to the annoyance, the pavements
were broken up, and provender much advanced in price. "Wherefore,"
says a proclamation, "we expressly command and forbid that no hackney
or hired coaches be used or suffered in London, Westminster, or the
suburbs thereof, except they be to travel at least three miles out of
the same. And also that no person shall go in a coach in the said
streets, except the owner of the coach shall constantly keep up four
able horses for our service when required."
The increasing wealth of the citizens made them covetous of honor, and
king James, to replenish his exhausted coffers, was willing to sell
them titles of knighthood. The attainment of these distinctions led to
some curious displays of human vanity, and excited those mean
jealousies which our fallen and debase nature is so apt to cherish. It
was a question keenly agitated among the civic dignitaries and their
ladies,--Whether a knight commoner should rank before an untitled
alderman--whether a junior alderman just knighted should take
precedence of a senior brother, without that distinction, who had long
passed the chair? A marshal's court was at length held to decide the
matter, and it was arranged that precedence in the city should be
attached to the aldermanic office, rather than the knightly name--an
instance of flattering respect to municipal rank.
While the wealthier classes were closely pressing on the heels of their
more aristocratic neighbors, the humbler orders were, in their own way,
seeking to imitate their superiors. The pride of dress was generally
indulged in, and manifested, as is always the case, in times and
countries distinguished by mercantile activity. To check extravagance
in this respect, sumptuary laws were adopted, after the fashion of
former ages, and with a like unsuccessful result. With tailor-like
minuteness, the dress of the inferior citizens was prescribed. No
apprentice was to wear a hat which cost more than five shillings, or a
neck-band that was not plainly hemmed. His doublet was to be made of
Kersey fustian, sackcloth, canvas, or leather, of two shillings and
sixpence a yard, and under; his stockings to be of woolen, and his hair
to be cut short and decent. Like minute directions were issued
relative to the attire of servant maids. Linen was to be their
clothing, and that not to exceed five shillings an ell.
Pageants, which had been so common in the days of the Tudors, reached
an unexampled stage of extravagant and absurd display under the first
two monarchs of the house of Stuart. Even grave lawyers, including the
great Mr. Selden himself, took part in getting up these exhibitions;
and a particular account is given of a masquerade of their devising,
which was performed at the expense of the inns of court, before king
Charles, in 1633.
Liveries, and dresses of gold and silver, glittering in the light of
torches, horses richly caparisoned, and chariots sumptuously fitted up,
were set off by contrast with beggars and <DW36>s, who were introduced
in the procession, riding on jaded hacks. Very odd devices,
illustrative of the taste of the period, and of the way in which
satirical feelings found vent, through the medium of emblematical
characters, were combined with the other quaint arrangements of this
show, such as boys disguised as owls and other birds, and persons
representing the patented monopolists, who were extremely unpopular. A
man was harnessed with a _bit_ in his mouth, to denote a projector who
wished to have the exclusive manufacture of that article; another, with
a bunch of carrots on his head and a capon on his wrist, caricatured
some one who wanted to engross the trade of fattening birds upon these
vegetables. The object was to convey to the king an idea of the
ridiculous nature of many of the monopolies then conferred. All sorts
of pageants and shows, with a dramatic cast in them, were exhibited at
Whitehall under royal patronage, and filled the edifice with revelry
and riot at Christmas and other festivals. The genius of Inigo Jones
was for many years chained down to the invention of scenery and
decoration for these trifles, while Ben Jonson exercised his muse in
writing verses and dialogues for the masquerades.
At a later period of the reign of Charles I., the year 1638, there was
much excitement produced in London by the grand entry of Mary
de'Medici, mother of the queen Henrietta, upon which occasion a
spectacle of unusual grandeur was exhibited. A very full account of
this was published by the Historiographer of France, the Sieur de la
Sierre.
After detailing the order of procession, reporting the speeches
delivered, and describing the rooms and furniture of the palace, and
the manner of the reception of the queen-mother by her daughter
Henrietta, the author dwells with wonderful delight on the public
illuminations and fireworks on the evening of the day: "For the
splendor of an infinite number of fireworks, joined to that of as many
stars, which shone forth at the same time, both the heavens and the
earth seemed equally filled with light. The smell had all its
pleasures of the cinnamon and rosemary wood, which were burning in a
thousand places, and the taste was gratified by the excellence of all
sorts of wine, which the citizens vied with each other in presenting to
passengers, in order to drink together to their majesties' health."
"Represent to yourself that all the streets of this great city were so
illuminated by an innumerable number of fires which were lighted, and
by the same quantity of flambeaux with which they had dressed the
balconies and windows, and from afar off to see all this light
collected into one single object, one could not consider it but with
great astonishment."
These festive transactions on the surface of London society little
indicated the awful convulsion that was near at hand. In the
chronicles of London pageantry, the waters look calm and bright, and no
stormy petrel flaps his wing as an omen of an approaching tempest. But
a time of controversy and confusion was near. A great struggle was
impending, both political and religious. What has just been noticed of
court and civic life was but
"The torrent's smoothness ere it dash below."
In some departments of London history, however, premonitions might have
been discovered of an approaching crisis. The anti-papal feelings of
the people had been aroused by the treaties between James and the king
of Spain, and the projected marriage of prince Charles with the
infanta. So turbulent was popular emotion on this subject, that on one
occasion the Spanish ambassador was assailed in the streets. When, in
the reign of Charles I., mass was celebrated in the ambassador's
chapel, and English <DW7>s were allowed to join in the ceremony, an
attack was made upon the house of the embassy, and the mob threatened
to pull it down. But a far deeper and stronger impression was produced
upon the minds of sound Protestants by the proceedings of archbishop
Laud and his friends. The consecration of St. Catherine Cree church,
on the north side of Leadenhall-street, was attended by ceremonies so
closely approximating to those of Rome, as to awaken in a large portion
of the clergy and laity most serious apprehension. The excitements of
later times on similar grounds find their adequate type and
representation in the troubled thoughts and agitated bosoms of a
multitude of Londoners in the early part of the year 1631. It was a
remarkable era in the ecclesiastical annals of London. The church
having been lately repaired, Laud, then bishop of London, came to
consecrate it. "At his approach to the west door," says Rushworth,
"some that were prepared for it cried, with a loud voice, 'Open, open,
ye ever-lasting doors, that the king of glory may enter in.' And
presently the doors were opened, and the bishop, with three doctors and
many other principal men, went in, and immediately falling down upon
his knees, with his eyes lifted up, and his arms spread abroad, uttered
these words, 'This place is holy, this ground is holy--in the name of
the Father, Son, and Holy Ghost, I pronounce it holy.' Then he took up
some of the dust, and threw it up into the air several times, in his
going up towards the church. When they approached near to the rail and
communion table, the bishop bowed towards it several times, and
returning they went round the church in procession, saying the
hundredth Psalm, after that the nineteenth." Then cursing those who
should profane the place, and blessing those who built it up and
honored it, he consecrated, after sermon, the sacrament in the manner
following: "As he approached the communion table, he made several lowly
bowings, and coming up to the side of the table, where the bread and
wine were covered, he bowed several times, and then, after the reading
of many prayers, he came near the bread, and gently lifted up the
corner of the napkin wherein the bread was laid; and when he beheld the
bread he laid it down again, flew back a step or two, bowed three
several times towards it, then he drew near again, and opened the
napkin, and bowed as before. Then he laid his hand on the cup which
was full of wine, with a cover upon it, which he let go, went back, and
bowed thrice toward it; then he came near again, and lifted up the
cover of the cup, looked into it, and seeing the wine he let fall the
cover again, retired back, and bowed as before: then he received the
sacrament, and gave it to many principal men; after which many prayers
being said, the solemnity of the consecration ended." The bishop of
London consecrated St. Giles's church in the same manner, and on his
translation to Canterbury, studiously restored Lambeth chapel, with its
Popish paintings and ornaments. The displeasure awakened by these
superstitious formalities and Popish tendencies was not confined to men
of extreme opinions. The moderate, amiable, but patriotic Lord
Falkland, the brightest ornament on the royalist side in the civil war,
sympathized with the popular displeasure, and thus pertinently
expressed himself in a speech he made in the House of Commons: "Mr.
Speaker, to go yet further, some of them have so industriously labored
to deduce themselves from Rome, that they have given great suspicion
that in gratitude they desire to return thither, or at least to meet it
half-way; some have evidently labored to bring in an English, though
not a Roman Popery. I mean not only the outside and dress of it, but
equally absolute, a blind dependence of the people on the clergy, and
of the clergy on themselves; and have opposed the papacy beyond the
seas, that they might settle one beyond the water, (_trans
Thamesin_--beyond the Thames--at Lambeth.) Nay, common fame is more
than ordinarily false, if none of them have found a way to reconcile
the opinions of Rome to the preferments of England, and be so
absolutely, directly, and cordially <DW7>s, that it is all that L1,500
a year can do to keep them from confessing it." This fondness for
Romish ceremonies, and these notions of priestly supremacy, cherished
and expressed by Laud and his party, were connected with the intolerant
treatment of those ministers who were of the Puritan stamp. Some of
them were silenced and even imprisoned. Mr. Burton, the minister of
Friday-street, preached and published two sermons in the year 1633
against the late innovations. For this he was brought before the High
Commission Court, and imprisoned.
About the same time, Prynne, a barrister of Lincoln's Inn, was
imprisoned, and had his ears cut off, for writing against plays and
masks; and Dr. Bastwick was also confined in jail for writing a book,
in which he denied the divine right of the order of bishops above
presbyters. These men were charged with employing their hours of
solitude in the composition of books against the bishops and the
spiritual courts, and for this were afresh arraigned before the
arbitrary tribunal of the Star Chamber. "I had thought," said lord
Finch, looking at the prisoner, "Mr. Prynne had no ears, but methinks
he has ears." This caused many of the lords to take a closer view of
him, and for their better satisfaction the usher of the court turned up
his hair, and showed his ears; upon the sight whereof the lords were
displeased they had been no more cut off, and reproached him. "I hope
your honors will not be offended," said Mr. Prynne; "pray God give you
ears to hear."[2] The sentence passed was, that the accused should
stand in the pillory, lose their ears, pay L5,000, and be imprisoned
for life. When the day for executing it came, an immense crowd
assembled in Palace-yard, Westminster. It was wished that the crowd
should be kept off. "Let them come," cried Burton, "and spare not that
they may learn to suffer." "Sir," cried a woman, "by this sermon God
may convert many unto him." "God is able to do it, indeed," he
replied. At the sight of the sufferer, a young man standing by turned
pale. "Son," said Burton, "what is the matter? you look so pale; I
have as much comfort as my heart can hold, and if I had need of more, I
should have it." A bunch of flowers was given to Bastwick, and a bee
settled on it. "Do you not see this poor bee?" he said, "she hath
found out this very place to suck sweet from these flowers, and cannot
I suck sweetness in this very place from Christ?" "Had we respected
our liberties," said Prynne, "we had not stood here at this time; it
was for the general good and liberties of you all, that we have now
thus far engaged our own liberties in this cause. For did you know how
deeply they have encroached on your liberties, if you knew but into
what times you are cast, it would make you look about, and see how far
your liberty did lawfully extend, and so maintain it." The knife, the
saw, the branding-iron, were put to work. Bastwick's wife received her
husband's ears in her lap, and kissed them. Prynne cried out to the
man who hacked him, "Cut me, tear me, I fear not thee--I fear the fire
of hell, not thee." Burton fainting with heat and pain, cried out,
"'Tis too hot to last." It _was_ too hot to last.
Sympathy with the principles of these Puritan sufferers pervaded, to a
great extent, the population of London. Side by side with, but in
stern contrast to, the gay merry-makings and pageants of the Stuart
age, there lay a deep, earnest, religious spirit at work, mingling with
political excitement, and strengthening it. The Puritan preachers of a
former age had been popular in London. Their sentiments had tended
greatly to mould into a corresponding form the opinions, habits, and
feelings of a subsequent generation. An anti-papal spirit, a love of
evangelical truth, a desire for simplicity in worship, a deep reverence
for the Lord's day, and a strict morality, characterized this
remarkable race of men. The strange doings of Archbishop Laud, the
doctrines they heard in some of the parish churches, the profanation of
the Sabbath, and the profligacy of the times, filled these worthies
with deep dismay, and vexed their righteous souls. Boldly did they
testify against such things; and when the Book of Sports came out, the
magistrates of London had so much of the Puritan spirit in them, that
they decidedly set their faces against the infamous injunctions, and
went so far as to stop the king's carriage while proceeding through the
city during service-time. King James, enraged at this, swore that "he
had thought there had been no kings in England but himself," and sent a
warrant to the mayor, commanding that the vehicle should pass; to which
his lordship, with great firmness and dignity, replied, "While it was
in my power I did my duty, but that being taken away by a higher power,
it is my duty to obey." In the reign of Charles, the chief magistrate
issued very stringent orders in reference to the Sabbath.
The proceedings of the Star Chamber, its barbarous punishments and
mutilations, with the accompaniments of fines and captivity, for
conscientious adherence to what was considered the path of duty, galled
the spirits and roused the indignation of many a Londoner. The
citizens went home from the public execution of iniquitous sentences,
from the sight of victims pilloried and mangled for their adherence to
virtuous principle, with a deep disquietude of soul, which swelled to
bursting as they reflected on the tragedies they had witnessed. The
avenging hand of Providence on injustice and oppression was about to be
manifested, visiting national iniquities with those internal calamities
and convulsions which so long afflicted the land. A significant scene,
prophetic of the new order of things, took place in London in the year
1640, just after the opening of the Long Parliament. Prynne, Burton,
and Bastwick, were restored to liberty. Crowds went forth to meet
them. "When they came near London," says Clarendon, "multitudes of
people of several conditions, some on horseback and others on foot, met
them some miles from town, very many having been a day's journey; so
they were brought about two o'clock of the afternoon in at Charing
Cross, and carried into the city by above ten thousand persons, with
boughs, and flowers, and herbs in the way as they passed, making great
noise and expressions of joy for their deliverance and return; and in
these acclamations mingling loud and virulent exclamations against
those who had so cruelly persecuted such godly men." The scarred
faces, the mutilated ears of the personages thus honored, would tell a
tale of suffering and heroism, sure to appeal to the popular sympathy,
and turn it in a stream of violent indignation against the mad
oppressors. What followed we shall see in the next chapter. Meanwhile
we may remark, that much of what has now been detailed furnishes a
singular historical parallel to the events of our own times, and
illustrates the observation of Solomon of old: "Is there anything
whereof it may be said, See, this is new? it hath been already of old
time, which was before us." Eccles. i, 10. We have lived in the
nineteenth century to witness the revival of superstitious mummeries
and popish errors; and taught by the past, the true Christian will
earnestly pray that they may be extirpated without the recurrence of
those awful calamities, of which their introduction in former times
proved the precursor. Meanwhile may each reader remember, that an
obligation is laid upon him to counteract these deviations from
Scriptural truth by maintaining that unceremonial and spiritual
religion which Christ taught the woman of Samaria, and by cultivating
that vital faith which rests on Him alone for acceptance, while it
works by love, purifies the heart, and overcomes the world!
[1] Howes, edit. 1631.
[2] State Trials. Guizot's English Revolution, page 64.
CHAPTER II.
LONDON DURING THE CIVIL WARS.
Charles I. unfurled his standard at Nottingham, in the month of August,
1642, and staked his crown and life on the issue of battle; a high wind
beat down the flag, an evil omen, as it was deemed by some who saw it,
and a symbol, as it proved, of the result of the unnatural conflict.
Sadly was England's royal standard stained before the fighting ended.
London took part at the beginning with the parliament. Its Puritan
tendencies; its awakened indignation at the assaults made by misguided
monarchs and their ministers on conscientious, religious, brave-hearted
men; its long observation of Stafford's policy, which had roused the
displeasure of the citizens, and led to riots; its jealousy of the
constitution being violated and imperiled by the arbitrary proceedings
of Charles, especially by his attempt to reign without parliaments;
and, added to these, a selfish, but natural resentment at the
exorbitant pecuniary fines and forfeitures with which it had been
visited in the exercise of royal displeasure, contributed to fix London
on the side of those who had taken their stand against the king. One
can easily imagine the busy political talk going on at that time in all
kinds of dwellings and places of resort--the eager expectancy with
which citizens waited for news--the haste with which reports, often
exaggerated, passed from lip to lip--the sensation produced by decided
acts on either side; as when, for example, Charles went down to the
House of Commons, demanding the arrest of five obnoxious members, and
when the House declared itself incapable of dissolution save by its own
will--the hot and violent controversies that would be waged between
citizens of opposite political and religious opinions--the separation
of friends--the divisions in families--the reckless violence with which
some plunged into the strife, and the hard and painful moral necessity
which impelled others to take their side--the mean, low, selfish, or
fanatical motives which influenced some, and the high, pure, and
patriotic principles which moved the breasts of others--the godless
zeal of multitudes, and the firm faith and wrestling prayer that
sustained not a few. These varied elements, grouped and arranged by
the imagination upon the background of the scenery of old London, in
the first half of the seventeenth century, form a picture of deep and
solemn interest.
After the battle of Edgehill, in October, Charles marched towards
London, anxious to possess himself of that citadel of the empire. So
near did the royal army come, that many of the citizens were scared by
the sound of Prince Rupert's cannon. The horrors of a siege or
invasion of a city, penned in by lines of threatening troops, expected
every hour to burst the gates or scale the walls--the spectacle of
soldiers scouring the streets, slaying the peaceful citizen, pillaging
his property, and burning his dwelling--such were the anticipations
that presented themselves before the eyes of the Londoners in that
memorable October, creating an excitement in all ranks, which the
leaders of the popular cause sought to turn to practical account.
Eight speeches spoken in Guildhall on Thursday night, October 27th,
1642, have come down to us; and as we look on the old reports, which
have rescued these utterances from the oblivion into which the earnest
talking of many busy tongues at that time has fallen, we seem to stand
within the walls of that civic gathering-place, amidst the dense mass
of excited citizens assembled at eventide, their faces gleaming through
the darkness, with the reflected light of torches and lamps, and to
hear such sentences as the following from the lips of Lord Saye and
Sele, whose words were applauded by the multitude, till the building
rings again with the echo: "This is now not a time for men to think
with themselves, that they will be in their shops and get a little
money. In common dangers let every one take his weapons in his hand;
let every man, therefore, shut up his shop, let him take his musket,
offer himself readily and willingly. Let him not think with himself,
Who shall pay me? but rather think this, I will come forth to save the
kingdom, to serve my God, to maintain his true religion, to save the
parliament, to save this noble city." The speaker knew what kind of
men he was appealing to; that their feelings were already enlisted in
the cause; that they had already given proofs of earnest resolution to
support it, and of a liberal and self-denying spirit. While his
majesty had been getting himself "an army by commission of array, by
subscription of loyal plate, pawning of crown jewels, and the
like--London citizens had subscribed horses and plate, every kind of
plate, down to women's thimbles, to an unheard-of amount; and when it
came to actual enlisting, London enlisted four thousand in one day."
As might have been expected, therefore, the audience responded to Lord
Saye and Sele, and prepared themselves to obey the summons of their
leaders; so that a few days afterwards, on hearing that Prince Rupert
with his army had come to Brentford, and on finding that the roar of
his cannon had reached as far as the suburbs, the train bands, with
amazing expedition, assembled under Major-General Skippon, and
forthwith marched off to Turnham Green. Besides enlistment of
apprentices and others, and contributions of all kinds for raising
parliament armies, measures were adopted for the permanent defence of
London. The city walls were repaired and mounted with artillery; the
sheds and buildings which had clustered about the outside of the city
boundaries in time of peace were swept away. All avenues, except five,
were shut up, and these were guarded with military works the most
approved. The first entrance, near the windmill, Whitechapel-road, was
protected by a hornwork; two redoubts with four flanks were raised
beside the second entrance, at Shoreditch; a battery and breastwork
were placed at the third entrance, in St. John's street; a two-flanked
redoubt and a small fort stood by the fourth entrance, at the end of
Tyburn, St. Giles's Fields; and a large fort with bulwarks overlooked
the fifth entrance, at Hyde Park Corner. Other fortifications were
situated here and there by the walls, so as to fit the city to stand a
long siege. A deep enthusiasm moved at least a considerable party in
the performance of these works. They were not left to engineers or
artillerymen and the paid artificers, who in ordinary times raise
bastions and the like. "The example of gentlemen of the best quality,"
says May, "knights and ladies going out with drums beating, and spades
and mattocks in their hands, to assist in the work, put life into the
drooping people." While warlike harangues, enlistments, contributions,
and the building of fortifications, were going on, and the bustle and
music of military marches were heard in the street, while the walls and
gates bristled with cannons and soldiery, there were those within that
war-girdled city who sympathized indeed in the popular cause, but who
were far differently employed in its defence and promotion.
There was at this time residing in London one
"Whose soul was like a star, and dwelt apart;
Who had a voice whose sound was like the sea."
His place of abode was in Aldersgate-street, in an humble house, with a
small garden--"the muses' bower," as he called it; and there his
marvelous mind was searching out the foundations of laws and
governments, breathing after liberty, civil and religious, and
picturing an ideal commonwealth of justice, order, truth, purity, and
love, which he longed and hoped to see reduced to a reality in his own
native land; he was preparing, also, for some high work, which should
be "of power to imbreed and cherish in a great people the seeds of
public virtue and public civility, to allay the perturbation of the
mind, and set the affections in right tune--a work not to be raised
from the heat of youth, or the vapors of wine, nor to be obtained by
the invocation of dame Memory and her syren daughters, but by devout
prayer to that eternal Spirit, who can enrich with all utterance and
knowledge, and sends out his seraphim, with the hallowed fire of his
altar, to touch and purify the lips of whom he pleases."
John Milton, who thus describes his employment in grand and sonorous
English, such as he alone could write, was by birth a Londoner, having
first opened his eyes in one of the houses of old Bread-street, and
received the elements of his vast and varied learning at St. Paul's
School. Antiquarian research has traced him through successive
residences in St. Bride's Churchyard, Aldersgate-street, Barbican,
Holborn, Petty France, Bartholomew-close, Jewin-street, Bunhill-fields,
to his last resting-place in the upper end of the chancel of St.
Giles's, Cripplegate. (Knight's London, vol. ii, p. 97.) In youth he
had pursued his studies in his native city, after his removal from
Cambridge,
"I, well content, where Thames with refluent tide
My native city laves, meantime reside,
Nor zeal, nor duty, now my steps impel
To reedy Cam, and my forbidden cell.
If peaceful days in lettered leisure spent
Beneath my father's roof be banishment,
Then call me banished: I will ne'er refuse
A name expressive of the lot I choose;
For here I woo the muse, with no control;
For here my books, my life, absorb me whole."
In the maturity of his manhood, at the outbreak of the civil war,
Milton was pursuing his favorite studies at his house in
Aldersgate-street, combining with his literary researches and sublime
poetic flights, deep theological inquiries and lofty political
speculations. At a time when the rumors of invasion were afloat, and
the inroads of an incensed enemy expected, he appealed to the
chivalrous cavalier in his own classic style:--
"Lift not thy spear against the muse's bower.
The great Emathian conqueror bid spare
The house of Pindarus, when temple and tower
Went to the ground; and the repeated air
Of sad Elecha's poet had the power
To save the Athenian walls from ruin bare."
Relieved from the fears of invasion, he continued to occupy his pen in
the production of those wonderful prose works, which, scarcely less
than his poetry, are monuments of his enduring fame. Probably it was
in his house in Barbican--the queer old barbican of that day, with a
portion of the Barbican, or tower, still standing, and picturesquely
gabled and carved dwellings crowded close against it--that Milton,
musing on his native city, wrote some of his most stirring political
tracts. He was the representative of a large class of London citizens,
who, without taking up arms on either side, earnestly entered into the
great struggle, and thought and talked, and worked and wrote, as men
agitated and in travail for the restoration and welfare of their
distracted and bleeding country.
It is interesting, in connection with this illustrious man, to notice
one of his London contemporaries, also distinguished in English
literature, but in another way, presenting an opposite character, and
the type of a different class. While Milton was exercising his lofty
intellect and plying his mighty pen on divinity and politics, Isaac
Walton, so well known as the author of the Complete Angler, and the
lives of Dr. Donne and others, was, besides pursuing his occupation as
a Hamburgh merchant, busily amusing himself with his favorite sport,
and preparing materials for his celebrated work, (which was published
in 1653,) as well as writing two of his lives, that of Donne and
Wotton, which appeared in 1640 and 1651. When London was moved from
one end to the other by storms of political excitement, Walton,
undisturbed by the commotion in public affairs, quietly sought
enjoyment on the banks of the Thames with his rod and line, below
London Bridge, where he tells us "there were the largest and fattest
roach in the nation;" or, taking a longer excursion, rambled by the Lea
side, or went down as far as Windsor and Henley. It is certainly
(whatever opinion we may form of the pursuits which engrossed so large
a portion of Walton's time) a relief, amidst scenes of strife, to catch
a view of little corners in English society, which seem to have been
sheltered from the sweeping tempest. Curious it is also to observe how
little some men are affected by the great changes witnessed in their
country. Moderation is frequently, however, nearly allied to
selfishness, and Walton apparently belonged to a class of individuals,
from whom society may in vain look for any improvements which involve
the sacrifice of personal ease or comfort. He could, to use the
language of Dr. Arnold, "enjoy his angling undisturbed, in spite of
Star Chamber, ship-money, High Commission Court, or popish ceremonies;
what was the sacrifice to him of letting the public grievances take
their own way, and enjoying the freshness of a May morning in the
meadows on the banks of the Lea?"
However the great conflict might be regarded or forgotten, it waxed
hotter every day, and London became increasingly involved in the
strife. For a while the parliament and the army were united in their
efforts against the king, and the city of London continued to lend them
efficient aid. But at length disagreements arose between the
legislative and military powers, the former being in the main composed
of Presbyterians, while the latter were strongly leavened by the
Independents. The rent became worse as time rolled on, till these two
religious parties, diverging in different directions, tore the
commonwealth asunder, and from having been allies became decided
antagonists.
The Presbyterians were strong in London; Presbyterians occupied the
city pulpits--Presbyterians ruled in the corporation. The Westminster
Assembly, which began to sit in 1642, and continued their sessions
through a period of six years, numbered a large majority of that
denomination, and in the measures for the establishment of their own
views of religion throughout the country, met with the sympathy and
encouragement of a considerable portion of London citizens. In the
church of St. Margaret's, Westminster, under the shadow of the
venerable abbey, the members of this assembly, with the Scots'
commissioners, and representatives from both houses of parliament, met
on the 25th of September, 1643, to take the Solemn League and Covenant,
the chosen symbol and standard of the Presbyterian party. It was
certainly one of the most remarkable scenes in the ecclesiastical
history of our country; and whatever opinion may be formed of the
ecclesiastical principles which moved that memorable convocation, no
person of unprejudiced mind can fail to admire the piety, the
earnestness, zeal, and courage, which many of them evinced in the
performance of their task. Solemn prayers were offered, addresses were
delivered in justification of the step they were taking, and then, as
the articles of the Covenant were read out from the pulpit, distinctly
one by one, each person standing uncovered, with his hand lifted bare
to heaven, swore to maintain them. On the Lord's-day following, the
Covenant was tendered to all persons within the bills of mortality of
the city of London, and was welcomed by a number of ministers and a
great multitude of people. Of the excitement which prevailed, some
idea may be gathered from the narrative of a royalist historian. We
are informed by Clarendon, that the church of St. Antony, in Size-lane,
Watling-street, being in the neighborhood of the residence of the
Scotch commissioners, was appropriated to their use during their stay,
and that Alexander Henderson, a celebrated preacher, and one of their
chaplains, was accustomed to conduct service there. "To hear these
sermons," he says, "there was so great a conflux and resort by the
citizens out of humor and faction, by others of all qualities out of
curiosity, by some that they might the better justify the contempt they
had of them, that from the first appearance of day in the morning of
every Sunday to the shutting in of the light the church was never
empty; they, especially the women, who had the happiness to get into
the church in the morning, (those who could not hang upon or about the
windows without, to be auditors or spectators,) keeping the places till
the afternoon exercises were finished."
As discussions arose between the parliament and the Presbyterians on
the one side, and the army and Independents on the other, the city of
London showed unequivocally its attachment to the former. In addition
to difficulties arising from an embargo laid by the king on the coal
trade between Newcastle and London, difficulties met by parliamentary
orders for supplying fuel in the shape of turf or peat out of commons
and waste grounds, and also out of royal demesnes and bishops' lands;
in addition to other difficulties, commercial, municipal, and social,
springing from the disjointed state of public affairs--the Londoners
were plunged into new difficulties, ecclesiastical and political, by an
important step which they conceived it their duty to take. The
Presbyterian ministers of London, upheld by their flocks, were zealous
for the full and unrestricted establishment of their own scheme of
discipline through the length and breadth of the city. In June, 1646,
the ministers met at Zion College, contending for the Divine right of
their form of government, and maintaining that the civil magistrate had
no right to intermeddle with the censures of the Church. The lord
mayor and common council joined them in a petition to the parliament to
that effect; but the political powers would not allow them that
uncontrolled and supreme ecclesiastical constitution which they craved.
However, they were authorized to carry out their Church polity
according to the law enacted for the whole kingdom, and to have
presbyteries in every parish, which parochial bodies should be
represented in a higher assembly called the classes, the classes again
in the provincial synod, and the synod in the general assembly. London
formed a province with twelve classes, each containing from eight to
fifteen parishes. Nowhere else but in London and in the county of
Lancashire did the Presbyterian establishment come into full operation,
and even in the metropolitan city, with all the zeal of the ministers
to support it, and with the majority of the people which they could
command, the success of the plan was very limited. On the 19th of
December, 1646, the lord mayor and his brethren went up to Westminster
with a representation of grievances, including first the contempt that
began to be put upon the Covenant; and secondly, the growth of heresy
and schism, the pulpits being often usurped by preaching soldiers, who
infected all places where they came with dangerous errors. Of these
grievances they desired redress. In the next year, 1647, the synod at
Zion College published their testimony to the truth, as it was termed,
in which a passage occurs curiously illustrative of the opinions on the
subject of toleration that were then prevalent. The last error they
witness against is called, they say, "the error of toleration,
patronizing and promoting all other errors, heresies, and blasphemies,
whatsoever, under the grossly-abused notion of liberty of conscience."
The Independents, who, though a minority, were a considerable body in
the city of London, being advocates for an extended toleration, as well
as for the enjoyment of liberty themselves, greatly displeased the
Presbyterian brethren, and materially thwarted the success of their
plans. On both sides, no doubt, there were sincere, earnest, and holy
men, nor did they disagree as to the essential truths of our blessed
religion. They were worshipers of the same everlasting Father, through
the same Divine Mediator, and trusted to the aid of the same gracious
Spirit. They looked not to any morality of their own, as the ground of
their acceptance with their Creator, but, conscious of manifold sins,
rested on the sacrifice of "the Lamb of God, which taketh away the sin
of the world." Yet it is grievous to think, that in some instances a
difference, which extended no further than to the outward polity of the
Church, could dissever and almost alienate those whom grace had made
one. And yet more grievous is it that good men who had only just
escaped from persecution themselves, should have been ready to fasten
the yoke upon brethren who could not see as they did. However, in this
imperfect state of existence, such things have been and still are; but
it is consoling to remember, that a state of being shall one day exist,
when these sad anomalies will prevail no more. Freed from prejudice,
passion, and infirmity, souls united by the tie of a common faith in
the essentials of the gospel, shall then rejoice in a perfect and
unbroken unity.
While the earlier stages of the struggle to which we have referred were
going on, some distinguished men in London, on both sides, were removed
from the scene of strife into the peaceful mansions of their Father's
house. Two in particular are worthy of mention here as of the gentler
cast, who, though they differed, felt that charity had bonds to bind
the souls of godly men together, stronger than any difference of
ecclesiastical opinion could break. Dr. Twiss, an eminent and learned
Presbyterian clergyman, the prolocutor of the assembly of divines, died
in London in 1646. He had refused high preferment and flattering
invitations to a foreign university. Forced from his living at Newbury
by the royalist party, and detained in London by his duties in the
assembly, for which he received but a very small allowance, he had to
struggle with poverty. Indeed, he was so reduced, that when some of
the assembly were deputed to visit him, they reported that he was very
sick and in great straits. He was buried in the Abbey, "near the upper
end of the poor folk's table, next the vestry, July 24th; thence, after
the Restoration, he was dug up and thrown into a hole in the churchyard
of St. Margaret's, near the back door of one of the prebendaries'
houses." In the same year died Jeremiah Burroughs, of the Independent
school, and preacher to two of the largest congregations about London,
Stepney, and Cripplegate. "He never gathered a separate congregation,
nor accepted of a parochial living, but wore out his strength in
continual preaching, and other services of the Church. It was said the
divisions of the time broke his heart. One of the last subjects he
preached upon and printed was his Irenicum, or attempt to heal
divisions among Christians." Under the ascendency of the Presbyterians
in London, the old church ceremonies of course were abandoned--churches
were accommodated to the simplicity of worship preferred by the party
in power. Superstitious monuments, images, and paintings, were
removed; the crosses in Cheapside and Charing Cross pulled down. Even
St. Paul's Cross, because of its form and name, was not spared, though
hallowed by the remembrance of the great Reformers, who had there so
effectively preached. Religious festivals were abolished, not
excepting Christmas--a measure to which the citizens did not quietly
submit, old habits and predilections being too strong to be overcome by
law. In 1647, on that day most people kept their shops shut, and many
Presbyterian ministers occupied their pulpits. Time, however, was
allotted for recreation; and it was arranged "that all scholars,
apprentices, and other servants should, with the leave of their
masters, have such convenient reasonable relaxation every second
Tuesday in the month, throughout the year, as formerly they used to
have upon the festivals." It may be added, that stage plays were
forbidden, and the theatres in London closed; galleries, seats, and
boxes, were removed by warrant from justices of the peace, and all
actors convicted of offending against this law were sentenced to be
publicly whipped.
In consequence of the excitement of the times, the parliament issued an
order forbidding persons to appear in the streets of London armed, or
to come out of doors after nine o'clock at night. It was further
enjoined, that all persons coming into the city should present
themselves at Guildhall and produce their passes, and also enter into
an engagement not to bear arms against the parliament. The
misunderstanding between the legislature and the army becoming more
grave and ominous than ever, the city corporation besought the former
to disband the latter--a thing more easily proposed than accomplished.
The citizens desired to have a militia for their own defence, under
officers to be nominated by the common council; and were likewise
anxious that the king, now in the hands of the army, should be brought
to London, and a personal treaty entered into with him. Tumultuous
assemblages, gathered from London, took place round the doors of the
House of Commons, some of the mob thrusting in their heads, with their
hats on, and shouting out, "Vote, vote;" and even forcing the speaker,
when he was about to leave the chair, to remain at his post, violently
demanding that their petition should be granted. The army at the time
lay coiled up near London with most threatening aspect, and to add to
the terror of the city, the speaker of the Commons and a hundred
members withdrew from the metropolis, and repaired to the camp. Orders
were now given by the common council to the train bands to repair the
fortifications, and for all persons capable of bearing arms to appear
at the appointed places of rendezvous. Fairfax and Cromwell, the
commanders of the army, wrote an expostulatory letter to the city,
stating their grievances, and disavowing all desire to injure the
place. An answer was sent, very unsatisfactory to the parties
addressed, and things wore an increasingly alarming appearance. Still
the citizens seemed determined to oppose the army, and entered into an
engagement to promote the return of the king to London. Shops were
shut up, a stop was put to business, horses were forbidden to be sent
beyond the walls, and whole nights were spent in anxious deliberation.
The army, however, was pressing towards the gates on the Southwark
side, and while the citizens were debating and planning, showed in an
unmistakable manner that it at least was in action. The peril being
imminent, on the 4th of August the common council and committee
assembled in Guildhall, vast multitudes of the people repairing thither
to learn the result of the deliberations. An express arrived, stating
that Fairfax with the army had halted on their march. "Let us go out
and destroy them," cried a stentorian voice; but a second express, on
the heels of the first, ran in to correct the mistake of his
predecessor, and to assure them that Fairfax and his men were no
halters, but were marching on with great energy. This changed the tone
of the assembly, and all exclaimed, "Treat! treat!" The committee
spent most of the night in consultation, and the next morning
despatched a submissive letter to the general. The inhabitants of
Southwark not having sympathized with their brethren on the other side
of the water in their opposition to the army, privately intimated to
the general their willingness to admit him, and, accordingly, a brigade
took possession of the borough about two o'clock in the morning, and
thereby became masters of London Bridge. Another letter was despatched
from the city authorities, more submissive than the first, and
commissioners were speedily despatched to Hammersmith to wait upon
Fairfax, who had there taken up his quarters, and formally yield to him
all the forts on the west side of the metropolis. On the 6th of
August, 1647, the general was received in state by the corporation at
Hyde Park, and escorted in procession to the city, being the same day
constituted constable of the Tower by the ordinance of parliament.
Three days afterwards, he took possession of that old fortress, being
attended by a deputation from the common council, who complimented him
in the highest terms, and invited him and his principal officers to
dinner. After an interval of another three days, the city voted
L1,200, to be spent on a gold basin and ewer, as a present to this
distinguished officer. The fortifications were dismantled, ports and
chains taken away, and the army quartered in and about the city: many,
we are told, in great houses, though the season was rigorous, were
obliged to lie on the bare floor, with little or no firing. Orders
were issued to provide bedding for the cold and weary soldiers; and
when the city failed to fulfil its promise to pay money to the army,
troops were dispatched to Weavers', Haberdashers', and Goldsmiths'
Halls, the first of which they lightened of its treasure to the amount
of L20,000. Strict injunctions, however, were given for the orderly
and peaceable conduct of the military, on pain of death. London was
now reduced to dumb quietude, save that murmurings were heard from the
Presbyterians, who still insisted upon making terms with the king; but
it was all in vain. The torrent rolled on, and swept away monarch and
throne; of its devastations there are awful recollections associated
with Charing Cross and Whitehall.
The latter was made the prison-house of the monarch during his trial.
Hence he passed to the old orchard stair, to take boat for Westminster
Hall. A servant, whom he particularly noticed on these occasions, has
become an object of interest to the religious portion of the English
public, from his having been the father of the eminently holy Philip
Henry, and the grandfather of Matthew Henry, the commentator. When
Charles returned to the palace after the absence of a few years, which,
because of the sorrows that darkened them, seemed an age, he accosted
his old attendant with the inquiry, "Art thou yet alive?" "He
continued," says Philip Henry, speaking of his father, "during all the
war time in his house at Whitehall, though the profits of his place
ceased. The king passing by his door under a guard to take water, when
he was going to Westminster to that which they called his trial,
inquired for his old servant, Mr. John Henry, who was ready to pay his
due respects to him, and prayed God to bless his majesty, and to
deliver him out of the hands of his enemies, for which the guard had
like to have been rough upon him." The king was condemned by the court
of justice instituted for the occasion, and on the 30th of January,
1649, was publicly beheaded. The place which had been the scene of
many of his youthful revels with the Duke of Buckingham, and which had
witnessed the early pomp and pageants of his reign, having been
converted into his prison, now became the spot where his blood was to
be spilt. He had been removed to St. James's Palace, after his
sentence, and there spent Saturday, Sunday, and Monday. At ten o'clock
on Tuesday, he crossed the park to Whitehall, under military guard,
Juxon, bishop of London, walking on the right, and Colonel Tomlinson,
who was his jailer, on the left. Reaching the palace, he went up the
stairs leading to the long gallery into his chamber, where he remained
in prayer for an hour, and received the sacrament. Two or three dishes
of refreshments had been prepared, which he declined, and could only be
prevailed on to take a piece of bread and a glass of claret. All
things being prepared, and the hour of one arrived, he passed into the
Banqueting House, and thence proceeded, by a passage broken through the
wall, to the scaffold. It was covered with black, and exhibited the
frightful apparatus of death. There stood the block, and by it two
executioners in sailor's clothes, with vizards and perukes. Regiments
of horse and foot were stationed round the spot, while a dense
multitude crowded the neighboring avenues, and many a serious
countenance looked down from the windows and the roofs of houses. No
shouts of insult met the unhappy prince as he stepped on the stage of
death, but perfect and solemn silence pervaded the closely-pressed
throng, as well as the soldiers on duty. Pity for the fallen monarch
in his misfortunes, prevailed even with some who had condemned his
unconstitutional and arbitrary course; so completely do the gentler
feelings of our nature at such times master the conclusions at which
the judgment has before arrived. Nor should it be forgotten, that very
many there, who had regarded with alarm and indignation not a few of
the acts which Charles had performed, shrank from the thought of the
penalty to which he was doomed, as too severe, or decidedly impolitic.
Others, also, were present, royalists in heart, whatever might be their
caution at such a time in avowing their principles. It was the king's
wish to address the multitude; but not being able to make himself heard
so far, he delivered a speech to those who were near him, in which he
expressed his forgiveness of his enemies, and then proceeded to
maintain those high notions of kingly power which had proved his ruin.
At the suggestion of the bishop, he closed by declaring, "I die a
Christian, according to the profession of the Church of England, as I
found it left me by my father. I have on my side a good cause and a
gracious God." "There is but one stage more," said Juxon: "it is
turbulent and troublesome, but a short one. It will carry you from
earth to heaven, and there you will find joy and comfort." "I go," he
said, "from a corruptible to an incorruptible crown." "You exchange,"
rejoined the bishop, "an earthly for an eternal crown--a good
exchange." Taking off his cloak, he gave the insignia of the order of
the garter to the prelate, adding significantly, "Remember!" then
kneeling down by the block, his head was severed from his body at a
blow. Philip Henry, son of the old Whitehall servant, witnessed that
mournful tragedy. "There he was," says his son Matthew, "when the king
was beheaded, and with a very heavy heart saw that tragical blow given.
Two things he used to relate, that he took notice of himself that day,
which I know not if any historians mention. One was, that at the
instant the blow was given, there was such a dismal universal groan
among the thousands of people that were within sight of it, as it were
with one consent, such as he had never heard before, and desired that
he might never hear the like again, nor see such cause for it. The
other was, that immediately after the stroke was struck, there was,
according to order, one troop marching from Charing Cross towards
King-street, and another from King-street towards Charing Cross,
purposely to disperse and scatter the people, and to divert the dismal
thoughts with which they could not but be filled, by driving them to
shift every one for his own safety."
A commonwealth was established, and London submitted in form, if not in
heart, to the victorious Cromwell. Returning from Worcester, where he
fought his last great battle, he entered the city in triumph; speaker
and parliament, lord president and council of state, mayor, sheriff,
and corporation, with an innumerable multitude, rending the air with
their shouts, accompanied by cannon salutes; in the midst of which,
says Whitelock, "he carried himself with much affability, and now and
afterwards, in all his discourses about Worcester, would seldom mention
anything of himself, mentioned others only, and gave, as was due, the
glory of the action to God."
When the commonwealth had lasted four years, the government was changed
into the form of a protectorate, and Cromwell was installed lord
protector. Of all the grand ceremonials that have taken place in
London or Westminster, this was among the most remarkable, and
certainly quite unique. The coronation of princes within the walls of
St. Peter's Abbey has been of frequent occurrence; but the installation
of the chief of the English republic was without precedent, and without
imitation. On the 16th of December, 1653, soon after noon, Cromwell
proceeded in his carriage to Westminster Hall, through lines of
military, both horse and foot. The aldermen of London, the judges, two
commissioners of the great seal, and the lord mayor, went before, and
the two councils of state, with the army, followed. Entering the Court
of Chancery, Cromwell, attired in a suit and cloak of black velvet,
with long boots and a gold-banded hat, was conducted to a chair of
state, placed on a rich carpet. He took his place before the chair,
between the commissioners; the judges formed a circle behind, the
civilians standing on the right, the military on the left. The clerk
of the council read the instrument of government, consisting of
forty-two articles, which the lord protector, raising his right hand to
heaven, solemnly swore to maintain and observe. General Lamberth,
falling on his knees, offered him a civic sword in a scabbard, which he
received, putting aside his military weapon, to indicate that he
intended to govern by law and not by force. Seating himself in the
chair, he put on his hat, the rest remaining uncovered; then, receiving
the seal from the commissioners, and the sword from the lord mayor of
London, he immediately returned them to the same officers, and at the
close of this ceremony proceeded again to the palace at Whitehall. He
was soon afterwards invited by the city to dine at Guildhall, where he
was received with as much honor as had been formerly paid to
sovereigns, the companies in their stands lining the streets through
which he passed, attended by the lord mayor and aldermen on horseback.
After the protector had been sumptuously entertained, he conferred the
honor of knighthood on the chief magistrate of the city. Standing in
the Painted Chamber at Westminster, with his first parliament before
him, he alludes with special satisfaction to this city visit. "I would
not forget," he says, "the honorable and civil entertainment I found in
the great city of London. Truly I do not think it folly to remember
this; for it was very great and high, and very public, and included as
numerous a body of those that are known by names and titles, the
several corporations and societies of citizens in this city, as hath at
any time been seen in England,--and not without some appearance of
satisfaction also." Cromwell returned the compliment paid him by the
city, and invited the mayor and court of aldermen to dine with him. A
good understanding seems to have been maintained between the lord
protector and the metropolitan authorities. When plots were formed to
take away his life, he called the corporation together, and gave them
an extraordinary commission to preserve the peace, and invested them
with the entire direction of the municipal militia. He also relieved
the citizens from some of their taxes, revived the artillery company,
and granted a license for the free importation of four thousand
chaldrons of coals from Newcastle for the use of the poor--measures
which made his highness popular in London.
"Subsequently to the annihilation of the royal authority, or between
that and the protectorate, the city became the grand focus of the
parliamentary government, as is abundantly testified by the numerous
tracts and other records of the period. Guildhall was a second House
of Commons, an auxiliary senate, and the companies' halls the
meeting-places of those branches of it denominated committees. All the
newspapers of the day abound with notices of the occupation of the
companies' premises by their committees. Goldsmiths' Hall was their
bank, Haberdashers' Hall their court for adjustment of claims,
Clothworkers' Hall for sequestration, and all the other halls of the
great companies were offices for the transaction of other government
business. Weavers' Hall might properly be denominated the exchequer.
From this place parliament was accustomed to issue bills, about and
before 1652, in the nature of exchequer bills, and which were commonly
known under the name of Weaver-Hall bills."--_Herbert's Hist. of Livery
Companies_, vol. i. During the melancholy time that the civil war
raged in England, the London companies were much oppressed, and spoiled
of their resources by the arbitrary exactions made by those in power;
but they seem to have enjoyed a better condition under the
protectorate, when a season of comparative rest and quietude returned.
Cromwell's state residence in London was Whitehall. With much less of
splendor and show than had been exhibited by the former occupants of
that palace, the protector maintained a degree of magnificence and
dignity befitting the chief ruler of a great country.[1] He had around
him his court--composed of his family, some leading officers of the
army, and a slight sprinkling of the nobility; but what interests
posterity the most, it included Milton, Marvell, Waller, and Dryden.
Foreign ambassadors and other distinguished personages were entertained
at his table in sober state, the dinner being brought in by the
gentlemen of his guard, clothed in gray coats, with black velvet
collars and silver lace trimmings. "His own diet was spare and not
curious, except in public treatments, which were constantly given the
Monday in every week to all the officers in the army not below a
captain, when he used to dine with them. A table was likewise spread
every day of the week for such officers as should casually come to
court. Sometimes he would, for a frolic, before he had half dined,
give order for the drum to beat, and call in his foot-guards, who were
permitted to make booty of all they found on the table. Sometimes he
would be jocund with some of the nobility, and would tell them what
company they had kept, when and where they had drunk the king's health
and the royal family's, bidding them when they did it again to do it
more privately; and this without any passion, and as festivous, droll
discourse."[2] In the neighboring parks, the protector was often seen
taking the air in his sedan, on horseback, and in his coach. On one
occasion he turned coachman, with a rather disastrous result, which is
amusingly told by Ludlow, whose genuine republicanism prejudiced him
against Cromwell after he had assumed the supreme power. "The duke of
Holstein made Cromwell a present of a set of gray Friesland
coach-horses, with which taking the air in the park, attended only by
his secretary Thurloe and a guard of janizaries, he would needs take
the place of the coachman, not doubting but the three pair of horses he
was about to drive would prove as tame as the three nations which were
ridden by him, and, therefore, not content with their ordinary pace, he
lashed them very furiously; but they, unaccustomed to such a rough
driver, ran away in a rage, and stopped not till they had thrown him
out of the box, with which fall his pistol fired in his pocket, though
without any hurt to himself: by which he might have been instructed how
dangerous it was to meddle with those things wherein he had no
experience." In connection with these anecdotes of Cromwell may be
introduced an extract from the Moderate Intelligencer, illustrative of
the public amusements in London at that time:--
"Hyde Park, May 1, 1654.--This day there was a hurling of a great ball
by fifty Cornish gentlemen of the one side, and fifty on the other; one
party played in red caps and the other in white. There was present,
his highness the lord protector, many of his privy council, and divers
eminent gentlemen, to whose view was presented great agility of body,
and most neat and exquisite wrestling, at every meeting of one with
another, which was ordered with such dexterity, that it was to show
more the strength, vigor, and nimbleness of their bodies, than to
endanger their persons. The ball they played withal was silver, and
was designed for that party which did win the goal." Coach-racing was
another amusement of the period, perhaps something of an imitation of
the old chariot races; races on foot were also run.
The author of a book entitled, "A Character of England, as it was
lately presented to a Nobleman of France," published in 1659, further
describes Hyde Park in the manner following: "I did frequently in the
spring accompany my lord N---- into a field near the town, which they
call Hide Park; the place not unpleasant, and which they use as our
course, but with nothing of that order, equipage, and splendor, being
such an assembly of wretched jades and hackney coaches, as, next a
regiment of carmen, there is nothing approaches the resemblance. The
park was, it seems, used by the late king and nobility for the
freshness of the air and the goodly prospect; but it is that which now
(besides all other exercises) they pay for here, in England, though it
be free in all the world besides, every coach and horse which enters
buying his mouthful, and permission of the publican who has purchased
it, for which the entrance is guarded with porters and long staves."
During the commonwealth, what may be called a drab- tint
pervaded London life, absorbing the rich many- hues which
sparkle in the early picturesque history of the old metropolis. The
pageantries of the Tudors and Stuarts were at an end; civic processions
lost much of their glory; maskings and mummings were expelled from the
inns of court; May-day became as prosaic as other days; Christmas was
stripped of its holly decorations, and shorn from its holiday revels.
The companies' halls were divested of royal arms, and the churches
purified from images and popish adornments. But the preceding
particulars show that the tinge of the times was not quite so drab as
it seems on the pages of some partial and prejudiced writers. London
had not the sepulchral look, and commonwealthmen had not the
funeral-like aspect commonly attributed to them. They had, as we have
seen, their cheerfulness and festivity, their banquets, recreations,
and amusements; and, no doubt, in the mansions and houses of the city
folk, both Presbyterian and Independent, there was comfort and taste,
and pleasure, far different from what would be inferred from the
accounts of them given by some, as if they were all starched
precisians, a formal and woe-begone race. There was a dash of humor in
Cromwell, to many about him quite inconsistent with that lugubriousness
so often described as the characteristic of the times. With the
suppression of the rude, boisterous, profligate, and vicious amusements
of earlier times, there was certainly an improvement of the morals of
the people. London was purified from a good deal of pollution by the
change. The order, sobriety, and good behavior of the London citizens,
during the period that regular government existed under Cromwell,
appear in pleasing contrast to the confusion and riots of earlier
times. There was a general diffusion of religious instruction, an
earnestness in preaching, and an example of reverence for religion,
exhibited by those in authority, which could not but operate
beneficially. No doubt in London, as elsewhere, there were formalism
and hypocrisy; the length of religious services had sometimes an
unfavorable influence upon the young; severity and force, too, were
unjustifiably employed in controlling public manners; but when all
these drawbacks are made, and every other which historical impartiality
may demand, there remains in the condition of London in those times, a
large amount of genuine virtue and religion.
The night of the 2d of September, 1658, was one of the stormiest ever
known. The wind blew a hurricane, and swept with resistless violence
over city and country; many a house that night was damaged, chimneys
being thrown down, tiles torn off, and even roofs carried away. Old
trees in Hyde Park and elsewhere were wrenched from the soil. Cromwell
was lying that night on his death-bed, and the Londoners' attention was
divided between the phenomena of the weather, and the great event
impending in the history of the commonwealth. The royalists said that
evil angels were gathering in the storm round Whitehall, to seize on
the departing spirit of the usurper; his friends interpreted it as a
warning in providence of the loss the country was about to sustain.
Amidst the storm and the two interpretations of it, both equally
presumptuous, Cromwell lay in the arms of death, breathing out a
prayer, which, whatever men may think of the character of him who
uttered it, will be read with deep interest by all: "Lord, though a
miserable and wretched creature, I am in covenant with thee, through
thy grace, and may and will come to thee for thy people. Thou hast
made me a mean instrument to do them some good and thee service. Many
of them set too high a value upon me, though others would be glad of my
death. Lord, however thou disposest of me, continue and go on to do
good for them. Teach those who look too much upon thy instruments to
depend more upon thyself, and pardon such as desire to trample upon the
dust of a poor worm, for they are thy people too."
Cromwell was not by any means given to excessive state and ceremony,
but after his death his friends evinced their fondness for it by the
singularly pompous funeral which they appointed for him. Somerset
House was selected as the scene of the lying in state, and thither the
whole city flocked to witness the spectacle of gorgeous gloom. They
passed through three ante-chambers, hung with mourning, to the funeral
apartment. A bed of state covered the coffin, upon which, surrounded
by wax lights, lay Cromwell's effigy, attired in royal robes. Pieces
of his armor were arranged on each side, together with the symbols of
majesty, the globe and sceptre. Behind the head an imperial crown was
exhibited on a chair of state. Strikingly did the whole portray the
fleeting and evanescent character of earthly pomp and power. It being
found necessary to inter the body before the conclusion of the public
funereal pageant, the effigy was removed to another room, and placed in
an erect instead of a recumbent position, with the emblems of kingship
in its hands, and the crown royal on its head. This exhibition
continued for eight days, at the conclusion of which period there was a
solemn procession to Westminster Abbey. The streets were lined with
military, and the principal functionaries of the city of London, the
officers of the army, the ministers of state, the foreign ambassadors,
and some members of Cromwell's family, composed the cortege, which
conducted the funeral car bearing the effigy to the place where the
body was interred.
The city of London acknowledged Richard Cromwell as lord high protector
on his father's death. Probably an address of congratulation from the
metropolis on the event of his accession, was included among the
contents of the old trunks, filled with such documents, to which
Richard humorously referred when his short career of rulership reached
its close. "Take particular care of these trunks," he said to his
servant, when giving some directions about them; "they contain no less
than the lives and fortunes of all the good people of England." The
corporation of London having played a conspicuous part in all the
changes of those changeful times, was particularly consulted by the
parties who seized the reins of government when they had fallen from
the hands of Oliver, and could not be held by his incompetent son. So
cordial seemed the understanding between the city magistrates and the
ruling authorities--consisting of the rump parliament, the council of
state, and the officers of the army--that an entertainment was given to
the latter at Grocers' Hall, on the 6th of October, 1659, by the lord
mayor and corporation, to celebrate Lambert's victory over Sir George
Booth, who had raised an insurrection in the west of England. At these
festivities there was, on the part of the city, more of the semblance
than the reality of friendship; for in the disjointed state of public
affairs, and the manifest impotence of those who had undertaken to
rule, London shared the general sentiments of dissatisfaction and
alarm. It was felt that the parliament was but a name, and the
re-establishment of a military despotism by the army was the object of
apprehension. In the disagreement between parliament and army the city
wished to stand neutral, though the apprentices rose in riotous
opposition to the committee of safety, which was formed of republican
officers. The feelings of this youthful part of the community were
sympathized in by many others, though they prudently desired to avoid
any infraction of the public peace. A general wish pervaded the city
that a free parliament might be called; and when the rump parliament
required the collection of the taxes, the citizens refused the impost,
and objected to the power which had levied it. General Monk was
ordered to march on the refractory citizens, which he did. He
forthwith stationed guards at the gates of the city, and then broke
them down, destroying the portcullises and removing the posts and
chains. While Monk was thus chastising the Londoners, he fell out with
the parliament, in whose service he professed to act, and at once
changing sides, sought the forgiveness of the city for his deeds of
violence, which, as he alleged, had been done, not from his own
inclination, but at the command of the parliament. Mutual engagements
and promises were now exchanged between the general and the citizens.
Posts, gates, chains, portcullises, were replaced and repaired; and the
corporation being let into the secret of Monk's design to promote the
restoration of the monarchy, cordially acquiesced in the object. When
messengers from Charles, who was at Breda, reached the city, they were
joyfully welcomed, and L10,000 was voted out of the civic coffers to
assist his majesty. While preparations for the king's return were
proceeding prosperously, a solemn thanksgiving-day was held on the 10th
of May, 1660, on which occasion the lord mayor and aldermen and the
several companies assembled at St. Paul's Cathedral, when the good
Richard Baxter preached to them on "Right Rejoicing: or, The Nature and
Order of rational and warrantable Joy." Feeling deeply as he did for
the political welfare of the city and the country, and deeming the
restoration of the monarch conducive to that end, yet the preacher,
filled as he was with love to souls and zeal for God, would not let the
occasion pass without wholly devoting it to the highest ends of the
Christian ministry. It was his compassion, he says, to the frantic
merry world, and to the self-troubling melancholy Christian, and his
desire methodically to help them in their rejoicing, which formed his
exhortation, and prompted the selection of his subject. No doubt men
of all kinds thronged old St. Paul's to hear the Puritan preach on the
king's return; and on reading over his wonderfully earnest and
conscience-searching sermon, one cannot help feeling how many there
must have been there to whom his warnings were as appropriate as they
still are to multitudes in our own day, perhaps even to some person now
perusing this sketch of the history of London. "Were your joy," said
he, "but reasonable, I would not discourage it. But a madman's
laughter is no very lovely spectacle to yourselves. And I appeal to
all the reason in the world, whether it be reasonable for a man to live
in mirth that is yet unregenerate and under the curse and wrath of God,
and can never say, in the midst of his greatest pomp and pleasure, that
he is sure to be an hour out of hell, and may be sure he shall be there
forever, if he die before he have a new, a holy, and a heavenly nature,
though he should die with laughter in his face, or with a jest in his
mouth, or in the boldest presumption that he shall be saved; yet, as
sure as the word of God is true, he will find himself everlastingly
undone, as soon as ever his soul is departed from his body, and he sees
the things that he would not believe. Sirs, is it rational to dance in
Satan's fetters, at the brink of hell, when so many hundred diseases
are all ready to mar the mirth, and snatch away the guilty soul, and
cast it into endless desperation? I exceedingly pity the ungodly in
their unwarrantable melancholy griefs, and much more an ungodly man
that is bleeding under the wounds of conscience. But a man that is
merry in the depth of misery is more to be pitied than he. Methinks it
is one of the most painful sights in all the world, to see a man ruffle
it out in bravery, and spend his precious time in pleasure, and melt
into sensual and foolish mirth, that is a stranger to God, and within a
step of endless woe. When I see their pomp, and feasting, and
attendance, and hear their laughter and insipid jests, and the fiddlers
at their doors or tables, and all things carried as if they made sure
of heaven, it saddeneth my heart to think, alas! how little do these
sinners know the state that they are in, the God that now beholdeth
them, the change that they are near. How little do they think of the
flames that they are hastening to, and the outcries and lamentations
that will next ensue." Baxter knew that he would have, in all
probability, many a light and careless mortal to hear him at St. Paul's
that day, whose every thought and feeling would be engrossed in the
anticipation of the gayeties that were about to return and supersede
the strictness of Puritan times; he anticipated the presence of men
who, like moths round a candle, were darting about in false security on
the borders of everlasting fire, and thus he sent the arrows of his
powerful eloquence direct at their consciences. Imagination can
scarcely refrain from picturing some dissipated merry-maker arrested by
such appeals, trembling under such tremendous and startling truths,
quailing with terror, pale with anguish, melted into repentance,
fleeing to the Saviour for mercy, and going home to pour forth in
secret tears and prayers before God.
On the 26th of May, King Charles II. landed at Dover, and on the 29th
entered the metropolis. He was met by the corporation in St. George's
fields, Southwark, where a grand tent had been fitted up for receiving
him. A sumptuous collation was ready, and the lord mayor waited to
place in the hands of the monarch the city sword. Arrived and welcomed
by his subjects, Charles conferred the honor of knighthood on the chief
magistrate, and then proceeded to London, amidst a display of rejoicing
such as brought back the remembrance of other days. The streets were
lined with the companies and train bands; the houses were adorned with
tapestries and silks; windows, balconies, roofs, and scaffolds, were
crowded with spectators; and the conduits ran with delicious wines.
The procession was formed of a troop of gentlemen, arrayed in cloth of
silver; two hundred gentlemen in velvet coats, with footmen in purple
liveries; another troop in buff coats and green scarfs; two hundred in
blue and silver, with footmen in sea-green and silver; two hundred and
twenty, with thirty footmen in gray and silver, and four trumpeters;
one hundred and five, with six trumpets; seventy, with five trumpets;
two troops of three hundred, and one of one hundred, all mounted and
richly habited. Then followed his majesty's arms, carried by two
trumpeters, together with the sheriff's men and six hundred members of
the companies on horseback, in black velvet coats and gold chains.
Kettle-drums and trumpets, twelve ministers at the head of the
life-guards, the city marshal, sheriffs, aldermen, all in rich
trappings, the lord mayor, and last of all, the king, riding between
the Dukes of York and Gloucester. The rear of the procession was
composed of military. An entertainment at Guildhall followed, on the
5th of July. Nothing could exceed the rapture of the old royalist
party in London. Cavaliers and their followers, restrained by the
regulations and example of the governing powers during the
commonwealth, and now freed from all restriction on their indulgence,
were loud and extravagant in their demonstrations of joy. London was
transformed into a scene of carnival-like festivity. There were
bonfires and the roasting of oxen, while the rumps of beef divided
among hungry citizens suggested many a joke on the rump parliament.
Revelry and intemperance were the order of the day. The taverns rang
with the roundelay of the licentious and intemperate--"The king shall
enjoy his own again." At night, the riotous amusement continued,
amidst illumination of the most brilliant kind which at that time could
be supplied. The whole was a fitting prelude to the reign that
followed, and an affecting commentary on the moving exhortations of
Baxter, to which we have before referred.
A band of wild and crazy enthusiasts, denominated Fifth Monarchy men,
troubled the peace of the city in the beginning of the following year.
Led on by a fanatic named Venner, they insisted on the overthrow of
King Charles, and the establishment of the reign of King Jesus. Though
only between sixty and seventy in number, they were so feebly opposed
by the authorities who had the safety of the city intrusted to them,
that they marched from street to street, bearing down their opponents,
and engaging in successful skirmishes, both with train-bands and
horse-guards. For two days this handful of misguided men kept up their
insurrection, and at last intrenched themselves in an ale-house in
Cripplegate, where, after severe fighting, the remnant of them were
captured. About twenty persons were killed on each side during the
whole fray, and eleven of the rebels were afterwards executed. Soon
after this, on the 23d of April, the coronation took place, which
occasioned another gala day for the citizens, who now, in addition to
other demonstrations of joy, erected four triumphal arches--the first
in Leadenhall-street, representing his majesty's arrival; the second in
Cornhill, forming a naval representation; the third in Cheapside, in
honor of Concord; and the fourth in Fleet-street, symbolical of Plenty.
The old national amusements were revived in London on the restoration.
May-day and Christmas resumed their former appearance. The May-pole in
the Strand was erected in 1661. The theatres were re-opened, pouring
forth a flood of licentiousness. The love of show and decoration was
cherished afresh. Dresses and equipages shone in more than their
ancient splendor. In 1661, it was thought necessary to repress the
gilding of coaches and chariots, because of the great waste and expense
of gold in their adorning.
London also witnessed other accompaniments of the restoration. The
regicide trials took place soon after the king's return, and could not
fail deeply to interest, in one way or the other, the mass of the
citizens, many of them personally acquainted with the parties, and
perhaps abettors of the acts for which they were now arraigned.
Charing Cross was the scene of the execution of Harrison, Scrope,
Jones, Hugh Peters, and others. The spirit in which they met their
deaths was very extraordinary. "If I had ten thousand lives," said
Scrope, "I could freely and cheerfully lay them down all to witness in
this matter." Jones, the night before he died, told a friend that he
had no other temptation but this, lest he should be too much
transported, and carried out to neglect and slight his life, so greatly
was he satisfied to die in that cause. Peters, whom Burke styles "a
poor good man," said, as he was going to die, "What, flesh, art thou
unwilling to go to God through the fire and jaws of death? This is a
good day; He is come that I have long looked for, and I shall be with
him in glory; and so he smiled when he went away." Others were
executed at Tyburn; and there, too, the bodies of the protector Oliver
Cromwell, Treton, and Bradshaw, were ignominiously exposed on a gibbet,
having been dug out of their tombs in Westminster Abbey.
[1] He loved paintings and music, and encouraged proficients in elegant
art. "I ventured," says Evelyn, in 1656, "to go to Whitehall, where of
many years I have not been, and found it very glorious and well
furnished."
[2] Perfect Politician, quoted in "London," vol. i, p. 360.
CHAPTER III.
THE PLAGUE YEAR IN LONDON.
Terrific pestilence had often visited London, and swept into the
eternal world multitudes of victims; but no calamity of this kind that
ever befel the inhabitants can be compared with the awful visitation of
the great plague year. It broke out in Drury-lane, in the month of
December, 1664. For some time it had been raging in Holland, and
apprehensions of its approach to the shores of England had for months
agitated the minds of the people. Remarkable appearances in the
heavens were construed into Divine warnings of some impending
catastrophe; and the common belief in astrology led many, in the
excited state of feeling, to listen to the prognostications that issued
from the press, in almanacs and other publications of the day. Defoe,
in his remarkable history of the plague, which, though in its form
fictitious, is doubtless in substance a credible narrative, describes a
man who, like Jonah, went through the streets, crying, "Yet forty days,
and London shall be destroyed." Another ran about, having only some
slight clothing round his waist, exclaiming, with a voice and
countenance full of horror, "O, the great and dreadful God!" Yet the
forebodings which were excited by reports from the continent, the
traditions of former visitations of pestilences, the actual breaking
out of the disease in a few instances, together with the superstitious
aggravations just noticed, only shadowed forth, in light pale hues, the
dark and intensely gloomy colors of the desolating providence which the
sovereign Ruler of all events brought over the city of London.
Head-ache, fever, a burning in the stomach, dimness of sight, and livid
spots on the chest, were symptoms of the fatal disorder. These signs
became more numerous as the months of the year 1665 advanced; yet the
cases of plague were comparatively few till the month of June. "June
the 7th," says an observant writer of that period in his diary, "the
hottest day that ever I felt in my life. This day, much against my
will, I did see in Drury-lane two or three houses marked with a red
cross upon the doors, and 'Lord, have mercy upon us!' writ there, which
was a sad sight to me, being the first of that kind that to my
remembrance I ever saw." Again, on the 17th of June: "It struck me
very deep this afternoon, going with a hackney coach down Holborn from
the lord treasurer's, the coachman I found to drive easily, and easily,
at last stood still, and came down hardly able to stand, and told me he
was suddenly struck very sick, and almost blind he could not see; so I
light, and went into another coach, with a sad heart for the poor man,
and myself also, lest he should have been struck with the plague."
This description of the first sight of the marked door, and the coach
going more and more easily till it stood still, with its plague-struck
driver, places the reader in the midst of the scene of disease and
sorrow, awakening sympathetic emotions with those sufferers in a now
distant age.
The alarm increased as the deaths multiplied, and people began to pack
up and leave London with all possible haste. The court and the
nobility removed to a distance, and so also did vast numbers beside who
had the means of doing so, and were not confined by business; yet the
general terror was so great throughout the kingdom that friends were
sometimes far from being welcomed by those whom they visited. "It is
scarcely possible," says Baxter, "for people who live in a time of
health and security to apprehend the dreadful nature of that
pestilence. How fearful people were thirty or forty, if not a hundred
miles from London, of anything they brought from mercers' or drapers'
shops, or of goods that were brought to them, or of any persons who
came to their houses. How they would shut their doors against their
friends; and if a man passed over the fields, how one would avoid
another, how every man was a terror to another. O, how sinfully
unthankful are we for our quiet societies, habitations, and health!"
But the bulk of the people, of course, were compelled to remain in the
city, and, pent up in dirty, close, unventilated habitations, while the
weather was burning hot, were exposed to the unmitigated fury of the
contagion. The weekly bills of mortality rose from hundreds to
thousands, till, in the month of September, the disease reached its
height, and no less than ten thousand souls were hurried into eternity.
The operations of business were of course checked, and in many cases
entirely suspended by the terrific progress of the calamity. Several
shops were closed in every street; dwellings were often left empty, the
inmates having been smitten or driven away by the fatal scourge. Some
of the public thoroughfares were nearly deserted. The markets being
removed beyond the city walls, to prevent the people as much as
possible from coming together in masses; the erection of houses also
being unnecessary, and therefore discontinued for a while--carts and
wagons, laden with provision, or with building materials, no longer
frequented the highways, which, a few short months before, had been the
scene of busy activity. Coaches were seldom seen, except when parties
were hurrying away from the city, or when some one, affected by the
disorder, was being conveyed home, with the curtains of the vehicle
closely drawn. The grass growing in the streets, and the solemn
stillness which pervaded many parts of the great city, in contrast with
its previous state, are circumstances particularly mentioned in the
descriptions of London in the plague year, and they powerfully serve to
give the reader an affecting idea of the awful visitation. Few
passengers appeared, and those few hurried on, in manifest fear of each
other, as if each was carrying to his neighbor the summons of death.[1]
The daughters of music were brought low; the din of business, and the
murmur of pleasant talk, and the London cries were silenced. The
shrieks, however, of sufferers in agony, or of maniacs driven mad by
disease, broke on the awful quietude. People might be heard crying out
of the windows for some to help them in their anguish--to assuage the
burning fever, or to carry their dead away. Occasionally, some rushed
towards the Thames, with bitter cries, to seek relief from their
torments by suicide. The Rev. Thomas Vincent, who was residing in
London at the time, describes some touching examples of sorrow, which
were only specimens of what prevailed to an indescribable extent.
"Amongst other sad spectacles," he says, "two, methought, were very
affecting; one of a woman coming alone, and weeping by the door where I
lived, (which was in the midst of the infection,) with _a little coffin
under her arm_, carrying it to the new churchyard. I did judge that it
was the mother of the child, and that all the family besides were dead,
and that she was forced to coffin up and to bury with her own hands
this her last dead child!" The second case to which this writer
alludes is even more terrible than that now given, but out of regard to
our readers' feelings we refrain from quoting it. A passenger, the
same eye-witness adds, could hardly go out without meeting coffins; and
Defoe gives us a picture, as graphic as it is awful, of the mode of
sepulture adopted when the plague was at its height. He informs us
that a great pit was dug in the churchyard of Aldgate parish, from
fifteen to sixteen feet broad, and twenty feet deep; at night, the
victims carried off in the day by death were brought in carts by
torchlight to this receptacle, the bellman accompanying them, and
calling on the inhabitants as they passed along to bring out their
dead. Sixteen or seventeen bodies, naked, or wrapped in sheets or
rags, were thrown into one cart, and then huddled together into the
common grave.
The king of terrors sweeping into the eternal world so many thousands,
is a picture which must excite in the mind of the Christian solemn
emotions. It is pleasing, however, to learn from Vincent how
tranquilly God's people departed in that season of Divine judgment.
"They died with such comfort as Christians do not ordinarily arrive
unto, except when they are called forth to suffer martyrdom for the
testimony of Jesus Christ. Some who have been full of doubts, and
fears, and complaints, whilst they have lived and been well, have been
filled with assurance, and comfort, and praise, and joyful expectations
of glory, when they have been laid on their death-beds by this disease;
and not only more growing Christians, who have been more ripe for
glory, have had their comforts, but also some younger Christians, whose
acquaintance with the Lord hath been of no long standing." There were
persons, however, who had lived through a course of profligacy, who, so
far from being led to repentance by the awful dispensation they
witnessed, only plunged into deeper excesses, driving away care by riot
and intemperance, or availing themselves of the confusion of the times
to commit robbery. The immorality, daring presumption, and reckless
wickedness of a portion of the people during the London plague, as in
the plague at Florence in 1348, and the plague at Athens, described by
Thucydides, prove the depravity of the human heart, and the inefficacy
of afflictions or judgments, if unaccompanied by Divine grace, to melt
or change it. We learn, however, that by the preaching of the gospel
some were graciously renewed and saved. Baxter informs us, that
"abundance were converted from their carelessness, impenitency, and
youthful lusts and vanities, and religion took such a hold on many
hearts as could never afterwards be loosed." The parish churches were
in several instances forsaken by their occupants, but many godly men
who had been ejected by the Uniformity Act, now came forward, with
their characteristic disinterestedness and zeal, to supply their
brethren's lack of service. Vincent, already mentioned, with Clarkson,
Cradock, and Terry, distinguished themselves by holy efforts for the
conversion of sinners at that dreadful time. A broad sheet exists in
the British Museum, containing "short instructions for the sick,
especially those who, by contagion, or otherwise, are deprived of the
presence of a faithful pastor, by Richard Baxter, written in the great
plague year, 1665." Preaching was the principal method of doing good.
Large congregations assembled to hear the man of God faithfully
proclaim his message. The imagination readily restores the timeworn
Gothic structure in the narrow street--the people coming along in
groups--the crowded church doors, and the broad aisles, as well as the
oaken pews and benches, filled with one dense mass--the anxious
countenances looking up at the pulpit--the divine, in his plain black
gown and cap--the reading of the Scriptures--the solemn prayer--the
sermon, quaint indeed, but full of point and earnestness, and
possessing that prime quality, adaptation--the thrilling appeals at the
close of each division of the discourse--the breathless silence, broken
now and then by half-suppressed sobs and lamentations--the hymn,
swelling in dirge-like notes--and the benediction, which each would
regard as possibly a dismissal to eternity; for who but must have felt
his exposure to the infection while sitting amidst that promiscuous
audience? It is at times like these that the worth of the soul is
appreciated, and a saving interest in Christ perceived to be more
valuable than all the accumulated treasures of earth. So far as their
health was concerned, the prudence of the people in congregating
together in such crowds, at such a season, has been often and fairly
questioned; yet who that looks at the imminent spiritual peril in which
multitudes were placed, but must commend the religious concern which
they manifested; and who that takes into account the peculiar
circumstances of the preachers, laboring without emolument at the
hazard of their lives, but must applaud their apostolic
zeal?--_Spiritual Heroes_, p. 289.
The plague reached its height in September--during one night of that
month ten thousand persons died. After this the pestilence gradually
diminished, and by the end of the year it had ceased. The visitation
has acquired additional interest for us of late from the occurrence of
cholera to an alarming extent. The former, like the latter, was
increased by poverty and filth, and to a much greater degree; for,
badly as houses have been ventilated, of late, and defective as may be
our drainage, our fathers were incomparably worse off than we are in
these respects. Houses were crowded together, and left in a state of
impurity which would shock the least delicate and refined of the
present day. There were scarcely any under sewers. Ditches were the
channels for carrying off refuse; and as supplements to these imperfect
methods of cleansing a great city, there were public dunghills. The
effluvia from such sources was, indeed, humanly speaking, enough to
cause a pestilence, and at the time of the plague must have been
intolerable from the heat of the weather; while some means, also,
adopted by the authorities for stopping the ravages of mortality, only
promoted the evil--such as the shutting up of houses, and the kindling
fires in the streets. The state of the metropolis then, and even now,
may be assigned as an auxiliary cause of the spread of plague and
cholera; but it must be confessed, there lies at the bottom of these
visitations much of mystery, inexplicable by reference to mere human
agencies. There is a power at work in the universe deeper far than any
of those which our poor natural philosophy can detect. Not that these
extraordinary occurrences show us the presence of a Divine providence
which does not operate at other, and at all times; not as if the
mysterious agency of God were sometimes in action, and sometimes in
repose; not as if the Almighty visited the earth yesterday, and left it
to-day; not as if his kingly rule over the world were broken by
interregnums;--by no means; still these events are like the lifting up
of the veil of second causes, and the disclosure of depths of power
down which mortals ought to look with reverence. They suggest to the
devout solemn views of nature and man--of life and death--of God ruling
over all. Loudly, also, do they remind us of the malignity of sin, and
the evils which it has brought on a fallen world. Happy is he who,
amidst desolations such as we have now described, can, through a living
faith in Christ, exclaim, "The Lord is my refuge and fortress: my God;
in him will I trust. Surely he shall deliver me from the snare of the
fowler, and from the noisome pestilence."
[1] Judge Whitelock came up to London from Buckingham to sit in
Westminster Hall. He reached Hyde Park Corner on the morning of the
2d, "where he and his retinue dined on the ground, with such meat and
drink as they brought in the coach with them, and afterwards he drove
fast through the streets, which were empty of people and overgrown with
grass, to Westminster Hall, where he adjourned the court, returned to
his coach, and drove away presently out of town."--_Whitelock_, p. 2.
CHAPTER IV.
THE FIRE OF LONDON.
"One woe is past, another woe cometh quickly." Just a year after the
plague was at its height, the great fire of London occurred. On
Sunday, September 3d, 1666, soon after midnight, the house of Farryner
the king's baker, near London-bridge, was discovered to be in flames.
Before breakfast time no less than three hundred houses were consumed.
Such a rapid conflagration struck dismay throughout the neighborhood,
and unnerved those who, in the first instance, by prompt measures might
have stayed the mischief. Charles II., as soon as he heard of what had
happened, displayed a decision, firmness, and humanity, which relieve,
in some degree, the dark shades Of his character and life; and gave
orders to pull down the houses in the vicinity of the fire. Soon
afterwards he hastened to the scene of danger, in company with his
brother, the duke of York, using prudent measures to check the
conflagration, to help the sufferers, and inspire confidence in the
minds of the people. But the lord mayor was like one distracted,
uttering hopeless exclamations on receiving the royal message, blaming
the people for not obeying him, and leaving the scene of peril to seek
repose; while the inhabitants ran about raving in despair, and the
fire, which no proper means were employed to quench, went on its own
way, devouring house after house, and street after street. By Monday
night, the fire had reached to the west as far as the Middle Temple,
and to the east as far as Tower-street. Fleet-street, Old Bailey,
Ludgate-hill, Warwick-lane, Newgate, Paul's-chain, Watling-street,
Thames-street, and Billingsgate, were destroyed or still wrapped in
flame.
On Tuesday the fire reached the end of Fetter-lane and the entrance to
Smithfield. Around Cripplegate and the Tower, the devouring element
violently raged, but in other directions it somewhat abated. Engines
had been employed in pulling down houses, but this process was too slow
to overtake the mischief. Gunpowder was then used to blow up
buildings, so that large gaps were made, which cut off the edifices
that were burning from those still untouched. By these means, on the
afternoon of Tuesday, the devastation was curbed. The brick buildings
of the Temple also checked its progress to the west. Throughout
Wednesday the efforts of the king and duke, and some of the lords of
the council, were indefatigable. Indeed, his majesty made the round of
the fire twice a day, for many hours together, both on horseback and on
foot, giving orders to the men who were pulling down houses, and
repaying them on the spot for their toils out of a money-bag which he
carried about with him. On Thursday, the fire was thought to be quite
extinguished, but in the evening it burst out afresh near the Temple.
Renewed and vigorous efforts at that point, however, soon stayed its
ravages, and in the course of a short time it was finally extinguished.
The space covered with ruins was four hundred and thirty-six acres in
extent. The boundaries of the conflagration were Temple-bar,
Holborn-bridge, Pye-corner, Smithfield, Aldersgate, Cripplegate, near
the end of Coleman-street, at the end of Basinghall-street, by the
postern at the upper end of Bishopsgate-street, in Leadenhall-street,
by the Standard in Cornhill, at the church in Fenchurch-street, by the
Clothworkers' Hall, at the middle of Mark-lane, and at the Tower-dock.
While four hundred and thirty-six acres were covered with ruins, only
seventy-five remained with the property upon it uninjured. Four
hundred streets, thirteen thousand houses, eighty-seven parish
churches, and six chapels; St. Paul's Cathedral, the Royal Exchange and
Custom House, Guildhall and Newgate, and fifty-two halls of livery
companies, besides other public buildings, were swept away. Eleven
millions' value of property the fire consumed, but, through the mercy
of God, only eight lives were lost.
The rapid spread of the devastation may be easily accounted for in the
absence of timely means to stop it. The buildings were chiefly
constructed of timber, and covered with thatch. The materials were
rendered even more than commonly combustible by a summer intensely hot
and dry. Many of the streets were so narrow that the houses facing
each other almost touched at the top. A strong east wind steadily blew
for three days over the devoted spot, like the blast of a furnace, at
once fanning the flame and scattering firebrands beyond it. It was
like a fire kindled in an old forest, feeding on all it touched,
curling like a serpent round tree after tree, leaving ashes behind, and
darting on with the speed of lightning to seize on the timber before.
Into the origin of the calamity the strictest investigation was made.
Some ascribed it to incendiaries. Party spirit led to the accusation
of the <DW7>s, as perpetrators of the deed. One poor man was
executed, on his own confession, of having a hand in it, but under
circumstances which pretty clearly prove that he was a madman, and was
really innocent of the crime of which, through a strange, but not
incredible hallucination of mind, he feigned himself guilty. Other
persons ascribed it to what would commonly be called an accidental
circumstance--a great stock of fagots in the baker's shop being
kindled, and carelessly left to burn in close contiguity with stores of
pitch and rosin. Many considered that the providence of Almighty God,
who works out his own wonderful purposes of judgment and mercy by means
which men call accidental, overruled the circumstances out of which the
fire arose, as a source of terrific chastisement for the sins of a
wicked and godless population, who had hardened their necks against
Divine reproof administered to them in another form so shortly before.
A religious sentiment in reference to the visitation took possession of
many minds, habitually undevout; and even Charles himself was heard, we
are told by Clarendon, to "speak with great piety and devotion of the
displeasure that God was provoked to."
Eye-witnesses have left behind them graphic sketches of this spectacle
of terror. "The burning," says Vincent, in his tract called "God's
Terrible Advice to the City by Plague and Fire,"--"the burning was in
the fashion of a bow; a dreadful bow it was, such as mine eyes never
before had seen--a bow which had God's arrow in it with a flaming
point." "The cloud of smoke was so great, that travelers did ride at
noon-day some six miles together in the shadow of it, though there were
no other clouds to be seen in the sky." "The great fury of the fire
was in the broader streets in the midst of the night; it was come down
to Cornhill, and laid it in the dust, and runs along by the stocks, and
there meets with another fire, which came down Threadneedle-street, a
little farther with another which came up from Wallbrook, a little
farther with another which came up from Bucklersbury, and all these
four joining together break into one great flame, at the corner of
Cheapside, with such a dazzling light and burning heat, and roaring
noise by the fall of so many houses together, that was very amazing."
One trembles at the thought of these blazing torrents rolling along the
streets, and then uniting in a point, like the meeting of wild
waters--floods of fire dashing into a common current. Evelyn observes
that the stones of St. Paul's Cathedral flew about like granadoes, and
the melted lead ran down the pavements in a bright stream, "so that no
horse or man was able to tread on them." "I saw," he says in his
Diary, "the whole south part of the city burning, from Cheapside to the
Thames, and all along Cornhill, (for it likewise kindled back against
the wind as well as forward,) Tower-street, Fenchurch-street,
Gracechurch-street, and so along to Baynard's Castle, and was taking
hold of St. Paul's Church, to which the scaffolds contributed
exceedingly." He saw the Thames covered with goods floating, all the
barges and boats laden with such property as the inhabitants had time
and courage to save; while on land the carts were carrying out
furniture and other articles to the fields, which for many miles were
strewed with movables of all sorts, and with tents erected to shelter
the people. "All the sky," he adds, "was of a fiery aspect, like the
top of a burning oven, and the light seen for above forty miles around
for many nights; the noise and cracking of the impetuous flames, the
shrieking of women and children, the hurry of people, the fall of
towers, houses, and churches, was like a hideous storm; and the air all
about so hot and inflamed, that at last one was not able to approach
it, so that they were forced to stand still, and let the flames burn
on, which they did for nearly two miles in length and one in breadth.
The clouds also of smoke were dismal, and reached upon computation
nearly fifty miles in length."
A great fire is a most sublime, as well as appalling spectacle, and
generally presents some features of the picturesquely terrible.
Guildhall, built of oak, too solid and old to blaze, became so much
red-hot charcoal, as if it had been a palace of gold, or a building of
burnished brass. There were circumstances, too, connected with the
destruction of magnificent edifices, full of a sort of poetical
interest. The flame inwrapped St. Paul's Cathedral, and rent in pieces
the noble portico recently erected, splitting the stones into flakes,
and leaving nothing entire but the inscription on the architrave,
which, without one defaced letter, continued amidst the ruins to
proclaim the builder's name. In remarkable coincidence with this, at
the same time that the fire entered the Royal Exchange, ran round the
galleries, descended the stairs, compassed the walks, filled the
courts, and rolled down the royal statues from their niches, the figure
of the founder, Sir Thomas Gresham, was left unharmed, as if calmly
surveying the destruction of his own munificent donation to the old
city, and anticipating the certainty of the re-edification of that
monument of his fame, as well as the revival of that commerce, in the
history of which his own is involved. As we think of this, we call to
mind another interesting incident, which occurred when the building was
burned down a second time in 1838. Some readers, perhaps, will
remember, that the bells in the tower rang out their last chime to the
tune of "There's na' luck about the house," just as they were on the
point of coming down with a tremendous crash; as though uttering
swanlike notes in death.
The area devastated by the fire may be estimated, if we fancy a line
drawn from Temple Bar to the bottom of Holborn-hill, then through
Smithfield across Aldersgate-street to the end of Coleman-street, then
sweeping round by the end of Bishopsgate and Leadenhall-streets, and
taking a curve till it touches the Tower, the river forming the
southern boundary of this large space. Within these limits, after the
fire, there arose a new London, of nobler aspect, and formed for
grander destinies than the old one, relieved by that very fire, under
the blessing of Divine Providence, from liability to the recurrence of
the dreadful plague, which had from time to time recruited its
death-dealing energy from the filth of old crowded streets, with all
their noxious exhalations. If a panic seized the citizens when the
first alarm of the conflagration spread among them, they redeemed their
character by the self-possession and activity which they evinced in
repairing the desolation. Not desponding, but inspired with the hope
of the future prosperity of their venerable city, they concurred with
king and parliament in the zeal and diligence requisite for the
emergency. Scarcely were the flames extinguished, when they set to
work planning the restoration. "Everybody," observes Evelyn, "brings
in his idea; amidst the rest, I presented his majesty my own
conceptions, with a discourse annexed. It was the second that was seen
within two days after the conflagration, but Dr. Wren had got the start
of me." This Dr. Wren had been spoken of by the same writer, fourteen
years before, as a miracle of a youth. Having made wonderful
attainments in science, he had devoted himself with enthusiasm to the
study of architecture, and now, in the wide space in which at once a
full-grown city was to appear, a field presented itself worthy of the
exercise of the greatest powers of art--a field, indeed, which could
rarely in the world's history be looked for. Doubtless Wren's mind was
all on fire with the grand occasion, and put forth all its marvelous
ability to meet so unparalleled a crisis. Before the architect's
imagination there rose the view of a city, built with scientific
proportions, with a broad street running in a perfect line from a
magnificent piazza, placed where St. Dunstan's church stands, to
another piazza on Tower-hill, with an intermediate piazza corresponding
with these, from each of which streets should radiate. Then, on the
top of Ludgate-hill, over which the broad highway was to run, the new
cathedral was to rise, in the midst of a wide open space, displaying to
advantage its colossal form; and on its northern side there was to
branch out, at a narrow angle with the other main thoroughfare, an
avenue of like dimensions, leading to the Royal Exchange--the site, in
fact, (but intended to cover a wider space,) of our present Cheapside.
The Royal Exchange was to be an additional grand centre, adorned with
piazzas, whence a third vast thoroughfare was to sweep along to
Holborn. All acute angles were to be avoided. The great openings were
to exhibit graceful curves, parochial edifices were to be conspicuous
and insulated, the halls of the twelve great companies were to be
ranged round Guildhall, and architecture was to do the utmost possible
in every street. A like vision dawned on the fancy of Sir John Evelyn,
who in this respect was no unworthy compeer of Wren. But, though the
architect showed the practicability of the scheme, without any loss of
the property, or infringement of the rights of the citizens, their
obstinacy in not allowing the old foundations to be altered, and their
determination not to give up the ground to commissioners for making out
the new streets and sites of buildings, defeated the scheme; "and
thus," writes Wren, (with a deep sigh one thinks he penned the words
while his darling dream melted away,) "the opportunity, in a great
degree, was lost, of making the new city the most magnificent, as well
as commodious for health and trade, of any upon earth." Sir
Christopher Wren could do nothing as he wished. The Monument was not
what he meant it to be. The churches were not placed as he would have
had them, so as to exhibit to advantage their architectural character.
Even St. Paul's was shorn of the glory with which it was enriched in
the architect's mind. It was narrowed and altered by incompetent
judges, especially the Duke of York, who wished to preserve in it
arrangements convenient for a popish cathedral, which he wildly hoped
it would ultimately become. When Wren was compelled to give way, he
even shed tears in the bitterness of his disappointment and grief. He
finally had to do on a large scale, what common minds are ever doing in
their little way--sacrifice some fondly cherished ideal to a stern
necessity.
But, crippled as his genius was by the untoward position in which he
was placed, he accomplished marvelous works of art in the churches so
numerous and varied, built from his designs, and especially in the
grand cathedral, which rises above the rich group of towers, domes,
steeples, and spires, with a lordly air. It is related, in connection
with the building of St. Dunstan's church in the east, the steeple of
which is constructed upon quadrangular columns, that so anxious was he
respecting the result, that he placed himself on London-bridge,
watching through a lens the effect of removing the temporary
supporters, by the aid of which the building was reared. The ascent of
a rocket proclaimed the stability of the structure, and Sir Christopher
smiled at the thought of his having for a moment hesitated to trust to
the certainty of mathematical calculations. Informed one night
afterwards, that a hurricane had damaged all the steeples in London, he
remarked, "Not St. Dunstan's, I am quite sure." St. Stephen's,
Wallbrook, is generally considered the _chef-d'oeuvre_ of Sir
Christopher Wren. "Had the materials and volume," to quote the opinion
of two celebrated architects, "been so durable and extensive as those
of St. Paul's Cathedral, he had consummated a much more efficient
monument to his well-earned fame than that fabric affords." But the
beauty of the edifice is in the interior. "Never was so sweet a kernel
in so rough a shell--so rich a jewel in so poor a setting." The cost
of the fabric was only L7,652. 13_s._ (Cunninghame's Handbook of
London.)
The first stone of St. Paul's was laid on the 21st of June, 1675, by
the architect; and he notices in his Parentalia a little circumstance
connected with the preparations, which was construed by those present
into a favorable omen, and which evidently interested and pleased his
own mind. When the centre of the dimensions of the great dome was
fixed upon, a man was ordered to bring a flat stone from the heap of
rubbish, to be laid as a mark for the masons. The piece he happened to
take up for the purpose was the fragment of a grave-stone, with nothing
of the inscription left but the words, "_Resurgam_," "I shall rise
again." And, true enough, St. Paul's did rise again, with a splendor
which posterity has ever admired. It is, undoubtedly, the second
church in Christendom of that style of architecture, St. Peter's at
Rome being the first. Inferior in point of dimensions, and sadly
begrimed with smoke, in contrast with St. Peter's comparatively
untarnished freshness--destitute, too, of its marble linings, gilded
arches, and splendid mosaics'--it is, on the whole, as Eustace, a
critic prejudiced on the side of Rome, acknowledged, a most extensive
and stately edifice: "It fixes the eye of the spectator as he passes
by, and challenges his admiration, and, even next to the Vatican,
though by a long interval, it claims superiority over all the
transalpine churches, and furnishes a just subject of national pride
and exultation." It was not until 1710 that the building was complete,
when the architect's son laid the topmost stone on the lantern of the
cupola.
In the prospectus published by Evelyn for the rebuilding of London, he
observed, that if the citizens were permitted to gratify their own
fancies, "it might possibly become, indeed, a new, but a very ugly
city, when all was done." The citizens were permitted to have their
own way, and the result was very much what he anticipated. The old
sites of streets and public buildings were, to a great extent, adopted.
The former remained narrow, winding, inconvenient--indeed, more
inconvenient than ever; for what might be borne with when even ladies
of quality traveled on horseback, became scarcely endurable when
lumbering coaches were all the fashion. Churches and other edifices of
importance were planted in inappropriate situations, and were blocked
up by houses and shops. In Chamberlayne's _Angliae Notitia_ for 1692,
he laments that within the city the spacious houses of noblemen, rich
merchants, the halls of companies, and the fair taverns, were hidden
from strangers, the room towards the street being reserved for
tradesmen's shops; but from his account and that of others, it appears
plain enough that the men of that day felt that London, as rebuilt
after the fire, was far superior to what it had been in the times of
their fathers. The old wooden lath and plaster dwellings gave place to
more substantial habitations of brick and stone, and the public
structures appeared to those who were contemporary with their erection,
proud trophies of skill, art, and wealth. "Notwithstanding," exclaims
the author just noticed, "all these huge losses by fire,
notwithstanding the most devouring pestilence in the year immediately
foregoing, and the then very chargeable war against three potent
neighbors, the citizens, recovering in a few months their native
courage, have since so cheerfully and unanimously set themselves to
rebuild the city, that, (not to mention whole streets built and now
building by others in the suburbs,) within the space of four years,
they erected in the same streets ten thousand houses, and laid out
three millions sterling. Besides several large hospitals, divers very
stately halls, nineteen fair solid stone churches were all at the same
time erecting, and soon afterwards finished, and now, in the year 1691,
above twenty churches more, of various beautiful and solid architecture
are rebuilt. Moreover, as if the late fire had only purged the city,
the buildings are becoming infinitely more beautiful." The author
speaks with immense satisfaction of the new houses, churches, and
halls, richly-adorned shops, chambers, balconies, and portals, carved
work in stone and wood, with pictures and wainscot, not only of fir and
oak, but some with sweet-smelling cedar, the streets paved with stone
and guarded with posts; and ends by observing, that though the king
might not say he found London of brick and left it of marble, he could
say, "I found it wood and left it brick."
CHAPTER V.
FROM THE RESTORATION OF THE CITY TO THE CLOSE OF THE CENTURY.
Great as was the consternation described in the foregoing chapter,
scarcely less terror was produced in the minds of the citizens by the
apprehension of a Dutch invasion about the same time. In 1666, even
before the fire, this feeling was excited. The ships of France and
Holland approached the Thames, and engaged with the English fleet.
"After dinner," says Lady Warwick, whose entry in her journal, under
date, July 29, brings the occurrence home to us--"after dinner came the
news of hearing the guns that our fleet was engaged. My head was much
afflicted by the consideration of the blood that was spilt, and of the
many souls that would launch into eternity." There is a fine passage,
descriptive of the excitement at this time, in Dryden's Essay on
Poesie: "The noise of the cannon from both navies reached our ears
about the city, so that men being alarmed with it, and in dreadful
suspense of the event, which we knew was then deciding, every one went
following the sound as his fancy led him, and leaving the town almost
empty, some took towards the park, some cross the river, others down
it, all seeking the noise in the depth of the silence. Taking, then, a
barge, which the servant of Lisidenis had provided for them, they made
haste to shoot the bridge, and left behind them that great fall of
waters, which hindered them from hearing what they desired; after
which, having disengaged themselves from many vessels which rode in
anchor in the Thames, and almost blocked up the passage to Greenwich,
they ordered the watermen to let fall their oars more gently; and then
every one favoring his own curiosity with a strict silence, it was not
long ere they perceived the air breaking about them, like the noise of
distant thunder, or of swallows in the chimney, those little
undulations of sound, though almost vanishing before they reached them,
yet still seeming to retain somewhat of their first horror, which they
had betwixt the fleets. After they had listened till such time as the
sound, by little and little, went from them, Eugenius, lifting up his
head, and taking notice of it, was the first who congratulated to the
rest that happy omen of our nation's victory, adding, we had but this
to desire in confirmation of it, that we might hear no more of that
noise, which was now leaving the English coast." This passage, which
Montgomery eulogizes most warmly in his Lectures on English Poetry, as
one of the most magnificent in our language, places before us, with
graphic force, the state of curiosity, suspense, and solicitude, which
was experienced by multitudes of citizens at the period referred to.
In the following year, fresh excitement from the same source arose.
The monarch was wasting upon his pleasures a considerable portion of
the money which parliament had voted for the defence of the kingdom.
The national exchequer was empty, and the credit of the navy
commissioners gone. No loans could be obtained, yet ready money was
demanded by the laborers required in the dockyards, by the sailors who
were wanted to man the vessels, and by the merchants from whose stores
the fleet needed its provisions. Not a gun was mounted in Tilbury
Fort, nor a ship of war was in the river ready to oppose the enemy,
while crowds thronged about the Admiralty, demanding their pay, and
justly upbraiding the government. The Dutch ships, under De Ruyter,
entered the Thames, sailed up the Medway, and seized the Royal Charles,
besides three first-rate English vessels. One can easily conceive the
second panic which this event must have produced among the citizens;
nor is it difficult to imagine the suspension of business, the general
exchange of hasty inquiries in that hour of terror, and the flocking of
the people to the river-side to learn tidings of the fleet. Though the
Dutch ships, unable to do further mischief on that occasion, returned
to join the rest of the naval force anchored off the Nore; yet the
citizens could not be relieved from their anxiety by this circumstance,
for they knew that the foe would remain hovering about their coasts,
and they could not tell but that in some unlooked-for moment the
invaders might approach the very walls of their city. Some weeks of
painful apprehension followed, and twice again did the admiral threaten
to remount the Thames. An engagement between the English squadron and
a portion of the invading armament of Holland prevented the
accomplishment of that design, and saved London for the present from
further fear.
Strong political excitement was produced in the city of London, at a
later period of Charles II.'s reign, by another kind of invasion. The
monarch and court, finding themselves thwarted in their arbitrary
system of government by the spirit of the citizens, who were jealous of
their own liberties, ventured, in defiance of the national constitution
and the charters of the city, to interfere in the municipal elections.
They attempted to thrust on the people as sheriffs men whom they knew
they could employ as tools for despotic purposes. In 1681, a violent
attempt of this sort was made, when the city returned in opposition to
the wishes of king and court, two patriotic and popular men, Thomas
Pilkington and Samuel Shaw. The king could not conceal his chagrin at
this election, and when invited to dine with the citizens, replied,
"Mr. Recorder, an invitation from the lord mayor and the city is very
acceptable to me, and to show that it is so, notwithstanding that it is
brought by messengers so unwelcome to me as those two sheriffs are, yet
I accept it." Many of the citizens about the same time, influenced by
fervent Protestant zeal, and by attachment to the civil and religious
liberties of the country, were apprehensive of the consequences if the
Duke of York, known to be a Roman Catholic, were allowed to ascend the
British throne. The anti-papal feelings of the nation had been
increased by the belief of a deeply-laid popish plot, which the
infamous Titus Oates pretended to reveal; and in London those
sentiments had been rendered still more intense by the murder of Sir
Edmondbury Godfery, the magistrate who received Oates's depositions.
His death, over which a large amount of mystery still rests, was
attributed to the revenge of the <DW7>s for the part he had taken in
the prosecution against them. The hatred of which, in general, Roman
Catholics were the objects, centered on the prince, from whose
succession to the crown the restoration of the old religion of the
country was anticipated. His name became odious, and it was difficult
to shield it from popular indignity. Some one cut and mangled a
picture of him which hung in Guildhall. The corporation, to prevent
his royal highness from supposing that they countenanced or excused the
insult, offered a large reward for the detection of the offender, and
the Artillery Company invited the prince to a city banquet. The party
most active in opposing his succession determined to have a large
meeting and entertainment of their own, to express their opinion on the
vital point of the succession to the crown; but the proceeding was
sternly forbidden by the court, a circumstance which only served to
deepen the feelings of discontent already created to a serious extent
in very many breasts. This was followed up by the lord mayor
nominating, in the year 1682, a sheriff favorable to the royal
interests, and intimating to the citizens that they were to confirm his
choice. The uproar at the common hall on Midsummer-day was tremendous.
The citizens contended for their right of election, and nominated both
sheriffs themselves, selecting two persons of popular sentiments.
Amidst the riot, the lord mayor was roughly treated, and consequently
complained to his majesty, the result of which was, that the two
sheriffs already in office, and obnoxious to the court, were committed
to the Tower for not maintaining the peace. Papillion and Dubois, the
people's candidates, were elected. The privy council annulled the
election, and commanded another; when the lord mayor most arbitrarily
declared North and Box, the court candidates, duly chosen. Court and
city were now pledged to open conflict; the former pursuing thoroughly
despotic measures to bring the latter to submission. One rich popular
citizen was fined to the amount of L100,000, for an alleged scandal on
the popish duke, and at length it was resolved to take away the city
charter. Forms of law were adopted for the purpose. An information,
technically entitled a _quo warranto_, was brought against the
corporation in the court of King's Bench. It was alleged, in support
of this suit at the instance of the crown, that the common council had
imposed certain tolls by an ordinance of their own, and had presented
and published throughout the country an insolent petition to the king,
in 1679, for the calling of parliament. The court, swayed by a desire
to please the king, pronounced judgment against the corporation, and
declared their charter forfeited; yet only recorded that judgment, as
if to inveigle the corporation into some kind of voluntary submission,
as the price of preserving a portion of what they were now on the point
of altogether losing. Such an issue, of course, was regarded by the
court as more desirable than an act of direct force, which was likely
to irritate the citizens, and arouse wrath, which might be treasured up
against another day. The city, to save their estates, yielded to the
law, and submitted to the conditions imposed by the king--namely, that
no mayor, sheriff, recorder, or other chief officer, should be admitted
until approved by the king; that in event of his majesty's twice
disapproving the choice of the citizens, he should himself nominate a
person to fill the office, without waiting for another election; that
the court of aldermen might, with the king's permission, remove any one
of their body, and that they should have a negative on the election of
the common council, and, in case of disapproving a second choice on the
part of the citizens, should themselves proceed to nominate such as
they themselves approved. "The city was of course absolutely
subservient to the court from this time to the revolution." (Hallam's
Constitutional History, chap. ii, p. 146.)
The unconstitutional proceedings of the king and court, of which the
circumstances just related are a specimen, aroused some patriotic
spirits in the country; but the power which inspired their indignation
crushed their energies. Two illustrious men, who fell victims to that
power, were connected with the city of London as the place of their
abode, and the scene where they sealed their principles by death.
Russell and Sydney both perished there in 1683. They were accused of
participation in the notorious Rye House plot, and upon evidence, such
as would convince no jury in the present day, were found guilty of
treason. Lord Russell was conveyed from Newgate on the 21st of July,
1683, to be beheaded in Lincoln's-inn-fields. The duke of York, who
intensely hated the patriot, wished him to be executed in
Southampton-square, before his own residence; but the king, says
Burnet, "rejected that as indecent." Lord Russell's behavior on the
scaffold was in keeping with his previous piety and fortitude. "His
whole behavior looked like a triumph over death." He said, the day
before he died, that the sins of his youth lay heavy on his mind, but
he hoped God had forgiven them, for he was sure he had forsaken them,
and for many years had walked before God with a sincere heart. The
faithful lady Rachel, who had so nobly acted as his secretary on his
trial, and had used her utmost efforts to save his life, attended him
in prison, and sought to strengthen his mind with the hopes and
consolations of the gospel of Christ. Late the last night he spent on
earth their final separation in this world took place; when, after
tenderly embracing her several times, both magnanimously suppressing
their indescribable emotions, he exclaimed, as she left the cell, "The
bitterness of death is past." Winding up his watch the next morning,
he observed, "I have done with time, and am going to eternity." He
earnestly pressed upon Lord Cavendish the importance of religion, and
declared how much comfort and support he derived from it in his
extremity. Some among the crowds that filled the streets wept, while
others insulted; he was touched by the tenderness of the one party,
without being provoked by the heartlessness of the other. Turning into
Little Queen-street, he said, "I have often turned to the other hand
with great comfort, but now I turn to this with greater." "A tear or
two" fell from his eyes as he uttered the words. He sang psalms a
great part of the way, and said he hoped to sing better soon. On being
asked what he was singing, he said, the beginning of the 119th Psalm.
On entering Lincoln's-inn-fields, the sins of his youth were brought to
his remembrance, as he had there indulged in those vices which
characterized the court of Charles II. "This has been to me a place of
sinning, and God now makes it the place of my punishment." As he
observed the great crowds assembled to witness his end, he remarked, "I
hope I shall quickly see a better assembly." He walked round the
scaffold several times, and then delivered to the sheriffs a paper,
which had been carefully prepared, declaring his innocence of the
charge of treason, and his strong attachment to the Protestant faith.
After this, he prayed by himself, and then Dr. Tillotson prayed with
him. Another private prayer, and the patriot, having calmly unrobed
himself, as if about to lie down on his couch to sleep, placed his head
upon the block, and with two strokes of the axe was hastened into the
eternal world. The faith, hope, patience, and love of his illustrious
lady surpassed even his own, and her letters breathe a spirit redolent
of heaven rather than earth. After a severe illness, she wrote, in
October, 1680: "I hope this has been a sorrow I shall profit by; I
shall, if God will strengthen my faith, resolve to return him a
constant praise, and make this the season to chase all secret murmurs
from grieving my soul for what is past, letting it rejoice in what it
should rejoice--His favor to me, in the blessings I have left, which
many of my betters want, and yet have lost their chiefest friend also.
But, O! the manner of my deprivation is yet astonishing." Five years
afterwards she says, "My friendships have made all the joys and
troubles of my life, and yet who would live and not love? Those who
have tried the insipidness of it would, I believe, never choose it.
Mr. Waller says--
'What know we of the bless'd above.
But that they sing, and that they love!'
And 'tis enough; for if there is so charming a delight in the love, and
suitableness in humors, to creatures, what must it be to the clarified
spirits to love in the presence of God!"
Algernon Sydney was a man of very powerful mind and of great eloquence,
in these respects utterly eclipsing his noble compatriot; but in his
last days it is painful to miss that Christian faith, tenderness of
heart, and beautiful religious hope, which shone with such serene
brightness amidst the sorrows of his friend. Sydney was a staunch
republican, and his patriotism was cast in the hard and severe mould of
ancient Rome. He was another Brutus. This distinguished man was
executed on Tower-hill, December the 7th, 1683, and faced death with
the utmost indifference, not seeking any aid from the ministers of
religion in his last moments, nor addressing the assembled multitude,
but only remarking to those who stood by that he had made his peace
with God, and had nothing to say to man.
Another sufferer in the same cause, less known to history, but more
closely connected with London, was alderman Cornish. From his great
zeal in the cause of Protestantism, he had become peculiarly odious to
the reigning powers. He was suddenly accused of treason, and hurried
to Newgate on the 13th of October. On the following Saturday he
received notice of his indictment, and the next Monday was arraigned at
the bar. Having been denied time to prepare his defence, he was
completely in the hands of his persecutors, who wreaked on him their
vengeance with merciless intensity and haste. On the 23d of the same
month, he was hanged, drawn, and quartered, in front of his own house,
at the end of King-street, Cheapside. After his death his innocency
was established, and it is said that James, who now occupied the
throne, lamented the injustice he had done. The duke of Monmouth, the
king's nephew, perished on Tower-hill, July, 1685, for his rebellion in
the western counties. The awful tragedy of an execution, with which
the citizens had become so familiar, was in this instance rendered
additionally horrid by the circumstance that the headsman, after
several ineffectual attempts to decapitate his victim, who, with the
gashes in his neck, reproached him for his tardiness, flung down the
axe, declaring he could not go on; forced by the sheriffs, the man at
length fulfilled his bloody task.
The arbitrary and cruel government of the country for many years was
now on the point of working out its remedy. The trial and acquittal of
the seven bishops at Westminster hastened on a crisis, and nothing
could exceed the joy which the city evinced on that occasion. On their
way to the Tower by water, the most enthusiastic demonstrations of
sympathy were evinced by the multitudes who lined the banks of the
Thames, and on reaching the fortress itself, the garrison knelt and
begged their blessing. Their subsequent discharge on bail, and
especially their final acquittal, excited boundless joy throughout the
city, and were celebrated by bonfires and illuminations. The king,
observing the tide of popular feeling set in so decidedly against him,
endeavored to reconcile the city of London by restoring to it the
charter, which, in his brother's reign, had been so unjustly taken
away. But though this brought votes of thanks in return, it
established no confidence towards the sovereign on the part of the
people. The prince of Orange, invited over by several distinguished
persons, wearied by the long continuance of tyranny, landed at Torbay,
when James, having committed the care of the metropolis to the lord
mayor, marched forth to meet his formidable rival. The result belongs
to the history of England. The lords spiritual and temporal held one
of their important meetings, during the interregnum, at Guildhall, and
summoned to it the chief magistrate and aldermen. Judge Jeffreys, of
infamous memory, was brought before the lord mayor, and committed to
the Tower, where he died through excessive drinking. Disturbances
broke out in the city, and the populace plundered the houses of the
<DW7>s. The mayor, aldermen, and a deputation from the common
council, were summoned to attend the convention parliament, which
raised the prince of Orange to the throne. These are the principal
incidents in the history of London, as connected with the glorious
revolution of 1688.
William and Mary were soon welcomed by the citizens to a very splendid
entertainment, the usual token of loyalty offered by them to new
sovereigns; and no time was lost by their majesties in reversing the
_quo warranto_, and fully restoring to the city its ancient charter.
When a conspiracy against William was discovered, in 1692, the city
train bands displayed their loyalty, and marched to Hyde Park to be
reviewed by the queen; and again, when an assassination plot was
detected, an association was formed among the citizens to defend his
person. These occurrences, with sundry rejoicings and entertainments
upon the king's return to this country, after the Irish and foreign
campaigns in which he engaged, are the principal civic events connected
with the reign of William III.
On turning from the political history of London to look at the manners
and morals of society during the latter part of the seventeenth
century, our attention is immediately arrested by the scenes at
Whitehall during the reign of Charles II. There the monarch fixed his
court, gathering around him some of the most profligate persons of the
age, and freely indulging in the most criminal pleasures. The palace
was adorned with the greatest splendor, the ceilings and walls being
decorated, and the furniture and other ornaments being fashioned
according to the French taste, as it then prevailed under Louis XIV.
Courtiers and idlers here flocked together from day to day, to lounge
in the galleries, to talk over public news and private scandal, and to
listen to the tales and jests of the king, whose presence was very
accessible, and whose wit and familiarity with his courtiers made him a
great favorite. Banquets, balls, and gambling, formed the amusements
of the evening, often disgraced by open licentiousness. "I can never
forget," says Evelyn, "the inexpressible luxury and profaneness, gaming
and all dissoluteness, and as it were total forgetfulness of God, (it
being Sunday evening,) which this day se'nnight I was witness of."
This was at the close of the sovereign's wretched career. "Six days
after," adds the writer, "was all in the dust!" This passage cannot
but call up in the Christian mind, awful thoughts of the eternal
condition of such as spend their days in the pleasures of sin, and then
drop into that invisible world, on the brink of which they were all
along "sporting themselves with their own deceivings." Sinful
practices, such as stained the court of Charles II., are too often
attempted to be disguised under palliative terms; but the solemn
warning of Scripture remains, "Let no man deceive you with vain words,
for because of these things cometh the wrath of God on the children of
disobedience." It is pleasing here to remember, that among those whom
their dignified station, or their duties towards the sovereign and
royal family, brought more or less into contact with the court, there
were persons of a very different character from the gay circle around
them, and whose thoughts, amidst the most brilliant spectacles, were
lifted up to objects that are beyond earthly vision. "In the morning,"
says lady Warwick, in her diary, April 23, 1667, "as soon as dressed,
in a short prayer I committed my soul to God, then went to Whitehall,
and dined at my lord chamberlain's, then went to see the celebration of
St. George's feast, which was a very glorious sight. Whilst I was in
the Banqueting House, hearing the trumpets sounding, in the midst of
all that great show God was pleased to put very mortifying thoughts
into my mind, and to make me consider, what if the trump of God should
now sound?--which thought did strike me with some seriousness, and made
me consider in what glory I had in that very place seen the late king,
and yet out of that very place he was brought to have his head cut off.
And I had also many thoughts how soon all that glory might be laid in
the dust, and I did in the midst of it consider how much greater glory
was provided for a poor sincere child of God. I found, blessed be God!
that my heart was not at all taken with anything I saw, but esteemed it
not worth the being taken with."--_Lady Warwick's Memoirs_. Lady
Godolphin was another beautiful instance of purity and piety amidst
scenes of courtly splendor, and manifold temptations to worldliness and
vice; and the more remarkable in this respect, that her duties required
her frequent attendance at Whitehall, and brought her into close
contact with the perils of the place.
The parks were favorite places of resort. "Hyde Park," observes a
cotemporary writer, "every one knows is the promenade of London;
nothing was so much in fashion during the fine weather as that
promenade, which was the rendezvous of magnificence and beauty; every
one, therefore, who had a splendid equipage, constantly repaired
thither, and the king seemed pleased with the place. Coaches with
glasses were then a late invention; the ladies were afraid of being
shut up in them." Charles was fond of walking in the parks, which he
did with such rapidity, and for such a length of time as to wear out
his courtiers. He once said to prince George of Denmark, who was
corpulent, "Walk with me, and hunt with my brother, and you will not
long be distressed with growing fat." Playing with dogs, feeding
ducks, and chatting with people, were occupations the king was much
addicted to, and were thought by his subjects to be so condescending,
familiar, and kind, that they tended much to promote his personal
popularity with the London citizens and others. Along St. James's
Park, at the back of what are now Carlton Gardens, there ran a wall,
which formed the boundary of the king's garden. On the north side of
it was an avenue, with rows of elms on one side, and limes on the
other, the one sheltering a carriage road, the other a foot-path.
Between lay an open space, called Pall Mall, which designation was
derived from a game played there, consisting of striking a ball through
an iron hoop suspended on a lofty pole. This was a favorite sport in
the days of Charles, and many a gay young cavalier exercised himself,
and displayed his dexterity among those green shades, where now piles
of houses line the busy street, still retaining the name it bore nearly
two centuries ago.
The pleasures of the parks and Whitehall, with all the licentious
accompaniments of the latter, were not always enough to meet the
vitiated appetite for amusement which then prevailed among the
courtiers. Lord Rochester--whose end formed such a striking contrast
to his life; whose sorrow for his sins was so intense, and his desire
for forgiveness and spiritual renewal so earnest--was prominent in
these extravagances, and set himself up in Tower-street as an Italian
mountebank, professing to effect extraordinary cures. Sometimes, also,
he went about in the attire of a porter or beggar. This taste was
cherished and indulged by the highest personages. "At this time,"
(1668,) says Burnet, "the court fell into much extravagance in
masquerading; both the king and queen and all the court went about
masked, and came into houses unknown, and danced there with a great
deal of wild frolic. In all this people were so disguised, that
without being in the secret none could distinguish them. They were
carried about in hackney chairs. Once the queen's chairman, not
knowing who she was, went from her. So she was alone, and was much
disturbed, and came to Whitehall in a hackney coach; some say a cart."
Scenes of dissipation at Whitehall, with occasional excesses of the
kind just noticed, make up the history of the court at London during
the reign of Charles II. The palace, under his brother James, who,
with all his popish zeal, was far from a pure and virtuous man, though
cleansed from some of its pollution, was still the witness of lax
morals. The habits of William III. and his queen Mary, greatly changed
the aspect of things at Whitehall, till its destruction by fire, (the
Banqueting House excepted,) in the year 1691. Afterwards the royal
residence was either at Kensington or Hampton Court.
The riotous pleasures of Charles II. and his favorites, naturally
encouraged imitation among the citizens of London, and during the whole
reign of Charles it was full of scenes of revelry. The excesses which
had been restrained during the commonwealth, and the abandoned
characters who, to escape the churchwardens and other censors of public
morals, sought refuge in retired haunts of villany, now appeared in
open day. The restoration had introduced a sort of saturnalia; and no
wonder, then, that the event was annually celebrated by the lovers of
frivolous pleasure in London, with the gayest rejoicings, in which the
garland and the dance bore a conspicuous part. While habits of
dissipation were too common among the inhabitants generally, vice and
crime were encouraged among the abandoned classes, by the existence of
privileged places, such as Whitefriars, the Savoy, Fuller's Rents, and
the Minories, where men who had lost all character and credit took
refuge, and carried on with impunity their nefarious practices. Other
persons, also, who ranked with decent London tradesmen, would sometimes
avail themselves of these spots; and we are informed that even late in
the seventeenth century, men in full credit used to buy all the goods
they could lay their hands on, and carry them directly to Whitefriars,
and then sending for their creditors, insult them with the exhibition
of their property, and the offer of some miserable composition in
return. If they refused the compromise, they were set at defiance.
The flood of licentiousness which rolled through the city in the time
of Charles II. happily proved insufficient to break down the religious
character of a large number of persons, who had been trained under the
faithful evangelical ministry of earlier times, or had been impressed
by the teaching of earnest-minded preachers and pastors who still
remained. The fire, as well as the plague, in connection with the
fidelity of some of God's servants, was, no doubt, instrumental, under
the blessing of his Holy Spirit, in turning the hearts of many from
darkness to light. The black cloud, as Janeway calls it, which no wind
could blow over, till it fell in such scalding drops, also folded up in
its skirts treasures of mercy for some, whose souls had been
unimpressed by milder means.
By the Act of Uniformity many devoted ministers had been silenced in
London--Richard Baxter, among the rest, whose sermons had attracted, as
they well might, the most crowded auditories;[1] but in private they
continued to do the work of their heavenly Master; and when spaces of
toleration occurred in the persecuting reigns of Charles and James II.,
they opened places of worship, and discharged their holy functions with
happy effects on their numerous auditories. After the fire, they were
for a little time in the enjoyment of this privilege; but, in 1670, an
act was passed for the suppression of conventicles, and the buildings
were forthwith converted into tabernacles, for the use of the
establishment while the parish churches were rebuilding. Eight places
of this description are mentioned, of which may be noticed the
meeting-house of the excellent Mr. Vincent, in Hand-alley,
Bishopsgate-street, a large room, with three galleries, thirty large
pews, and many benches and forms; and also Mr. Doolittle's
meeting-house, built of brick, with three galleries, full of large pews
below. Dr. Manton, a celebrated Presbyterian divine, was apprehended
on a Sunday afternoon, at the close of his sermon, and committed a
prisoner to the Gate-house. His meeting-house in White-yard was broken
up, and a fine of L40 imposed on the people, and L20 on the minister.
It is related of James Janeway, that as he was walking by the wall at
Rotherhithe, a bullet was fired at him; and that a mob of soldiers once
broke into his meeting house in Jamaica-row, and leaped upon the
benches. Amidst the confusion, some of his friends threw over him a
coat, and placed a white hat on his head, to facilitate his
escape. Once, while preaching in a gardener's house, he was surprised
by a band of troopers, when, throwing himself on the ground, some
persons covered him with cabbage leaves, and so preserved him from his
enemies. (Spiritual Heroes, p. 313.) In secresy the good people often
met to worship, according to the dictates of their consciences; and
until lately there remained in the ruins of the old priory of
Bartholomew, in Smithfield, doors in the crypt, which tradition
reported to have been used for admission into the gloomy subterranean
recesses, where the persecuted ones, like the primitive Christians in
the catacombs of Rome, worshiped the Father through Jesus Christ. The
Friends, or Quakers, as they were termed, at this time manifested great
intrepidity, and continued their worship as before, not stirring at the
approach of the officers who came to arrest them, but meekly going all
together to prison, where they stayed till they were dismissed, for
they would not pay the penalties imposed on them, nor even the jail
fees. On being discharged, they went to their meeting-houses as
before, and finding them closed, crowded in the street around the door,
saying "they would not be ashamed nor afraid to disown their meeting
together in a peaceable manner to worship God, but in imitation of the
prophet Daniel, they would do it more publicly because they were
forbid." _Neale's Puritans_, vol. iv, p. 433. William Penn and
William Mead, two distinguished members of the Society of Friends, were
tried at the Old Bailey in 1670, and were cruelly insulted by the
court. The jury, not bringing in such a harsh verdict as was desired,
were threatened with being locked up without "meat, drink, fire, or
tobacco." "We are a peaceable people, and cannot offer violence to any
man," said Penn; adding, as he turned to the jury, "You are Englishmen,
mind your privileges, give not away your rights." They responded to
the noble appeal, and acquitted the innocent prisoners.
When, in the next year, Charles exercised a dispensing power, and set
aside the persecuting acts, wishing to give freedom to the <DW7>s,
most of the London nonconformist ministers took out licences, and great
numbers attended their meetings. In 1672, the famous Merchants'
Lecture was set up in Pinner's Hall, and the most learned and popular
of the dissenting divines were appointed to deliver it. Alderman Love,
member for the city, in the name of such as agreed with him, stood up
in the House of Commons, refusing to take the benefit of the dispensing
power as unconstitutional. He said, "he had rather go without his own
desired liberty than have it in a way so destructive of the liberties
of his country and the Protestant interest, and that this was the sense
of the main body of dissenters." The indulgence was withdrawn.
Toleration bills failed in the House of Commons. The Test Act was
brought in; fruitless attempts were made for a comprehension; and
London was once more a scene of persecution. Informers went abroad,
seeking out places where nonconformists were assembled, following them
to their homes, taking down their names, ascertaining suspected
parties, listening to private conversation, prying into domestic
scenes, and then delivering over their prey into the hands of miscalled
officers of justice, who exacted fines, and rifled their goods, or
carried them off to prison. Such proceedings occurred at several
periods in the reigns of Charles and James II., after which the
revolution of 1688 brought peace and freedom of worship to the
long-oppressed nonconformists in London and throughout the country.
Popery lifted up its head in London on the restoration of Charles II.
Many professors of it accompanied the king on his accession to the
throne, and crowded round the court, being treated with conspicuous
favor. The queen-mother came from France, and took up her abode at
Somerset House, where she gathered round her a number of Roman Catholic
priests. The foreign ambassadors' chapels were used by English
<DW7>s, who thus obtained liberty of worship, while the London
Protestant nonconformists were shamefully persecuted. Jesuit schools
and seminaries were established, under royal patronage, and popish
bishops were consecrated in the royal chapel of St. James's. At
Whitehall, the ecclesiastics appeared in their canonical habits, and
were encouraged in their attempts to proselyte the people to the
unreformed faith. A diarist of the times, under date January 23, 1667,
records a visit he paid to the popish establishment in St. James's
Palace, composed of the chaplains and priests connected with Catharine
of Braganza, Charles II.'s queen: "I saw the dormitory and the cells of
the priests, and we went into one--a very pretty little room, very
clean, hung with pictures, and set with books. The priest was in his
cell, with his hair-clothes to his skin, barelegged, with a sandal only
on, and his little bed without sheets, and no feather bed, but yet I
thought soft enough, his cord about his middle; but in so good company,
living with ease, I thought it a very good life. A pretty library they
have: and I was in the refectory where every man had his napkin, knife,
cup of earth, and basin of the same; and a place for one to sit and
read while the rest are at meals. And into the kitchen I went, where a
good neck of mutton at the fire, and other victuals boiling--I do not
think they fared very hard. Their windows all looking into a fine
garden and the park, and mighty pretty rooms all. I wished myself one
of the Capuchins."
But it does not appear that the London commonalty were infected with
the love of the Papal Church, whatever might be done at court to foster
it. On the contrary, a strong feeling was cherished by multitudes in
opposition to all the popish proceedings of their superiors.
Ebullitions of popular sentiment on the question frequently appeared,
especially in the annual burning of the pope's effigy, on the 17th of
November, at Temple Bar. This was to celebrate the accession of Queen
Elizabeth; and after the discovery of the so-called Meal Tub plot, in
the reign of Charles II., it was performed with increased parade and
ceremony. The morning was ushered in with the ringing of bells, and in
the evening a procession took place, by the light of flambeaux, to the
number of some thousands. The balconies, and windows, and tops of
houses, were crowded with eager faces, reflecting the light that blazed
up from the moving crowds along the streets. Mock friars, bishops, and
cardinals, with the pope, headed by a man on horseback, personating the
dead body of Sir Edmondbury Godfery, composed the spectacle. It
started from Bishopsgate, and passing along Cheapside and Fleet-street
terminated at Temple Bar, where the pope was cast into a bonfire, and
the whole concluded with a display of fireworks. While anti-popish
proceedings of this description might be leavened with much of the
ignorance and intolerance which mark the odious system thus assailed,
and can, therefore, be regarded with little satisfaction, it must be
remembered that there was abundant cause at that time for those who
prized the liberties of their country, as well as those who valued the
truths of religion, to regard with alarm and to resist with vigor the
incursions of a political Church, which sought to crush those
liberties, and to darken those truths. The evils of Popery, inherent
and unchangeable, obtruded themselves most offensively, and with a
threatening aspect, at a period when they were defended and maintained
in high places; and it was notorious that the successor to the English
crown was plotting for the revival of Popish ascendency. During the
reign of James II., the grounds of excitement became stronger than
before. Everything dear to Englishmen as well as Protestants was at
stake. The destinies of Church and state, of religion and civil
policy, were trembling in the balance. Men's hearts might well fail
them for fear, and only confidence in the power of truth, and the God
of truth, with earnest prayer for his gracious succor and protection,
could still and soothe their agitated bosoms. Weapons of the right
kind were employed. The best divines of the Church of England manfully
contended in argument against the baneful errors of Romanism.
Dissenting divines, especially Baxter, threw their energies into the
same conflict. Political measures were also adopted vigorously and
with decision--their nature we can neither criticise nor describe--and
through the good providence of God our fathers were delivered from an
impending curse, which we pray may neither in our times, nor in future
ages, light on our beloved land.
In approaching the termination of this chapter, it is desirable to
insert some account of the extent and state of buildings in London at
the close of the seventeenth century, and a few notices of other
matters relating to that period, which have not yet come under our
consideration. Chamberlayne, in his _Angliae Notitia_, 1692, dwells
with warm delight upon the description of the London squares, "those
magnificent piazzas," as he terms them; and then enumerates
Lincoln's-inn-fields, Convent Garden, St. James's-square,
Leicester-fields, Southampton-square, Red Lion-square, Golden-square,
Spitalfields-square, and "that excellent new structure, called the
King's-square," now Soho. These were all extramural, and beyond the
liberties of the municipality, and they show how the metropolis was
extending, especially in the western direction. As early as 1662, an
act was passed for paving Pall Mall, the Haymarket, and St.
James's-street. Clarendon, in 1604, built his splendid mansion in
Piccadilly, called in reproach Dunkirk House by the common people, who
"were of opinion that he had a good bribe for the selling of that
town." Others, says Burnet, called it Holland House, because he was
believed to be no friend to the war. It was much praised for its
magnificence, and for the beautiful country prospect it commanded.
Evelyn's record of an interview with the builder of the proud palace,
is an affecting illustration of the vanity of this world's grandeur,
and of the disappointments and mortifications that follow ambition.
Clarendon had lost the favor of his sovereign, and the confidence of
the public. "I found him in his garden," says Evelyn, "at his
new-built palace, sitting in his gout wheel-chair, and seeing the gates
set up towards the north and the fields. He looked and spake very
disconsolately. After some while, deploring his condition to me, I
took my leave. Next morning, I heard he was gone." The house was
afterwards pulled down. In 1668, Burlington House was finished, placed
where it is because it was at the time of its erection thought certain
that no one would build beyond it. "In London," says Sir William
Chambers, "many of our noblemen's palaces towards the streets look like
convents; nothing appears but a high wall, with one or two large gates,
in which there is a hole for those who are privileged to go in and out.
If a coach arrives, the whole gate is open indeed, but this is an
operation that requires time, and the porter is very careful to shut it
up again immediately, for reasons to him very weighty. Few in this
vast city suspect, I believe, that behind an old brick wall in
Piccadilly there is one of the finest pieces of architecture in
Europe." All to the west and north of Burlington House was park and
country, where huntsmen followed the chase, or fowlers plied their
toils with gun and net, or anglers wielded rod and line on the margin
of fair ponds of water. "We should greatly err," observes Mr.
Macaulay, "if we were to suppose that any of the streets and squares
then wore the same appearance as at present. The great majority of the
houses, indeed, have since that time been wholly or in part rebuilt.
If the most fashionable parts of the capital could be placed before us,
such as they then were, we should be disgusted with their squalid
appearance, and poisoned by their noisome atmosphere. In Convent
Garden a filthy and noisy market was held, close to the dwellings of
the great. Fruit women screamed, carters fought, cabbage stalks and
rotten apples accumulated in heaps, at the thresholds of the countess
of Berkshire and of the bishop of Durham." Shops in those days did not
present the bravery of plate glass and bold inscriptions, with all
sorts of devices, but exhibited small windows, with huge frames which
concealed rather than displayed the wares within; while all manner of
signs, including Saracens' heads, blue bears, golden lambs, and
terrific griffins, with other wonders, swung on projecting irons across
the street, an humble resemblance of the row of banners lining the
chapels of the Garter and the Bath, at Windsor and Westminster. Though
a general paving and cleansing act for the streets of London was passed
in 1671, they continued long afterwards in a deplorably filthy
condition, the inconvenience occasioned by day being greatly increased
at night by the dense darkness, at best but miserably alleviated by the
few candles set up in compliance with the watchman's appeal, "Hang out
your lights." Glass lamps, known by the name of convex lights, were
introduced into use in 1694, and continued to be employed for
twenty-one years, after which there was a relapse into the old system.
It was dangerous to go abroad after dark without a lantern, and the
streets, with a few wayfarers, guided by this humble illumination, must
have presented a spectacle not unlike some gloomy country path, with
here and there a traveler.
Inns, of course, which still wore the appearance of the old hotels, and
have left a relic for example in the yard of the Spread Eagle, and a
more notable one in that of the Talbot, Southwark, had their
conspicuous signs, including animals known and unknown, and heads
without end. From their huge and hospitable gateways all the public
conveyances of London took their departure; and in an alphabetical list
of these, in 1684, the daily outgoings average forty-one, but the
numbers in one day are very unequal to those in another, seventy-one
departing on a Thursday, and only nine on a Tuesday. As there was only
one conveyance at a time to the same place, we have a remarkable
illustration in this record of the public provision for traveling, as
well as the stay-at-home habits of our good forefathers of the middle
class, about a century and a half ago. The gentry and nobility were
the chief travelers, and they performed their expeditions on horseback,
or in their own coaches. As to the number of the inhabitants in
London, at the close of the century, only an approximation to the fact
can be made, for no census of the population was taken. According to
the number of deaths, it is computed there were about half a million of
souls--a population seventeen times larger than that of the second town
in the kingdom, three times greater than that of Amsterdam, and more
than those of Paris and Rome, or Paris and Rouen put together. Though
the amount of trade was small compared with what it is now, yet the sum
of more than thirty thousand a year, in the shape of customs, (it is
more than eleven millions now,) filled our ancestors with astonishment.
Writers of that day speak of the masts of the ships in the river as
resembling a forest, and of the wealth of the merchants, according to
the notions of the day, as princelike. More men, wrote Sir Josiah
Child in 1688, were to be found upon the Exchange of London, worth ten
thousand pounds than thirty years before there were worth one thousand.
He adds, there were one hundred coaches kept now for one formerly; and
remarks, that a serge gown, once worn by a gentlewoman, was now
discarded by a chambermaid. The manufactures of the country were
greatly increased and wonderfully improved by the arrival of multitudes
of French artisans in 1685, on the revocation of the edict of Nantes.
"An entire suburb of London," says Voltaire, in his _Siecle de Louis
XIV._, "was peopled with French manufacturers of silk; others carried
thither the art of making crystal in perfection, which has been since
this epoch lost in France." Spitalfields is the suburb alluded to;
thousands besides were located in Soho and St. Giles's. "London,"
observes Chamberlayne, in 1692, "is a large magazine of men, money,
ships, horses, and ammunition; of all sorts of commodities, necessary
or expedient for the use or pleasure of mankind. It is the mighty
rendezvous of nobility, gentry, courtiers, divines, lawyers,
physicians, merchants, seamen, and all kinds of excellent artificers of
the most refined arts, and most excellent beauties; for it is observed,
that in most families of England, if there be any son or daughter that
excels the rest in beauty or wit, or perhaps courage or industry, or
any other rare quality, London is their north star, and they are never
at rest till they point directly thither."
[1] He mentions his preaching once at St. Dunstan's church, when an
accident occurred, which alarmed the vast concourse, and was likely to
have occasioned much mischief. He relates the odd circumstance of an
old woman, squeezed in the crowd, asking forgiveness of God at the
church door, and promising, if he would deliver her that time she would
never come to the place again.
CHAPTER VI.
LONDON DURING THE FIRST HALF OF THE EIGHTEENTH CENTURY.
From Maitland, who published his History of London in 1739, we learn
that there were at that time, within the bills of mortality, 5,099
streets, 95,968 houses, 207 inns, 447 taverns, and 551 coffee-houses.
In 1681, the bills included 132 parishes; 147 are found in those for
the year 1744. Judging from the bills of mortality, which however
cannot be trusted as accurate, population considerably increased in
that portion of the century included in Maitland's history. During the
seventeen years from 1703 to 1721, the total number of burials was
393,034. During the next seventeen years, to 1738, they amounted to
457,779. The extension of London was still towards the west. In the
Weekly Journal of 1717 it is stated, the new buildings between
Bond-street and Marylebone go on with all possible diligence, and the
houses even let and sell before they are built. In 1723, the duke of
Grafton and the earl of Grantham purchased the waste ground at the
upper end of Albemarle and Dover-streets for gardens, and turned a road
leading into May Fair another way. (London, vol. i, p. 310.)
Devonshire House remained for some time the boundary of the buildings
in Piccadilly, though farther on, by the Hyde Park Corner, there were
several habitations. Lanesborough House stood there by the top of
Constitution-hill, and was, in 1773, converted into an infirmary, since
rebuilt, and now known as St. George's Hospital. It may be added, that
Westminster Hospital, the first institution of the kind supported by
voluntary contributions, was founded in 1719. Several churches were
erected in the early part of the eighteenth century. In the year 1711,
an act was passed for the erection of no less than fifty, but only ten
had been built on new foundations when Maitland published his work.
These ecclesiastical edifices exhibit the architectural taste of the
age. The finest specimen of the period is the church of St.
Martin-in-the-fields, built by Gibbs. It was commenced in 1721, and
finished in 1726, at a cost of nearly L37,000. In spite of the
drawback in the ill-placed steeple over the portico, without any
basement tower, the building strikes the beholder with an emotion of
delight. St. George's, Hanover-square, and St. George's, Bloomsbury,
(the latter exhibiting a remarkable campanile,) were also built about
the same time, the one in 1724, the other in 1731. Almost all the
churches built after the fire are in the modern style, imported from
Italy. In its colonnades, porticoes, architraves, and columns, this
style presents elements of the Greek school of design, but differently
arranged, more complicated in composition, more florid and ambitious in
detail. Taste must assign the palm of superiority to the Grecian
temple, with its severe beauty and chastened sublimity. The one style
indicates the era of original genius, and exhibits the fruits of
masterminds in that line of invention, while the other marks an epoch
of mere imitation, supplying only the degenerate produce of
transplanted taste.
Feeble attempts were made to improve the state of the streets, but they
remained pretty much in their former condition till the Paving Act of
1762. Stalls, sheds, and sign-posts obstructed the path, and the
pavement was left to the inhabitants, to be made "in such a manner, and
with such materials, as pride, poverty, or caprice might suggest. Curb
stones were unknown, and the footway was exposed to the carriage-way,
except in some of the principal streets, where a line of posts and
chains, or wooden paling, afforded occasional protection. It was a
matter of moment to go near the wall; and Gay, in his Trivia, supplies
directions to whom to yield it, and to whom to refuse it."--_Handbook_,
by Cunninghame, xxxi. "In the last age," says Johnson, "when my mother
lived in London, there were two sets of people--those who gave the wall
and those who took it, the peaceable and the quarrelsome. Now it is
fixed that every man keeps to the right; and if one is taking the wall
another yields it, and it is never a dispute." The lighting, drainage,
and police, were all in a wretched condition.
To attempt to give anything like a detailed chronological account of
events in London during the first half of the eighteenth century, is
neither possible nor desirable in a work like this. Indeed, the far
greater part of the incidents recorded in the city chronicles relates
to royal visits, city feasts, celebration of victories, local tumults,
and remarkable storms and frosts. All that can be done, or expected,
in this small volume, is to fix upon a few leading and important scenes
and events, illustrative of the times.
In the reign of queen Anne, the chief matter of interest in connection
with London was the political excitement which prevailed. It turned
upon questions relating to the Church and the toleration of dissenters.
Dean Swift, in a letter dated London, December, 1703, tells a friend,
that the occasional Conformity Bill, intended to nullify the Toleration
Act, was then the subject of everybody's conversation. "It was so
universal," observes the witty dean, "that I observed the dogs in the
street much more contumelious and quarrelsome than usual; and the very
night before the bill went up, a committee of Whig and Tory cats had a
very warm debate upon the roof of our house." Defoe, the well-known
author of Robinson Crusoe, and a London citizen, rendered himself very
conspicuous by his advocacy of the rights of conscience; and in
consequence of writing an ironical work, which then created great
excitement, entitled, "The Shortest Way with the Dissenters," he was
doomed to stand three successive days in the pillory, at the Royal
Exchange by the Cheapside Conduit, and near Temple Bar. Immense crowds
gathered to gaze on the sufferer; but "the people, who were expected to
treat him ill, on the contrary pitied him, and wished those who set him
there were placed in his room, and expressed their affections by loud
shouts and acclamations when he was taken down."--_Life of Defoe_, by
Chalmers, p. 28.
The political excitement of London reached its height during the trial
of Dr. Sacheverell. He had preached two sermons, one of which was
delivered in St. Paul's Cathedral, on the 5th of November, 1709, in
which he inculcated the doctrine of passive obedience and
non-resistance, and inveighed with great bitterness against all
nonconformists. The drift of his sermon was to undermine the
principles of the Revolution, though he professed to approve of that
event, pretending to consider it as by no means a case of resistance to
the supreme power. The ministry, considering that his doctrine struck
a fatal blow at the constitution, as established in 1688, prosecuted
him accordingly. With Sacheverell numbers of the clergy sympathized,
especially Atterbury, the leader of his party. It was supposed that
the queen was not unfriendly to the arraigned divine. He was escorted
to Westminster Hall, the place of his trial, by immense crowds of
people, who rent the air with their huzzas. The queen herself attended
at the proceedings, and was hailed with deafening shouts, as she
stepped from her carriage, "God bless your majesty; we hope your
majesty is for Dr. Sacheverell." The spacious building in which he was
tried, the scene of so many state trials, was fitted up for the
occasion, benches and galleries being provided for peers and commoners,
peeresses and gentlewomen, who crowded every seat; the lower classes
squeezing themselves to suffocation into the part of the old building
allotted to their use. The London rabble were so much excited by what
took place, or were so completely swayed by more influential
malcontents, that on the evening of the second day of the trial they
attacked a meeting-house in New-Court, tearing away doors and
casements, pews and pulpit, and proceeding with the spoil to
Lincoln's-inn-fields. In the open space--where was then no fair garden
inclosed with palisades, it being a rendezvous for mountebanks, dancing
bears, and baited bulls--the populace kindled a bonfire, and consumed
the ruins of the conventicle. They went forth in quest of the
minister, Mr. Burgess, in order to burn him and his pulpit together.
Happily disappointed of their victim, they wreaked their vengeance upon
six other dissenting places of worship. An episcopal church in
Clerkenwell shared the same fate, being mistaken for one of the hated
structures through want of a steeple; for steeple and no steeple
probably constituted the only difference in religion appreciable by
these infatuated mortals. The advocates of toleration, even though
they might be good Churchmen, as Bishop Burnet for example, were also
in danger. Indeed, the tumult became of such grave importance, that
queen and magistrates, court and city, felt it a duty to combine in
order to quell the disgraceful outbreak. A few sword cuts, and the
capture of several prisoners, put down the insurrection; but
ecclesiastical politics still ran high in London, and whigs and
dissenters were in low estimation in many quarters, till the Hanoverian
succession brightened the prospects of the liberal party. While Queen
Anne lay ill, deep anxiety pervaded the political circles in London.
It is not generally known, but it is stated on the authority of
tradition, that the first place in which the decease of Anne was
publicly announced, and the accession of George I. proclaimed, was the
very meeting-house in New Court which had been formerly attacked by the
mob. The day on which the queen died was a Sunday; and as Bishop
Burnet was riding in his coach through Smithfield, he met Mr. Bradbury,
then the minister of the chapel, and told him that immediately upon the
royal demise, then momentarily expected, he would send a messenger to
give tidings of the event. Before the morning service was over a man
appeared in the gallery, and dropped a handkerchief, being the
preconcerted signal; whereupon the preacher, in his last prayer,
alluded to the removal of her majesty, and implored a blessing on King
George and the house of Hanover.
The most striking feature in the history of London in the reign of
George I., was the extraordinary spirit of speculation which then
existed. The moderate gains of trade and commerce did not satisfy the
cupidity of the human breast, which then, as it has done since, burst
out into a fever, that consumed all reason, prudence, and principle.
Men made haste to be rich, and consequently fell into temptation and a
snare. In 1717, an unprecedented excitement pervaded the money market.
Every one familiar with the city knows the plain-looking edifice of
brick and stone which stands in Threadneedle-street, not far from the
Flower-pot, and which is so well described by one whose youth was
passed within it, as "deserted or thinly peopled, with few or no traces
of comers-in or goers-out, like what Ossian describes, when he says, I
passed by the walls of Balclutha, and they were desolate." That
grave-looking edifice, now like some respectable citizen retired from
business, was at one time the busiest place in the world. A scheme was
planned and formed for making fortunes by the South Sea trade. A
company was incorporated by government for the purpose, and the house
in Threadneedle-street was the scene of business. Stock rapidly
doubled in value, and went on till it reached a premium of nine hundred
per cent. People of all ranks flocked to Change-alley, and crowded the
courts in riotous eagerness to purchase shares. The nobleman drove
from the West-end, the squire came up from the country, ladies of
fashion, and people of no fashion, swarmed round the new El Dorado, to
dig up the sparkling treasure. Swift compares these crowds of human
beings to the waters of the South Sea Gulf, from which their
imagination was drawing such abundant draughts of wealth.
"Subscribers here by thousands float,
And jostle one another down,
Each paddling in her leaky boat,
And here they fish for gold, and drown.
Now buried in the depths below,
Now mounted up to heaven again;
They reel and stagger to and fro,
At their wits' end like drunken men."
The mania spread so that the South Sea scheme itself could not satisfy
the lust for money. Maitland enumerates one hundred and fifty-six
companies formed at this time. Among some which look feasible, there
were the following characterized by extravagant absurdities:--An
association for discovering gold mines, for bleaching hair, for making
flying engines, for feeding hogs, for erecting salt-pans in Holy
Island, for making butter from beech trees, for making deal boards out
of saw-dust, for extracting silver from lead, and finally, (which seems
to have been much needed to exhaust the maddening vapors that had made
their way into it,) for manufacturing an air pump for the brain.
Some of them were surely mere satires on the rest; yet Maitland says,
after giving his long list, "Besides these bubbles, there were
innumerable more that perished in embryo; however, the sums intended to
be raised by the above airy projects amounted to about three hundred
million pounds. Yet the lowest of the shares in any of them advanced
above cent. per cent., most above four hundred per cent., and some to
twenty times the price of subscription." The bulk of these speculators
must clearly have been bereft of their senses, and the madness was too
violent to last long. The evil worked its own cure. The golden bubble
was blown larger, and larger, till it burst. Then came indescribable
misery. Thousands were ruined. Revenge against the inventors now took
the place of cupidity, and indignation aroused those who had looked
patiently on during the rage of the _money_ mania. One nobleman in
parliament proposed that the contrivers of the South Sea scheme should,
after the manner of the Roman parricide, be sown up alive in sacks, and
flung into the Thames. A more moderate punishment was inflicted in the
confiscation of all the estates belonging to the directors of the
company, amounting to above two millions, which sum was divided among
the sufferers. The railway speculation in our own time was a display
of avarice of the same order; and all such indulgence in the inordinate
lust of gain is sure to be overtaken, in the end, by its righteous
penalty. The laws of Divine providence provide for the punishment of
those who thus, under the influence of an impetuous selfishness, grasp
at immoderate possessions. Covetousness overreaches itself in such
cases, and misses its mark. How many instances have occurred in the
present day illustrative of that wise saying in Holy Scripture: "As the
partridge sitteth on eggs and hatcheth them not, so he that getteth
riches and not by right, shall leave them in the midst of his days, and
at the end shall be a fool!" The solemn lessons thus suggested should
be practically studied by the man of business, and while he is taught
to moderate his desires after the things of this world, he is also
instructed to turn the main current of his thoughts and feelings into a
far different channel, to seek durable riches and righteousness--bags
which wax not old--treasures which thieves cannot break through and
steal; and to "so pass through things temporal, as not to lose the
things which are eternal."
The history of London in the reign of George II. is remarkable for the
excitement which was produced by the northern rebellion, and for a far
different excitement, which we shall presently notice with great
delight. The progress of the arms of Prince Edward, the pretender, in
the year 1745, created much alarm in all parts of the country,
especially in London, the seat of government. When the invading army
was found to have proceeded as far as Derby, it was generally expected
it would advance to the metropolis. The loyalty of the citizens was
called forth by the impending peril, and all classes hastened to
express their attachment to the sovereign, and their readiness to
support the house of Hanover in this great emergency. The corporation,
the clergy, and the dissenting ministers, presented dutiful addresses.
Several corps of volunteers were raised, large sums of money were
contributed, and even the peace-loving body of Friends came forward to
furnish the troops with woolen waistcoats to be worn under their
clothing. As the cause of Popery was identified with that of the
pretender, the <DW7>s in London were regarded with great apprehension.
A proclamation was issued for putting the laws in force against them
and all non-jurors. Romanists and reputed Romanists were required to
remove out of the city, to at least ten miles off. All Jesuits and
priests who, after a certain time, should be found within that distance
were to be brought to trial. The pretender was defeated at Culloden,
and the news took off a heavy burden of fear from the minds of the
London citizens. Many prisoners were brought to the metropolis, and
among them the Earl of Kilmarnock, Lord Balmerino, and Lord Lovat, who
were all executed for treason on Tower-hill. The beheading of the last
of these brought to a close the long series of sanguinary spectacles of
that nature, which had gathered from time to time such a vast concourse
of citizens, on the hill by the Tower gates.
The other kind of excitement in London, hinted at above, relates to the
most important of all subjects. Spiritual religion had been at a low
ebb for a considerable period among the different denominations of
Christians. A cold formalism was but too common. It is not, however,
to be inferred that men of sound and earnest piety did not exist, both
among Churchmen and dissenters. One beautiful specimen of religious
fervor and consistency may be mentioned in connection with the earlier
part of this century. Sir Thomas Abney, who filled the office of lord
mayor in 1701, and also represented the city in parliament, is
described as having been an eminent blessing to his country and the
Church of God. He died in 1722, deeply regretted, not only by his
religious friends, but by his fellow-citizens in general. We have seen
or heard it stated respecting him, that during his mayoralty he
habitually maintained family worship, without suffering it to be
interrupted by any parties or banquets. On such occasions prayer was
introduced, or he retired to present it in the bosom of his family.
Many other beautiful instances of a devout spirit, of faith in Christ,
and of love to God, were, no doubt, open at that time to the eye of Him
who seeth in secret; but neither then, nor for some time afterwards,
were any vigorous efforts made to bring religion home with power to the
mass of the London population. That distinguished man, the Rev. George
Whitefield, was an instrument in the hand of God of effecting in the
metropolis, before the close of the first half of the century, an
unprecedented religious awakening. He came up to officiate in the
Tower in 1737, but his first sermon in London was delivered in
Bishopsgate church. On his second visit, crowds climbed the leads, and
hung on the rails of the buildings in which he was engaged to minister,
while multitudes went away because not able to get anywhere within the
sound of his voice. Nothing had been seen like it since the days of
such men as Baxter and Vincent. When collections were needed,
Whitefield was eagerly sought, as the man capable above all others of
replenishing the exhausted coffers of Christian beneficence. The
people sat or stood densely wedged together, with eyes riveted on the
speaker, and many a tear rolled down the cheeks of citizen and
apprentice, matron and maiden, as the instructions and appeals of that
wonderful preacher, expressed in stirring words and phrases, fell upon
their ears, in tones marvelously rich, varied, and musical. With an
eloquence, which now flashed and rolled like the elements in a
thunder-storm, and then tenderly beamed forth like the sun-ray on the
flower whose head the storm had drenched and made to droop, did he
enforce on the people truths which he had gathered out of God's
precious word, and the power of which he had evidently himself realized
in all the divinity of their origin, the sublimity of their import, the
directness of their application, and the unutterable solemnity of their
results. As a man dwelling amidst eternal things, with heaven and hell
before him, the eye of God upon him, and immortal souls around him,
hastening to their account,--in short, as every minister of Christ's
holy gospel ought to deliver his message, did he do so. The holiness
of God, as a Being of purer eyes than to behold iniquity; the perfect
excellence of the Divine law; its demand of entire obedience; its
adaptation, if observed, to promote the happiness of man; its
spirituality, reaching to the most secret thoughts and affections of
the heart; the corruption of human nature; the alienation of man from
God, and his moral inability to keep the Divine law; the sentence of
everlasting condemnation, which, as the awful, but righteous
consequence, falls upon our race; the marvelous kindness of God in so
commending his love to us, "that while we were yet sinners Christ died
for us;" the Saviour's fulfillment of the law in his gracious
representative character; the perfect satisfaction for sin rendered by
his atoning sacrifice; the unutterable condescension and infinite love
with which he receiveth sinners; the grace of the Holy Spirit; the
necessity of an entire regeneration of the soul by his Divine agency;
the full and free invitations of the gospel to mankind at large;
forgiveness through the blood of Christ offered to all who believe; the
universal obligation of repentance; the requirement of holiness of
heart and life, as the evidence of love to Christ, and the indwelling
of the Spirit, as the Author of holiness; such were the grand truths
which formed the theme of Whitefield's discourses, and which, in
numerous instances, fell with startling power on ears unaccustomed to
evangelical statements and appeals. The preacher was a man of prayer
as well as eloquence, and in his London visits poured out his heart in
earnest supplication to God for the effusion of his Holy Spirit upon
the vast masses of unconverted souls, slumbering around him in the arms
of spiritual death. Whitefield could not confine himself to churches,
and his out-door preaching soon increased the interest which his former
services had produced. "I do not know," said the celebrated Countess
of Hertford, in one of her letters, "whether you have heard of our new
sect, who call themselves Methodists. There is one Whitefield at the
head of them, a young man of about five-and-twenty, who has for some
months gone about preaching in the fields and market-places of the
country, and in London at May Fair and Moorfields to ten or twelve
thousand people at a time." Larger multitudes still are said to have
been sometimes convened; on Kennington Common, for example, the number
of Whitefield's congregation has been computed at sixty thousand.
The notice taken of the young preacher by this lady of fashion, is only
a specimen of the interest felt in his proceedings by many persons in
the same rank of life. The nobility attended in the drawing-room of
the Countess of Huntingdon to listen to his sermons, or accompanied her
to the churches where he had engaged to officiate. Long lists of these
titled names have been preserved, in which some of the unlikeliest
occur, such as Sarah, Duchess of Marlborough, the Earl of Chesterfield,
Lord Bolingbroke, Bubb Doddington, and George Selwyn. Indeed, it seems
to have been quite the fashion for the great ones of the land to
cluster round this man of God. He was the theme of their conversation.
By all he was marveled at; by some he was censured or ridiculed; by
more he was praised and caressed; by a few he was honored and blessed
as the means of their spiritual renewal or edification. Among the
middle and lower classes in London, as elsewhere, did he reap his
richest harvests. How many hundreds and thousands were melted down
under the power of the word which he proclaimed! How many of that
generation in our old city are now before the throne of the Lamb,
adoring the gracious Providence which brought them within the sound of
Whitefield's voice!
A remarkable occurrence in London, in the year 1750, gave occasion for
a singular display of this great preacher's holy zeal. Shocks of an
earthquake were felt in different parts of London and the vicinity,
especially in the neighborhood of the river Thames. Such visitations
are sure to produce violent terror, and on this occasion the feeling
reached its highest pitch. The people, apprehending there was greater
danger in their own houses, and in the streets lined with buildings,
than in wide spaces open and unencumbered, rushed, in immense crowds,
to Hyde Park, and there waited, in fearful foreboding of the judgments
of the Almighty. One night, when the excitement was overwhelming, and
a dense multitude had congregated there under the dark arch of heaven,
Whitefield, regarding it as a signal opportunity for preaching the
gospel to his fellow-countrymen, hastened to the spot, and delivered
one of his most powerful and pathetic discourses. He called the
attention of the throngs before him to the coming advent of the Son of
God, to judge the world in righteousness, when not the inhabitants of
one city only, but all of Adam's race, in every clime, would be
gathered together, to receive from the lips of Eternal Justice their
final and unalterable sentence. Nor did he fail to point out the
character of Christ in his relation to man as a Saviour as well as
Judge, urging his hearers to flee from the wrath to come, and to lay
hold on the hope set before them in the gospel. "The awful manner in
which he addressed the careless, Christless sinner, the sublimity of
the discourse, and the appearance of the place, added to the gloom of
night, continued to impress the mind with seriousness, and to render
the event solemn and memorable in the highest degree." While the
shades of night rendered him invisible to his audience, his clear
voice--which could be heard distinctly at the distance of a mile,
passing through a marvelous variety of intonations, in which the very
soul of the speaker seemed to burst out in gushes of terror or
love--must, as it sounded over the park, and fell upon the eager
listening thousands, have seemed to them like the utterance of some
impalpable and unseen spirit, who, with unearthly powers of address,
had come down from heaven to warn and invite. "God," he observed, in
writing to Lady Huntingdon, "has been terribly shaking the metropolis;
I hope it is an earnest of his giving a shock to secure sinners, and
making them to cry out, 'What shall we do to be saved?' What can shake
a soul whose hopes of happiness in time and in eternity are built upon
the Rock of ages? Winds may blow, rains may and will descend even upon
persons of the most exalted stations, but they that trust in the Lord
Jesus Christ never shall, never can be totally confounded." Charles
Wesley was in town during this dispensation of Providence, (which
happily passed off without inflicting any serious injury,) and he also
employed himself in faithful and earnest preaching. So did Mr.
Romaine, whose ministry will be noticed more particularly in the next
chapter. The only additional information we can give respecting this
religious revival, is that the Rev. John Wesley, equally distinguished
with Whitefield, but by gifts of a different order, began his course in
London as the founder of the Methodist Connection, in 1740, and spent
among the London citizens a large portion of his apostolic and
self-denying labors, with unconquerable perseverance and eminent
success. He was accustomed, at the commencement of his career, to meet
with the Moravians for religious exercises in their chapel in
Fetter-lane; thus associating that edifice, which still remains, with
the early history of Methodism. "There the great leaders in this
glorious warfare, with their zealous coadjutors--persons whose whole
souls were consecrated to the cause of God our Saviour--often took
sweet counsel together. They have all long since gone to their rest,
to meet in a better temple together, as they have often worshiped in
the temple below, and to go out no more."
In further illustration of the state of London at the time now under
our review, we will turn to consider some other of its social aspects.
Literary society presents some curious and amusing facts. The
booksellers before the fire were located, for the most part, in St.
Paul's Church-yard. It is stated that not less than L150,000 worth of
books were consumed during that conflagration. The calamity proved the
ruin of many, and was the occasion of raising very enormously the price
of old books. Little Britain, near Duck-lane, became the rendezvous of
the trade, which remained there for some years afterwards. "It was,"
says Roger North, "a plentiful and perpetual emporium of learned
authors." The shops were spacious, and the literati of the day gladly
resorted thither, where they seldom failed to find agreeable
conversation. The booksellers themselves were intelligent persons,
with whom, for the sake of their bookish knowledge, the most brilliant
wits were pleased to converse. Before 1750, the literary emporium of
London was transferred to Paternoster-row. Up to that time the
activity in the publishing business was very great, especially in the
pamphlet line; perhaps there were more publishers then than even now.
Dunton, a famous member of the fraternity, wrote his own life, in which
he enumerates a long list of his brethren, with particulars relating to
their character and history. The authors of London were computed by
Swift to amount in number to some thousands. While a Swift, a Pope, an
Addison, a Steele, a Bolingbroke, a Johnson, and other world-known
names in that Augustan age of letters, produced works of original
genius, the bulk of the writers who supplied the trade were "mere
drudges of the pen--manufacturers of literature." A whole herd of
these were dealers in ghosts, murders, and other marvels, published in
periodical pamphlets, upon every half sheet of which the tax of a
halfpenny was laid on in the reign of Queen Anne. "Have you seen the
red stamp the papers are marked with?" asks Dean Swift, in a letter to
Mr. Dingley--"methinks the stamping is worth a half-penny." These
panderers to a vitiated taste, which is far from having disappeared in
our own day, and other writers of the humbler class, were so numerous
in Grub-street, that the name became the cognomen for the humblest
brethren of the book craft. There and elsewhere did they pour forth
their lucubrations in lofty attics, which led Johnson to make the
pompous remark, "that the professors of literature generally reside in
the highest stories. The wisdom of the ancients was well acquainted
with the intellectual advantages of an elevated situation; why else
were the muses stationed on Olympus or Parnassus, by those who could,
with equal right, have raised them bowers in the vale of Tempe, or
erected their altars among the flexures of Meander?" The favorite
places of resort for poets, wits, and authors, were the coffee-houses,
especially Wills', in Russell-street, Convent Garden, where Dryden had
long occupied the critics' throne, and swayed the sceptre over the
kingdom of letters. Thither went the aspirant after fame, to obtain
subscribers for his forthcoming publication, or to secure the approving
nod of some literary Jupiter; and there many an offspring of the muse
was strangled in the birth, or if suffered to live, treated with
merciless severity. In the same street lived Davies, the bookseller,
at whose house Boswell, the biographer of Johnson, became acquainted
with his hero. "The very place," he says, "where I was fortunate
enough to be introduced to the illustrious subject of this work,
deserves to be particularly marked. It was No. 8. I never pass by
without feeling reverence and regret."
Pope was the most successful author of his time, and realized L5,320 by
his Iliad. The keenness of his satire in the Dunciad threw literary
London into convulsions. On the day the book was first vended, a crowd
of authors besieged the shop, threatening to prosecute the publisher,
while hawkers crushed in to buy it up, with the hope of reaping a good
harvest from the retailing of so caustic an article. The dunces held
weekly meetings to project hostilities against the satirical critic,
whose keen weapon had cut them to the quick. One wrote to the prime
minister to inform him that Mr. Pope was an enemy to the government;
another bought his image in clay to execute him in effigy. A
surreptitious edition was published, with an owl in the frontispiece,
the genuine one exhibiting an ass laden with authors. Hence arose a
contest among the booksellers, some recommending the edition of the
owl, and others the edition of the ass, by which names the two used to
be distinguished. In 1737, Dr. Johnson came up to the metropolis with
two-pence halfpenny in his pocket--David Garrick, his companion, having
one halfpenny more. Toiling in the service of Cave, and writing for
the Gentleman's Magazine, then a few years old, the former could but
obtain a bare subsistence, which forced from him the well-known lines
in his poem on London:--
"This mournful truth is everywhere confessed,
Slow rises worth by poverty depressed."
He lodged at a stay-maker's, in Exeter-street, and dined at the Pine
Apple, just by, for eight-pence. An odd example of the intercourse
between bookmakers and bookvenders, is preserved in the anecdote of
Johnson beating Osborne, his publisher, for alleged impertinence. Of
the genial habits of literary men in London, we have an illustration in
the clubs which he formed, or to which he belonged. That which still
continues to hold its meetings at the Thatched House, is the
continuation of the famous one established at a later period than is
embraced in this chapter, at the Turk's Head, where Johnson used to
meet Reynolds, Burke, and Goldsmith.
But it is time to glance at fashionable London. As to its locality, it
has been anything but stationary. Gradually, however, it has been
gliding westward for the last three centuries and more. First breaking
its way through Ludgate, and lining the Thames side of the Strand with
noble houses, then pushing its course farther on, and spreading itself
out over the favored parishes of St. James and St. George. Here,
during the first half of the last century, might be seen the increasing
centralization of English patricians. The city was deserted of
aristocratic inhabitants, and Devonshire-square was the spot "on which
lingered the last lady of rank who clung to her ancestral abode." But
this westward tendency, flowing wave on wave, was checked for awhile in
Soho and Leicester-squares, which remained till within less than a
hundred years ago, the abode or resort of the sons and daughters of
fashion. St. James's, Grosvenor, and Hanover-squares, were, however,
of a more select and magnificent character. The titled in Church and
state loved to reside in the elegant mansions which lined and adorned
them, so convenient for visits to court, which then migrated backwards
and forwards between St. James's and Kensington. Still, though these
anti-plebeian regions were scenes of increasing convenience, comfort,
and luxury, some of the nuisances of former days lingered amidst them;
and as late as 1760, a great many hogs were seized by the overseers of
St. George's, Hanover-square, because they were bred, or kept in the
immediate neighborhood of these wealthy abodes.
On the levee day of a prime minister, a couple of streets were
sometimes lined with the coaches of political adherents, seeking power
or place, when favored visitors were admitted to an audience in his
bedchamber. The royal levees were thronged with multitudes of
courtiers, who thereby accomplished the double purpose of paying their
respect to the sovereign and reviving their friendships with each
other. It is very melancholy to read in dean Swift's letters such a
passage as the following, since it evinces so painful a disregard of
the religious character and privileges of the Lord's-day, very common,
it is feared, at the time to which it relates: "Did I never tell you,"
he says, "that I go to court on Sundays, as to a coffee-house, to see
acquaintances whom I should not otherwise see twice a year."
"Drawing-rooms were first introduced in the reign of George II., and
during the lifetime of the queen were held every evening, when the
royal family played at cards, and all persons properly dressed were
admitted. After the demise of the queen in 1737, they were held but
twice a week, and in a few years were wholly discontinued, the king
holding his 'state' in the morning twice a week."--_Cunninghame_.
Promenading in Pall Mall and the parks on foot was a favorite
recreation of the lords and ladies of the first two Georges' reigns, at
which they might be seen in court dresses, the former with bag wig and
sword, the latter with hooped petticoats and high-heeled shoes,
sweeping the gravel with their trains, and looking with immense
contempt on the citizens east of Temple-bar who dared to invade the
magic circle which fashion had drawn around itself. These gathering
places for the gay were often infested by persons who committed
outrages, to us almost incredible. Emulous of the name, as of the
deeds of the savage, they took the title of Mohawks, the appellation of
a well-known tribe of Indians. Their sport was, sword in hand, to
attack and wound the quiet wayfarer. On one occasion, we find from
Swift's letters, that he was terribly frightened by these inhuman
wretches. Even women did not escape their violence. "I walked in the
park this evening," says Swift, under date of March 9th, 1713, "and
came home early to avoid the Mohawks." Again, on the 16th, "Lord
Winchelsea told me to-day at court, that two of the Mohawks caught a
maid of old lady Winchelsea's at the door of their house in the park
with a candle, who had just lighted out somebody. They cut all her
face, and beat her without any provocation."
Another glimpse of the London of that day, which we catch while turning
over its records, presents a further unfavorable illustration of the
state of society, both in high and in low life. In May Fair there
stood a chapel, where a certain Dr. Keith, of infamous notoriety,
performed the marriage service for couples who sought a clandestine
union; and while the rich availed themselves of this provision, persons
in humbler life found a similar place open to them in the Fleet prison.
Parliament put down these enormities in 1753.
Ranelagh and Vauxhall were places of frivolous amusement resorted to
even by the higher classes. From these and other haunts of folly,
lumbering coaches or sedan chairs conveyed home the ladies through the
dimly lighted or pitch dark streets, and the gentlemen picked their way
over the ruggedly paved thoroughfares, glad of the proffered aid of the
link boys, who crowded round the gates of such places of public
entertainment or resort as were open at night, and who, arrived at the
door to which they had escorted some fashionable foot passenger,
quenched the blazing torch in the trumpet-looking ornament, which one
now and then still sees lingering over the entrance to some house in an
antiquated square or court, a characteristic relic of London in the
olden time. A walk along some of the more quiet and retired streets at
the west end of the metropolis, which were scenes of fashion and gayety
a hundred years ago, awaken in the mind, when it is in certain moods,
trains of solemn and healthful reflection. We think of the generations
that once, with light or heavy hearts, passed and repassed along those
ways, too many of them, we fear, however burdened with earthly
solicitudes, sadly heedless of the high interests of the everlasting
future. Led away by the splendid attractions of this world, its
wealth, power, praise, or pleasure, they too surely found at last that
what they followed so eagerly, and thought so delightful, was only a
delusion, like the gorgeous mirage of the desert. Some few years
hence, and we shall have ourselves gone the way of all the earth.
Other feet will tread the pavement, and other eyes drink in the light,
and look upon the works and ways of fellow-mortals; and other minds
will call up recollections of the past, and moralize with sombre hues
of feeling as we do now; and where then will the reader be? It is no
impertinent suggestion in a work like this, that he should make that
grave inquiry--nor pause till, in the light which illumines the world
to come, he has duly considered all the materials he possesses for
supplying a probable answer.
CHAPTER VII.
LONDON DURING THE LATTER HALF OF THE EIGHTEENTH CENTURY.
"In the latter half of the century few public buildings were erected,
yet among them were two of the noblest which the city even now
possesses, namely, the Excise Office and Newgate. The end of the last
century was, however, marked by the erection of the East India House,
more decidedly Grecian than anything else which preceded it. Compared
with what it has since been, architecture then was rather at a low ebb,
for although one or two of the buildings above mentioned are noble
works, they must be taken as exceptions to the meagre, insipid, and
monotonous style which stamps this period, and which such erections as
the Adelphi and Portland-place rather confirm than contradict. With
the exception of St. Peter-le-poor, 1791, and St. Martin Outwich, 1796,
not one church was built from the commencement of the reign of George
III., till the regency."--_Penny Cyclopaedia, art. London_. This remark
applies to the city. Paddington church was built during that period,
and opened in 1791. The chief public buildings of the period, besides
those noticed, are the Mansion House, finished in 1753; Middlesex
Hospital, built 1756; Magdalen Hospital, 1769; Freemasons' Hall, 1775;
Somerset House, in its present state, 1775; and Trinity House, 1793.
Westminster bridge was finished in 1750, and Blackfriars begun ten
years afterwards; these, with London bridge, were the only roadways
over the Thames during the eighteenth century.
The extremities of London continued to extend. Grosvenor-place, Hyde
Park Corner, was reared 1767; Marylebone-garden was leased out to
builders 1778; Somers-town was commenced 1786. "Though London
increases every day," observes Horace Walpole in 1791, "and Mr.
Herschel has just discovered a new square or circus, somewhere by the
New-road, in the _via lactea_, where the cows used to feed; I believe
you will think the town cannot hold all its inhabitants, so
prodigiously the population is augmented." "There will be one street
from London to Brentford, ay, and from London to every village ten
miles round; lord Camden has just let ground at Kentish-town for
building 1,400 houses; nor do I wonder; London is, I am certain, much
fuller than ever I saw it. I have twice this spring been going to stop
my coach in Piccadilly, to inquire what was the matter, thinking there
was a mob; not at all, it was only passengers."
The Westminster Paving Act, passed in 1762, was the commencement of a
new system of improvement in the great thoroughfares. The old signs,
posts, water-spouts, and similar nuisances and obstructions, were
removed, and a pavement laid down for foot passengers.
But until the introduction of gas, in the present century, the streets
continued to be dimly lighted, and the services of the link boy at
night to be in general requisition. In 1760, names began to be placed
on people's doors, and four years subsequently, the plan of numbering
houses originated. Burlington-street was the first place in which this
convenient arrangement was made. In Lincoln's-inn-fields it was next
followed.
The history of London, during the latter half of the eighteenth
century, was emphatically that of an age of public excitements, some of
them specially pertaining to the city, while in others the whole
country shared. The removal of Mr. Pitt, afterwards Earl of Chatham,
from the high ministerial position he had occupied--an event which
occurred in 1757--produced very strong ebullitions of feeling in the
hearts of his numerous admirers. London largely participated in the
popular admiration of that extraordinary man, and expressed a sense of
his services by voting him the freedom of the city, which was presented
to him in an elegant gold box. The success of the British arms during
the next year, in the taking of Louisbourg, led to great rejoicings,
illuminations, and the presentation to the king of loyal congratulatory
addresses. In the year following, the wants of the army being found
very urgent, and men being unwilling to enlist, a subscription was
opened at Guildhall to meet the exigency by raising a fund, out of
which the amount of premium on enlistment might be augmented. The
taking of Quebec, in 1759, again awakened enthusiastic joy; and the
record of bonfires, ringing of bells, and kindred demonstrations, are
conspicuous in the civic annals for that year. The accession of George
III., in 1760, was marked by the full payment to the young sovereign of
all those loyal dues, which are tendered by the metropolitan
authorities and community when such an important event occurs as the
transfer of the sceptre into new hands. But the public excitement in
his favor was soon exchanged for feelings equally intense of an
opposite character. John Wilkes appeared on the stage of public life
in 1754--a man utterly destitute of virtue and principle, but possessed
of certain qualities likely to render him popular, especially an
abundance of humor, and a wonderful degree of assurance. By attacking
Lord Bute, the favorite of the king, but no favorite with the people,
he gained applause, and was set down as a patriot. In No. 45 of the
"North Briton," a newspaper which he edited, a violent attack on his
majesty appeared; indeed, it went so far as to charge him with the
utterance of a falsehood in his speech from the throne. The house of
Wilkes was searched, and his person seized for this political offence;
but sheltering himself under his parliamentary privileges, he obtained
his dismissal from custody. Upon an information being filed against
him by the attorney-general, he declined to appear, when the House of
Commons took the matter in hand, and declared Wilkes's paper to be a
false, seditious, and scandalous libel, and ordered it to be burned by
the common hangman. The sympathies of many in London being with
Wilkes, a riot ensued upon the attempt which the sheriffs made to
execute the parliamentary sentence. Wilkes's disgrace was turned into
a triumph, and the metropolis rang with the applause of this worthless
individual. Unhappily, the proceedings against him had involved
unconstitutional acts, which are sure to produce the indignation of a
free people, and to transform into a martyr a man who is really
criminal. He was next convicted of publishing an indecent poem; but
again the improper means adopted to secure his conviction placed him
before the people as a ministerial victim, and diverted attention from
his flagrant vices. But the reign of this demagogue in London,
properly speaking, did not begin till 1768, when he returned to
England, after a considerable absence, and offered himself as a
candidate for the city. Though exceedingly popular, he failed to
obtain his election, but afterwards, with full success, he appealed to
the Middlesex constituency. Then came the tug of war between the
electors and the House of Commons. The latter invalidated the return,
in which the former persisted. Riots were the consequence. One
dreadful outbreak took place in St. George's-fields, when the military
were ordered to fire, and some were killed or wounded. Three times
Wilkes was returned by the people to parliament, and three times the
parliament returned him to the people. This violation of popular
rights was deeply resented in London, and throughout the country. It
also made Wilkes's fortune; L20,000 were raised for him; all kinds of
presents were showered on the favorite; and his portrait, in every form
of art, was in universal request. In the Common Pleas, he afterwards
obtained a verdict against Lord Halifax for false imprisonment and the
illegal seizure of papers. He was subsequently elected sheriff,
alderman, and mayor of London; and finally, in 1779, sank down into
neglect much more comfortably than he deserved, as chamberlain of the
city. His history singularly illustrates how illegal proceedings
defeat their object, though it be right; and how a rash eagerness in
pursuing the ends of justice overturns them.
In connection with the Wilkes affair, there is a remarkable episode in
the municipal history of the metropolis. A most serious
misunderstanding took place between the monarch and the corporation.
The proceedings of ministers in reference to the Middlesex election,
led the civic authorities to present to the king a very strong
remonstrance, begging him to dissolve the parliament, and dismiss the
ministry. The monarch took time to consider what reply he should make
to so formidable an application, and at length informed the corporation
that he was always ready to receive the requests and listen to the
complaints of his subjects, but it gave him concern to find that any
should have been so far misled as to offer a remonstrance, the contents
of which he considered disrespectful to himself, injurious to
parliament, and irreconcilable with the principles of the constitution.
Among the aldermen, there were some who disapproved of the
remonstrance, and now strongly protested against it; but Beckford, who
then, for the second time, filled the office of lord mayor, and
strongly felt with the common council, livery, and popular party,
earnestly resisted such opposition, and encouraged the citizens to
maintain their stand against what was considered an exercise of
arbitrary power on the part of government. The mayor summoned the
livery, and delivered a speech just adapted to the assembly. Another
remonstrance was drawn up, to be presented to his majesty by the lord
mayor and sheriffs. To this the king replied, that he should have been
wanting to the public and himself, if he had not expressed his
dissatisfaction at their address. Beckford, who must have been a bold
and eloquent man, breaking through all the rules of court etiquette,
delivered an extempore speech to the sovereign, which he concluded by
saying, "Permit me, sire, to observe, that whoever has already dared,
or shall hereafter endeavor, by false insinuations and suggestions, to
alienate your majesty's affections from your loyal subjects in general,
and from the city of London in particular, and to withdraw your
confidence in, and regard for, your people, is an enemy to your
majesty's person and family, a violator of public peace, and a betrayer
of our happy constitution, as it was established at the glorious and
necessary revolution." Of course, no reply was given to this impromptu
address, but it seemed to have excited no little wonder among the
courtiers present on the occasion. On the birth of the princess
Elizabeth, a short and loyal address of congratulation, avoiding all
controversial topics, was presented by the same chief magistrate; to
which his majesty answered, that so long as the citizens of London
addressed him with such professions, they might be sure of his
protection. The stormy agitation was of brief continuance. The
ripples on the stream soon subsided. With this interview the good
understanding between the king and the city appears to have been
restored, though the bold remonstrance the latter had presented
produced no practical effect. The popular lord mayor, who signalized
himself especially by his speech in the royal closet, was removed by
Divine Providence out of this life before the term of his mayoralty
expired. After his decease, the citizens, to mark their esteem for his
character, erected a monument to him in Guildhall, and engraved on it
the speech which had given him so much celebrity.
The great dispute between the mother country and America, which began
as early as 1765, could not fail to excite a deep interest in the
capital of the empire. "The sound of that mighty tempest," as it was
termed by Burke, was heard with deep concern at first by the London
merchants, as threatening to injure their commercial interests; and
when the Stamp Act, so odious from its influence in that respect, was
repealed soon after it was passed, the whole city beamed with gladness
and satisfaction. When, however, America asserted her independence,
many in London, as well as in other parts of the country, felt their
national pride so much wounded, that they encouraged the war, till
finding the conflict with so distant and powerful a colony all in vain,
they were willing to hear of peace, though at the expense of losing the
chief part of the British territory in the western hemisphere. But in
the feelings that the protracted struggle awakened, the metropolis only
shared in connection with the provinces; they must, therefore, be
passed over with this cursory notice, that we may attend to what
particularly constitutes the history of the city.
This plunges us at once amidst scenes of excitement, much more serious
and shocking than any others that have lately come under review. In
1779, the Protestant Association was formed, in consequence of some of
the Roman Catholic disabilities being removed. The society met at
Coachmakers' Hall, Noble-street, Foster-lane, under the presidency of
lord George Gordon, whose general eccentricity bordered upon madness,
and whose professed abhorrence of Popery sank into fanaticism. The
association, in May, 1780, determined to petition for a repeal of the
Act just passed, and it was resolved that the whole body should attend
in St. George's-fields, on the second of June, to accompany lord George
with the petition to the House of Commons. His lordship enforced this
motion with vehement earnestness, and said that if less than 20,000 of
his fellow-citizens attended him, he would not present the document.
At the time and place appointed, an immense multitude assembled,
computed at 50,000 or 60,000, wearing blue ribbons in their hats,
marshaled under standards displaying the words "No Popery." In three
divisions they marched six abreast, over Londonbridge, towards
Westminster, being reinforced at Charing Cross by great numbers on
horseback and in carriages. The then narrow avenues to the houses of
parliament were thronged by these crowds, and such members of the
legislature as they disliked were treated with insult, as they made
their way through the dense concourse. The petition was presented; but
when that business was finished for which the populace had been invited
by the foolish nobleman, he found it impossible to disperse them.
Harangues, so potent in convening the host, were utterly powerless when
employed for their separation. Nor did the magistracy attempt a timely
interference; but the mob was left to its own wild will, and like a
swollen torrent, which bursts its banks, it poured over the city with
destructive havoc. The chapels of the Bavarian and Sardinian embassy
were pulled down that night. On the next day, Saturday, they committed
no violence; but on Sunday they assailed a popish chapel and some
houses in Moorfields, within sight of the military, who stood by unable
to do anything, because they had no commands from the chief magistrate,
who alone could authorize them to act. All that was done was to take a
few of the rioters into custody, while the rest were left without any
attempt at their dispersion. Utterly unnerved, the lord mayor
virtually surrendered the city at this momentous crisis into the hands
of the mob. Encouraged by the impunity with which they were left to
pursue their own course, they attacked on the next day the house of Sir
George Sackville, in Leicester-square, because he had moved the
Catholic Relief Bill. On Tuesday, waxing bolder than ever, they
besieged the old prison of Newgate, where a few of their associates
were confined. Breaking the roof, and tearing away the rafters, they
descended into the building by ladders, and rescued the prisoners. Two
eye-witnesses, the poet Crabbe and Dr. Johnson, have left their
impressions of this extraordinary scene: "I stood and saw," says the
former of these writers, "about twelve women and eight men ascend from
their confinement to the open air, and conducted through the streets in
their chains. Three of them were to be hanged on Friday. You have no
conception of the frenzy of the multitude. Newgate was at this time
open to all; anyone might get in, and what was never the case before,
anyone might get out."
"On Wednesday," says Dr. Johnson, "I walked with Dr. Scott, (lord
Stowell,) to look at Newgate, and found it in ruins, with the fire yet
glowing. As I went by, the Protestants were plundering the
sessions-house at the Old Bailey. There were not, I believe, a
hundred, but they did their work at leisure, in full security, without
sentinels, without trepidation, as men lawfully employed in full day."
Besides Newgate, lord Mansfield's house in Bloomsbury-square was pulled
down, and his valuable library burned. The Fleet, King's Bench, the
Marshalsea, Wood-street Compter, and Clerkenwell Bridewell, were all
opened, and such a jail delivery effected as the citizens had never
witnessed before. A stop was put to business on the Wednesday; shops
were closed; pieces of blue, the symbol of Protestant truth and zeal,
were required to be hung out of the windows, and "No Popery" chalked on
the doors. Before night, even the Bank was assailed, but not without a
dreadful and destructive repulse from the military who garrisoned it,
and were ordered to act. It is stated that the king, alarmed at the
danger of his capital, and indignant at the inaction of the
magistrates, took upon himself to command the services of the military
for putting down the riot. While thirty fires were blazing in the
streets, and the inhabitants passed a sleepless night, full of anguish,
a large body of soldiers was engaged in the terrible, though necessary
work of suppressing the riot by force. This was accomplished at the
expense of not less than five hundred lives. By Friday, quietude was
restored. Lord George Gordon was apprehended, but was acquitted upon
trial, his conduct not coming within the limits of the statute of
treason. Sixty of the deluded creatures, who at first were excited by
his mischievous agitation however, had to pay the extreme penalty of
the law. A happy contrast to this brutal kind of excitement has been
recently (1850-51) displayed in the calm, deep, and, for the most part,
intelligent resistance made to a far different measure--the papal
aggression, in the creation of territorial bishoprics; one really
calculated to excite far greater opposition. The years 1780 and 1850,
stand out at the extremes of a period which has witnessed, in London
and elsewhere, a change in public thought and habit of the most
gratifying kind; and to what can this be so fairly ascribed, under the
providence and blessing of God, as to the increase of instruction,
especially religious instruction, through the medium of Sabbath and
other schools, together with the distribution of the Bible and tracts,
as well as other meliorating agencies operating on society?
Eight years after the anti-popery riots, another excitement, of a
different kind, rolled its waves over the public mind in London; not,
indeed, confined to the metropolis, but concentrating its force there,
as the scene of the occurrence which produced it. This was the trial
of Warren Hastings, for his alleged mal-administration of Indian
affairs. But the great length to which it was extended wearied out the
public patience, and ere the forensic business came to its close the
court was forsaken, and the numerous London circles, at first thrown
into a storm of feeling by the occurrence, resumed their former
quietude, and almost forgot the whole matter.
The same year that Hastings' trial commenced, the public sympathy and
sorrow were aroused in London, and throughout the nation, by the
melancholy mental illness of George III., but the next year his sudden
recovery created universal joy, which was demonstrated in the
metropolis, after the usual fashion.
Then loyalty, with all his lamps
New trimmed, a gallant show,
Chasing the darkness and the damps,
Set London in a glow.
It was a scene, in every part,
Like those in fable feigned,
And seemed by some magician's hand
Created and sustained.
On the 23d of April, a general thanksgiving was held for the king's
recovery, and on that account his majesty, accompanied by the royal
family, went in procession to attend public worship in St. Paul's
Cathedral; thus reminding us of the words of the Babylonish monarch,
"Mine understanding returned unto me, and I blessed the Most High, and
I praised and honored him that liveth forever, whose dominion is an
everlasting dominion, and his kingdom is from generation to generation."
At the close of the eighteenth century, the proceedings of
revolutionary France sent a fresh stream of excitement through the
public mind of England. On one side or the other, in sympathy with or
in aversion to the measures adopted on the opposite side of the
channel, most politicians, high and low, eagerly ranged themselves.
The efforts of Mr. Pitt to prevent anything like the enactment here of
what our neighbours were doing, were condemned or applauded by the two
parties according to the principles they espoused. "The trials of
Hardy, Tooke, Thelwall, and others," says a minister, then a student
near the metropolis, "which took place not long after my entrance on
college life, agitated London to an extent which I have never seen
equaled, though my life has fallen on times and events of the most
prodigious and portentous character."--_Autobiography of the Rev. W.
Walford_. Clubs were formed of a more than questionable description,
of which we remember to have received an illustrative anecdote from a
citizen of London, now gray-headed, but then in the flower of his
youth. Invited by a person of about his own age to attend a meeting,
held in some obscure street, he was surprised on entrance to find a
number of men, ranged on either side a room, sitting beside long
tables, with one at the upper end, where sat the president for the
evening. Several foaming tankards were brought in, when the president
calling on the company to rise, took up one of the vessels, and
striking off with his hand the foam that crested the porter, gave as a
toast, "So let all ---- perish." The blank was left to be filled up as
each drinker pleased. The avowed dislike to kings, entertained by the
boon companions there assembled, suggested to the visitor the word
intended for insertion, and he gladly left the place, not a little
alarmed lest he should be suspected of sympathy in treasonable designs.
Following political excitement came a monetary crisis, which struck a
panic through the body of London merchants; for, in 1797, the Bank of
England suspended its cash payments. But after all these storms, which
severely tested its strength, the vessel of the state, under the
blessing of the Almighty, righted itself, and scenes of political calm
again smiled, and tides of commercial prosperity flowed upon old London.
In passing on to notice the general state of society in the metropolis
during the last half of the eighteenth century, it is painful to notice
the continuance of some of the revolting features which mark an earlier
age. The old-fashioned burglaries, with the robberies and rogueries of
the highway, were still perpetrated. A walk out of London after dark
was by no means safe; and therefore, at the end of a bill of
entertainment at Bellsize House, in the Hampstead-road, St.
John's-wood, there was this postscript--"For the security of the
guests, there are twelve stout fellows, completely armed, to patrol
between London and Bellsize, to prevent the insults of highwaymen and
footpads who infest the road." To cross Hounslow-heath or
Finchley-common after sunset was a daring enterprise; nor did travelers
venture on it without being armed, and even ball-proof carriages were
used by some. At Kensington and other places in the vicinity of
London, it was customary on Sunday evenings to ring a bell at
intervals, to summon those who were returning to town to form
themselves into a band, affording mutual protection, as they wended
their way homewards. Town itself did not afford security; for George
IV. and the Duke of York, when very young men, were stopped one night
in a hackney-coach and robbed on Hay-hill, Berkeley-square. The state
of the police, as these facts indicate, was most inefficient; but when
the law seized on its transgressors, it was merciless in the penalty
inflicted. Long trains of prisoners, chained together, might be seen
marching through the streets on the way to jail, where the treatment
they received was cruel in the extreme, and much more calculated to
harden than to correct. The number of executions almost exceeds
belief; and every approach to town exhibited a gibbet, with some
miserable creature hanging in chains. These public spectacles missed
their professed object, and the frequent executions did anything but
check the commission of crime. The lowest classes constantly assembled
to witness such spectacles, regarded them generally as mere matters of
amusement, or as affording opportunities for the indulgence of their
vices.
Some startling revelations of the state of things among London
tradesmen, as well as the lowest orders, were made before a select
committee of the House of Commons in 1835, relative to the period fifty
years earlier. "The conduct of tradesmen," said one of the witnesses,
"was exceedingly gross as compared with that of the same class at the
present time. Decency was a very different thing from what it is now;
their manners were such as scarcely to be credited. I made inquiries a
few years ago, and found that between Temple-bar and Fleet-market,
there were many houses in each of which there were more books than all
the tradesmen's houses in the streets contained when I was a youth."
He mentions, also, the open departure of thieves from certain
public-houses, wishing one another success--"In Gray's-inn-lane," he
remarks, "was the Blue Lion, commonly called the Blue Cat. I have seen
the landlord of this place come into the room with a large lump of
silver in his hand, which he had melted for the thieves, and pay them
for it. There was no disguise about it. It was done openly." "At the
time I am speaking of, there were scarcely any houses on the eastern
side of Tottenham-court-road; there, and in the long fields, were
several large ponds; the amusement here was duck-hunting and
badger-baiting; they would throw a cat into the water, and set dogs at
her; great cruelty was constantly practised, and the most abominable
scenes used to take place. It is almost impossible for any person to
believe the atrocities of low life at that time, which were not, as
now, confined to the worst paid and most ignorant of the populace."
Turning to look for a moment at the opposite extreme of society, it is
delightful to mark the improvement which had there taken place. While
drawing-rooms and levees were held as before, though less frequent, the
former being confined to once a week; while equipages of similar
fashion as formerly continued to roll through the parks, Piccadilly,
and the Mall; while the costumes and habits of courtiers exhibited no
great variation; while theatres, and other places of amusement, were
frequented by the fashionables; while gossiping calls in the morning,
and gay parties at night, were the common and every-day incidents of
West-end life--a very obvious improvement arose in the morals and
general tone of feeling of people about court, in consequence of the
exemplary and virtuous character of George III. and Queen Caroline.
Fond of quiet and domestic repose, retiring into the bosom of their
family, surrounded by a few favorite dependents, encouraging a taste
for reading and music, and ever frowning upon vice in all its forms,
they exerted a powerful influence upon those around them, and turned
the palace into a completely different abode from what it had been in
the time of the earlier Georges. Religion, too, if not in its earnest
spirituality, yet in its decorous observances and its moral bearings,
was maintained and promoted, both by royal precept and example. The
monarch and his family were accustomed to attend regularly upon the
services in the chapel attached to St. James's Palace.
The revival of religion in London, to which we adverted in a former
chapter, produced permanent results. During the last half of the
century, Christian godliness continued to advance. Whitefield's
labors, as often as he visited the metropolis, produced a deep
impression on the multitudes who, in chapels or the open air, were
eager to hear him. Whitefield died in America, but a monument is
erected to his memory in Tottenham-court Chapel, the walls of which
often echoed with his fervid oratory. Wesley's exertions were
prolonged till the year 1792. After a life of most energetic effort in
the cause of Christ, this remarkable man expired at his house in
London, 1791, in the eighty-eighth year of his age.
The countess of Huntingdon, Whitefield's early friend, exerted in
London a powerful religious influence, "scattering the odors of the
Saviour's name among mitres and coronets, and bearing a faithful
testimony to her Divine Master in the presence of royalty itself." She
has left behind her in the metropolis two remarkable proofs of her
religious liberality and zeal, in Zion and Spafields Chapels, both of
which she was the means of transforming out of places of amusement into
houses for the service and praise of God.
The labors of Mr. Romaine, the minister of St. Andrew-by-the-Wardrobe
and St. Anne, Blackfriars, claim special notice. Previous to his
induction to those parishes, he had preached at St. Dunstan's and St.
George's, Hanover-square, exciting great attention, and, by the
benediction of God, enjoying great success. The parishioners in the
latter church were sometimes incommoded by the vast concourse who came
to hear this evangelical clergyman. On one occasion, the Earl of
Northampton rebuked them for complaining of the inconvenience,
observing that they bore with patience the crowded ball-room or
play-house. "If," he said, "the power to attract be imputed as matter
of admiration to Garrick, why should it be urged as a crime against
Romaine? Shall excellence be considered exceptionable only in Divine
things?" Mr. Romaine was strongly opposed by some who disapproved of
his sentiments, and was soon turned out of St. George's Church; after
which the countess of Huntingdon made him her chaplain for awhile, in
which office he preached in her drawing-room to the nobility, in her
kitchen to the poor. Her house, where these services were performed,
was in Park-street. Settled, at length, as the rector of the two
churches above-named, this eminent servant of Christ--of whom it has
been said that he was a diamond, rough often, but very pointed, and the
more he was broken by years the more he appeared to shine--pursued
uninterruptedly his holy and edifying ministrations till the time of
his death in 1795. He was interred in St. Andrew's Church, where a
monument, not devoid of artistic beauty, and executed by the elder
Bacon, a well-known sculptor of that day, distinguishes the place of
his remains. In 1780, there came to minister in the parish of St. Mary
Woolnoth another individual, whose praise is in all the churches. This
was John Newton, the friend of the poet Cowper. He lies buried in the
edifice where he loved to proclaim the glorious Gospel of the blessed
God; and on the tablet raised as a memorial of his worth is inscribed
the following succinct account of his eventful life and of his
character, so illustrative of Divine grace, in words written by
himself: "John Newton, clerk, once an infidel and libertine, a servant
of slaves in Africa, was, by the rich mercy of our Lord and Saviour,
Jesus Christ, preserved, restored, pardoned, and appointed to preach
the faith he had long labored to destroy."
Rowland Hill, originally a clergyman of the establishment, and never
fully sympathizing with any dissenting denomination, though confessing
to many clerical irregularities, occupies a distinguished place among
the men who devoted themselves to the faithful preaching of the Gospel
in the metropolis. Surrey Chapel, which has proved a school in which
many spirits have been trained for the celestial world, was erected by
him in Blackfriars-road, 1782, and there till his death he continued to
preach.
Two very celebrated prelates filled the see of London during this
eventful period in the history of religion: Dr. Lowth, the elegant
scholar and able commentator, who was translated to London in 1777; and
Dr. Porteus, who succeeded him on his death in 1786, and though
inferior in talents and learning, earned for himself a considerable
literary reputation as a Christian divine, and distinguished his
episcopate, which lasted till 1808, by his pious diligence and catholic
charity.
Science, literature, and art, were promoted in London during the period
before us, by the establishment of several well-known institutions.
The British Museum was formed in 1753, in consequence of the will of
Sir Hans Sloane, who bequeathed his large collection of curiosities to
government for L20,000, which was L30,000 less than they cost him. An
act of parliament was passed for their purchase, and Montague House,
Bloomsbury, was taken and fitted up for the reception of Sloane's
treasures, and other collections, scientific and literary, upon which
great sums of money were expended. The Royal Academy, for the
encouragement and improvement of British artists and sculptors, was
constituted in 1768, and the first public exhibition was made at
Somerset House in 1780. The Royal Institution in Albemarle-street was
opened in 1799. The College of Surgeons was incorporated in 1800.
Other institutions, sacred to humanity and benevolence, and fraught
with great benefit to multitudes of our suffering race, were originated
within the last fifty years of the eighteenth century. In 1755,
Middlesex Hospital was founded, the generous exertions which led to it
having begun some years earlier. Three years later, the Magdalen
Hospital, for the reformation and relief of penitent females, was
opened in Prescott-street, Goodman-fields, and afterwards transferred
to an appropriate building, erected for the purpose in St.
George's-fields, in 1709. The foundation-stone of the Lying-in
Hospital, on the Surrey side of Westminster-bridge, was laid in 1765;
and a similar institution was begun in the City-road in 1770. The
Royal Humane Society, for the recovery of persons from drowning,
commenced in 1774. The Royal Literary Fund, for the relief of poor
authors, was instituted in 1790.
The religious societies of London, whose character adorns the English
capital, eclipsing its artistic and commercial splendour, chiefly
belong to the present century. The London Missionary Society, however,
for preaching the Gospel of Christ among the heathen, began as early as
1795. The declaration of the Society was signed at the Castle and
Falcon, Aldersgate-street. In the year 1709 was formed, also, the
institution by which the present volume is issued--the Religious Tract
Society. Commencing with small beginnings, it has, through the
prospering hand of God upon its labors, been privileged to proclaim the
unsearchable riches of Christ in one hundred and ten languages and
dialects; and, in the course of half a century, to circulate its varied
messengers of mercy to the vast amount of five hundred millions of
copies.
Since the conclusion of the eighteenth century, London has undergone an
unprecedented change, upon which the limits of this volume will not
allow us to touch. The city, which is still swelling every year, in a
degree which, if Horace, Walpole were living, would fill him with
greater surprise than ever, is really new London. Few of the principal
streets exhibit the appearance they did fifty years ago, and the
architectural alteration is but a type of the social one. The superior
sanitary arrangements, the more efficient police, the better education
of most classes of society, the augmented provision for religious
instruction and worship, the more decidedly evangelical tone of
preaching in the metropolitan pulpits, and the increase of real piety
amongst the population, must strike everyone, on even a superficial
comparison of the past and present; and when we consider the great
change wrought in half a century, it inspires encouragement in relation
to the future. The impulse which things have received of late has been
so mighty, that there is no calculating the acceleration of their
future progress. Thus the remembrance of the past yields advantage,
and we pluck hopes, "like beautiful wild flowers from the ruined tombs
that border the highways of antiquity, to make a garland for the living
forehead."--_Coleridge_. On taking a longer reach of comparison, an
amount of wonder is inspired not to be adequately expressed. Had some
sage in the Roman senate, two thousand years ago, proclaimed that the
day would come, when an obscure town, situated on the Thames, a river
scarcely known then to the Latin geographer, would vie with the city in
which they were assembled on the Tiber, nay, eclipse it, and wax in
glory while the other waned, that prediction would have strangely
crossed their pride, and would have been indignantly pronounced
incredible. Yet that day has come. The British town, then a mere
inclosure, containing a few huts, has swelled into a city teeming with
a population of above two millions, crowded with public buildings and
costly habitations, filled with commerce, wealth, and luxury, the
mirror of modern civilization, the metropolis of a mighty empire, and
the wonder of the world--while the Roman city, then the mightiest and
most splendid on the face of the earth, and the mistress of the globe,
so far as its regions were discovered, retains no traces of her glory,
and is chiefly interesting on account of her ancient name and
associations.
Happily the genius of civilization in the two cities is completely
diverse. In the early days of the Roman kingdom and republic, the
people fought in self-defence; in later times, from a pure thirst for
glory and dominion. In the best periods of its history, the virtues of
the citizens were of the martial cast, and found a fostering influence
in all the institutions of the state. To Rome, which then cradled a
warlike people, London presents a contrast on which we look with
satisfaction. London is the type of commercial civilization. The
merchant, not the soldier, is most prominent and influential. The
inhabitants of the English metropolis and country, it may be safely
asserted, are looking not to armies as sources of greatness, and
objects for gratulation, but to the busy thousands who are deepening
and spreading the resources of national wealth by their commercial and
manufacturing industry. The spirit of mercantile enterprise is as
strongly stamped upon the English character, in their metropolis of the
nineteenth century, as the spirit of war was stamped upon the character
of the Romans in their metropolis before the Christian era. Rome had
her trade as well as her army--her Ostia, whither her vessels brought
for her use the luxuries of the East; but it was not there, but to the
Campus Martius, where their legions performed their evolutions, that
the stranger would have been taken to see the greatness of the
republic. So the metropolis of the British empire is the rendezvous of
a great military establishment, as well as an emporium of merchandise;
but it is to the scenes on the borders of the Thames, to her spacious
docks, her crowded shipping, her stores and warehouses, with all the
accompaniments of busy commerce, presenting a spectacle which perfectly
overpowers the mind with wonder--it is to those scenes that we should
take the stranger, to impress him with an idea of the greatness of our
chief city. The Hyde Park review, with cuirasses and swords glittering
in the sun, and martial music floating through the air, affords a
brilliant holiday entertainment, but all must feel that the English
spirit of the nineteenth century is not there expressed. It is very
true that the love of war has not lost its hold entirely on the public
mind; that there are many who still pant for the conflict, and for the
honors and prizes which successful warfare brings; but, we repeat it,
the spirit of the nineteenth century is not there expressed, but it
finds its exponent in the earnest activity which is ever witnessed
round the neighborhood of London-bridge and the Exchange. The time is
coming--is already come, when, as most intelligent men turn over the
pages of the world's history, they award the palm of the noblest
civilization to London, a city full of merchants and artisans, rather
than to Rome, a city full of soldiers, flushed with the pride of
victory, and drunk with the blood of the slain.
In all that relates to the state of society, the genius of the people,
public opinion, general intelligence, taste, feeling, character--the
comparison is decidedly in favor of the English capital. This is to be
ascribed to many causes--to the intermingling of races, an insular
position, political revolutions, enlarged experience, providential
discoveries, and the creation of sentiments and opinions during
centuries of mental activity; but, above all, it is to be ascribed to
Christianity, which has long had a strong hold upon the hearts of
multitudes, and which has indirectly exercised a most beneficial reflex
influence upon the character of others, who have little regard for its
doctrinal principles. The richest forms of modern civilization in
London are founded on our religion. The elevation of woman to her
proper rank, the improved character of the judicial code, the
extinction of domestic slavery, the elevation of serfs of the soil to
freemen having an estate in their own labor, the value set on life, the
philanthropic institutions which abound--are all the results of
evangelical light and principle. Let any one walk through the streets
of London, and compare the aspect of things with what was exhibited to
the man who walked through the streets of ancient Rome--and with all
the vice and misery which exist in the former, there are found elements
of social welfare, the acknowledged creation of Christian morals, at
work, unknown in the latter. Indications of intelligence, peace,
freedom, and charity, are found here, which were wanting there. The
power and permanence of London must depend upon her morality and
religion.
We look with intense interest to the young men of London. With pain,
such as we cannot describe, we regard the gay, the dissolute, the
intemperate--those who drown the higher faculties of the soul in
sensual indulgence, who degrade their mental, moral, and spiritual
nature, and, forgetting their relationship to angels, sink to the level
of the brutes that perish. With pleasure, however, equally
indescribable, we turn to the steady, the sober, the virtuous, the
enlightened--those who labor after mental improvement, and especially
those who seek spiritual excellence, who ask and practically answer the
question, "While I am attending to the intellectual culture of the
mind, ought I not to prepare for that eternity to which I am hastening,
where moral and spiritual character will be all in all?" and who,
repairing to the word of God, the source of all religious wisdom, have
become the subjects of a discipline, which adorns the intellect with
the beauties of sanctity, and prepares the soul for the vision and
worship of heaven. Of such, London may well say with the mother of the
Gracchi, but in a far more important sense, "These are my jewels."
Let it be the endeavor, as it is the duty of London citizens, to aid
all wise schemes for its physical and intellectual amelioration, but
especially such as relate to morals and religion. With a clear eye, a
loving heart, a steady hand, and a determined will, each must apply
himself to pulling down the evil, and building up the good. The moral
health of a city should be the care of all its members. The most
precious object amidst the multitude of precious things in the chief
city of England is the citizen himself. Man, out of whose intellect,
energy, and power, all the rest has grown--man, in whose capacities are
found the germs of a greatness, the cultivation of which will a
thousand times repay the toil it involves. The noblest of enterprises,
be it remembered, is to be found, not in commercial speculation, or
political reform, or even literary and scientific knowledge, but in the
promotion of Christ's holy and saving religion, and in the recovery and
purification of the soul, through faith in him, and its preparation for
other realms of being in the infinite Hereafter. The enduring
magnificence of such labor and its results exceeds all the doings of
earthly ambition, even as the mighty Alps and Andes surpass the houses
of ice and snow which children in their sports build up, and which are
melting away before that sun in whose rays they glitter.
THE END.
BOOKS FOR SUNDAY-SCHOOLS.
200 Mulberry-street, New York.
LONDON IN MODERN TIMES;
Or, Sketches of the English Metropolis during the Seventeenth and
Eighteenth Centuries. 18mo., pp. 222.
THE RODEN FAMILY;
Or, the Sad End of Bad Ways. Reminiscences of the West India Islands.
Second Series, No. II. Three Illustrations. 18mo., pp. 159.
LEARNING TO FEEL.
Illustrated. Two volumes, 18mo., pp. 298.
LEARNING TO ACT.
Three Illustrations. 18mo., pp. 144.
ROSA, THE WORK GIRL.
By the Author of "The Irish Dove." Two Illustrations. 18mo., pp. 138.
THE FIERY FURNACE;
Or, the Story of Shadrach, Meshach, and Abednego. By a Sunday-School
Teacher. Two Illustrations. 18mo., pp. 64.
ELIZABETH BALES:
A Pattern for Sunday-School Teachers and Tract Distributers. By J. A.
JAMES. 18mo., pp. 84.
SOCIAL PROGRESS;
Or, Business and Pleasure. By the Author of "Nature's Wonders,"
"Village Science," etc. Sixteen Illustrations. 18mo., pp. 269.
MINES AND MINING.
18mo., pp. 212.
BLOOMING HOPES AND WITHERED JOYS.
By Rev. J. T. BARR, Author of "Recollections of a Minister,"
"Merchant's Daughter," etc. Five Illustrations. 18mo., pp. 286.
NINEVEH AND THE RIVER TIGRIS.
Two Illustrations. 18mo., pp. 210.
MOUNTAINS OF THE PENTATEUCH.
Conversations on the Mountains of the Pentateuch, and the Scenes and
Circumstances connected with them in Holy Writ. 18mo., pp. 202.
MEMOIR OF ELIZA M. BARKER.
By A. C. ROSE. Two Illustrations. 18mo., pp. 108.
IDLE DICK AND THE POOR WATCHMAKER.
Originally written in French, by Rev. CESAR MALAN, of Geneva. With
Illustrations. 18mo., pp. 82.
MY GRANDFATHER GREGORY.
With Illustrations. 18mo., pp. 118.
LITTLE WATER-CRESS SELLERS.
18mo., pp. 80.
SUNDAY AMONG THE PURITANS;
Or, the First Twenty Sabbaths of the Pilgrims of New England. By DR.
W. A. ALCOTT. 18mo., pp. 95.
IRISH STORIES FOR THOUGHTFUL READERS.
Five Illustrations. 18mo., pp. 285.
UNCLE WILLIAM AND HIS NEPHEWS.
Nine Illustrations. 18mo., pp. 64.
End of the Project Gutenberg EBook of London in Modern Times, by Unknown
***
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Q: Combinatorics alphabet If say I want to arrange the letters of the alphabet a,b,c,d,e,f such that e and f cannot be next to each other.
I would think the answer was $6\times4\times4\times3\times2$ as there are first 6 letters then 4 as e cannot be next to f.
Thanks.
A: The $6$ numbers without any restriction can be arranged in $6!$ ways.
If we put $e,f$ together, we can arrange the $6$ numbers in $2!(5!)$ ways, as $e,f$ can arranged in $2!$ ways.
So, the required number of combinations is $6!-2(5!)$
A: Count all the ways e and f can be together.
Subtract this from the total number of permutations.
A: You can, without loss of generality, choose to place $e$ first and then consider where to place $f$. However you will need to consider two cases, since if $e$ is at either end it only restricts one position and otherwise it restricts two.
The more direct way is to consider the number of ways to get what you don't want and then subtract it from the total. Of the 30 ways to arrange $e$ and $f$, 2 have distance 5, 4 have distance 4, 6 have distance 3, 8 have distance 2, and 10 have distance 1. So you should multiply the number of unrestricted arrangements by $\frac{20}{30}$ which should produce $\frac23 \cdot 6!$ which is $4 \cdot 5!$or 480.
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"redpajama_set_name": "RedPajamaStackExchange"
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Der Bahnhof Roma-Areeiro, auch Roma/Areeiro, ist ein viergleisiger Bahnhof in der portugiesischen Hauptstadt Lissabon, gelegen an der Linha de Cintura auf der Grenze zwischen den beiden Stadtgemeinden Alvalade und Areeiro. Am Bahnhof enden und beginnen die Fertagus-Züge in Richtung Setúbal, außerdem halten und enden dort auch teilweise dort die Züge der CP-Linien Linha de Sintra sowie der Linha da Azambuja.
Der Bahnhof wurde am 18. Juni 1972 als ein einfacher Haltepunkt unter dem Namen Areeiro an der Linha de Cintura, der Ringstrecke um das Lissabonner Zentrum, eröffnet.
Um den wachsenden Ansprüchen gerecht zu werden und den ansteigenden Zugverkehr aufnehmen zu können, ließ der Infrastrukturbetreiber des portugiesischen Schienennetzes, die REFER, den Bahnhof zwischen 2002 und 2003 sanieren und erweitern. Die Sanierung des Bahnhofes war in das Gesamtprojekt des Ausbaus der Linha de Cintura eingebettet, in diesem Rahmen erhielt die Strecke beispielsweise auch zwei zusätzliche Gleise und einen komplett neuen Oberbau. Der Bahnhof besitzt seitdem zwei weitere Bahnsteige und einen langen Gang, der zur Avenida de Roma führt. Damit ergeben sich unter anderem auch bessere Umsteigemöglichkeiten zu den beiden U-Bahnhofstationen Roma und Areeiro. Ebenso ließ die REFER einen großen Park-and-Ride-Parkplatz errichten. Mit der Eröffnung des Bahnhofes im September 2003 verlängerte auch der private Zugbetreiber Fertagus den Zugverkehr vom Nachbarbahnhof Entrecampos nach Roma-Areeiro.
Der Bahnhof besitzt heute vier Bahnsteige, der Bahnsteig 1 ist 191 Meter lang, die Bahnsteige 2 und 3 234 Meter sowie der Bahnsteig 4 218 Meter.
Einzelnachweise
Weblinks
Informationen der Comboios de Portugal zum Bahnhof
Roma-Areeiro
Bauwerk in Alvalade (Lissabon)
Bauwerk in Areeiro
Avenida de Roma
Lisboa Roma-Areeiro
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Charles Pahud de Mortanges (La Haia, Països Baixos 1896 - íd. 1971) fou un genet neerlandès, guanyador de cinc medalles olímpiques en el concurs complet d'equitació.
Biografia
Va néixer el 13 de maig de 1896 a la ciutat de La Haia, població situada a la província d'Holanda Meridional.
Va morir a la seva residència de la Haia el 7 d'abril de 1971.
Carrera esportiva
Va participar, als 27 anys, en els Jocs Olímpics d'Estiu de 1924 realitzats a París (França), on va aconseguir guanyar la medalla d'or en la prova per equips del concurs complet i on a més finalitzà quart en la prova individual d'aquesta modalitat amb el cavall Johnny Walker. En els Jocs Olímpics d'Estiu de 1928 realitzats a Amsterdam (Països Baixos) aconseguí guanyar sengles medalles d'or en la prova individua i en la prova per equips amb el cavall Marcroix. En els Jocs Olímpics d'Estiu de 1932 realitzats a Los Angeles (Estats Units) aconseguí revalidar el seu títol individual i guanyà la medalla de plata en la prova per equips. En els Jocs Olímpics d'Estiu de 1936 realitzats a Berlín (Alemanya nazi) participà en les dues proves, si bé no finalitzà la prova per equips i fou desqualificat en la prova individual.
Enllaços externs
www.olympic.org - Charles Pahud de Mortanges
www.sports-reference.com - Charles Pahud de Mortanges
Esportistes de la Haia
Genets neerlandesos
Medallistes neerlandesos als Jocs Olímpics d'estiu de 1924
Medallistes neerlandesos als Jocs Olímpics d'estiu de 1928
Medallistes neerlandesos als Jocs Olímpics d'estiu de 1932
Morts a Leiden
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Q: Programmatically converting an integer into bits with graphical output I just stumbled upon this interesting question about "how to automatically draw tree diagrams of prime factorization with LaTeX" and it rang a bell.
I 'd like to create a command that displays the conversion of an integer value into a bits string (which otherwise is a tedious operation to do "by hand") to use when preparing the exams of FOundation of Computer Science. This command needs 2 parameters, the integer to convert (213, for instance) and the desired number of bits for the result. The command should also be able to convert negative values by using Two's complement. The following pictures for values 137 (basic problem), -136 (negative problem) and -17 (problem requiring an 8 bits solution) should help you understand what kind of result I would like to get.
As a plus, I would like to introduce two variables to hold the min and max value allowed so that I can get the translation of a random integer value in [min, max] if I call the above command omitting the integer value. One could do the same with the number of desired bits and introduce a variable to hold an increment (4, for instance) so that it generates results with 4 bits and if a number requires 5 bits, for example, it automatically returns a solution that uses 8 bits. Not to mention that with an additional parameter one could convert to octal, hexadecimal, etc.
The problem is that I don't understand Tikz and I have no idea how to make LaTeX do maths! I read this on integers in TeX with interest, but I still miss too many things. Can someone help please? Thanks in advance!
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"redpajama_set_name": "RedPajamaStackExchange"
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Q: Can't run cordova commands on Windows 10 I have created a new project application using Sencha Touch and I want to run it on my Android phone using cordova. I have installed cordova globally on my computer (Windows 10), but none of the commands related to cordova work. Whenever I try to run the create command, all I get is:
Node Commands
Syntax:
node {operator} [options] [arguments]
Parameters:
/? or /help - Display this help message.
list - List nodes or node history or the cluster
listcores - List cores on the cluster
view - View properties of a node
online - Set nodes or node to online state
offline - Set one or more nodes to the offline state
For more information about HPC command-line tools,
see http://go.microsoft.com/fwlink/?LinkId=120724.
The commands I tried to run are:
cordova create hello com.example.hello HelloWorld
and
cordova-cli create hello com.example.hello HelloWorld
but not even cordova -v works.
I must say that I have added all the necessary environment variables, tried running the commands using the absolute path, or right from the cordova folder in AppData\Roaming\npm and from most of its subfolders.
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{"url":"https:\/\/physics.stackexchange.com\/questions\/559023\/deriving-position-mathbfr-in-two-body-problem-with-composite","text":"# Deriving position $\\mathbf{r}$ in two-body problem with composite\n\nIn classical mechanics, we know that accelerations are oppositely directed and inversely proportional to the masses:\n\n$$m_1 \\mathbf{a}_1 = -m_2 \\mathbf{a}_2.$$\n\nLet's say that we have a three-body system, where none of the masses of the bodies are equal. If two of the bodies (say, body 2 and 3) form a composite, then, since $$m_1 \\mathbf{a}_1 = -m_2 \\mathbf{a}_2$$ must remain true, how do we know what the position $$\\mathbf{r}$$ of the composite is?\n\nI am told that it must be $$\\mathbf{r} = \\dfrac{m_2 \\mathbf{r}_2 + m_3 \\mathbf{r}_3}{m_2 + m_3}$$, but I don't understand how this can be derived from the basic equations of classical mechanics.\n\nIf I had to guess, I'd say that, since acceleration is the second derivative of position, we get something like\n\n$$m_1 \\ddot{\\mathbf{r}} = -(m_2 + m_3) \\ddot{\\mathbf{r}} \\Rightarrow -\\dfrac{m_1}{m_2 + m_3}\\ddot{\\mathbf{r}} = \\ddot{\\mathbf{r}}.$$\n\nThis looks similar to the correct derivation, so I'm guessing that I'm somewhat on the right track.\n\nI would greatly appreciate it if people would please take the time to explain how this is derived from the basic equations of classical mechanics.\n\n\u2022 The title mentions a 3 body problem, but the question is about the 2 body problem. Please edit and clarify. \u2013\u00a0John Alexiou Jun 12 '20 at 21:51\n\u2022 @ja72 oh, is it? It was referred to as a three-body problem. Does it become a two-body problem due to the composite? \u2013\u00a0The Pointer Jun 12 '20 at 21:52\n\u2022 Then it is just a two-body problem. You took away the degrees of freedom between two of the three bodies. It just confuses the issue here. Just ask about how the center of mass arises from the equations of motion on the two-body problem. \u2013\u00a0John Alexiou Jun 12 '20 at 21:58\n\u2022 @ja72 Doing further research on two-body problems, I found this en.wikipedia.org\/wiki\/\u2026 ${\\displaystyle {\\ddot {\\mathbf {R} }}\\equiv {\\frac {m_{1}{\\ddot {\\mathbf {x} }}_{1}+m_{2}{\\ddot {\\mathbf {x} }}_{2}}{m_{1}+m_{2}}}.}$ Clearly, this is the equation in question. However, the Wikipedia article (1) assumes it by definition, which is not clarifying for us, and (2) for some reason has the acceleration $\\ddot{\\mathbf{r}}$ instead of the position $\\mathbf{r}$, which I find confusing. \u2013\u00a0The Pointer Jun 12 '20 at 22:51\n\u2022 @ja72 I found it here as well: en.wikipedia.org\/wiki\/Center_of_mass#Barycentric_coordinates , hyperphysics.phy-astr.gsu.edu\/hbase\/cm.html \u2013\u00a0The Pointer Jun 12 '20 at 23:30\n\nThe two composite bodies, can be reduced down to one body with combined mass, and the location where forces are applied being the barycenter (the center of mass). Then we have the following two body problem.\n\nConsider two free massive bodies located at $$\\boldsymbol{r}_1$$ and $$\\boldsymbol{r}_2$$ at some moment in time. A central force exists $$\\boldsymbol{F}(r)$$ that is applied in equal and opposite measure to each body, that depends only on the distance $$r$$. The equations of motion are\n\n\\begin{aligned} m_1 \\ddot{\\boldsymbol{r}}_1 & = -\\boldsymbol{F}(r) \\\\ m_2 \\ddot{\\boldsymbol{r}}_2 & = \\boldsymbol{F}(r) \\end{aligned} \\tag{1}\n\nwhere $$r = \\sqrt{ (\\boldsymbol{r}_2-\\boldsymbol{r}_1) \\cdot ( \\boldsymbol{r}_2 - \\boldsymbol{r}_1)} \\tag{2}$$\n\nThis is a hard problem to solve, as $$r$$ depends on the two positions.\n\nNow let us do a change of variables. I am going to pick two vector quantities, and then I am going to show how this specific choice diagonalizes the equations of motion and makes them solvable.\n\n\\begin{aligned} \\boldsymbol{\\Delta r} & = \\boldsymbol{r}_2 - \\boldsymbol{r}_1 \\\\ \\boldsymbol{r}_C & = \\frac{m_1 \\boldsymbol{r}_1 + m_2 \\boldsymbol{r}_2}{m_1 +m_2} \\end{aligned} \\tag{3}\n\nThe first is the vector separation and the second is the center of mass. You can immediately restate the distance as $$r=\\sqrt{ \\boldsymbol{\\Delta r} \\cdot \\boldsymbol{\\Delta r} }$$.\n\nNow use (3) to solve for the position vectors\n\n\\begin{aligned} \\boldsymbol{r}_1 & = \\boldsymbol{r}_C + \\frac{m_1}{m_1+m_2} \\boldsymbol{\\Delta r} \\\\ \\boldsymbol{r}_2 &= \\boldsymbol{r}_C - \\frac{m_1}{m_1+m_2} \\boldsymbol{\\Delta r} \\end{aligned} \\tag{4}\n\nNow consider the accelerations\n\n\\begin{aligned} \\ddot{\\boldsymbol{r}}_1 & = \\ddot{\\boldsymbol{r}}_C + \\frac{m_1}{m_1+m_2} \\ddot{\\boldsymbol{\\Delta r}} \\\\ \\ddot{\\boldsymbol{r}}_2 &= \\ddot{\\boldsymbol{r}}_C - \\frac{m_1}{m_1+m_2} \\ddot{\\boldsymbol{\\Delta r}} \\end{aligned} \\tag{5}\n\nUse (5) in (1) and solve for $$\\ddot{\\boldsymbol{r}}_C$$ and $$\\dot{\\boldsymbol{\\Delta r}}$$. The solution is\n\n\\begin{aligned} \\ddot{ \\boldsymbol{r}}_C & = 0 \\\\ \\ddot{\\boldsymbol{\\Delta r}} &= \\left( \\tfrac{1}{m_1} + \\tfrac{1}{m_2} \\right) F(r) \\end{aligned} \\tag{6}\n\nSo half the solution is the center of mass moves with constant velocity. $$\\dot{\\boldsymbol{r}}_C = \\text{(const.)}$$. We just found the special point in space which helps us solve this problem.\n\nThe rest of the solution is really an equation only in terms of $$\\boldsymbol{\\Delta r}$$ which can be solved for special cases of $$\\boldsymbol{F}(r)$$.\n\n\u2022 But here you're assuming $\\mathbf{r} = \\dfrac{m_2 \\mathbf{r}_2 + m_3 \\mathbf{r}_3}{m_2 + m_3}$ in the first place, right? My question was about how to derive this in the first place, using the basic force equations of classical mechanics. \u2013\u00a0The Pointer Jun 12 '20 at 23:15\n\u2022 The logic is this: If you use $\\boldsymbol{r}_C$ then the problem becomes solvable. therefore it is an important point in space. But as I said, it is all a trick. It is a special coordinate system where $$\\sum_i m_i \\boldsymbol{r}_i = 0$$ is true. You can reverse the logic and start from the mass balance above and find $\\boldsymbol{r}_C$, if that is what you wanted. \u2013\u00a0John Alexiou Jun 13 '20 at 0:47\n\u2022 I am trying to carefully follow your reasoning. Can you please explain how (4) is valid? \u2013\u00a0The Pointer Jun 16 '20 at 2:49\n\u2022 Take the two equations in (3) and solve for $r_1$ and $r_2$. Use $r_2 = r_1 + \\Delta r$ in the first expression to get $r_c = r_1 + \\Delta r \\frac{m_2}{m_1+m_2}$. Solve for $r_1$ and then back substitute to get $r_2$. \u2013\u00a0John Alexiou Jun 21 '20 at 1:08","date":"2021-08-03 19:30:43","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\": 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\": 22, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.9630438089370728, \"perplexity\": 372.2391294752183}, \"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\/1627046154471.78\/warc\/CC-MAIN-20210803191307-20210803221307-00239.warc.gz\"}"}
| null | null |
{"url":"https:\/\/zbmath.org\/?q=an:1133.47050","text":"zbMATH \u2014 the first resource for mathematics\n\nExamples\n Geometry Search for the term Geometry in any field. Queries are case-independent. Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact. \"Topological group\" Phrases (multi-words) should be set in \"straight quotation marks\". au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted. Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff. \"Quasi* map*\" py: 1989 The resulting documents have publication year 1989. so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14. \"Partial diff* eq*\" ! elliptic The not-operator ! eliminates all results containing the word elliptic. dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles. py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses). la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.\n\nOperators\n a & b logic and a | b logic or !ab logic not abc* right wildcard \"ab c\" phrase (ab c) parentheses\nFields\n any anywhere an internal document identifier au author, editor ai internal author identifier ti title la language so source ab review, abstract py publication year rv reviewer cc MSC code ut uncontrolled term dt document type (j: journal article; b: book; a: book article)\nIterative methods for strict pseudo-contractions in Hilbert spaces. (English) Zbl\u00a01133.47050\nThis article deals with two iterative algorithms of finding a common fixed points for $N$ strict pseudo-contractions $\\{T_i\\}_{i=1}^N$ defined on a closed convex subset $C$ of a real Hilbert space $H$ (an operator $T: C \\to C$ is a strict pseudo-contraction, if there exists a constant $0 \\le k < 1$ such that $\\Vert Tx - Ty\\Vert ^2 \\le \\Vert x - y\\Vert ^2 + k\\Vert (I - T)x - (I - T)y\\Vert ^2$). The first algorithm, called parallel, is defined by the formula $$x_{n+1} = \\alpha_nx_n + (1 - \\alpha_n) \\sum_{i=1}^N \\lambda_i^{(n)} T_ix_n, \\ x_0 \\in C,\\ \\lambda_i^{(n)} > 0, \\ \\lambda_1^{(n)} + \\cdots + \\lambda_N^{(n)} = 1;\\tag1$$ the second one, called cyclic, by the formula $$x_{n+1} = \\alpha_nx_n + (1 - \\alpha) T_{[n]}x_n, \\quad x_0 \\in C, \\quad T_{[n]} = T_i, \\ i = n(\\text{ mod} \\, N), \\ 1 \\le i \\le N.\\tag2$$ The main results describe (provided that $F = \\bigcap_{i=1}^N \\text{Fix} (T_i) \\ne \\emptyset$) conditions on the control sequence $\\{\\alpha_n\\}$ so that the approximations $x_n$ converge weakly to a common fixed point of $\\{T_i\\}_{i=1}^N$. At the end of the article, some modifications of algorithms (1) and (2) are proposed; it is proved that approximations $x_n$ for these modified algorithms converge strongly to $P_Fx_0$, where $P_F$ is the nearest point projection from $H$ onto $F$.\n\nMSC:\n 47J25 Iterative procedures (nonlinear operator equations) 47H09 Mappings defined by \u201cshrinking\u201d properties 65J15 Equations with nonlinear operators (numerical methods)\nFull Text:\nReferences:\n [1] Bauschke, H.: The approximation of fixed points of compositions of nonexpansive mappings in Hilbert space. J. math. Anal. appl. 202, 150-159 (1996) \u00b7 Zbl\u00a00956.47024 [2] Browder, F. E.; Petryshyn, W. V.: Construction of fixed points of nonlinear mappings in Hilbert spaces. J. math. Anal. appl. 20, 197-228 (1967) \u00b7 Zbl\u00a00153.45701 [3] Byrne, C.: A unified treatment of some iterative algorithms in signal processing and image reconstruction. Inverse problems 20, 103-120 (2004) \u00b7 Zbl\u00a01051.65067 [4] Genel, A.; Lindenstrauss, J.: An example concerning fixed points. Israel J. Math. 22, 81-86 (1975) \u00b7 Zbl\u00a00314.47031 [5] Goebel, K.; Kirk, W. A.: Topics in metric fixed point theory. Cambridge studies in advanced mathematics 28 (1990) \u00b7 Zbl\u00a00708.47031 [6] Goebel, K.; Reich, S.: Uniform convexity, hyperbolic geometry, and nonexpansive mappings. (1984) \u00b7 Zbl\u00a00537.46001 [7] G\u00fcler, O.: On the convergence of the proximal point algorithm for convex optimization. SIAM J. Control optim. 29, 403-419 (1991) \u00b7 Zbl\u00a00737.90047 [8] Halpern, B.: Fixed points of nonexpanding maps. Bull. amer. Math. soc. 73, 957-961 (1967) \u00b7 Zbl\u00a00177.19101 [9] Ishikawa, S.: Fixed points by a new iteration method. Proc. amer. Math. soc. 44, 147-150 (1974) \u00b7 Zbl\u00a00286.47036 [10] Kamimura, S.; Takahashi, W.: Strong convergence of a proximal-type algorithm in a Banach space. SIAM J. Optim. 13, 938-945 (2003) \u00b7 Zbl\u00a01101.90083 [11] Kim, T. H.; Xu, H. K.: Strong convergence of modified Mann iterations. Nonlinear anal. 61, 51-60 (2005) \u00b7 Zbl\u00a01091.47055 [12] Kim, T. H.; Xu, H. K.: Strong convergence of modified Mann iterations for asymptotically nonexpansive mappings and semigroups. Nonlinear anal. 64, 1140-1152 (2006) \u00b7 Zbl\u00a01090.47059 [13] Lions, P. L.: Approximation de points fixes de contractions. C. R. Acad. sci. S\u00e8r. A--B Paris 284, 1357-1359 (1977) \u00b7 Zbl\u00a00349.47046 [14] Mann, W. R.: Mean value methods in iteration. Proc. amer. Math. soc. 4, 506-510 (1953) \u00b7 Zbl\u00a00050.11603 [15] Marino, G.; Xu, H. K.: Convergence of generalized proximal point algorithms. Comm. pure appl. Anal. 3, 791-808 (2004) \u00b7 Zbl\u00a01095.90115 [16] G. Marino, H.K. Xu, Weak and strong convergence theorems for strict pseudo-contractions in Hilbert spaces, J. Math. Anal. Appl. (2006), in press (doi:10.1016\/j.jmaa.2006.06.055). Available online 27 July 2006 [17] Matinez-Yanes, C.; Xu, H. K.: Strong convergence of the CQ method for fixed point processes. Nonlinear anal. 64, 2400-2411 (2006) \u00b7 Zbl\u00a01105.47060 [18] Nakajo, K.; Takahashi, W.: Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups. J. math. Anal. appl. 279, 372-379 (2003) \u00b7 Zbl\u00a01035.47048 [19] O\u2019hara, J. G.; Pillay, P.; Xu, H. K.: Iterative approaches to finding nearest common fixed points of nonexpansive mappings in Hilbert spaces. Nonlinear anal. 54, 1417-1426 (2003) \u00b7 Zbl\u00a01052.47049 [20] O\u2019hara, J. G.; Pillay, P.; Xu, H. K.: Iterative approaches to convex feasibility problems in Banach spaces. Nonlinear anal. 64, 2022-2042 (2006) \u00b7 Zbl\u00a01139.47056 [21] Reich, S.: Weak convergence theorems for nonexpansive mappings in Banach spaces. J. math. Anal. appl. 67, 274-276 (1979) \u00b7 Zbl\u00a00423.47026 [22] Reich, S.: Strong convergence theorems for resolvents of accretive operators in Banach spaces. J. math. Anal. appl. 75, 287-292 (1980) \u00b7 Zbl\u00a00437.47047 [23] Scherzer, O.: Convergence criteria of iterative methods based on Landweber iteration for solving nonlinear problems. J. math. Anal. appl. 194, 911-933 (1991) \u00b7 Zbl\u00a00842.65036 [24] Shioji, N.; Takahashi, W.: Strong convergence of approximated sequences for nonexpansive mappings in Banach spaces. Proc. amer. Math. soc. 125, 3641-3645 (1997) \u00b7 Zbl\u00a00888.47034 [25] Solodov, M. V.; Svaiter, B. F.: Forcing strong convergence of proximal point iterations in a Hilbert space. Math. program. Ser. A 87, 189-202 (2000) \u00b7 Zbl\u00a00971.90062 [26] Tan, K. K.; Xu, H. K.: Approximating fixed points of nonexpansive mappings by the Ishikawa iteration process. J. math. Anal. appl. 178, No. 2, 301-308 (1993) \u00b7 Zbl\u00a00895.47048 [27] Tan, K. K.; Xu, H. K.: Fixed point iteration processes for asymptotically nonexpansive mappings. Proc. amer. Math. soc. 122, 733-739 (1994) \u00b7 Zbl\u00a00820.47071 [28] Wittmann, R.: Approximation of fixed points of nonexpansive mappings. Arch. math. 58, 486-491 (1992) \u00b7 Zbl\u00a00797.47036 [29] Xu, H. K.: Iterative algorithms for nonlinear operators. J. London math. Soc. 66, 240-256 (2002) \u00b7 Zbl\u00a01013.47032 [30] Xu, H. K.: Remarks on an iterative method for nonexpansive mappings. Comm. appl. Nonlinear anal. 10, No. 1, 67-75 (2003) \u00b7 Zbl\u00a01035.47035 [31] Xu, H. K.: Strong convergence of an iterative method for nonexpansive mappings and accretive operators. J. math. Anal. appl. 314, 631-643 (2006) \u00b7 Zbl\u00a01086.47060 [32] Xu, H. K.: Strong convergence of approximating fixed point sequences for nonexpansive mappings. Bull. austral. 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| null | null |
<?php
namespace Publero\Component\CodeGenerator\Tests;
use Publero\Component\CodeGenerator\Md5HashGenerator;
class Md5HashGeneratorTest extends \PHPUnit_Framework_TestCase
{
public function testGenerate()
{
$generator = new Md5HashGenerator();
$codes = array();
for ($i = 0; $i < 10; $i++) {
$code = $generator->generate();
$this->assertRegExp('/^[a-f0-9]{32}$/', $code);
$this->assertNotContains($code, $codes);
$codes[] = $code;
}
}
}
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 7,974
|
\section{Introduction}\label{sec:intro}
Word embeddings represent words and phrases in continuous low-dimensional vector spaces. They are usually trained with neural language models or word collocations~\cite{bengio, collobert2, mikolovb, levy}, such that similar assignments in a space reflect similar usage patterns. The rise of monolingual embeddings such as Word2Vec~\cite{mikolovb}, GloVe~\cite{glove}, and FastText~\cite{fasttext1}, coupled with the need to transfer lexical knowledge across languages, has also led to the development of cross-lingual word embeddings, in which different languages share a single distributed representation and are mapped into the same vector space. Such methods use different bilingual supervision signals (at the level of words, sentences, or documents) with varying levels of strength~\cite{ruder}.
A central task in the study of word embeddings is finding metrics to evaluate their quality. These metrics can either be \textit{extrinsic}, where embeddings are used as input features for downstream NLP tasks and evaluated on their performance, or \textit{intrinsic}, where embeddings are directly tested for how well they capture syntactic or semantic properties in their own right~\cite{qiu}. Extrinsic methods are not always feasible for low-resource languages due to a lack of annotated data. Moreover, downstream model components can be fine-tuned to achieve higher performance on certain tasks without necessarily indicating improvement in the semantic representation of words in an embedding space~\cite{leszczynski}.
This paper presents \textit{categorical modularity}, a low-resource intrinsic evaluation metric for both monolingual and cross-lingual word embeddings based on the notion of graph modularity. The underlying principle is that \textit{in good embeddings, words in the same semantic category should be closer to each other than to words in different categories}. We quantify this by building the $k$-nearest neighbor graph with a fixed set of words' semantic categories and computing the graph's modularity for a given embedding space. \textit{Modularity} measures the strength of division of a graph with densely connected groups of vertices, with sparser connections between groups~\cite{newman}.
We source our semantic categories from ~\citet{binder}. In contrast to other semantic and ontological categories in the literature, these have been motivated by a set of experiential attributes with neurobiological consistency, covering sensory, motor, spatial, temporal, affective, social, and cognitive dimensions. We refer to these attributes collectively as \textit{Binder categories}. The resulting dataset consists of 500 English words, each labeled with three categories at three levels of semantic granularity. For example, the word \textit{chair} belongs to \textit{Concrete Objects} (Level~1), \textit{Artifacts} (Level~2), and \textit{Furniture} (Level~3). 442 words are pulled from Binder, on top of which we add a few words to even out distributions of categories and replace a few English-specific words with words that are more easily translated to non-English languages.
We then translate these 500 English words into 28 more languages, selected based on their availability in the form of pre-trained vectors from the MUSE library~\cite{muse}. We produce 300-dimensional embeddings for these words using three popular embedding models: the monolingual FastText~\cite{fasttext1} and subs2vec~\cite{subs2vec} models and the cross-lingual MUSE~\cite{muse} model. Using these embeddings, we obtain the nearest-neighbor sets among the 500 words within each (language, model) pair and use those relationships to calculate a modularity score for the pair. We compare modularity scores to performance on three downstream tasks: sentiment analysis (monolingual classification), word similarity (monolingual regression), and word-level bilingual lexicon induction (BLI, cross-lingual regression) both to and from English. We obtain moderate to strong positive correlations on all three tasks, with slightly stronger results on the monolingual tasks. We also provide an analysis of correlations broken down by individual model and explore potential meta-predictive properties of categorical modularity.
We further show that estimating modularity on Binder categories yields relevant information that cannot simply be derived from naturally occurring distributions of word clusters in embedding spaces. We show this by replicating all three downstream task correlation analyses with modularity scores based on clusters obtained with unsupervised community detection methods~\cite{clauset}, which we henceforth refer to as \textit{unsupervised clusters}.
After establishing the utility of categorical modularity, we show some of its use cases for comparing and selecting models for specific NLP problems, and we discuss preliminary results about the individual categories we find to be most predictive of downstream task performance.
Our code and data are available to the public.\footnote{\url{https://github.com/enscma2/categorical-modularity}}
\section{Related Work}
\subsection{Word Embedding Evaluation Metrics}
While word embeddings have become crucial tools in NLP, there is still little consensus on how to best evaluate them. Evaluation methods commonly fall into two categories: those motivated by an \textit{extrinsic} downstream task and those motivated by the \textit{intrinsic} study of the nature of semantics and the cognitive sciences~\cite{survey}. Intrinsic and extrinsic metrics do not always align, as some models have high quality as suggested by intrinsic scores but low extrinsic performance, and vice versa~\cite{schnabel, glavas}.
Some commonly used methods of extrinsic evaluation include named entity recognition~\cite{collobert1} ---including the datasets \textit{CoNLL-2002} and \textit{CoNLL-2003}~\cite{tjong}---, sentiment analysis~\cite{schnabel}, semantic role labeling, and part-of-speech tagging~\cite{collobert1}. Intrinsic evaluation methods include word semantic similarity~\cite{baroni}, concept categorization~\cite{baroni}, and experiments on neural activation patterns~\cite{sogaard}.
Our categorical modularity metric is inspired by ~\citet{modularity}. They study the modularity of cross-lingual embeddings based on the premise that different languages are well-mixed in good cross-lingual embeddings and thus have low modularity with respect to language. Our metric improves upon the modularity proposed in ~\citet{modularity} by overcoming the problem caused by low modularity potentially occurring with a purely random distribution of word vectors and being mistaken for high embedding quality, as it is unlikely for a random distribution to coincidentally have highly modular clusters corresponding to Binder categories. Moreover, our metric is able to evaluate both monolingual and cross-lingual word embeddings and allow for comparisons between these types of embeddings (e.g., FastText and MUSE), and it incorporates cognitive information through the use of brain-based semantic categories.
\subsection{Cognitive Approaches to NLP}
Recent work on word embeddings has explored the connections between NLP word representations and cognitively grounded representations of words. Such connections enrich both computational and neuroscientific research: external cognitive signals can enhance the capacity of artificial neural networks to understand language, while language processing in neural networks can shed light on how the human brain stores, categorizes, and processes words~\cite{muttenthaler}.
Cognitive approaches to lexical semantics propose a model in which words are defined by how they are organized in the brain~\cite{lakoff}. Based on this premise,~\citet{nora} propose \textit{CogniVal}, a framework for word embedding evaluation with cognitive language processing data. They evaluate six different word embeddings against a combination of 15 cognitive data sources acquired via eye-tracking, electroencephalography (EEG), and functional magnetic resonance imaging (fMRI). In a similar line of work, both~\citet{sogaard} and~\citet{beinborn} evaluate word embeddings using fMRI datasets.
The use of cognitive data in NLP goes well beyond the evaluation of word embeddings. ~\citet{utsumi} uses the neurosemantically inspired categories from~\citet{binder} to identify the knowledge encoded in word vectors. Among other conclusions, they find that the prediction accuracy of cognitive and social information is higher than that of perceptual and spatiotemporal information.
\section{Modularity and \boldmath$k$-NN Graphs}\label{sec:graphs}
The concept of modularity has origins in the field of network science, as first introduced by Newman~\cite{newman}. The goal of the modularity measure is to quantify the strength of the division of a network into clusters. Usually, such networks are represented with graphs. Intuitively, the modularity of a graph measures the difference between the fraction of edges in the graph that connect two nodes of the same category and the expected corresponding fraction if the graph's edges were distributed at random. Thus, the higher the proportion of edges between nodes that belong to the same category, the higher the modularity.
In our case, we construct the pertinent graph with the $k$-nearest neighbors algorithm. Given a set $S_w$ of $N$ words and a set $S_c$ of categories such that each of the $N$ words belongs to exactly one of the categories in $S_c$, we map each of the $N$ words into a $d$-dimensional word embedding vector space and obtain a $d$-dimensional vector for each word. For each pair $(w_i, w_j)$, where $w_i, w_j \in S_w$ and $1 \leq i, j \leq |S_w|$, with corresponding $d$-dimensional vectors $v_i$ and $v_j$, we compute their cosine similarity (the cosine of the angle between them), which we denote by \texttt{similarity}$(i, j)$.
We create a matrix $M_D$ of dimensions $|S_w| \times |S_w|$, where entry $(M_D)_{i, j}$ is $\texttt{similarity}(i, j)$. For a given $k \in \mathbb{Z}_{>0}$, we build the $|S_w| \times |S_w|$ $k$-nearest neighbor matrix (denoted $k$-NNM) as follows: entry $(i, j)$ of $k$-NNM is equal to $1$ if and only if word $j$ is one of the $k$ nearest neighbors of word $i$ (i.e., if \texttt{similarity}$(i, j)$ is among the $k$ largest cosine similarities between $i$ and all other words in $S_w$). We note that $M_D$ and $k$\nobreakdash-NNM are not necessarily symmetric, as word $i$ being the $k$\nobreakdash-th nearest neighbor of word~$j$ does not imply the reverse. Finally, we define the $k$-NN graph of $S_w$ as the graph defined by $k$-NNM viewed as an adjacency matrix. We can now describe how to compute the modularity score following the schema in~\citet{modularity}.
Let $d_i$ denote the degree of node $i$, that is, $d_i = \sum_j (k$-NNM$)_{i, j}$, and let $g_i$ denote the category of word $i$. For each category $c \in S_c$, the expected number of edges within $c$ is
\begin{equation}
a_c = \dfrac{1}{2m} \sum_i d_i \, I[g_i = c],
\end{equation}
where $m$ is the total number of edges in the $k$-NN graph and $I$ is the indicator function that evaluates to 1 if the argument is true and to 0 otherwise.
The fraction of edges $e_c$ that connect words of the same semantic category $c$ is
\begin{equation}
e_c = \dfrac{1}{2m} \sum_{i, j} (k\textrm{-NNM})_{i, j} \, I[g_i = c] \, I[g_j = c].
\end{equation}
By weighting the $|S_c|$ different semantic categories together, we calculate the overall modularity $Q$ as follows:
\begin{equation}
Q = \sum_{c = 1}^{|S_c|} (e_c - a_c^2).
\end{equation}
Finally, we normalize $Q$ by setting
\begin{equation}\label{eq:qnorm}
Q_{max} = 1 - \sum_{c=1}^N a_c^2, \quad Q_{norm} = \dfrac{Q}{Q_{max}}.
\end{equation}
In our setting, $Q_{norm}$ indicates the modularity score of one (language, model) pair overall, but we denote by $Q_c$ the modularity of said (language, model) pair with respect to category $c \in S_c$. The definition of $Q_c$ (normalized) is deduced from Equation~\ref{eq:qnorm}:
\begin{equation}\label{eq:Qc}
Q_c = \dfrac{e_c - a_c^2}{Q_{max}}.
\end{equation}
A higher value of $Q_{norm}$ indicates that a higher number of words that belong to the same categories appear connected in the $k$-NN graph. In Sections~\ref{sec:modularity} and \ref{sec:experiments}, we analyze the values $Q_{norm}$ for each of the languages, and in Section~\ref{sec:futurework}, we make some observations about the different values of $Q_c$.
\begin{figure}%
\centering
\subfloat[][\centering A high-modularity semantic $k$-NN graph.]{\includegraphics[width=6.2cm]{high_modularity.png}}%
\qquad
\subfloat[][\centering A low-modularity semantic $k$-NN graph.]{\includegraphics[width=5.6cm]{low_modularity.png}}%
\caption{A toy visualization of the meaning of categorical modularity with some words pertaining to the Binder categories \textit{Body Parts} (purple ovals), \textit{Plants} (peach rectangles), and \textit{Emotions} (green rhombi). Dotted edges connect nodes of different categories, while solid edges connect nodes of the same category.
\label{fig:example}%
\end{figure}
In our conclusions about how our categorical modularity scores correlate with downstream task performance, we also want to prove that our selected neurosemantic-based categories are non-trivial and are better predictors than the unsupervised clusters that emerge from the embeddings. To find these clusters, we use the Clauset-Newman-Moore greedy modularity method~\cite{clauset}. This algorithm iteratively joins the pair of communities that most increases modularity until no such pair exists. For each value of $k$, we obtain the unsupervised communities in this manner and compute their modularity scores. In Section~\ref{sec:experiments}, we show that Binder categories are significantly better predictors than the unsupervised clusters using the same set of 500 words.
\section{Dataset}
In this section, we define the sets $S_N$ and $S_c$ of words and their semantic categories, respectively, that we use to compute categorical modularity scores for 29 languages.\footnote{The 29 languages are: Arabic, Bulgarian, Catalan, Croatian, Czech, Danish, Dutch, English, Estonian, Finnish, French, Greek, Hebrew, Hungarian, Indonesian, Italian, Macedonian, Norwegian, Polish, Portuguese, Romanian, Russian, Slovak, Slovenian, Spanish, Swedish, Turkish, Ukrainian, and Vietnamese.} As outlined in Section~\ref{sec:intro}, our motivation to take a cognitive approach in the study of word embeddings prompts us to use words and categories that reflect a brain-based computational model of semantic representation as in~\citet{binder}. We have 500 words (comprised of nouns, adjectives, and verbs) with 3 levels of categories, from most general (Level~1) to most specific (Level~3). Each word is tagged with 3 categories (one per level), which are listed in Table~\ref{table:binder}. After lifting 442 English words from Binder and adjusting the word set to optimize evenness of distribution across categories and translatability of concepts across languages, we manually translate the words to the 28 non-English languages\footnote{For languages with which we were not familiar, we solicited translations from colleagues, whom we compensated fairly for this work.} mentioned in footnote 2.
\begin{table}[h!]
\centering
\begin{tabular}{ |p{7cm}| }
\hline
\setstretch{0.9}
{\footnotesize
\textbf{Level 1.} Concrete Objects, Concrete Events, Abstract Entities,
Concrete Actions, Abstract Actions, States, Abstract Properties, Physical Properties.}
\\
\hline
\setstretch{0.9}
{\footnotesize
\textbf{Level 2.} Living Things, Other Natural Objects, Artifacts,
Social Events, Nonverbal Sound Events, Weather Events, Miscellaneous, Concrete Events, Abstract Constructs, Cognitive Entities, Emotions,
Social Constructs, Time Periods, Body Actions, Locative Change Actions,
Social Actions, Miscellaneous Actions, Abstract Actions,
States, Abstract Properties, Physical Properties.}
\\
\hline
\setstretch{0.9}
{\footnotesize
\textbf{Level 3.} Animals, Body Parts, Humans, Human Groups, Plants,
Natural Scenes, Miscellaneous Natural Objects, Furniture, Hand Tools, Manufactured Foods, Musical Instruments, Places/Buildings, Vehicles, Miscellaneous Artifacts, Social Events, Nonverbal Sound Events, Weather, Events, Miscellaneous Concrete Events, Abstract Constructs, Cognitive Entities, Emotions, Social Constructs, Time Periods, Body Actions, Locative Change Actions, Social Actions, Miscellaneous Actions, Abstract Actions, States, Abstract Properties, Physical Properties.}
\\
\hline
\end{tabular}
\caption{Three levels of Binder categories.}
\label{table:binder}
\end{table}
\section{General Categorical Modularity}\label{sec:modularity}
\label{sec:categorical}
With the dataset of 500 words that belong to three levels of semantic categories, we compute the modularity scores of each of the 29 languages for each of the three word embedding models (which we refer to as 87 (language, model) pairs): FastText,\footnote{\url{https://fasttext.cc/docs/en/crawl-vectors.html}} MUSE,\footnote{\url{https://github.com/facebookresearch/MUSE\#download}} and subs2vec.\footnote{\url{https://github.com/jvparidon/subs2vec}} We briefly summarize the properties of each of these embeddings.
\textbf{FastText.} Monolingual embeddings for 157 languages trained on Common Crawl and Wikipedia that use CBOW with position-weights and character $n$-grams~\cite{fasttext1}.
\textbf{MUSE.} Cross-lingual embeddings resulting from the alignment of 30 FastText embeddings into a common space under the supervision of ground-truth bilingual dictionaries~\cite{muse}.
\textbf{subs2vec.} Monolingual embeddings for 55 languages trained on the OpenSubtitles corpus of speech transcriptions from television shows and movies using the FastText implementation of the skipgram algorithm~\cite{subs2vec}. The authors claim that subtitles are closer to the human linguistic experience~\cite{subs2vec}.
Information about the sizes of each (language, model) pair can be found in Appendix~\ref{app:b}. For each pair, we build the $k$-NN graph and compute modularity for different values of $k$ and different levels of categories, which we treat as our 2 hyperparameters. We consider small values for $k$ (namely $k \in \{2, 3, 4\}$) due to the fact that categories such as \textit{States} have as few as 4 words.
\section{Downstream Task Experiments}\label{sec:experiments}
We test the reliability of categorical modularity by running a few downstream tasks and computing the Spearman rank correlations between categorical modularity scores and performance on these tasks.
After determining the optimal set of hyperparameters ($k$ and level of semantic categories) for each task, we then compare the correlation produced by that set of hyperparameters with the correlation produced by the corresponding value of $k$ with the modularity of the unsupervised clusters constructed by the community detection algorithm described in Section~\ref{sec:graphs} to establish the non-triviality of the predictive properties of these chosen semantic categories. Table~\ref{table:spearman} provides a summary of correlation values for four tasks: movie review sentiment analysis (Sentiment), word similarity (WordSim), bilingual lexicon induction from English (BLI from), and bilingual lexicon induction to English (BLI to). Appendix~\ref{sec:appa} contains full tables with the correlation results. A visual summary of the results can be found in Figure \ref{fig:main}.
\begin{figure*}[h!]
\centering
\includegraphics[width=\linewidth]{chb_main_nheb_h.png}
\caption{Summary of modularity vs performance metrics across tasks. Each language is represented with its 2-letter ISO 639-1 code. Hebrew, an outlier on the low end, is not included in this plot. Full modularity and performance data is included in our public GitHub repository.}
\label{fig:main}
\end{figure*}
\begin{table}[h!]
\centering
\begin{tabular}{ccccc}
\hline
\textbf{Task} & $\mathbf{\rho}$ & $\mathbf{\rho_{ft}}$ & $\mathbf{\rho_m}$ & $\mathbf{\rho_s}$ \\[0.05cm]
\hline
Sentiment & 0.54 & 0.44 & 0.68 & 0.46 \\
WordSim & 0.71 & 0.59 & 0.34 & 0.80 \\
BLI from & 0.55 & 0.40 & 0.54 & 0.76 \\
BLI to & 0.50 & 0.29 & 0.56 & 0.82 \\
\hline
\end{tabular}
\caption{Summary of Spearman correlations of categorical modularity with downstream task performance for Binder categories, aggregated across all models ($\mathbf{\rho}$) and broken down within FastText ($\mathbf{\rho_{ft}}$), MUSE ($\mathbf{\rho_m}$), and subs2vec ($\mathbf{\rho_s}$).}
\label{table:spearman}
\end{table}
\subsection{Sentiment Analysis}\label{sec:sentiment}
We first test our modularity scores through correlations with performance on the binary classification task of sentiment analysis, where the input is a movie review and the output is a binary label that corresponds to either positive or negative sentiment for that review. For this task, our data consists of $5{,}000$ randomly selected positive movie reviews and $5{,}000$ randomly selected negative reviews from the IMDB Movie Reviews dataset~\cite{imdb}. We randomly partition these $10{,}000$ reviews into 80\% training and 20\% testing data. Because this dataset is only available in English, we use the Google Translate API\footnote{\url{https://pypi.org/project/google-trans-new/}} to translate the data to 15 more languages (Arabic, Bulgarian, Catalan, Croatian, Czech, Danish, Dutch, Estonian, Finnish, French, Greek, Hebrew, Hungarian, Indonesian, and Italian) for a total of $n = 48$ observations. The languages and the dataset size of $10{,}000$ are chosen due to Google Translate API rate limits.
For each (language, model) pair, we convert the raw text of each review to a 300-dimensional embedding vector. We use the built-in black-box position-weighted continuous bag-of-words embedding model for FastText and subs2vec~\cite{fasttext1}, and we use a simple mean of individual word embeddings for MUSE, as the MUSE library does not have multi-word phrase embeddings built into its functionality. Using a vanilla linear support vector machine model with scikit learn's default settings,\footnote{\url{https://scikit-learn.org/stable/modules/svm.html}} we run the task on each language-model pair 30 times and record the mean accuracy and precision scores for each pair. We then calculate the Spearman correlations of each of the 9 modularity scores with both the accuracy and precision values. Furthermore, we analyze the overall merged correlations (taking all 48 data points for a given modularity score and performance metric) as well as the correlations within models (taking only the 16 data points within each single model), giving us a total of 72 Spearman correlation values.
We find that the optimal set of hyperparameters is Level 3 categories with $k = 2$, which gives a Spearman correlation of $\mathbf{\rho} = 0.54$ with the accuracy metric. Breaking it down by individual model, we have $\mathbf{\rho_{ft}} = 0.44$ for FastText, $\mathbf{\rho_m} = 0.68$ for MUSE, and $\mathbf{\rho_s} = 0.46$ for subs2vec. For $k = 2$, the correlations of unsupervised clusters with accuracy are $\mathbf{\rho} = 0.09$ for all 48 observations merged, $\mathbf{\rho_{ft}} = 0.1$, $\mathbf{\rho_m} = 0.4$, and $\mathbf{\rho_s} = 0.35$, providing evidence that Binder categories contain non-trivial predictive information that is not present in naturally emerging clusters.
\subsection{Word Similarity}\label{sec:wordsim}
Our next downstream task is the monolingual regression task of word similarity, in which the input is two words in one language and the output is a real number between 0 and 4 representing how similar the two words are (a higher score represents a greater degree of similarity). We use the English, Italian, and Spanish word pair datasets from SemEval-2017~\cite{camacho}, and we use the same Google Translate API from Section~\ref{sec:sentiment} to translate the English dataset into the remaining 26 languages. Each language's dataset then has 500 word pairs, which we randomly split into 400 training pairs and 100 testing pairs for each trial.
Given a language and a model, we take each word pair, compute the 300-dimensional embeddings of both words, and calculate the Euclidean distance, Manhattan distance, and cosine similarity between the embeddings. We then feed these three scalars as a vector of inputs into a standard linear regression model from Python's scikit-learn package with default settings,\footnote{\url{https://scikit-learn.org/stable/modules/linear\_model.html}} whose output is the similarity score given in the dataset. To evaluate task performance, we compute the Mean Squared Error (MSE) loss for each run and record the mean MSE loss over 30 trials per (language, model) pair.
We then calculate the Spearman correlations of each of the 9 modularity scores with the negatives of the losses (such that positive correlation means that high modularity predicts high performance), both merged (87 data points) and within individual models (29 data points per model), for a total of 36 correlation values.
We find that all of the merged correlations are moderately to strongly positive. In particular, with the optimal hyperparameters of Level 2, $k = 2$, we have $\mathbf{\rho} = 0.71$ overall, $\mathbf{\rho_{ft}} = 0.59$ for FastText, $\mathbf{\rho_m} = 0.34$ for MUSE, and $\mathbf{\rho_s} = 0.8$ for subs2vec. In comparison, the correlations of the unsupervised cluster modularities with mean MSE loss for $k = 2$ are $\mathbf{\rho} = 0.27$, $\mathbf{\rho_{ft}} = 0.36$, $\mathbf{\rho_m} = 0.3$, and $\mathbf{\rho_s} = 0.42$, all weaker than their Binder counterparts.
\subsection{Word-Level Bilingual Lexicon Induction}
In addition to both monolingual classification and monolingual regression tasks, we also test our modularity metric on the cross-lingual regression task of bilingual lexicon induction. Using the ground-truth bilingual dictionaries provided by the publishers of MUSE~\cite{muse}, we run this task with the 28 non-English languages listed in footnote 2 in two directions: translation to and from English. We use the $5{,}000$-$1{,}500$ train-test split provided in the MUSE dictionary dataset and formulate the tasks as multivariate, multi-output regression tasks: for each observation in each (language, model) pair, we convert the English source word to its 300-dimensional embedding specified by the English version of the model and feed this vector as input to the same scikit-learn linear regression model as in Section~\ref{sec:wordsim}, of which the output is a 300-dimensional vector in the target language model space representing the embedding of the target word.
We follow this procedure in the other direction as well by converting source non-English words to embeddings in the appropriate non-English model spaces, feeding those embeddings into the linear regression model, and computing 300-dimensional predictions for the target English word vectors in the English model spaces. To measure task performance in the ``from English'' direction, we convert the ground-truth non-English target words into vectors in the corresponding non-English embedding model space, compute the cosine similarities between each ground-truth vector and its corresponding predicted vector, and record the mean of those cosine similarities as a measure of how close we are to the ground truth on average. We run 30 trials per (language, model) pair and record the mean of the mean cosine similarities.
In the ``to English'' direction, we similarly convert the ground-truth English target words into vectors and compute the mean cosine similarity over the prediction-ground-truth pairs. We calculate the Spearman correlations of each of the 9 modularity scores with the 30-trial means of mean cosine similarities in both directions. Once again, we calculate the correlations both across all models and within each individual model, yielding 72 total correlation values.
The optimal set of hyperparameters for the merged correlation in the ``from English'' direction is Level 3, $k = 2$, giving a moderate $\mathbf{\rho} = 0.55$ overall, $\mathbf{\rho_{ft}} = 0.4$ for FastText, $\mathbf{\rho_m} = 0.54$ for MUSE, and a strong $\mathbf{\rho_s} = 0.76$ for subs2vec. For comparison, the corresponding $k = 2$ correlations for unsupervised cluster modularities are $\mathbf{\rho} = 0.35$, $\mathbf{\rho_{ft}} = 0.04$, $\mathbf{\rho_m} = 0.27$, and $\mathbf{\rho_s} = 0.65$ --- all weaker than their Binder counterparts.
The optimal set of hyperparameters for the merged correlation in the ``to English'' direction is also Level 3, $k = 2$, giving a moderate $\mathbf{\rho} = 0.5$ overall, a weak $\mathbf{\rho_{ft}} = 0.29$, a moderate $\mathbf{\rho_m} = 0.56$, and a very strong $\mathbf{\rho_s} = 0.82$. The corresponding unsupervised cluster correlations for $k = 2$ are $\mathbf{\rho} = 0.35$, $\mathbf{\rho_{ft}} = 0.04$, $\mathbf{\rho_m} = 0.27$, and $\mathbf{\rho_s} = 0.65$.
Notably, in both the word similarity and BLI tasks, $\mathbf{\rho_s}$ is significantly stronger than $\mathbf{\rho_{ft}}$ and $\mathbf{\rho_m}$. This may be due to the fact that compared to sources such as Wikipedia and Common Crawl, the subtitles used as training data for subs2vec are more representative of how the human brain semantically maps language, as suggested by the model's creators~\cite{subs2vec}.
Overall, these downstream task experiments suggest that categorical modularity is a non-trivially significant predictor of performance on both monolingual and cross-lingual NLP tasks (though it is stronger on monolingual tasks) and that it may have potential to be a meta-predictor of how well a particular model matches the information encoded in the human brain.
\section{Use Cases: Comparing and Selecting Models}
After having established substantial evidence of the predictive properties of categorical modularity, we present some examples of how the research community can make use of the metric for model evaluation and selection.
\subsection{Comparing Models within a Language}
The best hyperparameters for the tasks described in Section~\ref{sec:experiments} are Level 3 with $k = 2$ along with Level 2 with $k = 2$. Across the 29 languages at the latter, FastText has the highest modularity 9 times (Arabic, Catalan, Estonian, Finnish, Greek, Macedonian, Polish, Turkish, Ukrainian), while MUSE has the highest modularity 3 times (Hungarian, Russian, Spanish), and subs2vec has the highest modularity 17 times. For Level 3 with $k = 2$, FastText has the highest modularity 13 times, while MUSE has the highest modularity 2 times (Russian, Vietnamese), and subs2vec has the highest modularity 15 times. Though individual choices should be made with each language, this suggests that subs2vec may be a strong choice for monolingual tasks overall.
\subsection{Comparing Languages within a Model}
We also present some evidence that categorical modularity predicts bilingual lexicon induction performance moderately well, and predictive properties are especially strong within subs2vec. For the optimal set of hyperparameters found in that task within subs2vec (Level 2, $k = 2$, $\mathbf{\rho_s} = 0.77$ from English and $\mathbf{\rho_s} = 0.81$ to English), the languages with the highest modularities in subs2vec are Dutch ($0.84$), Portuguese ($0.81$), French ($0.80$), Bulgarian ($0.80$), Swedish ($0.80$), Indonesian ($0.79$), and English ($0.78$), while the languages with the lowest modularities are Catalan ($0.65$), Spanish ($0.58$), Hebrew ($0.58$), Greek ($0.56$), Finnish ($0.55$), Arabic ($0.53$), and Russian ($0.53$). This may suggest which languages have lower amounts of resources at this time and hence deserve more data collection efforts on the part of the NLP community, particularly within subs2vec's domain of subtitle and conversational data.
\subsection{Categorical Modularity as a Potential Meta-Predictor}
We find evidence that categorical modularity reveals some information about how well models map to the human brain, as suggested by subs2vec's significantly stronger correlations. This is particularly true with regression tasks. Given a new or existing embedding model, calculating its categorical modularities and assessing their correlations with regression tasks such as word similarity may reveal if the model space is representative of how linguistic information is encoded in the brain.
\section{Discussion and Future Work}\label{sec:futurework}
Categorical modularity shows promise as an intrinsic word embedding evaluation metric based on our preliminary experiments. We can envision extending this work in several directions. For one, we can calculate single-category modularities (denoted by $Q_c$ as defined in Equation~\ref{eq:Qc}) and test which individual categories contain the most predictive properties. Our limited experiments in this direction with the movie sentiment analysis task suggest that concrete and non-living categories have better predictive capabilities than abstract and living ones: for the sentiment analysis task, the 5 most strongly correlated categories are \textit{Nonverbal Sounds}, \textit{Artifacts}, \textit{Concrete Objects}, \textit{Vehicles}, and \textit{Manufactured Foods}, while the 5 least correlated categories are \textit{Abstract Properties}, \textit{Abstract Constructs}, \textit{Miscellaneous Actions}, \textit{Humans}, and \textit{Abstract Actions}.
We may also extend our work to more models and languages to see if the predictive properties truly hold across all languages and models. Additionally, as more multilingual research and data becomes available in this space, we may probe different sets of semantic categories, further downstream tasks (particularly multi-class classification, monolingual text generation, and sentence-level bilingual lexicon induction), and further variations of models used in downstream tasks (e.g., deeper neural networks instead of vanilla SVMs and linear regressions). We can also envision improvements upon the categorical modularity metric itself, perhaps by way of a lower-resource metric or a metric that works well on contextualized word embeddings for which the word-vector mappings may have more complex geometries. Our code and data, which are available to the public,\footnote{\url{https://github.com/enscma2/categorical-modularity}} can also enable researchers and practitioners to replicate our results and experiment with different models, words, languages, and categories.
\section{Conclusion}
In this paper, we introduce categorical modularity, a novel low-resource metric that may serve as a tool to evaluate word embeddings intrinsically. We present evidence that categorical modularity has strong non-trivial predictive properties with respect to overall monolingual task performance, moderate predictive properties with respect to cross-lingual task performance, and potential meta-predictive properties of model space similarity to cognitive encodings of language.
\section*{Acknowledgments}
This work was supported by the Radcliffe Institute for Advanced Study at Harvard University. SC and KH were supported by the School of Engineering and Applied Sciences at Harvard University under Prof. David Parkes. DEB acknowledges funding from the Branco Weiss Fellowship, administered by the ETH Zurich. DEB's research was also executed within the framework of the HSE University Basic Research Program and funded by the Russian Academic Excellence Project '5-100'.
\section*{Impact Statement}
\subsection*{Ethical Concerns}
All of the data used in this paper is either our own or from publicly released and licensed sources. Our data is mainly aimed towards researchers and developers who wish to assess the qualities of word embedding models and gain some intuition for embedding model selection for downstream tasks. In particular, our conclusions would be suited for researchers working among the 29 functioning languages given in the MUSE library, which are heavily skewed towards Indo-European languages. Though we do not directly introduce novel NLP applications, we provide resources that may be useful in selecting technologies to deploy and informing the development of word embedding systems.
Categorical modularity is intended to be an informational tool that sheds light on semantic representation of natural language information in computational word embeddings, and there are many aspects of its capabilities that can be improved upon, extended, or further explored. We would also like to emphasize that we have only tested our metric on three specific downstream tasks with basic downstream models, and these may not be representative of all NLP tasks in general. Categorical modularity also has not yet been shown to reveal information on representational harms inherent in word embedding spaces, so evidence of good downstream task performance should not be misconstrued as indicative of strong and beneficial performance across all NLP domains.
\subsection*{Environmental Impact}
We acknowledge the pressing threat of climate change and therefore record some statistics on the computational costs of our experiments. All of our experiments are run with a 13-inch 2019 MacBook Pro with a $1.7$ GHz Quad-Core Intel Core i7 processor running Python $3.8.3$ in Terminal Version $2.11$ on MacOS Big Sur Version $11.1$. For the English language, generating FastText embeddings for our 500 core words took $20.31$ seconds, generating the $500 \times 500$ $k$-NNM took 1 hour and 25.72 seconds, generating MUSE embeddings for the 500 words took $23.13$ seconds, and generating the $500 \times 500$ $k$-NNM took 7 minutes and $39.32$ seconds. For the downstream task of movie review sentiment analysis, it took $42.03$ seconds to generate FastText sentence embeddings for $10{,}000$ English reviews and 6 minutes and $38.32$ seconds to generate these embeddings with MUSE. It took $0.35$ seconds per review to translate from English to Spanish using the Google Translate API, and it took $2.6$ seconds to run 30 trials of the sentiment analysis task for English FastText using scikit-learn's LinearSVC. For the task of word similarity calculation, English FastText embeddings and 3-dimensional input data took $21.25$ seconds to generate for 500 word pairs, English MUSE-based embedding data took $33.47$ seconds to generate, and the word similarity task using scikit-learn's LinearRegression took $0.09$ seconds on the generated English FastText-based inputs. For bilingual lexicon induction, FastText English-Spanish embedding data took $55.87$ seconds to generate, MUSE English-Spanish embedding data took 27 minutes and $29.56$ seconds to generate, and the BLI task took a combined $4.35$ seconds for both directions of English-Spanish using FastText. All other tasks took less than one second per language/model pair.
\newpage
|
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"redpajama_set_name": "RedPajamaArXiv"
}
| 3,647
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Q: Google Map issue addressing location from DB this line is not working and no error in console.
position: new google.maps.LatLng( coordsArray[i].location ),
data confirmed by alert(coordsArray[i].location);location been database field returning LatLng -43.59670,172.38247 as a string.
This line works: position: new google.maps.LatLng( -43.59670,172.38247 ),
What is the same data as above, any ideas what wrong with my code?
var list_location = localStorage.getItem('myHouse');
var obj = JSON.parse(list_location);
var coordsArray = obj;
var marker;
var locX;
var image = 'http://apppics.weebly.com....png';
var map = Appery("googlemap_6").options.mapElement.gmap('get', 'map');
var CreateMarker = function(coordsArray, i){
var marker = new google.maps.Marker({
position: new google.maps.LatLng( coordsArray[i].location ),
//position: new google.maps.LatLng( -43.59670,172.38247 ),
title: coordsArray[i].storeName,
map: Appery("googlemap_6").gmap,
});
for (var i = 0, j = coordsArray.length; i < j-1; i++)
alert(coordsArray[i].location);
CreateMarker(coordsArray, i);
A: This is incorrect: new google.maps.LatLng(coordsArray[i].location).
You state: "location been database field returning LatLng -43.59670,172.38247 as a string."
the google.maps.LatLng constructor takes two numbers as arguments (not a comma separated string).
If coordsArray[i].location is a comma separated string, convert it to two numbers.
var coords = coordsArray[i].location.split(",");
var latLng = new google.maps.LatLng(parseFloat(coords[0]), parseFloat(coords[1]));
var marker = new google.maps.Marker({
position: latLng,
map: map
});
code snippet:
var geocoder;
var map;
function initialize() {
var map = new google.maps.Map(
document.getElementById("map_canvas"), {
center: new google.maps.LatLng(37.4419, -122.1419),
zoom: 13,
mapTypeId: google.maps.MapTypeId.ROADMAP
});
var location = "-43.59670,172.38247";
coords = location.split(",");
var latLng = new google.maps.LatLng(parseFloat(coords[0]), parseFloat(coords[1]));
var marker = new google.maps.Marker({
position: latLng,
map: map
});
map.setCenter(latLng);
}
google.maps.event.addDomListener(window, "load", initialize);
html,
body,
#map_canvas {
height: 100%;
width: 100%;
margin: 0px;
padding: 0px
}
<script src="https://maps.googleapis.com/maps/api/js?"></script>
<div id="map_canvas"></div>
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 4,031
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UNDERGROUND PACKAGE AND MAIL CONTAINER SYSTEM
WIPO Patent Application WO/2021/257861
Disclosed is an underground container system includes a container fixedly positioned underground and anchored to a concrete structure that is also fixedly positioned underground. The container includes a bottom, one or more sidewalls coupled to and extending upward from the bottom to form an internal chamber of the container, a lid coupled to at least one of the sidewalls, and an electronic lock configured to lock and unlock the lid. The internal chamber is configured to receive and hold one or more articles of mail and/or one or more packages. The lid is configured to move to an open position and to a closed position. The lid includes an exterior surface that is positioned at a height that is at least substantially flush with a ground surface when the lid is in the closed position.
MELANCON SEAN (US)
CAMCRETE LLC (US)
A47G29/124; A47G29/12; A47G29/122; A47G29/16
Foreign References:
JP2018140148A 2018-09-13
US8123113B1 2012-02-28
US3021996A 1962-02-20
DUMAIS, Brice S. et al. (US)
View/Download PDF PDF Help
Claims:
What is claimed is:
1. An underground container system, comprising: a container fixedly positioned underground, the container comprising: a bottom; one or more sidewalls coupled to and extending upward from the bottom to form an internal chamber of the container, the internal chamber being configured to receive and hold one or more articles of mail and/or one or more packages; a lid coupled to at least one of the sidewalls, the lid configured to move to an open position and further configured to move to a closed position, the lid comprising an exterior surface that is positioned at a height that is at least substantially flush with a ground surface when the lid is in the closed position; and an electronic lock configured to lock and unlock the lid; and a concrete structure fixedly positioned underground, the concrete structure covering an exterior surface of the bottom of the container and further covering at least a portion of an exterior surface of each of the one or more sidewalls, the container being anchored to the concrete structure.
2. A method for installing an underground container system, comprising: fixedly positioning a container underground, the container comprising: a bottom; one or more sidewalls coupled to and extending upward from the bottom to form an internal chamber of the container, the internal chamber being configured to receive and hold one or more articles of mail and/or one or more packages; a lid coupled to at least one of the sidewalls, the lid configured to move to an open position and further configured to move to a closed position, the lid comprising an exterior surface, wherein the container is fixedly positioned at a location where the exterior surface of the lid is at a height that is at least substantially flush with a ground surface when the lid is in the closed position; and an electronic lock configured to lock and unlock the lid; and fixedly positioning a concrete structure underground, the concrete structure covering an exterior surface of the bottom of the container and further covering at least a portion of an exterior surface of each of the one or more sidewalls, the container being anchored to the concrete structure.
3. A method for delivering one or more articles of mail and/or one or more packages, comprising: approaching a container fixedly positioned underground, the container comprising: a bottom; one or more sidewalls coupled to and extending upward from the bottom to form an internal chamber of the container; a lid coupled to at least one of the sidewalls, the lid configured to move to an open position and further configured to move to a closed position, the lid comprising an exterior surface that is positioned at a height that is at least substantially flush with a ground surface when the lid is in the closed position; and an electronic lock configured to lock and unlock the lid, wherein the container is anchored to a concrete structure fixedly positioned underground, the concrete structure covering an exterior surface of the bottom of the container and further covering at least a portion of an exterior surface of each of the one or more sidewalls; communicating with the electronic lock to unlock the lid; and while the lid is in the open position, positioning the one or more articles of mail and/or the one or more packages within the internal chamber of the container.
4. The method of Claim 3, further comprising opening the lid so that the lid is in the open position.
5. The method of Claim 3, further comprising closing the lid so that the lid is in the closed position.
[0001] This disclosure relates generally to the field of package and mail delivery and more specifically to an underground package and mail container system.
[0002] Traditionally, mail is delivered into a mailbox attached to a house or to a standalone raised mailbox, while packages are traditionally delivered to a porch of the house or near the house. Such traditional systems for storing delivered packages and mail may be deficient.
[0003] According to one example, an underground container system includes a container fixedly positioned underground and anchored to a concrete structure that is also fixedly positioned underground. The container includes a bottom, one or more sidewalls coupled to and extending upward from the bottom to form an internal chamber of the container, a lid coupled to at least one of the sidewalls, and an electronic lock configured to lock and unlock the lid. The internal chamber is configured to receive and hold one or more articles of mail and/or one or more packages. The lid is configured to move to an open position and to a closed position. The lid includes an exterior surface that is positioned at a height that is at least substantially flush with a ground surface when the lid is in the closed position. The concrete structure covers an exterior surface of the bottom of the container and further covers at least a portion of an exterior surface of each of the one or more sidewalls.
[0004] For a more complete understanding of the present disclosure and one or more examples of the features and advantages of the present disclosure, reference is now made to the following description, taken in conjunction with the accompanying drawings, in which: [0005] FIG. 1A is a perspective of an example container of an underground container system; and [0006] FIG. IB is a cross-sectional view of the example container of FIG. 1A, installed underground.
[0007] Embodiments of the present disclosure are best understood by referring to FIGS. 1A and IB of the drawings, like numerals being used for like and corresponding parts of the various drawings.
[0008] FIG. 1A is a perspective of an example container 14 of an underground container system 10. Furthermore, FIG. IB is a cross-sectional view of the example container 14 installed underground.
[0009] As is illustrated, the underground container system 10 includes a container 14. The container 14 may be used to store one or more articles of mail and/or one or more packages (and/or other items), thereby keeping them safe and dry until they can be retrieved. In some examples, the container 14 (and the underground container system 10) may replace the standard mailbox. For example, the container 14 (and the underground container system 10) may be used as a mailbox at a house (e.g., stand-alone home, private residence), a small business, or any other location.
[0010] As is illustrated in FIG. IB, the container 14 may be installed underground. In particular, in some examples, the container 14 may be fixedly positioned underground. This fixed positioning may prevent the container 14 from being removed from its underground positioning. It may further prevent the container 14 from moving out of its underground positioning. As such, the container 14 may differ from traditional container systems that may temporarily pop out of the ground to receive an item, and that then move back underground after receiving the item. Such pop-up container systems tend to be prohibitively expensive, and further tend to break. When these pop-up container systems break, they may no longer move out of the ground. This prevents the pop-up container system from being useable to receive items. In contrast, the container 14 may be useable even when it is fixedly positioned underground. As a result, the container 14 may provide a safe and dry internal chamber 26 that can be used to deliver one or more articles of mail and/or one or more packages to the owner of the underground container system 10, in some examples.
[0011] The container 14 may be installed at any location underground. For example, the container 14 may be installed at an underground location outside a house (or other structure) and near a road (e.g., where a typical mailbox stands). This location may deter a thief from approaching the porch of the house (or any other location near the house). Furthermore, this location may be more visible to neighbors, traffic, and law enforcement. This location may also increase the efficiency of delivering packages and/or articles of mail, as the delivery person (or drone) may deliver them near the road (as opposed to having to approach the house). As such, the delivery person (or done) may not have to walk up to the doorstep of the house anymore, and may also not need to avoid obstacles in the way of the doorstep (e.g., a bicycle strewn across the house path).
[0012] The container 14 may be installed at any height underground. In some examples, the container 14 may be installed so that an exterior surface 32 of a lid 30 of the container 14 is positioned at a height that is at least substantially flush with a ground surface when the lid 30 is in the closed position. An example of this is illustrated in FIG. IB. The exterior surface 32 of the lid 30 is positioned at a height that is at least substantially flush with a ground surface when the exterior surface 32 is at the same height as the ground surface surrounding the container 14, plus or minus 1 inch. This may prevent the container 14 from sticking too far out of the ground, thereby calling attention to the presence of the container 14. In some examples, the lid 30 may also be colored (e.g., colored green) to allow the container 14 to blend in with its surroundings (e.g., lawn) to increase the aesthetic value of the underground container system 10. In some examples, this positioning may also provide easier access to the container 14, as the user, delivery person, or drone may not have to reach too far down below the ground surface to reach the container 14.
[0013] In an example of operation, a delivery person or drone (e.g., AMAZON, FEDEX, UPS, USPS) can approach the underground container system 10 with one or more articles of mail, one or more packages, and/or one or more other items. The delivery person or drone can unlock and open the lid 30 of the container 14 (manually or automatically), and position the items in the internal chamber 26 of the container 14. The delivery person or drone can then close and redock the lid 30 of the container 14 (manually or automatically). Later, the owner of the underground container system 10 (or the owner of the residence) may then approach the underground container system 10, unlock and open the lid 30 (manually or automatically), retrieve the stored items, and close and re-lock the lid 30 (manually or automatically). [0014] In some examples, the underground container system 10 may store the articles of mail and packages underground, thereby helping to prevent them from being stolen. As a result, homeowners, businesses, delivery services, and online retailers may save millions due to stolen packages and mail. Furthermore, it may result in a decrease in criminal activity, thereby limiting law enforcement having to investigate or stop package theft. In some examples, the underground storage may also reduce the risk of damage to packages, as those packages can be stored underground away from the weather. Furthermore, by storing the packages underground, the underground container system 10 may reduce clutter on front porches (i.e., where packages are traditionally delivered to).
[0015] As is illustrated, the container 14 includes a bottom 18. The bottom 18 may be the base of the container 14. The bottom 18 may have any shape. For example, the bottom 18 may be shaped as a circle, an oval, a square, a rectangle, a diamond, an irregular shape, any other shape, or any combination of the preceding. As is illustrated, the bottom 18 is shaped as a square. The bottom 18 may further have any size. For example, the bottom 18 may have any length, width, height, diameter, thickness, and/or other dimension. As is further illustrated in FIG. IB, the bottom 18 includes an internal surface 19 and an external surface 20
[0016] The container 14 further includes one or more sidewalls 22 coupled to the bottom 18. The sidewall(s) 22 may surround the bottom 18, and may extend upward from the bottom 18 so as to form an internal chamber 26 of the container 14. The sidewall(s) 22 may extend upward from the bottom 18 at any upward extending angle. For example, the sidewall(s) 22 may extend upward at 90 degrees, 85 degrees, 80 degrees, 70 degrees, 60 degrees, 45 degrees, 95 degrees, 100 degrees, 110 degrees, 120 degrees, 135 degrees, or any other upward extending angle. As is illustrated, the sidewall(s) 22 extend upward at 90 degrees from the bottom 18.
[0017] The container 14 may include any number of sidewalls 22. For example, the container 14 may include one sidewall 22, three sidewalls 22, four sidewalls 22, five sidewalls, or any other number of sidewalls 22. As is illustrated, the container 14 includes four sidewalls 22: 22a, 22b, 22c (not shown), and 22d (not shown). The sidewall(s) 22 may have any shape. For example, a sidewall 22 may be shaped as a circle, an oval, a square, a rectangle, a diamond, an irregular shape, any other shape, or any combination of the preceding. As is illustrated, each of the sidewalls 22 is shaped as a square. The sidewall(s) 22 may further have any size. For example, the sidewall(s) 22 may have any length, width, height, diameter, thickness, and/or other dimension. As is further illustrated in FIG. IB, the sidewall(s) 22 include an internal surface 23 and an external surface 24.
[0018] The sidewall(s) 22 may be coupled to the bottom 18 in any manner. As one example, the sidewall(s) 22 and the bottom 18 may be formed as one integral piece. As another example, the sidewall(s) 22 may be coupled to the bottom 18 via one or more connectors (e.g., nails, screws, adhesive).
[0019] The container 14 further includes the lid 30 that is coupled to at least one of the sidewalls 22. The lid 30 may seal the container 14 and may also open the container 14. For example, the lid 30 may move to a closed position (shown in FIG. IB) to seal the container 14, and the lid 30 may also move to an open position (shown in FIG. 1A) to open the container 14.
[0020] When the lid 30 is in the open position, one or more items (e.g., one or more articles of mail, one or more packages, and/or one or more other items) may be positioned within or removed from the internal chamber 26. For example, a delivery person or drone may position one or more articles of mail and/or one or more packages into the internal chamber 26. As another example, a person (e.g., a homeowner) may remove one or more articles of mail and/or one or more packages from the internal chamber 26.
[0021] When the lid 30 is in the closed position, the lid 30 (and the remainder of the container 14) may protect the items contained within the internal chamber 26. For example, the lid 30 may prevent the items from being removed from the container 14. As another example, the lid 30 (and the remainder of the container 14) may prevent dirt and water from entering the container 14 and damaging the items.
[0022] The lid 30 may have any shape. For example, the lid 30 may be shaped as a circle, an oval, a square, a rectangle, a diamond, an irregular shape, any other shape, or any combination of the preceding. As is illustrated, the lid 30 is shaped as a square. The lid 30 may further have any size. For example, the lid 30 may have any length, width, height, diameter, thickness, and/or other dimension. As is further illustrated in FIG. IB, the lid 30 includes an internal surface 31 and the external surface 32. In some examples, the external surface 32 may be a non-skid surface, so as to prevent people from slipping if they step on the lid 30. The non-skid surface may be created by adding a pattern (e.g., lozenge, direction, cyclical, etc.) to the external surface 32 (e.g., via a mold and thermoform). [0023] As is discussed above, the lid 30 may move to a closed position (shown in FIG. IB) and the lid 30 may also move to an open position (shown in FIG. 1 A). The lid 30 may be configured in any manner that allows it to move to a closed position and to an open position. As an example of this, the lid 30 may be movingly coupled to a sidewall 22 by one or more hinges 34. The hinge(s) 34 may be any movable joint or mechanism that connects the lid 30 to one or more sidewalls 22 and that further allows the lid 30 to move to a closed position and to an open position. In the illustrated example, the hinge(s) 34 allow the lid 30 to rotate upward from the closed position to the open position, and further allow the lid 30 to rotate downward from the open position to the closed position. The hinge 34 may be a standard hinge that is coupled to both the lid 30 and the sidewall 22. In other examples, the hinge 34 may be a living hinge that is formed integral with the lid 30 and the sidewall 22. As an example of this, the lid 30, sidewall 22, and the hinge 34 may be a single integral structure (e.g., a single integral structure made of plastic, such as Ultra-High Molecular Weight Polyethylene). In such an example, the hinge 34 may be thinner (e.g., it is thermoset thinner) than the lid 30 and sidewall 22 (or the hinge 34 may be modified in any other way) so as to be flexible. This may allow the lid 30 to flex open and close with less moving parts.
[0024] As another example, the lid 30 may alternatively (or additionally) be movingly coupled to a sidewall 22 (or any other portion of the container 14) by one or more moveable arms (not shown). These arm(s) may be rotating arms that rotate around a pivot point, allowing the lid 30 to rotate upward from the closed position to the open position, and further allowing the lid 30 to rotate downward from the open position to the closed position. In other examples, these arms(s) may be swinging arms that allow the lid 30 to be lifted upward away from sidewalls 22 and further allow the lid 30 to then move horizontally away from the sidewalls 22, so as to move to an open position (and vice versa to a closed position).
[0025] The movement of the lid 30 to a closed position and to an open position may be a manually assisted movement. For example, a user may pull upward on the lid 30 (via a handle) to move the lid 30 to an open position, and the user may push downward on the lid to move the lid 30 to a closed position.
[0026] The movement of the lid 30 to a closed position and to an open position may be an automated movement. For example, the container 14 may include a mechanical/electrical/pneumatic system that can automatically move the lid 30 to a closed position and to an open position. As an example of this, the container 30 may include a motor and a battery (or other power source). The motor may be attached to one or more rotating arms (e.g., rotating coil rods). When in operation, the motor may force the rotating arms to rotate, thereby causing the lid to move to an open position or a closed position. The motor may be operated via a remote device, such as the user's Smartphone, a delivery person's digital device, and/or a drone. As another example of an automated movement, the lid 30 and hinge 34 may utilize elasticity (e.g., the law of elasticity) to cause the lid 30 to automatically spring (via potential energy) from the closed position to the open position when the lid 30 is unlocked. In such an example, the container 14 may include a barrier that stops the movement of the lid 30, thereby preventing it from extending past the open position (e.g., past 90 degrees).
[0027] In some examples, the movement of the lid 30 to a closed position and to an open position may be combination of a manually assisted movement and an automated movement. For example, the automated movement (e.g., pneumatic movement) may be used to move the lid 30 to an open position, and the manually assisted movement may be used to move the lid 30 to a closed position (or vice versa). As an example of this, the lid 30 may automatically spring (via potential energy) from the closed position to the open position when the lid 30 is unlocked (e.g., when a magnetic lock 38 is unlocked), and then a user may manually push the lid 30 back down to the closed position and redock the lid (e.g., re-lock the magnetic lock 38).
[0028] As is illustrated, the lid 30 is a single solid lid that rotates upward and downward at a single end. In other examples, the lid 30 may be multiple lid pieces. For example, the lid 30 may be made of two lid pieces that interconnect at a mid-point along the width or length of the container 14, and that individually rotate upward and downward at opposing ends. Furthermore, any other configuration of the lid 30 may be used in the container 14.
[0029] In some examples, the lid 30 may include a mail slot that allows articles of mail to be inserted into the container 14 even when the lid 30 is closed. In such examples, the lid 30 may also include a weather guard that prevents water from dripping into the mail slot.
[0030] The bottom 18, sidewall(s) 22, lid 30, hinge 34, and/or any other portion of the container 14 may be made of any material(s) that may allow the container 14 to be used to store one or more articles of mail, one or more packages, and/or other items. For example, the bottom 18, sidewall(s) 22, lid 30, hinge 34, and/or any other portion of the container 14 may be made plastic (e.g., Ultra-High Molecular Weight Polyethylene). The plastic may be thermoset plastic or thermoplastic. The plastic may 100% recycled plastic (e.g., post industrial plastic), thereby allowing this reusable plastic to be put to good use (as opposed to ending up in the landfill or in the ocean). The plastic may be impervious to moisture, extreme temperatures, and may be tough. This may allow the container 14 to last for the life of a home (and for potential future buyers of the home), in some examples. As such, the container 14 may be advantageous over typical mailboxes that need to be replaced periodically.
[0031] In other examples, the bottom 18, sidewall(s) 22, lid 30, hinge 34, and/or any other portion of the container 14 may be made of aluminum, steel (such as stainless steel and/or carbon steel), copper, clad metal, cast iron, any other metal, pottery materials, other non-metallic materials, any other material(s) that may allow the container 14 to be used to store items, or any combination of the preceding.
[0032] The container 14 further includes a lock 38. The lock 38 may be configured to lock and unlock the lid 30. When the lid 30 is unlocked, the lid 30 may be opened to the open position. When the lid 30 is locked, the lid 30 may remain in the closed position and may be prevented from opening. The lock 38 may be any locking system that can lock and unlock the lid 30. As an example, the lock 38 may be a manual lock (e.g., a combination lock, a key lock). As another example, the lock 38 may be an electronic lock that can lock and unlock the lid 30 based on a communication signal received from a remote device, such as the user's Smartphone, a delivery person's digital device, and/or a drone. The lock 38 may lock and unlock the lid 30 via one or more deadbolts, latches, magnets, cylinders (e.g., mortise cylinder), any other locking and unlocking system, or any combination of the preceding.
[0033] In some examples, the lock 38 and the opening/closing of the lid 30 may be automated. For example, the container 14 may include one or more processors, storage mediums, network interfaces, and software that cause the lock 38 to unlock/lock the lid 30 automatically and further cause the lid 30 to open/close automatically. In such an example, a user may utilize their phone (e.g., utilizing an "app" on the phone, accessing a website on the phone, texting a code to the underground container system 10), a remote control, or any other device to cause the lock 38 to unlock the lid 30 and further cause the lid 30 to open, and/or to cause the lid 30 to close and further cause the lock 38 to lock the lid 30. This access to the underground container system 10 may be protected by a password or code, in some examples. Furthermore, a one-time use password or code may be created and given to another person (e.g., a neighbor), thereby allowing the person to retrieve packages and articles of mail when the homeowner is not available.
[0034] The lid 30 may also include an interface (e.g., a keypad) that may allow the lid 30 to be unlocked/locked and opened/closed automatically. As such, the container 14 can be opened/closed directly from the container 14 itself, without a remote device. This interface may be hidden behind a movable panel.
[0035] When delivering articles of mail or packages, the delivery person (or drone) may be able to unlock/lock and open/close the lid 30. In such an example, when the container 14 is automated, the delivery person (or drone) may utilize a delivery password or code that may be transmitted to the container 14 (via the interface or using a remote device). This may allow the container 14 to be opened and closed so that the articles of mail or packages may be delivered. The delivery password or code may be periodically changed, thereby preventing it from being stolen. In some examples, the password or code may only be accessible to the delivery person's remote device. As such, the delivery person (himself) may not know the password or code.
[0036] In some examples, the container 14 may utilize global positioning system (GPS) coordinates for the automatic unlocking/locking and opening/closing of the lid 30. In such examples, the lid 30 may unlock and open automatically when the delivery person (or drone) approaches the container 14, and may also close and lock automatically when the delivery person (or drone) moves away from the container 14. This automation may be triggered by the communication (from a digital device to the container 14) of the GPS coordinates of the delivery person (or drone) themselves, the GPS coordinates of a device carried by the delivery person (or drone), and/or the GPS coordinates of the vehicle driven by the delivery person (or drone). For a flying delivery drone, the automation may be triggered when the drone flies near the container 14 and/or hovers over the container 14. The drone may then drop the articles of mail or packages into the internal chamber 26 from a height of, for example, 1 to 2 feet, preferably.
[0037] In order to provide power to the automatic features of the container 14, the container 14 may include a battery, solar panel(s), and/or an electrical hookup. The solar panel(s) may be included on (or in) the lid 30. These solar panel(s) may charge a battery in (or attached to) the container 14, allowing the container 14 to operate at night. [0038] As is discussed above, the container 14 includes the internal chamber 26. The internal chamber 26 may be configured to receive and hold one or more articles of mail, one or more packages, any other items, or any combination of the preceding. As an example, the internal chamber 26 may have a shape and/or size that allows it to receive and hold one or more articles of mail, one or more packages, any other items, or any combination of the preceding. The internal chamber 26 may have any shape and/or size that allows it to hold any number of articles of mail, packages, other items, or any combination of the preceding. As another example, the internal chamber 26 may be entirely enclosed (when the lid 30 is closed), thereby providing a safe and dry environment for the articles of mail, one or more packages, any other items, or any combination of the preceding.
[0039] In some examples, the internal chamber 26 may include a letter size rack placed at the top of the internal chamber 26, so as to hold articles of mail. The internal chamber 26 may also (or alternatively) have a self-lowering shelf that causes packages to remain near the top of the internal chamber 26. As more packages are added to the self-lowering shelf, the shelf may adjust downward in height, allowing the packages to be stacked. As packages are removed, the shelf may adjust upward in height. The self-lowering shelf may utilize a counterweight in order to move upward and downward. The internal chamber 26 (and its features, such as the shelf) may be padded, in some examples. This may protect packages that are dropped into the internal chamber 26 from a height by, for example, a drone. The internal chamber 26 may also (or alternatively) be insulated, so as to protect its contents from cold, heat, wind, and/or moisture.
[0040] In some examples, the internal chamber 26 may include one or more compartments. For example, the internal chamber 26 may include narrow (e.g., 2 inch - 12 inch) compartments (e.g., on both sides of the internal chamber 26) that may house a battery, motor, opening/closing arms, wires, or any other device. The internal chamber 36 may also include a central part for placement of packages, a slot or container for incoming articles of mail, and/or a slot or container for outgoing articles of mail (e.g., envelopes only), in some examples.
[0041] The container 14 may also include a lighting system, in some examples. The lighting system may be on a visible portion of the container 14. This may illuminate the container 14 during nighttime, so that people can find and use it. The lighting system may also (or alternatively) be in the internal chamber 26. In such an example, the lighting system may turn on when the lid 30 is opened during nighttime. This lighting system can light up any portion of the internal chamber 26 (e.g., 2 feet of depth into the internal chamber 26), allowing a user to see into the internal chamber 26 at night. The lighting system(s) can be used to provide visibility to the contents of the container 14, to allow users to find the container 14 (e.g., to light up the underground container system 10), to provide lighting in areas of the world that do not have long days or that have inclement weather, to provide security and/or lighting to streets, any other reason, or any combination of the preceding. The lighting system(s) may installed via a universal serial bus (USB). The lighting system(s) may be powered by a battery and/or solar panels. Excess energy created by the solar panels may be provided back to the electrical grid, in some examples.
[0042] As is illustrated in FIG. IB, the underground container system 10 further includes a concrete structure 42 that is also fixedly positioned underground. The concrete structure 42 may be positioned underground so as to cover the exterior surface 20 of the bottom 18 of the container 14. The concrete structure 42 may also cover at least a portion of the exterior surface 24 of one or more of the sidewalls 22 of the container 14. In some examples, the concrete structure 42 may provide protection for the container 14, and may channel water away from the container 14.
[0043] The concrete structure 42 may cover any portion of the exterior surface 24 of a sidewall 22. For example, the concrete structure 42 may cover 50% of the surface area of the exterior surface 24, 75% of the surface area of the exterior surface 24, 90% of the surface area of the exterior surface 24, 100% of the surface area of the exterior surface 24, or any other amount. As is illustrated, the concrete structure 42 covers 100% of the surface area of the exterior surface 24 of the sidewalls 22. Furthermore, the concrete structure 42 may cover the exterior surface 24 of all of the sidewalls 22, or may only cover the exterior surface 24 of a portion of the sidewalls 22 (e.g., it may cover 3 out of 4).
[0044] The concrete structure 42 may have any size and/or shape that allows it to cover the exterior surface 20 of the bottom 18 of the container 14 and/or that allows it to cover at least a portion of the exterior surface 24 of one or more of the sidewalls 22 of the container 14. As an example of this, the concrete structure 42 may be 1 inch thick on each of the bottom and sides of the concrete structure 42. In other examples, the concrete structure 42 may be less than 1 inch thick, or more than 1 inch thick. [0045] The container 14 may be anchored to the concrete structure 42. This anchoring may assist in keeping the container 14 fixedly positioned underground. Furthermore, it may prevent the container 14 from being stolen out of the ground, in some examples. For example, the weight of the concrete structure 42 may prevent the container 14 from being stolen out of the ground.
[0046] The container 14 may be anchored to the concrete structure 42 in any manner. As an example, the container 14 may be anchored to the concrete structure 42 by being encased in the concrete structure 42. In such an example, the concrete may be poured under and around the container 14, causing it to harden around and encase the container 14 as the concrete structure 42 dries and forms. This encasement may be done prior to the container 14 being positioned underground, or after. In some examples, the sidewalls 22 of the container 14 may include ridges, bumps, or appendages that the concrete can form around. This may further anchor the container 14 to the concrete structure 42.
[0047] As another example, the container 14 may be anchored to the concrete structure 42 by one or more connectors that are attached to both the container 14 and the concrete structure 42. Examples of the connectors include coil rods, chains, adhesives, and/or any other device that may attach the container 14 to the concrete structure 42.
[0048] In some examples, the underground container system 10 may not include a concrete structure 42. In such an example, the container 14 may be anchored directly to ground (via connectors). In other examples, the container 14 may not be anchored at all. Instead, the container 14 may have a weight and/or size sufficient to prevent it from being stolen out of the ground, in some examples
[0049] Modifications, additions, and/or substitutions may be made to the underground container system 10 of FIGS. 1A-1B without departing from the scope of the specification. For example, although the container 14 has been described above as being positioned underground, in other examples, all or a portion of the container 14 (or any other portion of the underground container system 10) may be positioned above ground. As an example of this, the container 14 may be installed into an above ground structure (e.g., into a wall that may also operate as the concrete structure 42). In such an example, the container 14 may be installed in a location that is near the porch/door area of a house, and the container 14 may also blend in with the materials that protect and add aesthetics to the house, such as brick, insulating concrete form (ICF), masonry, etc. Such a placement may allow the container 14 to be installed in a higher location, thereby limiting the amount of bending a user may have to perform to reach the internal chamber 26. In some examples, the container 14 may have a second lid or door that is positioned on the inside of house. As such, the delivery person (or drone) could deliver packages from the outside of the home, but the user could retrieve those same packages without having to go outside. This may be a preferable feature for seniors, handicapped or disabled persons, for locations with inclement weather, for higher end homes, etc.
[0050] As another example, the underground container system 10 could be used to replace city mailboxes (e.g., the blue mailboxes at the comers of streets). In other examples, the underground container system 10 can be used to store items that are not related to articles of mail or packages. For example, the underground container system 10 can be used to contain city meter systems, electrical systems, water systems, any other system that is contained underground, or any combination of the preceding.
[0051] As a further example, the underground container system 10 could be used to store any other items (e.g., any items that are not related to articles of mail or packages). For example, the underground container system 10 could be used to store medical supplies, weaponry, ammunition, computer equipment, food (e.g., meals ready-to-eat), water, batteries, or any other items. In some examples, the underground container system 10 may be installed at or near military outposts, refugee outposts, or any other location (including locations that are hard to reach, or hard to deliver supplies to). In such examples, the underground container system 10 may be used to re-supply military personnel, medical personnel, or any other person. In some examples, the underground container system 10 may include a refrigeration/cooling device to keep the items cool, an electrical connection (e.g., for re charging phones and/or other electrical device), solar panels (e.g., on the lid 30) to power one or more components of the underground container system 10, or any combination of the preceding.
[0052] As a further example, the underground container system 10 may further allow for one or more items (e.g., one or more articles of mail, one or more packages, and/or one or more other items) to be positioned within or removed from the internal chamber 26 through access points other than an open lid 30. For example, one or more of the sidewalls 22 and/or the bottom 18 may include an access point (e.g., a door or lid) that allows the items to be positioned within or removed from the internal chamber 26. These access points may be used for underground delivery, such as if delivery tunnels are positioned below the underground container system 10.
[0053] This specification has been written with reference to various non-limiting and non-exhaustive embodiments or examples. However, it will be recognized by persons having ordinary skill in the art that various substitutions, modifications, or combinations of any of the disclosed embodiments or examples (or portions thereof) may be made within the scope of this specification. Thus, it is contemplated and understood that this specification supports additional embodiments or examples not expressly set forth in this specification. Such embodiments or examples may be obtained, for example, by combining, modifying, or reorganizing any of the disclosed steps, components, elements, features, aspects, characteristics, limitations, and the like, of the various non-limiting and non-exhaustive embodiments or examples described in this specification. In this manner, Applicant reserves the right to amend the claims during prosecution to add features as variously described in this specification.
Previous Patent: COMPLIANT SINGLE NET MARINE BARRIER
Next Patent: SALIVA COLLECTION DEVICE AND METHOD OF USING THE SAME
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In an interview with the UN News Centre on 30 July, the Secretary-General's Special Envoy for Syria, Staffan de Mistura explained his proposal of launching thematic discussions through intra-Syrian working groups to address key aspects of the Geneva Communiqué. "One is the humanitarian issue, which means access. People are requesting a format through which access can be guaranteed for many things: medicines, humanitarian aid, food. And there is, of course, the mother of all issues: the political process. And that means how to get into a [political] transition, through a transitional governing body, but do so in a way that you are not actually producing an immediate shake-up, rather, a scenario where you are getting, gradually but clearly, to a different political scenario, where everyone is included. All that can be part and should be part of this working group, so that when the right time comes, the working groups would be ready", the Envoy noted.
Within the framework of the Geneva Consultations, Deputy Special Envoy for Syria Ramzy Ezzeldin Ramzy met today with representatives of the Syrian civil society, including Mr. Zedoun Al Zoubi and Mr. Tawfik Chamaa of the Union of Syrian Medical Relief Organizations. They briefed Mr. Ramzy on the escalating armed conflict and deteriorating situation on the ground, including the dire conditions of medical facilities, as well as on the work of Syrian civil society organizations. They also shared perspectives for a political solution and discussed ways how the civil society could contribute to efforts in reaching a political solution to the Syrian conflict.
Within the framework of the ongoing Geneva Consultations, Deputy Special Envoy Ramzy Ezzeldine Ramzy met today in Geneva with representatives of the Union of Syriac Women and the International Committee of the Red Cross (ICRC), who briefed on the situation in Syria. They discussed ways to support people in Syria in their daily humanitarian needs. Mr. Ramzy also discussed with the representatives of the Union of Syriac Women perspectives on a political solution to the Syrian conflict which could meet the needs of diverse components, which make up integral parts of the Syrian society.
At the end of today's meetings, Mr. Ramzy stressed that, "all should put their differences aside to ensure that aid reaches all those in need, but ultimately only a political solution would allow to address the deepening humanitarian crisis in a sustainable manner." While highlighting the urgent need for a political solution to the Syrian conflict, he added that, "it is critical that women organizations are included in any political process, fully participate in it and contribute to it".
On 29 May, he met with a delegation of civil society organizations from the United States working on the Syrian crisis. He said afterward that listening to civil society organizations — especially those who work on advocacy and the medical doctors who put their lives at risk every day to save the victims of chemical attacks or shelling — was yet another reminder of the daily realities of the Syrian civilians who pay the highest toll of this conflict. He said it was also an opportunity to reflect on the aspirations of the diaspora. The Special Envoy also met with delegations of European countries, namely Belgium, Czech Republic, Denmark, Finland, Germany, Greece, Italy, Netherlands, Norway, Sweden and Switzerland.
On 24 May, Mr. de Mistura met with a delegation of the Assyrian Democratic Organization, and the Syrian Turkmen Council. He shared views with them on a political solution in Syria and the ongoing conflict on the ground. "Today I heard again about the importance of preserving Syria's social fabric and taking into account the diverse views from all corners of the country," Mr. de Mistura said. He stressed that "the United Nations will continue supporting efforts towards an all-inclusive Syrian-led political process."
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{"url":"https:\/\/quant.stackexchange.com\/questions\/15589\/portfolio-var-with-copula","text":"Portfolio VaR with Copula?\n\nLet the portfolio be given by: $$X=X_1+X_2$$ $(X_1,X_2)$ are dependent through a Copula function $C(u_1,u_2)$, such that the joint distribution is given by: $$F(x_1,x_2)=C(F(x_1),F(x_2))$$\n\nWhat is the VaR of this portfolio?\n\nUsually VaR is the inverse quantile: $VaR_\\alpha=F^{-1}_X(\\alpha)$.\n\nI am not sure how to determine it in this multivariate case?\n\nYou don't really have a multivariate case: we can only define VaR (in its usual sense) for a one-dimensional output. Recall that $$\\operatorname{VaR}_\\alpha(X) = \\inf\\{v:F_X(v)\\geq \\alpha\\}$$ and since in your case $X = X_1+X_2$ you just need to compute $F_X$ in terms of $X_1$ and $X_2$. For the notation of partial derivatives, I denote the generic variables of the copula function by $u_1$ and $u_2$. $$F_X(v) = \\mathbb P(X_1+X_2\\leq v) = \\int\\limits_{-\\infty}^\\infty \\frac{\\partial C}{\\partial u_1}\\left(F_{X_1}(x_1),F_{X_2}(v-x_1)\\right)\\mathrm dF_{X_1}(x_1). \\tag{1}$$ As long as you can compute\/estimate this function, you can get a value\/estimate for VaR. The formula $(1)$ can be obtained as follows: \\begin{align} F_X(v) &= \\mathbb P(X_1+X_2\\leq v) = \\int\\limits_{-\\infty}^\\infty \\mathrm dx_1 \\int\\limits_{-\\infty}^{v-x_1}\\frac{\\partial^2 C}{\\partial u_1\\partial u_2}\\left(F_{X_1}(x_1),F_{X_2}(x_2)\\right)F'_{X_1}(x_1)F'_{X_2}(x_2)\\mathrm dx_2 \\\\ &= \\int\\limits_{-\\infty}^\\infty \\mathrm dx_1 \\int\\limits_{-\\infty}^{v-x_1}\\frac{\\partial}{\\partial x_2}\\left(\\frac{\\partial C}{\\partial u_1}\\left(F_{X_1}(x_1),F_{X_2}(x_2)\\right)F'_{X_1}(x_1)\\right)\\mathrm dx_2 \\\\ &= \\int\\limits_{-\\infty}^\\infty \\left.\\frac{\\partial C}{\\partial u_1}\\left(F_{X_1}(x_1),F_{X_2}(x_2)\\right)F'_{X_1}(x_1)\\right|_{x_2=-\\infty}^{x_2=v-x_1}\\mathrm dx_1 \\\\ &= \\int\\limits_{-\\infty}^\\infty \\frac{\\partial C}{\\partial u_1}\\left(F_{X_1}(x_1),F_{X_2}(v-x_1)\\right)F'_{X_1}(x_1)\\mathrm dx_1 \\\\ &= \\int\\limits_{-\\infty}^\\infty \\frac{\\partial C}{\\partial u_1}\\left(F_{X_1}(x_1),F_{X_2}(v-x_1)\\right)\\mathrm dF_{X_1}(x_1). \\end{align} For the partial derivatives notation, consider the following example. If $g(u_1,u_2) = u_1 + u_2$ then $$\\frac{\\partial }{\\partial u_1}g(x_1^2,x_2^2) = 1,$$ $$\\frac{\\partial}{\\partial x_1}g(x_1^2,x_2^2) = 2x_1.$$\n\u2022 Can you explain how you get to this formula for $F_X(v)$? E.g. why is it $dF(x_1)$? I found this other link for the convolution pdf: stats.stackexchange.com\/questions\/21549\/\u2026 \u2013\u00a0emcor Nov 24 '14 at 9:03\n\u2022 Thank you, what is the upper limit for the first and second integrals? Can you please express $f(x)$ in pdf's, I cannot follow what is the difference between $F'(x_1)$ and $dF(x_1)$, and why in the second line $F'(x_2)$ suddenly vanishes? \u2013\u00a0emcor Nov 24 '14 at 9:22\n\u2022 @emcor: I've put the limits there, for some reason they have not appeared in the first version. Now, $\\mathrm dg(x) = g'(x)\\mathrm dx$ which is kinda fundamental theorem of calculus. Finally, $F'_{X_2}(x_2)$ has not vanished: it's just a chain rule for partial derivative. If $g(u,v)$ is some function, then $$\\frac{\\partial}{\\partial y}g(a(x),b(y)) =\\frac{\\partial g}{\\partial v}(a(x),b(y))\\cdot b'(y).$$ As often with partial derivatives, notation may be confusing, so let me make it more formal in my answer if that is confusing you. \u2013\u00a0Ulysses Nov 24 '14 at 9:38\n\u2022 @emcor: indeed, since $F_{X_2}(-\\infty) = 0$ and $C(u_1,0) =0$ regardless of $u_1$ \u2013\u00a0Ulysses Nov 24 '14 at 13:16","date":"2019-12-13 09:53:25","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\": 1, \"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\": 1, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.999929666519165, \"perplexity\": 437.30588436495935}, \"config\": {\"markdown_headings\": false, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 20, \"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-2019-51\/segments\/1575540553486.23\/warc\/CC-MAIN-20191213094833-20191213122833-00151.warc.gz\"}"}
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So we went on our first real family outing to Nanna and Pappa's house yesterday. Eisley got to hang out with Ayla and Indy. Ayla calls Eisley "The Cousin", and was apparently under the impression at one point that Ayla and Indy would each have their own... maybe someday!
So we got some good pictures of Eisley and her maternal side of the family.
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{"url":"https:\/\/www.physicsforums.com\/threads\/boundary-value-problem.48064\/","text":"# Boundary Value Problem\n\n1. Oct 16, 2004\n\n### MathematicalPhysics\n\nI need some help starting off on this question.\n\nElectrostatic potential $$V (x,y)$$ in the channel $$- \\infty < x < \\infty, 0 \\leq y \\leq a$$ satisfies the Laplace Equation\n\n$$\\frac{\\partial^2 V}{\\partial x^2} + \\frac{\\partial^2 V}{\\partial y^2}= 0$$\n\nthe wall $$y = 0$$ is earthed so that\n\n$$V (x,0) = 0$$\n\nwhile the potential on the wall $$y = a$$\n\n$$V (x,a) = V_0 \\cos{kx}$$ where $$V_0 , k$$ are positive constants.\n\nBy seeking a soln of an appropriate form, find $$V (x,y)$$ in the channel.\n\n2. Oct 16, 2004\n\n### arildno\n\nWhen in doubt, try separation of variables!\nV(x,y)=F(x)G(y).\nInserting this into Laplace, yields, by rearrangement:\n$$\\frac{G''(y)}{G(y)}=-\\frac{F''(x)}{F(x)}$$\n\n3. Oct 16, 2004\n\n### MathematicalPhysics\n\nThanks, I was trying to get it in the form $$V (x,y) = F (a) V_0 \\cos{kx}$$ then sub the values into the Laplace eqn. Is that going about it the wrong way?\n\n4. Oct 16, 2004\n\n### arildno\n\nYou DO mean (in my notation!)\n$$V(x,y)=G(y)V_{0}\\cos(kx)$$???\nIf so, then it will work.\nNote that the separation of variables method in this case implies:\n$$G''(y)=k^{2}G(y)$$\n\n5. Oct 16, 2004\n\n### MathematicalPhysics\n\nHmm im not really keeping up with you here sorry. How can I find things out about F(x) and G(y) (in your notation) when we have just introduced them?\n\n--------edit----------\n\noh yes sorry im with you, then differentiate V (x,y) = G(y) V_0 cos (kx) to get the different bits to go in the Laplace eqn? ahh!\n\nLast edited: Oct 16, 2004\n6. Oct 16, 2004\n\n### arildno\n\nHint:\nYou should be able to see that G(y)=ASinh(ky), where A is some constant, and Sinh() the hyperbolic sine function.\n\n7. Oct 16, 2004\n\n### MathematicalPhysics\n\nNow I've got G''(y) - k^2 G (y) = 0, still on the right track yeh?\n\n8. Oct 16, 2004\n\n### arildno\n\nYes, you are.\n\n9. Oct 17, 2004\n\n### MathematicalPhysics\n\nFrom this how do I get to G(y)=ASinh(ky)?\n\n10. Oct 17, 2004\n\n### arildno\n\nNote that:\n$$\\frac{d}{dy}ASinh(ky)=kACosh(ky),\\frac{d^{2}}{dy^{2}}ASinh(ky)=k^{2}ASinh(ky)$$\nThis shows that ASinh(ky) is a solution for G(y).\nSimilarly, you may show that BCosh(ky) is another solution for G(y).\nG(y)=ASinh(ky)+BCosh(ky)\nApply the boundary condition at y=0 to prove that B=0\n\n11. Oct 17, 2004\n\n### MathematicalPhysics\n\nThanks for being so patient. How can I show that ASinh(ky) is a soln for G(y)? Im used to looking at the differential eqn and substituting\n\nG(y) = e^{ry} so G'(y) = re^{ry} and G''(y) = r^2. e^{ry}\n\nIs there no such substitution to show that ASinh(ky) & BCosh(ky) are solns?\n\n12. Oct 17, 2004\n\n### arildno\n\nDo you agree with the following result, using your method:\n$$r=\\pm{k}$$??\n\n13. Oct 17, 2004\n\n### MathematicalPhysics\n\nYeh which gives gen soln G (y) = Ae^{ky} + Be^{-ky}\n\nbut the boundary condition at y=0 doesnt allow for B so we are left with\n\nG(y) = Ae^{ky} ?\n\n14. Oct 17, 2004\n\n### arildno\n\nA bit too fast there..\nLet's write the general solution for G(y) as follows:\n$$G(y)=K_{+}e^{ky}+K_{-}e^{-ky}$$\nwhere the K's are constants to be determined by boundary conditions.\nPrior to that step, however, let's rewrite the general solution as:\n$$G(y)=(K_{+}+K_{-})\\frac{e^{ky}+e^{-ky}}{2}+(K_{+}-K_{-})\\frac{e^{ky}-e^{-ky}}{2}$$\n1. We now set $$B=K_{+}+K_{-},A=K_{+}-K_{-}$$\n(Clearly, A and B are as arbitrary as the K's!)\n2) We now recognize:\n$$Cosh(ky)=\\frac{e^{ky}+e^{-ky}}{2}$$\n$$Sinh(ky)=\\frac{e^{ky}-e^{-ky}}{2}$$\nOr, we may rewrite G(y) as:\n$$G(y)=ASinh(ky)+BCosh(ky)$$\n\n15. Oct 17, 2004\n\n### MathematicalPhysics\n\nright now I need to find\n\nB: iv done this and basically its because cosh can never be zero which implies B must be zero.\n\nA: at y=a V(x,a) = V_0 cos{kx}\n\ntherefore for y=a, G(y)=1\n\nASinh(ka) = 1 is that right?\n\n16. Oct 17, 2004\n\n### arildno\n\n$$V(x,y)=V_{0}\\frac{Sinh(ky)\\cos(kx)}{Sinh(ka)}$$","date":"2017-02-19 23:30:14","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\": 0.7547854781150818, \"perplexity\": 4058.6824539835284}, \"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-2017-09\/segments\/1487501170286.6\/warc\/CC-MAIN-20170219104610-00339-ip-10-171-10-108.ec2.internal.warc.gz\"}"}
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Q: How to install Autoconf, Automake and related tools on Mac OS X from source? I want to install autoconf, automake, m4, etc… from the source on a Mac OS X 10.7.2 machine running Xcode 4.2.1. The problem is anything that I try and install I have to rely on autoconf. Therefore, I am trying to install autoconf I get:
configure.ac:30: require Automake 1.11, but have 1.10
I try to install automake, the bootstrap reports:
configure.ac:20: error: Autoconf version 2.68 or higher is required
configure.ac:20: the top level
autom4te: /usr/bin/gm4 failed with exit status: 63
aclocal.tmp: error: autom4te failed with exit status: 63
Currently installed autoconf version: autoconf (GNU Autoconf) 2.61
Currently installed automake version: automake (GNU automake) 1.10
A: Update: Just use Homebrew to install these packages and move on with life.
Install Homebrew and just install the autoconf, automake and libtool packages like this:
brew install autoconf automake libtool
When I wrote this answer about 3+ years ago, it was to correct a previous answer that was outdated, link-only and vague in explanation. At that time I preferred to use raw source compilation on macOS for a task like this rather than a package manager like Homebrew because I simply found Homebrew and MacPorts to be a tad immature back then.
Now I use Homebrew (aka brew) on macOS as regularly as I use apt-get on Ubuntu and yum on CentOS. I would recommend avoiding compiling anything from raw source code on macOS unless you really have no choice.
Old answer content below for reference purposes.
I realize this question is about 3+ years old, but the accepted answer is a link only answer and that link is now dead. And the other answer is technically correct, but it still does not explain the actual hands-on process required to install the GNU versions of autoconf, automake and libtool in Mac OS X.
First, Xcode—since at least version 4.3 I believe—no longer includes the GNU versions of autoconf, automake and libtool. This doesn't mean you can't install GNU tools on your own. And here is how.
I've used this process on Mac OS X 10.6 (Snow Leopard), 10.7 (Lion), 10.8 (Mountain Lion) and 10.9 (Mavericks) without issue.
Install Xcode and Xcode command line tools.
The first prerequisite is to have Xcode installed along with the Xcode command line tools as well. Chances are if you need autoconf, automake and libtool installed, you already have Xcode and the command line tools installed, but just pointing that out for those who don't have that setup yet.
Now, onto the show! Just note that version numbers of downloads are based on what is current (as of April 2015) and works well as of the time of this post. Adjust to other versions if you need to:
Install autoconf 2.69.
Set the working directory to your home directory:
cd
Get the source code and decompress it:
curl -O -L http://ftpmirror.gnu.org/autoconf/autoconf-2.69.tar.gz
tar -xzf autoconf-2.69.tar.gz
Go into the uncompressed source code directory:
cd autoconf-*
Run the configure script on the source code:
./configure
Now run make to compile it:
make
Now install it:
sudo make install
Check the newly installed autoconf version to confirm all went well:
autoconf --version
Response should be something like this:
autoconf 2.69
Install automake 1.15.
Set the working directory to your home directory:
cd
Get the source code and decompress it:
curl -O -L http://ftpmirror.gnu.org/automake/automake-1.15.tar.gz
tar -xzf automake-1.15.tar.gz
Go into the uncompressed source code directory:
cd automake-*
Run the configure script on the source code:
./configure
Now run make to compile it:
make
Now install it:
sudo make install
Check the newly installed automake version to confirm all went well:
automake --version
Response should be something like this:
automake 1.15
Install libtool 2.4.6.
Set the working directory to your home directory:
cd
Get the source code and decompress it:
curl -OL http://ftpmirror.gnu.org/libtool/libtool-2.4.6.tar.gz
tar -xzf libtool-2.4.6.tar.gz
Go into the uncompressed source code directory:
cd libtool-*
Run the configure script on the source code:
./configure
Now run make to compile it:
make
Now install it:
sudo make install
Check the newly installed libtool version—via the man page—to confirm all went well:
man libtool
On the first page of the man page there should be something like this:
libtool - manual page for libtool 2.4.6
A: If you install autoconf from the git repository, you will need automake. However, if you instead download a distribution tarball for autoconf, you will not have that dependency. You should always install from a distribution tarball, and not from a vcs. In other words, if you want to install autoconf from source, just install it from source! But realize that "install from source" means "install from a distribution tarball"; it does not mean "install from git".
A: Just use Homebrew. It compiles everything for you. It worked like a charm for me.
brew install autoconf automake libtool
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"redpajama_set_name": "RedPajamaStackExchange"
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\section{Introduction} \label{sec:introduction}
Recent years have witnessed growing interest in exploring relationships between vision and language modalities. A wide range of applications have been boosted by its rapid development, such as multi-modal search engines~\cite{chen2017amc,elizalde2019cross,cao2017collective} and recommender systems~\cite{sun2020multi,wang2019learning,chen2020imram}. It motivates researchers to find semantic correspondence between two modalities and bridging their visual-semantic discrepancy. Some earlier works~\cite{radford2021learning,jia2021scaling,li2021align,gan2020large} focused on learning joint embeddings for these two modalities, while more recent ones~\cite{kamath2021mdetr,li2022grounded,zhang2021vinvl} have turned to considering latent vision-language alignments at the level of regions and words.
\newcommand{\addff}[1]{\includegraphics[width=0.48\linewidth]{fig/fig1/#1.png}}
\begin{figure}
\centering
\small
\renewcommand{\arraystretch}{1.1}
\setlength\tabcolsep{1.2mm}
\begin{tabular}{cc}
\addff{retrieval}&\addff{cap}\\
(a) Image-text Retrieval&(b) Image Caption\\
\addff{det3}&\addff{grounding}\\
(c) Object Detection&(d) Phrase Grounding\\
\end{tabular}
\caption{Visualization on four different tasks.
We visualize the activation map for text-to-image retrieval task in (a). As for the caption task in (b), we visualize regions selected by our model.
Besides cross-modal understanding task, SLAN can transfer to localization tasks, shown in (c) and (d), and we list the confidence score for each region.}
\label{fig:fig1}
\end{figure}
In order to achieve fine-grained cross-modal alignments, some works~\cite{lee2018stacked,kuo2022beyond,li2020oscar} use object detectors to extract key regions in images. Treated as black boxes, the detectors only support for fixed vocabulary object detection. Meanwhile, the extracted regions cannot adapt to different text information due to the freezing parameters of the detectors. To alleviates the problem, VinVL~\cite{zhang2021vinvl} applies a pre-trained object detector with more than $2000$ classes and attributes to enrich local visual representations. However, the extended label set still limits the perceptive capability of object detectors for cross-modal understanding compared to free-form text from real-world scenes.
Recently, more works have attempted to apply learnable region locators for cross-modal tasks, which extract regions of interest conditioned on different texts. Unlike previous methods using frozen object detectors, MDETR~\cite{kamath2021mdetr} builds an end-to-end framework on datasets with region-to-word annotations. GLIP~\cite{li2022grounded} directly proposes grounded language-image pre-training for learning object-level, language-aware, and semantic-rich visual representation. These methods demonstrate their effectiveness in cross-modal reasoning by introducing trainable locators. However, in order to supervise the training of locators, these methods require a certain amount of region-to-word grounding annotations (gold data), which are based on burdensome and expensive annotation efforts. It limits their applications on existing larger scale of cross-modal datasets which have abundant but coarse-grained image and text pairs.
To address the problems above, we propose Self-Locator Aided Network (SLAN) for cross-modal understanding. The designed self-locator is capable of accurately locating regions of interest based on different texts. Specifically, the self-locator consists of a region filter to select important regions and a region adaptor to update coordinates of regions with text guidance. By incorporating the self-locator into our framework, SLAN performs context-aware region extraction and cross-modal feature fusion. Moreover, SLAN is trained solely on datasets with paired images and texts, making it scalable to larger pre-training settings for further performance improvements. With fine-grained region-word alignments, SLAN has a more detailed understanding of interactions in vision and language modalities.
To sum up, our contributions have four aspects:
\begin{itemize}
\item We propose a framework termed SLAN to capture fine-grained interplay between vision and language modalities. A self-locator is introduced to perform text-guided region adaptation, enabling dynamic region-word alignments for cross-modal understanding tasks.
\item We demonstrate that SLAN can be easily applied to large-scale pre-training on cross-modal datasets, because it is free from training with gold data.
\item We naturally generalize SCAN to some localization tasks, such as object detection and phrase grounding, due to its ability to locate key regions in images.
\item Experiments on five cross-modal understanding and two localization tasks demonstrate the effectiveness of our method. For example, SLAN achieves state-of-the-art performance on COCO image-text retrieval.
\end{itemize}
\section{Related Work}
\subsection{Vision-language Task}
\begin{figure*}[!t]
\centering
\includegraphics[scale=0.215]{fig/all6_harley_1110.pdf}
\caption{Overall framework of our proposed SLAN, consisting of two unimodal encoders for embedding images and text and a self-locator for fine-grained region-word alignments. The self-locator performs saliency prediction with a region filter and progressive regression with a region adaptor. The learned vision and language features with cross-modal awareness are used for downstream tasks.
}\label{fig:main}
\end{figure*}
Many efforts have been made to explore relationships between visual and textual modalities, then apply the knowledge to various downstream multi-modal tasks. Some previous methods propose loss functions and network structure to learn semantic vision-language alignments. DeViSE~\cite{frome2013devise} first introduces a linear layer to unify image and text embeddings. TBNN\cite{wang2018learning} learns cross-modal features and applies contrastive losses. The instance loss is introduced in ~\cite{zheng2020dual} to train the dual encoder. Other methods introduce
some prior tools or knowledge to assist the image-text matching analysis. For example, SGG~\cite{xu2017scene} considers the internal relations between visual regions and compares them with the text structure. ViSTA~\cite{cheng2022vista} applies OCR~\cite{biten2019scene} to extract text from images for richer cross-modal labels.
In recent years, a prevailing direction applies cross-modal pre-training on some larger datasets. CLIP~\cite{radford2021learning} pre-trains with 400M image-text pairs collected from the web, building global relations between images and texts. BLIP~\cite{li2022blip} benefits from large-scale web data by filtering out noisy ones, and performs vision-language understanding and generation tasks. Beit-3~\cite{wang2022image} adopts mask-then-predict self-supervised training on large-scale monomodal data (\emph{i.e.,~} images, and texts) and multi-modal data (\emph{i.e.,~} image-text pairs) to learn internal cross-modal dependencies.
Aside from these attempts, exploring local relations between words in text and objects in the image works efficiently in cross-modal pre-training. It helps localize more accurate objects according to corresponding words, and provides cues for downstream tasks.
\subsection{Localization for Vision-language Task}
There are two kinds of methods whose differences are whether the detection module are frozen or trained to adapt to cross-modal tasks.
The first kind introduces a frozen object detector to extract detailed visual representations. SCAN uses Faster R-CNN pre-trained on Visual Genomes to choose key regions for matching with word embeddings.
Instead of using a traditional object detector trained with relatively few classes and data, some later works (e.g., VinVL~\cite{zhang2021vinvl}, Oscar~\cite{li2020oscar}) increase the number of detection labels and introduce some attribute information to complement previous visual concepts.
The other kind relies on fine-grained annotations of the cross-modal dataset to perform pre-training. MDETR~\cite{kamath2021mdetr} introduces a modulated detector with multi-modal datasets, which have precise alignments between phrases in text and objects in the images. GLIP~\cite{li2022grounded} applies grounded pre-training to learn object-level, language-aware, and semantic-rich visual representations. These methods link object detection with phrase grounding (region-word alignments), enabling models to learn from richer semantic knowledge from both modalities. However, these methods require cross-modal data with fine-grained annotations, limiting their application on larger-scale pre-training settings.
\section{SLAN}
We will introduce our proposed SLAN in this section. As shown in Figure~\ref{fig:main}, our framework consists of three components, two unimodal encoders and a self-locator. We first briefly introduce two unimodel encoders.
Then we introduce the detailed structures of SLAN which adaptively select informative regions with text guidance. Finally, we list our pre-training objectives.
\subsection{Unimodal Encoding}
We introduce the vision and text encoder to learn visual and textual representations with ${D}$ dimensions. For text feature extraction, we use BERT~\cite{kenton2019bert} as our text encoder, encoding words into a shared semantic space. A text [CLS] token is added to word embeddings to summarize the whole sentence. For image feature extraction, we encode images and obtain the vision feature map $V$ with high-level semantics.
\subsection{Self-locator for Cross-modal Understanding}\label{ss:mod}
Since fine-grained region-word alignments are important for cross-modal relation exploration, our self-locator is built on DETR~\cite{carion2020end} to output original regions. Region embeddings are extracted from the feature map $V$. A vision [CLS] token is then obtained from global average pooling of region embeddings.
Different from most traditional object detection tasks that use the pre-defined label set, cross-modal tasks usually have a wider vocabulary and free-form textual expressions. Therefore, our self-locator is adapted to introduce a region filter for region saliency prediction and a region adaptor for progressive region regression for cross-modal tasks. By replacing fixed vocabulary prediction with region saliency prediction, our self-locator assigns each region a saliency score to estimate the probability that the region is useful for the alignment process. For traditional detection settings, the regression targets are annotated region coordinates. Since there is no grounding (gold) annotations in our setting, we propose progressive region regression supervised by a weighted summation of updated regions.
\subsubsection{Vision Decoder: Pyramid Feature Extraction}
Our proposed self-locator is designed for regression in a coarse-to-fine manner, requiring visual features of multi-scale and pyramid hierarchy. Considering these characteristics, we adopt a vision decoder after the global visual feature to extract multi-scale feature maps. Let $F_i ~(i \in {1,2,...,L})$ denotes the $i$-th level of decoder features separately, where $L$ is the number of layers of the self-locators. Then $F_i$ is fed to the $i$-th level of self-locator regression.
\subsubsection{Region Filter: Region Saliency Prediction}
When describing images, people usually focus on limited salient regions in the images. However, original detection models (e.g., DETR) output a relatively large number of region proposals (e.g., 100) for images, which are mostly redundant for text descriptions. If we directly select all detected regions, it will lead to unnecessary computational cost and might cause the model to learn some meaningless region-to-word pairs. The strategy to control the maximum number of selected regions. The strategy is as follows: (a) Normalize all saliency scores of these regions. After this process, the scores are represented as $S=\{S_1, ...,S_k\}, S_i \in \mathbb{R}$, with the maximum value of 1. (b) Sort these regions in descending order according to their saliency scores. (c) Select regions with saliency scores above the threshold $h$ ($S_i>h$). (d) If the number of selected regions is greater than hyper-parameter $T$, the self-locator picks the first $T$ regions. Finally, we weight region embeddings by the scores.
\begin{figure}[!t]
\centering
\includegraphics[scale=0.3]{fig/adaptor.pdf}
\caption{Illustration of one level of the region adaptor to update each region's coordinate with text guidance. We use the feature map from vision decoder to extract region embeddings and explore latent region-word alignments.
}\label{fig:ada}
\end{figure}
\begin{algorithm}[h]
\renewcommand{\algorithmicrequire}{\textbf{Input:}}
\renewcommand{\algorithmicensure}{\textbf{Output:}}
\caption{Self-localization}
\label{alg::ba}
\begin{algorithmic}[1]
\Require
Image $x$, region embeddings $E_0^G$, text embeddings $E_0^T$, pyramid feature map $F_i$, neighbour size $(NH_i, NW_i)$, total region regression layers $L$.
\Ensure
Updated regions $G_{out}$, region supervision on detection head $\overline{G}$, visual token $v_{cls}$, textual token $t_{cls}$.
\State $G_0, S, E_0^G$ ← Detection($x$)
\State $G_0, E_0^G$ ← Region Saliency Prediction ($G_0, S, E_0^G$)
\For{$i\in$ $\{1,2,...,L\}$}
\State $E^G_i, E^T_i$ ← Cross attention($E^G_{i-1},E^T_{i-1}$)
\State $ R_i $ ← $(NH_i,NW_i)$
\State $ E^{Ne}_i $ ← Neighbour Embedding($R_i,G_{i-1}$)
\State $Sim_i$ ← Similarity($E^{Ne}_i$,$E^T_i$)
\State $\Delta$$x_i$,$\Delta$$y_i$ ← $Offset$($Sim_i$)
\State $p_{w_i}, p_{h_i}$ are learnable parameters.
\State $G_i$ ← Update($G_{i-1}$,$\Delta$$x_i$,$\Delta$$y_i$,$p_{w_i}, p_{h_i}$)
\State $E^G_i$ ← Embedding($G_i,f_i$)
\EndFor
\State $v_{cls}, t_{cls}$ ← ExtractCLS($E^G_{out}, E^T_{out}$)
\State $G_{out}$ ← $G_{L}$, ~$\overline{G}$ ← $(\sum_{i=1}^{L}G_i)/L$
\end{algorithmic}
\end{algorithm}
\label{ss:ba}
\subsubsection{Region Adaptor: Progressive Region Regression}
This module aims at adjusting the coordinates of proposed regions to align with words with the same semantics. The difficulty comes from no annotated text-referenced regions as ground truths. We transform this problem into the $L$ cascaded coarse-to-fine progressive regression. We set $L$ to 3 in default. As shown in Figure~\ref{fig:ada}, the $i$-th level of the region regression receives three inputs: word embeddings $E_{i-1}^T \in \mathbb{R}^{N^T \times D}$, region embeddings $E_{i-1}^G \in \mathbb{R}^{N^G \times D}$ with their coordinates $G_i \in \mathbb{R}^{N^G \times 4}$, and a global decoder feature map $F_i \in \mathbb{R}^{H_i \times W_i \times D}$, where $N^T$ and $N^G$ denotes the number of words and selected regions respectively.
We describe the procedure for progressive region regression in Algorithm~\ref{alg::ba}. The cross-modality multi-head attention layers fuse region and word embeddings and model their interactions as follows:
\begin{equation}
\begin{aligned}
\label{eqn:ca}
Attn &= \frac{E_{i-1}^G E_{i-1}^{T\top}}{\sqrt{D}}\\
E^G_{i} &= Softmax(Attn) E^T_{i-1}\\
E^T_{i} &= Softmax(Attn^\top) E^G_{i-1} \\
\end{aligned}
,
\end{equation}
where $D$ denotes the dimension of embeddings. With cross-modal semantics, the updated vision-aware word embeddings $E^T_{i}$ are able to guide region coordinate updates by searching for highly correlated regions around the original one. Specifically, the neighborhood of the region $g=(x,y,w,h)$ is defined as a region of size $(NH_i, NW_i)$ centered on it, where $NH_i$ and $NW_i$ are pre-defined parameters for the $i$-th level in region regression. And the neighborhood is split to $K \times K$ regions to compute region-word similarities, as shown in Figure~\ref{fig:ada}, where each region embedding is extracted with RoIAlign and average pooling from $F_i$. With different response scores to words, neighbor regions aggregate context information to the central one. The coordinate update for the central region is in the form of weighted summation of coordinates of neighbor center points as follows:
\begin{equation}
\begin{aligned}
\label{eqn:wo}
w' &= p_w w, ~ ~ h' = p_h h, \\
x' &= x + \Delta x, ~ ~ y' = y + \Delta y, \\
\Delta x &= \sum_{j=0}^{K^2-1}s_j H_j (\lfloor\frac{j}{K}\rfloor-\lfloor\frac{K}{2}\rfloor), \\
\Delta y &= \sum_{j=0}^{K^2-1}s_j W_j ((j~ mod~K) -\lfloor\frac{K}{2}\rfloor), \\
\end{aligned}
\end{equation}
where $\lfloor \cdot \rfloor$ is the round down operation, $p_w$ and $p_h$ are learnable parameters, and $s_j$ is the maximum similarity between the embedding of the $j$-th neighbor region and all word embeddings.
For each original region $g$, let $g_i$ denotes the updated version after the $i$-th layer of region regression. We take the average of them as the ground truth and apply the $L_1$ and GIoU regression loss:
\begin{equation}
\begin{aligned}
\label{eqn:re}
\overline{g} &= \frac{\sum_{i=1}^{L}g_i}{L}\\
\mathcal{L}_{reg}(g) &= \mathcal{L}_{L1}(g,\overline{g})+\mathcal{L}_{GIoU}(g,\overline{g})\\
\end{aligned}
.
\end{equation}
\subsection{Pre-training Objectives with SLAN}
Our SLAN pretrains on image-text pairs and learns fine-grained region-word alignments, supervised by three common losses.
\minisection{Image-Text Matching Loss (ITM)} predicts whether a given image-text pair is positive or not, which can be viewed as a binary classification problem. The visual and textual [CLS] tokens $(v_{cls}, t_{cls})$ are concatenated and sent to a linear layer $f_c$. The ITM loss is formalized as follows:
\begin{equation}
\begin{aligned}
\label{eqn:itm}
\mathcal{L}_{itm} (I,T) &= H(f_c(cat(v_{cls}, t_{cls})),y_{v,t}),
\end{aligned}
\end{equation}
where $y_{v,t}$ denotes the matching relation (1 for matched and 0 for unmatched), and $H$ is the cross-entropy loss for classification.
We directly select positive pairs from the dataset and build hard negative samples with batch sampling, following ALBEF~\cite{li2021align}.
\minisection{Image-Text Contrastive Loss (ITC)} ensures that visual and textual embeddings share the same semantic space and the positive (matched) image-text pairs are pulling closer than negative (unmatched) ones. We use two queues $I_q, T_q$ to save the latest visited image and text samples. For each image-text pair $(I, T)$, the softmax-normalized cross-modal similarity is computed as as:
\begin{equation}
\begin{aligned}
\label{eqn:itm}
p_{i2t} (I,T,T_q) &= \frac{exp(sim(I,T)/ \tau)}{\sum_{T' \in T_q} exp(sim(I,T')/\tau)}\\
p_{t2i} (T,I,I_q) &= \frac{exp(sim(T,I)/\tau)}{\sum_{I' \in I_q} exp(sim(T,I')/\tau)}\\
\end{aligned}
,
\end{equation}
where $\tau$ is a temperature parameter and $sim(\cdot)$ measures cross-modal similarity, which is implemented by the dot product between image and text embeddings.
Following ALBEF \cite{li2021align}, we compute ITC loss as:
\begin{equation}
\begin{aligned}
\label{eqn:itc}
\mathcal{L}_{itc}(I,T) &= -log(p_{i2t}(I,T,T_q))-log(p_{t2i}(T,I,I_q)).
\end{aligned}
\end{equation}
\minisection{Language Modeling Loss (LM)} encourages the model to predict masked words with context information. We randomly mask $15\%$ text tokens and apply the masked language modeling loss as follows:
\begin{equation}
\begin{aligned}
\label{eqn:mlm}
\mathcal{L}_{lm}(I,T) &= H(p_{mask}(I,T),y_{mask}),
\end{aligned}
\end{equation}
where $y_{mask}$ denotes the masked word to predict and $p_{mask}(I,T)$ is its predicted probability.
The full pre-training objective is the combination of the downstream loss and our constraint on progressive region regression, computed as follows:
\begin{equation}
\begin{aligned}
\label{eqn:itm}
\mathcal{L}_{all}&= \mathcal{L}_{ds} +\mathcal{L}_{reg} \\
\end{aligned}
\end{equation}
where $\mathcal{L}_{all}$ is the downstream loss and $\mathcal{L}_{reg}$ denotes the summation of the regression loss in Equation~\ref{eqn:re} for all regions.
\begin{equation}
\begin{aligned}
\label{eqn:itm}
\mathcal{L}_{ds} (I,T) &= \mathcal{L}_{itm} (I,T)+\mathcal{L}_{itc}(I,T)+\mathcal{L}_{lm}(I,T).
\end{aligned}
\end{equation}
\section{Experiments} \label{sec:experiments}
We first pre-train our method on a combined dataset of 14M image-text pairs from five datasets: COCO~\cite{lin2014microsoft}, Visual Genome~\cite{krishna2017visual} (excluding
COCO images), Conceptual Captions~\cite{changpinyo2021conceptual}, Conceptual~\cite{changpinyo2021conceptual}, and SBU Captions~\cite{ordonez2011im2text}. The data statistics are described in supplementary. We evaluate the proposed SLAN by comparing it to other state-of-the-art cross model methods on several downstream tasks. The ablation studies are further conducted to study how each component of our method influences the performance.
\begin{table*}[t]
\centering
\small
\renewcommand{\arraystretch}{1.1}
\setlength\tabcolsep{1.2mm}
\begin{tabular}{cc|cccccc|cccccc} \whline{1pt}
\multirow{2}{*}{Method} & \multirow{1}{*}{Pre-train} & \multicolumn{6}{c|}{Zero-shot}&\multicolumn{6}{c}{Fine-tune} \\
&\# Images &\multicolumn{3}{c}{Image $\rightarrow$ Text}&\multicolumn{3}{c|}{Text $\rightarrow$ Image}&\multicolumn{3}{c}{Image $\rightarrow$ Text}&\multicolumn{3}{c}{Text $\rightarrow$ Image} \\
\whline{0.7pt}
&&R@1&R@5&R@10&R@1&R@5&R@10&R@1&R@5&R@10&R@1&R@5&R@10\\
ALIGN~\cite{li2021align} &1.8B&88.6& 98.7& 99.7& 75.7& 93.8& 96.8& 95.3& 99.8& 100.0& 84.9& 97.4& 98.6\\
FILIP~\cite{yao2021filip} &300M& 89.8& 99.2& 99.8& 75.0& 93.4& 96.3& 96.6& 100.0& 100.0& 87.1& 97.7& 99.1\\
BLIP~\cite{li2022blip} &14M& 94.8& 99.7& 100.0& 84.9& 96.7& 98.3& 96.6& 99.8 &100.0& 87.2& 97.5& 98.8\\
BEIT-3~\cite{wang2022image}&21M& 94.9 &99.9& 100.0& 81.5& 95.6& 97.8& 98.0& 100.0& 100.0& 90.3& 98.7& 99.5\\
Ours&14M&96.0&100.0&100.0& 86.1&97.0&98.5&98.1&100.0&100.0 &90.2&99.0&99.6\\
\whline{1pt}
\end{tabular}
\caption{\label{tab:ftr}Comparison with state-of-the-art image-text retrieval methods on Flickr30k. We use Recall@k scores as the evaluation metric under zero-shot and fine-tuning settings.}
\end{table*}
\begin{table*}[t]
\centering
\small
\renewcommand{\arraystretch}{1.1}
\setlength\tabcolsep{1.2mm}
\begin{tabular}{cc|cc|cccc|cc|cc} \whline{1pt}
\multirow{2}{*}{Method}&\multirow{1}{*}{Pre-training} &\multicolumn{2}{c|}{Retrieval(COCO)} &\multicolumn{4}{c|}{Caption(COCO)}&\multicolumn{2}{c|}{VQA(VQAv2)}&\multicolumn{2}{c}{NLVR(NLVR2)} \\
&Data&I2T R@1&T2I R@1&B@4&M&C&S&test-dev&test-std&dev&test-P
\\
\whline{0.7pt}
Oscar~\cite{li2020oscar} &6.5M&73.5&57.5& 37.4&30.7& 127.8&23.5& 73.6& 73.8& 79.1& 80.3\\
VinVL~\cite{zhang2021vinvl} &8.85M&75.4&58.8& 38.5&30.4&130.8&23.4& 76.5& 76.6& 82.6& 83.9\\
SimVLM~\cite{wang2021simvlm}&1.8B &-&-& 40.6&33.7& 143.3&25.4& 80.0& 80.3& 84.5& 85.1\\
GLIPv2-H~\cite{zhang2022glipv2}&16M & -&-&-&-&131.0&-&74.6 & 74.8&-&-\\
CoCa~\cite{yu2022coca} &4.8B&-&-& 40.9&33.9& 143.6&24.7& 82.3& 82.3& 86.1& 87.0\\
BLIP~\cite{li2022blip} &14M&82.4&65.1& 40.4&-& 136.7&-& 78.2& 78.3& 82.1&82.2\\
Ours&14M&85.7&69.2&43.7&34.1& 144.3&25.6&83.4 &83.5&90.4&91.3\\
\whline{1pt}
\end{tabular}
\caption{\label{tab:od}Comparison on more downstream tasks. For COCO retrieval, I2T and T2I represent image to text and text to image retrieval task, respectively. For COCO image captioning, we report BLEU@4 (B@4), METEOR (M), CIDEr (C), and SPICE (S) on the Karpathy test split. For VQA, we evaluate the vqa-score on VQAv2 test-dev and test-standard (test-std) splits. For NLVR, we report accuracy on NLVR2 development set (dev) and public test set (test-P).}
\end{table*}
\subsection{Implementation Details}
We choose $BERT_{base}$~\cite{kenton2019bert} as our text encoder, which is initialized from HuggingFace~\cite{wolf2020transformers}.
For the vision encoder, we explore four options: one is the CNN model ResNet50, and three kinds of ViT:
ViT-Base, ViT-Large and ViT-Huge, which are all random initialized. As for the neighbour size for each region adaptor, we use a ratio $r_i$ to denote them: ($NH_i$, $NW_i$) = ($r_i H_i$, $r_i W_i$), where $r_1, r_2, r_3 = 1, 0.5, 0.25$, respectively.
We pre-train SLAN for 20 epochs. For different options of the vision encoder, the batch size is set to 1280, 960, 640, 640 for ResNet50, Vit-B, Vit-L and Vit-H, respectively.
The AdamW optimize is adopted with the initial learning rate 3e-4, and the learning rate is linearly decayed to 0. We resize the input images to 224$\times$224.
\subsection{Comparison on The Downstream Tasks}
We compare our approach with state-of-the-art methods on five challenging cross-modal understanding tasks, including image-text retrieval, image captioning, visual question answering, natural language visual reasoning, zero-shot video-text retrieval. Besides, we transfer our method to two localization tasks: object detection and phrase grounding. The default vision encoder is Vit-Huge, if not specified.
\subsubsection{Image-Text Retrieval}
Given an image, the task expects to retrieve the corresponding text from the text gallery through the input image, and vice versa. We evaluate our method on Flickr30k~\cite{plummer2015flickr30k} under zero-shot and fine-tune settings with Karpathy split and the performance is evaluated in terms of Recall@k. The comparative results are shown in Table~\ref{tab:ftr}.
Specifically, on the same pre-training setting, SLAN also outperform BLIP~~\cite{li2022blip} by 3.3\% in average recall@1 on COCO. This performance gain explains the efficiency of learning fine-grained alignments from coarse annotations.
\subsubsection{Image Captioning}
Given an input image, this task generates a sentence description to describe the image in detail. We use COCO Karpathy split to fine-tune and evaluate our method. Our SLAN outperforms most previous methods under this efficient setting, as shown in Table~\ref{tab:od}.
\begin{table}[tp]
\centering
\small
\setlength\tabcolsep{1.3mm}
\renewcommand{\arraystretch}{1.3}
\begin{tabular}{c|cccc}
\whline{1pt}
Method & R@1 $\uparrow$ & R@5 $\uparrow$ & R@10 $\uparrow$ & MdR $\downarrow$ \\ \hline
ClipBERT~\cite{lei2021less}& 22.0& 46.8& 59.9& 6\\
VideoCLIP~\cite{xu2021videoclip}& 30.9& 55.4 &66.8& -\\
FiT\dag~\cite{bain2021frozen}&43.3& 65.6& 74.7& 2\\
BLIP\dag~\cite{li2022blip} &43.3& 65.6& 74.7& 2 \\
Ours\dag &46.8&70.5& 83.6& 1.5\\
\whline{1pt}
\end{tabular}
\caption{\label{tab:vr}Comparisons with state-of-the-art methods for text-video retrieval on the 1k test split of the MSRVTT~\cite{xu2016msr-vtt} dataset. \dag denotes the zero-shot settings, while others are fine-tuned ones.
}
\end{table}
\begin{table*}[t]
\centering
\small
\renewcommand{\arraystretch}{1.1}
\setlength\tabcolsep{1.2mm}
\begin{tabular}{ccc|cc|cc|p{11mm}p{11mm}p{11mm}} \whline{1pt}
\multirow{2}{*}{Method} & \multirow{2}{*}{Backbone}&\multirow{2}{*}{Params(M)}&\multicolumn{2}{c|}{Pretrain Data(M)}& \multicolumn{2}{c|}{Object Detection(COCO)}&\multicolumn{3}{c}{Phrase Grounding(Flickr30k)}
\\
&&&Image-Text&Region-Word&Zero-shot&Fine-tune&R@1&R@5&R@10
\\
\whline{0.7pt}
DETR~\cite{carion2020end}&ResNet50&42&0&0&-&42.0&-&-&-\\
MDETR~\cite{kamath2021mdetr}&ResNet101&185&0&0.2&-&-&84.3&93.9&95.8\\
GLIP~\cite{li2022grounded} &Swin-Large&430&24&3& 49.8& 60.8& 87.1& 96.9&98.1\\
GLIPv2~\cite{zhang2022glipv2} &Swin-Huge&870&16&3& -& 60.2& 87.7&97.3&98.5\\\hline
Ours &ResNet50&322&14&0& 46.9& 59.2& 86.8&96.6&97.4\\
Ours &Vit-Base& 383&14&0&47& 59.6& 87.4&96.9&98.2\\
Ours&Vit-Large&601&14&0& 48.5& 60.5& 89.1&98.0&98.9\\
Ours&Vit-Huge&929&14&0& 50.1& 63.5& 90.6&98.6&99.3\\
\whline{1pt}
\end{tabular}
\caption{\label{tab:det}Comparison on two localization tasks: Object Detection on COCO and Phrase Grounding on Flickr30k. The pre-training data covers: image-text pairs and word-specific region annotations. we evaluate zero-shot and fine-tune settings on object detection. We use recall@k scores to evaluate phrase grounding task.
}
\end{table*}
\begin{table}[t]
\centering
\small
\renewcommand{\arraystretch}{1.1}
\setlength\tabcolsep{1.2mm}
\begin{tabular}{cccccccc} \whline{1pt}
\multirow{1}{*}{Trainable} & \multirow{1}{*}{Adaptor}& &\multicolumn{2}{c}{COCO}&&\multicolumn{2}{c}{Flickr30k}
\\
Detector&Number&&TR@1&IR@1&&TR@1&IR@1
\\
\whline{0.7pt}
\ding{56}&0&&68.5&53.5&&85.0&74.1\\
\ding{52}&0&&69.1&53.8&&86.7&76.2\\
\ding{52}&1&&70.0&57.2&&88.3&77.4\\
\ding{52}&2&&70.8&57.5&&88.7&78.1\\
\ding{52}&3&&72.1&58.3&&90.3&78.9\\
\whline{1pt}
\end{tabular}
\caption{\label{tab:ba}Effect of training detection module and region adaptor. \ding{56} in the first coloum denotes applying a frozen detection module and no self-locator. TR@1 and IR@1 denote recall@1 of image to text and text to image retrieval. To evaluate the effect of the self-locator against a frozen detection module, we load the pre-trained weight from COCO Detection to compare with our method for line 1. The remaining experiments train from scratch. We use Vit-Base as the vision encoder.}
\end{table}
\begin{table}[t]
\centering
\small
\renewcommand{\arraystretch}{1.1}
\setlength\tabcolsep{1.2mm}
\begin{tabular}{cccccccc} \whline{1pt}
\multirow{2}{*}{Top K} & \multirow{2}{*}{Threshold}& &\multicolumn{2}{c}{COCO}&&\multicolumn{2}{c}{Flickr30k}
\\
&&&TR@1&IR@1&&TR@1&IR@1
\\
\whline{0.7pt}
-&-&&69.4&54.1&&85.9&74.7\\
10&-&&70.6&56.8&&87.5&77.3\\
10&0.3&&71.2&57.6&&89.1&78.2\\
10&0.5&&72.1&58.3&&90.3&78.9\\
\whline{1pt}
\end{tabular}
\caption{\label{tab:bf}Different settings of the region filter.}
\end{table}
\subsubsection{Visual Question Answering}
Visual Question Answering (VQA)~\cite{antol2015vqa} requires the model to predict an answer from an image and a question. We follow ~\cite{li2022blip} and treat VQA as an open-ended question-generation task. We fuse the image embedding with the question embedding and send them to the question decoder to get the result. As shown in Table~\ref{tab:od}, SLAN outperform other method by at least 1.1\% on VQAv2 test-dev and test-std with less or equal pre-training data.
\subsubsection{Natural Language Visual Reasoning}
Natural Language Visual Reasoning (NLVR2)~\cite{suhr2018corpus} measures whether a sentence describes a pair of images. We extract the image and text embeddings from the image-text input, which are fused by a cross-attention layer. We use a binary classification module to predict their relations. As shown in Table~\ref{tab:od}, our results surpass others by a large margin, showing the importance of learning fine-grained cross-modal alignments.
\subsubsection{Zero-shot Video-Text Retrieval}
Besides the image-text tasks mentioned above, our method can generalize to the video-text retrieval task. We randomly select $m$ frames of the video input and concatenate them to get an image-text sequence, then we feed them directly into our image-text retrieval model. The performance in Table~\ref{tab:vr} is comparable to others, demonstrating the cross-modal knowledge learned in our method is semantic-rich.
\subsubsection{Localization Tasks}
We conduct two localization tasks: object detection on COCO, and phrase grounding on Flickr30k.
For the text input on the object detection task, we use a prompt composed of concatenated labels of COCO (e.g. detect: person, bicycle, car, ... , toothbrush). We adopt the output from the last layer of the Table~\ref{tab:det} has exciting results about SLAN on localization tasks.
For example, in the task of object detection with Vit-Base as the backbone, SLAN achieves comparable results to GLIP using a larger backbone and 3M gold data, i.e., Swin-Large, only slightly worse on object detection task, but still slightly better on grounding task. When applying a larger backbone Vit-Huge, our method significantly outperforms all comparison methods.
\subsection{Ablation Study}
\subsubsection{Effect of Self-locator
}
\minisection{Importance of learnable detection module.} As shown in the first row of Table~\ref{tab:ba}, we replace our self-locator with a frozen detector pre-trained on COCO Detection, and the second row is the result of our learnable detector. We do not load the detector with pre-trained weights, but only fine-tune on the downstream task datasets. Our method improves on average about 0.5\% and 2\% on COCO and Flickr30k's image-to-text
and text-to-image retrieval tasks, respectively.
\minisection{Number of region adaptors for region regression.} The region adaptor performs progressive regression on the regions output by the detector to provide more accurate region localization for cross-modal understanding tasks. As shown in Table~\ref{tab:ba}, as the number of region adaptors increases from 0 to 3, the retrieval performance can be significantly improved by an average of more than 3\%.
\minisection{Region filter for saliency prediction.}
Table~\ref{tab:bf} illustrates how the region filter affects the performance on COCO and Flickr30k retrieval tasks. Learnable detector is trained from scratch and the number of region adaptors is set to 3. The first and second rows show that when the regions are sorted by saliency score and selected by a certain number, we can achieve an performance gain of ~2\% on each dataset. When using the saliency score threshold, our region filter is able to remove redundant regions that negatively affect cross-modal adaptation with higher performance.
\subsubsection{Computational Cost}
Table~\ref{tab:com} illustrates the computational cost of our method and other state-of-the-art methods. Our method has the smallest amount of parameters and FLOPS because in this experiments our vision backbone is a relatively lightweight ResNet50. However, our retrieval performance significantly outperforms other methods. As far as our concerned, our method is efficient and high-performance.
\begin{table}[t]
\centering
\small
\renewcommand{\arraystretch}{1.1}
\setlength\tabcolsep{1.2mm}
\begin{tabular}{cccccc} \whline{1pt}
\multirow{2}{*}{Method}&\multirow{2}{*}{Backbone} & \multirow{2}{*}{Params(M)}& \multirow{2}{*}{FLOPS(G)}&\multicolumn{2}{c}{COCO}
\\
&&&&TR@1&IR@1
\\
\whline{0.7pt}
BLIP&Vit-Base&370&558&81.9&64.3\\
BLIP&Vit-Large&810&1594&82.4&65.1\\
Coca&Vit-Huge&2100&4103&83.0&65.5\\
Beit-3&Vit-Huge&1900&-& 84.8&67.2\\
Ours&ResNet50&322&324&85.1&68.9\\
\whline{1pt}
\end{tabular}
\caption{\label{tab:com}Comparison of model parameter and FLOPS on cross-modal retrieval task. The FLOPS is calculated with the image of 384x384 resolution. The Backbone denotes the vision encoder.}
\end{table}
\subsection{Visualization Analysis}
\subsubsection{Text-guided Region Adaptation}
As shown in Figure~\ref{fig:tg}, our region adaptor produces text-specific results with relatively high confidence. When we change the detailed description of the sentence, e.g., ``a man in a red coat" to ``a man in black pants", the interesting phenomenon is that the attention regions of our self-locator are also shifted accordingly with relatively high confidence.
\subsubsection{Region adaptation during training phases}
SLAN learns to localize accurate regions given input sentences. As illustrated in Figure~\ref{fig:pha}, as training progresses, the regions of interest outputed by our model gradually become accurate. This demonstrates that our model can be trained without grounding annotation and can gradually learn fine-grained image-text alignment information.
\newcommand{\addtg}[1]{\includegraphics[width=0.47\linewidth]{fig/tg/#1.jpg}}
\begin{figure}
\centering
\small
\renewcommand{\arraystretch}{1.1}
\setlength\tabcolsep{1.2mm}
\begin{tabular}{cc}
\addtg{insa}&\addtg{insb}\\
\end{tabular}
\caption{Illustration of text-specific region adaptation. We colorize three words per sentence and use the corresponding colors to mark the regions with the highest matching scores. This denotes the interpretable region adaptation of our method, which brings fine-grained cross-modal feature fusion for downstream tasks.}
\label{fig:tg}
\end{figure}
\newcommand{\addtrb}[1]{\includegraphics[width=0.31\linewidth]{fig/trb/#1.jpg}}
\begin{figure}
\centering
\small
\renewcommand{\arraystretch}{1.1}
\setlength\tabcolsep{1.2mm}
\begin{tabular}{ccc}
\addtrb{ph0}&\addtrb{ph3}&\addtrb{ph1}\\
0&1/2&1\\
\end{tabular}
\caption{Visualization of region proposal during pre-training. The numbers under images denote the relative training duration, where $1$ represents the whole pre-training procedure. The referenced text is "A \textcolor{yellow}{man} in a green \textcolor{blue}{shirt} is doing the trick on a \textcolor{red}{skateboard}."}
\label{fig:pha}
\end{figure}
\begin{figure}[!t]
\centering
\includegraphics[scale=1.55]{fig/trb/boxadapt2.jpg}
\caption{ \label{fig:cba}Coarse-to-fine process of the region adaptation. We also list the matching score between the regions and counterpart words.
}
\end{figure}
\subsubsection{Coarse-to-fine Region Adaptation}
To verify the calibration effect of region adaptation, we visualize an image with its text in Figure~\ref{fig:cba}. Model locates more accurate regions of interest with higher similarity scores after three levels of region adaptor. This shows that our self-locator hierarchically refines the related regions of provided words.
\section{Conclusions and Future Work}
In this paper, we present the Self-Locator Aided Network (SLAN), which incorporates the self-locator to adapt proposed regions for cross-modal alignments without extra grounding (region-to-word) annotations. Experimental results show that our method achieves a strong performance on many cross-modal understanding tasks. Besides, the self-locator can also be transferred to some localization tasks, and demonstrates its potential on them. We hope SLAN provides a new direction for learning fine-grained cross-modal alignments without relying on expensive grounding annotations.
\clearpage
{\small
\bibliographystyle{ieee_fullname}
\section{Introduction}
After receiving paper reviews, authors may optionally submit a rebuttal to address the reviewers' comments, which will be limited to a {\bf one page} PDF file. Please follow the steps and style guidelines outlined below for submitting your author response.
Note that the author rebuttal is optional and, following similar guidelines to previous CVPR conferences, it is meant to provide you with an opportunity to rebut factual errors or to supply additional information requested by the reviewers. It is NOT intended to add new contributions (theorems, algorithms, experiments) that were not included in the original submission. You may optionally add a figure, graph or proof to your rebuttal to better illustrate your answer to the reviewers' comments.
Per a passed 2018 PAMI-TC motion, reviewers should not request additional experiments for the rebuttal, or penalize authors for lack of additional experiments. This includes any experiments that involve running code, e.g., to create tables or figures with new results. \textbf{Authors should not include new experimental results in the rebuttal}, and reviewers should discount any such results when making their final recommendation. Authors may include figures with illustrations or comparison tables of results reported in the submission/supplemental material or in other papers.
The rebuttal must adhere to the same blind-submission as the original submission and must comply with this rebuttal-formatted template.
\subsection{Response length}
Author responses must be no longer than 1 page in length including any references and figures. Overlength responses will simply not be reviewed. This includes responses where the margins and formatting are deemed to have been significantly altered from those laid down by this style guide. Note that this \LaTeX\ guide already sets figure captions and references in a smaller font.
\section{Formatting your Response}
{\bf Make sure to update the paper title and paper ID in the appropriate place in the tex file.}
All text must be in a two-column format. The total allowable width of the text
area is $6\frac78$ inches (17.5 cm) wide by $8\frac78$ inches (22.54 cm) high.
Columns are to be $3\frac14$ inches (8.25 cm) wide, with a $\frac{5}{16}$ inch
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Please number all of your sections and any displayed equations. It is important
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Wherever Times is specified, Times Roman may also be used. Main text should be
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List and number all bibliographical references in 9-point Times, single-spaced,
at the end of your response. When referenced in the text, enclose the citation
number in square brackets, for example~\cite{Authors14}. Where appropriate,
include the name(s) of editors of referenced books.
\begin{figure}[t]
\begin{center}
\fbox{\rule{0pt}{1in} \rule{0.9\linewidth}{0pt}}
\end{center}
\caption{Example of caption. It is set in Roman so that mathematics
(always set in Roman: $B \sin A = A \sin B$) may be included without an
ugly clash.}
\label{fig:long}
\label{fig:onecol}
\end{figure}
\subsection{Illustrations, graphs, and photographs}
All graphics should be centered. Please ensure that any point you wish to make is resolvable in a printed copy of the response. Resize fonts in figures to match the font in the body text, and choose line widths which render effectively in print. Many readers (and reviewers), even of an electronic copy, will choose to print your response in order to read it. You cannot insist that they do otherwise, and therefore must not assume that they can zoom in to see tiny details on a graphic.
When placing figures in \LaTeX, it's almost always best to use \verb+\includegraphics+, and to specify the figure width as a multiple of the line width as in the example below
{\small\begin{verbatim}
\usepackage[dvips]{graphicx} ...
\includegraphics[width=0.8\linewidth]
{myfile.eps}
\end{verbatim}
}
{\small
\bibliographystyle{ieee_fullname}
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 2,910
|
Always give a shock as soon as a defibrillator is available, don't give a round of compressions first.
With initial VF/VT, wait with drugs until you've done 4 mins of Advanced CPR.
In pregnant patients in cardiac arrest, perimortem caesarian should be initiated after 4 mins of unsuccessful CPR.
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 7,452
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Coming Soon (26)
Under 1 Hour (388)
1-3 Hours (381)
6-10 Hours (528)
10-20 Hours (311)
Audiobook (1,897)
Radio & TV Program (23)
Periodical (14)
Abridged (40)
Unabridged (1,833)
Whispersync
Whispersync for Voice (839)
What the New Science of Psychedelics Teaches Us About Consciousness, Dying, Addiction, Depression, and Transcendence
By: Michael Pollan
Narrated by: Michael Pollan
When Michael Pollan set out to research how LSD and psilocybin (the active ingredient in magic mushrooms) are being used to provide relief to people suffering from difficult-to-treat conditions such as depression, addiction, and anxiety, he did not intend to write what is undoubtedly his most personal book. But upon discovering how these remarkable substances are improving the lives not only of the mentally ill but also of healthy people coming to grips with the challenges of everyday life, he decided to explore the landscape of the mind in the first person as well as the third.
A delightful trip
By Paul E. Williams on 05-19-18
Answers to Eczema, Psoriasis, Diabetes, Strep, Acne, Gout, Bloating, Gallstones, Adrenal Stress, Fatigue, Fatty Liver, Weight Issues, SIBO & Autoimmune Disease
By: Anthony William
Narrated by: Sarah Coomes
Medical Medium Liver Rescue offers the answers you should have had all along. With his signature compassion, Anthony William, the Medical Medium, shares unparalleled insights into undiscovered functions of our life-saving livers, explains what's behind dozens of health issues that hold us back, and offers detailed guidance on how to move forward so we can live our best lives. Find out for yourself what liver rescue is all about: being clearer-headed, more peaceful, happier, and better able to adapt to our fast-changing times.
I wish there was a pdf of the 3:6:9 cleanse
By Lindsey DeLeo on 02-22-19
Being Mortal
Medicine and What Matters in the End
By: Atul Gawande
Narrated by: Robert Petkoff
In Being Mortal, bestselling author Atul Gawande tackles the hardest challenge of his profession: how medicine can not only improve life but also the process of its ending. Medicine has triumphed in modern times, transforming birth, injury, and infectious disease from harrowing to manageable. But in the inevitable condition of aging and death, the goals of medicine seem too frequently to run counter to the interest of the human spirit.
Required Reading!
By Jeffrey on 10-13-14
Medical Medium Celery Juice
The Most Powerful Medicine of Our Time Healing Millions Worldwide
From celebrities posting about their daily celery juice routines to people from all walks of life sharing pictures and testimonials of their dramatic recovery stories, celery juice is revealing itself to ignite healing when all odds seem against it. What began decades ago as a quiet movement has become a global healing revolution.
I can't stop talking about this!!!
By Jennifer Rivera on 06-23-19
History's Worst Plagues and the Heroes Who Fought Them
By: Jennifer Wright
In 1518, in a small town in Alsace, Frau Troffea began dancing and didn't stop. She danced until she was carried away six days later, and soon 34 more villagers joined her. Then more. In a month more than 400 people had been stricken by the mysterious dancing plague. In late-19th-century England an eccentric gentleman founded the No Nose Club in his gracious townhome - a social club for those who had lost their noses, and other body parts, to the plague of syphilis for which there was then no cure.
Human Reactions to Historical Disasters
By N. Rogers on 08-12-17
Medical School for Everyone
Grand Rounds Cases
By: Roy Benaroch, The Great Courses
Narrated by: Roy Benaroch
There's an art and science behind how doctors diagnose and treat medical patients. Where do doctors get these skills? The Grand Rounds experience, where they practice how to make accurate diagnoses by examining real patients. And with Dr. Benaroch's 24 unique lectures, you'll explore how a master physician solves medical problems just like a detective.
Be a Medical Sherlock's Watson
By Jacobus on 05-17-14
Series: The Great Courses: Better Living
Complex PTSD
By: Pete Walker
Narrated by: Paul Brion
The causes of Complex Post-Traumatic Stress Disorder range from severe neglect to monstrous abuse. Many survivors grew up in houses that were not homes-in families that were as loveless as orphanages and sometimes as dangerous. If you felt unwanted, unliked, rejected, hated, and/or despised for a lengthy portion of your childhood, trauma may be deeply engrained in your mind, soul, and body. This book is a practical guide to recovering from lingering childhood trauma. It is copiously illustrated with examples of the author's and his clients' journeys of recovering.
Neurofitness
A Brain Surgeon's Secrets to Boost Performance & Unleash Creativity
By: Dr. Rahul Jandial
Narrated by: Graham Winton
This fascinating book draws on Dr. Jandial's broad-spectrum expertise and brings together the best of various fields - surgery, science, brain structure, the conscious mind - all to explain the bigger picture of brain health and rejuvenation. It is a journey into his operating room, around the world on his surgical missions, inside his laboratory, and to the outer edges of neuroscience to reveal the latest brain breakthroughs that are turning science fiction into reality, translating their implications for everyday life.
Fantastic! Wonderful book and a fab performance
By Lisa M. Ludwig on 07-02-19
Narrated by: Scott Brick
"What should we have for dinner?" To one degree or another, this simple question assails any creature faced with a wide choice of things to eat. Anthropologists call it the omnivore's dilemma. Choosing from among the countless potential foods nature offers, humans have had to learn what is safe, and what isn't. Today, as America confronts what can only be described as a national eating disorder, the omnivore's dilemma has returned with an atavistic vengeance.
Great presentation of a moral dilemma
By MCRedding on 02-07-09
The Secret History of Lyme Disease and Biological Weapons
By: Kris Newby
Narrated by: Coleen Marlo
A riveting thriller reminiscent of The Hot Zone, this true story dives into the mystery surrounding one of the most controversial and misdiagnosed conditions of our time - Lyme disease - and of Willy Burgdorfer, the man who discovered the microbe behind it, revealing his secret role in developing bug-borne biological weapons and raising terrifying questions about the genesis of the epidemic of tick-borne diseases affecting millions of Americans today.
Ban up job
By Kristina Bauer on 05-16-19
A Step-By-Step Guide to Reverse Polycystic Ovary Syndrome, Regulate Your Hormones and Restore Your Fertility
By: Simon Lloyd
Narrated by: Scott Clem
Most people's busy lives, combined with the absence of information on the subject of PCOS, has led many women to an unexplainable, uphill battle against acne, depression, irregular menstrual cycles, and weight gain. Even worse, infertility can be a very possible, albeit reversible, symptom of PCOS. In this book, you will find everything you need to know about reversing PCOS.
I needed this book
By Trixie Aguilar on 10-30-18
My Month of Madness
By: Susannah Cahalan
Narrated by: Heather Henderson
In 2009, Susannah Cahalan woke up in a strange hospital room strapped to a bed, under guard, and unable to move or speak. Her medical records - from a month-long hospital stay of which she had no memory - reported psychosis, violence, and dangerous instability. Yet, only weeks earlier she had been a healthy, ambitious twenty-four-year-old, six months into her first serious relationship and a sparkling career as a cub reporter
For those interested in neurology & psychology
By Brian Quaranta on 01-07-14
Deep Medicine
How Artificial Intelligence Can Make Healthcare Human Again
By: Eric Topol
Medicine has become inhuman, to disastrous effect. The doctor-patient relationship - the heart of medicine - is broken: doctors are too distracted and overwhelmed to truly connect with their patients, and medical errors and misdiagnoses abound. In Deep Medicine, leading physician Eric Topol reveals how artificial intelligence can help. AI has the potential to transform everything doctors do, from notetaking and medical scans to diagnosis and treatment, greatly cutting down the cost of medicine and reducing human mortality.
By Philip Yaghmai on 05-04-19
Medical Medium Thyroid Healing
The Truth behind Hashimoto's, Graves', Insomnia, Hypothyroidism, Thyroid Nodules & Epstein-Barr
The thyroid is the new hot topic in health. Across age groups, from baby boomers (and their parents) to millennials, more and more people - women especially - are hearing that their thyroids are to blame for their fatigue, weight gain, brain fog, memory issues, aches and pains, insomnia, hair loss, hot flashes, sensitivity to cold, and more. Everyone wants to know how to free themselves from the thyroid trap. As the thyroid has gotten more and more attention, though, these symptoms haven't gone away - people aren't healing.
Convincing...
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The Emperor of All Maladies
A Biography of Cancer
By: Siddhartha Mukherjee
Narrated by: Fred Sanders
The Emperor of All Maladies reveals the many faces of an iconic, shape-shifting disease that is the defining plague of our generation. The story of cancer is a story of human ingenuity, resilience, and perseverance but also of hubris, arrogance, paternalism, and misperception, all leveraged against a disease that, just three decades ago, was thought to be easily vanquished in an all-out "war against cancer".
By S.R.E. on 03-02-16
By: Beth Macy
Narrated by: Beth Macy
In this masterful work, Beth Macy takes us into the epicenter of America's 20-plus year struggle with opioid addiction. From distressed small communities in Central Appalachia to wealthy suburbs; from disparate cities to once-idyllic farm towns; it's a heartbreaking trajectory that illustrates how this national crisis has persisted for so long and become so firmly entrenched. Through unsparing, yet deeply human portraits of the families and first responders struggling to ameliorate this epidemic, each facet of the crisis comes into focus.
Amazingly sad scary and informative.
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Bottle of Lies
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By: Katherine Eban
Narrated by: Katherine Eban
From an award-winning Fortune reporter, an explosive narrative investigation of the generic drug boom that reveals the life-threatening dangers posed by globalization - The Jungle for pharmaceuticals.
A Call to Action - Citizens Awake!
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In the Realm of Hungry Ghosts
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By: Gabor Maté
Narrated by: Daniel Maté
In this timely and profoundly original book, best-selling writer and physician Gabor Maté looks at the epidemic of addictions in our society, tells us why we are so prone to them, and what is needed to liberate ourselves from their hold on our emotions and behaviours.
Anyone in the helping field must read
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Nine Pints
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Narrated by: Karen Cass
Blood carries life, yet the sight of it makes people faint. It is a waste product and a commodity pricier than oil. It can save lives and transmit deadly infections. Author Rose George is renowned for her intrepid work on topics that are invisible but vitally important. In Nine Pints, she takes us from ancient practices of bloodletting to modern "hemovigilance" teams that track blood-borne diseases. She probes the lucrative business of plasma transfusions and looks to the future, as researchers seek to bring synthetic blood to a hospital near you.
Surprisingly Entertaining
By Diana Zou on 06-10-19
A Terrifying True Story
By: Richard Preston
Narrated by: Richard M. Davidson
A highly infectious, deadly virus from the central African rain forest suddenly appears in the suburbs of Washington, D.C. There is no cure. In a few days, 90 percent of its victims are dead. A secret military SWAT team of soldiers and scientists is mobilized to stop the outbreak of this exotic "hot" virus. The Hot Zone tells this dramatic story, giving a hair-raising account of the appearance of rare and lethal viruses and their "crashes" into the human race. Shocking, frightening, and impossible to ignore, The Hot Zone proves that truth really is scarier than fiction.
If you love viruses and gore and non-fiction...
By aaron on 01-05-12
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{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
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Florentino és una entitat de població de l'Uruguai, ubicada al centre-nord del departament de Salto.
Es troba a 112 metres sobre el nivell del mar. Té una població aproximada de 100 habitants cal remarcar que les dades es van prendre l'any 1996 per lo qual no és sap si ha disminuït o augmentat la població.
Referències
Entitats de població de Salto
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{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 3,522
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Q: machine froze during upgrade to 12.04 I tried upgrading from 11.10 to 12.04. It got to the point of installing packages then I stepped away. When I got back the screen was black (possibly due to the screen saver). I left it for about 8 hours and there was no change. I then power-cycled and now it won't boot to a login screen. I tried hitting <Esc> repeatedly while powering up (to get to the Grub menu) but that has no effect.
What should I do now?
EDIT:
I can see the files on the hard disk once I boot from a Live CD. I saw some stuff online about using chroot and dpkg to continue an aborted upgrade from the command line. Is there any comprehensive guide on this?
A: The original poster here, SplashHit, indicated in a comment that this question on SuperUser answered the question.
*
*In that question, the OP followed this "guide" posted on Launchpad (which is actually the original version of this bug report by TJ).
*rumtscho, the OP of that SuperUser question, had attempted to chroot into the installed system from a live CD system and run dpkg --configure -a, but there were lots of Permission denied error messages.
*The accepted answer (by Darth Android) was that the OP needed to mount the /proc and /dev filesystems in the chroot before running dpkg ....
It's unclear from SplashHit (the original poster here)'s comment whether the Launchpad "guide" was sufficient to solve this problem here, or if the answer to that question was also necessary.
In any case, it appears that this question is now effectively answered for the OP (and abandoned).
@SplashHit, if I am mistaken and you still need help with this problem, please let us know (you can post a comment here, and of course if there is additional information then you can add that to your question).
A: Try holding down Shift to get to the GRUB2 menu. If that works, see if you can boot any of the options. (You can then provide more information in your question.)
If that doesn't work, or you do get a GRUB2 menu but you can't boot into Ubuntu, try reinstalling the GRUB2 boot loader to your Master Boot Record (MBR), using any of these methods.
Once you've booted into Ubuntu, you can attempt to repair and finish the upgrade by running sudo apt-get dist-upgrade.
A: About using chroot, you can take a look at this Gentoo guide:
*
*Chroot from a livecd
It says how you can reinstall grub, but you can run dpkg --configure -a instead of grub2-install.
The main idea of the chroot approach is to mount your original / partition on the live CD filesystem, probably on /mnt/mysystem, then chroot to /mnt/mysystem. After chrooting, your / will be actually /mnt/mysystem, your original /. It's like you CHanged your ROOT.
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{
"redpajama_set_name": "RedPajamaStackExchange"
}
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Family law matters are often complex and very personal. From the breakdown of a marriage to property settlements, navigating family affairs requires skill and experience to guide parties through these difficult times. Resolving issues involving children and child support can be particularly stressful.
Where possible, most family law matters should be resolved through negotiation and mediation. Family law court cases are often time-consuming and very expensive – it can take years to obtain a court judgment. On the other hand, resolving a family law matter outside the court system often results in a more amicable outcome in a shorter time frame.
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{
"redpajama_set_name": "RedPajamaC4"
}
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House Speaker Nancy Pelosi described the Climate Action Now Act as one of many steps toward Democratic efforts to confront global warming. In particular, the bill aims to prevent President Donald Trump from removing the United States from the non-binding Paris Climate accord.
The bill is a watered-down version of New York Rep. Alexandria Ocasio-Cortez's Green New Deal, which called for shifting completely away from fossil fuels and toward green energy. The GND was torpedoed in the Senate on Tuesday after Republicans voted en masse against the resolution while Democrats voted present.
The GND was introduced in February and called for "10-year national mobilizations" toward a series of goals aimed at fighting global warming. A fact sheet posted online during the introduction claimed the plan would "mobilize every aspect of American society on a scale not seen since World War 2." It also became an object of ridicule as a draft suggested the end of cows and drastically curbing airplane travel.
Not a single Democrat (including 6 running for President) supported the Green New Deal when put up for a vote in Senate. AOC tries to pivot from climate change to pollution.
House Democrats along with most of the Democratic Party's quickly expanding 2020 presidential field have voiced support for the measure. Democratic Sens. Elizabeth Warren of Massachusetts and Cory Booker of New Jersey, who both announced their bids for the 2020 nomination, for instance, signed on as Senate co-sponsors of the proposal.
|
{
"redpajama_set_name": "RedPajamaC4"
}
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Q: Unable to get product_id with $package['contents'][0]['product_id'] Manually creating a custom plugin database:
CREATE TABLE wp_pppzpc_shipping_rates (
id INT(11) UNSIGNED NOT NULL AUTO_INCREMENT,
product_id INT(11) NOT NULL,
country_code VARCHAR(2) NOT NULL,
zone_id INT(11) NOT NULL,
shipping_rate DECIMAL(10,2) NOT NULL,
PRIMARY KEY (id)
);
I then populate the database like so:
INSERT INTO wp_pppzpc_shipping_rates (product_id, country_code, zone_id, shipping_rate)
VALUES (29303, "AU", 1, 255.95);
PHP in /wp-content/plugins/my-plugin:
function get_pppzpc_shipping_rate( $product_id, $country_code, $zone_id ) {
global $wpdb;
$table_name = $wpdb->prefix . 'pppzpc_shipping_rates';
$query = $wpdb->prepare(
"SELECT shipping_rate FROM $table_name WHERE product_id = %d AND country_code = %s AND zone_id = %d",
$product_id,
$country_code,
$zone_id
);
$result = $wpdb->get_var( $query );
return $result ? $result : false;
}
add_filter( 'woocommerce_package_rates', 'pppzpc_modify_shipping_rates', 10, 2 );
function pppzpc_modify_shipping_rates( $rates, $package ) {
foreach ( $rates as $rate_key => $rate ) {
if ( $rate->method_id == 'flat_rate' ) {
$product_id = $package['contents'][0]['product_id'];
$country_code = $package['destination']['country'];
$zone_id = WC_Shipping_Zones::get_zone_matching_package( $package )->get_id();
$shipping_rate = get_pppzpc_shipping_rate( $product_id, $country_code, $zone_id );
if ( $shipping_rate ) {
$rates[$rate_key]->cost = $shipping_rate;
}
}
}
return $rates;
}
Woocommerce does not appear to use my custom shipping rate in cart and checkout contexts. It fails somehow.
For debugging, I add into pppzpc_modify_shipping_rates():
error_log( print_r( compact( 'product_id', 'country_code', 'zone_id' ), true ) );
which gives
(
[product_id] =>
[country_code] => AU
[zone_id] => 1
)
suggesting that product is not being obtained successfully.
It appears I am unable to get the $product_id of the current product with
$product_id = $package['contents'][0]['product_id'];
Please explain why this is failing and advise a solution.
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 3,071
|
{"url":"http:\/\/mathhelpforum.com\/pre-calculus\/76133-vector-function-problem.html","text":"Math Help - vector function problem\n\n1. vector function problem\n\nI have the following vector function:\n\n$\\overrightarrow{r}(t)=\\binom{2\\cdot \\cos t}{-3+4\\cdot \\sin t} , t\\in [0;2\\pi]$\n\nI need to find the intersections with the x-axis.\nI found the first one (the green cross in the image) by doing the following:\n\n$y(t)=0$\n$0=-3+4\\cdot \\sin t$\n$t=0.848$\n$x(0.848)=2\\cdot \\cos (0.848)=1.323$\n\nSo the intersection is $P(1.323;0)$\n\nMy question is, how do I find the other intersection? I have tried to subtract with $\\pi$ but didn't help.\n\n2. Your two solutions are: $\nt = \\arcsin \\left( {\\frac{3}\n{4}} \\right)\\;\\& \\;t = \\pi - \\arcsin \\left( {\\frac{3}\n{4}} \\right)$\n\n3. but of course!! thanks a lot!\n\n4. It should also be evident from the symmetry that the other point is (-1.323, 0)","date":"2016-05-06 10:09:33","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\": 8, \"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\": 0.8479971885681152, \"perplexity\": 478.7357907840104}, \"config\": {\"markdown_headings\": false, \"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-2016-18\/segments\/1461861743914.17\/warc\/CC-MAIN-20160428164223-00210-ip-10-239-7-51.ec2.internal.warc.gz\"}"}
| null | null |
Q: How to convert PNG image to grayscale using java? I have a problem with regards to changing my PNG image to grayscale. I wanted to make a method that would accept byte[] image as a parameter and return back as a newly modified grayscale image as byte[] also.
I found some links that make images grayscale with JPEG images using below snippet.
private byte[] makeItGray(byte[] img, String contentType) throws IOException, Exception{
InputStream in = new ByteArrayInputStream(img);
BufferedImage bimg = ImageIO.read(in);
for(int y=0; y < bimg.getHeight(); y++){
for(int x=0; x < bimg.getWidth(); x++){
Color color = new Color(bimg.getRGB(x,y));
int graylevel = (color.getRed() + color.getGreen() + color.getBlue()) / 3;
int r = graylevel;
int g = graylevel;
int b = graylevel;
int rgb = ( r<<16 ) | ( g<<8 ) | b;
bimg.setRGB(x, y, rgb);
}
}
in.close();
ByteArrayOutputStream baos = new ByteArrayOutputStream();
if(contentType.equals(MediaType.IMAGE_PNG_VALUE)){
ImageIO.write(bimg, "png", baos);
System.out.println("PNG!!!");
}
else if(contentType.equals(MediaType.IMAGE_JPEG_VALUE)){
ImageIO.write(bimg, "jpg", baos);
}
else
throw new Exception();
baos.flush();
byte[] grayImage = baos.toByteArray();
baos.close();
return grayImage;
}
My references were on below :
How can I use ImageJ as a library for a separate Java application?
https://www.mkyong.com/java/how-to-convert-byte-to-bufferedimage-in-java/
It works on JPEG images but on PNG, it sends me a transparent image.
// converting orig image to grayscale in byte[]
imageBytes = makeItGray(imageBytes, file.getContentType());
Path path = Paths.get("some path here that would overwrite existing image");
Files.write(path, imageBytes);
When I try to open the image manually to check if it is grayscale, it gives me transparent image or no image is showing but not null since it returns byte[] data. I was wondering if the above method is ok with PNG formats?
Please let me know for any questions. Thanks!
A: Actually, the getRGB and setRGB methods, despite their names, actually returns and accepts a pixel in 32 bit packed ARGB format. That means that if the color model of your BufferedImage actually contains an alpha channel, leaving the alpha values of the pixel empty (0x00) as you do, will result in an all transparent image...
The PNG format supports alpha, while JPEG normally don't use it, that is why you see the results you do, and why it seems to work different for the different formats.
The fix is simple though, just prepend the pixel value with all opaque alpha:
int rgb = 0xff000000 | (r << 16) | (g << 8) | b;
bimg.setRGB(x, y, rgb);
If you want to retain the alpha of the original, you can do that too (I simpliedfied the code a little):
int oldrgb = bimg.getRGB(x,y);
Color color = new Color(oldrgb);
int gray = (color.getRed() + color.getGreen() + color.getBlue()) / 3;
int rgb = (oldrgb & 0xff000000) | (gray << 16) | (gray << 8) | gray;
bimg.setRGB(x, y, rgb);
PS: Note that your way of computing gray values by averaging isn't the recommended way to convert RGB to grayscale, so your images may look off compared to other tools. See for example Converting color to grayscale.
A: public class GrayScaleImage{
public static void main(String[]args)throws IOException{
BufferedImage img = null;
File f = null;
try{
f = new File("D:\\Image\\image.jpg");
img = ImageIO.read(f);
} catch(IOExeption e){
System.out.println(e);
}
int width = img.getWidth();
int height = img.getHeight();
for(int y = 0; y < height; y++){
for(int x = 0; x < width; x++){
int p = img.getRGB(x,y);
int a = (p>>24)&0ff;
int r = (p>>16)&0ff;
int g = (p>>8)&0ff;
int b = p&0ff;
int avg = (r + g + b)/3;
p = (a<<24) | (avg<<16) | (avg<<8) | avg;
img.setRGB(x, y, p);
}
}
try{
f = new File("D:\\Image\\output.jpg");
ImageIO.write(img, "jpg", f);
} catch(IOException e){
System.out.println(e);
}
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 6,111
|
\section{Introduction}
Let $P$ be a set of participants, among whom we would like to share a secret.
An {\it access structure} $\Gamma$ on $P$ is the collection of all
subsets of $P$ that are {\it qualified}, i.e., allowed to reconstruct the secret. An access structure
$\Gamma$ is fully determined by its {\it minimal qualified subsets},
which are those qualified sets for which no proper subset is qualified. Any subset of $P$ not in $\Gamma$
is called {\it unqualified}. We assume that each participant in $P$ belongs to some minimal qualified subset.
We may think of the secret as belonging to a special participant called the {\it dealer}.
Intuitively, a secret sharing scheme for $\Gamma$ is a way for the dealer to select a secret and deal out
one or more {\it shares} to each participant
in such a way that qualified sets are able to reconstruct the secret by combining their shares,
while unqualified sets cannot learn any information about the secret.
The efficiency of a secret sharing scheme can be measured in terms of its {\it information rate},
a value which indicates the size of participants' shares relative to the size of the secret.
The information rate will always be between zero and one \cite{Csirmaz}.
Mart\'i-Farr\'e and Padr\'o \cite{MFP} showed that any
access structure with information rate greater than $\frac{2}{3}$ is induced by a matroid.
It is not yet known how to determine the information rates of the access structures induced by a particular matroid.
One matroid currently under consideration is the Vamos matroid,
which induces two non-isomorphic access structures $V_1$ and $V_6$.
Each of these access structures is known to have an information rate of at least $3/4$ \cite{MFP}, and
Beimel, Livne, and Padr\'o showed that the information rates of $V_1$
and $V_6$ have upper bounds of $10/11$ and $9/10$ respectively \cite{BLP}
(Beimel et. al. refer to $V_8$ rather than $V_1$, but the two are isomorphic and
$V_1$ is notationally more convenient for our purposes).
Here we improve those upper bounds to $19/21$ for $V_1$ and $17/19$ for $V_6$.
\section{Secret Sharing Schemes}
We now give a more precise definition of a secret sharing scheme, following the ideas of
Csirmaz \cite{Csirmaz} and Mart\'{i}-Farr\'{e} and Padr\'{o} \cite{MFP}.
Let $\Sigma$ be a collection of random variables consisting of one random variable $S$ for the secret and,
for each participant $x \in P$, a random variable for the share belonging to $x$.
For any participant $x \in P$, we use $H(x)$ to denote the Shannon entropy of the corresponding
random variable, and for any nonempty
subset $X \subseteq P \cup \{S\}$, we use $H(X)$ to denote the joint entropy of the
random variables for all elements of $X$. We use $H(X|Y)$ to denote conditional entropy for nonempty sets
$X,Y \subseteq P \cup \{S\}$. Recall that by definition $H(X|Y)=H(X \cup Y)-H(Y)$.
We call $\Sigma$ a {\it (perfect) secret sharing scheme for $\Gamma$} if it has the following properties:
\begin{itemize}
\item If $X \in \Gamma$ then $H(S|X)=0$, that is, the participants in $X$ are able to combine their shares to
completely determine the value of the secret.
\item If $X \notin \Gamma$ then $H(S|X)=H(S)$, that is, the uncertainty about the secret does not change even when all participants in $X$ pool their shares.
\end{itemize}
Given a secret sharing scheme $\Sigma$ and a participant $x \in P$, the {\it information rate of $x$} is defined by
\begin{equation*} \rho(x)=\frac{H(S)}{H(x)} .\end{equation*}
The information rate of $\Sigma$, $\rho(\Sigma)$, is the minimum information rate over all participants in $P$.
For an access structure $\Gamma$, the information rate $\rho(\Gamma)$ is the supremum of $\rho(\Sigma)$ over all
$\Sigma$ that are secret sharing schemes for $\Gamma$.
\section{Normalized Entropy}
Fix a (perfect) secret sharing scheme $\Sigma$.
We define the {\it normalized entropy} of a nonempty set $X \subseteq P$ by
$$h(X)=\frac{H(X)}{H(S)}$$
and the {\it conditional normalized entropy of $X$ given $Y$} for nonempty sets $X,Y \subseteq P$ by
$$h(X|Y)=\frac{H(X|Y)}{H(S)}.$$
The entropy function $H$ is nonnegative.
We may assume that $H(S)$ is strictly positive, because if $H(S)=0$ then $H(S|X)=0$ for every $X \subseteq P$, meaning that every
set of participants is qualified and there is nothing left to investigate. Thus the normalized entropy and conditional normalized entropy are
well-defined. We observe that
the information rate for a participant $x \in P$ is the reciprocal of the normalized entropy for that participant:
\begin{equation}\label{h_and_rho}\rho(x)=\frac{1}{h(x)}.\end{equation}
The normalized entropy is monotone and submodular, as can be shown by dividing through the appropriate
inequalities for the entropy function by the positive quantity $H(S)$.
Some additional useful facts about $h$
are described in the following lemmas. We assume that $X,Y$ are nonempty subsets of $P$. We will frequently omit the
symbol for set union, writing $XY$ for $X \cup Y$.
\begin{la}\label{addSqual} If $X \in \Gamma$ then $h(X)=h(XS)$.
\end{la}
\begin{proof}
From the definitions of (perfect) secret sharing scheme and conditional entropy, if $X \in \Gamma$ then
$$0 = H(S|X) = H(XS)-H(X).$$
Dividing through by $H(S)$ and rearranging gives the desired result.
\end{proof}
\begin{la}\label{addSunqual} If $X \notin \Gamma$ then $1 = h(XS)-h(X)$.
\end{la}
\begin{proof}
From the definitions of (perfect) secret sharing scheme and conditional entropy, if $X \notin \Gamma$ then
\begin{equation*} H(S)=H(S|X)=H(XS)-H(X). \end{equation*}
Dividing through by $H(S)$ gives the desired result.
\end{proof}
\begin{la}\label{add1unqual} If $X \notin \Gamma$ but $XY \in \Gamma$ then $1 \leq h(XY) -h(X)$.
\end{la}
\begin{proof}
Using the monotonicity of $h$ and lemmas \ref{addSqual} and \ref{addSunqual},
\begin{equation*}1 = h(XS)-h(X) \leq h(XYS) - h(X) = h(XY)-h(X).\end{equation*}
\end{proof}
Lemma \ref{add1unqual} says that if $X$ is unqualified and adding the participants in $Y$ produces a qualified
set, then the participants in $Y$ must contribute at least 1 to the normalized entropy of $X$.
A slight reformulation of this is the following lemma, which says that
if adding a participant $r$ to an unqualified superset of $X$ produces a qualified set,
then $r$ must contribute at least 1 to the
normalized entropy of $X$.
\begin{la}\label{supersetunqual} If $XY \notin \Gamma$ but $XY \cup \{r\} \in \Gamma$ then
$1 \leq h(X \cup \{r\}) - h(X).$
\end{la}
\begin{proof}
By lemma \ref{add1unqual}
\begin{eqnarray*}
1 &\leq& h(XY \cup \{r\})-h(XY)
\end{eqnarray*}
and by the submodularity of $h$
\begin{eqnarray*}
h(X) + h(XY \cup \{r\}) &\leq& h(XY) + h(X \cup \{r\}).
\end{eqnarray*}
If we add these inequalities, cancel terms, and rearrange, we get the desired result.
\end{proof}
\begin{la}\label{qual2ways} If $X\cap Y \notin \Gamma$ but $X, Y \in \Gamma$ then
\begin{eqnarray*}
h(X\cap Y) + h(XY) + 1 &\leq& h(X) + h(Y). \end{eqnarray*}
\end{la}
\begin{proof}
By the submodularity of $h$,
\begin{eqnarray*}h((X\cap Y)S) + h(XYS) &\leq& h(XS) + h(YS).\end{eqnarray*}
Since $X, Y, XY \in \Gamma$, adding $S$ to any of these sets
does not change their normalized entropy. However, by lemma \ref{addSunqual}
$$h((X\cap Y)S) = h(X\cap Y)+1.$$
\end{proof}
\section{Matroids and Secret Sharing Schemes}
A {\it matroid} $M$ over a finite set $Q$ is a collection $\mathfrak{I}$, called the {\it independent}
subsets of $Q$, such that
\begin{itemize}
\item the empty set is independent,
\item subsets of independent sets are independent, and
\item if $X,Y$ are independent with $|X|=|Y|+1$ there is $x \in X\setminus Y$ such that $Y \cup \{x\}$ is independent.
\end{itemize}
Any set that is not independent is {\it dependent}. Maximal independent sets are called {\it bases}, and
minimal dependent sets are called {\it circuits}. A matroid may also be specified in terms of its bases or
circuits. For a more thorough introduction to matroids we refer the reader to \cite{Welsh}.
Given a matroid $M$ over $Q$, each element $x \in Q$ induces an access structure $\Gamma_x$ over the participants
$Q \setminus \{x\}$.
The minimal qualified sets of $\Gamma_x$ are those subsets $Y \subseteq Q\setminus\{x\}$ for which
$Y \cup \{x\}$ is a circuit in the matroid $M$.
Intuitively, if $Y \cup \{x\}$ is a circuit then the value of $x$ can be determined from the elements of $Y$.
More discussion of matroids and access structures may be found in \cite{MFP}.
\section{The Vamos Matroid}
We define the Vamos matroid on the set $\{v_1, \dots, v_8\}$ as follows.
First define the {\it Vamos pairs} $A$, $B$, $C$, and $D$ by
$A=\{v_1, v_2\}$, $B=\{v_3, v_4\}$, $C=\{v_5, v_6\}$, and $D=\{v_7, v_8\}$.
The Vamos matroid on $ABCD$ is the matroid
whose independent sets are all sets of size less than 5 except for the sets $AB$, $AC$, $BC$, $BD,$ and $CD$.
Thus the sets $AB$, $AC$, $BC$, $BD$, and $CD$ are circuits in the Vamos matroid. Any set of fewer than 4 elements is
independent, and any set with more than four elements is dependent.
In the following discussion when we speak about circuits, independent sets, and dependent sets,
we mean these terms with respect to the Vamos matroid.
Because of symmetries there are, up to isomorphism, two access structures induced by the Vamos matroid.
One is the structure $V_1$, where $v_1$ is the dealer. The other is $V_6$, where $v_6$ is the dealer.
For convenience we shall consider each of $V_1$ and $V_6$ to be an access structure on eight participants, thinking of the dealer
as a participant who is individually qualified to recover the secret. Recall that the other minimal qualified sets will be
those sets of participants who, with the inclusion of the dealer, form a circuit in the Vamos matroid.
Note that this means any qualified set which does not contain the dealer must include at least 3 participants.
As in \cite{BLP}, for a fixed secret sharing scheme $\Sigma$ on $V_1$ or $V_6$ we define
\begin{equation*}
\lambda = \left( \displaystyle\max_{1 \leq i \leq 8}h(P_i) \right) - 1
\end{equation*}
so that for each participant
\begin{equation}\label{lambda}
h(v_i) \leq 1 + \lambda.
\end{equation}
We note that by equation \eqref{h_and_rho} the information rate of the scheme will then be
\begin{equation}\label{schemeinfo}
\rho(\Sigma)=\min_{1 \leq i \leq 8}\frac{1}{h(P_i)} = \frac{1}{1+\lambda}.
\end{equation}
\begin{la}\label{upbounds} Let $X, Y$ be distinct Vamos pairs with $XY$ a circuit. If the dealer is a member of $Y$, then
\begin{enumerate}[(i)]
\item $h(Y|X) \leq 1 + \lambda$
\item $h(X|Y) \leq 1 + 2\lambda.$
\end{enumerate}
\end{la}
\begin{proof}
Let $Y=\{s,t\}$ where $s$ is the dealer, and let $X=\{p,q\}$.
\begin{enumerate}[(i)]
\item Since $XY$ is a circuit containing the dealer, $X\cup\{t\}$ is a qualified set. Thus by lemma \ref{addSqual},
the submodularity of $h$, and equation \eqref{lambda},
\begin{equation*}
h(Y|X)=h(\{t\}|X) \leq h(\{t\}) \leq 1 + \lambda.
\end{equation*}
\item The set $\{p,t\}$ is unqualified, as it is a set of size 2 that does not include the dealer.
The set $X \cup \{t\}$ is qualified. Thus by lemma~\ref{qual2ways},
\begin{equation*} h(\{p,t\})+h(XY)+1 \leq h(\{p\} \cup Y) + h(X \cup \{t\}). \end{equation*}
Subtracting $h(Y)$ from both sides, rearranging, and using equation \eqref{lambda} gives us
\begin{eqnarray*}
h(X|Y) &\leq& h(\{p\}|Y) + h(\{q\}|\{p,t\}) -1 \\
&\leq& h(\{p\}) + h(\{q\}) -1\\
&\leq& 2(1+\lambda) - 1\\
&=&1 + 2\lambda.
\end{eqnarray*}
\end{enumerate}
\end{proof}
\begin{la}\label{3lambda}Let $X,Y$ be distinct Vamos pairs with $XY$ a circuit.
If neither $X$ nor $Y$ contains the dealer, then
\begin{equation*}h(Y|X) \leq 1 + 3\lambda.\end{equation*}
\end{la}
\begin{proof}
Let $Y=\{p,q\}$. Take $r$ to be one of the two participants that is neither in $XY$ nor in the Vamos pair of
the dealer. Then we will have $X \cup \{r\} \notin \Gamma$, since adding the dealer to these three elements does not
produce a circuit.
We will have $X \cup \{p,r\}, X \cup \{q,r\} \in \Gamma$, since each of these is an independent set with four
participants. Then by lemma~\ref{qual2ways} we have
\begin{eqnarray*}
h(X \cup \{r\}) + h(XY \cup \{r\}) +1 &\leq& h(X \cup \{p,r\}) + h(X \cup \{q,r\}).
\end{eqnarray*}
Since $XY \notin \Gamma$, by lemma \ref{add1unqual} we have
\begin{eqnarray*}
h(XY) + 1 &\leq& h(XY \cup \{r\}).
\end{eqnarray*}
We get the following from the submodularity of $h$:
\begin{eqnarray*}
h(X \cup \{p\}) &\leq& h(X) + h(\{p\})\\
h(X \cup \{p,r\}) &\leq& h(X \cup \{p\}) + h(\{r\})\\
h(X \cup \{q,r\}) &\leq& h(X \cup \{r\}) + h(\{q\}).
\end{eqnarray*}
Finally, from equation \eqref{lambda},
\begin{eqnarray*}
h(\{p\}) &\leq& 1 + \lambda\\
h(\{q\}) &\leq& 1 + \lambda\\
h(\{r\}) &\leq& 1 + \lambda.
\end{eqnarray*}
Adding the inequalities above, canceling terms, and writing as conditional entropy gives us the bound specified.
\end{proof}
\begin{la}\label{at_least_2}Let $X,Y$ be distinct Vamos pairs with $XY$ independent. If the dealer is not a member of $X$, then
\begin{equation*} 2 \leq h(Y|X). \end{equation*}
\end{la}
\begin{proof}
{\it Case 1:} Assume that the dealer is not a member of $Y$.
Let $Y=\{p,q\}$. Since $XY$ is qualified but $X \cup \{p\}, X \cup \{q\}$ are not, by lemma \ref{add1unqual} we get
the inequalities
\begin{align*}
1 \leq& h(XY) - h(X \cup \{p\})\\
1 \leq& h(XY) - h(X \cup \{q\}).
\end{align*}
By the submodularity of $h$,
$$ h(XY) + h(X) \leq h(X \cup \{p\}) + h(X \cup \{q\}).$$
Adding the above three inequalities, canceling terms, and rearranging gives the desired result.
{\it Case 2:} Assume that $Y=\{s,t\}$ where $s$ is the dealer.
Since $XY$ is independent, $X \cup \{t\}$ is unqualified. Thus by lemma \ref{addSunqual}
\begin{equation*}
1 \leq h(XY) - h(X \cup \{t\}).
\end{equation*}
Let $r$ be any participant not in $XY$. Then $X \cup \{r\}$ is also unqualified. Since $X \cup \{t,r\}$ is
qualified, lemma \ref{supersetunqual} tells us that
\begin{equation*}
1 \leq h(X \cup \{t\}) -h(X).
\end{equation*}
Adding the above two inequalities gives the desired result.
\end{proof}
Although the previous lemma is stated in general terms, it will only apply to the Vamos pairs $A$ and $D$, as any other two
distinct Vamos pairs are dependent.
\section{New Bounds For Lambda}
In \cite{BLP} Beimel, Livne, and Padr\'o found by looking at the Zhang-Yeung non-Shannon inequality \cite{ZY}
that when $v_6$ is the dealer, $1/9 \leq \lambda$, and when $v_1$ is the dealer,
$1/10 \leq \lambda$. Here we improve those bounds by looking at other non-Shannon inequalities from \cite{Dougherty}.
\begin{thm}\label{C}
If the dealer is a member of $C$, then $2/17 \leq \lambda.$
\end{thm}
\begin{proof}
We use Dougherty, Freiling, and Zeger's inequality (i) from \cite{Dougherty}, which may be written
\begin{align*}\tag{DFZi}\label{Di}
0 \leq& - 3h(A) - 5h(B)- 3h(C) + 8h(AB) \\
& + 6h(AC) - 2h(AD) + 6h(BC)+ 2h(BD)\\
& + 2h(CD)- 9h(ABC)- 2h(BCD).
\end{align*}
Since $A, AB, BD \notin \Gamma$ and $ABC, BCD, AD \in \Gamma$,
from lemmas \ref{add1unqual}, \ref{supersetunqual}, and \ref{at_least_2} we obtain the following inequalities, which we add
to \eqref{Di} with the indicated multiplicities:
\begin{eqnarray*}
9[1 &\leq& h(ABC)-h(AB)]\\
2[1 &\leq& h(BCD)-h(BD)]\\
2[2 &\leq& h(AD)-h(A)]\\
1 &\leq& h(AB)-h(A).
\end{eqnarray*}
After canceling terms, the sum of inequalities yields
$$16 \leq -6h(A) -5h(B) -3h(C) + 6h(AC) +6h(BC) +2h(CD).$$
Rearranging, we obtain
\begin{eqnarray*}
16 &\leq& 6[h(AC)-h(A)] + 5[h(BC)-h(B)] \\
&& + [h(BC)-h(C)] + 2[h(CD)-h(C)]
\end{eqnarray*}
which may be further rewritten as
$$16 \leq 6h(C|A) + 5h(C|B) +h(B|C) +2h(D|C).$$
Replacing each conditional normalized entropy by its upper bound from lemma \ref{upbounds},
we get
$$16 \leq 6(1+\lambda) + 5(1+\lambda) + (1 + 2\lambda) + 2(1 + 2\lambda).$$
This simplifies to
$$16 \leq 14 + 17\lambda$$
and we conclude that $2/17 \leq \lambda.$
\end{proof}
\begin{thm}\label{A}
If the dealer is a member of $A$, then $2/19 \leq \lambda.$
\end{thm}
\begin{proof}
We begin with inequality (iv) from \cite{Dougherty}, which is
\begin{align*}\tag{DFZiv}\label{Div}
0 \leq& -h(A) -5h(B) -5h(C) +6h(AB)\\
& + 6h(AC) - 2h(AD) +8h(BC) +2h(BD)\\
& + 2h(CD) -9h(ABC)-2h(BCD).
\end{align*}
To this we add four inequalities (with indicated multiplicities) to cancel out the terms with $h(AD),$ $h(ABC),$ and $h(BCD)$.
Since $AD \in \Gamma$ but $D \notin \Gamma$, by lemma \ref{at_least_2}
\begin{eqnarray*}2[2 &\leq& h(AD) - h(D)].\end{eqnarray*}
Since $ABC, BCD \in \Gamma$ and $BC, CD \notin \Gamma$, by lemma \ref{add1unqual}
\begin{align*}9[1 \leq& h(ABC)-h(BC)]\\
2[1 \leq& h(BCD) - h(CD)].\end{align*}
Finally, since $C$ combined with either participant in $D$ will still be an
unqualified set, by lemma \ref{supersetunqual} we have
\begin{eqnarray*}1 &\leq& h(BC)-h(C).\end{eqnarray*}
After adding the above inequalities to \eqref{Div}, simplifying, and canceling terms we are left with
\begin{eqnarray*}
16 &\leq& -h(A)-5h(B) - 6h(C) - 2h(D) + 6h(AB)\\
&& + 6h(AC) + 2h(BD)
\end{eqnarray*}
which can be rearranged into
\begin{eqnarray*}
16 &\leq& 5h(A|B) + h(B|A) + 6h(A|C) + 2h(B|D).
\end{eqnarray*}
Using the bounds found in lemmas \ref{upbounds} and \ref{3lambda},
we have
\begin{eqnarray*}
16 &\leq& 5(1+\lambda) + (1+2\lambda) + 6(1+\lambda) + 2(1+3\lambda)
\end{eqnarray*}
and we conclude that $2/19 \leq \lambda$.
\end{proof}
The method of canceling terms used here was generalized and
applied to the other inequalities in \cite{Dougherty}, after appropriate permutations of letters in the
other inequalities. However, only bounds for $\lambda$ weaker than those shown here were obtained.
\section{Conclusion}
By theorem \ref{C} and equation \eqref{schemeinfo}, for any secret sharing scheme $\Sigma$ on $V_6$ we have
\begin{equation*}\rho(\Sigma)=\frac{1}{1+\lambda} \leq \frac{17}{19}\end{equation*}
and thus by the definition of information rate for an access structure,
\begin{equation*}
\rho(V_6) \leq \frac{17}{19}.
\end{equation*}
Similarly, by theorem \ref{A} and equation \eqref{schemeinfo},
\begin{equation*}
\rho(V_1) \leq \frac{19}{21}.
\end{equation*}
These are improvements to the best previously known upper bounds for the information rates of the access structures induced
by the Vamos matroid.
\section{Acknowledgments}
The author would like to thank Andreas Blass.
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 7,874
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The Huawei E303 dongle now goes for Ugx 55,000. The Huawei E3251 dongle is sold at Ugx 99,000, down from Ugx 139,000.The products are available at all MTN service centres and dealer shops across the country.During May 2014, MTN launched the "Join the fastest internet in the New World", a new thematic internet campaign highlighting how you can use the internet strategically for your personal and business success.According to MTN's Chief Marketing Officer, Ernst Fonternel, the campaign showcases the real beauty and benefits of the internet when you join Uganda's fastest network. MTN Uganda boasts of the latest and most innovative mobile internet and digital value offerings with the widest coverage and fastest speeds across the country."Oh, the things you'll learn" is positioned in their new advertising to showcase how important the internet is for self-education, discovering and learning new things.Last year, MTN, Uganda's number one telecom company, became the first operator to launch the LTE service. The launch of LTE represented a major jump in mobile connectivity capabilities with very fast internet connection speeds in ranges of 100Mbps. MTN is further covering the country with speeds up to 42Mbps and ensuring great quality internet and speeds for the broader Uganda population.In 2013, the company more than doubled its internet utilization, driven by innovative solutions enabling the over 2.6 million data customers gain access to 15MB free internet each month and free unlimited Facebook use through 0.Facebook.com and the number of users is projected to exponentially grow by end of 2014.With deliberate effort, MTN Uganda is indeed a telecom provider that offers internet geographical redundancy by providing three internet uplinks that guarantee business continuity for its customers. This means that whenever there is a local fibre cut within Uganda or a fibre cut in Kenya or Rwanda, or an undersea cable cut, MTN can use an alternative route to continue providing its customers with world-class internet.
The launch of internet technologies through the 3G 42Mbps, 4G LTE and WiFi hotspots saw the company's total data subscribers growing by 124%, up to 2.4 million.
Huawei E3276 LTE dongle that was being sold at Ugx 269,000 now goes for Ugx 175,000 while Huawei E3131 dongle now goes for Ugx 69,000. The dongles comes with 1GB free internet bundle for three months, EDGE and 3G support, internet speed of between 7.2Mbps and 122Mbps depending on the type you buy.
The router prices have also been reduced. You can now get a Huawei E5832 at Ugx 99,000 while the Huawei E5375 LTE is sold at Ugx 399,000, down from Ugx 403,000. The routers come with free SIM and airtime, 10GB free internet bundles for three months, internet speeds of up to 112Mbps and support up to 10 wireless connections on EDGE, 3G and 4GLTE.
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 1,217
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Praise for
THE 3O-DAY SOBRIETY SOLUTION
* * *
The Experts
"If you are concerned about your drinking and looking for answers, look no further. The 30-Day Sobriety Solution will change your life. Dave Andrews and Jack Canfield have integrated powerful new tools and techniques for recovery, many of which have been inexplicably left out of current recovery programs, with what we know already works. And by tightly integrating a full-featured and interactive website, which includes multimedia content and is regularly updated with breakthroughs in the field of recovery, The 30-Day Sobriety Solution is a comprehensive program that works, all for the price of a book."
—JUSTIN LUKE RILEY, president and CEO, Young People in Recovery
"Disguised as a book, this is a brilliantly effective lifestyle makeover for anyone fighting the lonely battle with alcohol. Dave and Jack's dynamic program culls from the very best tools for personal change—mindfulness, EFT tapping, visualization, journaling, and more—to provide effective and commonsense solutions that can be implemented immediately. They don't judge, and they don't insist on permanent abstinence. They understand deeply, and with a compassionate and encouraging tone, show you how to "reboot" your body for a healthy relationship with alcohol. The multimedia program on the book's companion website, and the supportive community you'll find there, will support you in lasting change, even if you've failed with other approaches. Follow their coaching, and you can put your drinking problems behind you forever."
—DAWSON CHURCH, PhD, author of the award-winning bestseller The Genie in Your Genes
"The 30-Day Sobriety Solution is a great book. It combines the best techniques of the human potential (EFT Tapping, neurolinguistic programming, life purpose exercises, goal setting, meditation, guided visualization, affirmations, journaling), with the best approaches from recovery counseling and coaching in a comprehensive approach that works to overcome alcohol abuse and addiction."
—John Gray, #1 New York Times bestselling author of Men Are from Mars, Women Are from Venus; What You Feel You Can Heal; and Staying Focused in a Hyper World
"Alcoholism and addiction are so complicated. Getting and staying sober is a monumental challenge for those struggling with the problem. Other diseases and afflictions usually bring sympathy and empathy to those suffering, but with alcoholism and addiction there is still an undercurrent of moral judgment, affecting not only the person suffering but also their family, friends, and colleagues—shame all around. The 30 Day Sobriety Solution by Dave Andrews and Jack Canfield provides an elegant, compassionate, and "easy-to-follow" road map to sobriety and a fulfilling life. This is all grounded in Jack Canfield's proven success principles. This book is the Apple computer for recovery and long-term sobriety!"
—DAN MARKEL, CEO and founder of MyLife Recovery Centers
"Since society reinforces drinking, being sober can be a huge challenge. The 30-Day Sobriety Solution offers a lifeline to those ready to take charge of their drinking behavior. Jack Canfield and Dave Andrews have created a practical guide that fills an important niche in the literature on recovery."
—PAUL R. SCHEELE, PhD, cofounder of Learning Strategies; CEO of Scheele Learning Systems; and author of Natural Brilliance
"If you know anyone who is struggling with alcohol and addiction, please give them this book. It offers a breakthrough approach, combining the very best of the human potential movement with the very best of recovery programs. The 30-Day Sobriety Solution will take people beyond recovery, helping them experience deep and lasting happiness in life."
—MARCI SHIMOFF, #1 New York Times bestselling author of Happy for No Reason and Chicken Soup for the Woman's Soul
"The 30-Day Sobriety Solution is a classic book that gives the reader powerful tools to overcome any addiction. I highly recommend it."
—TONY O'DONNELL, PhD, ND, addiction expert and author of Miracle Detox Secrets
"Finally, a book that combines the best of timeless success principles with potent recovery and therapeutic practices and coaching strategies, making it a comprehensive, inspiring, and powerful recovery resource."
—JANET BRAY ATTWOOD, New York Times bestselling author of The Passion Test and Your Hidden Riches
"This is a wonderful, thoughtful book that will guide you and inspire you to get complete control over your drinking problem once and for all."
—BRIAN TRACY, bestselling author of No Excuses, Maximum Achievement, and Change Your Thinking, Change Your Life
"The 30-Day Sobriety Solution brings the power of positive psychology to recovery, and by integrating it with other proven techniques and tools for life change, Jack and Dave have created the new standard for achieving sobriety."
—SHAWN ACHOR, happiness researcher and bestselling author of The Happiness Advantage
The 30-Day Graduates
"Wine was always my drink of choice, and even after facing serious health consequences from drinking excessively, I still couldn't face quitting. After my last emergency room visit, I actually went to the liquor store on the way home, telling myself I needed alcohol to "relax." I've attended a six-week AA treatment facility in the past and have tried AA meetings. The 30-Day Sobriety Solution is the only thing that has helped. I felt like I was reading a program written specifically for me. Not only have I completely quit drinking, but I used the same methods to quit smoking. My nineteen-year-old daughter even told me how happy and proud she was of me, and for the first time since I can remember, I actually feel like a good role model."
—NATHALIE, 30-Day Graduate from Winnipeg, Canada
"All areas of my life started to slowly improve at the very beginning. I was very skeptical at first, but the more solutions I completed, the more clear things became. Within two months of starting The 30-Day Sobriety Solution, I was closer to my family, performing better at work, coping with stress much more easily, had lost thirty pounds, was training for a marathon, and, most interesting, my social life actually improved."
—ROBERT, sales executive, 30-Day Graduate from Vienna, Austria
"When I heard about The 30-Day Sobriety Solution, my interest was instantly piqued. The habit of a glass of wine with dinner had crept into my life, and that one glass was enough to diminish my motivation to work out, meditate, or even read. And being a doctor, I felt that this was a contradiction to what I believe and teach others. I also wanted to drop some extra weight, reduce toxicity, and explore my desire to drink that glass of wine in the first place. Not only did The 30-Day Sobriety Solution help me successfully navigate my initial goals, but as a result of doing each day's action steps, I really felt different. I became less stressed, more centered, and there was no longer a craving to "take the edge off" toward the end of my day. I was also thrilled about how so much of what I learned improved other areas of my life as well. I feel great, and highly recommend The 30-Day Sobriety Solution, whether your goal is to quit drinking completely or just to cut back on the nightly ritual of drinking wine."
—DR. LIZ ANDERSON-PEACOCK, author, professional speaker, and coach, 30-Day Graduate from Ontario, Canada
"Having my doctorate in psychology not only meant that I was able to study some of the most celebrated psychologists in the field but also that I learned what really drives human behavior and how to change it. What was so exciting about The 30-Day Sobriety Solution was how effectively it "translated" and applied so many of these critical concepts, techniques, and teachings to cutting back and quitting drinking, as well as integrated countless other transformational tools taught by leading authors, trainers, and self-help experts. The end result is a comprehensive, holistic program that will become the new standard for sobriety—all for the price of a book."
—BYRON, PhD in psychology, 30-Day Graduate from Phoenix, Arizona
"When I started The 30-Day Sobriety Solution, I had one goal—to remove my desire to drink. In the past, I had been able to string together some continuous sobriety, but the desire to drink always remained. After recently turning fifty, I knew I wanted to live the rest of my life differently, and The 30-Day Sobriety Solution ended up being exactly what I needed to help me accomplish this. By the time I finished the program, the desire to drink was amazingly gone, and it continues to be to this day. In fact, when I think about drinking, I wonder why it ever seemed so important to me in the first place."
—LENORE, 30-Day Graduate from Dallas, Texas
"The solutions I learned from The 30-Day Sobriety Solution have been extremely effective in maintaining sobriety and thriving in it; they are the foundation upon which my sobriety is based."
—DAN, lawyer, 30-Day Graduate from Jackson, Wyoming
"The 30-Day Sobriety Solution did what I didn't think was possible: it made getting and staying sober fun. Prior to discovering this program, I tried many things, from AA to therapy to other recovery programs, but none of them freed me from the prison alcohol was holding me in like The 30-Day Sobriety Solution."
—MISSY, 30-Day Graduate from Grand Rapids, Michigan
"I am still amazed, looking back on the way I was when I first started The 30-Day Sobriety Solution, to see how far I've come. And all without Alcoholics Anonymous, without inpatient or outpatient rehabilitation, and even without anybody to cheer me on. It is truly amazing, and I just want to thank you for The 30-Day Sobriety Solution. It has given me everything I need to thrive in sobriety."
—JAMES, retired military, 30-Day Graduate from Istanbul, Turkey
"With eleven years of sobriety, I know that the key to ongoing happiness is embracing personal growth, whether it is related to creating more success in my career, developing and maintaining more fulfilling relationships, or being more emotionally and physically healthy. What surprised and excited me were the results I experienced when I completed The 30-Day Sobriety Solution. Not only did my life improve in each of these areas, but more importantly, it helped me have even more fun and passion in my life without alcohol. I believe that The 30-Day Sobriety Solution is a groundbreaking program that will help anyone who wants to get and stay sober and be happy in life without feeling the need to drink."
—SHEIRA MACKENZIE, speaker, trainer, and coach, 30-Day Graduate from Portsmouth, Rhode Island
"I might even venture to say that half of the value I have gotten out of this program has been outside of just controlling my drinking. Once I control the drinking, I have a fairly large amount of time in the evenings and on the weekends where I would have gotten blasted before, but now I have to fill that time with productive or enjoyable activities. A lot of the lessons The 30-Day Sobriety Solution taught during the 30 days were stuff that was applicable in terms of staying positive, ways to grow and expand your horizons, and how to basically crawl out of the small little tunnel I have been in for so many years with drinking."
—MIKE, engineer, 30-Day Graduate from San Diego, California
"I felt like The 30-Day Sobriety Solution was breathing life back into me. Every day, I learned new tools and techniques that actually worked. I was finally able to imagine a happy life without alcohol, something that had always escaped me. And one of the surprising results was that for the first time in my life, I felt like I was not alone, even though I was doing the program alone at home."
—HANNAH, business owner and life coach, 30-Day Graduate from Sydney, Australia
"When I started The 30-Day Sobriety Solution, I was skeptical because my past attempts to quit drinking using "conventional" treatment methods didn't work for me. So I doubted this book and the additional content and recordings on the companion website were going to result in the breakthrough I was searching for to finally overcome my excessive drinking. Within the first week, I experienced more progress than in all my other previous treatment attempts combined, and I can honestly say after completing the program that the positive impact it had in my life was phenomenal. For the first time in over a decade, I actually can see a happy and fun future that doesn't include drinking."
—JERRY, 30-Day Graduate from San Antonio, Texas
"In the past, I always connected drinking to immediate gratification, not realizing I was only trying to fill a void in my life. Now I clearly see that over time drinking guarantees I will always feel empty inside, where sobriety opens up the possibility to experience true happiness, joy, and fulfillment."
—SUSAN, business owner and entrepreneur, 30-Day Graduate from Philadelphia, Pennsylvania
"I tried willpower to quit drinking on my own. I tried switching to beer and wine. I tried Alcoholics Anonymous several times, but found the program was too ambiguous. However, The 30-Day Sobriety Solution was something I could sit down and do every night. And the "homework" not only helped keep me on track, it helped me get clear and understand how I was feeling and provided me with tools and techniques to change."
—MATT, IT project manager, 30-Day Graduate from Kansas City, Missouri
"Taking an honest look at where I was at in my life was hard. I was in my midforties, divorced, and no matter how hard I tried or how many promises I made, my attempts to quit drinking over the last year never lasted for more than three days. My greatest accomplishment was my two teenage children, but I felt ashamed and guilty for not being the parent they deserved. The 30-Day Sobriety Solution helped me get to the "why" that always led me back to drinking. And once I uncovered that, and was able to use the various techniques in the program to resolve it, not only did I easily overcome the three-day sobriety "wall" I always ran into, but my desire to drink was gone."
—TAMARA, 30-Day Graduate from Kansas City, Missouri
"Some of my earliest memories were of being terrified of my father's drunken rages, and despite my childhood promises to never drink like my father did, I discovered I had an almost undeniable compulsion to drink excessively. After recently turning sixty, and my nightly drinking reaching an embarrassing fifth of scotch every night, I knew I had to change. I had always been a successful entrepreneur, and even maintained a healthy, active lifestyle, but I just couldn't seem to escape my addiction to alcohol. The 30-Day Sobriety Solution finally freed me from my decades of drinking. Working through the daily program was a wonderful journey, and the end result is I have complete confidence in my ability to live the rest of my life sober."
—BRIAN, business owner, 30-Day Graduate from Trenton, New York
"The 30-Day Sobriety Solution is really a powerful program that's targeted at taking a whole new approach to life."
—ANN, MBA graduate, 30-Day Graduate from New York City
"Sobriety has become second nature. I can't really explain it, other than that soon after completing The 30-Day Sobriety Solution, I just stopped thinking about drinking, even though I still go to the pub with friends."
—THOMAS, teacher and aspiring author, 30-Day Graduate from London, England
"For many years, I tried to give up drinking, both on my own and working with counselors, but nothing seemed to break the bond until I read and dedicated myself to working through The 30-Day Sobriety Solution. This fantastic program gave me a huge variety of tools to work with, and it has enabled me not only to find relief, joy, and happiness in sobriety, but also to find real meaning and direction in my life. I recommend this book to anyone who is serious about giving up problem drinking and waking up to experience life's true potential."
—CHRISTINA, 30-Day Graduate from Greece
Thank you for downloading this Atria Books eBook.
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## CONTENTS
Note to Readers
Introduction
Getting Started
PHASE I
MASTERING THE ABSOLUTE BASICS TO GET FROM WHERE YOU ARE TO WHERE YOU WANT TO BE
Day 1: The 100% Solution
Building Your Foundation for Thriving in Sobriety
Day 2: The Purpose Solution
Identify, Acknowledge, and Honor Your Thriving-in-Sobriety Vision
Day 3: The Pendulum Solution
Embracing Your Painful Past to Unleash Pleasure and Joy in the Present
Day 4: The Forgiveness Solution
Embracing Forgiveness and Creating an Abundance of Love and Happiness
Day 5: The Believe-in-Yourself Solution
Believing in Yourself and Believing It Is Possible
Day 6: The Outcome Solution
The Power of an Outcome-Focused, Purpose-Driven, Goal-Setting Strategy
Day 7: The Review Day and Bonus Solution
Embracing the Power of Repetition to Master the Basics
PHASE II
REMOVING THE MENTAL AND EMOTIONAL BLOCKS THAT PREVENT YOU FROM THRIVING IN SOBRIETY
Day 8: The "Why Can't You Just Quit?" Solution
The Truth About Willpower
Day 9: The Action Solution
Getting Out of Your Head and Into Action
Day 10: The Core Values Solution
Discovering Your Core Values
Day 11: The Lie Detector Solution
Confronting Your Limiting Beliefs
Day 12: The Subconscious Mind Solution
Leverage the Power of Your Subconscious Mind
Day 13: The Tapping Solution
Tapping Away Your Desire to Drink
Day 14: The Review Day and Bonus Solution
Acknowledging, Celebrating, and Reviewing Your Accomplishments
PHASE III
CREATING AN UNSHAKABLE BELIEF IN YOURSELF AND YOUR DREAMS
Day 15: The 4-Minute-Mile Solution
Using the Power of Creative Visualization
Day 16: The Quality Question Solution
Change Your Questions to Change Your Life
Day 17: The Eternal Optimist Solution
Practicing Positive Expectation and Optimism
Day 18: The Affirmation Solution
The Power of Affirmations
Day 19: The Attraction Solution
Using the Law of Attraction to Accelerate Your Success
Day 20: The Gratitude Solution
Awakening the Power of Gratitude and Appreciation
Day 21: The Review Day and Bonus Solution
Using the Secrets of Advertising to Create an Unshakable Belief in Yourself and Your Dreams
PHASE IV
CULTIVATING COURAGE AND POSITIVE RELATIONSHIPS TO THRIVE IN MIND, BODY, AND SPIRIT
Day 22: The Courage Solution
Successfully Confronting Your Fears
Day 23: The Emotional Sobriety Solution
Successfully Handling Your Emotions
Day 24: The Meditation Solution
Meditate to Release Stress and Develop Inner Peace
Day 25: The Mind and Body Solution
Thriving in Your Mind and Body Through Nutrition
Day 26: The Positive Addiction Solution
Adding Fun, Healthy, and Confidence-Building Activities to Your Life
Day 27: The Love and Relationship Solution
Surrounding Yourself with Positive and Supportive Relationships
Day 28: The Review Day and Bonus Solution
Nurturing Your Body, Mind, and Spirit
PHASE V
CREATING YOUR PERSONALIZED PLAN TO THRIVE IN LIFE
Day 29: The Vision Solution
Discovering Your Life Purpose and Vision
Day 30: The Sobriety for Life Solution
Wrapping Up The 30-Day Sobriety Solution
Wrapping Up The 30-Day Sobriety Solution—Now What?
The 30-Day Graduates: Share Your Story
Acknowledgments
30-Day Resources
Permissions
About the Authors
Notes
Index
## NOTE TO READERS
This publication contains the opinions and ideas of its authors. It is intended to provide helpful and informative material on the subjects addressed in the publication. It is sold with the understanding that the authors and publisher are not engaged in rendering medical, health, or any other kind of personal professional services in the book. The reader should consult his or her medical, health, or other competent professional before adopting any of the suggestions in this book or drawing inferences from it.
The authors and publisher specifically disclaim all responsibility for any liability, loss, or risk, personal or otherwise, which is incurred as a consequence, directly or indirectly, of the use and application of any of the contents of this book.
Important: According to a recent government study, 90 percent of heavy drinkers are not actually physically addicted to alcohol; however, you may be among the 10 percent who are. If you suffer withdrawal symptoms such as sweating, shaking, vomiting, or hallucinations after you've stopped drinking—for example, going for one or two days without alcohol—or you drink to avoid these withdrawal symptoms, you have a serious addiction problem, and suddenly stopping without medical supervision can cause potentially fatal withdrawal symptoms such as seizures, heart failure, and stroke.
This book is dedicated to the memory of Dr. Bryan Duke, without whom this program might never have been written.
We hope The 30-Day Sobriety Solution will help inspire and teach millions of people how to thrive in sobriety and avoid years of unnecessary pain and suffering.
Bryan Jefferson Duke, 1966–2008
## INTRODUCTION
I want to share with you why I devoted the better part of two years of my life to coauthoring this book.
Before I learned to read, I had learned the dark side of drinking. My earliest childhood memories are of my father's drunken rages—he could drain almost an entire bottle of whiskey in one evening. And when he drank too much, he always became angry and violent.
I can still remember in vivid detail being a terrified five-year-old, hiding in the bottom half of the console of an old stand-up radio that I could crawl into, praying that he wouldn't find me and hit me. But even though I had found the perfect hiding spot, I still had to listen in fear as he physically and emotionally abused my mother and my younger brother. And on the occasions when he found me before I was able to hide, he would severely whip me with a thick leather belt or a heavy pig-bristle hairbrush, which hurt and stung more than any bare hand ever could.
Thankfully, when I was six, my mother filed for divorce, and with that my life forever changed. I finally felt unafraid and free to be a child again. However, as she attempted to hide from the pain and embarrassment of her failed marriage and her inability to cope with the stress and anxiety of raising three kids by herself, my mother went from moderately drinking—primarily during multifamily picnics and other social occasions—to turning to alcohol as her daily way of coping.
It was all she knew to do. And to be fair, there weren't a lot of options at that time—but whatever options there were, such as Alcoholics Anonymous, they were public, and my mother was very private. In our family you didn't "air your dirty laundry in public." My aunt and my grandmother were also alcoholics, often passing out at dinner, but it was a family issue that was never openly discussed—or addressed.
The scary part is that this story of mine is not unique. Today more than seven million children in the United States live in a household where at least one parent is alcohol dependent or is abusing alcohol, and even though there is not always physical abuse as there was in my case, the result is all too often some form of childhood wounding that needs to be healed in later life.
If there is such a thing as an "alcohol gene," it skipped my youngest brother and me, but emerged in the next generation, gripping the lives of two of my three children. So I have seen firsthand the ravages of alcohol addiction and drug abuse—both on the alcoholic and on the extended family members. It is because of these very painful personal experiences that I am so committed to this book and to helping you, the reader.
While there have been great advances in personal development, psychology, and neuroscience over the past twenty years, most people are still not getting the help they need to overcome their abuse of alcohol. Society in general has failed to provide the proper tools and techniques for people to successfully overcome their problem drinking. David Sheff, in his book Clean: Overcoming Addiction and Ending America's Greatest Tragedy, states, "Prevention efforts have failed, and so too has what passes for a treatment system. Ninety percent of people who need help never receive it." Ninety percent!
A few years ago while I was conducting a workshop in Philadelphia, I met Dave Andrews. When I mentioned the devastating effects alcohol had had on my family, he excitedly told me about the extraordinary success he was having with an online coaching program he had developed called "The 30-Day Sobriety Solution." I was instantly intrigued, especially when he told me how much of my work on success principles he had integrated into his program.
In my Breakthrough to Success seminars, workshops, and trainings, I have taught these same principles to well over a million people of all ages, races, religions, and income levels in forty-seven different countries. I have had many participants in every country who were struggling with the negative effects of their drinking and wanted to cut back or quit. And when they learned the principles and participated in the exercises I taught, I consistently witnessed incredible breakthroughs, which were usually followed up by letters and emails expressing how those breakthroughs had led to long-term sobriety.
When I met Dave, I was thrilled to learn he was using these same principles and techniques to help people quit or cut back their drinking—and he was consistently seeing positive results. Once I reviewed the program and saw how brilliantly it was structured, I asked Dave to write a book with me so this revolutionary approach to sobriety or cutting back could reach more people.
Dave and I spent the next two years turning the program into a book. When The 30-Day Sobriety Solution was complete, we then tested it with a group of volunteers who were struggling with problem drinking or who were currently in recovery, and discovered that the book format—based on the most current research and insights gleaned from Dave's hundreds of hours of successful private coaching—was decidedly as effective. In fact, the most common feedback we received from the participants after they completed the program was that their desire to drink was completely gone.
Other affirming feedback from the book-only test group led us to implement a free complementary website with many of the features of Dave's original online program. This "companion" for your sobriety journey includes powerful tools such as soundtracks of guided visualizations and meditations, inspirational and instructional videos, and supplemental chapters.
I have dedicated my life to helping people change their lives. Now that I have seen the results of combining my success principles with Dave's effective approach to achieving sobriety, I am confident that The 30-Day Sobriety Solution is indeed a breakthrough program that will help you successfully create a life where alcohol is no longer in control.
I am honored and humbled that you have picked up this book, and I wish you all the best for a sober and fulfilling life!
—Jack Canfield
## Getting Started
My recovery is the single greatest accomplishment of my life. And without that, the rest of my life would have fallen apart.
—JAMIE LEE CURTIS
Award-winning actor and bestselling author
The 30-Day Sobriety Solution is filled with life-changing, lasting ways to cut back or quit drinking. We developed these highly effective methods over eight years of research into cutting-edge scientific findings about addiction and through thousands of hours of working with people who wanted to stop drinking heavily. By combining timeless success principles with potent recovery and therapeutic practices and coaching strategies, we created the most comprehensive, inspiring, and powerful recovery resource ever published.
If you are not sure if this book is for you, answer these questions:
• Do you want to have fun and be naturally inspired and passionate about life without always feeling like you have to drink to be happy and fit in?
• Are you concerned about the effects of your drinking on your finances, family, relationships, health, weight, and/or career? Do you have legal problems as a result of your drinking?
• Are you frustrated because you have not lived up to promises that you made to yourself and to others to finally cut back or quit drinking? Are you discouraged that you have failed multiple times to cut back or quit?
• Are you a "work-hard, party-hard" type of person or a "weekend warrior"? Do you know deep down that your drinking habits are holding you back from what you really want to accomplish in life?
• Do you want to cut back or quit drinking, but you're leery of some of the conventional "public" methods of recovery such as Alcoholics Anonymous (AA) and rehab? Are you looking for a more private solution that you can work on at home?
• Are you afraid that if people knew how much you really drank, they would no longer respect or like you?
• Are you concerned about what you are going to do when you go to the next office party or wedding, or when you go on your next vacation, and whether you will be able to get through it without alcohol?
• Are you in recovery but feel stuck? Are you wondering what you can do to create more passion and enthusiasm in your life and your sobriety?
If you answered yes to some or all of these questions, then you are in the right place! Throughout this book, you will find stories of people just like you who had these same questions and were able to get the answers they were searching for from The 30-Day Sobriety Solution, even after trying and failing with past attempts to cut back or quit drinking.
If you are still not sure if you have a problem with drinking, consider this recent finding. A US government report released in November 2014 found that 29.3 percent of the adult population—that's almost one out of every three adults—meets the definition for excessive drinking.
The reality is that if you think you might have a problem, or if you think changing your drinking would benefit you, you are probably right.
Although this book is geared toward the problem drinker, excessive drinker, or alcoholic (whatever term you prefer to use), and people living in recovery, these solutions can be and have been used to recover from addictions to drugs (legal and illegal), gambling, sex, shopping, smoking, overeating, and other really self-destructive habits. Rather than attempt to address all of these in this book, however, we will focus solely on the problem drinker who is struggling to cut back or quit drinking and on the individual who is looking to be reinspired in recovery.
Last, we know some of you are ready to get started now, and we appreciate your enthusiasm. This "Getting Started" chapter includes relevant information that will help you understand the layout of this book and program. So feel free to quickly browse through it before getting right to Day 1 of the program.
### The Inspiration Behind The 30-Day Sobriety Solution
In this book, you are going to get to know us through our stories, including the challenges we have faced, our lowest points, and our greatest accomplishments. Jack Canfield is perhaps best known as America's #1 Success Coach; the author and editor of more than two hundred inspirational and self-help books, including The Success Principles and the Chicken Soup for the Soul® series (with over five hundred million copies sold and sixty New York Times bestsellers); a professional speaker; and a teacher to well over a million people around the world. Dave Andrews is best known for being a "sobriety expert" and America's #1 Sobriety Coach. As a recovered alcoholic, he knows firsthand what it is like to struggle with the fear and helplessness of trying to overcome the grip of alcoholism to eventually achieve the state of mind that he calls "thriving in sobriety."
We first met over five years ago, and it became instantly clear how much we had in common. We are both unabashedly enthusiastic about human potential and people's ability to transform their lives in a dramatic fashion. We are both committed to growing and learning, to serving others, and contributing to the greater good. We are both passionate about our families, maintaining balance, and being positive and inspirational role models to those around us. We teach those same principles, solutions, and techniques that have worked for us to anyone who wants to make profound changes, and we love doing this through coaching, training, and the written word. But most importantly, we both have been touched in profound ways by alcoholism and addiction.
Jack's mother, father, grandmother, aunt, sister, two of his children, and one of his stepchildren have struggled with alcoholism and addiction. Jack knows what it is like to be one of the more than a hundred million people in the United States whose lives have been turned upside down by a loved one struggling with alcohol abuse. Dave knows firsthand what it's like to struggle with alcoholism. He knows what it's like to desperately want to quit drinking, but to be terrified at the same time that a life without alcohol would be unhappy and boring.
Together we combine our personal experiences with our extensive collective knowledge of human potential and transformation to overcome addictive behaviors in a way that has never been done before.
We are absolutely convinced that applying the solutions taught in this program will enable you to live the life you've always dreamed of but deep down knew was impossible until you overcame your greatest challenge—your self-defeating relationship with alcohol.
The same solutions and techniques taught in The 30-Day Sobriety Solution have not only worked for us, they have helped our clients and students all over the world achieve breakthrough success in accomplishing everything they dreamed, including lasting sobriety; permanently cutting back on their drinking; propelling their careers to new heights; looking and feeling younger and sexier; and attaining greater financial wealth, greater health and fitness, greater passion and joy in their relationships, and greater overall happiness and fulfillment. When you work with the solutions in this book to finally cut back or quit drinking, you will be surprised at how easily you will also accomplish all of the rest of your goals.
### These Solutions Work, Even if You Have Tried Before and Failed
Amazingly, as soon as I stopped drinking and drugging, I became a successful actor. Hollywood called. The rest is history.
—SAMUEL L. JACKSON
Actor whose films have grossed over $8 billion
You, too, can successfully cut back or quit drinking even if you have tried before and failed. Why? Because our experience with our clients has shown us that these techniques and solutions work—as long as you always work the solutions. That means you need to complete the exercises in each chapter and consistently practice the techniques you learn.
Take Chris's story, for example. Over four years ago, Chris found The 30-Day Sobriety Solution online. Like many of the people we have helped, Chris had already tried Alcoholics Anonymous, therapy, inpatient and outpatient rehab, and several other methods to get sober. He had come to the conclusion that nothing would work; he was also afraid that sobriety would be boring and make him unhappy. However, he was about to lose his house and knew that he might lose his marriage and access to his two young children next. In a recent letter, he shared the following:
For once, it felt like I found a program that spoke the same language I spoke that was able to remove the stigma of my addiction and find solutions that actually worked. And not only worked to help me get and stay sober, but worked in every aspect of my life. It was something that I could do on my own, privately, and the more effort I put into the work, the more positive results I gained in my life.
In a nutshell, the program made sobriety easy and second nature for me. With that, my finances, health, and relationships all changed in dramatic fashion for the positive.
Today Chris is celebrating more than four years of sobriety. For the first time in his life, he broke the six-figure-salary barrier—not just once, but three years in a row. He is still married, and his relationships with his wife and kids have changed in ways that he always wanted but feared were impossible. Chris also went through a complete physical transformation and is in better shape than he has been in for over a decade—all of which he attributed to completing The 30-Day Sobriety Solution.
If Chris's story was the exception, you would not be reading this book. In fact, we have received countless letters and emails sharing inspiring stories of recovery from individuals with a range of sobriety goals: some quit for good and never looked back; some were able to return to moderate drinking; and some already in recovery became reinspired and excited about staying sober. We will share many of their stories with you.
The fact is that anyone can learn to consistently produce these same kinds of results. We know this because for over eight years, we researched, developed, tested, and improved the principles and techniques that we present in The 30-Day Sobriety Solution. We used them in hundreds of hours of coaching people who were struggling with problem drinking, and by integrating feedback from those sessions, we created a life-changing recovery program that works.
Throughout this book, we'll tell you the stories of some of the people we've helped who have struggled with the same issues as you. In many cases, their names and/or identifying details have been changed. However, the problems they faced and the solutions they implemented are real.
You will also find quotes from many high-profile individuals in recovery—actors, musicians, authors, and athletes—who have shared their stories of addiction and recovery in memoirs and interviews. The people we work with are often deeply inspired to hear that they are not alone in their struggles and that some of the most successful, well-known people also had issues with drinking and drugs and overcame them. Many of them share that some of their greatest accomplishments came only after they finally got sober.
### Can I Become a Normal Drinker Again?
I found getting sober surprisingly easy with The 30-Day Sobriety Solution, even after never going more than two days without alcohol for over fifteen years. As long as I did the solutions, it wasn't difficult.
—THOMAS
30-Day Graduate from London, England
Without fail, almost every client asks us, "Can I become a normal drinker again?" We will cover this in greater depth in Day 1, but briefly, we do believe it is possible for some people to cut back their drinking to that of a normal—or social—drinker. These people can have one or two drinks and not want more—the defining characteristic of a "normal drinker." They get to the point in their sobriety where they can take it or leave it. But this is true for only a very small percentage of problem drinkers. And although numerous studies and other successful recovery programs advocate cutting back on drinking and provide case studies to prove that this option is viable for some people, we know that this position is controversial. If you find yourself feeling frustrated or angry about this assertion, we just ask that you suspend judgment for now.
Even though many past graduates of The 30-Day Sobriety Solution have successfully cut back drinking, our experience has also shown us that everyone has to abstain from alcohol for at least 30 days. We will review this further in Day 1, including some options around when you can begin abstaining.
You are likely wondering if you are one of the few who can return to drinking after the program. At this stage, it is too early to know. But don't worry; we will cover this topic more thoroughly in Day 1 and Day 30.
### How We Structured This Book
I've never seen an approach to getting sober that makes you enthusiastic about sobriety. In other programs, it seems like sobriety is a sentence into purgatory, but The 30-Day Sobriety Solution is so attractive because not only does it actually work, it gets you excited about being sober.
—ANN
30-Day Graduate from New York City
The 30-Day Sobriety Solution presents you with an easy-to-follow 30-Day plan to recover, reclaim, and reinvent your life. It is organized in a proven format that has regularly resulted in feedback from participants that each solution was "almost eerily" delivered at the exact time it was needed.
To help you effectively learn and assimilate these powerful solutions, we have organized the book into thirty chapters, to be read one per day. The chapters unfold in five phases. Most participants complete the program within 30 days. But you can decide to complete it in a 30-, 60-, or 90-day period. We will tell you how on Day 1. You'll be introduced to one solution each day, with exercises you can complete at the end of reading that day's content. As you take yourself through each phase of this program, you will learn how to thrive in sobriety, whether your goal is to cut back your drinking, quit drinking, or get reinspired in your recovery.
———
Let's review the content of the book and its organization to give you a sense of what to expect. Feel free to skim this section, as it is meant only to give you a brief overview of what you will learn.
The 30-Day Sobriety Solution begins with Phase I, which contains the absolute basics that you must master to get from where you are to where you want to be. This phase is covered in six days and is often completed during the first week of reading this book, with a review day on Day 7. However, if you have chosen the 60-day or 90-day option, you would complete this phase over the first two or three weeks. Here is some of what you will learn in Phase I:
• The magic of 30 days and the "30-Day Reboot," and why this specific time frame works.
• One of the fundamental principles of sobriety: how to create a belief and vision for your new sober self that makes it much easier to stick to your decision to change your drinking habit.
• How to apply the psychological drivers of pain and pleasure to move yourself toward your new thriving-in-sobriety vision.
• How to set your sobriety goals to ensure that they don't backfire.
• How to identify the real reasons for your drinking and why your addictive nature is actually your greatest gift.
• The art of forgiveness and how to let go of the past to embrace the present.
• Some basic nutritional guidelines and recommendations you can follow to reduce your cravings for alcohol and facilitate the physical and mental recovery process.
Phase II addresses the important inner work you will need to do to help remove the mental and emotional blocks and beliefs that prevent you from thriving in sobriety. This section is covered in Days 8 through 13 and is most commonly completed during the second week of the program, with a review day on Day 14. Here is some of what you will learn in the second week:
• The willpower illusion and how your willpower actually hurts your chances of cutting back or quitting drinking.
• How to align your values, thoughts, beliefs, and feelings to ensure that the actions you take are actually the right ones for long-term happiness and fulfillment.
• The lies you've been telling yourself that have kept you from achieving and thriving in sobriety.
• How your subconscious mind has been sabotaging your success for most of your adult life and how to reprogram your subconscious to make sobriety easier and more natural.
• The power of tapping and how to use this simple technique to help you overcome some of your greatest obstacles to cutting back or quitting drinking.
Phase III reveals the most effective methods for changing your thinking to create an unshakable belief in yourself and your dreams. This section is covered in Days 15 through 20 and is most commonly completed in the third week of the program, with a review day on Day 21. Here is some of what you will learn in the third week:
• How to harness the incredible power of visualization—a secret to the success of Olympic athletes, top entrepreneurs, world leaders, and people who have gone from excessive drinking to thriving in sobriety.
• The transformative effect of asking questions and how changing the questions you ask yourself can change your life.
• The power of the law of attraction and how "drinking thinking" has repeatedly tricked you into believing that you need alcohol in your life to be happy, and why the opposite is actually true.
• How and why affirmations can be one of the most powerful techniques to create positive change and lasting fulfillment.
• How to develop and cultivate an attitude of gratitude—a necessary component for achieving lasting sobriety.
Phase IV gives you the tools and techniques you need to more easily create physical health and wellness, along with mental and emotional balance. It concludes by teaching you how to build and maintain meaningful and fulfilling relationships. This section is covered in Days 22 through 27 and is most commonly completed during the fourth week of the program, with a review day on Day 28. Here is some of what you will learn in the fourth week:
• What creates your fears and doubts and how to overcome them so that you can live with courage every day.
• The incredible power of meditation to heal addiction and promote health and wellness.
• The five fundamentals of healing your physical body and how to eat and exercise to decrease your cravings and increase your energy and passion.
• The truth about "positive addiction" and how to get in touch with fun, inspiring, healthy, and confidence-building activities to make negative addictions disappear forever.
• What "crabs in a bucket" can teach you, and how your new team of friends, peers, alliances, and networks can build lasting success in sobriety and help you fulfill your dreams.
• How to heal the relationships that have been damaged by your drinking, and how to identify, change, and, when necessary, eliminate the relationships that continue to hold you back.
Phase V covers how you can apply what you have learned to customize your own plan for thriving in sobriety without feeling overwhelmed or stopped by a fear of failure. This section is covered in Days 29 and 30 and wraps up The 30-Day Sobriety Solution. Here is some of what you will learn in this section:
• How to create a powerful and inspiring vision for your future life thriving in sobriety, including proven techniques to help you implement and manifest this vision in your life.
• The mind-sets and strategies of people who have learned how to thrive in sobriety and life despite facing unbelievable challenges.
• Your answer to the question "Can I ever drink again?"
### The Companion Website
One of the things I loved about The 30-Day Sobriety Solution was the ease of learning and implementing the daily solutions. Past attempts to quit drinking had always led to delaying when I would stop drinking or rationalizing why I deserved to drink, but with this program I found myself naturally motivated to read each day's solution and complete the action steps. I also loved how each solution built on the previous ones, which all led to my finally happily embracing sobriety.
—BRIAN
30-Day Graduate from Trenton, New York
This book comes with free access to The 30-Day Sobriety Solution companion website. Throughout the book, we will be referring you to the website. Not only will you find great supplemental content for every day's solution but also a forum where you can interact with past and present clients of The 30-Day Sobriety Solution. This website also includes critical recordings, such as guided visualizations related to the day's exercises. This has allowed us to dramatically extend the value of The 30-Day Sobriety Solution—enabling us to give you a comprehensive multimedia program all for the price of a book. You may want to visit the website now at www.The30DaySolution.com just to get a feel for what is there.
Lastly, we include four additional bonus solutions on the companion website that are integrated with the review days on Day 7, Day 14, Day 21, and Day 28. As we worked with people struggling to get and stay sober, we identified four solutions that virtually everyone on this path needs at some point or another.
• Day 7—The Social Solution covers the top 11 excuses that you can use to avoid drinking and feeling judged by others in any social situation. If you are planning to attend a party or a social event where people will be drinking, this is a must-read for you.
• Day 14—The Relapse Solution teaches you how to beat the odds of relapse and provides you with real solutions that work if you do relapse.
• Day 21—The Frequently Asked Sobriety Questions Solution includes the top questions that we have received from our sobriety coaching clients. It gives you answers to questions you did not even realize you wanted to ask, without having to pay the thousands of dollars others have paid for expensive coaching services.
• Day 28—The Sobernomics Solution teaches you the basics of what we call "sobernomics," a path to creating financial wealth and security with your newfound sobriety.
### How to Read This Book
I was a trained coach, and successful at helping facilitate positive change in others, but I still turned to excessive drinking late in life to deal with some of my personal challenges. And no matter what I tried, I just couldn't seem to let go of alcohol as the answer. Then I found The 30-Day Sobriety Solution, and I realized the answers were right in front of me. Although I was familiar with most of the tools and techniques in the program, the unique way they had been adapted to quitting drinking, as well as the strategic order in which they were taught, led to the exact breakthrough I needed to finally overcome my drinking problem.
—TAMARA
30-Day Graduate from Kansas City, Missouri
Everyone learns differently, and you probably know how you learn best. Nonetheless, we would like to make a few suggestions that you might find helpful.
The solutions are presented in a specific order, and they build on one another. Think of them like the numbers to a combination lock—all of the numbers are needed, and they are needed in the right order. Remember, if you know the combination to a lock, regardless of your IQ, ethnicity, race, gender, or age, the lock has to open for you.
As you read each day's solution and complete the exercises, we strongly urge you to take notes in the margins, highlight on your tablet or smartphone, or underline or circle anything that stands out to you. Find things that are important to you and that you want to take action on. Then go back and review your notes or highlighted text as often as possible. Remember, repetition is absolutely necessary to the learning process. Most people have to hear or see things multiple times in order to remember them, so by repeatedly exposing yourself to the ideas and techniques in this book, you will begin to change the way you think and live in the world. Every time you go back and read something you've marked, you'll be reminded of what you most need to do to get from where you currently are to a life thriving in sobriety. Reading the additional material, listening to the audios, and watching the videos on the companion website will also help you accomplish this.
As you go through the program, you might find that some of the solutions presented in this book sound familiar. That's good! Even if they do sound familiar, don't skip over them. Make sure to take a look at your life to see if you are currently practicing them. If not, commit to take action today!
The solutions will work on you only if you work on them.
If you're hesitating to take action on some of the steps or feeling resistant, that's okay. Our experience has shown that the steps you most resist are the ones you most need to take. If you are only going to read this book and not do the exercises, you will not get the same transformational experience as you would from actually doing the work—not even close.
### It Can Be Yours
Sober is sexy!
—DEMI LOVATO
Platinum-selling recording artist and founder of the Lovato Treatment Scholarship Program
As you embark on this journey, take a second to realize what can be yours in your new life if you just follow the simple steps laid out for you in this book:
• Whether it is having fun and excitement in your life without alcohol—it can be yours!
• Whether it is health and completely reversing the damage you have done with alcohol, finally losing the weight you always wanted, and looking younger and sexier—it can be yours!
• Whether it is finally feeling free from needing alcohol and waking up feeling naturally energized instead of tired and crappy—it can be yours!
• Whether it is taking your career to the next level and finding, embracing, and creating a new career in your life—it can be yours!
• Whether it is restoring your relationships with family and friends, and becoming the parent and spouse you always dreamed of being—it can be yours!
• Whether it is getting that spark back that you had in early recovery but have lost over the years—it can be yours!
• Or whether it is simply going to a party or going on a vacation and having an awesome time without needing alcohol—it can be yours!
We will show you how you can do all of this, and we will prove to you that others just like you were able to change their lives from top to bottom and blow away every myth that they held on to about how being sober sucks.
### Your New Life Awaits . . .
It's time to start living the life you've imagined.
—HENRY JAMES SR. (1811–1882)
American philosopher
It is completely normal if you feel both excited and afraid. In fact, we would be concerned if you were not a little afraid at this stage. Giving up or changing a habit that is as pervasive as drinking can be terrifying. After all, you may have been using alcohol daily for years just to get by. By quitting or changing your drinking habit, you put yourself out of your comfort zone, and fear is the natural reaction to such an act.
Take a deep breath and realize that we are here to guide you through this process. Millions of people around the world have already done what you want to do, and there is no reason that you cannot follow in their footsteps.
Your new life awaits—so don't hesitate. Turn the page and start Day 1 now.
# PHASE I
* * *
# Mastering the Absolute Basics to Get from Where You Are to Where You Want to Be
* * *
The beginning is the most important part of the work.
—PLATO (428–c. 348 BC)
Greek philosopher
We are excited to welcome you to Phase I of The 30-Day Sobriety Solution. This first phase is often completed over the first week of the program, and it will show you how to live a happy and fulfilling life without the desire to drink. These techniques have already worked for countless others just like you, who were either trying to cut back or quit drinking, or get reinspired in their recovery.
Before you turn the page (or swipe, tap, or click, if you are reading an ebook) to Day 1 of The 30-Day Sobriety Solution, it is important that you know this first solution sets the foundation for the whole program. It will hopefully address all of your questions, explain the tools and resources available to you and how to make best use of them, and, most importantly, start you along what most 30-Day Graduates consider a fun, exciting, and, of course, at times, challenging journey. We also want to give you advance notice that this first solution is the longest one in the book. This is just to make sure you have everything you need to successfully complete the program. We promise you the other solutions are much shorter, so hang in there. Let's get started now.
## Day 1
## The 100% Solution
## Building Your Foundation for Thriving in Sobriety
Take the first step in faith. You don't have to see the whole staircase. Just the first step.
—DR. MARTIN LUTHER KING JR. (1929–1968)
Clergyman and civil rights leader
As the above quotation from Martin Luther King Jr. says, all you have to do is take the first step. And congratulations—you have already taken the first step by picking up this book and starting to read it. Don't worry about how far you have to go or what you have to do. You have just opened the door to a life full of unlimited potential and possibility, and we invite you to walk through that door with us now.
### The Golden Buddha
We would like to start by having you read this story by Jack that appeared in the first Chicken Soup for the Soul book:
In the fall of 1988, my wife and I were invited to give a presentation on self-esteem and peak performance at a conference in Hong Kong. Since we had never been to Asia, we decided to extend our trip and visit Thailand.
When we arrived in Bangkok, we decided to take a tour of the city's most famous Buddhist temples. Along with our interpreter and driver, my wife and I visited numerous Buddhist temples that day, but after a while, they began to blur in our memory.
However, one temple left an indelible impression in our hearts and minds. It is called the Temple of the Golden Buddha. The temple itself is very small, probably no larger than thirty feet by thirty feet. However, as we entered, we were stunned by the presence of a ten-and-a-half-foot-tall solid gold Buddha. The statue weighs more than two and a half tons and is valued at approximately $196 million. It was an awesome sight—the kindly and gentle yet imposing solid gold Buddha smiling down at us.
As we immersed ourselves in normal sightseeing tasks (taking pictures while oohing and ahhing over the statue), I walked over to a glass case that contained a large piece of clay about eight inches thick and twelve inches wide. Next to the glass case was a typewritten page describing the history of this magnificent piece of art.
Back in 1957, a group of monks from a monastery had to relocate a large clay Buddha from their temple to a new location. The monastery was to be relocated to make room for the development of a highway through Bangkok. When the crane began to lift the giant statue, the weight of it was so tremendous that it began to crack. Rain also began to fall. The head monk, who was concerned about possible damage to the sacred Buddha, decided to lower the statue back to the ground and cover it with a large canvas tarp to protect it from the rain.
Later that evening, the head monk went to check on the Buddha. He shined his flashlight under the tarp to see if the Buddha was staying dry. As the light reached the crack, he noticed a little gleam of light shining back and found that strange. As he took a closer look at this gleam of light, he wondered if something was underneath the clay. He fetched a chisel and hammer from the monastery and began to chip away at the clay. As he knocked off shards of clay, the little gleam grew brighter and bigger. After many hours of labor, the monk stood face-to-face with the extraordinary solid gold Buddha.
Historians believe that several hundred years before the head monk's discovery, the Burmese army was about to invade Thailand (then called Siam). The Siamese monks realized that their country was about to be attacked and covered their precious golden Buddha with an outer layer of clay to keep their treasure from being looted by the Burmese. Unfortunately, the Burmese apparently slaughtered all of the Siamese monks, and the well-kept secret of the golden Buddha remained intact until that day in 1957.
As we flew back to Los Angeles on Cathay Pacific Airways, I began to think to myself, Just like the clay Buddha, we are all covered with a shell of hardness created out of fear, anger, resignation, and self-doubt, and yet underneath that outer layer, each of us is really a "golden Buddha," a "golden Christ," or a "golden essence," which is our real self. Somewhere along the way, between the ages of two and nine, we begin to cover up our "golden essence"—our natural self. Much like the monk with the hammer and the chisel, our task now is to discover our true essence once again.
What about you? What have you been using drinking to cover up or hide from? What "golden" parts of yourself have you let alcohol conceal? Today we will start to uncover the answers to these two important questions and help you get back in touch with the parts of you that may have become lost due to your problem drinking.
### The 30/60/90 Day Plan
In the early eighties, Maine's legislature enacted a returnablebottle-and-can law. Instead of going into the trash, my sixteen-ounce cans of Miller Lite started going into a plastic container in the garage. One Thursday night, I went out there to toss in a few dead soldiers and saw that this container, which had been empty on Monday night, was now almost full. And since I was the only one in the house who drank Miller Lite—Holy shit, I'm an alcoholic, I thought, and there was no dissenting opinion from inside my head—I was, after all, the guy who had written The Shining without even realizing (at least until that night) that I was writing about myself. My reaction to this idea wasn't denial or disagreement; it was what I'd call frightened determination.
—STEPHEN KING
Author of over fifty novels selling more than 350 million copies
As we mentioned in "Getting Started," this book was designed for you to read and implement over 30 days. We have repeatedly found that people who are serious about cutting back or quitting drinking will experience the greatest likelihood of success by completing one solution a day for 30 consecutive days.
Mike, a graduate of The 30-Day Sobriety Solution, discovered how effective it was for him to have a solution a day to turn to. He would come home every day from work and have the urge to drink, but instead of giving in to that urge, he would dive into that day's solution. So instead of going to happy hour, he replaced that with doing the program.
We have also found that a couple of alternatives can work just as well, including completing a solution every two or three days. The key to being successful is to decide the frequency that works best for you, and then hold yourself accountable for following through with that discipline. In fact, research has shown that you are more likely to follow through with something if you have set up a structured plan of action.
For example, if you plan to complete this program in 30 days, you need to set aside approximately forty-five minutes to an hour each day, which at first might sound like a lot of time. However, put it into perspective by thinking about the amount of time that you used to spend drinking every week. Often, the time you spent thinking about drinking, planning the next drinking event, doing the actual drinking, and then recovering from your drinking adds up to far more than an hour a day. Some of our graduates have shared that simply cutting out or cutting down their time spent on social media websites was more than enough to free up the necessary time to complete the program.
To help you succeed, we have created three email lists that you can join for free and that will help you complete The 30-Day Sobriety Solution in either 30, 60, or 90 days. For example, if you sign up for the 30-day list, you will receive an email every day for 30 days that briefly outlines that day's content and provides links to optional online resources. If you select the 60- or 90-day option, you will receive an email every second day or every third day. You can even track your progress and what you completed each day. We strongly recommend you use this free support system to keep you on track. To sign up for one of these email support systems, simply go to <http://Day1.Solutions>.
### Can You Ever Drink Again?
I found myself drinking two bottles of wine on the couch and said, "Jada, I think we've got a problem here." From that day on, I went cold turkey. I haven't had a drink in eight years.
—JADA PINKETT SMITH
Actor and singer-songwriter
We are always asked two questions when working with people in The 30-Day Sobriety Solution: "Can I ever drink again?" and "Do I need to quit drinking right now?"
Cutting back is a viable option for some people, as proven by past graduates who were able to achieve a take-it-or-leave-it attitude toward alcohol; in addition, numerous studies have confirmed that cutting back works for some people.
Nonetheless, in order for you to become a social drinker, you will need to abstain from alcohol for at least 30 days. In a minute, we will discuss the magic of 30 days and why this minimum period of time is necessary for making any profound change in your life.
But you do not have to stop drinking completely today. In fact, we often tell people we work with to pick a time during the first week when they will stop drinking. However, the caveat is that you must not be under the influence of alcohol while reading this book and completing the exercises. For example, during the first week, many clients complete the program during the day, before having anything to drink.
Most importantly, depending on how much you drink, we must remind you that quitting drinking abruptly can be dangerous. Daily excessive drinkers, such as those who drink around a fifth or a liter of hard liquor a day, can experience life-threatening seizures when they quit drinking all of a sudden. So please be sure to consult a doctor before you quit.
If you decide to quit later in the first week, do not "go all out" in the days leading up to that moment. For instance, do not suddenly decide to drink twice as much as you usually do by making the excuse that you want to "make the most" of the last time that you drink. Anytime that you increase your use of a mind-altering substance, bad things can happen. You make poor decisions, drive when you should not, or drink so much that you pass out (and if you pass out lying on your back, you risk asphyxiation). Because no one knows your drinking habit like you do, be smart about how you go about quitting.
Also, our experience has shown us that cutting back works for only a very small percentage of problem drinkers. Don't worry today about whether or not you are in this minority because, right now, you cannot know. On Day 30 we will address this question in far more detail, but for now, simply understand that you need to quit drinking completely for at least 30 days, even if only cutting back is your goal. If you are doing this program to be reinspired in your recovery, you may find the mention of a cutting-back option upsetting. We understand and respect this point of view and ask only that you don't let your belief about this hold you back from moving forward with this program. The 30-Day Sobriety Solution can help you enrich your life in recovery and ensure your continuing success.
Last, we want to share with you a definition of sobriety: "moderation in or abstinence from consumption of alcoholic liquor or use of drugs." We use the word sobriety throughout this program; however, we want to be clear that the use of this word does not exclude those who desire to only cut back. Although some dictionaries define sobriety as complete abstinence, we prefer this definition because it isn't important if you drink or abstain, as long as alcohol no longer has a negative impact on your life and you can drink responsibly.
### The 30-Day Reboot
I haven't gone back to drinking, and the thought of ever having another hangover gives me chills. I feel great, and I can't believe that I wasted a lot of my life trying to avoid life.
—MATT
30-Day Graduate from Kansas City, Missouri
At this point, you may be wondering what is so special about 30 days. In their book The Answer: Your Guide to Achieving Financial Freedom and Living an Extraordinary Life, John Assaraf and Murray Smith describe an experiment conducted by the National Aeronautics and Space Administration that demonstrates why it takes 25 to 30 days to successfully reprogram the brain. NASA was preparing to send astronauts into space and wanted to determine the mental and physical long-term effects of disorientation that the human brain and body experienced in zero gravity. It created goggles with convex lenses that turned everything upside down. Then it picked several subjects, who wore the goggles twenty-four hours a day for several weeks and attempted to function as normally as possible during this time, including eating, reading, and working, all while seeing the world upside down.
After 25 to 30 days, an amazing thing happened. One by one, the subjects started to see things right side up while still wearing the goggles. Effectively, their brains formed enough new neural connections to re-create reality in a more useful way.
The results of this experiment really are astonishing. The brain, after a few short weeks, "rewired" itself to ensure that one could not only survive but even thrive in a new environment. So, how long do you have to do something new to really change how you think—but not just to change how you think, but to actually change the neural connections in your brain to facilitate such a change in thinking? This study shows that such a change can occur in as little as three to four weeks.
Why does this matter? The bottom line is that you take daily action. We have outlined daily actions for you throughout The 30-Day Sobriety Solution, so that you can truly change the way you think and act for the long term. However, if you don't take regular, repeated action to implement the solutions in this book, you will greatly reduce your chance to succeed.
We call this concept the 30-Day Reboot. By taking the positive action laid out in this program, including 30 days of abstinence, you are essentially "rebooting" your system. Whether your goal is to cut back or quit drinking or simply to get reinspired in your recovery, this 30-Day Reboot will provide you with the foundation you need for sobriety.
### Your Destiny Is the Consequences of Your Daily Decisions
It is in your moments of decision that your destiny is shaped.
—TONY ROBBINS
World-renowned speaker and author of Awaken the Giant Within
Our goal for this program and our promise to you is to provide you with all of the information, inspiration, tools, and techniques that you need to recover, reclaim, and reinvent your life without alcohol, or, as we like to say, to thrive in sobriety.
We want sobriety to become second nature to you, so that the idea of taking a drink rarely enters your mind. And even when the thought of drinking does occur, it will seem more like an echo from an old habit and time rather than a serious consideration. We also want to be clear: we cannot help you achieve this goal without your commitment and desire. We are here today asking to be your role models, coaches, and mentors on your road to reclaiming your life from alcohol. We are asking you to make the decision today to change your life and your self-destructive relationship with alcohol. Give yourself a gift today: the gift of making a clear decision to get and stay sober—the gift of committing to work for as long as it takes to learn how to thrive in sobriety.
This clarity in your decision making will give you the power to produce the results that you really want. Here's a little secret. When you fully commit to thriving in sobriety, the answers you seek come a lot more quickly than you could ever expect. Some of the greatest moments in life come when we make very clear, committed decisions. This is one of those moments.
Your destiny is the consequences of your daily decisions. Read this sentence a few times and make sure it really sinks in. Remember, even when you do not make a decision, you just made a decision. You decided not to decide. So why not make a decision that empowers you? Today, make that choice to move toward your new future—one in which alcohol no longer defines who you are.
### The 100% Solution
Ninety-nine percent commitment is not possible. We are either 100% or not committed at all. I was amazed to discover this, because I had made a lifestyle out of tepid commitments that turned out to be noncommitments. I was just conning myself that I was partly committed. I had adapted to the pain of early rejection with the decision "Don't play." If I didn't play, I wouldn't have to face losing. And if I were forced to play, I could always play halfheartedly. If I lost, I could say it didn't matter, because I wasn't trying. It took me many years to realize that I wasn't even in the game if I was not committed. My body might have been out on the field, but my soul was on the bench. Soulless play is worse than no play at all.
—GAY HENDRICKS
Author of Conscious Living: Finding Joy in the Real World
If you want to cut back or quit drinking, and if you truly want to thrive in sobriety and life, you must choose to take 100% responsibility for all your life experiences, including the quality of your relationships, your health, your accomplishments, your failures, your debts, your physical state, your feelings, and, most importantly, your drinking habits.
This is not easy! No one really wants to do it. It's easier and more convenient to blame someone else—the weather, your horoscope, your friends, your husband or wife, your parents, your children, your lack of finances, your boss, your colleagues, the economy, or even the people who make, serve, and sell alcohol. We are afraid to acknowledge the real source of our problem—ourselves.
The truth is that you, and only you, are responsible for the quality of your life. This is the core idea on which this book is built.
Many years ago, Dr. Robert Resnick, a psychotherapist in Los Angeles, taught us a very simple but very important formula that has had a profound effect on our lives and work. It is a core principle we have taught to hundreds of thousands of people around the world that clarifies what 100% responsibility really means:
### E (Event) + R (Response) = O (Outcome)
Every outcome you experience in life—sobriety or alcoholism, excessive drinking or "normal" drinking, financial success or poverty, health or sickness, happiness or dissatisfaction—is the result of how you have responded to an earlier event or events in your life. The formula states that if you don't like the outcomes you are experiencing in your life today, you have two options:
1. You can blame the event (E) for your lack of results (O). In other words, you can blame anything and everything else: the presence of a liquor store and bar on every corner, your lack of education, racism, not having enough money, your friends, your family's drinking history, your past failed attempts at quitting drinking, the death of a loved one, losing your job, and so on. Without a doubt, these factors exist. But if any one of them was so absolute in deciding how your life would unfold, nobody would ever succeed. Actor Robert Downey Jr. would never have finally gotten sober to star in the Iron Man movies, Jackie Robinson would never have become the first African American to play major league baseball, and Samuel L. Jackson would not have become one of the top-ten-grossing actors of all time after the age of forty (after he went to rehab and got sober).
For every difficult circumstance in which someone ended up failing, thousands of other people faced the same circumstance and succeeded. The external conditions and circumstances are not stopping you—you are stopping yourself!
2. Or you can change your responses (R) to the events (E)—the way things are—until you get the outcomes (O) you want. You can't change the past, but you can change how you respond to the past. To do this, you must regain control of your thoughts, your beliefs, your desires, and, ultimately, your actions. You need to stop responding to events by drinking, whether it is drinking to celebrate, drinking to forget, or drinking to socialize, and respond with thoughts and actions that are aligned with your values, goals, and purpose. Don't worry. We know this is easier said than done. We will give you the tools and techniques you need to regain control of your thoughts and choose more effective actions.
### You Have to Give Up All Blaming
All blame is a waste of time. No matter how much fault you find with another, and regardless of how much you blame him, it will not change you.
—WAYNE DYER
Author of Your Erroneous Zones
As long as you continue to blame something or someone else for your lack of accomplishments in any area of your life, you will never become successful. This concept is particularly critical to your drinking. It is easy to outsource the blame to someone or something else because change is scary. It is far easier to place blame instead of taking responsibility and risking the uncertainty and discomfort of facing the unknown. Most importantly, blaming others takes away your power to make any lasting change.
If you are going to cut back or quit drinking for good and continue to stay inspired once you are sober, you have to acknowledge the truth—that you are the one who thought the thoughts, created the feelings, made the choices, and took the actions that got you to where you are now.
### You Have to Stop All Your Complaining
The man who complains about the way the ball bounces is likely the one who dropped it.
—LOU HOLTZ
Legendary college football coach
Everyone complains, but why? If you complain about someone or something, you must believe that there is someone or something better. If you didn't actually believe that something better was possible in your life—more friends, more money, a larger house, a more fulfilling job or career, more joy, a more loving spouse—you wouldn't complain. In your mind, you have a picture or an image of what you prefer because it's better. And you know you would prefer that something better, but you aren't willing to take the risks that are required to create it.
Let this really sink in. Every circumstance you complain about is something that you can change but have chosen not to. Problem drinking is a perfect example of this. You have the ability to cut back or quit drinking; however, you have to accept that doing this requires you to change.
So why haven't you changed yet? It's because it involves risks—you run the risk of being bored, not being liked, being ridiculed and judged by other "normal drinkers," or not being able to deal easily with stress or the uncomfortable feelings that might come up. You also run the risk of failure, and of disappointing (yet again) your parents, your friends, your spouse, or your children if you fail.
Making a change might be a struggle and take extra effort, time, and money that you don't think you have. Making a change might be distressing, unnerving, and unpleasant. So, instead of experiencing any of these uncomfortable feelings, you avoid taking any risks and stay put and complain about your situation. And, of course, you drink. You drink and complain to anyone that will listen. You drink to numb out your uncomfortable feelings.
In order to grow, you need to make the decision to stop complaining and to stop spending time with complainers, and get on with creating the life of your dreams.
### 99% Is a Bitch, 100% Is a Breeze
There is a difference between interest and commitment. When you're interested in doing something, you do it only when it's convenient. When you're committed to something, you accept no excuses, only results.
—KEN BLANCHARD
Coauthor of The One Minute Manager
One of the most important components of the 100% Solution is the No-Exceptions Rule. This rule means that once you are 100% committed, there are no exceptions and no renegotiating. Not only does this rule make life easier and simpler, it frees you from inner conflict. Instead of internally debating over and over about whether you will or won't do something, like drinking, your decision is already made. The real power and value from this come from all the energy you can now redirect to focus on what you actually want to create and accomplish in your life.
However, the moment your commitment drops to 99%, you open the door for the internal debate to begin, and when it comes to alcohol, this is a debate that usually ends in a rationalization to drink again.
Think about this from another perspective. Have you ever been somewhere where you knew there was absolutely no way you could drink? For example, you went somewhere where no one was drinking and no alcohol was available, and the option was 100% closed off to sneak in any alcohol or even have a single drink. What was your reaction? Most likely, leading up to the event, you were annoyed; but when you got there, you accepted it and found that you were not obsessing about drinking. Why? Because you knew without question the option didn't exist, so you didn't even start down the "what-if" path of whether you should drink. When you commit 100%, you create "the-option-doesn't-exist" event in your life every day. But when you are less than 100% committed and times get tough, you end up giving in to your cravings.
Here's Dave's story of his last drink and how this led him to apply the 100% Solution to his life:
I remember the last time I drank as if it happened yesterday. It was a warm and humid day just outside of Seattle. I had just flown in from Denver for a week of technical training for my job. I had forty-two days of sobriety, was going to Alcoholics Anonymous, and even had a sponsor. As soon as I got into my rental car, I felt this overwhelming shift inside, and all of a sudden my craving for alcohol reached an all-time high.
I called my sponsor and was able to refrain from drinking that first night, but the obsession was growing. The moment I stepped out of that first day of training, I knew that I was going to find the nearest liquor store and start drinking. With a liter of Captain Morgan rum and a liter of Absolut vodka in hand, I planned to drink that night, without question, and likely every night that week. What I did not know was how life-threatening that week would end up being for me.
My first night of drinking was uneventful, and I made it to my training session the next day. But all I could think about during the training was my next drink. Once I returned to my hotel room, I immediately started drinking again. Because of my previous stint with sobriety, and the fact that I was drinking more than usual because I wanted to "make the most of my drinking freedom," I woke up with a severe hangover and puked—something that I rarely did. I skipped the training that day, and by noon, I was feeling better and started drinking again. The previous two days seemed to be just a warm-up, because from noon to nine that night, I drank excessively. The last thing I remember from that evening was watching the television show So You Think You Can Dance while lying in bed, slightly propped up on my back.
The next morning, I awoke with vomit all over my clothes, the floor, and the bathroom. At that moment, I knew I was lucky to be alive. I suddenly recalled all the stories that I had heard about people who'd asphyxiated while intoxicated. I remember looking at myself in the mirror and barely recognizing the person staring back at me—overweight, face bloated, and puffy-eyed. I knew that if I did not commit 100% to getting sober at that moment, I might not have another chance.
The evening of August 15, 2007, was the last time I ever drank. That moment also marked the culmination of almost eighteen years of excessive drinking. This story represents the importance of the 100% Solution. Not until this last experience did I truly become committed to getting sober. I was finally ready to stop blaming and complaining about why I could not get sober, and I owned up to the truth—that I had complete control over my life and my decisions. It was also the first time in my life when I committed 100% instead of 99%. If I had been 100% committed to staying sober when I arrived in Seattle, the thought of drinking might still have entered my mind, and the craving might not have instantly disappeared, but the internal debate in my head never would have started because my decision would have already been made. That is the power of 100% commitment—while it might be challenging, it makes life far less complicated.
Today drinking represents to me total and complete pain, and sobriety represents absolute pleasure. The thought of drinking is the equivalent of causing great physical and mental harm to myself. I know that you might find this difficult to believe, depending on the stage you are at, but this program will show you, step by step, exactly how I and others got sober and went on to be truly happy and successful.
### The Myth of "Rock Bottom"
I was lost. Emotionally lost, physically lost, mentally lost. I didn't know where to turn or what to do. Part of my problem, although I didn't know it yet, was denial.
—JOSH HAMILTON
American League Baseball MVP, author of Beyond Belief: Finding the Strength to Come Back, and in recovery from alcohol and drugs
You often hear about an alcoholic needing to hit "rock bottom" before getting sober. In reality, the rock bottom that everyone envisions—the homeless drunk begging for money on the street—is not close to the real meaning of hitting rock bottom. Have you wondered why some people can drink normally, but you don't seem to be able to? One reason is because others define their rock bottom very differently than you do. For example, "normal" drinkers might go out once every six months, drink too much, feel miserable, and say, "I will never do that again." That was their rock bottom, and they simply chose not to allow alcohol to play a more significant role in their lives.
By embracing the 100% Solution, you are acknowledging that you have reached your rock bottom and that you will no longer allow alcohol to play a controlling role in your life—you will no longer live in denial. Because "rock bottom" is whatever you decide to make it, you can decide now that you have suffered all of the negative consequences that you are ever willing to suffer from drinking—that today you have hit your rock bottom.
There is a great analogy we love to share. We often ask the people we work with if they shoplift. The answer is almost always no. We then follow up with the question "Do you have a debate with yourself about shoplifting when you are in a store and you see the perfect opportunity to get away with it?" Of course, the answer is still no, and the reason is simple. If you are 100% opposed to stealing, then you never engage in a debate on whether or not to steal. But if you did have a history of shoplifting and you had never committed 100% never to steal again, when the opportunity presented itself, the internal debate of whether or not to steal could start. And once the debate has started, especially when it's related to an addictive behavior, the ability to say no is much more difficult.
So when you decide that you have hit your rock bottom, you will have reached that empowered 100% attitude, and you will stop wasting time and energy debating about when, where, and how much you will be drinking. Instead, when the thought to drink enters your mind, you won't even entertain the debate because you are now 100% committed to not drinking.
### Why Do You Drink?
No matter how many negative consequences I suffered or how many times I promised to quit drinking, I always returned back to my drink of choice—wine. The 30-Day Sobriety Solution finally changed all of that. Every solution seemed to bring me more clarity and wisdom about why I was drinking, and as I worked through the exercises, I was able to solve what was really driving me to drink.
—NATHALIE
30-Day Graduate from Winnipeg, Canada
We have some great news for you! Contrary to what you might believe, you do not have a problem with alcohol, which is exactly why we don't like to use the words alcoholism and alcoholic.
We use "problem drinker, "excessive drinker," and other terminology rather than alcoholic because this word has negative connotations for most people. Given what we know about the brain and self-actualization, labeling yourself an alcoholic can ultimately be counterproductive to thriving in sobriety.
So if your problem is not with alcohol, what is your problem? Simply put, drinking alcohol is the symptom of a deeper problem, or what is often referred to as a symptomatic behavior. The real problem is why you use. The deceased actor Patrick Swayze discussed this in his book The Time of My Life: "In all my life, I never drank for the sake of drinking; it was always a response to some kind of emotional difficulty I was going through. Drinking for me was a symptom of a problem, not the problem itself."
Drinking alcohol is the symptom, and the real problem lies elsewhere. Although various programs and therapists discuss this point, they often do not state it as clearly as it should be stated. Alcohol abuse, drug addiction, overeating, and other compulsive negative behaviors are responses to one of a variety of factors in your life.
For example, the average American watches almost five hours of TV a day. If you're watching too much TV, what is the real problem? The TV itself is not the problem; the reason you watch TV is the problem. You watch too much TV because you are bored, you want to live the lives of the people on the shows rather than your own life, or you believe it helps reduce your stress or distract you from your feelings. The same is true for your drinking. The alcohol itself is not the problem—the reason you drink is the problem.
Part of the challenge with cutting back or quitting drinking is that people often become too focused on stopping their drinking instead of understanding and identifying why they drink, and then changing that reason. Addressing the underlying causes of why you drink is a critical component to stopping your desire to drink in the first place or, equally important, your desire to switch your problem drinking to some other addictive behavior. If you simply attempt to cut back or quit drinking without addressing your why, you will only go down the path of manifesting other addictive behaviors. Even if you do manage to stop your addictive behavior but fail to work on the "why," you will likely not be very fulfilled in life.
### "You Can't Hire Someone Else to Do Your Push-ups for You!"
If you want to see the benefits from doing anything of value in life, you have to do it yourself. As Jim Rohn, pioneering success coach and motivational expert, states, "You can't hire someone else to do your push-ups for you." No one else can do it for you. We can show you the way, but you will have to do the work. You can choose to embrace the solutions and the action steps, even if you have some doubt, or you can choose to always look for reasons and rationalizations for why what we are teaching won't work for you.
We are not saying that every single solution will be a perfect fit for you, and you may choose to disregard some of them; however, as one 30-Day Graduate shares below, you will find some solutions that will work wonders for you:
What I love about The 30-Day Sobriety Solution is that it gives dozens, if not hundreds, of tools and techniques you can use to help you get sober. In Day 1 it acknowledges that everyone is unique, and that is why some solutions result in incredible breakthroughs for one person but not for another. I found this statement refreshingly honest, and logical, and experienced that most of the solutions really helped me to "thrive in sobriety." And the few that I didn't get as much value from, I simply didn't integrate into my life beyond the program.
Another 30-Day Graduate said that she felt like she opened up a "supercharged Craftsman tool kit of things to use for sobriety," and as a result, she started seeing amazing shifts happen within only the first two weeks. For the first time in her life, she was able to say, "I don't see myself drinking. I don't see choosing feeling the way I felt before when I know I can feel like this." The solutions that do work for you will change your relationship with drinking for the rest of your life, as long as you embrace them with passion, purpose, and a positive expectation.
### A Vote for Living
The thing I really like about The 30-Day Sobriety Solution is that it's focused on getting you to thrive in sobriety and getting you really excited about it. Up until I found The 30-Day Sobriety Solution, it always seemed like to conquer alcohol I needed to have a boring and somewhat painful life that would not involve much with social activities. And that I probably would be committing myself to life with not much fun. But The 30-Day Sobriety Solution actually got me excited about being sober.
—ANN
30-Day Graduate from New York City
You are now ready for your first exercise, which we refer to as an action step. Assuming you've already gotten approval from your health care professional to quit drinking, this first one is optional, especially if you already have some extended sobriety. But don't get used to action steps being optional. We recommend that you schedule an appointment with your qualified health professional to get your standard blood work, weight, blood pressure, and other vital signs measured.
This is important for two reasons. First, the people we have helped often have two things in common: they are great at rationalizing that they do not have a problem with drinking—at least most of the time. Second, health-related consequences of excessive drinking are some of the most common and the most difficult to hide from because your blood work does not lie.
Dave's blood work tests showed the typical bad numbers for his liver, the fats known as triglycerides, and other indicators that go hand in hand with a drinking problem. Every time Dave got his blood work done, the doctor asked him the same question: "How much do you drink?" His temporary solution was to lie to the doctor about how much he was actually drinking, and then to eventually switch doctors—or to simply not go at all. He rationalized that drinking was okay, but ultimately he could not overcome his fears about his alcohol abuse cutting his life short, and particularly how that would affect his two young daughters.
Another reason for getting a physical is that by going to the doctor, you are taking a stand and telling the world that you want to survive and that you are making an effort in that direction, which is a vote for living. And this is one vote you don't want to miss. So as soon as you stop reading this, pick up the phone and schedule an appointment with your doctor or qualified health professional to get a complete physical and blood panel.
The photos of Dave below show him before and after sobriety, and indicate what is possible by completing The 30-Day Sobriety Solution. Our graduates consistently report very similar results, and these dramatic outer physical changes are a manifestation of the inner changes that also occur as a result of the program.
Dave Andrews in 2006 and Dave Andrews after getting sober and completing the Denver Marathon with Bill Phillips (bestselling author of Body for Life: 12 Weeks to Mental and Physical Strength).
### The Heart of The 30-Day Sobriety Solution
Through the 30-Day solutions and action steps, I was able to deal with and overcome many issues in my life that in the past I had to mask with alcohol. Fully grasping the concept of being excited about life and having the gratitude for it propelled me into areas of my life I had never been to or even knew were possible to reach within myself.
—DESIREE
30-Day Graduate from Harare, Zimbabwe
The heart of The 30-Day Sobriety Solution can be summed up in one word: action.
When you read the solutions, we would love to be able to say to you, "Just think about the answer, and you will be on your way to thriving in sobriety." However, the reality is that you have likely spent years "strengthening" your dependence on alcohol. To reverse this, you must take the time to actually complete the action steps at the end of each day's solution, and, most importantly, this includes writing down your answers. Something happens when the ink (whether real ink or "electronic ink," if you are using a computer, smartphone, or tablet) hits the "paper."
Believe us when we tell you that our clients have tried to prove us wrong on this. However, once we convinced them to start journaling and writing down the answers to the action steps and their notes on the content covered, they began to see real change happen. Several powerful things happen when you put your thoughts on paper.
First, you remove ambiguity and gain clarity. Your thoughts can be unorganized and unclear, but putting them on paper forces you—in many ways—to get clearer, and clarity is incredibly powerful. Second, writing things down removes the thoughts from your head, essentially freeing your mind and reducing your inner conflict and clutter. Your brain knows it can now release some of those thoughts because you have written them down. Third, writing things down engages more of your senses, which is extremely powerful. When you write things down, you are physically taking action, and you experience visually what you have written. Simply, writing is the doing part of thinking.
You might be asking, "What if someone reads my personal thoughts without my permission?" Trust us, we understand your fears related to writing down the details of your personal thoughts and feelings, and how violated, ashamed, or embarrassed you might feel if someone discovered and read them. Our recommendation is to find a safe place to record and store your writing. For example, you can use Google or Hotmail documents, which allows you to create and store Word documents online that are protected by your user name and password. You can even set up a new account just for your writing activity. Alternatively, if you really like the touch and feel of a physical journal, you can get one just for this program and keep it hidden and locked. On the companion website, we provide these various journaling solutions, as well as the results of a research study that proves the incredible value of journaling.
To further understand the importance of writing in your journal (and completing each day's action steps), look at the Cone of Learning, developed by American educationist Edgar Dale. The Cone of Learning shows the effects of different kinds of learning on human memory. Simply stated, the more you engage actively in the learning process, the more you will retain. If you only read the solutions but don't do the exercises and don't experience any of the material in any other way, you will end up remembering only about 10 percent of it two weeks later. That will not make a huge impact on your cutting back or quitting drinking.
### The Cone of Learning
I see and I forget.
I hear and I remember.
I do and I Understand.
—Confucius
We have therefore created a companion website for each solution that will help make sure the solutions work for you by involving you in written exercises, guided visualizations, supplemental audio content, and more. The bottom line is that the more fully you engage in this program with all of the exercises and resources, the more fully you will experience the transformations you are seeking. The impact will be much more powerful than if you only read the material. And here is the best part: it doesn't take a lot of time to do the writing exercises and other activities that are in the book and on the website. You can do all of this work in the same amount of time that you might have spent at happy hour or while partying over a weekend.
### Day 1 Action Steps
The money I saved from not drinking well exceeded the cost of The 30-Day Sobriety Solution, but the changes it helped me make in my life were priceless.
—ROBERT
30-Day Graduate from Vienna, Austria
At the end of every day's solution, we will summarize the action steps that we covered. You can choose to do them as you go or wait until the end of the chapter. We recommend that you do them at a time when you will most likely follow through. For example, you may feel that stopping and doing the first action step when it is first presented for the day propels you forward to complete the other ones, or you might feel that you need to read the entire chapter before doing any of the action steps. Unless we mention that an action step is optional, it is required because it is essential for your success in this program. You may need to access the free companion website for some of these action steps; however, reading the additional content and resources on the site is optional. They are just there for additional support if you want to go deeper.
One of the benefits of the companion website is that it allows us to give you a wide range of content, such as new breakthrough research, additional success stories, specially recorded videos from experts, online tools and resources, and multimedia content that we otherwise could not deliver.
If you prefer listening over reading, we highly recommend purchasing the audio version of the book, which is integrated seamlessly with the companion website for ease of use. Many of our graduates have told us that listening to the material was effective and enjoyable for them because they could take notes easily and be more engaged in the content. If you are interested in finding out more about this, simply visit the companion website for today's solution at <http://Day1.Solutions>.
Now let's review today's action steps:
• Start a journal. Whether you keep an online journal using Google Docs or Hotmail SkyDrive or a physical journal, start one right now. In your journal, write down your answers to the exercises, your thoughts on the content for the day, and your progress and setbacks along your path to thriving in sobriety. Remember, you don't need to worry about grammar or spelling in your journal, but you do want to write in it every day, even when there isn't an action step that tells you specifically to do so. If you have chosen to do this in 60 or 90 days, you still need to write in your journal daily. The same is true for all "daily" action steps in future solutions.
• Decide your time frame. Choose whether you will finish this program in 30, 60, or 90 days and then sign up for a free email reminder on the companion website to help keep you accountable. Then decide the day during the first week of this program on which you will quit drinking for at least 30 days. Write this date in your new journal. And decide right now that you are 100% committed to this plan and write it down in your journal.
• Begin to use the equation E + R = O in your life. Simply begin to pay attention to moments when you are complaining about or blaming an event rather than focusing on creating a new response that can change the outcome.
• Capture the "before you." Take a photo of yourself, or find a good recent "before" photo of yourself, and then schedule a visit to the doctor or health professional's office to get your blood work done (this last part is optional). You will be amazed at the end of 30 days how much sobriety can make your face look years younger and bring back the sparkle in your eyes.
• Listen to the Time Travel Technique. Through all of the coaching we have done and the feedback we have received, this guided exercise, which can be found on the companion website, has proven to create incredible leverage, clarity, and purpose. It is critical you do this exercise. One 30-Day Graduate shared with us, "In Day 1 of The 30-Day Sobriety Solution, I did the Time Travel Technique, which was life changing. This process gave me a level of clarity around my drinking that I had never experienced before. I finally knew, and accepted, that continuing to drink was going to keep me from everything I wanted in life, and sobriety was going to lead to true happiness and fulfillment." Immediately after you finish listening to the Time Travel Technique, write about your experience in your new journal.
Congratulations! You have just finished the longest chapter in the book. We promise the remaining solutions are much shorter. Be sure to access the companion website for the Time Travel Technique, to sign up for your free email reminders, and to find out more about this program, at <http://Day1.Solutions>.
## Day 2
## The Purpose Solution
## Identify, Acknowledge, and Honor Your Thriving-in-Sobriety Vision
Great minds have purposes, others have wishes.
—WASHINGTON IRVING (1783–1839)
American author
Each of us is born with a unique life purpose. Possibly the most important action you will ever take to cut back or quit drinking for good and truly thrive in sobriety is to identify, acknowledge, and honor your purpose. When you understand and know what you are here to do and pursue that with enthusiasm and passion, your desire to drink fades naturally. The Purpose Solution takes you through exactly how to do this.
Before we get started with identifying your life purpose, we have to ask an important question: Did you complete the action steps on Day 1 in the 100% Solution? If not, please stop reading right now and go back and complete them. If you completed them, congratulations! You have taken that critical first step, and you are on your way to creating a new and exciting life for yourself. Did you realize that completing Day 1 already puts you in the top 10 percent? Less than 10 percent of the people who buy a nonfiction book read past the first chapter. By getting this far, you have proven already that you are willing to take more action than the other 90 percent, and with this continued action, you will inevitably reap the rewards you are seeking.
### One Day at a Time
As I completed each day in The 30-Day Sobriety Solution, I often found myself torn between wanting to spend more time focusing on that one solution rather than moving on to the next. What I quickly realized was that the future solutions built on the previous ones, as well as answered many of the questions that came up on those previous days. This organization of the solutions really helped me create a new, strong foundation for my sobriety.
—LENORE
30-Day Graduate from Dallas, Texas
Yes, we know that "live your life one day at a time" is one of the most overused clichés of our time, but when it comes to overcoming an addictive habit, it couldn't be more appropriate. One day, one hour, one minute at a time—whatever it takes to help keep you moving forward.
As you go through The 30-Day Sobriety Solution, questions will inevitably come up. Questions about the content we included (and didn't include). Questions about certain action steps. And questions about your personal experience, and if others are experiencing similar challenges and breakthroughs like you. We assure you that most, or even all, of these questions will be answered by the end of the program. We can say this with confidence because we frequently receive this feedback from 30-Day Graduates. So as questions come up, feel free to make note of them in your journal, and if your questions aren't answered, you can use the companion website or the Frequently Asked Sobriety Questions Solution, which is a bonus solution on Day 21, to get answers.
As we mentioned on Day 1, you want to begin your 30 days of continuous abstinence, or the 30-Day Reboot, sometime in this first week. One of the easiest ways to dramatically improve your odds of abstaining successfully is by removing all alcohol from your house. If you live with others who are not willing to do this, consider using a locked cabinet. For example, when one of Jack's family members was struggling with problem drinking, Jack added a lock to an existing cabinet and stored all liquor, beer, and wine in it.
This simple step will create an important barrier between you and alcohol—giving you some time to really consider your decision, rather than being able to react instinctively to a desire to drink. If you have already started your reboot, that is fantastic; just make sure you complete this step of removing all alcohol from your house. Otherwise remember to complete this step before starting your 30-Day Reboot.
### Change Comes at the Edge of Your Comfort Zone
I will begin one of the most exhilarating, liberating, and exciting four weeks of my life. Scary, yes, and filled with unspeakable emotional discomfort, but for me it's an unquantifiable relief that I am being shown a different way to live. I am so tired of the lying, my inability to keep my word, the bullshit relationships, the hangovers, the cover-ups, and the helplessness to stop doing the things I truly want to stop doing.
—ROB LOWE
Actor and author of Stories I Only Tell My Friends: An Autobiography
Most people are initially fearful of cutting back or quitting drinking. This is because you are comfortable with drinking. It has become your trusted friend. And sobriety is a challenge for you and most likely not in your comfort zone. Fear is the natural reaction when you step out of your comfort zone. At this stage, a typical response that we hear from our clients is that they are afraid to quit drinking, yet at the same time, they are afraid to continue drinking. These conflicted feelings are completely normal.
For you to achieve your goal, you have to embrace fear and change. There is simply no other way around it. We will teach you what you need to know—you just need to be open to learning and applying these lessons and embracing change. The choices you make today, and every day, create your future, and real change comes at the edge of your comfort zone.
William James, a Harvard University psychologist, philosopher, and doctor, said, "It is our attitude at the beginning of a difficult undertaking that, more than anything else, will determine its successful outcome." Make the choice today to embrace a positive attitude about the journey on which you are embarking.
Remember, the only way that you can fail at cutting back or quitting drinking is to give up. If you don't give up, and if you keep searching for the solutions that best fit you, you will find the answers you seek. If you continue to take small steps right now, you will develop the momentum you need to build the life you most desire.
### The Story of "The Alcoholic King"
A great irony exists among drinkers, one that Dave frequently experienced firsthand during his drinking days, and one that you might be able to relate to as well. Some refer to it as the "King's Reflection," although it is not usually used in relation to problem drinkers. We prefer to call it "The Alcoholic King."
A very common scenario exists—a ritual, in many ways—that is played out at the start of the "drinking day" for many problem drinkers. Somewhere in the neighborhood of two to five drinks, you often reach what may be referred to as an "optimal buzz." It is that moment in which the euphoria of drinking starts to manifest—the warm, tingling sensation in your stomach, the feelings of relaxation moving through your body, and the temporary letting go of all of your problems.
This peak state, one that you often "chase" the entire night to maintain, usually leads to daydreaming about all of the exciting and amazing accomplishments that you will achieve in life and how everyone will be so proud of you. During this peak state, problem drinkers dream of the life that they believe they are meant to live, including achieving financial goals, optimal physical fitness, various career accomplishments, and engaging in philanthropic efforts. Can you remember having this experience when you drank?
The ultimate irony is that this temporary state of mind is an alcohol-induced mirage that is virtually guaranteed to never manifest in your life. The reflection that you see during this peak state could not be further from reality. The sad truth is that the same thing that fuels this mirage is the same thing that ensures you will never accomplish these things—alcohol.
Just as this picture depicts, the image looking back at you from the mirror is a lie. Not only are you not that person looking back at you, but you never will be the person you want to be as long as alcohol continues to be in your life the way it is today. There simply isn't room in your life for drinking to excess and accomplishing all of your goals.
When you drink, you usually play out a very different story than what you really want. Problem drinkers start drinking and reach that peak state where they daydream about everything they want. Eventually they shift out of that peak state of mind but continue to try to regain it by drinking more. They eventually go to sleep, or pass out, only to wake up hungover and too tired and unenthusiastic to take any real action toward accomplishing their goals.
They get through the day, do the bare minimum they need to, and as they begin to feel better, they start to think, "Wouldn't it be nice to have a few drinks tonight?" or "I am so sick of my life, so maybe I will just have a drink to take the edge off." The process repeats itself, ensuring that the future will be the same as the past, bringing you no closer to your goals tomorrow than you were today. In fact, the opposite is often true, and you move further from the person you desire to be. At times, you may recognize how far you are from the person you want to be, which only creates more pain related to the choices you have made. So, in order to escape this reality, you drink more.
Deep down, do you know that you are meant for something better and that alcohol is keeping that "better life" from ever manifesting? Today you will discover how to create a powerful vision that will accelerate your desire to thrive in sobriety.
### The Power of Vision
Throughout the centuries, there were men who took first steps down new roads armed with nothing but their own vision.
—AYN RAND (1905–1982)
Novelist and philosopher
One of the themes of this book is how to get from where you are to where you want to be, or more specifically, how to cut back or quit drinking and thrive in sobriety. To accomplish this goal, you need to know where you are today and where you want to be in the future. And to get there you need a vision or a detailed description of what your destination looks and feels like.
Problem drinkers have several things in common. First, if they do have some idea of their vision, it often is not very clear. Second, they have never taken the time to write down their vision. Third, their vision is very different from the vision they are living, and alcohol has become the main coping mechanism for this disconnect. Today is all about clarifying and resolving these disconnects in your life.
### Your Thriving-in-Sobriety Vision
The secret of getting ahead is getting started. The secret of getting started is breaking your complex, overwhelming tasks into small, manageable tasks, and then starting on the first one.
—MARK TWAIN (1835–1910)
Author of The Adventures of Huckleberry Finn
Figuring out a vision for your life is not as easy as it might sound, especially at the beginning of a new undertaking such as this one. When alcohol has played such a profound role in your life, uncovering your life's vision and purpose takes time and, most importantly, some extended sobriety.
At this stage, one approach works better than anything else, and that is simply to create a vision statement for yourself 30 days from today. These 30 days are setting the stage for a profoundly new and exciting life thriving in sobriety, and we know that if you can get through these 30 days, then anything is possible. This is your first action step for today.
#### The Vision Statement Guidelines
A dream is your creative vision for your life in the future. You must break out of your current comfort zone and become comfortable with the unfamiliar and the unknown.
—DENIS WAITLEY
Author of The Psychology of Winning: Ten Qualities of a Total Winner
Here are some basic guidelines that you need to follow when writing a vision statement:
• Write it in the present tense. Write your vision as if you are already living it. For example, "I am . . ."
• Be as clear, concise, and specific as possible. Ask yourself, "What will I be doing, experiencing, seeing, touching, and feeling?"
• Write in the positive. For example, do not write, "I do not drink every day." Studies have shown that your subconscious mind does not register the negative of a statement; it doesn't "hear" the not. Therefore, when you say, "I do not drink," the subconscious mind receives this statement as "I do drink," and focuses on that. As Carl Jung, the founding father of analytic psychology, stated, "What you resist persists," which is why you need to always focus on what you do want rather than what you don't want. Instead, write, "I wake up every day feeling vibrant and excited about being sober."
• Keep it short. Some people prefer to keep their vision statement short, like a headline in a newspaper, while others prefer to add more details, as you'll see with the examples below.
• Focus on the what, not the how. Getting clear on your vision of sobriety is all that matters right now. The "how" will come later as a natural result of doing this and other exercises.
#### Writing Your Thriving-in-Sobriety Vision
If you want to change the fruits, you will first have to change the roots. If you want to change the visible, you must first change the invisible.
—T. HARV EKER
Author of Secrets of the Millionaire Mind: Mastering the Inner Game of Wealth
Here are some examples of vision statements from graduates of The 30-Day Sobriety Solution. As long as you get energized and inspired when you read your vision statement, the length is not important.
• Every day I wake up feeling excited, vibrant, and passionate about living a meaningful and fulfilling sober life.
• I am grateful to be solving my drinking dilemma and am excited to be creating a life of quality.
• Physically, spiritually, emotionally, and mentally, I am making decisions and choices that manifest sobriety every day in my life, and doing so allows me to live the life that I have always dreamed of—one of excitement, purpose, and giving back.
• I am full of life, love, and energy. I radiate as bright as the sun. I am strong, self-confident, healthy, and happy again. The more I fuel my body with the right things, the more alive I become. This is the best gift I am giving to life. Life is to be lived, and I am living it to the fullest—doing all of those things that used to be put off to the tomorrow that never came.
• I am vibrant, healthy, and energetic, like I was before the drinking thing, and what's amazing, it's even better than I imagined. I am happy and joyful and wake up with zest for each day.
• I am living my purpose, and my relationships are improving in ways that are amazing and will only get better. I am proud of myself, and it's so refreshing experiencing all the people who are so happy right along with me.
• I am full of gratitude for the immense learnings and beautiful gifts I have received from my "failures."
• I am healthy. I run without stopping and sometimes turn off the music just to be in the moment—fully aware and alive.
As you can see, these statements are written as if you have already turned your vision into reality. They are clear, concise, written in the present tense, and positive in nature. They also can vary in length—simply pick a length that feels right to you. We want you to know that the vision statement you write today is just for these 30 days and is not a vision statement for your entire life. We will help you discover and write that on Day 29. What is important now is that you focus on what you want to feel and what you want to be by the end of The 30-Day Sobriety Solution.
Once you have written your vision statement, review it several times a day, every day. For example, you can put your statement at the beginning of your journal, and every time you open your journal (whether physical or electronic), it will be the first thing you see, and you can quickly reread it. Or you can put your vision statement on an index card and tape it to your bathroom mirror, refrigerator, or near your work area. You can also print it and put it in your wallet and occasionally take it out to review. Or laminate it and tape it on the shower wall or on the inside cover of a notebook. You can even make your vision statement a screen saver on your computer, iPad, or smartphone. Dave puts his on the sill in front of the speedometer in his car, where he can easily flip it up and read it out loud when he is stopped at a red light. Get creative—the end goal is simply to consistently remind yourself of your vision so you are continually aligning with it.
### What's the "Why" Behind Everything You Do?
Decide upon your major definite purpose in life and then organize all your activities around it.
—BRIAN TRACY
Author of Goals! How to Get Everything You Want—Faster than You Ever Thought Possible
Yesterday we addressed the fact that your problem is not with alcohol, but rather that drinking alcohol is the symptomatic behavior of a deeper issue. One of the keys to cutting back or quitting drinking is identifying the reasons why you drink. One of the most effective methods to do this is to discover and embrace your life purpose.
Without a clear purpose as the compass to guide you, the achievement of your goals and action plans may not ultimately fulfill you. As Stephen Covey writes in The 7 Habits of Highly Effective People, you don't want to get to the "top of the ladder" in life only to find out that the ladder was leaning against the wrong wall.
When Jessica found The 30-Day Sobriety Solution, she quickly discovered that her "ladder" was leaning up against the wrong wall. By most people's standards, Jessica was very successful. She had an undergraduate degree and a master's degree from highly regarded educational institutions and a successful career in which she was excelling and recognized for her invaluable contributions. She also had a boyfriend she loved and with whom she could see a bright future.
Even with all of that, Jessica was unhappy. She drank alone regularly, binge drank on weekends, and experienced the occasional blackout. She constantly worried about her health, her safety when she blacked out, her relationship with her boyfriend, and her career. And every time she drank to escape those feelings, they only came back stronger when she sobered up. She felt like she was wasting her potential, and the easiest way to avoid her worries was by drinking.
As Jessica worked through The 30-Day Sobriety Solution, she started to really look at the "why" behind her drinking. One thing stood out above everything else—her career. She took time to look back over her life to analyze what had made her the happiest. She then thought about what her ideal day would look like if she could create it just the way she wanted, without getting caught up in the things that masked her true passion in life—things such as income, prestige, and what her parents thought was best for her. All of a sudden she gained clarity. As she reviewed the times in her life that had brought her the greatest joy, she realized she had a passion for fitness and a passion to help others achieve their goals, and that combining these two passions by becoming a fitness instructor and trainer excited her.
Buoyed by her new insight, she began to research a career in the fitness field. She talked to other trainers and looked into various certifications and training programs, and she realized that she was actually getting excited about her future for the first time. As a result, her whole life started to improve—her relationship with her boyfriend was better than ever, and she finally felt "authentic" in her life. She was much happier than before and, interestingly, her desire to drink faded quickly. For the first time, Jessica could envision a future without drinking. Sobriety became almost easy, and with every step she took toward creating this new life path, the universe seemed to respond by opening doors that previously had seemed closed.
Within eight months, Jessica became a Certified CrossFit Trainer, enrolled in a weight-lifting certification program, and was working on her certification as a group fitness instructor. Along with these new certifications and her passion about her opportunities in life, her existing job started to transform into one that she truly enjoyed and in which she found meaning where she was previously unable to. She was given opportunities at work that were not available to her when she was drinking, including a promotion. Although Jessica's dream is to eventually leave her existing job and pursue her life purpose, she no longer feels trapped in the life she is living. She has over two years of sobriety and, most importantly, is happy and excited in life without alcohol, and is even engaged to be married. Jessica's story is a testament to the power that clarity of purpose can create in your life.
### What Were You Put on This Earth to Do?
There is one great truth on this planet: whoever you are, or whatever it is that you do, when you really want something, it's because that desire originated in the soul of the universe. It's your mission on earth. . . . And when you want something, all the universe conspires in helping you to achieve it.
—PAULO COELHO
Author of The Alchemist
Now, let's figure out what it is that you really want, because without a purpose, you can easily get sidetracked. You can wander and drift, accomplishing little, and easily get pulled back into the desire to drink. However, if you have a purpose, everything in life seems to become aligned. When you are truly following your purpose, you are doing something you are good at, something that has the most meaning for you, something that has importance to you, and something that you love. As a result, the opportunities, people, and resources naturally move toward you. The world also benefits because when you are "on purpose," everything you do automatically serves others. And when you are on purpose, the desire to drink simply begins to fade away.
The goal of the Purpose Solution is to help you understand why you want to get and stay sober. When you understand the "why," you often also come to understand why you want to or need to cut back or quit drinking. For this reason, the Purpose Solution is broken down into two simple action steps that will each move you closer to discovering your life purpose.
### The "Before You"
Getting my third DUI wasn't the miracle I was expecting, but it was the one I had been waiting for. It led me to The 30-Day Sobriety Solution and ultimately freed me from the one prison I feared the most—the one I had created with alcohol.
—BYRON
30-Day Graduate from Phoenix, Arizona
In this second action step, we want you to capture the "before you." Spend at least five minutes, or longer if you need it, to write down what caused you to want to cut back or quit drinking. This can include embarrassing or humiliating events (drunken arguments, making mean or hurtful comments, gossiping or sharing inappropriate information), ultimatums (from loved ones, employers, friends), legal challenges (DUIs, divorce, bar fights), health concerns (concerning blood work, weight issues, enlarged liver or heart), noticeable physical changes (bloated face, bloodshot eyes, skin discoloration), financial challenges (excessive bar expenses, poor decision making while drinking), or alarming changes in your drinking habits (increases in alcohol consumption, hiding your drinking, drinking alone more frequently).
For example, part of Dave's "before" story came during the holiday season. His in-laws were visiting, and while they were helping his wife move a bookshelf out of the guest bathroom, two empty bottles of vodka rolled out from underneath. Dave had hidden them there a year before when he was drunk and subsequently forgot. This was not only embarrassing to Dave but also led to his wife calling him at work and giving him an ultimatum not to come home unless he was serious about getting help. So Dave's "before" story included this event, as well as the other existing circumstances and challenges that drinking had created, including an emergency room visit for a heart attack scare, an enlarged liver, increasing debt related to spending money irresponsibly (on alcohol, going to bars, and unnecessary spending when under the influence), and drinking alone more frequently.
Use the following questions as you write down your "before you" story in your journal. If you need help getting started, we provide some additional questions as well as a guided audio version of how to capture this "before you" on the companion website at <http://Day2.Solutions>, so you can focus on writing your answers while listening to the questions. Remember, this is not an exercise in grammar or punctuation, but rather an exercise in writing down as much information as possible without self-judgment.
• Do you believe that you need alcohol to have fun in life, or that alcohol is necessary for you to feel like you fit in?
• Are you concerned with the consequences of your drinking, whether financial, legal, family related, health related, or career related?
• Are you sick of not living up to all of the promises that you made to yourself and to others about your plan to finally cut back or quit drinking, only to fail again?
• Are you the work-hard, party-hard or weekend-warrior type of person, but deep down you know that your drinking habits are holding you back from what you really want to accomplish in your career or your life?
• Do you want to be a better role model to your family and children? Do you want to attract a relationship that is not based on drinking or getting drunk to have fun? If the answer is yes, write down the ways in which you haven't been a good role model or how you have attracted the wrong kind of people in your life.
• Are you depressed? Have you been using drinking as the way to escape your depression?
As you go through these questions, be as specific as possible. Write about what keeps you up at night and what scares you the most about your drinking. Refer to the Time Travel Technique you completed yesterday—specifically, what you would become in the future and look like if you continued with your current drinking habits.
We know this can be a difficult exercise, and we wouldn't ask you to do it unless we felt it was critical in your path to recovery. After you complete it, you will be able to look back after 30 days and see how far you have come. Like many people, you are probably unjustly hard on yourself and don't recognize and acknowledge your accomplishments. Having a picture of this "before you" will help you see more clearly where you were when you started and enable you to appreciate your progress more fully.
This exercise also plants an important "pain point" regarding why you do not want to drink. For most of this program, you will be looking at what you do want instead of what you don't want. However, reminding yourself why you started down this path in the first place is important at times. Remember, you never have to be this person again. Consider this action step a good-bye ceremony to the old you. One that will open the door for the "new you" to shine through.
If you want to deepen the psychological impact of this ceremony of saying good-bye to your old self, you can turn it into a ritual by burning, shredding, or burying a copy of the "before you." The more energy you put into the ritual or ceremony, the more impact it will have.
### The "New You"
I would complete a solution every day and know that I was becoming a better person—not just in relation to drinking but in every area of my life. I started to get my self-confidence back, and, more importantly, I started to see a happier, healthier, future version of myself that I could become.
—MATT
30-Day Graduate from Kansas City, Missouri
We now come to the fun part, and what the Purpose Solution is all about—to identify, acknowledge, and honor your purpose, or your "why" for cutting back or quitting drinking. Today's third action step is to write down what you really want in life and specifically what sobriety will give you and what doors it will open up for you. This is similar to the "before you" exercise you just completed, but instead of focusing on what you don't want and your concerns about drinking, you focus on all the things you do want in order to thrive in sobriety.
For example, Dave wanted to be a better husband and father, wanted to be fit and healthy, and wanted to be free from feeling like he needed alcohol in his life to be happy. He wasn't happy in his career as a computer systems engineer and wanted to be a positive role model and leader, and to inspire, teach, and coach others. But he knew this would never be possible with alcohol in his life. When he was finally able to see a future without drinking, he realized he had virtually an unlimited number of ways he could embrace a more meaningful and fulfilling path—from being a more present father, loving husband, engaged employee, and inspirational leader. He never imagined that his life purpose would be fulfilled by working in the field of recovery, but as thriving in sobriety became a reality for him, he realized his life purpose was to help lead others to do the exact same thing.
So let's discover your "why" for cutting back or quitting drinking, which will lead to your "new you." Write down your answers to the following questions in your journal. If you need additional questions or want to use the guided recording, remember to go to the companion website for today at <http://Day2.Solutions>.
• How will you really feel when you are thriving in sobriety? What will your energy level be like? How will you feel about yourself? What will going to bed sober and waking up without a hangover feel like and be like?
• What are you going to finally be able to accomplish now that you are not compelled to drink so frequently? Will you learn a new sport, take up a new hobby, learn how to speak a new language, do rewarding volunteer work, or engage in new, enjoyable activities with your friends and loved ones?
• How will your career change? Will you look for a new career, start your own business, or simply start performing much better at your existing job? Will you be more upbeat, personable, and confident at work with your newfound attitude and energy level?
• How will your finances change? Will you be saving money from not drinking and not engaging in drinking-related activities? Will you be able to earn more money?
• Will you find a loving and supportive partner because your sobriety is attracting into your life people that you really want? Or will you be able to rekindle the passion and love in an existing relationship? Will you feel sexy or more attractive as a result of your newfound health and energy?
Be as specific as you can and use your notes from the Time Travel Technique when you write down your answers to these questions. You want to build the biggest "why" possible here, so that you can begin to see why drinking equals pain and sobriety equals immense pleasure. The Purpose Solution works because it reminds you of the many great things you are able to accomplish when you are sober, and it helps you continue to take action, almost effortlessly.
### Staying on Purpose
Now that you have written down what really inspires and excites you—specifically, what becomes possible in life when you cut back or stop your drinking and are thriving in sobriety—the fourth action step is to take some time every day to read what you wrote, preferably in the morning. To be clear, we do not want you to reread the "before you" notes, because completing that exercise has already given you its intended value; however, we will refer back to it later. We do want you to review your "new you" journal entry every day, at least for the next three weeks, along with the vision statement that you wrote for these 30 (or 60 or 90) days.
You might find yourself becoming irritated with how often we use the phrase "thriving in sobriety," but we assure you that there is a very important reason for this, which we will explain in Day 12.
### Day 2 Action Steps
I don't put pressure on myself. I let things happen how they should naturally. That's how I am today. I'm a recovering alcoholic and addict, and I don't drink and I don't do drugs. I live my life one day at a time.
—NAOMI CAMPBELL
Supermodel
As we close the chapter on Day 2, we want to share a passage from The Alchemist by Paulo Coelho:
It's the thought of Mecca that keeps me alive. That's what helps me face these days that are all the same . . . I'm afraid that if my dream is realized, I'll have no reason to go on living . . . You're different from me, because you want to realize your dreams. I just want to dream about Mecca . . . I'm afraid that it would all be a disappointment, so I prefer just to dream about it.
Are you afraid to live the life of your dreams? It's not enough to simply dream about your ideal life. You have to take the necessary actions to create it. You have to stop dreaming and start living! Creating and pursuing your vision of thriving in sobriety takes courage, and the simple act of writing down your answers to the questions in today's action steps is an important first step in achieving this new vision for yourself. If you have not yet purchased a journal or started an online journal, stop reading and do so now.
• Write your 30-Day Vision Statement. Follow the guidelines and the sample vision statements we provided, and come up with your own statement that captures the "you" that you desire to be, thriving in sobriety, by the end of this program.
• Capture the "before you." Write down in your journal your thoughts about all of the driving forces that got you to look for ways to cut back or quit drinking. You can refer to the questions under the "before you" heading, use your notes from the Time Travel Technique, or use the guided recording from the companion website.
• Capture the "new you." Write down in your journal all the positive "whys" regarding what sobriety will bring to your life. You can refer to the questions under the "new you" heading as well as the thoughts and feelings that you experienced when completing the Time Travel Technique, or use the guided recording on the companion website.
• Review your 30-Day Vision Statement and your "new you" journal entry. Keep your vision statement visible and accessible so that you can read it often and review the "new you" notes every day for at least the next two weeks. One easy way to make sure you remember to do this is by adding a recurring private calendar meeting for every day (with your vision statement written into the meeting details) on your computer or smartphone.
As always, we have some fantastic additional content on the companion website, including the optional guided recordings to help you through the action steps. Go to <http://Day2.Solutions>.
## Day 3
## The Pendulum Solution
## Embracing Your Painful Past to Unleash Pleasure and Joy in the Present
Everyone recognizes beauty only because of ugliness. Everyone recognizes virtue only because of sin.
—LAO TZU
Sixth-century BC Chinese philosopher and author of Tao Te Ching
When Dave was eleven years old, he got sick with the flu. He experienced many of the typical symptoms, including high fever, vomiting, chills, body aches, and fatigue. But this time, when he got sick, he asked his mom a question that changed his perspective on life forever: "Mom, why do people get sick?" Without hesitation his mother responded, "If you never got sick, you would never know how great it is to feel healthy."
This simple story perfectly captures the essence of the Pendulum Solution: you can understand your problem drinking or alcohol dependency only in the context of its opposite—sobriety. We are going to show you how learning and applying this concept in your life will accelerate your ability to make and maintain not only sobriety but also countless other positive changes in your life.
### All or Nothing
I can't remember drinking. When I stopped, I would look at a beer and think how great it would be. I'd get this pang in my stomach to go back out and have fun, but then I'd remember that I used up that right—that I did a full life's worth of drinking between fourteen and twenty-seven.
—GERARD BUTLER
Actor
Most problem drinkers can relate to a lack of balance in life. In fact, you might operate from an all-or-nothing attitude. But this type of thinking can lead to a challenge we often see in early sobriety. In the first two days of this program, we asked you to start imagining what is possible in your life when you are finally thriving in sobriety. As you start to wake up and energize that part of you, we often find that you might get tempted to start setting all sorts of goals along with your goal to get sober. Don't do this! Even if you have been sober and are doing this program to get reinspired in your recovery, don't start setting other goals.
Inevitably, we see two negative outcomes when you set too many goals at once. First, your focus on sobriety wanes or disappears, and you slip back into your old tendencies. Second, you take on so much in your life that you become overwhelmed and begin missing deadlines. This last one is the most common and usually makes you feel like a failure, which often takes you right back to drinking, ensuring that none of your goals will be accomplished.
Therefore, do yourself a big favor and stay focused on your sobriety during this 30-Day program. You will have plenty of time to work on your other life goals later. And the great thing about accomplishing your sobriety goal is the domino effect that occurs afterward. This first domino of achieving sobriety can seem unmovable and insurmountable, but once you learn how to push it over, the rest of the dominos fall more easily, and you will be amazed at your newfound ability to overcome challenges that used to hold you back.
### The Law of Duality
Life is a tennis match between polar opposites: winning and losing, love and hate, open and closed. It helps to recognize that painful fact early. Then recognize the polar opposites within yourself, and if you can't embrace them or reconcile them, at least accept them and move on. The only thing you cannot do is ignore them.
—ANDRE AGASSI
Tennis champion who overcame his crystal meth addiction
At the core of the Pendulum Solution is the law of duality, which states that two different feelings, characteristics, or features cannot exist without each other. Common examples include good and evil, hot and cold, and right and wrong. When considering "good" in the context of "evil," the definition of "good" becomes clear.
So what does the law of duality have to do with your drinking? First, this law helps you understand sobriety because sobriety is typically defined only in the context of alcoholism or addiction. Without the existence of alcohol dependency, you would not be able to understand sobriety. It is the same thing with thriving in sobriety—you can understand what it means only through its opposite. Everyone has his or her own definition of what the opposite of thriving in sobriety is. For Dave, this was drinking despite knowing what it was taking from him—his health, his wife, his kids, his career, and his passion and purpose.
When you are able to finally cut back or quit drinking for good, you are given this gift of knowing what the exact opposite of thriving in sobriety is. You are able to experience and appreciate the highs of sobriety because you have experienced the lows of drinking.
### Your Problem Drinking Is Your Greatest Gift!
I consider my journey in recovery to be one of the greatest gifts of my life.
—BRENÉ BROWN
Author of The Gifts of Imperfection: Let Go of Who You Think You're Supposed to Be and Embrace Who You Are
When John found The 30-Day Sobriety Solution, everything seemed to be going well for him. He owned and operated a flourishing financial firm that he'd built from the ground up. At age forty-six, he could easily have sold his firm and never have to work another day in his life. He had an eight-year-old son, was happily married, and was a respected member of his community.
But John also had a secret. He drank more than a half liter of vodka every night. Over time, his drinking changed from being a social and enjoyable experience to a private and compulsive behavior. He tried acupuncture, hypnotherapy, willpower, counseling, and various supplements to help cure himself of his drinking compulsion, none of which worked. He felt isolated and alone, and doubted whether he would ever be able to quit drinking. He was terrified to quit, and he was terrified of what might happen if he kept drinking.
As John worked through The 30-Day Sobriety Solution, he began to see and experience a new life without alcohol, one in which he was actually happy. He completed one solution a day, embracing and applying what he learned with passion and perseverance, and he started to see his daily compulsions dissipate. He was able to stay completely sober using what he learned. At first, he found that staying sober became easy during the week; however, weekends remained a challenge. But as the weeks passed and the solutions continued to stack up and build in his life, he suddenly found it less challenging to stay sober on the weekends as well.
Enjoying extended sobriety for the first time in decades, he found that he was ready to start tackling new goals in his life. John was always passionate about health and fitness, even though over the years he had let his drinking take priority over his passion for taking care of his body. So as sobriety became easier, John decided to start P90X, an intense 90-day workout program that he had always dreamed of doing but never had the time or determination to pursue, given his nightly drinking habit. But this time he finished the program and regained a level of fitness and health that he had not experienced since college. He lost more than twenty-five pounds of fat and put on more than ten pounds of muscle.
For the first time in decades, John felt like the person that people saw on the outside matched how he felt on the inside. He felt a renewed passion for every aspect of his life and experienced firsthand how the power of perspective he had gained from his past excessive drinking allowed him to truly appreciate and embrace his new life in sobriety. John's story is a testament to the polar opposites that you can experience in life, all in a relatively short period of time.
These polar opposites are like two sides of a pendulum, as the image below depicts. Excessive drinking is like pulling the pendulum all the way up to one side—to the "dark side," where depression, addiction, and unhappiness flourish. However, when you are able to finally let go of the pendulum, as John did, it naturally propels you to the top of the other, positive side, where you experience and appreciate being healthy and sober.
You might have heard that "pain is the currency of transformation." But perhaps for you, your excessive drinking is the currency of your transformation. With excessive drinking eventually come pain and hurt, and when you experience pain and hurt, ironically, you enable yourself to more quickly go to the opposite of those feelings—pleasure and happiness.
The graduates of The 30-Day Sobriety Solution, like John, regularly share how their problem drinking has been a gift in many ways. They share how today they spend much of their lives on the other side of the pendulum, thriving in sobriety, and even when they do experience pain and sadness, they are able to use the tools they learned in this program to deal effectively with these emotions. They are able to truly appreciate and value the lives they have today because they have such vivid memories and pain associated with the days when drinking was controlling their decisions and their relationships. The crazy mood swings they experienced during their times of excessive drinking are gone, and they are able to reach wonderful, natural highs without having to experience the incredible lows. The accomplishment of overcoming excessive drinking has propelled them forward in many other areas of their lives, and goals they once considered unattainable, or were too afraid to take on, all of a sudden became far less scary and overwhelming in the context of the changes they made getting sober.
We understand this can be hard to believe at this stage, so all we ask is that you remain open to the possibility—as John did, even though he had doubts initially. Today John has over two years of sobriety, and although he has faced his share of life challenges since getting sober, the tools he learned in this program have allowed him to do it without turning to vodka to cope.
What about you? When you think about actually being happy in sobriety, what do you think is possible in your life? American author, lecturer, and advocate for the blind Helen Keller, who certainly understood duality in life, said, "Character cannot be developed in ease and quiet. Only through experiences of trial and suffering can the soul be strengthened, vision cleared, ambition inspired, and success achieved."
Whether you are aware of it or not, your past really has been perfect. What brought you to this exact point in your life is exactly what was meant to be. Over time, you will realize that it was a gift. What you do with this gift is up to you, but know that it is a gift that can keep on giving your entire life. Once again, we know this might be hard to believe right now, but we are asking you to trust us.
### How the Greatest Gift Keeps On Giving
Sobriety was the greatest gift I ever gave myself. I don't put it on a platform. I don't campaign about it. It's just something that works for me. It enabled me to really connect with another human being—my wife, Sheryl—which I was never able to do before.
—ROB LOWE
Shortly after we signed the publishing deal for The 30-Day Sobriety Solution, Dave received a letter from his daughter that demonstrates the "greatest gift" concept from a completely different perspective. When you finally overcome your problem drinking and thrive in sobriety, you get to see the positive impact this has on your loved ones. Here is what Briana wrote:
Your words help me through times that are so difficult. You say the best things to make me feel special, wanted, and loved. I'm so proud to tell people that you're my dad. You are fun, brave, and adventurous. I am so happy that after all of your work you finally are out there doing it! It makes me feel overjoyed to think that you're finally getting your book published and you're helping others! I am so glad that you stopped drinking. And to be honest, I'm glad that you had a problem with it before. I am glad of this because you have taught me so much from it! I have learned that people can be one way and change in an instant, whether it's a good change or a bad one. I have to be honest to say that I was a little bit scared about your addiction, and after you stopped, even though I was young, I realized that by you overcoming it, I could/can do anything I want to in life. It must be hard to push through a "wall" that is so heavily bearing on you. Once you pushed through that "wall," I felt like I was also capable of pushing through walls that block me from my dreams.
At first you may understandably feel embarrassed or ashamed of your past and want to hide from it, or act like it never even happened. However, eventually this will change, and your shame and embarrassment will transform into confidence and pride, and you will become an inspiration to those around you.
### The Pleasure Principle
Every negative event contains within it the seed of an equal or greater benefit.
—NAPOLEON HILL (1883–1970)
Author of Think and Grow Rich
Every decision you make in life is to either avoid pain or gain pleasure. Sigmund Freud, the founding father of psychoanalysis, first described this phenomenon as the pleasure principle. Right now you are probably trying to prove this statement wrong, but we challenge you to find any action that you take that cannot be traced back to this simple concept. Whether you are volunteering your time for a worthy cause, sitting in front of the TV, going to your job, or spending time with family, at the root of all of these actions is the desire to either avoid pain or experience pleasure. Similar to the previous examples, pain and pleasure are opposites of each other. More importantly, every decision that you make regarding whether or not to drink comes back to satisfying one of these two basic needs.
Why is this concept so important? Let's look at Dave's story again. Dave drank for many reasons. Early on, he drank to fit in and to feel connected to a group of friends. Later on, he drank because he wanted to hide from the painful things going on his life, as well as from the pain that he felt as the result of not following through with his dreams and goals. Drinking also allowed him to avoid the pain of knowing he was not being the husband, father, and son he wanted to be. The further along he got in his "drinking career," the more pain his drinking created in his life. Finally, he reached his bottom, where the pain was significant enough for him to act to avoid further pain and to finally get sober for good.
Dave finally created enough pain around his drinking to get sober, but it took him years longer than it needed to. All he, or anyone, has to do to get sober now is to make sure that enough pain is associated with drinking and enough pleasure is associated with staying sober. It really is that simple. Sobriety becomes second nature if you associate strong feelings of pleasure with sobriety and strong feelings of pain with excessive drinking.
### Addiction Explained
Dr. William Glasser, known for pioneering reality therapy and choice therapy, offers one of the simplest and most powerful explanations of addiction. In his highly acclaimed book Positive Addiction, Glasser discusses negative addiction in depth and shares the following: "The reason addiction is powerful and difficult to break is that it alone of all the choices consistently both completely relieves the pain of failure, and provides an intensely pleasurable experience." Glasser goes on to explain, "It is this peculiar, unique combination of pain relief first and then, quickly, a 'rush' of pleasure that is necessary for an addiction."
Consider this statement in relation to what we just covered. In the short term, drinking eliminates pain and provides pleasure—almost instantly. How many things are so effective at almost instantly relieving pain in your life, while adding pleasure (albeit short term) at the same time? When you consider your drinking in this context, are you surprised that you have a problem? You shouldn't be. The effect of drinking is powerful and quick acting, and tempts even the strongest-willed individual. But don't let this discourage you; The 30-Day Sobriety Solution shows you exactly how to remove pain and create lasting pleasure, all without alcohol.
### Putting the Pleasure Principle to Work for You
In the end, some of your greatest pains become your greatest strengths.
—DREW BARRYMORE
Actor-director and author of Little Girl Lost
If you want to thrive in sobriety, you have to make sure you link enough pleasure to staying sober and you link enough pain to drinking. During these first three days, our primary focus has been doing exactly this.
You have already done part of the first action step for today. On Day 2 in the Purpose Solution, you captured in your journal a snapshot of the "before you" and the "new you." We are going to build on this by first reviewing what you wrote yesterday. The reason we want to review the "before you" one more time is because we want to reinforce the link of pain to drinking. And not just pain, but massive pain. Studies show that you will do as much as two times more to avoid pain than to gain pleasure. By reviewing your journal notes of your "before you" again, you are taking a powerful initial step toward linking pain to your drinking.
The key to doing so is not merely to reread what you wrote but also to experience it emotionally. It is one thing to recognize that if you drink, you might push away your loved ones. But it is a completely different thing to acknowledge the pain and feelings you experience when you push away your loved ones—the loneliness, the sense of failure, the disappointment, and the fear of potentially losing them from your life. When you really feel these feelings, you "anchor" the pain associated with your drinking.
Your second action step is to do the same exercise with your "new you" journal notes. Feel what it feels like to thrive in sobriety and to finally accomplish so many positive changes in your life. Really experience how it feels in your body, how you look, and the energy you have to move forward in so many areas of your life that you always dreamed of. One of our graduates told us how valuable this exercise was to his ongoing sobriety:
I have always been a very visual person, but I never realized how useful this strength was until I started applying it in The 30-Day Sobriety Solution. Today I have two collections of images—one of the future me that kept drinking, and one of the future (and current) me thriving in sobriety—that I can easily recall in vivid detail. Whenever I am struggling, I simply recall these pictures and find I am naturally inspired to take positive action.
We recommend that you close your eyes while doing this, put on some relaxing music in the background, and focus on creating images and movies in your mind that really evoke your feelings. You can even play music that induces negative feelings while reviewing your journal notes for the "before you" and music that elicits passion and excitement while reviewing your journal notes for the "new you."
### Breaking Through When Others Break Down
Wouldn't it be great if you could increase your odds of success twofold? New York Times business reporter Charles Duhigg, in his bestselling book The Power of Habit: Why We Do What We Do in Life and Business, references one study that tells you exactly how to do this.
Patients who were recovering from knee or hip surgery were each given a booklet with their rehab schedules and instructed to write their goals and a detailed action plan for each of the thirteen weeks of recovery. Three months later, the patients who had written out plans were walking well before those who had not, recovering almost twice as fast. They were also able to get in and out of their chairs without assistance almost three times faster than those who didn't write down their goals or action plan.
Those who recovered faster had written very specific, detailed plans for their recovery, including the exercises they would do, when and where they would do them, the places they would go, and the friends and family they would meet with and at what times. They wrote what they would do if the pain was too great, and specifically how they would deal with the movements they knew would cause pain (which was important because these were the times they would be most tempted to quit). They also defined rewards for certain milestones, no matter how small, such as being able to meet their spouse at the bus stop. One person put a bowl of M&Ms next to his bathroom door and rewarded himself with one M&M every time he walked into the bathroom and one M&M every time he walked out.
So, your third action step for today is to write in your journal a detailed plan for how you are going to overcome the temptation to drink. Include things like driving home along a different route to avoid bars and liquor stores, listing various activities you can engage in when the craving to drink is strongest, and deciding on a time of day that you are going to complete the solution and action steps for the day. List several people you will spend time with who are positive influences, and, of course, choose what kinds of rewards you can give yourself during the day or at the end of every day to celebrate abstaining from alcohol. Most importantly, focus on the time of the day you would usually drink and plan alternative activities for that time. This simple written plan of action works! It should take less than ten minutes to complete, but once you have written it down, refer to it daily and stick to it.
### Day 3 Action Steps
The fallacy about drinking, however, is that when people say they drink to forget, all it does is magnify the problem. I would have a drink to banish the problem and then, when it didn't go away, have another one . . .
—ERIC CLAPTON
Singer-songwriter, author of Clapton: The Autobiography, and founder of Crossroads Centre Antigua
When you are tempted to drink—and the odds are high that you will be tempted to drink again—remind yourself of the pain you will experience by drinking and the pleasure you will gain by choosing to stay sober. Remember that how you feel drives the choices you make in your life. At some level, you believed that drinking equaled more pleasure than pain or was simply less painful than not drinking, which led you to drink.
Either way, because the balance was skewed in favor of drinking, you ended up doing just that. Shifting that pain-pleasure balance in your favor to match the new vision of yourself is not difficult and—guess what—in only three days, you have taken incredible steps to accomplish that. If you find yourself craving alcohol, simply come back to these action steps, or you can jump ahead to Day 13, the Tapping Solution, and use the tapping techniques to lessen or even completely remove your craving.
• Review the "before you" journal notes from Day 2. Remember, the key is to really feel what you wrote—not simply to read it. Experiencing the feeling creates a powerful link between drinking and pain. Imagine your experience with all five senses: what it feels like, sounds like, tastes like, looks like, and smells like. Feel free to add any additional insights to this list.
• Review the "new you" journal notes from Day 2. Once again, experience the positive feelings of this "new you" thriving in sobriety. Allow yourself to really feel amazing about the changes. Congratulate yourself out loud and tell yourself how great it is to be the person you knew you were always meant to be. Feel free to add any additional insights to this list.
• Write down in your journal your quit-drinking strategy. Make a detailed list of when you are going to complete The 30-Day Sobriety Solution, what you will do to overcome cravings to drink, activities you can do, good role models you can spend time with, people you can call, and small rewards you can give yourself for following through.
Be sure to visit the companion website, where we include an extremely funny and enlightening video of a famous late-night talk-show host sharing how absurd his drinking was before he got sober, at <http://Day3.Solutions>. We have also included on the website an optional guided version of today's first two action steps.
## Day 4
## The Forgiveness Solution
## Embracing Forgiveness and Creating an Abundance of Love and Happiness
When we forgive, we set a prisoner free and discover that the prisoner we set free is us.
—LEWIS B. SMEDES (1921–2002)
Author of Forgive and Forget: Healing the Hurts We Don't Deserve
Some people live as if they have a heavy ball and chain tied to them. And if they could finally free themselves from this extra weight, their future would be full of promise and opportunity. Perhaps this rings true for you—maybe you are tied to past anger, fear, or pain, or are full of regret from not doing the things you said you would. Releasing this ball and chain is often the final step in completing your past so that you can embrace your future.
We have found that something as simple as forgiving a parent, best friend, or even yourself for past hurts and transgressions can be one of the single most effective solutions to cutting back or quitting drinking for good. The truth is, we need to let go of the past to embrace the future, and the Forgiveness Solution will provide you with proven techniques to finally accomplish this.
### We Accept the Sobriety We Think We Deserve
I think we all wish we could erase some dark times in our lives. But all of life's experiences, bad and good, make you who you are. Erasing any of life's experiences would be a great mistake.
—LUIS MIGUEL
Singer-songwriter
"We accept the love we think we deserve." Stephen Chbosky's quote from his book, and later the movie, The Perks of Being a Wallflower, is brilliant in its simplicity, yet it doesn't apply just to love. You also accept the sobriety you think you deserve. If you don't think you deserve to be sober or you don't think you deserve to thrive in sobriety, you will never attract it or accept it in your life. You might get close to reaching the coveted thriving-in-sobriety state of mind, but then self-sabotage will inevitably kick in.
As we said on Day 1 in the 100% Solution, alcohol is not the problem; rather, it is the symptom. To get and stay sober, or to successfully cut back on drinking, you need to solve the problem, or the "why," behind your drinking. One of the most common whys that problem drinkers struggle with are overwhelming feelings of guilt and shame. Guilt about things they have done when drinking and shame about not being able to cut back or quit drinking on their own. These feelings of guilt and shame keep the problem drinker coming back to alcohol to cover up the problem, which only adds to the guilt and shame. When you are finally able to forgive yourself and heal this pain, you can move forward.
What are guilt and shame? Guilt is best explained as a feeling that occurs when you behave in ways that don't match your beliefs. For example, you believe you should stop drinking, you say you are going to stop drinking, but then you drink again, so you feel guilty. Shame is a much stronger feeling and is usually defined by a conscious or subconscious belief, at some level, that you are a "bad" person. Guilt comes from your behavior. Shame comes from a belief that you are somehow flawed. Often, shame is a constant negative feeling about yourself, an overall feeling of emptiness. Shame can manifest in your life in many ways, although quite often it comes from a traumatic event or series of events from your childhood and ultimately leads to an ongoing experience of suffering.
One of the greatest challenges of this suffering is that you can become addicted to it. You hold on to it like a close friend. Over time, it becomes a part of you that is hard to let go of. Today you will learn an effective technique that is at the core of the Forgiveness Solution—the Total Truth Process, a powerful emotional healing process we learned from bestselling authors John Gray and Barbara DeAngelis.
### The Total Truth Process
Originally I was a happy drunk. But later I was miserable because it's a depressant. I was just ashamed of myself, really.
—EWAN MCGREGOR
Actor
This simple but powerful tool will help you release those ball-and-chain negative emotions from the past and return to your natural state of joy and love in the present. For many of you, finally freeing yourself from your past hurts, humiliations, guilt, shame, and resentments will be one of the most important things that you do in The 30-Day Sobriety Solution.
The reason this process is called the "total truth" is that when we're upset, we often don't communicate the totality of our true feelings—especially to the person we're the most upset with. We get stuck in the negative emotions of anger or hurt and are rarely able to move past those to a more complete emotional state. The Total Truth Process helps you gain access to a more natural emotional state that brings back the closeness, thoughtfulness, and caring you truly feel toward someone else. The intention of this process is not to purge or dump your negative emotions on another person but to move through those emotions, releasing them and returning to your natural state of being—one of love and acceptance. Creativity and joy can easily flow from you in this natural state. And it is only in this state of mind that thriving in sobriety can become a full reality in your life.
One of the reasons the Total Truth Process is so incredibly effective is because it includes all the stages of the natural process you need to go through to reach a true state of forgiveness. When you apply this process, you ensure that you don't get "stuck" on any one stage, especially the initial stage of anger or resentment, which can easily happen. When you get stuck at this stage, your desire to drink often increases because drinking helps you temporarily escape these negative feelings. Of course, drinking is an ineffective solution because it masks these feelings only momentarily—it cannot resolve or release them. When you use the Total Truth Process, you will clear all the feelings, so that you can be at peace with the issue.
### The Stages of the Total Truth Process
As long as you don't forgive, who and whatever it is will occupy rent-free space in your mind.
—ISABELLE HOLLAND (1920–2002)
Children's book author
You can do the Total Truth Process verbally or write it as a letter or a journal entry. However you decide to do the process, your goal is to communicate and release your anger and hurt, which allows you to move toward love and forgiveness.
In the early stages of cutting back or quitting drinking, you may find yourself on a bit of an emotional roller coaster. And when you are in an emotionally volatile state, it is best that you don't do the Total Truth Process verbally with another person. Instead, we recommend that you wait until after completing The 30-Day Sobriety Solution to do this particular process in person. You might also find that the simple act of writing down your emotions in the form of a Total Truth Letter—which you don't send to the person—is all you need to do in order to move yourself back into your natural state of love and joy.
Here are the six steps or stages of the Total Truth Process:
Acknowledge your anger and resentment.
I'm angry that . . .
I'm fed up with . . .
I hate it when . . .
I resent . . .
Acknowledge the hurt and pain that it created.
It hurt me when . . .
I feel hurt that . . .
I felt sad when . . .
I feel disappointed about . . .
Acknowledge the fears and self-doubts that it created.
I was afraid that . . .
I get afraid of you when . . .
I feel scared when . . .
I'm afraid that I . . .
Own any part that you might have played in letting it occur or letting it continue.
I'm sorry that . . .
I'm sorry for . . .
Please forgive me for . . .
I didn't mean to . . .
Express what you wanted that you didn't get and/or what you want now.
All I ever want(ed) . . .
I want(ed) . . .
I want you to . . .
I deserve . . .
Understand where the other person was/is coming from and forgive him or her.
Now put yourself in the other person's shoes and attempt to understand where he or she was coming from at that time. Also acknowledge what needs that person was trying to meet—however inelegantly—by his or her behavior.
I understand that . . .
I forgive you for . . .
I appreciate . . .
Thank you for . . .
I love you for . . .
Get out your journal, whether it is electronic or paper, and start your first action step for today, right now. Think about the person you hold the most anger or resentment toward and begin with that one person. Don't be surprised if the first two stages are painful to work through. John Green, the author of the young-adult novel The Fault in Our Stars, captures this best when he writes, "That's the thing about pain. It demands to be felt." As we mentioned yesterday in the Pendulum Solution, sometimes you have to feel those painful emotions to move forward.
In order to really have a breakthrough today, you, like most problem drinkers, need to focus on forgiving yourself. So you may want to do the Total Truth Process with yourself. Also, make sure to write a Total Truth Letter to each of your parents or the guardians who raised you. Make sure to address any feelings left over from your childhood—especially any that were traumatic.
Finally, if you are really ready to live a life of love, passion, and joy, make a list of everyone you have any anger toward and anyone who may have hurt you—family members, teachers, classmates, friends, employers, coworkers, ex-spouses and ex-lovers, the police, the military, or the legal system. Over time, work through that list. You don't need to do it all today. That's not possible, and even though you do want to work through your whole list eventually, this can be such an emotionally intense and time-consuming process that the most important thing is to just get started with at least one person today. And don't worry, because of the importance of this topic, we revisit some key parts of it on Day 27 in the Love and Relationship Solution.
### Forgive and Move On
Life demands these hurtful experiences for you to learn how forgiveness feels. It could be no other way. If there is anyone in your life that you must forgive, instead of seeing them as someone who has hurt you, try to see them as someone who was sent to teach you forgiveness and thank them for this precious gift—then forgive them, and let it go.
—JACKSON KIDDARD
Author and philosopher
In order to let go and move on, you need to come from a place of forgiveness and love, especially when dealing with your family, your individual relationships, and your career. Maybe your best friend lied to you. Maybe a coworker gossiped about you or took full credit for your project. Maybe your spouse had an affair and then treated you badly during the divorce. Or maybe a business partner made a bad decision and ruined you financially. You need to forgive each and every one of these people who hurt you somehow in the past. Forgiving someone does not mean that you need to forget what happened, condone the person's actions or behaviors, or ever trust him or her again, but in order to move on, you do need to forgive the person for whatever he or she did or didn't do, learn whatever lessons you can from the situation, and then let it go.
### Forgive Yourself
In order to attain total freedom, you also need to forgive yourself. Forgive yourself for the pain and harm you may have caused others. Forgive yourself for continually telling your loved ones that you would cut back or quit drinking but never following through. Forgive yourself for the mistakes you might have made under the influence of alcohol. Forgive yourself for the harm you might have done to your body, your career, or your finances by drinking.
When you forgive yourself and others, you release the past and bring yourself back to the here and now. Tony Robbins, one of the most influential teachers of this generation, reminds us constantly that "the past does not equal the future." You always have the opportunity to change your life—right this minute. The past is the past. It does not determine who you are or what you will be in the future. Your power is in the present moment. And if you are living in the present, then you are able to choose and attract good things into your life. You can focus on taking action now to create what you really want for the future—for yourself, for your family, and, of course, for your sobriety. If you are stuck in your story of how the past should have been different, your energy is stuck, and you can't move forward. You have to forgive and let go in order to reclaim the power and the energy that you need to move ahead and create the life that you really want—a life thriving in sobriety.
Thousands of people in our seminars and our coaching practice have experienced enormous and unexpected benefits when they finally, truly forgave someone. They've released migraine headaches they've had for years within minutes, found immediate relief from persistent physical ailments, slept through the entire night for the first time in years, and felt their overwhelming compulsion to drink fade away. Believe us, working on forgiveness is definitely worth the effort, as Desiree's story illustrates so beautifully.
### Desiree's Story of Forgiveness
Even though it has only been three weeks, my whole life has turned around completely! I have been struggling almost all my life with this each and every day, and it is wonderful realizing when I wake up each morning that the way I used to live my life is in the past and I can greet each day with excitement instead of the habitual cycle hanging over me . . . I am more energized, happier, and healthier!
—DESIREE
30-Day Graduate from Harare, Zimbabwe
Desiree had her first drink when she was just eight years old. One of her earliest father-bonding memories was sitting with her dad, pouring him drinks, and having a special little glass to herself. As the youngest child of four, Desiree had to grow up quickly. When she was sixteen years old, her mother died in a car accident, and just two years later, her father, who had been a bedridden alcoholic most of his life, passed away from cirrhosis of the liver.
Desiree knew only one way to cope with all of this loss so early in her life—drinking. Even though she was drinking to excess nightly, she managed to stay employed, but the rest of her life was in shambles. Three broken marriages, two illegal abortions, and losing custody of her four-week-old son through an ugly divorce left her desperate and suicidal.
She knew that alcohol was only making things worse, but no matter what she tried, she couldn't quit. Desiree said, "I tried self-discipline, abstinence, willpower, AA, and so many other things that would last for a while, and then I was off the wagon again! AA may work for others, but it never did for me . . . I felt as though I was reduced to less of a person and had no right or place on the face of the earth, and was even more suicidal."
While Desiree was desperately searching online for an answer that would finally help her, she found The 30-Day Sobriety Solution. In early sobriety, she wrote to us, "Through the 30-Day solutions and action steps, I was able to deal with and overcome many issues in my life that in the past I had to mask with alcohol. Fully grasping the concept of being excited about life and having the gratitude propelled me into areas of my life I had never been to or even knew were possible to reach within myself."
Desiree has been sober for over three and a half years. In sobriety, with all the newfound tools and techniques she now has at her disposal, Desiree was finally able to forgive—not only all those people who had hurt her in life, but also herself. And not just forgiving, but actually starting to love herself. She discovered quickly that all of these changes propelled her forward in every other area of her life as well.
Desiree became recognized for her exceptional contributions at work. Her love life flourished, and her friendships and family ties became stronger. Instead of always being the "problem child" in her family, she became the one who encouraged, supported, and led others to make positive changes. Today she is considering becoming a full-time recovery coach and told us, "I am forty-five and feeling fabulous!"
### The Forgiveness Affirmation
One final technique for helping you forgive is to recite this affirmation several times each day:
I release myself from all the demands and judgments that have kept me limited. I allow myself to be free—to live in joy, love, peace, and sobriety. I allow myself to create fulfilling relationships, to have success in my life, to experience pleasure, to know that I am worthy and deserve to have what I want. I am now free. I release all others from any demands and expectations I have placed on them. I choose to be free. I allow others to be free. I forgive myself, and I forgive them. And so it is.
Just like the 30-Day Vision Statement you have already written, we recommend that you include this at the beginning of your journal and read it out loud at least once a day for the next two weeks. Many of our clients prefer to condense this affirmation so that they can easily memorize it, so feel free to edit it as you see fit.
### Bryan Had It All
It's taken me years to let go of the terrible shame. I wouldn't change a thing, because it brought me here today—and without all that pain, would I be the same person? However, I speak to many addicts all the time, and what I probably tell them most often is: it's not your fault. I know it feels like your fault. I know everyone else tells you it's your fault. I know everyone's hurt and angry with you. I know you've done bad things. But the only thing within your control is seeking help to stop.
—KRISTEN JOHNSTON
Actor, author of Guts: The Endless Follies and Tiny Triumphs of a Giant Disaster, and founder of SLAM, NYC (Sobriety, Learning and Motivation)
We would like to share with you a moving story that shaped Dave's life, demonstrates the power of guilt and shame, and played an enormous role in creating The 30-Day Sobriety Solution.
You know those people who seem like they have everything going for them? My friend Bryan was one of those people. Prestigious brain surgeon, great-looking, charismatic, beautiful wife, and two amazing kids. I was envious.
We met at a fantasy football draft party in 2002. We became casual friends, seeing each other at various parties and get-togethers. I met his wife and two kids, who were the same ages as my two kids.
Years later, there was one time we met up that I still vividly recall—it was just after receiving a disturbing phone call from my doctor. Dr. Lee sounded strangely somber as he said to me on the phone, "I have the results of your blood work, and there are some concerning numbers." There was an awkward pause as he followed up with the question "Dave, how much do you drink?"
This was not a new question to me. My response to doctors in the past was to lie—and then find a new doctor. But I knew something was different this time. I downplayed my drinking to Dr. Lee, agreed to not drink as much, and to come back in two months to get my blood work done again.
Then, after that concerning phone call, I reached into my big bag of coping skills and decided to go to the bar.
And Bryan was there—Bryan the prestigious brain surgeon. I thought, Who better to ask advice from? I shared my doctor's concern, and his response was simple and to the point. He said, "Dave, all of these people in this bar have a lot worse numbers than that; you don't need to worry about it."
What a relief! All I wanted to be told was that I had nothing to worry about. It didn't matter to me whether it was true. Of course, it didn't cross my mind that using the population of the bar might not be the best baseline for health and wellness.
About a month later, I walked into the same bar, and a friend came up to me. "Dave, you are not going to believe this. Bryan almost died. He had complete organ failure. He has been drinking vodka out of a Gatorade bottle in his car on a regular basis and taking all kinds of prescription medications without a prescription. He is going to be in the hospital for ten days and then is going to a 90-day rehab program."
I was speechless. Not only was Bryan's life never going to be the same, but this was also a wake-up call for me. Drinking was creating havoc in my life. I was having marriage problems and health issues, and even though I didn't even really enjoy drinking anymore, I couldn't imagine stopping.
As I was struggling to turn things around with my drinking, I watched Bryan come back from rehab—he was a new person. He looked amazing; he had that sparkle in his eyes, had lost some weight, and all the puffiness in his face was gone.
Once again, I was envious.
I had figured out enough to get some sobriety under my belt but just barely enough to keep my family off my back about my drinking. I reached out to Bryan for help, but, unfortunately, he chose to be private about it and was not willing to help.
About eight months later, on April 25, 2008, I got an email that would change my life forever—Bryan had relapsed and had taken his life with a shotgun.
Right then I knew that my future could easily mirror Bryan's. I knew that with the suicidal thoughts I was having, and with all my failed attempts at sobriety prior to that, my next drink really could be my last—just like it was for Bryan.
At the funeral, seeing his heartbroken wife and two kids, and watching the slide show of all the memories of Bryan with his family, I knew that it could be my family sitting there at my funeral.
In that instant, I made several decisions.
I decided that I would never forget the path that drinking and addiction can lead you down. I decided that I would never take my sobriety, or the sobriety of others, for granted. I decided that if anyone ever asked for help and I was in the position to help them, I would never turn them away. And I decided that if drinking for seventeen years had any kind of upside, it was that the firsthand experience would help me know how to help others.
A short time later, I made another decision that changed my life forever: I decided that there had to be other solutions for recovery—and that was the moment where the initial idea to research and eventually create The 30-Day Sobriety Solution came from.
Over the years, I have given a lot of thought to what might have been going through Bryan's mind in those final hours before he took his own life. It isn't hard for me to imagine the overwhelming guilt and shame that he must have felt after failing again—after letting down his wife, kids, family, and friends, and putting his career as a doctor in jeopardy.
In the end, I believe the reason he took his life was that he was unable to truly recover from the guilt and shame of his past, unable to truly forgive himself and others, and, therefore, unable to truly love himself.
If you asked me if I felt much guilt or shame over my drinking before I got sober, I would have said no. Overall, I didn't think that I was in denial about my drinking issues, but clearly I was in denial about how much guilt and shame I had.
Once I realized that so many other "normal" people struggled with drinking and addiction, I felt a light turn on inside of me as I heard their stories. I realized I had been dimming that light through my drinking years because of how much blame and shame I held on to. I felt like a failure because I couldn't get and stay sober.
Bryan's story helped me understand this. His tragic death helped free me, and I will always be grateful to him for the lessons he taught me, even though they came from such a heartbreaking incident that I would do anything to go back and change.
### Love Your Addiction, Love Yourself
Holding on to anger and resentment is like drinking poison and expecting someone else to die.
—SOURCE UNKNOWN
This brings us to the final topic of the day—loving yourself. Poisoning your body with alcohol on an almost daily basis, judging yourself for your inability to quit or control your drinking, and beating yourself up for your mistakes all lead to one end result—you stop loving yourself, and, worse yet, you may even begin to hate yourself.
Loving yourself can sound a bit hokey, but don't let the importance of this concept slip by just because it sounds woo-woo or clichéd. If you don't love yourself, how will you ever treat your body and mind with respect? If you don't love yourself, how can you ever truly reach the level of fulfillment and meaning in your life that you deserve? If you don't love yourself, how can you ever expect anyone else to truly love you?
You cannot change the fact that you spend every minute of every day of your life with yourself. Accept who you are, accept that you make mistakes, and decide right now to make a conscious decision to love yourself. Slipups in life are normal and are not unforgivable sins. The only sin in your life is to spend time remembering and focusing on your sins. You will find that as your love for yourself becomes more real, your thoughts will become more positive, and you will attract more people, places, and things that bring joy and prosperity into your life.
Remember, the "new you" is one that is thriving in sobriety, living a meaningful and fulfilling life, and inspiring and supporting your friends and family every day. What is not to love about the "new you"? Better yet, the old you that suffered from drinking and the old you that made selfish decisions offer a much-needed perspective to truly appreciate and celebrate the "new you." So take a second and thank that old you for validating and confirming how amazing it is to live this new life of sobriety and excitement.
You are empowered every time you choose love and weakened every time you choose hatred, anger, guilt, or shame. Love lifts you up. Hatred, anger, guilt, and shame bring you down, and there is no way that you can overcome addictive behavior when you are constantly feeling anger, resentment, guilt, or shame. Martin Luther King Jr. said that the only way to convert an enemy to a friend is through love, not through hatred or anger. You may have heard the saying "At the end of our lives, there will be only two things that matter: who we loved and who loved us." Yes, love really is the answer, and it all starts with loving yourself.
### "I Love Myself"
Love loves people right where they are.
—MASTIN KIPP
Founder of TheDailyLove.com
It is important to understand that your desire to drink actually comes from a positive intention—your desire to feel good. It is human nature to want to feel good. The problem is that using drinking as the solution to feeling good is flawed. Over time, drinking ruins your health, contributes to depression, and causes accidents. Rather than connecting you to others, it separates you from others. Most importantly, it disconnects you from loving and taking care of yourself.
The first way you can start to love yourself and others more is to stop judging yourself. Accept yourself right where you are. Not where you are going to be in 30 days, or where you were last year, but right where you are today—at this very moment. Which brings us to our second action step for today.
Many books over the years have taught techniques to love yourself where you are, but one book, Love Yourself Like Your Life Depends on It, by Kamal Ravikant, focuses on how to transform your life by teaching just one powerful life-changing concept—loving yourself.
To do this, Ravikant teaches a simple technique—to repeat the three-word mantra "I love myself." Use this mantra in your daily life. Say it out loud when you are at home alone, in your car, or simply going for a walk. And better yet, when you look in the mirror over the course of the day, say, "I love you," as you look into your own eyes.
We know this sounds strange. We are asking you to trust us and all the other people that have confirmed that this technique changed their life. And what do you have to lose by trying it? After you read this chapter, go into the bathroom, look in the mirror, and do it. As easy as it sounds, you might be surprised to find that it is harder than you think to say those three words to yourself and mean them. If you experience discomfort saying "I love you" to yourself, it only validates the importance of doing this. If it is awkward and uncomfortable at first (and it probably will be), keep practicing it and saying it to yourself in the mirror until it feels natural and normal. There will be a moment when you break through, and when you do, you will experience a dramatic shift in your life. This is an important action step to take—and repeat—until it feels natural and true to you.
Also ask yourself, What would you do with your life if you were deeply and truly in love with yourself? What would you do if you loved yourself like a parent loves a child or like a child loves his or her mother? Would you want your child, spouse, or loved one to drink as much as you drink? Close your eyes and consider this for a moment. Until we really think about it, we often don't even realize how little love we have for ourselves.
### Day 4 Action Steps
In life, pain is inevitable but suffering is optional. There are no victims, only volunteers.
—TONY ROBBINS
What you need to take away from today is simple and powerful. You drink for many reasons, and, over time, these reasons undoubtedly include guilt, shame, and pain from past events. Every time you drink, guilt and shame weigh more heavily on you, and eventually alcohol stops working as a solution to mask your problems and instead amplifies them.
To thrive in sobriety, you need to accept and become aware of this, forgive yourself and others, and begin loving yourself again.
• Complete the Total Truth Process. Go through the six steps of the Total Truth Process to address at least one past resentment, guilt, anger, or shame you might have. Be sure to focus on forgiving yourself and forgiving others who are responsible for any traumatic events you experienced in childhood. Although you can eventually do this process with the person you are forgiving, you may want to wait until after you have attained more long-term sobriety. For now, just write a Total Truth Letter to the person (but do not send it), making sure to give all six steps equal attention. Create a list of all people you need to complete this process with for later.
• Practice the forgiveness affirmation and the "I love myself" mantra. Review these regularly. Post them at the beginning of your journal with the other key items to review for at least two weeks. Consider putting a reminder in your bathroom, such as a Post-it note or a string around your toothbrush that prompts you to say "I love myself," or, as you look into your eyes in the mirror, "I love you." Let go of any judgments that this technique is silly or any thoughts that it won't work, and just trust us that it does.
Be sure to visit the companion website at <http://Day4.Solutions> to review the additional supporting material, which includes the important topic of the stigma of alcohol addiction and how to overcome it, as well as information on a fantastic documentary film, The Anonymous People, which examines the personal and societal value of recovery through the moving stories of people who are public about what their lives are like now that they're no longer using alcohol or drugs.
## Day 5
## The Believe-in-Yourself Solution
## Believing in Yourself and Believing It Is Possible
The thing always happens that you really believe in, and the belief in a thing makes it happen.
—FRANK LLOYD WRIGHT (1867–1959)
American architect
If you are going to be successful in cutting back or quitting drinking and creating the life of your dreams, you first have to believe that it's possible—that you have what it takes to make it happen. Simply put, you have to believe in yourself. You can call this belief self-confidence, self-assurance, or self-esteem, and it consists of an absolute certainty that you have the ability and the inner means and skills to create whatever you want.
### Believing in Yourself Is the Starting Point for All Achievement
I used alcohol as a friend, companion, and protector over the years. I made it into whatever it needed to be, whenever I needed it. I acted like it was the answer to my emptiness and loneliness, instead of realizing it was actually the source. In the end, it was all a lie that lasted well over a decade. Alcohol left me with self-doubt, guilt, shame, depression, anxiety, and fear. The 30-Day Sobriety Solution helped me take off the mask I had been hiding behind, freeing me to finally thrive in sobriety.
—BYRON
30-Day Graduate from Phoenix, Arizona
When you think about yourself, in particular about the "you" before you started this 30-Day program, what are the predominant thoughts or images that come to mind? Did you think of yourself as a drunk, alcoholic, or problem drinker? Did you think of yourself as someone who would never be able to figure out how to bring sobriety into your life in a positive way?
You have probably had thoughts similar to these, maybe quite frequently. Having a positive self-image is vital to your success. Psychology teaches us that a large portion of our behaviors are driven by how we see ourselves. When we have a healthy self-esteem, we take healthy risks, we are more goal-directed and driven, and we face fears head-on. When we have low self-esteem, we don't take risks, we stop when faced with the slightest roadblock, and we don't believe in ourselves.
Neuropsychologists say this is true because we spend our whole lives becoming conditioned. Through a lifetime of events, our brain learns what to expect—whether it eventually happens that way or not. And because our brain expects that something will happen a certain way, we often create exactly what we anticipate.
To sum it up, believing in yourself is the starting point for all achievement, and today is all about making massive progress in shifting your beliefs about yourself and your ability to thrive in sobriety. When you have fully installed a new belief system of thriving in sobriety, your odds of accomplishing it are forever in your favor.
### The Number One Reason You Are Not Sober Today
I felt like The 30-Day Sobriety Solution was breathing life back into me. Every day, I learned new tools and techniques that actually worked. I was finally able to imagine a happy life without alcohol, something that had always escaped me. And one of the surprising results was that for the first time in my life, I felt like I was not alone, even though I was doing the program alone at home.
—HANNAH
30-Day Graduate from Sydney, Australia
We have discussed this before, and certainly will again, because it is that important. If you have tried to cut back or quit drinking in the past and failed, part of the reason is due to the fact that on some level you don't believe it is possible. Maybe you don't believe it is possible for you to be sober and happy at the same time. Maybe you don't believe you can go more than a few days without craving alcohol to the point where you know you will give in. Maybe you don't believe you can be successful in life without alcohol. Or maybe you just don't believe in yourself. The bottom line is that if you don't believe you have what it takes to get sober, you won't. You must choose to believe in yourself!
When was the last time you wanted to do something but because you didn't believe that you could do it, you never even tried? Maybe a friend whom you don't consider as smart or talented as you accomplished that same goal, and you said to yourself, If they can do it, I certainly can. Then you actually went out and accomplished it.
What changed to make you do it? Maybe you learned something new. Maybe now you had a role model you could follow. However, the most likely answer is that you simply started to believe you were able to do it—you started to believe in yourself. And once you believe in yourself, everything changes. You overcome fear. You find solutions when you come up against challenges. And you naturally leverage your strengths and talents.
### Does a Sober Vacation Seem Impossible?
People become really quite remarkable when they start thinking that they can do things. When they believe in themselves, they have the first secret of success.
—DR. NORMAN VINCENT PEALE (1898–1993)
Author of The Power of Positive Thinking
Can you imagine vacationing at a tropical resort in Mexico and not drinking? Diane certainly couldn't, yet that is exactly what she did after completing The 30-Day Sobriety Solution. And she actually had fun on the vacation, something she doubted would ever be possible. Diane started drinking the way most people start drinking—socially. Her entire social circle drank, and she believed that being an adult meant drinking alcohol. She also believed that being able to "hold your liquor" was an admirable trait. She was proud to excel at it.
Over the years, Diane had three daughters and managed to stay sober through her pregnancies; however, her two marriages were created and destroyed by alcohol. By the time she reached her midfifties, she was a widow and surrounded by people who drank heavily. She knew it was time for a change but wasn't quite ready—until she returned from a vacation and felt compelled to drink excessively. That night, she passed out, smashed her head on the floor, and almost bled to death.
Shortly after that, Diane found The 30-Day Sobriety Solution and felt like she had opened up a "supercharged Craftsman tool kit of things to use for sobriety." Within the first two weeks, amazing shifts started happening in her life. She was sober, and it wasn't a struggle. She connected with her children and used the tools she was learning to communicate more effectively with them, including helping them solve some challenges they were having. For the first time in her life, she said, "I don't see myself drinking. I don't see choosing feeling the way I felt before when I know I can feel like this."
Today she believes in herself like never before. She now has a sense of calmness and peace that previously eluded her. When she looks in the mirror, she sees a completely different image of herself—someone who is healthy and happy and has a radiant glow in her eyes.
In fact, when we recently reached out to Diane to see how she was doing, we found that she was able to return to "normal" drinking. Two full years after completing the program, Diane is able to have the occasional martini and not feel the urge to get drunk or go back to her previous excessive levels of drinking. She loves to do her own version of the 30-Day Reboot by abstaining for 30 days and reviewing her favorite solutions and exercises from the program.
Like many people in recovery, Diane found that some of her friendships had to change. Certain friends were not as funny or compatible when she removed drinking from the relationship. Today she is thriving in sobriety, spending time tutoring, volunteering for a local food bank and homeless shelter nonprofit organization, and maintaining wonderful relationships with her children.
### Teetotalism
I don't drink. I've never tried a drug. It's just something that I genuinely don't have a desire for.
—BLAKE LIVELY
Award-winning actor
The first action step today is simple and fun. It is all about shifting your beliefs so that you truly believe it is possible to thrive in sobriety. Whether your goal is to cut back or quit drinking, it is critical that you believe that you can do it. Part of this belief is also believing that sobriety will add joy and happiness to your life, not boredom and sadness.
By now it is highly likely that your beliefs about the benefits of not drinking have already shifted. With each sobriety success story and every quote from someone thriving in sobriety, you simply start to believe that changing your life is possible. And the powerful processes you have used this first week dramatically expand your self-awareness and help you let go of past guilt, anger, and resentments. To continue this progress, we are going to give you more examples of people who are actually thriving in sobriety. This brings us to the term teetotalism.
Teetotalism is the practice or promotion of complete abstinence from alcoholic beverages. And it will surprise you to know who is actually on this list. It includes past leaders of countries, rock stars, athletes, politicians, CEOs, and well-known TV personalities. People such as Jennifer Lopez, Jim Carrey, Warren Buffett, Natalie Portman, Brett Favre, Eddie Murphy, Diana Ross, Donald Trump, Muhammad Ali, and Albert Pujols. So take a minute right now to review this list on today's companion website: <http://Day5.Solutions>.
The next time you feel embarrassed about your drinking past, or you think that not drinking at a party makes you stand out negatively, remind yourself of this list of high-profile people. You are not alone. Whether you consider some of the people on this list role models or not, it is hard to ignore the accomplishments of these famous teetotalers.
### The Placebo Effect
Hundreds of scientific studies have validated the placebo effect, or the benefit that results from a patient believing in a treatment that has no substance or active ingredients—in other words, a fake treatment. But the patient doesn't know the treatment is a sham. According to Dr. Irving Kirsch of the University of Connecticut, placebos are about 55 to 60 percent as effective as most active medications like aspirin and codeine for controlling pain.
One study, for instance, tested thirteen people who were extremely allergic to poison ivy. Each person was rubbed with a harmless leaf on one arm and told it was poison ivy. Each was also rubbed on the other arm with poison ivy and told it was harmless. Interestingly, all thirteen people broke out in a rash where the harmless leaf was rubbed, whereas only two had a reaction to the poison ivy.
In another study, surgeons performed arthroscopic knee surgery on patients with osteoarthritis, but only two-thirds actually underwent surgery. One-third of the patients' surgeries were faked. Their surgeons made the incisions but did nothing to repair the knees. All of the participants were aware that they might receive the placebo surgery, but no one was told if they'd actually received it until after the study was over. Two years after the surgery, the patients who had undergone the placebo surgery reported the same amount of relief as the patients who underwent the actual operation. Their brains had expected that "surgery" would improve the knee, so it did.
In another story from early investigations into the placebo effect, in 1957 a patient was diagnosed with advanced cancer of the lymph nodes and had painful cancerous tumors throughout his body. "Mr. Wright" was given only a short time to live, but he had heard of an alternative cancer treatment whose creator claimed it worked on people as well as on animals, and begged to receive it. His own physician, after much persuasion, finally agreed to administer it. The patient received an injection on Friday afternoon, and by the following Monday, his tumors had shrunk by half. Ten days later, after further treatment, doctors could find no trace of cancer, and the patient was released from the hospital. Interestingly, no other cancer patients who received the treatment showed any improvement.
Two months later, however, Mr. Wright read reports that the treatment was quackery. He suffered a relapse immediately, with the tumors returning. His physician, to try to buy him more time, told him that a new, much stronger version of the drug had been developed, and the patient agreed to have another injection. However, his physician did not have a new version of the drug, which had been thoroughly disproved, and so he gave Mr. Wright an injection of distilled water. The injection worked again—the patient believed he had received an effective cancer treatment, and his tumors disappeared.
Two more months passed, and the patient read a definitive report that the treatment was ineffective. Mr. Wright died two days later.
There is no question that your beliefs have a dramatic impact on your life. The placebo effect comes down to the power of expecting an outcome—really believing in it. When you expect results, your beliefs are in accordance with those expectations, and your thoughts, feelings, and actions align with them as well. When you believe it is possible to thrive in sobriety, and when you believe in yourself, sobriety will become a reality for you.
### The Choice of What to Believe Is Up to You
You have to give up "I can't." The phrase "I can't" is the most powerful force of negation in the human psyche.
—PAUL R. SCHEELE
Cofounder of Learning Strategies Corporation, author of Genius Code
If you are going to thrive in sobriety, you have to stop saying "I can't" and all of its relatives, such as "I wish I were able to." When you say "I can't," these two disempowering words actually make you weaker. We use a technique called muscle testing to test the effect of thoughts on physical strength. A person extends an arm as he says a positive or negative phrase. A tester pushes down on the arm. Invariably, when the tester pushes down on the arm after the person says something negative, like "I can't sing," he always tests weaker. When he says something positive, such as "I can sing," as the tester pushes down on the arm, he always tests stronger.
This is your second action step today. We want you to test this out, though, over the course of this program. Every time you catch yourself using the word can't, rephrase the sentence. For example, if you were to think, I can't quit drinking, because then I won't be happy, you can simply shift to I can stop drinking, and I am excited to learn how to be sober and happy. We know it can be challenging to even catch yourself using this word at first, so one effective option is to recruit a friend, coworker, or spouse as a partner. You can both agree to point out to each other when you use the word can't.
### We Believe in You
You have to believe in yourself when no one else does. That's what makes you a winner.
—VENUS WILLIAMS
Tennis champion
If having others believe in you was a requirement for sobriety, most of us would still be drinking excessively today. It is entirely possible that everyone around you gave up believing that you would ever get sober or permanently cut back your drinking. If you tried to cut back or quit in the past and made declarations to others about how you were going to change, only to go back to the way you were (or even worse), it is fair to assume that the people around you will stop believing in you. That is okay!
What they think about you has no impact on your ability to succeed. Too often we go through life letting the opinions of others hold us back. It doesn't matter what has happened up to this point in your life—the fact that you are still here and still reading says all we need to know.
We believe in you! Nothing in this book is too advanced or hard for you or anyone to do. It simply takes some dedication, commitment, and perseverance, which you have already demonstrated by getting this far.
If you have any people in your life who doubt your ability to cut back or quit drinking, decide this instant that you are not going to give their opinion any power. In fact, let their doubt fuel your desire to demonstrate how wrong they are.
### Why Did I Wait So Long?
At the worst of it, I no longer wanted to drink and no longer wanted to be sober, either. I felt evicted from life. At the start of the road back, I just tried to believe the people who said that things would get better if I gave them time to do so. And I never stopped writing.
—STEPHEN KING
People we coach through The 30-Day Sobriety Solution inevitably tell us, "I wish I hadn't waited so long to do this." They often say this after a breakthrough that makes them realize that being sober and happy is not as challenging as they had thought it was. Don't worry, this is a normal feeling.
In yesterday's solution, Dave shared his story about the time he went to the bar and discussed his worrisome blood work results with Bryan, who assured him that he was fine and had "nothing to worry about." That was exactly what Dave wanted to hear, but he didn't realize then that Bryan was giving him a perfect example of "confirmation bias." Confirmation bias is when you get the answer you want to a question, and you stop looking for other input. Most likely, you have practiced this. For example, you have a concern or worry, so you go to the internet and search for information. The first time you read something that validates that you have nothing to worry about, you stop looking, regardless of the source.
Confirmation bias is likely something that led you to wait before you even picked up a book like this. Dave wanted to deny the health impact of his drinking, so he listened to advice from someone who he knew was a heavy drinker—and a doctor, no less!
So, the third action step for today is to answer this question in your journal: Where have you used confirmation bias to hold you back? Here's how one 30-Day Graduate explained his experience with confirmation bias:
There were moments in The 30-Day Sobriety Solution that led to incredible clarity, and one of those for me was the concept of "confirmation bias." It was clear that despite all my education and knowledge about addiction, when it came to looking in the mirror, I only let in the information that confirmed I didn't have a problem. Once I changed this, everything started changing.
Another example might include searching online for "proof" that drinking red wine is healthy, even if you are drinking four or five glasses a night. Or you're always looking for validation that cutting back is actually possible for you, even though you drink a fifth of liquor a day. Most qualified experts would agree that drinking four glasses of red wine a day is never healthy, and that going from a fifth-a-day drinker to a "normal" drinker is not possible. As you continue your journey to sobriety, be sure to recognize when you are looking for the answer you want to hear rather than really seeking out the truth.
To end the day on an inspirational note, and to build your believing-in-yourself muscles, we want to share some stories regarding supersuccessful people and what they had to overcome to create success. While their stories may not involve overcoming problem drinking, they did have to overcome tremendous challenges.
• Walt Disney, the founder of Disney World, was fired by a newspaper editor because he "lacked imagination and had no good ideas." He was told by MGM studios that the idea to put a giant mouse on the screen (Mickey Mouse) would terrify women.
• J. K. Rowling, billionaire author of the Harry Potter series, was a divorced single mother on welfare while writing the first book in the series, which was rejected by twelve publishers. She was told not to quit her day job.
• Oprah Winfrey was told she was "unfit for TV" and fired from her job as coanchor on a local news station.
• Sidney Poitier, Oscar-winning actor, was told by a casting director, "Why don't you stop wasting people's time and go out and become a dishwasher or something?"
• Steven Spielberg, one of the most successful directors in Hollywood, was rejected from the University of Southern California School of Theater, Film and Television three times.
• The Beatles, looking for a record deal in 1962, were turned down by Decca Records, which said, "We don't like their sound, and guitar music is on the way out. They have no future in show business."
• Elvis Presley was fired by the manager of the Grand Ole Opry, who told him, "You ain't goin' nowhere, son. You ought to go back to drivin' a truck."
• Ronald Reagan, the fortieth president of the United States, didn't take office until one month before his seventieth birthday.
It is never too late, regardless of your age, how many setbacks you have had, or your drinking history—you, too, can overcome almost any obstacle life throws at you and live the life of your dreams.
### Day 5 Action Steps
You can be anything you want to be, if only you believe with sufficient conviction and act in accordance with your faith; for whatever the mind can conceive and believe, the mind can achieve.
—NAPOLEON HILL
The Believe-in-Yourself Solution can be summed up in three short sentences:
Believe it is possible. Believe in yourself. Go for it!
When Jack wrote The Success Principles, he interviewed hundreds of people. Almost all of them reflected that they weren't the most gifted or talented in their fields, but they chose to believe that anything was possible. They studied, practiced, and worked harder than the competition, and that's how they got to where they are today.
It really is that simple. When you decide what you want, believe it is possible, believe in yourself, and then work hard to get it, you take 100% control of your destiny. Not only does cutting back or quitting drinking become easier to achieve, but you'll also start to see what you want in the rest of your life falling into place right alongside it. Your dreams really do start coming true.
Along with completing these action steps, we want to remind you that you should be writing in your journal every day, even if you limit it to just a few bullet points.
• Review the list of famous teetotalers. If you haven't done so already, visit the companion website and review the list of teetotalers.
• Stop using the word can't. Remove the word can't from your vocabulary. Instead, substitute more empowering words and phrases. For example, if you find yourself saying, "I can't go to a party and have only a couple of drinks," change it to "I can find ways to have a ton of fun at this party and still not drink, or I can have only two drinks." Consider doing this with a friend or loved one you regularly spend time with, so you can point out to each other when you hear the word can't.
• Write down examples of using confirmation bias with your drinking. Think about times in the past you have used confirmation bias to avoid dealing with your drinking. Maybe you spent time with people who drank more than you, so you could believe your drinking wasn't an issue. Or maybe you exercise, eat well, and have healthy blood work in spite of excessive drinking, so you tell yourself that you must not have a problem.
On the companion website, you will learn more about the science behind the placebo effect and find the list of famous teetotalers, as well as some other great resources. Go to <http://Day5.Solutions>.
## Day 6
## The Outcome Solution
## The Power of an Outcome-Focused, Purpose-Driven, Goal-Setting Strategy
Man is a goal-seeking animal. His life only has meaning if he is reaching out and striving for his goals.
—ARISTOTLE (384–322 BC)
Greek philosopher
You have committed 100% to thriving in sobriety, determined your 30-Day Vision, and learned how to forgive yourself and believe in yourself. Now you are ready to leverage the incredible power of goal setting.
The human brain is designed as "a goal-seeking organism." Once you set a specific and measurable goal, your subconscious mind will work day and night to achieve it. This is true for any goal in your life, including cutting back drinking, quitting drinking, or simply completing the 30-Day Reboot.
### The Test
I got sober. I stopped killing myself with alcohol. I began to think, Wait a minute—if I can stop doing this, what are the possibilities? And slowly it dawned on me that it was maybe worth the risk.
—CRAIG FERGUSON
Talk-show host and author of American on Purpose
Before we jump into goal setting, let's take a moment to address some common experiences and challenges that often come up during the first week, especially after you've stopped drinking. In every problem drinker, there live two "people" or identities—the thriving sober person and the problem-drinker person. This week, you have been empowering your identification with the sober person and disempowering your identification with the problem drinker, which ultimately leads to an internal conflict. Before this program, the problem drinker part of you usually "won," and you would drink. Now that is no longer the case. However, sometimes the problem drinker part will essentially fight for its life. That part of you is afraid of disappearing after being in control for so many years, and this can lead to a temporary increase in the desire to drink. For now, just know that if you are actually experiencing an increased desire to drink, it is normal—and most importantly, short lived!
Another experience during the first six days is that "when it rains, it pours." You start making these wonderful changes in your life, and then you are suddenly faced with more challenges, including relationship issues, changes in your health, financial setbacks, work-related stresses, or a combination. For our clients on the cusp of making a breakthrough change in their life, one that will have positive ripple effects all around them, it's almost as if they're being tested one last time. If they pass this test, their lives change forever. If they don't, their old habits and self-defeating behaviors come back as strong as ever.
Trust us: if you are experiencing this, it means you are on the doorstep of something amazing, and all you need to do is push through. The truly wonderful life that awaits you on the other side is worth the effort and the discipline.
And remember, the initial desire to drink is often very intense when it is first triggered—say, by the smell of stale beer in a bar or the sight of your favorite liquor store—but that intensity usually drops significantly in as little as fifteen seconds. If you feel these urges, don't fight them. Simply accept that you are experiencing them and take a few deep breaths. This alone is often enough to move you beyond the initial temptation. If the deep breaths aren't effective enough, and you feel you need more reinforcement, we recommend you skip ahead to the tapping exercise, which you will find on Day 13 in the Tapping Solution.
### The Power of Goal Setting
If you want to be happy, set a goal that commands your thoughts, liberates your energy, and inspires your hopes.
—ANDREW CARNEGIE (1835–1919)
American industrialist and philanthropist
Goal setting is one of the most powerful tools at your disposal. Virtually every successful coach, trainer, and motivational expert teaches goal setting as a key component of creating a successful life.
Surprisingly, goal setting is underutilized in most recovery programs. The Outcome Solution addresses this oversight by teaching you the right techniques for goal setting, so that you actually get the results you desire. Today you will learn how to use an outcome-focused, purpose-driven method of goal setting to ensure that the 30-Day Thriving-in-Sobriety Vision you wrote on Day 2 in the Purpose Solution becomes a reality.
The Outcome Solution not only applies to accelerating your achieving your goal to cut back or quit drinking, but can also be used to set and accomplish goals in every area of your life, including losing weight, starting a new career, achieving financial freedom, making new friends, finding true love, excelling at sports, and mastering a new hobby.
### The Short-Term Trap
I just realized that drinking was counterproductive to what I was trying to do. Acting is very difficult in weird ways. You'd have to get to class by 8:00 a.m., work all day, rehearse all night, and it's not really good to do when you're hungover. I'd wanted to be an actress my whole life, that was my goal, that was all I cared about. Something had to go, so I chose drinking to go. Has it been difficult? Oh yeah. Sometimes it would be nice to just have some red wine with dinner, but it's not worth the risk. I have a great life, a great situation. Why would I want to risk self-destructive behavior?
—KRISTIN DAVIS
Actor who has been sober for over twenty years
Satisfying your short-term desires is often in conflict with accomplishing your long-term goals. This is one of the most important concepts we want you to take away from the Outcome Solution. Today you will identify and commit to at least three specific goals that, over time, will have a profoundly positive impact on your life—and that you can accomplish only through the choice to stay sober.
And let's be honest—it isn't easy to stay sober when you are used to drinking frequently. The temptation to satisfy your short-term desire to drink can feel overwhelming, but you will be less willing to give in to that temptation when you clearly know that doing so undermines achievement of your longer-term goals.
Take a second and think back to the greatest accomplishments in your life. Now ask yourself, What sacrifices did I have to make, especially in the short term, to create that success? Maybe you wanted to get an A in a class in school, make a sports team, break a record, become the top salesperson in your company, save money for a car, lose weight, get fit, perform in a play, create a rock band, become a cheerleader, or raise money for a favorite cause. Whatever it was, most likely you had to make some short-term sacrifices—working hard, getting up early, staying up late, giving up desserts, and saying no to distractions like television, video games, and socializing.
The question now is: Are you willing to forgo the short-term satisfaction that drinking brings to ensure the longer-term happiness and fulfillment you desire in your life? Every time you feel overwhelmed by the desire to drink, ask yourself that question. Consider the costs you will face from choosing to drink, in both the short term and the long term, and the benefits you will gain by choosing not to drink, especially in the long term.
### The Power of Positive Pressure
The pursuit of a goal brings order in awareness because a person must concentrate attention on the task at hand and momentarily forget everything else. These periods of struggling to overcome challenges are what people find to be the most enjoyable of their lives. . . . By stretching skills, by reaching toward higher challenges, such a person becomes an increasingly extraordinary individual.
—MIHALY CSIKSZENTMIHALYI
Psychologist and author of Flow: The Psychology of Optimal Experience
In his book Eat That Frog!: 21 Great Ways to Stop Procrastinating and Get More Done in Less Time, Brian Tracy, one of America's leading authorities on the development of human potential and personal effectiveness, writes: "Only about 3 percent of adults have clear, written goals. These people accomplish five and ten times as much as people of equal or better education and ability but who, for whatever reason, have never taken the time to write out exactly what they want."
As we said on Day 1 in the 100% Solution, your destiny is the consequences of your daily decisions. Along with your purpose and your beliefs, your goals will help you set the standards for these daily decisions. Remember, in every situation, there are only two choices. Your decision will either take you toward what you want or take you away from what you want. So always ask yourself, Is this action going to take me toward my goal or away from my goal?
Setting a goal means that you acknowledge, in your conscious and subconscious minds, that where you are is not where you want to be. Simply put, having goals creates positive pressure in your life. In virtually every study, written, time-bound goals are a key component of attaining high performance. Remember back to Day 3, the Pendulum Solution, where we shared with you the study of patients recovering from hip and knee surgeries, and how setting goals for their recovery helped them walk almost twice as fast as those that did not set goals. The same principle applies to you and your goal of thriving in sobriety.
### SMART Goals
You want to set a goal that is big enough that in the process of achieving it you become someone worth becoming.
—JIM ROHN (1930–2009)
Author of The Art of Exceptional Living
Zig Ziglar, one of the all-time great motivational speakers, once said, "What you get by achieving your goals is not as important as what you become by achieving your goals." As you move toward achieving your goals, you become the person you were meant to be—a healthy, vibrant, passionate, successful person who doesn't need alcohol to get through the day or the weekend. You become a person who is a great role model to peers, friends, family, and coworkers. A person who no longer needs to drink to fit in, have fun, or feel successful.
Here are some basic guidelines for writing your goals that will significantly improve your success in achieving them. A popular acronym used to remember the criteria for setting goals effectively is SMART, which is commonly attributed to the work of management consultant Peter Drucker.
• Specific—Who, what, and where. Be as specific as possible.
• Measurable—The criteria for measuring your goal should be clear to you and others.
• Attainable—The goal should stretch you while still being attainable.
• Realistic—You should be willing and able to achieve the goal. It needs to be believable.
• Time-bound—The goal should be bound to a specific time frame. By what specific date and time will you achieve it?
In short, you have to state specifically how much and by when in a way that an outside observer could verify that you have achieved it.
While this is just a brief overview of the key attributes of setting a SMART goal, you can find more information on setting your SMART goals on today's companion website.
### Goals and Thriving in Sobriety
In the past, I always connected drinking to immediate gratification, not realizing I was only trying to fill a void in my life. Now I clearly see that over time drinking guarantees I will always feel empty inside, where sobriety opens up the possibility to experience true happiness, joy, and fulfillment.
—SUSAN
30-Day Graduate from Philadelphia, Pennsylvania
On Day 2 we asked you to create a 30-Day Vision Statement for yourself. If for any reason you didn't do this, stop and go back and do it now. This book is not like a novel you simply read. It's a program you do. These solutions are all important, and they are designed strategically to build on one another, leading to a powerful transformation in just 30 days. The solutions always work for you if you always work the solutions. But if you skip over reading the content or doing the exercises, you are cheating yourself of the opportunity to experience the full power of this program.
It is important to write down your goals because they will support you as you take the steps to fulfill your life purpose—something we will talk about more on Day 29. Today, we are going to work with the 30-Day Vision Statement.
Let's say that your 30-Day Vision Statement is "Every day I wake up excited, vibrant, and passionate about living a meaningful and fulfilling sober life." Some SMART goals that support your vision might include the following:
• I will have stayed sober for 30 days in a row by January 31, [year], at midnight.
• Every night by 10:00 p.m., I will have completed that day's reading assignment for The 30-Day Sobriety Solution, finished that day's action steps, and spent five minutes or more writing in my private journal until I have completed the program by 11:00 p.m. on April 21, [year].
• After I have immersed myself fully in all of the content and solutions in The 30-Day Sobriety Solution, I will have manifested passion, purpose, and 30 days of continuous sobriety in my life by July 15, [year], at 5:00 p.m.
• I will be a "normal drinker," thriving in life with a take-it-or-leave-it attitude toward drinking, by November 1, [year], at 7:00 p.m.
• I will have an amazing group of friends that are supportive of my sobriety, and regularly find creative, healthy, and fun activities to do that make thriving in sobriety a reality in my life, by January 31, [year], at 9:00 a.m.
Each of these goals, in one way or another, supports your 30-Day Vision Statement and incorporates the SMART goal-setting recommendations. These goals are written from the perspective of what you want, not what you don't want. One of the most ineffective and self-destructive phrases you could use when setting your goals is "quit drinking" or "cut back drinking." The reason is that the subconscious mind does not hear negative words like no, not, never, don't, stop, or quit. What it hears is the word drinking. It then creates an image of drinking, which it then wants to fulfill through the action of drinking. If you say, "I am not thinking of a tiger," what image comes to mind? A tiger. So if you don't want to think of tigers, you'd say, "I am thinking about airplanes or a sunset in Hawaii"—anything but tigers.
Yourfirst action step today is to start writing the goals that will support your 30-Day Thriving-in-Sobriety Vision. Feel free to use our examples or create ones that speak more powerfully to you. In any case, remember that right now we are focused on one key vision—thriving in sobriety—and you should write down three or more goals that support this.
At least one goal should be similar to the first four examples we gave, but you can also write one or two other goals, such as what your career, friends, family, health, and love life might look like when you are thriving in sobriety. These should not be what you consider big goals outside of thriving in sobriety, like becoming the president of your company or going on an African safari; when you focus on accomplishing too many big goals at once, you often end up failing at all of them. By concentrating on this one main goal of thriving in sobriety, you set yourself up for long-term success. This strategy of focusing on three goals that support this one main goal works! Time and time again, we see our clients get to the end of these 30 days having fully accomplished their goal of thriving in sobriety, and then go on to manifest other achievements in virtually every area of their lives.
### How Military Veteran James Embraced Goals
I am still amazed, looking back on the way I was when I first started The 30-Day Sobriety Solution, to see how far I've come. And all without Alcoholics Anonymous, without inpatient or outpatient rehabilitation, and even without anybody to cheer me on. It is truly amazing, and I just want to thank you for The 30-Day Sobriety Solution. It has given me everything I need to thrive in sobriety.
—JAMES
30-Day Graduate from Istanbul, Turkey
James is one of our heroes. When he was fresh out of high school, he knew he wanted to serve his country, so he joined the United States Air Force. James was surprised by his own success in this new environment, and was recruited by a highly selective, prestigious unit in the air force. As he served his country, his pride and self-worth reached an all-time high. When it came time for James to retire, at first he was excited about having new career opportunities, and he had a great sense of accomplishment from his military career. But he hadn't realized how much of his identity and self-worth were tied to his air force career, and before long, even though he became successful in his new job, drinking had become a nightly routine.
By the time James reached his early fifties, he was shocked to realize he had been drinking excessively for thirteen years. Somehow he believed, like many military retirees, that "the best days of my life were in the past." And because his postmilitary career required frequent traveling and gave him a lot of autonomy, he couldn't imagine what it would be like to travel sober.
James tried Alcoholics Anonymous and other recovery options that didn't work for him, but when he came across The 30-Day Sobriety Solution, he recognized some of the same principles and techniques that had helped him be successful in the military and his current career. When he completed the program, he told us, "The program took every positive characteristic and every personal strength I have succeeded with in the past, improved them, and applied them in positive ways to live a sober and happy life."
Because so many of the 30-Day solutions helped James create breakthroughs, he was surprised that he had never considered applying the simple act of goal setting to his sobriety. After all, in the air force and his later career, setting and accomplishing goals was a fundamental technique he used to create success. As he continued to focus on his vision of thriving in sobriety and setting supporting goals to accomplish this, his life changed. James said, "Your program absolutely cured me. That's the best way to put it. The thought of drinking might enter my mind—rarely—just like any other thought would, but there was an instantaneous reaction, and in less than a second, I was thinking, Why in the world would I ever do that? And that's the end of it—no internal debate."
James was sober for almost a year before he decided to experiment with drinking again. He quickly realized that being a "normal drinker" was not something that would work in his life, so he decided to go through The 30-Day Sobriety Solution a second time. Once again, he discovered that he was able to have new insights and breakthroughs. Today he is truly thriving in sobriety, and recently emailed, "I'm happier than I've ever been in my whole life."
### Stupid Juice
One day, while James was at a restaurant with a friend who was drinking, he looked at his friend's beer and internally referred to his beer as "stupid juice." It surprised him, as he had never used that phrase before, and it led to a profound realization:
Alcohol makes you do stupid things. You make stupid decisions, say inappropriate things, and offend people. The more you drink, the dumber you get. And what's really crazy about it is that you don't realize how stupid you are. And you keep drinking more of it and become stupider and stupider. It wears off, and the next day you look back and feel stupid because of the things you did.
Anytime that James thought of drinking or heard a radio commercial for one of his favorite drinks, he just referred to it as "stupid juice," and any desire he had to drink vanished. He realized that, over the years, the multimillion-dollar advertising campaigns for his favorite liquors had created strong associations with pleasure, freedom, and "good times." As James put it, "You might say I created my own brand image for alcohol, one that was personal to me. And believe me, there's no pleasure attached to it."
We recommend that you try out this powerful way to attach "pain" to the idea of drinking.
### Why You Set Goals and Sometimes Nothing Happens
If you are bored with life, if you don't get up every morning with a burning desire to do things—you don't have enough goals.
—LOU HOLTZ
Have you ever set a goal that you failed to achieve? You're not alone. Even though we often want something better, we often fail to produce it. Here are a few of the most common reasons.
• You are not fully committed to the goal and attempt to accomplish it only if it's convenient.
• You don't have a big enough reason why—why it will be painful not to accomplish the goal and why it will be pleasurable and rewarding to accomplish it.
• You don't feel you deserve to achieve the goal—that you are not worthy or good enough.
• You don't believe it's possible—or you believe it is possible only for someone else.
• You are somehow different—a special case.
• You don't know what to do or how to go about it—you don't know whom to ask, or you are too proud or scared to ask.
Can you relate to any of these reasons? Can you identify any of these reasons behind past goals you failed to accomplish? You can set all the goals in the world and have every intention of accomplishing them, but if you haven't addressed these internal roadblocks, you will fail. That is the reason the Outcome Solution is on Day 6 and not on Day 1 or 2. Everything in The 30-Day Sobriety Solution before today has set you up for success in setting and accomplishing your goals. And everything that follows will reinforce and build on today's solution, including removing the blocks and limiting beliefs listed above.
On Day 1, the 100% Solution, you committed fully to let go of blaming and complaining. On Day 2, the Purpose Solution, you created a 30-Day Vision for your life and a powerful emotional connection to that vision to help keep you moving forward despite obstacles and challenges that will inevitably come up. On Day 3 in the Pendulum Solution you leveraged and applied the power of pain and pleasure in your life, so that the thought of drinking equals pain and the thought of sobriety equals ultimate joy and pleasure. On Day 4 in the Forgiveness Solution you forgave others—and most importantly—yourself, so that you could accept the love and sobriety you deserve in your life. On Day 5 in the Believe-in-Yourself Solution you chose to shift your beliefs and believe in the possibility of living in sobriety and to believe that you can do it.
That is why the goals you set today will be unlike any goals you have ever set. You have set yourself up for success, and the "magic" of this program is that each day, each solution, builds one upon the other to create massive positive change in just 30 days.
### Using Your New Goals
Goals. There's no telling what you can do when you get inspired by them. There's no telling what you can do when you believe in them. There's no telling what will happen when you act upon them.
—JIM ROHN
Once you've written down your goals, your second action step is to review your list at least two to three times a day, which will activate the power of your subconscious mind. If you are in an appropriate place, read your goals one at a time out loud with passion and enthusiasm. Otherwise read them silently. After you read each goal, close your eyes and picture each goal in your mind as if you had already achieved it, and then visualize what your life will look like when you accomplish your thriving-in-sobriety vision. Fill in as many details as you can. Then take a minute to feel, as deeply as you can, everything you would feel if you had already accomplished this vision. It doesn't matter if your visualization appears fuzzy or in high definition, as long as you make the effort to picture it as best you can.
If you do this as a daily discipline, it will activate what psychologists refer to as "structural tension" in your brain, which naturally wants to reconcile that tension between your vision and your current reality. By constantly repeating your goals and visualizing them as already accomplished, you will increase the structural tension, which your mind will work to resolve by making your vision come true. It does this by strengthening your motivation, boosting your creativity, and opening up your awareness to all the people, resources, and things around you that are there to help you attain your one main goal of thriving in sobriety, but that you may not have seen as accessible before.
You can use creative ways to constantly review your goals. For example, Jack puts his on three-by-five-inch index cards and keeps them by his bed to review every morning and evening. He also places his most important goal in his wallet where his driver's license would normally appear through the little plastic window, so he sees it every time he opens his wallet. Find something that works for you, so you are forced to habitually review your goals along with your 30-Day Thriving-in-Sobriety Vision. Also, we know these might be private, so find a way that protects your privacy while still enabling you to review them, such as keeping the list on your tablet or smartphone. This kind of repetition creates greater clarity, focus, and motivation to act, all of which will accelerate the accomplishment of your goals.
### Day 6 Action Steps
Getting sober was one of the three pivotal events in my life, along with becoming an actor and having a child.
—GARY OLDMAN
Actor
The Outcome Solution is all about creating an outcome-focused, purpose-driven, goal-setting, and reinforcement strategy to ensure that your thriving-in-sobriety vision becomes a reality in your life.
• Write down three goals that support your 30-Day Thriving-in-Sobriety Vision Statement from Day 2. Write these goals following the SMART guidelines and examples we gave, without using the words "quitting drinking" or "cutting back drinking."
• Determine a plan to review these goals, along with your vision, at least two times a day. Figure out a daily strategy for reviewing your goals. Read them (out loud when possible), visualize having accomplished them, and create the feelings you would feel if you had already accomplished them. Feeling the feelings is key.
• Optional: review the "new you" brainstorming notes from Day 2. To help you follow through, review what you wrote regarding the solutions from Day 2. This will remind you what you stand to gain by accomplishing these goals.
As always, you can visit the companion website for today's solution, where we have included more studies and strategies to supercharge your goals and underline the importance of having intrinsic goals, at <http://Day6.Solutions>.
## Day 7
## The Review Day and Bonus Solution
## Embracing the Power of Repetition to Master the Basics
Any idea, plan, or purpose may be placed in the mind through repetition of thought.
—NAPOLEON HILL
Congratulations! You have completed Phase I, "Mastering the Absolute Basics to Get from Where You Are to Where You Want to Be." Take a minute and celebrate your dedication. As Babe Ruth used to say, "It's hard to beat a person who never gives up." And by completing Phase I, you have proven that you are committed to doing the work to get from where you are to where you want to be.
Days 7, 14, 21, and 28 are review days. The significance of repetition in your life has been enormous. Repetition helped create your drinking problem; now it will help create your solution. Before moving on to Phase II, please trust us and make that little extra investment of time right now; the rewards that you will gain from doing this will far exceed the amount of time it takes. And don't worry, we never give you additional action steps on the review days.
In Phase I you learned why a 100% commitment is critical to your success in The 30-Day Sobriety Solution, and you wrote a 30-Day Thriving-in-Sobriety Vision Statement to accelerate your desire to get and stay sober. You learned about the law of duality and the role of pain and pleasure in your life, and why embracing forgiveness and letting go of guilt and shame are essential to your happiness. You explored the power of believing in yourself, and learned a proven process for writing empowering and exciting goals. On the companion website, we review each of these key concepts further, as well as share a special video from us.
You will also find access to your first bonus solution, the Social Solution, which covers the top 11 excuses you can use when you want to not drink and not feel judged in any social situation. If you are planning to attend a party or a social event where people will be drinking, this is a must-read for you. You will find all of this on the companion website at <http://Day7.Solutions>.
But before you visit the website, we have some information that we know you will find important as you are completing Phase I.
### The Foggy Brain
I hated every minute of training, but I said, "Don't quit. Suffer now and live the rest of your life as a champion."
—MUHAMMAD ALI
World champion heavyweight boxer
There is a common expectation that people have in early sobriety. After a few days or weeks of continuous sobriety, people tend to believe that they should feel great physically—have more energy, feel clearheaded, and be more alert. If you were drinking three to four glasses of wine a night or were the weekend-warrior type drinker, then this might be true. However, if you fall into the heavier-drinking category, you might experience "foggy brain"—where your energy is low and you are unable to think clearly. It can feel like you're driving down a curvy road on a foggy night—no matter how hard you concentrate on the road ahead, you struggle to see it clearly.
Please know that this can be completely normal at this stage. In fact, you may also find yourself feeling more irritable and becoming angry and frustrated more easily.
Remember, you are taking away an emotional and physical coping mechanism, and your body and mind need time to adjust. You are making a dramatic change in your life. If you were drinking heavily, your brain almost certainly stopped producing natural chemicals (like the neurotransmitters dopamine and serotonin) that are key to creating a good mood. But don't worry; the human body is amazing at self-healing. After some time, your body will resolve this imbalance on its own, and as that happens, your brain fog will lift and your mood will improve. If you would like to expedite this process, we have some basic nutritional recommendations.
### Serotonin and Dopamine
I don't drink anymore. I don't want to get old, and drinking really makes you old. I just got fed up with feeling slightly groggy in the morning when I went out and had too many drinks. Now I can go out until two or three in the morning and leap out of bed the next day and feel great.
—JEMIMA FRENCH
Fashion designer
Dopamine and serotonin have played critical roles in your drinking. Sometimes referred to as the "happiness hormone," serotonin helps regulate your mood and prevent depression. Dopamine also affects your mood, the brain's reward and pleasure centers, and your ability to focus. Drinking generally stimulates the release of these brain chemicals, so you feel good at first. You might have a feeling of euphoria, well-being, and reward, but, over time, heavy drinking will deplete the amounts of dopamine and serotonin, leading to a low or depressed mood. By drinking often, you become conditioned to believe that alcohol will improve your mood, even though it no longer does so.
This explains why many problem drinkers say that drinking eventually "stopped working." Even though you have stopped drinking, your brain's production of serotonin and dopamine does not immediately return to normal levels. In fact, some studies show that your brain may need up to 90 days—and in some cases, even longer—to return to normal levels of dopamine and serotonin production. During this time, your desire to drink in order to reexperience that good feeling can be heightened.
However, there are other natural and healthy ways to stimulate the brain's production of serotonin and dopamine. We will cover many of them throughout the rest of this program, but here are some you can start today. We have consulted several nutritional experts to find out which foods and nutritional supplements provide the greatest support for an easier journey, but we recommend that you consult your own doctor or health care professional before adding supplements to your diet. We will cover this topic in more depth on Day 25 in the Mind and Body Solution. Also, for supplement recommendations, we like to visit Consumer Lab's website (www.consumerlab.com). This independent lab has been testing supplements since 1999, and posts its results—much like a Consumer Reports of the unregulated dietary supplement industry.
• GABA supplements. Gamma-aminobutyric acid (GABA) acts as a serotonin reuptake inhibitor (it alters the balance of serotonin in the brain, often improving mood) and has often been used in early sobriety to help alleviate withdrawal. But do not take GABA supplements while drinking. You can also get GABA naturally from cherry tomatoes, shrimp, bananas, and kefir (a drink that contains probiotics—the "good" bacteria that help keep your digestive system healthy).
• Omega-3 fats. Omega-3s raise the brain's dopamine level by 40 percent, which increases alertness, focus, and mood. Fish is your best source, specifically wild-caught (not farm-raised) salmon, sardines, herring, anchovies, and mackerel. You can either eat two servings per week or take 2 grams of omega-3 fish oil with eicosapentaenoic acid (EPA) and docosahexaenoic acid (DHA) per day. EPA and DHA are two types of omega-3 fatty acids that are found in fish and fish-oil products.
### The Sugar Connection
Not only do you have a dependency on alcohol, but also you have a dependency on sugar, because alcohol is essentially fermented sugar. Sugar itself is extremely hard on your system and dangerous to your health, but we have found that for most people, quitting drinking while also dramatically cutting back on sugar is a recipe for failure, so generally we don't recommend it this early in sobriety. Regardless, we would be remiss not to address this topic and give some basic advice, because changing your diet can curb alcohol cravings. We will revisit and elaborate on this topic in Day 25.
The overall goal is to keep the amount of glucose found in the blood (your blood sugar levels) stable, which will help curb cravings for alcohol. Here are seven tips to help maintain stable blood sugar:
1. Never go hungry.
2. Eat at least every five hours.
3. Eat three healthy meals a day.
4. Always eat breakfast.
5. Never skip meals.
6. Ideally, get your vitamins and nutrients from food rather than supplements.
7. Fruit is a great alternative to candy bars and sweets to satiate sugar cravings.
On today's companion website, we have included a recipe for a wonderful alcohol detox smoothie you might want to try. Last, we want to remind you that by abstaining from alcohol, you are perhaps making one of the biggest changes to your diet in years or even decades. Your goal is to quit drinking, and many of our clients simply find it easier if they allow themselves to have some sweets during the transition phase, because by the end of The 30-Day Sobriety Solution, you will be far better prepared to embrace a more comprehensive and healthy nutritional strategy.
Be sure to visit the companion website right now to finish your Phase I review and watch the special video we've created for you at <http://Day7.Solutions>.
# PHASE II
* * *
# Removing the Mental and Emotional Blocks That Prevent You from Thriving in Sobriety
* * *
Every great work, every big accomplishment, has been brought into manifestation through holding to the vision, and often just before the big achievement, comes apparent failure and discouragement.
—FLORENCE SCOVEL SHINN
Welcome to Phase II of The 30-Day Sobriety Solution. This phase is often completed during the second week of the program, unless you have chosen the 60- or 90-day option. Like so many of our clients, if you continue forward, you will accomplish what you set out to do when you started this program. In fact, most graduates find that they actually exceed their original expectations. Just as spiritual teacher Florence Scovel Shinn says, it is all about holding to the vision, no matter what challenges and setbacks you face. Which leads us to an important question. Are you reviewing your 30-Day Vision Statement and goals several times a day? If not, you do need to make this part of your daily recovery process.
As you start Phase II, it is important to remind you of the 30-Day Reboot. When you work through the solutions and observe 30 days of abstinence, you are rebooting your mind and body. The end result is a surge of personal growth and transformation in a short period of time. On Day 1, we asked you to pick a time during the first week to quit drinking, as long as it was approved by your doctor or health care professional. We expect that you have already done that if you're this far along in the program, but if not, be sure to start today. This 30 days of abstinence is imperative for your success.
#### So You Slipped. Now What?
Whether you have already started the 30-Day Reboot or are starting it today, the reality is that you may give in to your desire to drink before completing 30 days of abstinence. This does not mean you have failed! The most important thing to do is to forgive yourself and then continue forward with the program. However, we do have a few recommendations if you slip.
First, go back to Day 1, the 100% Solution, and listen to the Time Travel Technique on the companion website. This will help remind you of the pain you will experience if you keep drinking, and it will reconnect you to your why—what you really want in life and how sobriety will help you accomplish it.
Second, on the companion website for Day 14, you can access the Relapse Solution, which specifically addresses this topic in depth and explains how to make sure you don't slip again. Although we recommend you review this solution if you relapse, it is optional.
Third, your best chance for successfully quitting or cutting back drinking is to keep making progress in the program. With each additional solution you complete, you will gain valuable new personal insights and learn powerful tools to create lasting change. Often one solution will result in the exact breakthrough you need to finally succeed, so by continuing with the program, you allow this to happen.
Before we jump into Day 8, let's briefly discuss dreams.
#### The Drunk Dream
I still dream, twice a week at least, that I've taken cocaine, and I have it up my nose. And it's very vivid, and it's very upsetting, but at least it's a wake-up call.
—ELTON JOHN
Singer-songwriter in recovery
Have you ever woken up in a panic after having a dream that you got drunk? For weeks, months, and even years after getting sober, it is not uncommon to dream about getting drunk—and for a moment when you wake up, you feel the disappointment of having actually relapsed. If this happens, use it as an opportunity to remind yourself of the inevitable pain that comes from drinking. The feelings you experienced in that drunk dream were real, even though you didn't actually get drunk. The best way to move forward is to be thankful that you didn't drink and realize that the negative emotions you experienced in, or after, your dream are very similar to how it will feel if you do drink. Now let's get started with the first solution in Phase II.
## Day 8
## The "Why Can't You Just Quit?" Solution
## The Truth About Willpower
Willpower can produce short-term change, but it creates constant internal stress because you haven't dealt with the root cause.
—RICK WARREN
Author of The Purpose Driven Life: What on Earth Am I Here For?
Willpower is often considered one of the greatest predictors of individual success, but it's not always your greatest asset for sobriety. The "Why Can't You Just Quit?" Solution explains the importance of willpower and how you can build and leverage it. It also reveals the truth about why strong willpower can actually stop you from thriving in sobriety.
### What Is Willpower?
Willpower is defined as a "strong determination that allows you to do something difficult (such as lose weight or quit smoking)." Isn't it telling that even the published dictionary definition of willpower includes an example of overcoming addictive behaviors? However, we prefer this definition from The Life You've Always Wanted, by John Ortberg: "Willpower is trying very hard to not do something you want to do very much." We're sure you can relate to that.
How many times have you decided that you were going to cut back or quit drinking? Dave can't even count how many times he said he was going to quit before his first sincere attempt. It was almost ten years later when he was actually able to accomplish long-term sobriety. During those years, he tried all kinds of ways to cut back and quit drinking; however, they all ended the same way—he went back to drinking at the same level or more within weeks or months.
The interesting thing is that everyone who knew Dave thought of him as someone who had incredible willpower and persistence, always being able to follow through with what he set out to accomplish. But when it came to changing his drinking, he always failed. He was unable to leverage his willpower to quit drinking as he had used it to power through other goals. This was hard for him to understand, and it also baffled his wife, who knew that Dave could accomplish anything when he set his mind to it.
After Dave had been sober for over two years, his wife asked him a question that plagues most loved ones of problem drinkers and alcoholics: "Why weren't we—me and our daughters—enough for you to quit drinking sooner?"
As any problem drinker or alcoholic knows, there is no easy answer. The truth is that unless you have struggled with highly addictive behaviors, it is almost impossible to explain. It is an addiction, an obsession, a habit, a way of life, and somehow you become convinced that the only life worth living is one that includes drinking.
And although today's solution is about willpower, we call it the "Why Can't You Just Quit?" Solution because this is the question that a hundred million or more family members, friends, and loved ones of alcoholics (just in the United States alone) ask over and over again. And at the center of the answer to this question lies willpower, both as part of the cause and the solution.
### The Truth About Willpower
I tried willpower to quit drinking on my own. I tried switching to beer and wine. I tried Alcoholics Anonymous several times, but found the program was too ambiguous. However, The 30-Day Sobriety Solution was something I could sit down and do every night. And the "homework" not only helped keep me on track, it helped me get clear and understand how I was feeling, and provided me with tools and techniques to change.
—MATT
30-Day Graduate from Kansas City, Missouri
There are certain days in The 30-Day Sobriety Solution that are going to create an "Aha!" moment for you. This is one of those days.
Take a minute right now and think about some of the times in your past when you decided to quit or cut back drinking. Maybe you had an embarrassing or frightening incident related to your drinking, or you were sick and tired of the emotional roller-coaster ride that alcohol takes you on, or you had a drunken confrontation with family or friends. Whatever the reason, you were ready to make a change. This is where your willpower kicks in.
The problem is that willpower alone will always fail over time. To understand why, first you have to look at what you are feeling the moment you decide to make this change. Your decision always has a common theme: you are cutting back or quitting drinking because you perceive that drinking is holding you back in some way or creating specific problems or challenges in your life. Or, as we discussed on Day 3, you associate more pain than pleasure with drinking, so you stop. The best way to explain this is by using a numbered rating system.
### Willpower and the Pain-Pleasure Balance in Your Sobriety
Imagine that you wake up one morning feeling miserable from a night of heavy drinking. Your head is pounding, and you can feel the blood pulsing in the veins in your forehead, making it hard to think clearly. Later that morning, your doctor calls to tell you that he is concerned about your blood work and that the numbers indicate some early signs of liver damage. At that moment, you feel disgusted with yourself, wondering, How could I have let it go this far? On a scale of 1 to 10, with 10 being the highest, your desire to drink is at an unusual low of 2. And your concerns and fears about the health implications of your drinking are at an all-time high of 9.
Right now, what these initial ratings mean is that you have more pain associated with drinking than you do with not drinking. The pain of staying sober is less than the pain of drinking, so you choose not to drink.
You stay sober for a couple of days, and an internal shift starts to occur. The more distance you have from the reason you decided not to drink in the first place, the further removed you are from the pain that led you to make that change. In fact, with the alcohol out of your system, you are feeling healthier, more confident, and more clearheaded. The pain that drove you to make that initial change is all but a distant memory—and now the desire to drink is starting to kick back in.
With your recent hiatus from drinking, your concern with your health has dropped from a 9 to a 5. At the same time, your desire to drink, which was down to a 2 because of your bad hangover and the call from your doctor, has risen to a 6. And with the weekend approaching, this number is quickly escalating as you start thinking about all of the fun things you can do over the weekend while drinking, and all the fun you'll miss if you don't.
This is where your willpower really starts to show up (or doesn't). Depending on how strong your willpower is, your sobriety may last through the weekend and beyond, or you might simply give in to the desire to drink, restarting the whole cycle again. Nevertheless, no matter how strong your willpower is, when there is greater pain associated with staying sober than there is with drinking, you will eventually give in to the desire to drink again—unless you have changed at a deeper and more fundamental level, which is what you are doing by going through The 30-Day Sobriety Solution.
Willpower can help initiate and sustain significant short-term changes in your life, but without doing the other, deeper work—the work you are doing in this program—willpower alone will never get you where you want and need to be. We all have limited willpower. It doesn't matter who you are. People who appear to have incredible willpower appear that way only because they have also set themselves up on the inside for "success."
### What Is Willpower in Your Life?
Think about something positive you do well that others struggle to do. Maybe it's eating healthy, or always showing up on time for meetings, or just being well organized. What separates you from the people who also want to be successful at these things but never seem able to? Willpower is certainly one factor, but the key difference is your beliefs. You have decided, consciously or unconsciously, that eating healthy equals pleasure, energy, and longevity, and that not eating healthy equals inflammation, pain, and illness.
When you go from not eating healthy to eating healthy, you'll often experience pain at first—the pain of eating foods you might not like as much, the pain of having to learn how to cook and prepare new meals, and the pain of going out with friends and not being able to enjoy the same unhealthy appetizers and desserts as everyone else. This is where using willpower is essential to your short-term success. However, long-term success only comes from truly changing yourself at a deeper level, and those who have successfully completed this transformation believe that eating healthy eventually equals ultimate pleasure—the pleasure of having more energy, the pleasure of looking and feeling better, and the pleasure of feeling more self-confident.
The 30-Day Sobriety Solution is about transforming yourself so that you no longer need willpower to stay sober in the long term. Sobriety should not be difficult to achieve and maintain, at least in the long term. Sobriety should not feel like a sacrifice or a curse; rather, it should simply be a choice you make because it is what you want. However, if you keep trying to quit and stay sober by using willpower alone, you will always ultimately fail. The only way to succeed and maintain that success over time is to change on the inside, which is what you are doing in this program.
Don't get us wrong. You need to use willpower early and often on your path to sobriety, but you also have to diligently continue with the inner work to make sure that you can overcome the urges to drink when willpower alone stops working. Rick Warren's quote from The Purpose Driven Life at the start of this chapter bears repeating. "Willpower can produce short-term change, but it creates constant internal stress because you haven't dealt with the root cause." The 30-Day Sobriety Solution is all about dealing with this root cause.
If you experienced significant emotional trauma in your childhood, for example, to some degree this is probably one of the root causes for your desire to drink. When you do the personal work necessary to heal from this past pain, such as the Total Truth Process that you learned on Day 4, you are dealing with the root cause. Doing this inner work is what makes long-term positive change a reality in your life.
We have seen many high-functioning alcoholics quit drinking for 30 days simply by leveraging their remarkable willpower, only to falsely "prove" to themselves and others that they don't have a drinking problem. Not only do they not do any personal growth work to deal with the root causes of their drinking, but also they actually spend a great deal of time during each of those 30 days thinking about and planning in detail when, where, and how much they are going to drink on Day 31.
So your first action step for today is to explore the role of willpower in your past attempts to quit drinking. Answer the following questions in your journal: Have you previously tried to quit or change your drinking without seeking any help or using any outside resources? If so, how did it work? Write down, as best as you can remember, the past times you quit drinking without support or without also doing the inner work. Address specifically how long you stayed sober, how your experience changed day by day, and, if you returned to drinking, what happened. The awareness you gain from this exercise often results in a greater willingness to do the personal-growth work necessary for long-term change.
### The Willpower Illusion
Depending upon where you are on the "drinking continuum," willpower has likely created another challenge for you. It takes an incredible amount of willpower to ignore that you actually have a problem with drinking—to ignore all of the problems that have occurred in your career, your financial life, and your relationships as a result of your drinking—and to ignore the fact that your drinking alcohol most nights will dramatically affect your health and shorten your life. We call this "the willpower illusion."
Your drinking mind constantly tricks you into thinking that drinking is not a problem, that you can drink "normally," and that you can quit whenever you want.
### Your "Movie Moment"
My heroes are the ones who survived doing it wrong, who made mistakes, but recovered from them.
—BONO
Twenty-two-time Grammy Award–winning musician
To really capture this, we want to share with you an analogy that we call the "Movie Moment." Think back to a movie where you were really invested in the main character—one you identified with and whose story you were really engrossed in. And then the character does something unbelievably dumb. Maybe he cheats on his girlfriend, who is clearly a perfect match. Or he walks into a dark house, ignoring many warning signs of danger. Or he lies about something that he has no chance of getting away with, making the situation far worse.
Whatever it is, you might find yourself getting emotionally triggered. In your mind, or even out loud, you might yell at the screen, "How can you be so dumb and not see what is going to happen next?! You have everything you ever needed, and now you are throwing it all away!" To you, the mistakes they are making are obvious, but they seem oblivious to their poor judgment.
The question we have for you is, what is your Movie Moment? What would someone in the audience yell at you if he or she were watching you starring in your current movie? Or, even more to the point, what would you be yelling at the screen if you were watching yourself in your own movie? Would you be yelling about your drinking and how much it negatively affects your life? The goal of this process is not for you to feel ashamed or embarrassed but to look at your life from a different and more neutral perspective—one that will help free you from any denial that might still be holding you back.
When you are a problem drinker, your mind is amazingly effective at creating the illusion that you do not have a problem. It is no coincidence that high-functioning alcoholics are the best at this, as they are some of the strongest-willed people you will ever find. High-functioning drinkers pride themselves on being able to do the work that many others give up on, pushing through challenges with their incredible willpower. Ironically, that same willpower keeps them from accepting their problem with drinking until they can no longer ignore it—and, tragically, for many that realization comes too late.
Your second action step for today is to act like you are watching a movie of your life that you are starring in. What about your character's actions, or inactions, upsets you the most? Is he or she clearly in denial? What if one of your trusted loved ones, such as a parent, sibling, good friend, or child, were to watch it? What would that person say? If you could pick any person in the world to mentor you, but he or she had to watch your movie first, what would he or she see that you are pretending not to see? Our experience is that this exercise is more effective and powerful when you can relax and let someone else take you through it, so we've provided a guided version of the Movie Moment exercise on today's companion website.
### Willpower and Decision Fatigue
In their book Willpower: Rediscovering the Greatest Human Strength, psychologist Roy Baumeister and journalist John Tierney share an important study about willpower and decision fatigue. After analyzing 1,100 decisions regarding prisoners' legal appeals over the course of one year, researchers uncovered a pretty amazing statistic: prisoners who appeared in front of the parole board early in the morning received parole 70 percent of the time, while those who appeared late in the day received parole less than 10 percent of the time. After analyzing the data and all the cases, researchers concluded that decision fatigue affected the judges' rulings. The mental effort necessary for deciding case after case simply wore down the judges as the day went on.
This is relevant to your drinking, because most people drink at night, even though many begin their day planning not to drink. When the evening comes around, their willpower drops, and decision fatigue kicks in. Your third action step for today is to think about how your willpower fades as your day goes on and to decide how you are going to avoid decision fatigue and successfully complete this 30-Day program.
Here are two options that we find work well. The first is to decide that from now on, you'll begin your day by reading that day's solution and doing the action steps before decision fatigue has time to set in. If, for any reason, that is not possible, the other highly effective approach is to read the solution and do the action steps immediately upon getting home from work—that time when you would have regularly started drinking or gone to happy hour.
### The Comparison Game
Despite all my education and knowledge about addiction, when it came to looking in the mirror, I only let in the information that confirmed I didn't have a problem. Once I changed this, everything started changing.
—BYRON
30-Day Graduate from Phoenix, Arizona
Have you ever looked at someone and thought, I don't drink as much as he does. Or, I might occasionally drink too much, but I am not an alcoholic like my [friend, cousin, parent, sibling]. Or, Look at what a great person she is; if only I had her life, all my problems would be solved.
Comparing yourself to someone else is a "sobriety killer." This brings us to the fourth action step. When you compare yourself to others, you get caught up in focusing on your differences rather than on your similarities. And often these differences go something like, "I don't have a problem with alcohol like they do," or "Look at how much Jen [or Eric] drinks." When you focus on the differences, you stop noticing the similarities. You tell yourself you are different and that you don't have a problem.
In fact, a common scenario in the recovery world is that someone will go to rehab and be surrounded by alcoholics and addicts who are much farther down the path of addiction than he or she is, and so the person focuses solely on those differences and leaves rehab believing that he or she must not have a problem because he or she is not like "those people." In David Sheff's book Clean: Overcoming Addiction and Ending America's Greatest Tragedy, Dr. Michael Pantalon, cofounder of the Center for Progressive Recovery, in New Haven, Connecticut, says, "Less severe people say that rehab made them feel their drug use was not that bad when compared to others in rehab and that this comparison led them back to use."
But when you focus on the similarities instead of the differences, you are less likely to get caught in denial. If you look for similarities, you can hear parts of your story in everyone else's story. That simple change has a profound impact on your awareness. You can better see your greatest challenges, which greatly helps you to quit or cut back drinking. So the next time you hear yourself saying that so-and-so is different from you, change your point of view and focus instead on what you have in common.
There are always going to be people better off and worse off than you, no matter where you are or what you're doing. Even though you are unique, and your story and your journey are different from everyone else's, you can embrace your individuality without getting caught in the illusion that those differences mean you don't have a problem. We have seen clients, friends, and even our own family members get stuck in this self-delusion. Everyone has to get over it in order to proceed with recovery.
### Day 8 Action Steps
Whether you have willpower or not, you have to be willing to change and not rely solely on your willpower to get yourself through these 30 days. Dr. James Gordon, a Harvard-educated psychiatrist and founder-director of the Center for Mind-Body Medicine, in Washington, DC, says that it isn't that "some people have willpower and some don't, but that some are willing to change and some are not."
Let yourself be open to the information in this program. Make time every day to do the action steps—especially the ones that make you a little uncomfortable. Just reading about the solutions won't get it done. As one of our friends said recently, "You can't get wet reading about the ocean." And you can't stay dry just reading about sobriety.
Don't let your willpower convince you that all you need is 30 days of sobriety to "cure" yourself from alcohol. Recognize that, during these 30 days, you are also becoming the person you have secretly dreamed of becoming—your true self. You are steadily transforming yourself into someone who can fully embrace all of life and thrive in sobriety.
Be sure to refer back to the text earlier in this chapter if you need to refresh your memory on the steps, as we only summarize them below:
• Write down in your journal what role willpower has played in cutting back or quitting drinking. Have you tried to quit drinking using only willpower? How, specifically, have those experiences worked out?
• Write down your Movie Moment. What bothers you the most about your actions, or inactions, as you watch an imaginary movie of your life from the perspective of an unbiased third party? Is your character clearly in denial about the negative impact of drinking on his or her (your) life? To really achieve a breakthrough in this action step, we highly recommend that you listen to the guided version on the companion website.
• Decide how you are going to avoid the negative impact of decision fatigue. What can you do differently now that you know your willpower weakens throughout the day? When will you read that day's solution and do the action steps? Is there something self-nurturing you can easily do at the same time you used to start drinking, like going for a walk?
• Get out of the comparison trap. Write the answers to the following questions in your journal. Do you regularly comment internally on other people's drinking habits? Do you believe that you do not have a problem like theirs? Do you regularly compare yourself to others, because you want what they appear to have or you want to reassure yourself that what you have is better? Think back to a time where you might have judged someone else for drinking or substance abuse. What similarities can you acknowledge you have or had with that person if you are completely honest?
As always, there is additional support material on the companion website at <http://Day8.Solutions>, including our top tips for building your willpower and the guided version of your Movie Moment.
## Day 9
## The Action Solution
## Getting Out of Your Head and Into Action
When you quit drinking, you stop waiting.
—CAROLINE KNAPP
Author of Drinking: A Love Story
There's a lasting adage of success that says, "The universe rewards action." Yet despite the simplicity and truth of this principle, it's amazing that so many of us seem to get hung up by continually planning, organizing, and considering all of our options rather than just taking action.
By taking action, you activate other dynamics that move you toward sobriety. When you take action, others around you know that you are sincere and determined with your intent. You start actively learning from your own life experiences instead of just learning from books. You become more receptive to the feedback you are receiving as the result of the actions you are taking, and all of a sudden you have more information on how to improve things in an easier, quicker, and more efficient manner. Things that puzzled you before suddenly become clear, and things that seemed impossible now seem possible. You attract people who reinforce your path and encourage you. Once you take action, support flows your way.
Quite simply, taking regular action toward your goal of cutting back or quitting drinking, like we have strategically set out for you in each solution, all but guarantees your success at thriving in sobriety.
### Take Action, Avoid Distraction
Over the years of teaching and coaching people, we have found that action is the one thing that separates those who successfully overcome problem drinking in the long term and those who don't. Those who are thriving in sobriety, even after having failed many times, are thriving because they took action and did what had to be done.
We can give you solutions for change and share inspirational stories of people who overcame seemingly impossible odds. We can convince you that you are no different from anyone else who has successfully quit drinking or achieved the "normal drinker" lifestyle. But none of this matters if you don't take action and do what has to be done.
We know you might be thinking, Wait, I have taken action every day. I have read the material, done the action steps, and reviewed the companion website. If so, that is fantastic. We applaud your accomplishments, and you should feel great about what you have done so far.
However, the Action Solution goes beyond just these 30 days. If you have found taking action in this program easier than usual, that is great and exactly what we intended. On the other hand, if you have found it challenging to take action so far, or if you are concerned about taking action beyond these 30 days, today will help you to take positive action, and avoid distraction, for the rest of your life.
And now it's time for you to take action.
### Your Bridge to Thriving in Sobriety
I don't drink anymore. I don't smoke anymore. I don't do drugs anymore. All of those come with an "anymore." I used to do everything and a lot of everything.
—KELLY PRESTON
Actor
Action is best explained as the bridge between your inner world and your outer world. Your outer world is a manifestation of your inner world, and, as you change on the inside (your thoughts, feelings, and beliefs), you also change on the outside.
Your inner world drives your actions, or inactions, to manifest in your outer world. Inaction is actually a kind of action because if you are not working the solutions, you are doing something else, even if that is just sitting in front of the TV.
So far in this program, we have been working primarily on your inner world, so that it changes your outer world. Results might include improved health, weight loss, better relationships, and a promotion at work or a new job, as well as your primary goal of cutting back or quitting drinking. At the end of these 30 days, if you do the solutions, you will find your inner world has changed so dramatically that the actions you take will become second nature in supporting your thriving in sobriety.
### The Definition of a Hero
The most successful people are long-term thinkers. They look into the future as far as they can to determine the kind of people they want to become and the goals they want to achieve. They then come back to the present and determine the things that they will have to do—or not do—to achieve their desired futures.
—BRIAN TRACY
When Dave's oldest daughter made the sixth-grade honor roll, he attended a school celebration. The principal gave a speech acknowledging the students and defining a hero as "somebody who does what needs to be done." His point was that a hero doesn't have to save lives or have some special superpower that no one else has—all heroes have to do is what they already know needs to be done. When you do what needs to be done, you, too, are a hero—and anyone who has curbed an addictive behavior such as drinking would readily agree.
The opposite of heroic action is inaction and procrastination—delaying something that you know should be done now. If you are like most problem drinkers, you have delayed addressing your drinking many, many times in the past. The bottom line is that we all procrastinate, but people who have mastered how to quickly overcome procrastination are happier, healthier, and more successful.
In a study published in Psychological Science in 1997, researchers rated college students on an established scale of procrastination and then tracked their academic performance, stress, and general health throughout the semester. Initially, there seemed to be some benefit to procrastination, as students put off work for more enjoyable activities, but the eventual cost of procrastination far outweighed the temporary benefits. Procrastinators earned lower grades and reported higher cumulative levels of stress and illness. The study concluded that procrastination is a self-defeating behavior with long-term costs.
This sounds similar to the "short-term trap" discussed on Day 6 in the Outcome Solution. By giving in to your short-term desires, you pay the ultimate price of never accomplishing your long-term dreams and goals. Focusing on the short term not only costs you your dreams, it creates more stress and illness in your life. When you choose to focus on the long term and make decisions based on those desires, however, you can more easily overcome procrastination and move toward your dreams, including thriving in sobriety.
### Sobriety Anxiety
If something is worrying you, always do something about it. It doesn't have to be the big thing that will make it disappear. It can be any small thing. But the positive effect it will have on you will be enormous.
—STEVE CHANDLER
Author of 100 Ways to Motivate Yourself: Change Your Life Forever
Think back to a time when you decided to quit drinking or change how you drink. Perhaps you decided to drink only on the weekends, not drink any hard liquor, or never have more than two glasses of wine. What were some of your initial thoughts right after deciding to make the change? Most likely they included thoughts such as:
• Maybe I will make one exception for the party next weekend, so I can have fun.
• If I quit drinking completely, my coworkers won't want to hang out with me, and that might cost me the upcoming promotion.
• If I stop at two glasses of wine, I should be fine, even if I drink every night.
• I will be too stressed if I can't get drunk at least once a week.
• I have too many challenges and concerns to do this right now, but maybe next month will be a good time.
Behind all of these thoughts is WORRY—worries about the bad timing of making this change, about not enjoying an upcoming party, about it being a career-limiting decision, and about not knowing how to deal with stress without alcohol. These worries, on top of the legitimate worries about your health and relationships that problem drinking brings, can completely paralyze you.
Worries are "sobriety killers." When you become consumed by worrying, the only action you may take is to escape through drinking. We refer to worry as sobriety anxiety: you have become accustomed to dealing with your worries and anxiety by drinking, so eventually your continued worrying pushes you past your breaking point, and you decide to drink.
Even though worrying does tell you that you need to do something, that is the only value it serves. To take action, you need to stop all the worrying. You have to decide to stop worrying. The easiest way to do this is to ask yourself one simple question: What can I do about this right now? And then take action—any action, however small, that moves you forward.
In the book Constructive Living, David Reynolds writes, "The mature human being goes about doing what needs to be done regardless of whether that person feels great or terrible. Knowing that you are the kind of person with that kind of self-control brings all the satisfaction and confidence you will ever need. Even on days when the satisfaction and confidence just aren't there, you can get the job done anyway." As Reynolds writes, taking action will give you the satisfaction you seek. Even if you are "not in the mood" to take action, the best way to change your mood is to do what you know needs to be done—you act like a hero does.
### Overcoming Resistance
At age thirty-nine, Mike felt that his life was on hold. He was a successful engineer, often recognized as a high performer, yet every night he came home unsatisfied. The only way he knew how to deal with this feeling was to drink. He would arrive home and immediately open a beer or pour a quadruple bourbon, and drink until he passed out, which was usually his only stopping point once he started drinking.
Mike knew there must be more to life, and he did have some dreams, but as his fortieth birthday neared, he started to doubt whether he would ever accomplish them. That is when he found The 30-Day Sobriety Solution. Mike was a little skeptical, but at the same time, he was inspired by the success stories, so he decided he had nothing to lose.
Instead of having a drink after work, he came home and immediately started the solution for the day even though he was usually not in the mood. He quickly realized that all he had to do was push through a little bit of resistance at first, and by the time he was done with the solution for the day, he found that his mood had improved completely. He felt encouraged and even excited at times about what he was learning. And more importantly, he was surprised to discover that his desire to drink was gone.
Mike cruised through the 30 days—not drinking once—something he hadn't done in many years. Shortly after completing The 30-Day Sobriety Solution, Mike gave us the following feedback:
I might even venture to say that half of the value I have gotten out of this program has been outside of just controlling my drinking. Once I control the drinking, I have a fairly large amount of time in the evenings and on the weekends to fill with productive or enjoyable activities.
Mike changed the course of his life over those 30 days. Within months of completing the program, he was promoted at work, something he knew would not have happened before doing the program. He became clear about what he really wanted in life, which was to work as an engineer at an amusement park and find a girlfriend. And now he had the time and motivation to go after those dreams.
It's been three years since Mike completed the program, and he has celebrated his one year anniversary at his dream job, working for one of the biggest amusement parks in the United States. He also has a serious girlfriend and told us recently, "I can't say that I'd change much about the transformation in my new life. I got pretty much everything I wanted."
Mike is one of our graduates who is able to have just one drink when he wants to and has a take-it-or-leave-it attitude about drinking. And it all started because he took that one simple step when he got home from work—pushing through the initial resistance he had and doing the work in the program instead of fulfilling his short-term desire to drink.
The first action step for today is to write down your top three worries related to your problem drinking, whatever they are. Then note anything you have done in the first nine days of this program that will help address those worries and anything you plan on doing for the remainder of this program. For example, one common worry is about the impact of your drinking on your health, so you might write down that abstaining from alcohol for 30 days will address this worry. The most important thing to do is to acknowledge your worry and then quickly move on to acknowledge that you are doing something, no matter how small, to deal with it.
### Ready Fire Aim
I knew I was lucky, and somehow I knew that if I didn't stop, everything would go tits up—my career, my family, my everything.
—EWAN MCGREGOR
You may have heard "Ready, aim, fire!" before. It's a familiar term for clearly focusing on your target before you shoot, but when you apply it to your life, the problem is that you might spend your entire life aiming at the target, but never firing. Do you know people who are always planning, preparing, or having to get things perfect before they even start? If you want to hit any target in the quickest way possible, you need to fire first, notice where the bullet ended up, and then modify your aim appropriately. If the bullet landed three inches above, aim lower and fire again. Where did it land now? Fire again and keep modifying. If you do this, you'll soon find yourself hitting the target square on. This same approach is true for everything in life.
Most successful people we know have a low tolerance for excessive planning. They are excited to get going. The 30-Day Sobriety Solution was developed with your success in mind. All the preparation and planning have already been done for you. All you need to do is read each chapter and complete the action steps for the day you are on in the order we provided. It's that simple. Just keep firing. And remember that there is rarely a "perfect" time or way to do anything. As long as you keep taking action and keep moving, you will experience profound changes over these 30 days.
Sir Isaac Newton's first law of motion, sometimes called the law of inertia, states that "objects in motion tend to stay in motion and objects at rest tend to stay at rest." This is true about the actions you take and don't take. If you wake up on Saturday morning and immediately wash the dishes, straighten the house, and work out, how do you think this will affect your mood for the rest of the day? But if instead you wake up on Saturday morning and plop down on the couch in front of the TV for several hours and eat junk food, how will your mood, and your day, differ?
We often find that people who struggle with problem drinking also struggle with an all-or-nothing mentality—the notion that something isn't worth doing unless you go all out at it. This couldn't be more false. Don't discount or ignore taking a step because it seems too insignificant or like it is "not enough." The forward momentum you get from even a small step is undeniable and worth the effort.
This takes us to the next action step of the day—"tiny habits" that can totally transform your ability to make and maintain significant changes in your life.
### "tiny habits"
A bicycle maintains its poise and equilibrium only so long as it is going forward toward something. You have a good bicycle. Your trouble is you are trying to maintain your balance sitting still, with no place to go. It is no wonder you feel shaky.
—MAXWELL MALTZ (1889–1975)
Author of Psycho-Cybernetics: A New Way to Get More Living out of Life
In 2007 the Hershey Company wanted to sell more Kit Kat bars. The marketing strategy it deployed was simple and brilliant. The company wanted to link eating Kit Kat bars to drinking coffee, since coffee was already a habit for much of its desired target market. This gave birth to the marketing message "a break's best friend" and an extensive radio and TV ad campaign repeatedly linking coffee with Kit Kat bars. The result? The $300 million brand grew to $500 million.
This campaign was so effective because it linked a new behavior to an existing behavior that was already firmly rooted. The best thing about this simple, brilliant, and proven marketing strategy is that you can implement it in your life to create amazing breakthroughs.
B. J. Fogg, PhD, the founder and director of the Persuasive Technology Lab at Stanford University, knows the power of tiny habits and developed a simple three-step method to create any new desired habit.
1. Start small. To defeat procrastination, you need to start small. In his book Time Warrior: How to Defeat Procrastination, People-Pleasing, Self-Doubt, Overcommitment, Broken Promises and Chaos, Steve Chandler writes, "Keep your life creative and simple: What needs to be done now in these three minutes? That's all you ever need to ask, and you'll never have anything like procrastination bother you again." Whatever needs to be done, make it easy and quick. Fogg notes that the new habit should seem like no big deal when beginning.
2. Find an anchor. Pick an existing routine or habit to act as a trigger for the new habit you want to create. Your life is full of routines, so just pick one. For example, Fogg began doing push-ups right after going to the bathroom. He started with just two each time, but today he does more than a hundred throughout the day. Other routines to link to a new habit might be brushing your teeth, washing your hair, getting in your car, hanging up the telephone, closing the refrigerator, checking your email, or turning on the TV.
3. Celebrate immediately. Whenever you find yourself doing your new behavior, give yourself kudos right away, whether it is a thumbs-up, saying "Good job!" out loud, affirming yourself in the mirror, or doing a fist pump. This simple acknowledgment acts as a very powerful reinforcement.
Implementing this tiny-habits method is the second action step for today. The key to succeeding with this method is to start small, so let's apply it to your 30-Day Vision Statement you wrote on Day 2. Pick a routine or behavior that you currently do at least five times a day as a trigger and reviewing your 30-Day Vision Statement as the new tiny habit. For example, after you use the restroom, immediately read your vision statement, or say it out loud or silently in your head if you have memorized it. The third step is to acknowledge your success immediately following the behavior. Soon it will become a new habit.
Now that you know this simple, effective technique, you might be tempted to use it to develop more than one new habit—and maybe even use it for a new habit that isn't directly related to your goal of quitting or cutting back drinking. Please don't do this. We know that we sound like a broken record on this topic, but trust us that you need to remain focused on these 30 days and your vision from Day 2. This focus will reap you incredible results in the long term.
### Day 9 Action Steps
The Action Solution is all about taking action and avoiding procrastination, not just throughout these 30 days but also for the rest of your life. When you replace worrying with action directed toward meeting the challenge or solving the problem, your life will start to improve, you'll achieve more of your goals, and you'll find yourself thriving in sobriety.
• Write down your top three worries related to problem drinking. Then write what you have done in this program to date, and what you will do over the remaining 30 days, to address these worries. The goal is to give yourself permission to stop worrying, since you are taking positive action that addresses those concerns. And when you find yourself worrying, come back to the question "What can I do about this right now?" And then take action—any action, however small, that moves you forward in addressing the issue you were worrying about.
• Start a tiny habit. Using the start-small strategy, link repeating your 30-Day Vision Statement (out loud when possible) to an existing routine in your life that you do at least five times a day. And to make it even more powerful, take twenty seconds to experience the feelings you will feel when you have made your vision a reality. Then remember to give yourself some sort of acknowledgment for completing it: a thumbs-up, a thank-you in the mirror, a fist pump, or just saying, "Good job!" out loud.
On the companion website, there are two fantastic, free online tools that we have found instrumental in helping you to take action and celebrate your successes. So be sure to visit <http://Day9.Solutions>.
## Day 10
## The Core Values Solution
## Discovering Your Core Values
When we honor our values, we feel an internal "rightness." It's as if each value produces its own special tone. When we live our values, the various tones create a unique harmony.
—From the book Co-Active Coaching: Changing Business, Transforming Lives by Henry Kimsey-House, Karen Kimsey-House, Phillip Sandahl, and Laura Whitworth
Integrity. Passion. Freedom. Honesty. There are hundreds of core values, and we each have our own personal set. When we let our lives be guided and directed by our values, we feel happy, fulfilled, and a deep sense of connection with others and ourselves.
We develop our core values throughout our lives. Your ability to cut back or quit drinking and to thrive in sobriety is related directly to whether you make decisions that align with your core values. When your actions express your values, you will achieve a state of inner and outer balance that will bring you peace, clarity, and joy. And when they don't, you will experience tension, confusion, guilt, shame, dissatisfaction, and even depression or chronic disease.
### Core Value Contradictions
Anyone who can't go five minutes without a cigarette, or can't stop drinking, or is strung out on drugs knows that after awhile there develops an attachment to the ritual of using it that has little to do with your original motive. The original impetus was to feel its effect, and the effect seemed positive at the time.
—ROBERT DOWNEY JR.
Actor in recovery
What are your core values? We rarely find people that can answer this question with any real clarity. We also know that when your behavior is out of alignment with your core values, it creates a deep disturbance in your psyche that can lead to lack of passion and loss of energy in your life.
When you look at someone who struggles with problem drinking, this issue becomes even more pronounced. Excessive drinking can numb your awareness of your core values and often leads to bad decision making, whether it's prioritizing your drinking over visiting a friend who needs your help, not finishing a task you promised to complete, or simply choosing to spend time at the bar instead of spending time at home with your family.
Dave's core values include honesty, generosity, success, passion, love, and fun. When Dave compared this list to his behavior when he was drinking heavily, it became clear why he was abusing alcohol. His decisions and his behavior contradicted almost all of his core values, except, at times, fun. When your life doesn't match what you say you care about, you're uncomfortable and unhappy. You look for a way to escape. Drinking was Dave's escape.
His excessive drinking kept him from living his core values. Honesty? Dave lied about his drinking and hid bottles of alcohol from his family. Generosity? Because of the time and money it took to support his habit, he never had the time or the money to be as generous toward others as he wanted—except for sometimes paying for a round of drinks at the bar. Success? Dave and everyone around him knew that he was never going to be truly successful when he was drinking almost every night of the week. Love and passion? Over time, drinking had drowned out most of the passion and love in his life—and eventually even the fun of drinking disappeared. Dave was trapped in a horrible state of imbalance, stress, and discomfort. Can you relate to any of this?
Today is about rediscovering and aligning with your core values so that you will never feel like you need alcohol to escape. Legendary civil rights leader Dr. Martin Luther King Jr. reminds us, "If we are to go forward, we must go back and rediscover those precious values."
### The Sobriety System
The Sobriety System, and specifically identifying my core values and the lies I have been telling myself, was a revelation for me. I didn't realize how out of alignment my actions were from my core values, and how many beliefs I was holding on to that were keeping me from ever getting sober. The action steps for these two days significantly changed my life—increasing my self-confidence, improving my self-worth, and ultimately making me believe that a life thriving in sobriety was possible.
—COURTNEY
30-Day Graduate from Newark, New Jersey
The 30-Day Sobriety Solution is based on the Sobriety System, a model of how your core values, thoughts, beliefs, feelings, emotions, and behaviors affect one another. You can see this dynamic in the diagram below. Over the next three days, you will learn how valuable this system is in helping you make sobriety second nature. This model is an effective tool for quickly identifying the predominant challenges and obstacles that are holding you back from accomplishing your goals.
Let's explore each component of the system. We'll work through it using a common limiting belief that many problem drinkers have—the belief that a sober life will be boring and unexciting. Be sure to refer back to the diagram above as you read through this. For additional examples, visit the companion website.
### The Sobriety System
• Core Values. Core values are the guiding principles—such as honesty, integrity, loyalty, respect, love, fun, family, faith, success, balance, creativity, and justice—that dictate your behavior and action. So if you hold the belief that a sober life is a boring and unexciting life, and one of your core values is "fun," this will inevitably result in your going out drinking and partying in order to fulfill your value of fun.
• Thoughts (Conscious and Subconscious). When you believe that a sober life will be boring and unexciting, your thoughts gravitate to all the various ways that drinking can be fun (drinking games, tailgate parties, uninhibited play and humor). And you think that a life without drinking will not be fun (feeling anxious, inhibited, and left out).
• Beliefs (Limiting Beliefs). The limiting belief is that sobriety is boring and unexciting. Note the double-sided arrows in the diagram above, which indicate that your beliefs affect your thoughts, and your predominant thoughts create your beliefs. For example, when you first started drinking, you probably didn't believe that being sober was boring, but as you went out drinking and had good times with your friends, you started to link fun with drinking and not drinking with not having fun. This created a new belief, which was reinforced by advertisements linking fun to drinking, or by role models who partied frequently. Once a limiting belief is in place, it significantly affects your thoughts and feelings.
• Feelings and Emotions. What you believe determines much of what you feel and experience, and your feelings contribute to and reinforce your beliefs. So once again, if you believe being sober is boring, and you think about going out with others and not drinking, you will likely feel disappointed, anxious, afraid, and resentful. These negative emotions reinforce your belief that not drinking is boring, represented by the double-sided arrow in the diagram. However, if you think about going out and drinking with friends, and remember the positive experiences you had doing this in the past, you will feel excited and happy.
• Actions (Behaviors and Habits). Predominant feelings (such as love, joy, fear, and anger) lead you to act and form habits. Your actions, in turn, also affect how you feel. However, after a certain point, you act automatically and unconsciously in response to your thoughts, beliefs, and feelings.
• Results and Outcomes. Your actions create outcomes, which can affect your core values. If one of your core values is fun, then drinking, at least in the early stages, reinforces this value. You are being run by thoughts, beliefs, and feelings that you are no longer aware of and that are reinforced by the results of your actions. You can get stuck in an endless loop of self-reinforcing, self-destructive thoughts, beliefs, feelings, and behaviors. But with the intervention of tools and processes like these in The 30-Day Sobriety Solution, you can change. By changing any part of the system (new thoughts, new beliefs, new images, new feelings, new behaviors), you can change the whole system.
Reviewing the Sobriety System may lead you to some "Aha!" moments, shedding light on why you do what you do. It may also lead to some scratch-your-head moments, stirring up more questions than answers. Although the system is simple, it can seem complicated initially. That is why today's focus is mainly on core values.
Core values are the starting point of the Sobriety System. If you don't clarify your core values, you cannot leverage the full value of this system. Lisa, a 30-Day Graduate from Minneapolis, Minnesota, shares how today's solution helped her to regain peace and happiness:
In revisiting the Core Values Solution, I have realized it is probably the most effective and powerful solution for me. When going through my journal, I noticed how I had slowly "slipped down the slippery slope" away from some of my core values, and this, in turn, created terribly uncomfortable negative emotions, which, of course, could only be temporarily relieved by a few glasses of wine. Welcoming back and embracing my core values has been the tipping point for me. When I am living in support of my core values, I experience inner peace and happiness, and the desire to drink in order to escape from negative emotions literally evaporates. I'm also feeling grateful today that I did not attend the "wild" Christmas party, which is a big step for me because it angered the hostess and I received a curt and cold email in response, but thanks to The 30-Day Sobriety Solution, I had the resolve to stay on purpose with my core values.
### How Robert Rediscovered His Freedom, Spirit, and Creativity
The 30-Day Sobriety Solution worked miracles for me.
—ROBERT
30-Day Graduate from Vienna, Austria
Robert's father was a workaholic who didn't get home most nights until ten o'clock. And as much as he loved his mother, she was strict, and he couldn't wait to be on his own. Once he turned eighteen, four years after he started drinking socially, Robert moved out.
Like many young adults, Robert was fearless. He knew there was a lot more to life, and his courage, passion for knowledge, and curiosity led him to explore an exciting, diverse world. He studied philosophy, and was drawn to Taoism and Buddhism. He trained in tai chi and kung fu, traveled to other countries and cultures, and discovered a strong spiritual connection to nature. He also embraced his creativity by writing and composing songs and performing.
Then one day, as he neared thirty, everything changed. He got involved with a woman, who got pregnant. Robert knew it was time to "grow up," and they married. His most influential role model was his workaholic father, so Robert's career in sales became his top priority. But his drinking, which had increased throughout his twenties, became a growing concern.
Over the next ten years, Robert worked during the day and drank eight to twelve high-alcohol-content beers (5.5 percent) every night. His occasional attempts to quit would last no more than three days, and whenever he went on business trips, which were frequent, he really let loose.
By the time Robert turned forty, he had two young children and knew he needed to change. He was drinking excessively almost every night, almost completely in private. Robert found The 30-Day Sobriety Solution, and even though he was uncertain and afraid, he was encouraged by some of the changes he made early on in the program. Before the program, the longest he had stayed sober was ten days; after starting the solutions and reconnecting with his passion for learning, he had two months of sobriety and shared this with us:
All areas of my life started to slowly improve at the very beginning. I was very skeptical at first, but the more solutions I completed, the more clear things became. Within two months of starting The 30-Day Sobriety Solution, I was closer to my family, performing better at work, coping with stress much more easily, had lost thirty pounds, was training for a marathon, and, most interesting, my social life actually improved.
Robert also shared that today, Day 10, was his favorite solution, because he rediscovered his core values of freedom, spirituality, creativity, health, and variety. He realized that when his life had abruptly changed by becoming both a husband and a father in less than a year, he had stopped expressing these core values. As he started to reconnect to them again, he became happier and more fulfilled, and his need to escape by drinking was reduced significantly.
Our last update from Robert is a great example of the power of perseverance. Robert has been sober for over two of the last two and a half years. He left his job in sales and has been working toward his MBA. Today he considers his drinking to be moderate. He doesn't get drunk and is excited about all the positive changes he has made. He also used his favorite solutions to give up caffeine and quit smoking. Even though Robert has had a couple of setbacks along the way, he is optimistic and committed to thriving in sobriety.
### Defining Your Core Values
The solutions I learned from The 30-Day Sobriety Solution have been extremely effective in maintaining sobriety and thriving in it; they are the foundation upon which my sobriety is based.
—DAN
30-Day Graduate from Jackson, Wyoming
Our lives are in harmony when we make decisions in line with our core values. But drinking to excess virtually ensures that our Sobriety System is broken and that many decisions will contradict our core values. When you have the self-awareness and courage to align your actions with your core values, you make better decisions, live a more fulfilling and purposeful life, and thrive in sobriety. Zig Ziglar says, "You cannot consistently perform in a manner which is inconsistent with the way you see yourself." Today is about getting in touch with your true identity and letting it shine through all you do.
That means it is time to rediscover your core values—the ones that will empower you in every aspect of your life. You can refer to your core values to help you make difficult decisions, choose a particular lifestyle, select a new career, or parent your children. Let's get started.
### Day 10 Action Steps
I was drinking quite often, and when I drank, it gave me permission to do things that I normally would not do. I had a moral frame of reference. I never played around or anything except when I drank.
—MARTIN SHEEN
Actor in recovery
The following four-step process is one of the most effective methods we have discovered for helping you get in touch with the core values that deep down you want to live by. Be sure to complete this process in your journal. You might enjoy listening to some relaxing music while you work through each step.
Action Step 1: Core Values Discovery Process
• Review and write down the core values that stand out in the list below. First, read through the values listed below. If one feels important to you, write it down. Be sure to trust your instincts. You can always eliminate it later if you decide it isn't a fit. You might find it valuable to view the much longer list on the companion website at <http://Day10.Solutions>. However, you do not want to add values to your list that you think you should have, want to have, or need to have. This is about only what actually matters to you.
accountability
achievement
appreciation
authenticity
comfort
courage
creativity
dependability
excitement
fame
family
freedom
friendship
fun
generosity
happiness
health
honesty
humor
influence
integrity
joy
justice
love
loyalty
openness
passion
patience
peace
power
privacy
recognition
reliability
security
self-reliance
spirituality
status
strength
success
tolerance
truth
vulnerability
wealth
wisdom
• Think of situations, people, movie, or TV characters that really upset, offend, or anger you. This might include coworkers, friends, family members, public figures, or other people in the public eye. You can also include situations or experiences you have had such as driving in heavy traffic, waiting in line, or a pet peeve. As you think of each one, write down which of your values was compromised in each situation. For example, someone who cuts in line might upset you because he violated your values of respect for others and fairness. Or someone who doesn't tip the waiter might upset you because she violated your values of generosity and appreciation. Take a minute to write down any values that apply.
The values you identify in this step are crucial for two reasons. First, these might include your core values, although that is not always the case. Second, and more likely, these are values that you are most guilty of violating, either now or in the past. If this is true, make sure you note which values you might be violating. If you are still doing this action today, underline it; if you were guilty of doing it in the past, put a star by it or boldface it. But be sure you make a note to revisit any actions you identify here that you are still doing. You want to change them.
• Think of the people (dead or alive) whom you admire the most. Include interactions that impressed you or touched your heart. You might include people like Oprah Winfrey, Tony Robbins, Mother Teresa, Taylor Swift, Bill or Melinda Gates, Tom Hanks, Michael Jordan, Nelson Mandela, Bono, Princess Diana, Pope Francis, John F. Kennedy, or a family member or friend. What experiences or activities do you admire? Mentoring others? Taking care of children? Kind teachers? Community activists? Charitable actions? Creative acts? Write down the values or emotions you respect most about these people or situations. For example, Dave and Jack both have had mentors, and some of their values included passion, discipline, love, integrity, and generosity.
The important thing is to make note of what values you see, not what values you think others might see in that person or situation.
• From your list, pick ten values you identify with most and write down how your drinking has played a role in contradicting or violating each of these. If you don't have ten or more, that is fine; just use the ones you have written down. For at least three minutes, make a list of every way your drinking helped make sure that you did not fulfill these values. You might be surprised to discover that drinking has compromised, to some degree, virtually every one of your core values. Here are some examples we have heard from our clients:
• Passion. "I am unable to have passion and enthusiasm in the morning when I am hungover, which sets the tone for the whole day and often has me craving to drink again that night."
• Success. "How can I be successful if I feel like I need to drink to be happy? Would I consider a great leader to be 'great' if he or she depended on alcohol as much as I do?"
• Happiness. "I feel a false sense of happiness when I drink, but in the morning, I realize that drinking only seems to fill this emptiness in my life. I know real happiness is finding my life purpose, but my drinking ensures I won't accomplish that."
• Honesty. "When I drink, I often exaggerate, lie, drive drunk, and make other choices that I find reprehensible."
• Responsibility. "I like to wallow in self-pity and negativity sometimes when I drink, and the mornings after I get really drunk, I feel sorry for myself and act like I am somehow the victim."
Action Step 2: Integrating Your Core Values
Now it is time to use the core values you identified. Update your 30-Day Vision Statement (Day 2) and goals (Day 6) with some of your core values. By integrating your core values into your vision and goals, you instantly create a more authentic and meaningful connection to them, which will dramatically accelerate your successful accomplishments. Please take a minute and complete this now in your journal. For example, if passion is one of your values, see where you might be able to add the words passion, passionate, or passionately into your 30-Day Vision Statement or goals.
———
In The 7 Habits of Highly Effective People, Stephen Covey says, "As you live your values, your sense of identity, integrity, control, and inner-directedness will infuse you with both exhilaration and peace. You will define yourself from within, rather than by people's opinions or by comparisons to others." And it is exactly the same for thriving in sobriety—you need to start making decisions that are in alignment with your core values.
Excessive drinking and core values don't mix! If your actions constantly contradict what you care most about, your attempts at getting sober won't last, and thriving in sobriety will be impossible. So, over the next twenty days, when you are presented with any important decision to make, we challenge you to think about which choice is most in sync with your core values. As this becomes a habit, you will make better decisions, and—most importantly—you will experience more inner peace, happiness, and joy.
On the companion website, you will find additional examples to help you understand and integrate the Sobriety System into your life, as well as the longer list of core values. You can find the site at <http://Day10.Solutions>.
## Day 11
## The Lie Detector Solution
## Confronting Your Limiting Beliefs
The biggest obstacle to creating a wonderful life is self-limiting beliefs. A self-limiting belief is an idea you have that you are limited in some way, in terms of time, talent, intelligence, money, ability, or opportunity.
—BRIAN TRACY
We all have beliefs that influence and often limit our lives. You have beliefs about your capabilities, what success means, how to relate to other people, and why you need alcohol in your life. Moving beyond the beliefs that limit you and hold you back is a critical step toward cutting back or quitting drinking. Today you will learn how to identify the limiting beliefs—the lies you tell yourself—and replace them with positive beliefs that support your path to sobriety.
### Your Beliefs
A core belief is defined as something you assume as true about reality, and as long as you hold on to it, your belief will hold your body's informational fields to certain parameters. You will perceive something as likable or unlikable, distressing or enjoyable, according to how it fits your expectations.
—DEEPAK CHOPRA
Coauthor of Freedom from Addiction: The Chopra Center Method for Overcoming Destructive Habits
Let's revisit the Sobriety System diagram and focus on today's solution—identifying and clearing limiting beliefs that are holding you back.
### The Sobriety System
Beliefs are ideas that you hold to be true. You have beliefs about yourself and the world, whether you are aware of them or not. Your beliefs determine your decisions and your behavior, which, in turn, create your future. A belief can be so powerful that if you are exposed to information that contradicts that belief, your brain will actually filter it out.
A part of your brain called the reticular activating system (RAS) acts as a filter for all incoming sensory data (sounds, sights, smells, taste, and touch). There are about eleven million bits of information per second vying for your attention. It's impossible to attend to all of that, so your RAS filters out most of it. The information that gets through the filter into your awareness includes your strongly felt needs, your stated goals, and your conscious (and unconscious) beliefs.
Just to get a feel for how this works, focus right now on what you are feeling in your right foot. You can feel that, right? But until we directed your attention to it, your RAS was filtering it out because it wasn't relevant to your reading, which was your focus. This filter is useful because it allows you to ignore most unimportant stimuli so that you can focus on the task at hand. The problem is that the RAS may also filter out important information, such as opportunities and resources that could help you achieve your sobriety goals, because that information does not match your dominant belief: I need alcohol to be relaxed, confident, funny, and fun in social situations, or I need alcohol to relax at the end of a long, hard workday.
From the Sobriety System, you can see how thoughts and beliefs are connected. Your thoughts create your beliefs, and your beliefs direct your thoughts. Your thoughts and your beliefs are constantly interacting, and the important point here is that they have a huge impact on your life, your state of mind, and—in particular—your ability to cut back or quit drinking.
Since your beliefs control your RAS (the doorway to your perception), if you are going to change your life, you first have to change the beliefs that are keeping you stuck.
### Believing in Yourself
Your worst enemy cannot harm you as much as your own unguarded thoughts.
—THE BUDDHA
As you learned on Day 5, what you believe about yourself shapes your life. Whether a belief is positive or negative, it affects how you see the world and determines your actions. Ask yourself this: If you believed that something was not possible, would you attempt to do it? For the majority of people, the answer is no, and the stronger your belief that you cannot do something, the more likely you never will. Of course, the opposite is also true. The greater your belief that you can accomplish something, the more likely you will. Why? The answer is simple. Your belief that you can accomplish something will lead you to take the action you need to take. In other words, if you believe you can, you will try. If you believe you can't, you won't.
Limiting beliefs are lies that hold you back. They are lies that you have told yourself, often unknowingly. They constantly conflict with what you really want. Today's solution will help you identify the lies about drinking that have stopped you from successfully cutting back or quitting drinking—until now.
### Change Your Limiting Beliefs, Change Your Life
A human being always acts and feels and performs in accordance with what he imagines to be true about himself and his environment.
—MAXWELL MALTZ
Here are some examples of common limiting beliefs:
• I'm not (intelligent, attractive, rich, old or young, happy) enough.
• Nothing I do is ever good enough.
• I'm not worthy of love (success, money).
• I need more education to be able to get a better job.
• I don't have enough experience.
• I never have the time (or the money) to do what I want to do.
• I'm not safe.
• I don't have what it takes.
Do any of these beliefs sound familiar to you? You most likely have some of these limiting beliefs, but there is another list of lies that may also be holding you back from cutting back or quitting drinking.
### The Lies That Limit You
Unless you become aware of limiting beliefs or lies you tell yourself, and then release them, they will virtually guarantee that you won't be able to cut back or quit drinking. Here are the 11 lies that will keep you from getting sober. We will start with number 11 and work our way up to number 1. As you read them, be sure to note which ones are applicable to you—we will come back to those in your action steps for today's solution.
11. Sex and sobriety suck.
Drinking lowers your inhibitions, so the perception is that sex is better with alcohol. When you drink, you have the false belief that you are braver, more confident, and more sexually open. The truth is that alcohol just lulls you into a false reality in which you often make bad decisions based on poor judgment. Drinking can also result in sloppy sex, poor hygiene, the inability to perform, and unsafe sex, which can lead to sexually transmitted diseases (STDs) and unwanted pregnancies. The bottom line is sober sex can be fantastic. Sobriety is a lot sexier than drunkenness. Sober people are healthier inside and out, maintain a better body weight, and have an attractive, natural energy and vibrancy that make sex much more appealing, enjoyable, and fulfilling.
10. Drinking reduces stress.
How many times have you come home from work thinking that you needed a drink to relax from the long day? We have all been programmed by TV, movies, and commercials to believe that drinking equals relaxation, fun, and reduced stress. The reality is that you create more stress in your life by excessive drinking. You put stress on your relationships and your family, stress on your health, stress on your career, and stress on your finances. Maybe you don't experience problems in every one of these areas of your life, but if you take an honest look at your drinking, we're sure it will be obvious where your drinking is creating more stress rather than reducing it.
9. I have to reach rock bottom to quit drinking.
Millions of people around the world quit drinking every year, and many of them did not wait until they lost their job, marriage, health, or wealth to finally quit. You can choose to quit drinking at any time. As we discussed in Day 1, you can choose your own rock bottom. All it takes is for you to make a clear decision and take action to make a lasting change in your life.
8. Alcoholics are losers.
We've avoided using the word alcoholic as much as possible in this program, but this label and its associated limiting belief often extend to excessive drinkers and problem drinkers. People struggling with addictive behaviors, whether they are full-blown alcoholics or "just" problem drinkers, are stigmatized and they feel embarrassed, guilty, and ashamed. Yet a US government report released in November 2014 found that 29.3 percent of the US adult population meets the definition for excessive drinking. Many are high achievers. This reminds us of a famous Harvard Law School address to incoming students: "Look to your left, look to your right; one of you will not be here by the end of the year." Thinking about it this way, you could say to an audience of US adults: "Look to your left, look to your right; one of you is an excessive drinker." Recovered alcoholics include presidents of countries and corporations, Grammy and Oscar winners, and very likely some of your neighbors and friends. See the list on the companion website.
7. Drinking wine is healthy.
Some drinkers like to quote studies that claim wine is healthy for the heart. More recent research indicates that these benefits are significantly overstated. But if you are honestly only drinking one or two glasses of wine a couple of nights a week (eight-ounce glasses, not a whole carafe of wine), then we would not readily classify you as a problem drinker. But the fact that you are reading this tells us that you are probably drinking a lot more. The truth is that alcohol is a poison—in fact, the word intoxicate originally meant "to poison" someone. Alcohol is used to fuel cars, and as a preservative, disinfectant, and anesthetic. Don't kid yourself into thinking that putting this poison into your body on a regular basis will somehow have a healthy impact. And by the way, you can get resveratrol (the healthy compound in red wine) from supplements.
6. I have an addictive personality.
Problem drinkers may rationalize their drinking by saying they have an addictive personality and can't do anything about it. Studies show that some people do have a genetic predisposition to addiction, but you are not born an addict, and you do have the choice and ability to live a nonaddicted lifestyle. Being human comes with a great gift—the gift of being able to make choices in your life.
5. I can't have a successful career without drinking.
This common myth is held by drinkers who work in sales or any job that requires a lot of networking. They believe that drinking socially with clients is key to establishing a relationship and winning a sale. Many people also believe that socializing with coworkers over drinks is invaluable for building positive and beneficial relationships at work. However, the truth is that drinking negatively affects your job performance by decreasing your ability to focus and your productivity. Would you want your surgeon to operate on you while nursing a hangover? Trust us, your manager, your business partner, your clients, and the accounts you handle do not want their reputation and their success in the hands of someone who drinks excessively. Even if you do need to socialize with clients or colleagues, you can always order a nonalcoholic beverage like a club soda and lime, or even get one that looks like an alcoholic beverage, like cranberry juice and tonic water. Refer back to the bonus solution on Day 7, the Social Solution, for ways to avoid drinking and being judged at parties and networking events.
4. I have a disease.
Many people embrace the concept that their alcoholism is a disease and that, therefore, they cannot change. But if you have diabetes, high blood pressure, or heart disease, you change your diet. You can do the same for alcoholism or excessive drinking. Do not undermine your ability to change your relationship with alcohol by holding on to the belief that you have a disease and cannot change your behavior or recover from it.
3. I am not fun or likable without alcohol.
When you first got drunk, did you feel like you belonged for the first time in your life? Did you feel like a switch had turned on inside of you that made you funny and more interesting, and like you finally belonged? Drinking might seem to make you feel this way, but this is a false perception. Over time, most people no longer find your excessive drinking amusing; instead, they feel sorry for you. They judge you for having a drinking problem, although they will rarely tell you about it. Trust us, when you do get sober, you will hear what many of these people really thought about your drinking. Your drinking was not as hidden, under control, or acceptable as you thought it was.
2. Getting sober is too hard.
Maybe you constantly feel overwhelmed by the desire to drink and plan your next drink—convinced that you will never be free from your compulsion to drink. We know, all of this is scary. If you weren't afraid, you wouldn't be human. Cutting back or quitting drinking requires a dramatic change in your life, and that evokes fear. Think about your greatest accomplishments. They, too, required you to overcome fear, take courageous risks, and push through some tough challenges. If getting sober were easy, you would have done it already. It is hard, and it can be a struggle, but it will also ultimately lead to greater success in virtually every area of your life. We can promise you one thing—you are no different from the countless others who have overcome their addiction or abuse of alcohol to live meaningful, productive, and happy lives. You do have what it takes to accomplish your goal of sobriety. Keep reminding yourself of that no matter how hard and challenging it might seem to you right now.
1. It is not possible to be sober and happy and excited in life.
This lie is the most pervasive among problem drinkers. You believe that you cannot get sober, and even if you could, you wouldn't love life sober. Out of the countless people we have worked with, we have never heard anyone say that he or she had no concerns about being able to enjoy life sober. Dave recalls in his very early sobriety looking into the eyes of people in disbelief as they shared that they were truly happy sober and that even the idea of drinking no longer burdened them. We know this truth can be hard to believe, but we ask you to trust us. You can be sober and have a life filled with incredible joy, meaning, and passion.
The first action step for today is to write down which of these top 11 limiting beliefs/myths/lies you have believed up until now. Then take a moment to add to this list. Think of any other limiting beliefs you might have that keep you from getting sober that are not on this top 11 list. Have you embraced any other limiting beliefs that are directly tied to your drinking? Here are a few more to consider and see if they fit:
• Drinking gives me freedom, and if I stop drinking, I will lose my freedom. I don't like anyone telling me what I can and cannot do.
• There is no way I can become a "normal" drinker because complete abstinence is the only thing that works for problem drinkers.
• What makes me successful in my career is the "reward" of drinking at the end of a long day or week.
• I just never thought I could be someone who didn't drink.
• It is going to be too physically painful to quit drinking.
• I need to drink to feel love and be connected.
• Not only do most people drink, they also drink at the same levels I do.
Go ahead and add any of these limiting beliefs that fit to your list, as well as any new ones that might occur to you. We will come back to them soon.
### How an MBA Graduate Learned to Cut Back Drinking
Ann couldn't imagine a life without alcohol, at least not a life where she was happy. She was in her early thirties, had an MBA from a prestigious Ivy League university, and was living in New York City. With no kids, she was enjoying the fast-paced life the city offered her. She was working hard, building her career, and going out with friends many nights of the week.
Ann started drinking in high school. It helped her feel like she fit in, she had more fun, and she felt more confident and independent. In college, she drank frequently and at times to excess, but so did her peers, so she wasn't concerned. But as she reached her midtwenties, she started to realize she was different—that her drinking had become a problem.
Before Ann found The 30-Day Sobriety Solution, she had already been to a therapist to deal with her drinking concerns and made attempts to quit and cut back, but nothing lasted. She continued to drink and continued to see it consume more and more of her life and her free time. But with The 30-Day Sobriety Solution, she started to see what her new life could look like, and realized that sobriety and having fun were not mutually exclusive.
Ann worked on the 30-Day solutions with the same tenacity with which she earned her MBA. Within weeks of starting the program, she found she was able to start socializing, and although it wasn't easy at first, she started having fun going out with friends and not drinking. And not just going out once a week, but going out as often as she did when she had been drinking. She even enjoyed the process of deciding which new nonalcoholic concoctions she would order.
After only a couple of months, Ann celebrated her first sober birthday in eighteen years. For the first time in her life, she was excited about sobriety. Fast-forward almost a year and Ann found that she was one of the few who was able to drink occasionally. She could go out and have a drink or two without any negative consequences. Ann's story is a testament to the fact that you can actually be happy and sober at the same time. And that for some, you might be able to return to a life of normal drinking.
### What Do You Think About Sober People?
The second action step for today is to consider what you see and believe when you imagine sober people. What are their predominant traits and characteristics? Do you think they are happy or sad? What do you think they do to have fun? Do you think they are boring? Do you think they would judge or dislike you? Go ahead and take a minute to write down your answers before moving on.
Now ask yourself the following question: Do you like the representation you have created in your mind of these sober people?
You probably don't. And how can you ever get sober if you don't even like the image of what sobriety represents to you? If you believe that being sober equals being unhappy, you will never take the steps to thrive in sobriety. Your beliefs create your future because ultimately we all are well-oiled self-fulfilling-prophecy machines.
This list may have similarities with the limiting beliefs you identified in the last action step, and it may help you identify some additional limiting beliefs that you overlooked. Be sure to add any new beliefs to your list.
Now that you have awareness of your limiting beliefs, you're ready for the next step, which is shifting those beliefs. In order to shift the limiting belief that you are not fun and likable without alcohol, you need positive models of sobriety. Think of all the people you know, or know of, who don't drink or drink very little and are positive role models. Most likely, even though your initial image of a sober person isn't positive, when you actually consider these specific people, you will realize how wrong your belief or image was regarding sober people. Now let's take a look at some high-profile examples.
### What Do Seven of the Top Ten Grossing Actors of All Time Have in Common?
I just decided that I pretty much got everything I could get out of it. I investigated wine and spirits thoroughly, and they certainly investigated me as well, and we found out that we got along beautifully, but maybe too well.
—JOHNNY DEPP
Actor
Consider the following statistic that shatters many of the top 11 lies that problem drinkers tell themselves. As of the writing of this book, at least seven of the top ten grossing actors of all time are either in recovery (Morgan Freeman, Samuel L. Jackson, Robert Downey Jr.), have talked openly about a history of alcohol abuse and either cut back dramatically or quit (Bruce Willis, Johnny Depp), or have chosen not to drink at all (Eddie Murphy, Tom Cruise).
Think about this for a minute. Seven of the top ten actors of all time don't drink. Yet they work in an incredibly stressful and competitive industry—one that requires lots of socializing and networking to be successful. If you are concerned with how you might be perceived by others for not drinking, remember this list. Do you think their peers judge them for their choice not to drink? Hardly!
And guess what the following celebrities all have in common: Jennifer Lopez, Jim Carrey, Natalie Portman, Warren Buffett, Brett Favre, Diana Ross, Andy Murray, Donald Trump, Elton John, Tobey Maguire, Muhammad Ali, Prince, and Shania Twain. None of them drinks
As you might recall from Day 5, teetotalers abstain from alcoholic beverages completely, and the list above contains just a few of the people who consider themselves teetotalers. And almost every one of them never had a problem with alcohol—they simply decided that sobriety made them happier and more fulfilled.
### Where Do Your Limiting Beliefs Come From?
I was afraid that I wouldn't be able to work anymore if I quit drinking and drugging, but I decided (again, so far as I was able to decide anything in my distraught and depressed state of mind) that I would trade writing for staying married and watching the kids grow up. If it came to that. It didn't, of course. The idea that creative endeavor and mind-altering substances are entwined is one of the great pop-intellectual myths of our time.
—STEPHEN KING
Before we show you how to change your limiting beliefs, let's look at where they come from. Limiting beliefs are created in many different ways, but mostly they are created during an emotionally powerful event that happened in your childhood. For example, the belief "I don't fit in" or "I am not good enough" may have stemmed from being made fun of, or losing your best friend to someone else, or getting picked last for the team in gym class. But when you had your first drinking experience and suddenly felt like you belonged, you felt, even if only temporarily, like you were good enough. Through these experiences, you created—and then reinforced—a strong belief that drinking alcohol meant having friendships and feeling connected to others, and that not drinking meant not being as funny or interesting, or being isolated and lonely.
When Dave took the time to look for the source of his belief that it was not possible to be sober and happy in life, he quickly found it. Throughout junior high and high school, Dave was unhappy, but when he got to college and made good friends, he started having lots of fun. He suddenly became happy. But all of this happened only after he started drinking, so he created a strong association (and ultimately a self-destructive belief) that being happy, having friends, and having fun all came from drinking. This belief was continually reinforced over most of his "drinking career," until he finally became aware of it and changed.
Another common experience is divorce, which shapes children's beliefs about love, self-worth, relationships, marriage, and success, which can all affect your tendency to drink. If you felt abandoned or unloved, or somehow blamed yourself for the divorce, then alcohol may help you feel connected and loved. Alcohol also might help you mask the pain of traumatic events from your childhood, giving you a sense of relief and pleasure. But that underlying pain still exists, waiting to resurface again and again until you face it, feel it, and heal it.
Here's the interesting thing about limiting beliefs—they form in response to an event that happens in your life, but the event itself has no inherent meaning. The only meaning any event has is the meaning you give it. It is how you uniquely interpret the event that gives it its meaning. That is why two people can experience the same thing and respond to it completely differently. You each form a different interpretation of the event and therefore attach a different meaning to it. The problem is that most of us assign negative meanings about ourselves or about life to events that don't turn out as we hoped. It is this negative interpretation or meaning that we assign to the event that creates a limiting belief. Here are some examples:
"I lost the race—I am not a good athlete."
"I got a bad grade on that test—I am not good at math."
"I failed at quitting drinking again—I will never be able to get sober."
"Jean broke up with me—I must not be lovable."
"I didn't get that promotion—I must not be good enough to deserve it."
Once you change the interpretation or meaning that you assign to the event, you empower yourself.
"I lost the race—I need to train harder next time."
"I got a bad grade on that test—I know I am as smart as the people that aced it. I just didn't prepare as much as I should have."
"I failed at quitting drinking again—I know I can beat this if I just persevere long enough. What can I learn from that experience and do differently in the future?"
"Jean broke up with me—we must not be well suited for each other. I'll keep dating and searching for my ideal mate."
"I didn't get that promotion—I know I have what it takes. I just need to learn some new skills and develop myself personally."
You can change the meaning of any event to something positive. Just like the examples above, you always have a choice. You can interpret the event in a negative context and create or reinforce a belief that will hold you back, or you can create a positive, empowering belief that will propel you forward.
Now we will look at the limiting beliefs you just uncovered, determine the source of those beliefs, and create new beliefs by giving new and more positive meanings to the events in your life. Imagine how your life would change if you started giving positive interpretations and meaning to the events in your life rather than negative ones.
### The Cross-Examination!
Both behavior and feeling spring from belief. To root out the belief which is responsible for your feeling and behavior, ask yourself, "Why."
—MAXWELL MALTZ
Let's do a quick review. The first action step for today was to note which of the top 11 lies were most prevalent in your life. Then you added to this list any that you uncovered by reviewing other common myths. Next, you captured what the characteristics and traits of a sober person look like to you, and you acknowledged how they might be in conflict with your goal to thrive in sobriety. And last, you acknowledged some positive sober role models.
Your third action step is to look at your own personalized list of lies and circle the top five that you think could hold you back the most from getting and staying sober. Then cross-examine each one, just like a lawyer would do. Make a strong case as to why that particular belief is not true and how it stops you from living a life that embodies the core values that you uncovered yesterday.
Alan Cohen, author of Why Your Life Sucks . . . and What You Can Do About It, suggests approaching it this way. "Imagine two lawyers in a courtroom inside your head. One is arguing for your possibilities and you achieving your goals. The other is arguing for your limits and why you don't deserve what you want. Who will win? The lawyer whom you pay the most. The way you pay these lawyers, however, is not with money; it is with your attention."
One of Dave's limiting beliefs was that he couldn't be successful in his career without drinking. When he started to question this belief, he came to some important realizations. He was more present on the job and was a better employee when he wasn't hungover. He recognized how consumed he was during the day with thinking about and planning when he would drink again. He realized that he overestimated the quality and depth of the relationships he developed with coworkers and clients while drinking; in fact, when he spent time with them and didn't drink, he realized how consumed he had been with his own drinking and hadn't noticed that they drank a lot less than he did. And those who drank as much as or more than he did were so into their drinking that they didn't really care about him. Those who did care had their own issues with alcohol, which eventually had an impact on their ability to succeed at their jobs. Ultimately, Dave realized that what every manager and coworker cares about most is the quality of your work and your ability to work well with others. He clearly saw that his drinking was hurting him more than helping him.
The bottom line is that when you begin to take an impartial point of view, it becomes painfully clear how false and limiting your old beliefs are and why you need to change them.
Now consider what will happen if you continue to let your old beliefs guide your choices. Where will you be six months, one year, or five years down the road? What will have happened to your health, your finances, and your relationships? Continuing to embrace your old beliefs will only create more pain. It also means you won't be living by your core values. You won't be a positive role model to your family, friends, and peers. You won't live a long, healthy, fulfilled life. The list of negatives is endless. Take the time to honestly recognize and acknowledge the pain in your life that comes from hanging on to your limiting beliefs.
### New Beliefs for Your New Life
If you believe you can, you probably can. If you believe you won't, you most assuredly won't. Belief is the ignition switch that gets you off the launching pad.
—DENIS WAITLEY
Now comes the fun part. It's time to create new beliefs to replace the lies that have been holding you back. New beliefs that support you thriving in sobriety. Beliefs that capture the way you want to be, act, and feel. Beliefs that support your core values, which you identified yesterday. Here are examples of new beliefs that address some of the limiting beliefs or lies we discussed today. You can use these or write your own.
Old Belief. It is not possible to be sober and still be happy and excited.
New Belief. It's easier to experience ultimate happiness, excitement, and fulfillment when I am sober. Or: It's easier to be happy and excited when I am sober.
Old Belief. I am not fun and likable without alcohol, and drinking reduces my stress.
New Belief. My sobriety makes me more fun, authentic, and present with my friends, family, and coworkers. Being sober gives me all the time and energy I need to manifest my goals.
Old Belief. Getting sober is too hard.
New Belief. I have everything I need to create a happy and fulfilling sober life.
Old Belief. I can't have a successful career without drinking.
New Belief. I can create a more successful career when I am sober because I am more awake, clearheaded, and focused.
As you can see, this is pretty straightforward. Write your new beliefs in a positive way (avoid negatives like no and not) and write them in the present tense. Follow the same guidelines from Day 2 that you learned in the Purpose Solution.
Once you have written your new beliefs, which support your values and goals, you are on your way to making some big changes. Hopefully you see how every solution builds on the previous solutions. Now recall the pleasure principle from Day 3 and the Pendulum Solution. The best way to make sure that these new beliefs stick is to link so much pleasure to them that you are highly motivated to act on them. And yes, we know we have asked you to do this before, but repetition is one of the keys to your success in this program.
So take a moment to close your eyes and dream about this "new you." Allow yourself to get excited and really feel what it will be like to be the "new you," as if it were happening right now. How are your friends, family, and coworkers responding to you? Have you lost weight? Are you in better physical shape? Are you more successful in your career? Have you saved more money or rewarded yourself with something you have always wanted but couldn't afford before? Really see it, feel it, and believe it. The more you can picture yourself acting on these new beliefs, the more the "new you" becomes real, which will cause you to make changes more easily and effortlessly. So stop reading now and take a few minutes to do this visualization exercise.
When you are done, be sure to put the list of your new beliefs somewhere where you will see it and review it every day.
### Day 11 Action Steps
For about ten years, I've been pretty much not drinking. I went through a normal kind of late-teens, early twenties drinking, but it was a choice I made, because I didn't think it was very good for my life.
—CHRISTINA RICCI
Emmy Award–nominated actor
Here is a brief review of today's action steps. Be sure to refer back to the text if you need help remembering how to complete each one.
• Capture your limiting beliefs. Review the 11 myths/lies/limiting beliefs and write down which ones you believe. Then add to this list any other beliefs that have held you back from getting sober. The best way to uncover these is to think about why you drink and what scares you most about not drinking, and then ask yourself if those fears are real or if they are simply limiting beliefs.
• Write down the characteristics and traits of a sober person. Be sure to note if any of these traits is also limiting beliefs that you overlooked in the first action step. Then list any friends, family members, or public figures that you respect who are sober or are "normal drinkers," and review the list of celebrity teetotalers on today's companion website.
• Cross-examine your limiting beliefs. Pick the top five limiting beliefs that have been keeping you from getting sober. Next, write down how each of them limits you and what your life will look like if you allow these limiting beliefs to continue to run you. Then approach each limiting belief like a lawyer and create a strong case for why it is not true. Be sure to write this down in your journal.
• Write new beliefs to replace your limiting beliefs. Capture the way you really want to be, act, and feel. And then take a minute to imagine how it will feel to be living your life in alignment with those beliefs. Keep a list of these new beliefs in a place where you can easily review it daily for the next nineteen days.
Be sure to visit the companion website for today at <http://Day11.Solutions>, where we walk you through additional examples for each of today's action steps.
## Day 12
## The Subconscious Mind Solution
## Leverage the Power of Your Subconscious Mind
I discovered that when we compete the conscious and the subconscious, the subconscious always wins. So we're functioning 95 percent of the day with a more powerful mind that was programmed by other people with limitations that will prevent us from going someplace, yet we can't see it unless we purposely become aware of it.
—DR. BRUCE LIPTON
Author of The Biology of Belief
Have you ever driven a car, arrived at your destination, and then realized you don't remember any of the details of driving there—the turns, lights, or traffic you just went through? This is one of the most common examples of the power of your subconscious mind.
Your subconscious mind is far more powerful than your conscious mind. Your subconscious mind directs your choices and your drinking habits more than your conscious mind does. Today, with the Subconscious Mind Solution, we conclude our deep dive into the Sobriety System by teaching you how to use the power of your subconscious to thrive in sobriety.
### The Recording of Your Life
The diagram of the Sobriety System illustrates how we want our life to be in harmony with our core values. When you contradict those values, you experience internal conflict, which contributes to your desire to drink. Yesterday we covered the importance of your beliefs and how they drive the decisions you make that either support or conflict with your core values. However, many of your beliefs are hidden in your subconscious—and are therefore harder to become aware of and change.
The subconscious is defined as "the mental activities [ideas, impressions, urges] just below the threshold of consciousness." It is a part of the mind that we are not fully aware of, but that influences our feelings, judgments, and behavior. Your subconscious contains all of your "programming." Like a video recording device with unlimited storage, it keeps a record of everything that happens to you and around you; however, it plays back only the most powerful recordings or programs from your past.
The most powerful programs in your subconscious are your beliefs. When you have a strong belief system that is in sync with your core values, the benefits are extraordinary. Strong limiting beliefs, like the ones you uncovered yesterday and others that are still buried in your subconscious, impede your ability to cut back or quit drinking. The Subconscious Mind Solution will teach you the power and significance of the subconscious and how to work with it to thrive in sobriety.
### Most of Your Behavior Is Unconscious
Your subconscious mind does not argue with you. It accepts what your conscious mind decrees. If you say, "I can't afford it," your subconscious mind works to make it true.
—DR. JOSEPH MURPHY (1898–1981)
Author of The Power of Your Subconscious Mind
Research suggests that most of your behavior is unconscious. Think of your consciousness like an iceberg, where the conscious mind is just the tip, and the rest of the iceberg below the water, which is most of it, represents your subconscious. The amount of mental activity occurring outside your conscious awareness is massive.
It is understandable to be a little skeptical about how much your subconscious directs the decisions you make every day. Up until recently, the study of the unconscious was often dismissed as pop psychology; however, recent science has proven that the influence of the subconscious in our life is immense.
Dr. Bruce Lipton, a leading researcher in psychology and the bestselling author of The Biology of Belief, explains that our subconscious is "more than a million times more powerful than the conscious mind." The subconscious mind can handle twenty million bits of information per second compared with the conscious mind, which can handle only forty bits of information per second.
Think about when you first learned to drive a car. The amount of information you had to absorb all at once was overwhelming, especially if you learned to drive a stick shift. You had to keep your eye on the road in front of you, regularly look in your rearview mirror, pay attention to the traffic around you, watch for traffic signs and traffic lights, stay under the speed limit, and follow the rules of lane changing, turning, yielding, and merging with other traffic.
Having a conversation with a passenger, changing the radio station, or drinking coffee was virtually impossible when you were learning to drive. Now fast-forward to today. When was the last time you went on an errand and didn't even remember the details of driving? Maybe you were "lost" in a great song or were in the middle of an important conversation, and the next thing you knew, you were at your destination. That happened because your subconscious took over. It had been programmed countless times over the years to drive safely. There is too much going on for your conscious mind to process it all, so when your focus shifts, your subconscious kicks in. And most of the time, you are not even aware it is happening.
You may believe that your conscious thoughts are creating your reality and that by changing your conscious thoughts, you can learn to thrive in sobriety. However, your behavior is far more representative of your subconscious than your conscious. Dr. Drew Pinsky, addiction expert and producer and star of the reality-TV show Celebrity Rehab, says that addiction "operates outside of consciousness."
Remember, your beliefs lead to your actions and behaviors, so until you can change your subconscious limiting beliefs, you will sabotage your efforts to become and remain sober. And you might not even know how or why you're sabotaging yourself, because just like when you are driving, your subconscious takes over without you consciously deciding when and where.
### Lottery Winners Going Bankrupt
According to a recent study, lottery winners declare bankruptcy at twice the rate of the general population. How is this possible? It's because the subconscious, which includes your limiting beliefs, sabotages you. Your subconscious works much like a thermostat—if you set the thermostat at 70 degrees, and the temperature goes up or down, your air-conditioning or heat will turn on. Similarly, if you are programmed to believe you don't deserve to have a lot of money, then when you come into a sudden windfall, your subconscious will kick in and bring you back to where it believes you should be—your comfort zone.
This operates the same way with sobriety. If deep down your self-concept and self-image are of being a "drunk" or high-functioning alcoholic, your subconscious will always work to bring you back to this core identity. If you don't first change these limiting beliefs and images in your subconscious, you will have a hard time making progress and staying sober.
In his book Subliminal: How Your Unconscious Mind Rules Your Behavior, bestselling author and physicist Leonard Mlodinow captures the importance of understanding the interaction between our awareness and subconscious when he writes, "Our subliminal brain is invisible to us, yet it influences our conscious experience of the world in the most fundamental of ways."
Mlodinow mentions an interesting study on how the subconscious can influence our actions, totally outside of our awareness. Ironically, this study was done on wine purchases.
In the study, four French and four German wines were placed in an English supermarket, and French or German music was played in the background on alternating days. On the days when French music was played, 77 percent of the wine sold was French. And on the days when German music was played, 73 percent of the wine purchased was German. This is a powerful example of how our subconscious can be influenced and how it can exert influence over our decisions without our conscious awareness.
Bill Wilson, the cofounder of Alcoholics Anonymous, writes, "How shall our unconscious, from which so many of our fears, compulsions, and phony aspirations still stream, be brought into line with what we actually believe, know, and want! How to convince our dumb, raging, and hidden Mr. Hyde becomes our main task." We agree. When you get your subconscious synchronized with what you really want—your conscious desires and dreams that you have started to identify during these first two weeks—it becomes much easier to achieve and maintain your desired results.
### Your First Six Years of Life
Many psychologists believe that the first six or seven years of a child's life completely form his or her personality, especially the most powerful beliefs, because during this time, the subconscious is easily programmable. Think of this programming as if you are writing notes with a pencil and you can use only one sheet of paper. The first time you write something, it's clear and easy to read, but once you fill up the page, you have to erase what you wrote earlier in order to write more. The more often you write on the paper, the harder it is to erase the previous writings. This is one of the reasons why early childhood is the best time to teach children languages and how to play instruments, and also why, as we explained on Day 4 in the Forgiveness Solution, traumatic events from your childhood leave such a lasting negative impact.
But don't worry; all of this can be changed. The great news is that a lot of the previous days' solutions have already started to reprogram your subconscious, and over the next two weeks, you will learn many other solutions that work at the subconscious level as well as at the conscious level. Let's look at the Sobriety System one last time.
### The Sobriety System
Even though we have placed the subconscious under thoughts, the subconscious really serves as the "engine" that powers both your thoughts and your beliefs.
For example, when Dave was five years old, his eight-year-old brother showed him a gallon jug of wine (with a screw cap) that was stored in a lower cabinet in the kitchen. His brother told Dave that if he wanted to "feel good," he could drink some of the wine. One night after Dave's parents had put him to bed, they discovered him in the kitchen, drinking from the wine jug. He doesn't know how many times he did this, but you can see how Dave's subconscious created a strong belief linking drinking to feeling good. While this is a common belief for many of us, the fact that this programming was formed at an early age made it much harder for Dave to break. However, once he understood this, he used the same techniques you are learning here to reprogram his subconscious with the belief that being sober is what really makes him feel good.
### The Elephant in the Room
When you wrote your 30-Day Vision Statement on Day 2 and set goals on Day 6, we instructed you not to write them in the negative. The conscious mind can understand the meaning of negative words such as no, not, don't, and won't. It also understands the meaning intended by the phrases "quitting drinking" and "cutting back drinking." However, numerous studies have proven that the subconscious mind does not understand negatives. So if you are saying to yourself, "Do not drink," or "I will not go to bars," or anything that you do not want yourself to do, your subconscious does not process the not. It hears those statements as "Drink" and "Go to bars," and will sabotage your intention to cut back or quit drinking.
When you read the words "Don't think about elephants," you most likely just pictured one or more elephants in your mind. (You did, didn't you!) And when you tell young children not to do something, quite often they do exactly what you told them not to do. This isn't necessarily because they are trying to defy you; it's because the prefrontal cortex (the part of the brain that is responsible for analyzing thoughts and regulating behavior) is not yet fully developed and they did not process the not or the don't. Think of it this way. If you tell a two-year-old not to slam the screen door, the subconscious forms a picture of slamming the screen door, and that's what the child does. Instead, you could say, "Please close the screen door gently."
Once you stop focusing on and talking about how to cut back drinking or quit drinking and put more energy into deleting old programming and installing new programming with the focus on the positive thoughts and images of a sober and happy life, you experience a dramatic shift in your desire to drink.
### Changing Your Subconscious
The solutions in The 30-Day Sobriety Solution have changed me in ways I never imagined possible. On a conscious level, the changes are easy for me to recognize, but the most unexpected and powerful result of this program is that I finally feel like I have changed my subconscious programming and limiting beliefs that were always sabotaging my ability to get and stay sober. Today my life and my new story are exciting, and I know these great changes are going to last.
—HANNAH
30-Day Graduate from Sydney, Australia
Whatever you consciously and repeatedly think about, accompanied by strong emotions, will reprogram your subconscious over time. It really is that simple. And throughout this entire program, we are teaching you the most effective techniques for accomplishing this.
For example, you might be sick of the phrase "thriving in sobriety." We use it a lot, but there is an important reason why. Although cutting back or quitting is the goal you started with, that is just a step toward the larger goal of living a happy and fulfilling sober life, or thriving in sobriety. And we want to continually activate that positive image and desire. On Day 1, we defined sobriety as "moderation in or abstinence from consumption of alcoholic liquor or use of drugs." So when we use the word sobriety, even if your goal is to cut back, this still applies. The strategy behind using the phrase "thriving in sobriety" repeatedly throughout each solution is to reprogram your subconscious to focus constantly on that outcome.
### Day 12 Action Steps
If there is one solution that can put thriving in sobriety on cruise control in your life, it is the Subconscious Mind Solution. And yet today we are not going to give you a lot of exercises to complete. Rather, we just want to stress the importance of working to reprogram your subconscious and the role that plays in creating and sustaining a life of thriving in sobriety.
• Reprogram yourself for success before bed. While you are lying in bed at the end of the day, spend five minutes focusing on your goals, dreams, and desires, including your thriving-in-sobriety goals. Doing this before you fall asleep is a very effective way of helping to reprogram your subconscious overnight, because unlike your conscious mind, your subconscious never sleeps. Simply take time to visualize all your dreams and goals as already completed. What would you be seeing, hearing, and feeling?
• Complete all of the guided recordings. On the companion website, we have included guided imagery exercises for many of the past solutions that are perfect for reprogramming your subconscious. If you haven't done them yet, please do so today. In addition, we review some past solutions and explore more deeply how they are already helping to reprogram your subconscious.
• Identify your subconscious drinking links. Set aside a few minutes to write in your journal the situations, times, places, and emotional states (happy, sad, angry, bored) you were in when you used to drink, and also note if any of those situations were times when you really craved drinking. Then take a minute and see if you can recall any incidents from your childhood that helped create these links. For example, maybe every night when your dad came home from work, he would have a drink to "take the edge off." Or maybe no one ever watched a football game on TV without a six-pack of beer. Or maybe someone in your home would become abusive when he or she drank. Or maybe the only times that your parents seemed to have fun and relax were when they drank. Or maybe Saturday night was always party night with lots of alcohol.
Take the time to acknowledge these subconscious "lessons" you learned as a child. They can reveal the source of the deep programming that has been causing your greatest struggles. However, don't worry if you can't recall any childhood events—just the process of consciously looking for those events now can lead to remembering some of them in the following weeks or months.
Be sure to visit the companion website at <http://Day12.Solutions>, where we address hypnotism, one of the concepts that relates directly to the topic of the subconscious—why it works for some, why it doesn't for others, and how we are all hypnotized.
## Day 13
## The Tapping Solution
## Tapping Away Your Desire to Drink
EFT tapping can make the entire recovery process both easier and shorter, potentially preventing relapses and giving addicts a way to treat themselves on a day-to-day, even moment-to-moment, basis.
—DAVID ROURKE
EFT tapping practitioner who specializes in addiction recovery
Cutting back or quitting drinking is not easy, but thanks to Roger Callahan, Gary Craig, and others, there is now a technique that can make it much easier. That technique is popularly known as EFT, Emotional Freedom Techniques, or tapping.
First developed as the Five Minute Phobia Cure by Dr. Roger Callahan to cure phobias, fears, and anxieties, it was later further developed and popularized by Gary Craig, Dawson Church, Nick Ortner, and others to relieve stress, release negative emotions, make physical symptoms (including pain) disappear, dissolve and replace limiting beliefs, and reduce or eliminate cravings and addictions.
Gary Craig called this new system of emotional healing EFT Tapping, or simply tapping, because it combines focused thought with gentle tapping with your fingers on a series of seven to twelve acupuncture points. These acupuncture points lie on a set of meridians, or pathways in the body where vital energy is thought to flow. It is simple to learn and easy to perform on yourself, and it can radically accelerate the process of recovery. Today we will teach you exactly why tapping works, share with you some breakthroughs that others have experienced using it, and show how you can use tapping to thrive in sobriety.
### The Stupidest Thing You'll Ever Do?
When we first introduce tapping to people, most of them think it's weird, too simple to actually work, and not something you would want anyone else to catch you doing. In the following excerpt from The EFT Manual by Dawson Church, a patient named Kari Reed describes her experience with—and her initial impressions of—the therapy:
Tapping is probably the stupidest thing you'll ever do. Think about it—there are "special places" all over your face and body, and if you bang on those long enough, while saying some words and imagining some stuff, all your problems will go away. And let's face it, you know that when you're sitting there, your eyes closed, trying to picture your inner four-year-old, touching your face like a crazy person with a nervous tic, and mumbling that you truly and deeply love and accept yourself anyway, you probably look pretty stupid. In fact, we can go ahead and remove the "probably"—you look stupid. The problem with this stupid thing is that it actually works.
Like many others, we were skeptical about tapping at first, but once we tried it on ourselves and with our families and friends, we were blown away by its speed and effectiveness. Since then, we have used it with thousands of people in both individual coaching sessions and large group trainings to release fears, anxieties, limiting beliefs, traumatic memories, and cravings. Almost everyone we have used tapping with experiences major breakthroughs in just minutes—results that would have previously taken hours, and even years in some cases. Jack became so impressed with the technique that he even teamed up with tapping expert Pamela Bruner to coauthor the book Tapping into Ultimate Success: How to Overcome Any Obstacle and Skyrocket Your Success.
### How Tapping Is Changing Recovery
Tapping is a technique that can help you successfully quit or cut back drinking in as little as 30 days. Breaking an addiction or a strong habit no longer has to be painful or require the same constant effort as it did just a few years ago. You don't have to rely solely on your willpower or confessional meetings. Tapping combines focused thought with gentle finger tapping on a few key acupuncture points on the hand, head, and chest to reduce cravings, reduce the physical symptoms of withdrawal, clear emotions such as guilt and shame, replace limiting beliefs, and resolve any original underlying emotional issues that led to the alcohol abuse in the first place.
Here's an example of how powerful tapping can be. A patient named Cath visited Mair Llewellyn-Edwards, a master at tapping, as a last resort in her fight against her alcohol addiction. At that time, she was only just managing to hang on to the threads of her life as a professional and a mother of two young children. Two months before her visit, she had been on Antabuse, a medication that makes alcohol unpalatable, to help her abstain. However, her problems and cravings remained, and without alcohol, she had no way of tranquillizing her anxiety. She was in an emotionally volatile state.
During her first session with Mair, she learned the basic tapping procedure, focusing on getting rid of a slight headache. After two rounds of tapping, Cath said her mind felt clearer and her headache felt different. On the third round, her headache was completely gone. Cath went home with the instruction to use tapping on every concern before her next appointment the following week.
At Cath's second session, she was exuberant. She had used tapping to reduce her anxiety about everything and everyone! Tapping made her calm and confident each time she used it. And it helped her realize that she had been masking her anxiety with alcohol, which is why she would drink on her way home before facing her family at the end of a hectic day.
Tapping throughout her busy day as well as on her way home enabled Cath to reduce the buildup of stress at its source. It gave her confidence to face situations she had previously feared.
### How It Works
When you experience emotional or physical pain, your brain's stress response kicks in. Whether you're upset by a current event or an old memory, the emotional part of your brain releases a cascade of stress hormones like cortisol and adrenaline, which then communicate the stress to your entire body in a matter of seconds.
But by gently tapping on a series of eight acupuncture points on your body when you feel stressed, a second signal travels to your brain, telling it that you're safe. This signal that you're safe breaks the brain's association between the bad event and the stress response. And once that link is broken, it usually stays broken.
Here's how it works in relation to reducing cravings for alcohol—when you get a physical craving, your body becomes stressed, and you feel anxious. In the past, drinking was a way to relieve that stress and anxiety. But by tapping, you can calm your anxiety more easily and with fewer harmful side effects than drinking. Specifically, you calm a part of your brain called the amygdala, which disrupts production of the stress hormones that were flooding your body, so your body and mind can relax. And when your body and mind relax, your "need" for a drink disappears.
Gloria Arenson, author of the book EFT for Procrastination, specializes in helping people overcome compulsive behaviors. She has found that people struggling with an addiction or abuse problem usually struggle with a kind of "superstress." This occurs when they feel totally powerless about something in their life and reflexively tell themselves, It's really awful, and there's nothing I can do about it!
Superstress creates an imbalance in the feel-good brain chemicals dopamine and serotonin, which produces a craving for any substance (such as alcohol) that will make you feel good by raising the level of those neurotransmitters. The problem is, the relief is only temporary, and when the stressful situation continues, the craving returns. The cool thing about tapping is that it replenishes your levels of dopamine and serotonin, and so the craving stops.
A good deal of scientific research shows that tapping is effective for reducing cravings and addictions. For a study published in the journal Integrative Medicine, Dawson Church and Audrey Brooks examined cravings among 216 health care workers before and after tapping. In the study, trays of alcohol, cake, and candy were brought into the room, so that the participants could get fully in touch with their cravings. The participants then identified childhood events linked to their cravings, such as "Mommy always gave me ice cream after my piano lesson" and "Dad always had a beer with me on weekend days after I turned fifteen. He died when I was eighteen, and I miss him so much." After about thirty minutes of tapping on the emotional intensity related to those childhood events, their cravings dropped by an astonishing 83 percent, and symptoms of anxiety and depression dropped by an average of 45 percent.
### Five Ways You Can Use Tapping
People have all kinds of reasons for drinking, but most involve unresolved emotions, including stress, anxiety, and fear. Drinking is one way to tranquilize difficult emotions and keep them under control. What we're discovering with EFT is that it's possible to eliminate stress, anxiety, and other damaging emotions altogether, so the need for self-medication simply disappears. When an addictive behavior serves no useful purpose, the behavior disappears too.
—GARY CRAIG
Founder of EFT and author of the first edition of The EFT Manual
Using tapping can help you accelerate your recovery process in the following five ways:
1. Reduces your desire to drink or your craving for alcohol. Tapping can often provide fast relief for cravings, which allows you to stop your use of alcohol with less pain.
2. Reduces your symptoms of withdrawal. Tapping can help free you from any physical or emotional side effects of alcohol withdrawal.
3. Releases any feelings and limiting beliefs about cutting back or quitting drinking. On Day 11, in the Lie Detector Solution, we asked you to make a list of all your limiting beliefs, including the lies you have told yourself about drinking. You can use tapping to clear these and any other limiting beliefs that you uncover.
4. Releases any painful feelings that are associated with drinking or trying to quit. Cutting back or quitting drinking can bring to the surface a wide range of emotions, such as guilt, shame, embarrassment, self-hatred, fear, anger, or low self-esteem. If these are not cleared properly, they can keep you "stuck" and eventually lead you back to drinking.
5. Identifies and resolves the original events, emotional issues, and underlying feelings that caused your problem drinking. Alcohol abuse is often the result of painful or traumatic experiences from your past and unresolved feelings that you have not dealt with. Tapping can help you identify and resolve those experiences.
The true cause of addictions is anxiety, an uneasy feeling that is temporarily masked, or tranquilized, by some substance or behavior.
—GARY CRAIG
### How Jose Tapped Away His Alcoholism
Jose was an alcoholic who drank four large bottles of beer, or the equivalent of eleven 12-ounce bottles, every night. He began at six o'clock, while he was still at the auto paint shop he owned, and continued at home until he eventually passed out.
Then Jose met EFT practitioner Javier Gomez, who was able to identify in only one session that drinking wasn't Jose's real issue. Rather, it was the loss of both his father and his brother, with whom he had been very close, about seven years earlier. Jose had not been able to let go of the pain from losing two of his closest family members. Javier decided to use a very simple tapping technique to help free Jose from his sadness and loneliness, which took less than twenty minutes. After this short tapping session, Jose reported feeling "liberated" as he headed back to work.
As he got ready for bed, Jose suddenly realized that he hadn't needed a drink that night—and hadn't even thought about it! He couldn't believe it. And each of the following three nights, he didn't drink either. On the fifth night after his first tapping session, some of his drinking friends showed up with lots of beer, which usually would have meant that Jose would drink even more than usual. But he declined their offer easily. He still had no desire to drink.
This story might sound unbelievable, but we have consistently seen these kinds of results with tapping. Jose dealt with his alcoholism by tapping on—and tapping into—his core issue, which was his grief over losing his father and brother.
By now you know that the key to thriving in sobriety is dealing with the root cause of your drinking—your unresolved emotional issues. If you went through a painful experience, such as flunking out of school, being passed over for a promotion, losing your job, declaring bankruptcy, discovering that your spouse cheated on you, getting divorced, or losing a loved one, you will ultimately need to deal with those feelings of loss, betrayal, unworthiness, or low self-esteem. Tapping is a perfect solution. In fact, tapping can free you from these painful feelings in a fraction of the time it would take with more traditional methods of therapy.
So let's get started.
### The Basic Tapping Protocol
The great thing about tapping is that it's easy. You can learn the basic protocol in under ten minutes. You can also learn how to tap by going to the companion website at <http://Day13.Solutions> and watching the Introduction to Basic Tapping video. As you watch the video, you may want to refer to the steps below as well as the diagram of the tapping points.
Start by practicing on yourself, but once you learn the basic protocol, you might want to practice it with your friends or family. When Dave first learned this basic tapping process, he used it with his daughters to help them overcome their test-taking anxiety and a fear they had of bad people hurting them or their family. Both of them thought it was weird at first, but when Dave checked in with them a week later, they acknowledged that it had actually worked.
1. Decide what issue you want to tap on. In tapping, the issue you're working on is sometimes referred to as your Most Pressing Issue, or your MPI. Decide if you want to tap on a craving, a physical discomfort, an uncomfortable or painful emotion, or a limiting belief that you would like to clear (let go of). Give it a name such as "This craving for a glass of wine," "My headache," "My fear of rejection," "My being upset with my husband," or "My belief that I can't relax without alcohol." We'll demonstrate the rest of the steps in the basic tapping protocol using the following fear or limiting belief: "I'm afraid that people will judge me and make fun of me if I don't drink with them."
2. Determine your level of discomfort—the intensity of the feeling or belief. Close your eyes and focus your attention on the MPI you have chosen to clear with tapping. For example, you could heighten your concentration on your fear that people will judge you if you don't drink by imagining being at a party with your friends where everyone is drinking. As you focus intently on the belief or fear, scan your body and notice what you are feeling and where. Determine on a scale of 0 to 10—0 meaning "no intensity at all" and 10 meaning "extremely intense"—the intensity of the discomfort you feel in your body when you focus on your craving, feeling, pain, or belief. By establishing a number before you begin to tap, you can measure any reduction in intensity after a few minutes of tapping.
3. Create your "setup statement." Now that you know your intensity level, the next step is to craft the "setup statement." The basic setup statement goes like this:
"Even though [fill in the blank with your MPI], I deeply and completely love and accept myself."
For example, you might say, "Even though I'm afraid people will judge me if I don't drink with them, I deeply and completely love and accept myself."
• If you were tapping to get rid of your headache, you might say, "Even though I have this headache, I deeply and completely love and accept myself."
• If you were tapping to get rid of a limiting belief, you might say, "Even though I have this belief that I can't relax without alcohol, I deeply and completely love and accept myself."
Once you have your setup statement, you can begin tapping. Looking at the diagram of the tapping points above, find the location of the karate chop point on the heel of one hand. (Either hand is fine.) With the other hand, using two or three of your fingers, start tapping on this spot firmly enough to feel it but not hard enough to bruise your hand, while you focus on your fear of being judged. While tapping on your karate chop point, say your setup phrase out loud three times.
4. Choose a "reminder phrase." Your reminder phrase consists of just a few words to remind you of your MPI, which you will say out loud as you tap on the sequence of the eight points in the tapping sequence. It can be as simple as "This urge to drink" or "This feeling of shame." Working with the MPI from above, your reminder phrase could be "This fear of rejection."
5. Tap through the points. We recommend that you begin by tapping on just one side of the body, using whichever hand is most comfortable for you. Using the index and middle finger, tap on each one of the eight points five to seven times while saying your reminder phrase out loud one time at each point before moving on to the next one. You have completed a "round" of tapping when you've tapped on each of the eight points. We recommend that you watch the video so that you're clear on the points, but don't worry about being too precise; tapping is very forgiving. Tap lightly but firmly. If you can't tap a certain point due to an injury, just skip that point. Tap on the eight points in the following order:
• Top of the Head: This fear of rejection.
• Eyebrow: This fear of rejection.
• Outside of the Eye: This fear of rejection.
• Under the Eye: This fear of rejection.
• Under the Nose: This fear of rejection.
• Chin: This fear of rejection.
• Collarbone: This fear of rejection.
• Under the Arm: This fear of rejection.
After three or four rounds of tapping on the points, stop, close your eyes, take a deep breath, and check to see what the level of intensity of the feeling (fear of rejection) is now. If your level is a 0, you can stop. If it is not yet a 0, keep tapping some more rounds until you bring it all the way down. Another option is to add in several "positive choice" rounds when the level of intensity is down to a 4 or below. We explain this in the next step.
6. Add a positive choice statement. When the intensity level drops to 4 or less, you can create one or more statements affirming a positive thought or action you could take. Use this structure:
"Even though [fill in the blank with your MPI], I choose to [fill in the blank with a positive action]."
For example, "Even though I'm afraid of being rejected if I don't drink with my friends, I choose to go and have a good time anyway."
A positive choice round might look like this:
• Top of the Head: Even though I'm afraid of being rejected if I don't drink . . .
• Eyebrow: I choose to go and have a good time anyway.
• Outside of the Eye: Even though I'm afraid of being rejected if I don't drink . . .
• Under the Eye: I choose to believe nobody will even notice, if I don't make a big deal about it.
• Under the Nose: Even though I'm afraid of being rejected if I don't drink . . .
• Chin: I choose to drink club soda and be myself.
• Collarbone: Even though I'm afraid of being rejected if I don't drink . . .
• Under the Arm: I choose to be happy knowing I don't have to worry about drinking and driving.
Now that you have learned the basic steps for tapping, let's look at a couple of different ways you can use it to help you cut back or quit drinking. Your first action step for today is to practice the basic tapping protocol and tap on one of your limiting beliefs that you identified on Day 11 in the Lie Detector Solution. Or try it with some cravings or negative emotions that you may be experiencing, using the following examples.
### Tapping Away Your Cravings
One of the most valuable uses of tapping is to reduce your desire or craving for alcohol. Using the basic tapping protocol, your tapping session might look like this:
1. Rate the intensity of your craving from 0 to 10.
2. Create a setup statement like the following and say it three times while tapping on the karate chop point: "Even though I really desire a drink so badly that I am not sure that I can control myself, I totally and completely love myself."
3. Tap three or four rounds as you get in touch with your craving, how much you want to drink, and how good you think it will make you feel. As you tap on each point in the order below, state your reminder phrase ("This desire to drink") out loud. (Notice that it is okay to change the wording of your reminder phrase as long as it keeps you focused on the same issue.)
• Top of the Head: This desire for alcohol.
• Eyebrow: This desire for alcohol.
• Outside of the Eye: This desire for alcohol.
• Under the Eye: This desire for alcohol.
• Under the Nose: This desire to have a drink.
• Chin: This desire to drink.
• Collarbone: This craving for a drink.
• Under the Arm: This desire for alcohol.
4. Stop and rate the intensity of your craving again. Is it the same, lower, or higher? Keep tapping until you reach 0 and the craving is gone. Or once you reach an intensity level of 4 or lower, add in a few rounds with a positive choice statement.
• Top of the Head: Even though I have this desire for alcohol . . .
• Eyebrow: I choose to be free from it.
• Outside of the Eye: Even though I want a glass of wine . . .
• Under the Eye: I choose to be free from it.
• Under the Nose: Even though I have this urge to have a drink . . .
• Chin: I choose to have a glass of club soda.
• Collarbone: Even though I have this craving for a drink . . .
• Under the Arm: I choose to be totally free from this desire.
Be aware that when you tap on a craving, troublesome thoughts and feelings might come up. Here are some common thoughts that often arise:
If I don't have a drink, I'll feel too deprived.
I don't have the strength to refuse a drink.
Overcoming my alcohol addiction is impossible.
I can't live without alcohol.
I can't be relaxed and happy without alcohol.
I cannot sleep without having a drink.
I don't know how to socialize without a drink.
I won't have any friends if I don't drink.
A drink is my reward for working hard all day.
I can't stop drinking because I have a lot of stress.
I don't like anyone telling me what I can and cannot do.
Even if tapping does work, I am afraid it won't last.
If thoughts like these do surface, take a few moments to tap on those as well. For example:
Setup phrase: "Even though I've lost all my money through my drinking, I deeply and profoundly love and accept myself."
Reminder phrase: "This sense of loss."
Setup phrase: "Even though I believe a drink is my reward for working hard all day, I totally and completely love and accept myself."
Reminder phrase: "This belief that drinking is my reward."
### Tapping Away Negative Emotions Associated with Your Drinking
As you work through the solutions in this 30-Day program, you might feel some of the following emotions: guilt or shame (because of your addiction), fear (that you won't be able to get a drink), anxiety (when you don't know what to do), unhappiness (because you don't have what you want), and anger (because you are not "allowed" to have a drink). Use the same tapping procedure to tap on these feelings as well. Here's an example:
Setup phrase: "Even though I feel ashamed because I'm addicted to alcohol, I totally and completely love myself."
Reminder phrase: "This shame."
Positive choice rounds: I choose to be free from this shame. I choose to be free from this desire for a drink.
### Tapping Away Pain and Discomfort
When physical symptoms or pain arises, you can use tapping to get them to subside. For example:
Setup phrase: "Even though I have this terrible tension in my chest when I don't have a drink, I deeply and profoundly love and accept myself."
Reminder phrase: "This tension in my chest."
### Identifying and Finally Resolving Your Core Issues
If someone can be traumatized in thirty seconds, why can't they be healed in a day, an hour, a minute?
—RICK WILKES
EFT expert
As they often say in psychology, "The problem is not the problem." In other words, for problem drinking or excessive drinking, drinking is not the problem. As we talked about several times in the first few days, drinking is a symptom of an earlier emotionally laden "problem" that you need to clear in order to truly be free.
Underlying any self-destructive habit are unresolved emotional issues that almost always stem from unmet needs and traumas that were experienced in childhood. Painful events such as excessive teasing, emotional shaming, bullying, physical or sexual abuse, abandonment (due to work, drug or alcohol addiction, divorce, or death), severe accidents, catastrophic illnesses, witnessing a violent crime such as a rape or a murder, being kidnapped, failing a class in school, or dropping the ball that caused the team to lose the game can leave a mountain of unexpressed and unresolved emotions: guilt, shame, grief, betrayal, anger, resentment, fear, low self-esteem. You are trying to cover up or numb these feelings with alcohol, but you need to neutralize or release them. Your second action step is to go back to your Day 4 list of people whom you need to forgive and practice tapping to neutralize and release your feelings.
For example, Emily, one of Jack's coaching clients, is a high-level executive in a bank in Paris. She drank heavily to relieve the pressure of her highly stressful life, and she was also a workaholic. In their first session working together, Emily described her intensely overcommitted life. In addition to her job, she was on several boards of directors, was a consultant to other financial institutions, and was planning her own wedding. As a perfectionist, she had to do everything at the highest level of excellence, which added more stress to her overly busy life.
When Jack began to explore where this pressure to do so much and do it so perfectly came from, Emily remembered an incident when she was five that occurred in the kitchen of her family's Paris apartment. The economy was in a recession, and her father blurted out to her mother, "I am not sure we are going to have enough money to feed all of the children." In Emily's five-year-old mind, she took her father's statement literally, and decided in that moment that she would become the perfect child in order to be one of the children who didn't go without eating. She would keep her room clean, say yes to every parental request, always do more than what was asked of her and do it perfectly, look for ways to contribute without being asked, and never express her own needs for fear of being a burden. Later, she also got straight A's in school, participated in every extracurricular activity she could, and was always "nice," never causing trouble.
When Emily tapped on her fear of being abandoned and not having enough food if she wasn't always perfect and overproducing, she neutralized the fear that had been driving her. She was able to reduce her perfectionism while still maintaining her excellent job performance, resign from two boards, reduce her consulting load, and hire a wedding planner. And, having eliminated the anxiety that had been her constant companion since she was five, she stopped drinking.
Tapping on cravings themselves is often successful, but identifying and clearing specific childhood events that underlie your drinking is the deepest, most thorough way to apply tapping to cravings and addictions.
### Day 13 Action Steps
• Practice the basic tapping procedure. Simply practice the tapping sequence using the diagram every day until you no longer need the diagram and the examples to guide you. The easiest way to begin is to watch the Introduction to Basic Tapping video on today's companion website to guide yourself through this basic tapping process.
• Revisit Day 4, the Forgiveness Solution. If you are still holding any judgments, anger, or resentment toward yourself or anyone else, tap to neutralize and release those feelings.
On the companion website at <http://Day13.Solutions>, you'll find more suggestions and examples of how you can use tapping to cut back or quit drinking, including tapping on negative thoughts that might come up when you are repeating your 30-Day Vision Statement or your affirmation from Day 4. You'll also find a fifteen-minute audio recording by Jack that will guide you through a powerful transformational process to help you identify and resolve any underlying emotions and unconscious limiting beliefs that may have been motivating and driving your excessive drinking. Lastly, you'll find some guided tapping sessions led by tapping experts.
## Day 14
## The Review Day and Bonus Solution
## Acknowledging, Celebrating, and Reviewing Your Accomplishments
We are what we repeatedly do. Excellence then, is not an act, but a habit.
—ARISTOTLE
Congratulations! Reaching the end of Phase II is a huge accomplishment, so close your eyes, take a few deep breaths, and really appreciate yourself for taking such massive positive action. Reaching Day 14 represents a significant milestone in your journey. You are well on your way to thriving in sobriety.
By completing Phase II, "Removing the Mental and Emotional Blocks That Prevent You from Thriving in Sobriety," you have learned and applied some critical concepts, including the Sobriety System. The Sobriety System can be life transforming, because when you reconnect with your core values, uncover and change your limiting beliefs around drinking, and utilize the power of your subconscious mind, you can make significant progress toward thriving in sobriety.
You uncovered the importance of your willpower, and why your past attempts to quit drinking might have failed. You learned specific solutions to overcome procrastination and take action. And you discovered the breakthrough technique of tapping to quit drinking.
Please make sure to visit the companion website for a quick review of each of these key concepts, as well as a special video from us that we have created for you.
Today's companion website also contains your second bonus solution—the Relapse Solution. This teaches you how to beat the odds of relapse and what to do if you find yourself returning to your excessive drinking habits. You can read this solution along with today's review content at <http://Day14.Solutions>, or you may prefer to save it for a rainy day—when you are feeling a little down or when you find yourself seriously considering drinking again.
Be sure to complete the Phase II review, as it is truly a critical component of your ongoing success. Before you know it, you will be on Phase III.
# PHASE III
* * *
# Creating an Unshakable Belief in Yourself and Your Dreams
* * *
Whatever the present moment contains, accept it as if you had chosen it. Always work with it, not against it. Make it your friend and ally, not your enemy. This will miraculously transform your whole life.
—ECKHART TOLLE
Author of The Power of Now: A Guide to Spiritual Enlightenment
Welcome to Phase III. This phase is often completed during the third week of The 30-Day Sobriety Solution, unless you have chosen the 60- or 90-day option. As you head into Phase III, we want to take a minute to review the ongoing action steps we have asked you to do daily. Let's be honest. We have asked you to do a ton. When we have participated in intense programs like this (and rest assured we have), we know how annoying and overwhelming it can feel. We get it! Our advice is to simply do your best.
We know you've been working hard when we hear feedback like, "Do you realize how many ongoing action steps you have given us?" Yes, we do. We put a huge amount of attention and effort into the design of this program, and we have been receiving and integrating feedback from people like you for years, all to make sure that what we are asking you to do gives you the greatest amount of value in the shortest amount of time. Still, we know it is a lot to ask. But we also know that what we are asking is very doable, given the feedback from our graduates who are now thriving in sobriety. So let's take a look at them.
#### The Top 11 Ongoing Action Steps (in Order of Importance)
I found getting sober surprisingly easy with The 30-Day Sobriety Solution, even after never going more than two days without alcohol for over fifteen years. As long as I did the solutions, it wasn't difficult.
—Thomas
30-Day Graduate from London, England
1. Journaling. We really can't overstate the importance of this ongoing practice in your early sobriety (Day 1).
2. Review your 30-Day Vision Statement, which now includes some of your core values (Day 2 and updated in Day 10).
3. Review your three goals supporting your 30-Day Vision Statement, which were updated with some of your core values (Day 6 and updated in Day 10).
4. Continue to work through your list of people you need to forgive or let go of with the Total Truth Process. Although this doesn't have to be a daily exercise, it is critical for you to get through your whole list eventually. For some people, this process turns out to be their highest priority (Day 4).
5. Use tapping to clear your cravings, negative feelings, and limiting beliefs. You can use tapping to address many different challenges (Day 13).
6. Use the forgiveness affirmation and the "I love myself" mantra (Day 4).
7. Review your new beliefs (Day 11).
8. Continue using the "tiny habit," anchoring your 30-Day Vision Statement to an existing behavior (Day 9). (This step could easily be combined with step 2.)
9. Stop using the words "I can't" (Day 5).
10. Have a short nightly ritual before bed where you focus on your vision, goals, dreams, and desires. This accomplishes several steps listed above at once (Day 12).
11. Review your "new you" notes (Day 2).
Whoa, that can make you tired just reading it. Do we honestly expect you to do every one of these every day? Not necessarily, but the more of these action steps you do consistently, the more you set yourself up for breakthrough success. Rest assured, we practice what we preach. Both of us read our vision statements, repeat our affirmations, and visualize our goals daily. We regularly use the tiny-habit technique and the Total Truth Process, and we have almost completely removed the word can't from our vocabularies. We use the "I love myself" mantra. Dave journals every day, and Jack uses tapping every day.
To make it easier for you to follow through, we recommend that you combine some of the action steps. For example, start a tiny habit to review your 30-Day Vision Statement, goals, new beliefs, "new you" notes, and the forgiveness affirmation. With this new habit alone, you will accomplish six of these top eleven action steps every day! Okay, enough said.
You are going to love Phase III. Many consider this set of solutions the most fun, effective, and easy to implement in the program. But before we get started, let's talk about the monkey trap.
#### Avoiding the Monkey Trap
A monkey trap is a glass jar that contains a piece of fruit under a lid with a hole in it. The hole is just large enough for a monkey to put its paw into. When the monkey grabs the fruit, his fist is too big to pull out through the opening. The only way to get it out is by dropping the fruit. But instead of giving up the fruit, he keeps holding on to it because he wants it. Now that he has that food in his possession, he treats it like it is actually part of him. He would rather suffer the consequence of being stuck than let go of it and look for food elsewhere.
In many ways, your behavior might be like that of the monkey—you have grabbed on to the habit of drinking, and you believe and act like you can't let it go. You may get caught up in justifying and rationalizing it, not realizing that all you have to do is just let go.
One of the reasons that most people don't let go is explained by what psychologists refer to as learned helplessness, which describes how we take on an attitude that we are helpless to change. So even if you are presented with a solution to a major problem, you have become so helpless that you will never recognize the solution or take action to change.
You are not helpless, and hopefully by today, you have fully accepted this fact. You have complete control of your life, and what you choose to hold on to and what you choose to let go of are totally up to you. The solutions in this next phase of the program will help you exercise that choice in regard to your drinking.
## Day 15
## The 4-Minute-Mile Solution
## Using the Power of Creative Visualization
Imagination is everything. It is the preview of life's coming attractions.
—ALBERT EINSTEIN (1879–1955)
Physicist
Visualization has always been around, but it didn't really become popularized until the 1980s. Now, even though it isn't taught in school, almost all athletes—professional and Olympic—as well as leading entrepreneurs and business leaders use visualization. When you visualize doing something, your brain functions as if you are actually performing the task. In other words, the brain doesn't distinguish between actually doing something and visualizing it. Performance experts and sports psychologists agree that this technique can greatly speed up the process of reaching your goals. And it's easy. You just close your eyes and imagine vivid, detailed pictures in your mind.
Visualization, like so many other solutions in The 30-Day Sobriety Solution, has rarely been used in the recovery process. In the 4-Minute-Mile Solution, you will learn not only how to use visualization to make thriving in sobriety a reality, but also how to accelerate the achievement of all your other goals in life.
### The 4-Minute-Mile Barrier
Experimental and clinical psychologists have proved beyond a shadow of a doubt that the human nervous system cannot tell the difference between an "actual" experience and an experience imagined vividly and in detail.
—MAXWELL MALTZ
On May 6, 1954, Roger Bannister did what most people believed was physically impossible—he became the first person to run one mile in under four minutes. How did Bannister do it? First, he believed he could do it; he did not listen to all the doubters. Second, he visualized the race in incredible detail over and over again. He pictured everything—where he would accelerate and vary his pace, how he'd round the curves, and what his time would be at every point in the race. He did this so many times that when he entered the race, he was crystal clear on what he had to do and how he would do it, and he believed without a doubt that he would break the four-minute mile.
His time that day was 3:59:40. That accomplishment alone is amazing, but others soon followed in his footsteps. Within a few weeks, John Landy had accomplished the same "impossible" feat. Within three years, sixteen runners had. How was it possible to go from no one running a four-minute mile to sixteen people doing it within three years?
It wasn't new shoes, a new track, or a new running style. It was simple—Bannister broke a limiting belief. Most limitations are mental, not physical. And once Bannister disproved this belief, other athletes thought, If he can do it, I can do it, too.
You can use the same technique that Roger Bannister used to break the four-minute mile to accelerate the manifestation of your goals—including to cut back or quit drinking for good and make thriving in sobriety a reality in your life. In fact, later today we will show that you can use visualization in almost every solution we have presented to accelerate its life-changing impact.
Today we will teach you the science behind this powerful technique and how to utilize it most effectively.
### See What You Want, Get What You See
I would visualize things coming to me. It would just make me feel better. Visualization works if you work hard. That's the thing. You can't just visualize and go eat a sandwich.
—JIM CARREY
Actor
When you envision a goal as already accomplished, the image (sobriety) and your current reality (abusing alcohol) don't match. This creates a conflict, or structural tension, in your mind. In order to resolve the tension, your mind either has to give up the vision of your accomplished goal or come up with a solution (ideas and behaviors) to make the vision a reality.
When you consistently visualize your goal as already accomplished, this image intensifies the structural tension, and three things begin to happen:
1. Your brain's reticular activating system (RAS) is programmed to bring to your awareness anything that will help you attain your goal.
2. Your subconscious mind's creative aspect is activated and starts developing solutions for accomplishing your goal. You'll find yourself frequently coming up with new ideas—upon waking up in the morning, while taking a shower, when you're waiting in a line at a store, and even when you're watching TV or a movie.
3. Your motivation increases. You'll suddenly and unexpectedly find yourself doing things and taking actions to move toward your goal because you want to, and not because you feel like you have to.
You might remember that we also covered some of this on Day 11 in the Lie Detector Solution. To determine what you will be aware of, the brain's RAS filters about eleven million bits of information per second. Another study even found that the RAS can filter nearly four hundred billion bits of information per second that enter your brain. Your RAS will let in anything that will help you achieve the goals that you constantly affirm and envision. It will also let in anything that matches and reinforces the beliefs and images you have about yourself, other people, and the world., Just think about when you started a new project, whether personal or professional, and how soon after that you started to notice things that had always been there but that you had previously filtered out. For example, if you decide to buy a new car, you will start noticing all kinds of different cars and what you like and don't like. You will naturally remember to ask others who know a lot about cars for advice. However, before that, you were probably oblivious to noticing cars, and would never consider initiating a conversation about them, because your RAS filtered it out, since you were not interested in that data.
So how does all this apply to your efforts to thrive in sobriety? It turns out that visualization is the most effective way to reprogram your RAS. When your brain has detailed, colorful, and vividly convincing pictures, it will seek out and capture all the essential information to make those pictures a reality. If you give it pictures of yourself thriving in sobriety, such as being in great physical shape, or laughing and smiling while spending time with close friends while drinking an iced tea, your RAS will be programmed to become aware of things that can help you do that. Your subconscious will also go to work on achieving this.
However, if you are constantly feeding your brain negative, fearful, and anxious images, such as drinking at a bar or sneaking alcohol at home, it will help you make those a reality, too. Unfortunately, most people often feed their brains images of what they don't want instead of what they do want. This is why it is so important to have a daily practice of visualization to plant positive mental images in your brain of you thriving in sobriety.
### The Process for Visualizing Thriving in Sobriety
Formulate and stamp indelibly on your mind a mental picture of yourself as succeeding. Hold this picture tenaciously. Never permit it to fade. Your mind will seek to develop the picture. . . . Do not build up obstacles in your imagination.
—DR. NORMAN VINCENT PEALE
Visualizing yourself thriving in sobriety is really simple—you close your eyes and imagine your goal as already complete. While a vision of a still picture is great, creating a short mental movie or scene can be more powerful. See yourself saying no to an alcoholic beverage that you're offered at a party. Or envision a whole weekend of fun activities without alcohol. Think about your 30-Day Vision Statement and supporting goals from Day 2 and Day 6. Create a detailed mental picture of exactly what you would be seeing through your eyes while you are already thriving in sobriety.
Vividly imagine all of the details—large and small—that you would see. Here are some questions you might want to focus on "seeing" the answers to:
• What does the thriving-in-sobriety version of you look like?
• What are you wearing?
• What is your weight?
• Who is with you, and what are you doing?
• What job do you have? How are you performing?
• How has your self-confidence changed?
• Are you more present and available for deep and meaningful conversations?
• How are people responding differently to you?
• Are you helping others more and giving back more to your community?
• How do you respond when people offer you a drink?
Your vision of thriving in sobriety will likely include multiple images or movies, such as one of you at work, where you feel alive and energetic while talking to your coworkers instead of being hungover. You see yourself with your spouse, kids, or family, doing something that represents how healthy and happy you are sober and how wonderful and fulfilling your relationships with them have become. You can create a scene with friends where you are doing an activity that you have always wanted to do, but drinking made it impossible. Or you even see yourself at a bar or party, having fun while sober, and when a friend offers you a drink, you see and hear yourself say—easily and confidently—"No, thanks" (or one of the excuses for not drinking that we shared in the Social Solution on the companion website for Day 7).
If you have trouble picturing what you would look and feel like when you are thriving in sobriety, you may find it helpful to review your 30-Day Vision again or go back to a time when you were not addicted to or abusing alcohol, even if you have to go back as far as your childhood. You can draw upon a positive memory and the positive feelings of pure joy and happiness you had without alcohol, such as when you were waiting in line to get on an exciting amusement park ride or having a pillow fight with your friends or family.
### Supercharging Your Images and Movies
Not only did visualization have a huge impact on helping me thrive in sobriety, I was also able to apply this technique to creating success in my job, my writing, and my relationships.
—THOMAS
30-Day Graduate from London, England
To deepen the impact of your visualization practice, add sounds, smells, tastes, and feelings to your pictures. What sounds, smells, and tastes would you experience, and—most importantly—what emotions and bodily sensations would you feel if you had already achieved your sobriety goals?
Focus on the smells and tastes that might replace the smells and tastes around drinking alcohol. For example, if one of your thriving-in-sobriety visualizations is of a sober you at a bar having fun with friends, then you would add the smells and tastes of your ginger ale or preferred nonalcoholic beverage.
Include in your visualizations the sensations you would feel—such as the satisfaction and pride at finally having achieved your goal of cutting back or quitting drinking, the warmth of the sun on your face as you look out over the ocean at a beautiful sunset and drink a fresh-squeezed lemonade, or the joy of waking up clearheaded and refreshed on a Sunday morning.
By creating these emotions in your mind and imagination, you provide fuel to propel your vision forward. Because your subconscious mind responds more to physical sensations and feelings than to logic, the stronger the feelings you create, the stronger the impact they will have. Research has shown that images or scenes that are tied to intense emotions become locked into your memory.
To validate this fact, you only have to think about some of the major events in your life, especially the traumatic ones, and then think of all the specific details you can still easily remember. For example, when the Twin Towers at the World Trade Center collapsed on September 11, 2001, most likely you remember where you were, what you were doing, whom you were with, and maybe even the clothes you were wearing.
You have a detailed memory of tragic events because of the intense emotions attached to them. Intense emotions stimulate the brain to create stronger and deeper neural connections, which firmly lock a memory. So add the sensations of strong emotions—joy, excitement, enthusiasm, pride—to your visualization. It will seal it in your mind.
You can also deepen the emotional intensity of your visualizations by hearing uplifting music, deeply feeling your passion for succeeding, and adding movement. In seminars, we have people stand up, spread out around the room, close their eyes, and then act out their visualization; for example being at a party, dancing, requesting a ginger ale at the bar, or being the designated driver. The more senses you engage, and the more you include your body in your visualization, the more your mind will retain it, and the quicker your results will be.
### Byron's 4-Minute Mile
The 30-Day Sobriety Solution helped me accomplish so many goals and "firsts" in my life, such as my first sober birthday as an adult. This success helped me believe that I don't need alcohol to celebrate special occasions, even New Year's Eve and the Fourth of July—two holidays I was certain I needed to drink to enjoy.
—BYRON
30-Day Graduate from Phoenix, Arizona
There are certain moments in life we never forget. For Byron, it was his third DUI, which he had promised himself would never happen. Details of that morning are forever etched in his memory. The cold sensation of the steel handcuffs being secured around his bony wrists; the jarring noise of the jail cell door slamming shut, and the terrifying silence that followed; the cold concrete of the cell; and the emotional heaviness that enveloped him as the gravity of his mistake set in.
Throughout high school, Byron struggled with panic attacks and depression, in spite of his good grades. All he really wanted was to feel "normal," and he would have gladly traded his academic aptitude to feel like he belonged. After he graduated from high school, Byron discovered that drinking alcohol made him feel normal. In college, he was still able to get good grades, but now he actually had friends and felt happy—like he belonged. His panic attacks lessened dramatically, and he rarely felt depressed. Byron also realized he wanted to pursue a career in psychology. His mother had struggled with mental illness most of his life, and he wanted to help her.
Even though Byron drank heavily during college, he excelled and was awarded a scholarship to a graduate school for psychology. But as Byron continued his studies, he started drinking alone and got his first DUI, which hardly fazed him. In fact, when Byron took his first graduate class on addiction, he realized that his mom didn't have just mental health issues, she was also an addict. But as he studied more about addiction, he convinced himself that if he was getting his PhD in psychology, he couldn't be an alcoholic.
As Byron continued working toward his career as a doctor of psychology, he worked with a therapist. This alleviated most of his panic attacks, although general anxiety and depression still plagued him. His heavy drinking was no longer helping. Eventually Byron got a second DUI, but he still wouldn't accept that he had a drinking problem. After he graduated with a doctorate, he continued drinking, sometimes heavily and only on weekends, and other times every night. Then, in his early thirties, Byron got his third DUI and could no longer hide from the truth. A concerned family member recommended The 30-Day Sobriety Solution to Byron, which led to a breakthrough on the first day. "In Day 1 of The 30-Day Sobriety Solution I did the guided Time Travel Technique, which was life changing. This process gave me a level of clarity around my drinking that I had never experienced before. I finally knew, and accepted, that continuing to drink was going to keep me from everything I wanted in life, and sobriety was going to lead to true happiness and fulfillment."
As Byron no longer lived in denial, every solution led to additional insights and progress toward sobriety. He recognized many of the concepts in The 30-Day Sobriety Solution from his education in psychology and was excited to apply them in a unique, powerful way. Byron discovered that he was particularly good at visualization, and he could create and recall images in his mind with a high level of detail. He hadn't realized how valuable this ability was until he started using it to attract the life he wanted. "Today I have two collections of images—one of the future me that kept drinking and one of the future (and current) me thriving in sobriety—that I can easily recall in vivid detail. Whenever I am struggling, I simply recall these pictures and find I am naturally inspired to take positive action."
Today when Byron thinks of alcohol, or sees a commercial for alcohol and drinking, it no longer has any power over him. He has been able to restore his self-confidence, learn new coping mechanisms, and for the first time he is truly excited about what the future holds. As Byron shared recently, "Getting my third DUI wasn't the miracle I was expecting, but it was the one I had been waiting for. It led me to The 30-Day Sobriety Solution and ultimately freed me from the one prison I feared the most—the one I had created with alcohol."
### The Exploding-Through Visualization
One of the most powerful techniques I did in The 30-Day Sobriety Solution was the guided visualization of the healthy, vibrant, thin, energetic, and excited version of me exploding out of the old, bloated, overweight, lethargic, and drunk me. To this day, every time I find myself struggling with the desire to drink, I just repeat this visualization in my head, and it leaves me feeling confident and back in control. And most importantly, my craving for alcohol diminishes.
—TESS
30-Day Graduate from Denver, Colorado
There is a very simple but powerful visualization technique that we recommend you use, especially in your early sobriety. Close your eyes and picture yourself as a problem drinker. Fill in all the details, which might include what you're wearing, your antagonistic or withdrawn demeanor, your slurred speech, and anything else that applies. Briefly hold that image in your mind's eye. Then vividly picture the sober, healthy, vibrant, and happy version of yourself nestled inside the problem drinker. Again, fill in all the details. Now clearly see the sober you explode from inside the alcoholic you, shattering the alcoholic you into a thousand little pieces, and leaving the thriving-in-sobriety version of you proudly and confidently standing tall—beaming with light and positive energy.
Now picture that thriving-in-sobriety version of yourself inside a large, clear bubble. Picture the bubble floating up into the sky, radiating a glowing white light and attracting everything you need in your life to fulfill your sober vision. You can even imagine yourself inside the bubble, multiplying and spreading out all over the globe until there are millions of them, each bubble of you on a mission to serve you and your vision of thriving in sobriety.
### Make a Vision Board
Once you have decided on the images that represent your goal of thriving in sobriety, you can also place them on a vision board. A vision board is a collage of various pictures, photos, outcome statements, motivational images, and phrases usually pasted or taped together on a bulletin board or poster board. You can even use Pinterest or one of the many digital vision board apps and software programs you can find online to create a vision board on your smartphone, tablet, or computer. These images are powerful reminders of what you want, and looking at them helps program your reticular activating system, accelerating the accomplishment of your goals.
Making and using vision boards are one of those things that people usually either love or hate, yet we are convinced of their power to speed up the process of achieving your goals. Using a vision board, along with the other solutions in this program, will lead to remarkable results.
You can create a vision board in many ways. Google "vision board" and click on the images tab along the top to find some examples you like. You can also use Google Images to find and copy a picture of almost anything you want to add to your vision board.
On the next page is a photo of a vision board that Dave created several years ago. This five-foot-by-four-foot vision board depicts goals on the left side and accomplishments on the right. On the goals side is a list of 101 goals he wants to accomplish in his life, and on the accomplishments side is a list of his greatest accomplishments to date. The accomplishments side also serves as a powerful expression of gratitude.
Use your board for all your goals—not just your goals for thriving in sobriety. Include work, play, family, financial, relationship, and service goals, because all of them are related to your sobriety in one way or another. If you are not sure what all your other goals are yet, don't worry. We'll explore this topic further on Day 29, and you can update your board as often as you like.
The more realistic you can make the photos of your ideal self, the better. For example, you can paste or Photoshop a picture of your head onto the ideal body you desire. You can include a photo of the company headquarters where you want to work. You can go to your local auto dealer and take a picture of yourself sitting in the car you want to own someday. But only include pictures of what you do want. For example, you don't want a picture with a bottle of wine crossed out.
We are so enthusiastic about the effectiveness of this technique that we have even hired graphic designers to create custom images that represent our most important goals. In fact, we paid a designer to create mock-up images of this book before the first version of the program was even released. And by the way, having custom images designed doesn't have to be expensive. Check out the websites Fiverr and Elance. You'll be surprised what you can get for five or ten dollars. We use them all the time.
### Lines, Traffic, and Meals
A large part of my successful career was due to my ability to really see, or visualize, that success. The 4-Minute-Mile Solution was eye-opening for me because I realized I could use this same technique to thrive in sobriety—simply by picturing the future person I desired to become, and seeing it as my current reality.
—BRIAN
30-Day Graduate from Trenton, New York
Perhaps the best thing about visualization is that it doesn't take any extra time. You have time every day that goes underutilized. Whenever you are sitting on the subway or as a passenger in a car, or when you are waiting—waiting on hold, waiting in lines, waiting to see a doctor, waiting for a friend or family member, or waiting for your food to be delivered—you can use this time to your benefit. Rather than being annoyed with someone in line who is taking too long, or feeling impatient about the time it is taking for your takeout food to be delivered, or feeling antsy about what you have to get done, visualize your goals. This will make you happier, and you will feel like you are accomplishing something (which you are!). It will also help you to accomplish your goals faster.
After you practice visualization for a while, you'll find you can do it even with your eyes open, which means that you can do it anytime and anywhere.
The two best times to visualize are right before you go to bed at night and right when you get up in the morning. When you visualize just before falling asleep, you are programming your subconscious to focus throughout the night on how to create that goal. You may wake up with insights and inspirations. When you watch a scary movie or the news right before bed, your dreams will often be related to what you watched or heard before you went to sleep. It is much more productive to "seed" your consciousness with positive, goal-oriented images rather than ones of violence and mayhem.
### Connecting the Solutions
As we have stated, all the solutions in this program are carefully sequenced and build upon one another. And when you visualize yourself thriving in sobriety, you are reinforcing and integrating many of the past solutions, which is a big reason why you are able to experience such a significant transformation in just 30 days. Let's quickly take a closer look at how using visualization can enhance the impact of the earlier solutions.
• The 100% Solution (Day 1). When you continually visualize what you want, your ability to maintain a 100% commitment to your new life is much easier.
• The Purpose Solution (Day 2). The images you use in your visualizations and on your vision board represent the fulfillment of your true purpose.
• The Pendulum Solution (Day 3). Your visualizations create a powerful emotional and psychological association between sobriety and pleasure.
• The Forgiveness Solution (Day 4). First visualizing having a successful conversation working through the Total Truth Process with a loved one is an effective way to prepare for an actual conversation.
• The Believe-in-Yourself Solution (Day 5). Visualizing yourself as the person you want to be and achieving your sobriety goals helps strengthen your belief in yourself and your ability to succeed.
• The Outcome Solution (Day 6). By purposely creating structural tension between your current reality and what you are picturing in your mind, visualization facilitates the achievement of your goals.
• The "Why Can't You Just Quit?" Solution and the Action Solution (Days 8 and 9). Your willpower is naturally stronger and action comes more easily when you have a clear mental image of what you want and why you want it. When your subconscious becomes deeply imprinted with your goal images, you will naturally take the actions you need to take.
• The Sobriety System (Days 10, 11, 12). Visualization combined with affirmations is one of the most rapid, effective methods for replacing limiting beliefs with powerful new thriving-in-sobriety beliefs.
• The Tapping Solution (Day 13). When limiting thoughts come up, you can tap on those limiting beliefs and let go of them.
### Day 15 Action Steps
• Create three to five mental images or movies to visualize. Get clear on your thriving-in-sobriety mental images or movies. Write them down in your journal and visualize them at least once a day. Include all five senses (touch, sight, taste, smell, and hearing). Always create the feelings and emotions you will feel when you have achieved this goal. Visualize an experience in your past where you had a great time sober, even if you need to go back to a time in your childhood, before you drank. Do this when you are waiting in line or sitting in a waiting room. Review the previous action steps and use visualization with them.
• Listen to the two guided visualizations on today's companion website. The first one guides you in creating powerful thriving-in-sobriety images, and the second one guides you through the Exploding-Through Visualization.
• Create a vision board. Take time to create a vision board in the next month, perhaps at night or on the weekends. But make sure to get started today by creating, cutting out, or printing out at least one image you can focus on that inspires you about your goal of thriving in sobriety. Schedule the date and time when you will complete your vision board. You might want to invite a friend or family member to make one with you. It can be a lot more fun.
The companion website at <http://Day15.Solutions> has additional content on visualization, including more studies and success stories that illustrate the power and effectiveness of this technique. There is also a short interactive video demonstration of the power of visualization, which we think will blow your mind.
## Day 16
## The Quality Question Solution
## Change Your Questions to Change Your Life
A major stimulant to creative thinking is focused questions. There is something about a well-worded question that often penetrates to the heart of the matter and triggers new ideas and insights.
—BRIAN TRACY
All day long, you ask yourself questions. What do I have to do at work today? What errands do I need to run? I haven't heard from Denise in months; is she okay? Is tonight the season finale of my favorite TV show? What am I going to eat for dinner? Can I find something to "celebrate" tonight so I can have an excuse to drink?
Asking questions is part of being human, but most of the time, the questions we ask ourselves keep us stuck in our current reality—including self-destructive patterns of drinking. However, there are a lot of questions that can help you break free from your current limitations and accelerate your transformation from a problem drinker to a person thriving in sobriety. The Quality Question Solution will teach you how to ask the right kinds of questions.
### The Roller Coaster of Life
I'm loving sobriety. I've been sober for forty-nine days now, and it feels like second nature. And just as you wrote in the program, pushing down that first domino seemed like a huge challenge, but now the dominos fall easily.
—JAMES
30-Day Graduate from Istanbul, Turkey
Before we jump into the Quality Question Solution, let's take a moment to address what you might be experiencing at this point in your 30-Day journey. As you know, life can be an emotional roller coaster. When you drink, you experience highs, and then you face challenging lows. The great thing about thriving in sobriety is that it removes the frequency and depth of those lows. During these 30 days, especially the first few weeks, you might still experience some emotional waves. At one moment, you might feel amazing—like you finally have your drinking issue handled, and you can't wait to impress everyone with your phenomenal turnaround. And then all of a sudden, you might get hit with a huge craving, or a letdown, and you feel sad, angry, or scared. Or maybe you even slip and drink, breaking your promise to quit—at least for these 30 days. If this does happen, remember the recommendations we made at the start of Phase II: listen to the Time Travel Technique again on the companion website for Day 1; consider reviewing the bonus solution on Day 14, the Relapse Solution; and continue the program where you left off.
If getting and staying sober were easy, you wouldn't have bought this book—you would have already accomplished your goal. The path to sobriety is a journey, and sometimes a difficult one. And even though at certain times thriving in sobriety might seem challenging or even impossible, when you do get beyond that point—and you will—it will have an incredible domino effect on every other area of your life.
The reality is that some people do slip along the way—some quite a bit. Others don't slip at all. Regardless, and even though this may sound clichéd, it's how you respond to these slips or setbacks that defines you and your ultimate outcome. If you pick yourself up and get back to doing the work, you will accomplish your goal of happiness and sobriety. But if you give up, you will have the opposite outcome. And since you've read this far, it is clear that you are committed to thriving in sobriety.
The fact that you showed up again today is another reason to celebrate your success. Problem drinkers love to beat themselves up when they feel like they are not making as much progress as they had hoped to or they're not recovering quickly. Problem drinkers also tend to overlook or downplay the personal growth they have made. Don't let this be you! Fully appreciate and celebrate that you have made it this far. And if you doubt that you have made any progress, go back and read your journal entries from Day 1.
Okay, let's look at today's solution and lock in another way to keep making progress.
### The Einstein Solution?
Albert Einstein, winner of the Nobel Prize in Physics, wrote, "The important thing is not to stop questioning. Curiosity has its own reason for existing." Einstein was not talking about questions such as "What am I going to wear today?" but about questions with answers that can dramatically change your life.
You see, Einstein knew something about questions that many people don't. The process of frequently asking questions engages your subconscious mind, which searches endlessly for an answer. In his book How to Think Like Leonardo da Vinci: Seven Steps to Genius Every Day, Michael Gelb writes, "Neuroscientists estimate that your unconscious database outweighs the conscious on an order exceeding ten million to one. This database is the source of your creative potential. In other words, a part of you is much smarter than you are. The wisest people regularly consult that smartest part."
When you put your subconscious to work by asking it the right questions, you will soon discover the answers that can change your life. As you might recall from Days 11 and 15, the right questions reprogram your brain's reticular activating system to allow information into your conscious awareness that might help you with the answer.
At some point, you have most likely experienced this by asking yourself a question and then, soon after, noticing something in your environment—a book, a song lyric, a newspaper headline, a picture—that had been right in front of you all along, but now you could see it in a way that sparked a new thought or association that led to an answer to your question. For example, maybe you want to start exercising more, so you ask yourself, What type of workout program should I do? A little later that same day, as you are quickly scanning your feed on Facebook, you notice a friend who lives nearby and you suddenly remember that he had posted about a great new gym he joined. Because you asked the question, your mind was able to connect the photo of that person to his previous post and bring it to your attention.
When you ask the right questions, your conscious and subconscious work together to provide you with answers. Today you will learn how to create better questions that will help you achieve your sobriety goals.
### Presuppositions: The Guaranteed Alcohol Attractor
If you ask the wrong question, of course, you get the wrong answer. We find in design it's much more important and difficult to ask the right question. Once you do that, the right answer becomes obvious.
—AMORY LOVINS
Physicist named by Time magazine as one of the world's one hundred most influential people
Have you ever asked yourself, Why can't I quit drinking? Or Why can't I drink normally? Or, in extremely frustrating times, maybe even Why am I a "loser drunk"? The problem with this type of question is that it contains presuppositions that keep you stuck. When you ask, Why can't I quit drinking? the question is already based on the presupposition (or assumption) that you can't quit drinking, which results in your mind searching for answers that confirm and reinforce that limiting belief. The answers your subconscious might respond with include Because you will never be able to succeed without alcohol, and Because if you didn't drink, your life would be boring. These "answers" are not helpful. They just reinforce your limiting belief that you can't change.
### The Quality of Your Life Equals the Quality of Your Questions
In The Biggest Loser—the reality TV show that helps contestants lose a large amount of weight in a relatively short time—a distraught contestant said she had asked herself thousands of times, Why am I so fat? Let's take a look at her question.
By asking "Why am I so fat?" she is confirming that she is too fat. She is creating negative feelings. Her question keeps her mind focused on being fat instead of on being or becoming healthy. She is telling her subconscious to keep focusing on being fat. This question will never yield a useful answer; she will just receive reasons and justifications for why she is fat. These answers will ultimately only reinforce her self-image as a "fat" person, so even if she does make progress in losing weight, her subconscious will most likely sabotage her because, deep down, she still identifies with a "fat" self-image. In addition, her asking this same question "thousands" of times made sure her focus was always on being fat, instead of on what she could do to be healthy and fit.
Imagine if, instead, she were to ask herself many times a day, How can I achieve my ideal weight? Or better yet, How can I eat healthy, exercise, and achieve my ideal weight while absolutely loving the process? This simple change in questions would have a dramatic impact because now she'd be focused on what she wants instead of what she doesn't want. She is instructing her conscious and subconscious minds to search for the answer of how to achieve her goal rather than to explain her unwanted condition.
It's easy to see that these two questions create radically different feelings. The question "Why am I so fat?" is likely to make you feel shame, resignation, and hopelessness, while the other question, "How can I achieve my ideal weight?" is likely to make you feel optimistic and hopeful because it presupposes that achieving your ideal weight is possible.
Your questions determine how you feel. And as you know from the Sobriety System diagram in Days 10, 11, and 12, how you feel determines the actions you take and the results you get. If you feel discouraged, sad, or angry, the actions you take will be completely different than if you feel optimistic, hopeful, and inspired.
One of the most important ideas to take away from today is this: The quality of your life is dramatically affected by the quality of the questions you ask yourself on a daily basis.
Dave used to constantly ask himself questions like, Why am I not able to be happy without drinking? How can I be so effective at accomplishing other goals, but when it comes to drinking, I can never quit or change? One day while he was journaling, it dawned on him that he had been asking all the wrong questions. He immediately stopped asking self-defeating and disempowering questions and replaced them with one life-changing question—How can I be sober and really happy and excited in life? From then on, whenever he caught himself asking the old self-defeating questions, which was still often at first, he would replace them with his new empowering question.
Within weeks, Dave started to experience astonishing changes. Just by changing the questions he asked and asking the new one numerous times a day, he began to get valuable answers. Even more exciting, he would simply ask the question and not consciously try to come up with an immediate answer, knowing his subconscious would take on that task. Before long, he was constantly finding answers and insights about exactly what he needed to do. Sometimes the answer was to reach out to a past friend, join a recreational sports league, or not watch a certain television show that triggered negative emotions.
In each case, the answers were clear and taking action was easy. And, even more interesting, he started noticing that he had naturally stopped doing some self-defeating behaviors, which he didn't even realize until much later because it never felt like he'd made a conscious decision to stop. The changes were unconscious and effortless. This is part of the dynamic we are constantly referring to when we talk about how this program eventually makes thriving in sobriety easy and effortless.
Now you can start asking the right questions to direct your subconscious.
### Why Do You Drink?
But if years down the road you are still saying, "Baby, I do it because it makes me happy," you don't really mean it.
—ROBERT DOWNEY JR.
You might have noticed that we don't want you to ask questions that start with the word why. This is a general rule in most types of therapy and coaching—do not ask "why" questions about a bad habit or something you want to change. When you ask "why" questions, the initial responses are usually rationalizations and justifications. The answers you get to "why" questions are booby prizes—they are just not useful.
So pay attention. When you hear yourself asking "why" questions, take note. If the question is, Why am I so unhappy when I am sober? then you need to change the question. If you are going to use a "why" question, change it to Why am I so amazing, loving, and smart when I am sober? That would be a great question to keep asking yourself. But you'll see in a moment that asking how is almost always better than asking why.
### Asking the Right Questions
Great minds ask great questions. The questions that "engage our thought" on a daily basis reflect our life purpose and influence the quality of our lives. By cultivating a Da Vinci–like, open, questioning frame of mind, we broaden our universe and improve our ability to travel through it.
—MICHAEL GELB
Virtually all spiritual traditions have a variation of this phrase: "Ask and you shall receive." But first you must know how to ask.
Just as there are guidelines for setting goals and writing effective affirmations, there are also guidelines for asking questions that empower you instead of disempower you. Here are the key guidelines for asking questions that will liberate you instead of imprison you:
• Ask "how," not "why." Always ask how you can achieve what you want rather than why you are stuck or don't already have it. Instead of asking yourself, Why can't I ever find the love I want? or Why do I always end up being rejected? you can ask How can I be sober while finding and falling in love with my soul mate?
• Ask frequently. Keep asking the question silently in your mind—and out loud when appropriate—until you get an answer. We have asked ourselves certain questions hundreds and even thousands of times over a long period. The repetition keeps your conscious awareness aligned with your desired outcome, and reprograms your subconscious to come up with answers and solutions to support your goals.
• Don't try to consciously answer the question. The answer will come to you when you are ready, and often when you least expect it. You can ask the question and then let it go, with complete confidence that your subconscious is hard at work seeking your answer, which it will often reveal to you at times when your conscious mind is less focused, such as when you are taking a shower, washing dishes, or walking in the park. Or as Dave often experiences, an answer will come to him right as he is falling asleep.
• Emotionally charge the question. Add empowering vocabulary to make the question engaging and exciting. Specifically, go back to Day 10, the Core Values Solution, and include some of your core values. For example, if you identified love as a core value, add the word love into the question where appropriate. Such as, How can I experience incredible love and joy in my sobriety?
Today we want you to write down one question in your journal that captures your 30-Day Vision Statement. Let's use the first example from Day 2. "Every day I wake up feeling excited, vibrant, and passionate about living a meaningful and fulfilling sober life." Now let's change it to a question. "How can I wake up every day feeling excited, vibrant, and passionate about living a meaningful and fulfilling sober life?" If excitement and passion are two of your core values, then this is the perfect question. Be sure to turn your updated 30-Day Vision Statement from Day 10 into a question that includes some of your core values.
Then ask your question multiple times a day, especially before you go to bed at night, which is the perfect time to "task" your subconscious with answering the question. Remember, whatever you focus on right before you fall asleep will actually get more attention from your subconscious than other things that occurred during the day.
### Day 16 Action Steps
There is one key takeaway for today—ask questions that will empower and excite you, and avoid questions that keep you focused on what you don't want.
• Make a list of the questions you ask yourself that contain negative presuppositions. Write down the questions you ask yourself that contain negative presuppositions about your problem drinking. These might include some of the examples we have just given you. You might want to also review the top five limiting beliefs you uncovered on Day 11 in the Lie Detector Solution. Most likely you are asking questions that contain presuppositions that reinforce those limiting beliefs. For example, if you believe you have an addictive personality, you might be asking yourself, How am I ever going to quit drinking if I have an addictive personality? This question presupposes that you have an addictive personality and (if that is even true) that it is permanent and unchangeable.
• Write empowering questions. Using the guidelines for asking quality questions, write down an alternative question to any presuppositions you identified, such as, How can I leverage my unique strengths and talents to thrive in sobriety? When you catch yourself asking a question with a limiting presupposition, simply re-ask the question in a way that doesn't presuppose you are stuck and can't change. Ninety percent of the time, you can simply change a "Why" question to a "How can I" question.
• Write your 30-Day Vision Statement question. In your journal, write your updated 30-Day Vision Statement in a question format using our guidelines. Ask yourself this question several times during the day, out loud when appropriate, and especially before you go to bed at night. In Day 2 we asked you to review your 30-Day Vision Statement and your "new you" journal entry for at least two weeks. Since today marks the end of those two weeks, you can stop doing this and simply replace that step with this question.
On the companion website at <http://Day16.Solutions> you'll find a questioning technique that you can use by yourself, and with others, to accelerate the accomplishment of your goals.
## Day 17
## The Eternal Optimist Solution
## Practicing Positive Expectation and Optimism
If you think in negative terms, you will get negative results. If you think in positive terms, you will achieve positive results.
—DR. NORMAN VINCENT PEALE
The quality of your thoughts determines your happiness, your feelings, and ultimately the actions you take and the results you experience. Today's focus is on how to harness the power of your thoughts to help you thrive in sobriety. When you think more positively and limit your negative self-talk, you greatly improve your ability to permanently cut back or quit drinking.
### Negativity Explained
I would say about 80 to 90 percent of most people's thinking is not only repetitive and useless, but because of its dysfunctional and often negative nature, much of it is also harmful. Observe your mind, and you will find this to be true. It causes serious leakage of vital energy.
—ECKHART TOLLE
The opposite of optimism is pessimism, or negativity. Negative thoughts such as complaining, blaming, worrying, and judging others result in feelings of anxiety, fear, anger, resentment, guilt, and shame. When you are caught up in negative thoughts and the negative feelings they create, you are not living in the present moment.
You might be thinking, No, that isn't true. I get angry in the present when I am stuck in traffic or when my boss gives me a project I hate. What is really bothering you in these examples? Have you ever been in bad traffic or been given projects you didn't like, yet you were still in a good mood? The difference was your interpretation of the situation—in particular, your interpretation of what was going to happen in the future because of this.
If you are listening to a great song in the car and have nowhere you need to be, the traffic might not bother you at all. In fact, you might even enjoy the time alone. But if the traffic is going to make you late, you might get angry or frustrated because you assume that being late is going to cause you future pain. The same goes for the project you hate. You make assumptions about the pain you are going to experience in the future when you work on that project.
Here's a story of three people that illustrates this. One person agreed to go outside with a coworker for a smoke break first thing in the morning, something she had never done before noon. Another overslept after staying up late watching football the night before. The third person was about to transfer from a local subway train to an express, as he did every morning, but he noticed how crowded it was and decided to stay on the less crowded local train and just be a little late for work. Each of these people worked at the World Trade Center, and because they were not in the towers on September 11, 2001, when terrorists flew planes into the buildings, they all survived, while their coworkers who were in the buildings did not.
We can't predict the future or change the past. Just because something might appear bad or good to us in that present moment, we really have no idea how to judge a single event without knowing the whole story. And we will never know the whole story.
But you can learn to control your thoughts in the present moment. You can choose to interpret everything that happens as a good thing and be optimistic about it. How much happier would you be if you didn't get caught up in the negativity around the perceived "uncontrollable" and "bad" things that happen to you every day? Would you be as likely to drink?
### Negative Drinking Thinking
Optimism is the faith that leads to achievement. Nothing can be done without hope and confidence.
—HELEN KELLER (1880–1968)
Today we are going to explore positive versus negative thoughts. Unfortunately, this topic is boring, hard to grasp, and most people don't find it useful.
How does reading that make you feel? Probably not too excited to keep reading. And if this chapter contained the single most effective solution that could help you achieve a huge breakthrough, you would probably miss it because your expectations were so negative.
Your expectations change how you feel in the present moment, as well as how you will feel in the future, as you do the thing you have expectations about, whether it is reading this book, going for a jog, or attending a party knowing that you won't be drinking. But many people have been conditioned to have negative expectations more often than positive. (By the way, this topic is not really boring.)
Problem drinkers often get caught up in what we call "negative drinking thinking." They focus on the problems and challenges of drinking, and not on the desire and ability to thrive in sobriety. With negative drinking thinking, your thoughts often come back to complaining, blaming, and resenting, instead of being grateful for all the good things in your life. Mark Twain, the celebrated American author, captured this concept when he said, "I am an old man and have known a great many troubles, but most of them never happened."
What about you? When this insight became really clear to Dave, he was newly sober and had decided to coach his daughter's first-grade basketball team. Five weeks after practices began, the league let a new girl, who had never played basketball before, join the team. And then the girl's mother informed Dave that her daughter would be able to make one of the two basketball practices before the first game. Dave decided to bench her for the first game because he didn't feel she would be prepared after only one practice, and because he thought that it wasn't fair to the rest of the players.
The girl's parents objected to this decision and contacted the league office to complain. It was the holidays, and there were delays in the league responding, which led to a lot of time for Dave to speculate on the eventual outcome. Fortunately, Dave had an insight during this time that dramatically changed his life.
Dave realized that he was being judgmental and resentful of the parents, and was also complaining about the situation. He even thought about how nice it would be to "fall off the wagon" and go drinking with friends and complain about it. He found himself playing out a variety of scenarios about what might happen, like how the league would respond or how the parents would respond, but he realized that all of these were negative. Not once did he think, "The league will support my decision, and the parents will be understanding."
Dave had always thought of himself as a positive person—a true optimist—but he realized now that this was a common theme in his life. When there was a potential conflict, instead of having an attitude of positive expectation, he focused on negative outcomes. This awareness was all Dave needed to change, and he found that once he had freed himself from this bad habit, it created a dramatic shift in the level of happiness he experienced.
Can you relate to this? Do you spend time thinking about negative outcomes or how things can go wrong before they even happen? The more you do this, the more you will have a desire to drink, and the more likely the negative outcomes you envision will happen.
### Negative Thinking Traps
The Eternal Optimist Solution opened my eyes to the fact that I am in control of the amount of negativity I let into my life, and that as long as I keep letting these negative thinking traps lead me back to feelings of self-loathing and anxiety, and ultimately back to drinking, I will never be happy. By implementing the action steps in today's solution, I was finally able to recognize and change my inner voice to support my goals and dreams of living a sober, happy life.
—COURTNEY
30-Day Graduate from Newark, New Jersey
Most everyone has some negative self-talk. To change it, you first need to identify what it sounds like to you. You may hear negative self-talk in interior dialogue in your own voice or in the voice of someone from your past or present who has put you down. Note the tone of the voice in your negative self-talk. The tone is far more important than the actual words. When self-talk is in the negative voice of someone who criticizes you, the overall impact of that self-talk is much more negative and hurtful. It can reinforce false beliefs and trigger a desire to drink. But you can change these negative messages.
The process of identifying and changing these destructive thought patterns or negative thinking traps, which can lead you back to drinking, is used in cognitive therapy, sometimes called talk therapy. This process has been successfully used to treat addiction. In many ways, the action steps for today are similar to the work a cognitive therapist would do with you. The action steps will help you see that your thoughts, feelings, and behavior are all connected. They will help you identify where your thinking is holding you back, and then help you shift that thinking. So if you find today especially valuable, we have included some additional cognitive therapy resources on the companion website, which you may want to check out.
When you actively stop negative thoughts and substitute positive thoughts, you also change negative, self-limiting beliefs and feelings that can trigger low moods and anxiety, which can trigger a desire to drink. Eventually positive self-talk leads to more positive behavior and experiences.
The first step in this process is to review the following list of negative thinking traps for many problem drinkers. Pay attention to the tone and voice of the self-talk in order to identify which traps are familiar to you and hurt your chances for thriving in sobriety.
• Perfectionism. When you are a perfectionist, you constantly judge and critique yourself. Instead, you want to acknowledge that, for most things, "good enough is good enough." Nothing will ever be perfect, so you are setting yourself up for an inevitable failure.
• Negative Labeling. When you define yourself or others with negative labels, such as "I'm a drunk" or "I'm a loser," it only strengthens your attachment to that label and makes it harder for you to change your behavior or your perspective. Avoid labels. You are not a drunk. Drinking is something you do, not who you are. A failure is something you experience, not who you are.
• Generalizing. This is the all-or-nothing trap. It is easy to say "I always" or "I never." You don't always do anything. For example, you don't drink when you are asleep. Instead, focus on specifics: for instance, exactly where and when do you feel uncomfortable, get anxious, and drink? Then use that information to better understand how to shift that behavior. Do you "always get drunk" when you have a drink, or are there times when you have just one or two drinks? Another form of generalizing is to use the words everything and nothing, as in "Nothing ever goes my way" or "I've tried everything, and nothing has worked." The truth is, you haven't tried everything. If you had, you'd already be sober. Generalization also uses the word only, as in "Drinking is the only way I can cope with stress." Of course it is not the only way. You can cope by exercising, dancing, meditation, massage, breathing techniques, tapping, and many more ways.
• Deletion. Deletion shows up with problem drinkers as "euphoric recall," which is the tendency to recall only the positive experiences of drinking and ignore the negative experiences and consequences. You delete all the negative experiences, so the idea of drinking becomes even more enticing.
When we are coaching someone, we generally ask this question: "When you think of some past times drinking, what comes to mind first?" Their answer usually contains mostly positive memories. But when we ask clients specific questions to elicit their bad experiences and the negative consequences of their drinking, they realize that euphoric recall plays a major role in this deletion trap. Euphoric recall also relates to why willpower alone doesn't work—the farther away you are from the pain of drinking, the harder it is to abstain, because you remember the good times and forget the bad times. This is why your journal is a fantastic tool. You can go back and read what really happened, like the "before you" that you wrote about on Day 2.
• Jumping to Conclusions. You jump to negative conclusions and assume that things will turn out badly, or you see something that starts out the way other negative experiences or failures have started out, and you immediately play out the rest in your head. It is important to recognize that every event or situation is unique and different, and to stay open to what is happening in the moment.
• Exaggeration/Minimization. You exaggerate the importance of the "bad" things in your life ("This is the worst thing that's ever happened to me" or "I'm ruined") and minimize or fail to celebrate the significance of good things. Flip this around! Exaggerate the positive and minimize the negative.
• Emotional Reasoning. You get caught up in negative emotions and assume that they reflect the way things really are. Acknowledge that emotions are temporary and can be changed. Notice how you are feeling and ask yourself how you might have come to feel that way. What thoughts are you thinking? What pictures are you imagining? Once you recognize what makes you feel the way you do, it is much easier to identify and change the false logic that created those feelings.
• "Should" Statements. When you say "I should stop drinking," part of you responds by resisting with an "I don't want to, and you can't make me" kind of energy. Replace the word should with the word want, as in "I want to stop drinking." Or "I want to be in control of my drinking." Drop the word should from your vocabulary. Nobody likes to be "should on," including you!
• Personalization. This is when you view yourself as the cause of events that may have nothing to do with you. If you come home to find that your spouse or partner is upset, don't immediately assume it is about or because of you. Ask. Likewise, if he or she is getting ready to go out and says, "Well, I guess the reason you can't go to the party with me is because you're working on that important project for work," you could also end up personalizing this statement by thinking, Why are you always so critical of my work when I'm just trying to make a living and support the family? In fact, your spouse or partner might actually have been feeling compassion and empathy for you.
• Mind Reading. You guess what someone else is feeling or thinking without asking. So just ask. You might be surprised how wrong your assumptions are. Remember: "When in doubt, check it out!"
All of these negative thinking traps, which most problem drinkers struggle with at one time or another, contribute to low self-esteem and cause feelings of overwhelm, disconnectedness, hopelessness, and anxiety—all of which increase the likelihood that you will drink to numb out those feelings. But when you recognize, challenge, and replace your negative thinking patterns with positive ones, you dramatically reduce your desire to drink. So let's look at how you can break out of these repeating patterns of self-defeating thoughts.
### The Power of Awareness
It is our desire that you become one who is happy with that which you are and with that which you have—while at the same time being eager for more. That is the optimal creative vantage point: to stand on the brink of what is coming, feeling eager, optimistic anticipation—with no feelings of impatience, doubt, or unworthiness hindering the receiving of it—that is the Science of Deliberate Creation at its best.
—ESTHER AND JERRY HICKS
Authors of Ask and It Is Given: Learning to Manifest Your Desires
It all starts with awareness. You can't change what you aren't aware of. When you are not conscious of what you're doing, you just keep repeating the same self-destructive habits. The best way to expand your awareness is by journaling every day. That is why we sound like a broken record about writing in your journal—it is a critical component of creating the personal awareness that will lead you to a breakthrough.
Successful people are optimistic. Even in the face of great challenges, they are almost always able to reframe a problem or "failure" as an opportunity to learn and grow. People who struggle usually get caught in negative thinking traps, unable to break the pattern once it begins.
For example, have you ever temporarily cut back or quit drinking, only to disappoint yourself and go back to your old drinking habits? When this happened, did you feel like a failure and revert to negative thinking traps, such as making generalizations and exaggerations ("I'll never be able to stop drinking"), or jumping to conclusions and using emotional reasoning ("I'll never be able to deal with stress without drinking")?
These negative thinking traps will lead you back to drinking, so you want to recognize that those thoughts don't work, and then ask yourself what you need to do differently. For example, ask yourself, How did I handle stress in my life before I started drinking? or What have I done to deal with stress when drinking wasn't an option, such as while at the office? Most likely you will discover that one, or several, negative thinking traps led you back to drinking. Matt's story is a perfect example of how identifying the negative thinking traps in his life led to the breakthroughs he needed to thrive in sobriety.
### Breaking Through Matt's Traps
I haven't gone back to drinking, and the thought of ever having another hangover gives me chills. I feel great, and I can't believe that I wasted a lot of my life trying to avoid life.
—MATT
30-Day Graduate from Kansas City, Missouri
In his early fifties, Matt had a successful career, beautiful wife, two smart and talented kids, and was a respected member of the community. Even though his career success had afforded him the freedom to never have to work another day in his life, he was terrified of not working. At the same time, no matter how successful he was at work, he never believed or felt he was "good enough." So Matt drank almost every night. He recalls how he felt toward the end of his drinking:
I was anxious, depressed, and unhappy, and alcohol helped me cope with my feelings—until it didn't. At that point, I felt desperation setting in, and I remember asking myself, Now what? I started going to Alcoholics Anonymous, where I was told, "Just quit drinking, and things will get better, but it might take a long time." I remember how scared I was to hear this. It painted a gloomy picture of my future—with months or even years of continued anxiety and depression. I knew there had to be a better approach for me, and that's when I found The 30-Day Sobriety Solution.
Within days of starting the program, Matt's life changed for the better. He said, "I would complete a solution every day and know that I was becoming a better person—not just in relation to drinking, but in every area of my life. I started to get my self-confidence back, and more importantly, I started to see a happier, healthier future version of myself that I could become."
During The 30-Day Sobriety Solution, Matt recognized his negative thinking traps, including perfectionism, exaggeration/minimization, jumping to conclusions, personalization, and making "should" statements.
• Since Matt believed he had to be perfect to be enough, he was constantly driving himself to do more and be better. Since "perfect" is never possible, and because his fear of not being perfect enough was always eating away at him, no matter how much he did and how much success it brought him, Matt always felt that "I was never 'good enough.' My self-esteem was dependent on getting praise from others, especially at work, since I had no self-esteem. No amount of praise was enough, and I lived my life in this fog that I tried to lift by drinking."
Because Matt needed to appear to be perfect, he exaggerated his accomplishments and minimized his failures in the hope of getting more approval. But in his heart, he knew he wasn't being authentic and truthful, which only further increased his desire to drink.
• Matt jumped to conclusions and personalized other people's actions. As a result, he was continually asking himself, What did they mean by that comment? Why didn't they give me the acknowledgment and recognition I deserved? Are they jealous, or are they trying to imply that I'm not good enough?
• Because he thought he was not good enough, Matt constantly felt that he should be doing more, and his self-talk contained a constant stream of "should" statements: I should make more money. I should get promoted. I should be the hero on the team, rescuing my coworkers by taking on their responsibilities. When he did rescue coworkers, and they didn't reciprocate, he ended up feeling angry and resentful.
As Matt changed his negative thinking traps, he dramatically curbed his desire to drink. Three years later, almost every aspect of Matt's life has markedly improved. He quit his old job and was inundated with more interesting opportunities. He changed his diet, started exercising regularly, and lost fifty-three pounds, which he has kept off. He also started spending more time with his wife and kids, something that had always come last, after his job and his drinking. As a result of all these positive changes, he decided that his life was much better when he completely abstained from alcohol, which was quickly validated after he briefly returned to drinking on two different occasions.
Matt's two returns to drinking were short-lived, lasting only a few days each time, and happened only at night. He said, "I knew I had a choice, but the few hours of semipleasure that drinking gave me was far outweighed by the self-contempt I felt afterward and the knowledge that drinking came at the ultimate cost of sacrificing my real happiness." Matt hasn't drunk any alcohol in over two years, enjoys attending AA meetings, and still revisits some of the 30-Day solutions in the program when he feels that he is getting off track.
### How Do You "Fix" a Dark House?
What you focus on expands, and when you focus on the goodness in your life, you create more of it. Opportunities, relationships, even money flowed my way when I learned to be grateful no matter what happened in my life.
—OPRAH WINFREY
Host and producer of the top-rated, award-winning The Oprah Winfrey Show
In their program "The 11 Forgotten Laws," Bob Proctor and Mary Morrissey ask, "What do you do when you walk into a dark house and you can't see?" The answer, of course, is simple—you turn on a light. You don't try to push away the darkness. You simply turn on a light. And then another, and another. The solution is exactly the same for overcoming negativity. Instead of trying to push away your negative thoughts, you replace them by choosing to think of something more positive. As you fill your mental "house" with the light of positive thoughts and expectations, there will be no room left for the darkness of your negative thoughts.
Similarly, instead of focusing on quitting drinking, focus on thriving in sobriety. Instead of focusing on resentment and anger toward the people who have hurt you, focus on understanding and forgiving them. Instead of focusing on your mistakes and your failures, focus on your lessons and your successes. Instead of focusing on your limiting beliefs, focus on the positive beliefs you have written to replace them. Instead of focusing on images of what you don't want, focus on images of what you do want. When you keep "turning on the lights," the rest will take care of itself!
Our clients tell us that when they finally "get this" and apply it regularly in their lives, they wonder how and why they ever got stuck in the mental trap of focusing on what they don't want. In retrospect, the positive-focus approach seems so obvious, yet their unexamined habitual thoughts and their drinking kept them from ever being able to see it clearly.
### Negative Traps in Your Life
A pessimist sees the difficulty in every opportunity; an optimist sees the opportunity in every difficulty.
—WINSTON CHURCHILL (1874–1965)
Prime minister of Great Britain
In his book The Power of Your Supermind, bestselling author Vernon Howard explains the importance of identifying negativity in your life. He writes, "Honest self-observation dissolves pains and pressures that formerly did their dreadful work in the darkness of unawareness. This is so important I urge you to memorize and reflect upon the following summary: Detection of inner negativity is not a negative act, but a courageously positive act that makes you a new person."
The first action step for today is to write down each of the negative thinking traps above in your journal and then write about how each one shows up in your life. Include specific examples, and be sure to add as many details as you can, such as when, where, and especially with whom. As you write about each, see if you can discern whose voice is speaking. Are there "should" statements coming from your father? Or negative labeling from your mother? Or your ex? Notice the tone of voice of these thoughts. Is it in your voice or someone else's? Is it accusatory, angry, or demanding? These are all clues to where the thoughts are coming from.
For example, we see many partners and spouses who try to read the other's mind—they try to discern how the other is feeling without asking. They may also struggle with deletion, where one will let a single negative comment completely delete other positive comments. Remember, even though you are looking at internal negative self-talk, negative comments can show up externally in a conversation or argument. For instance, you might use generalizations at times with your spouse or partner by internally getting annoyed with something he or she said and think to yourself, You always do this. Then you might eventually decide to say out loud, "You always do . . ." instead of, "It seems like at certain times you do . . ."
The next step is to write down how you can change each negative thinking trap. If you catch yourself thinking, I can never quit drinking (a generalization), then write down what is really true. When do you struggle the most not to drink? Weekends? Weekdays? When you are at a party, or when you are home alone? Also, is this really true? Do you know or have you read about people like yourself who have quit drinking and are happy? Last, what are the tone and voice of this generalization? Do you hear one of your parents' voices saying this in a condescending tone? Or an ex-spouse or former boss?
Another example might be a night where you almost always drink, but for whatever reason, you did not drink this time. What emotions did you experience? Did you feel frustrated, bored, or sad because you were not drinking? Did you feel that those emotions were permanent, like in the emotional reasoning trap, or were you able to recognize that they were temporary feelings and that you had the power to change them?
When you think about drinking and your past experiences of drinking, do you remember only how much fun you had (euphoric recall)? Do you delete the times you felt lonely and sad when drinking, or the mean and hurtful things you said while drinking, or how you felt the morning after a night of heavy drinking? Does your "drinking thinking" recall only the positive moments and delete all the negative ones?
This is a powerful process because you will start to recognize specific triggers, patterns, and places where you get caught up in negative thinking, which can lead you right back to drinking. Sometimes the awareness of these patterns in your life is all you need to make a lasting change.
For more examples of how these traps commonly show up for problem drinkers, you can visit today's companion website.
### The Positive Thinking Trap
You have to see things as they really are but not worse than they are—that view of life only gives you the excuse not to do something.
—TONY ROBBINS
Not all positive thinking is the same. As great as positive thinking is, it is possible for it to hold you back by basically tricking you into a state of complacency. Gabriele Oettingen, a professor of psychology at New York University, and her colleagues completed several studies of goal setting, and they discovered that by focusing only on positive thoughts, participants tricked themselves into believing they had already succeeded, which resulted in their having less drive to do the actual work required.
They discovered that the optimal approach is to practice a technique called "mental contrasting," which includes positive thinking. First, spend several minutes thinking of your goal and imagining your achievement of that goal. Then, think about the obstacles that you will have to overcome and how you will do so. This is similar to the strategy we recommended on Day 3 in the Pendulum Solution and the one that hip and knee surgery patients used to recover almost twice as fast as others who didn't envision specific goals and recovery methods.
Our message here is this. Don't let a simplistic or overly positive attitude blind you to the actual challenges you will face and the work you will have to do to accomplish your goal. Have a positive expectation that you will succeed and think about how you will handle these inevitable challenges (cravings, uncomfortable feelings, office parties, and peer pressure). And, of course, keep doing the action steps and solutions in The 30-Day Sobriety Solution.
### Day 17 Action Steps
One of the most powerful takeaways from The 30-Day Sobriety Solution, outside of finally removing my desire to drink, was all the notes I wrote in my journal throughout the program. Now when I start to feel my "drinking thinking" kick back in, I just read my journal, and specifically some of my favorite entries, which almost immediately gets me excited about my future and inspires me to take positive action.
—LENORE
30-Day Graduate from Dallas, Texas
Whether you call it positive self-talk, positive thinking, or simply optimism, the more you have in your life, the more you will thrive. Without a positive or optimistic outlook, the possibility of truly thriving in sobriety is almost nonexistent.
• In a bad mood? STOP—and analyze your thoughts. Ask yourself, What am I thinking about? What is my negative self-talk? Whose voice is it? What is the tone of voice? What visual images am I focusing on? Once you are aware of what is putting you in a bad mood, change your thoughts by using what you have learned today and in past solutions.
• Write down your negative thinking traps. Write down all the thinking traps in your journal and write about how each one shows up in your life. Include examples, such as when, where, and with whom, and be sure to include the euphoric recall trap if that is something you experience. Notice if those thoughts are in your voice or someone else's. For example, you may have started The 30-Day Sobriety Solution with the jumping-to-conclusions trap by saying or thinking, Everything else I have tried to stop drinking has failed, so this program is going to fail, too. Include examples in your life that show up in your conversations with friends and family.
• Write down how to change each of your traps. For example, if one of your traps is jumping to conclusions, ask yourself, What is different about this attempt to quit from the other times I have tried, and what is different about this program compared with others I have tried? If one of your traps is making "should" statements, ask yourself, What statements could I use that would demonstrate my willing choice to participate instead of using guilt to motivate myself? In a positive tone, ask, What specifically is holding me back from what I want? And if you find yourself making "should" statements to others about what they ought to do, change this by first asking them whether or not they would like any advice from you.
On the companion website, you will find a study that reveals the two most self-destructive words you can ever use, and the simple change you can make to eliminate them from your thinking and your speech. In addition, we explore a famous experiment with water that demonstrates how words and thoughts actually create a physiological change in your body. Be sure to visit <http://Day17.Solutions>.
## Day 18
## The Affirmation Solution
## The Power of Affirmations
I've always believed in magic. When I wasn't doing anything in this town, I'd go up every night, sit on Mulholland Drive, look out at the city, stretch out my arms, and say, "Everybody wants to work with me. I'm a really good actor. I have all kinds of great movie offers." I'd just repeat these things over and over, literally convincing myself that I had a couple of movies lined up. I'd drive down that hill, ready to take the world on, going, "Movie offers are out there for me, I just don't hear them yet." It was like total affirmations, antidotes to the stuff that stems from my family background.
—JIM CARREY
One of the best ways to thrive in life and sobriety is to bombard your subconscious with inspiring thoughts, images, and affirmations. See yourself joyfully attending a party, drinking a sparkling mineral water; having a trim and healthy sober body; enjoying exciting work; interacting with interesting and supportive friends; being a role model to your children; and experiencing all your goals as already complete.
An affirmation is a statement that describes a goal in its already completed state, such as your 30-Day Vision Statement that you wrote on Day 2 as part of the Purpose Solution. Today we will teach you exactly how to write and use affirmations to accomplish your sobriety goals.
### The Philosophy of Personal Achievement
Andrew Carnegie, the industrialist-turned-philanthropist, challenged a young and unknown journalist named Napoleon Hill to write a philosophy of personal achievement. Carnegie told Hill that if he committed to documenting and recording this philosophy of success over the next twenty years, he would introduce the journalist to the wealthiest, most successful men of the time. Hill immediately accepted the challenge.
Over the next two decades, Napoleon Hill interviewed 504 people, including business titans Henry Ford, Charles M. Schwab, King Gillette, and John D. Rockefeller; inventors Thomas Edison and Alexander Graham Bell; and three US presidents. In 1937 he published his findings in a thirteen-step formula called Think and Grow Rich: Teaching, for the First Time, the Famous Andrew Carnegie Formula for Money-Making, Based upon the Thirteen Proven Steps to Riches, which sold more than thirty million copies.
Saying the book was ahead of its time is an understatement. Since Hill's book, countless books and studies have validated and expanded on his findings. Think and Grow Rich has influenced the field of personal development. Yet the word rich is somewhat misleading, because this book is not simply about accumulating monetary or material wealth but also about having an abundance of loving relationships, health, and joy.
One of the key tools for success in Think and Grow Rich is the power of affirmations.
### Trust Us, Affirmations Actually Work!
Despite all the published research that affirmations work, many people still doubt their effectiveness. Not only do affirmations work, but we consider the use of affirmations to be one of the top five techniques that ensure success, happiness, love, and sobriety.
We have both experienced firsthand how writing and practicing a new affirmation brings a goal to fruition. We both first used affirmations to create quantum leaps in our careers—Jack went from earning $8,000 a year to $100,000 and later to over $1 million a year. Dave went from being an unemployed college graduate to becoming the first employee of a promising start-up to earning double his previous salary. In both cases, our new incomes were nearly identical to amount we had written down and practiced daily in our affirmations. These successes taught us early on that the daily practice of affirmations is powerful. We have continued to find validation of their effect in our own lives and the lives of our clients, and we believe that affirmations need to be a core component of every recovery program.
### The Magic of Affirmations
It's the repetition of affirmations that leads to belief. And once that belief becomes a deep conviction, things begin to happen.
—MUHAMMAD ALI
Napoleon Hill defines an affirmation as "repeated instructions to the subconscious mind, through the principle of auto-suggestion." Affirmations are also called declarations or mantras, but the clearest explanation is that they are your goals written down in a completed state.
The conscious mind is rational. It distinguishes right from wrong and directs many of your thoughts. The subconscious mind records everything from your five senses (touch, smell, hearing, sight, and taste), stores this information, and replays it during your daily life to influence your thoughts and actions. Affirmations can reprogram your subconscious to make sure that it helps you achieve your new goal.
By focusing your consciousness on affirmations, you remind yourself what you want. You engage in positive self-talk rather than negative self-talk. Repeating an affirmation numerous times a day improves its effectiveness, rewires your subconscious, and keeps you from getting sidetracked with negative self-talk. You maintain focus on your goals, and the repetition has a greater impact on your subconscious. All of this leads to a shift in beliefs, removes limitations, and drives your actions toward your goals.
In The Magic of Believing: The Science of Setting Your Goal and Then Reaching It, Claude M. Bristol writes, "Repetition of the same chant, the same incantations, the same affirmations leads to belief, and once that belief becomes a deep conviction, things begin to happen." Once you shift your beliefs, the accomplishments you seek will soon follow as you start taking actions that move you toward your goal without even consciously thinking about it.
### Eight Guidelines for Creating Effective Affirmations
To be effective, your affirmations should follow eight guidelines:
1. Start with the words "I am." The words "I am" are the two most powerful words in the English language. The subconscious takes any sentence that starts with the words "I am" and interprets it as a command—a directive to make it happen.
2. Use the present tense. Describe what you want as though you already have it and as though you've already accomplished it.
3. State it in the positive. Affirm what you want, not what you don't want.
4. Keep it brief. Make your affirmation short enough and clear enough that you can remember it easily.
5. Make it specific. Vague affirmations produce vague results.
6. Include an action word ending with -ing. The active verb adds power to the effect by evoking an image of doing it or experiencing it right now.
7. Include at least one dynamic emotion or feeling word. Include the emotional state you would feel if you had already achieved the goal. Some commonly used words are enjoyment, joy, happiness, celebration, pride, calm, peace, delight, enthusiasm, love, security, serenity, thrill, and triumph.
8. Make affirmations for yourself, not others. Your affirmations describe your behavior, not others' behavior. Instead of saying, "I am so happy my coworkers now accept and support my decision to live a sober lifestyle," you would say, "I am happily choosing to stand firm in my decision to live a sober lifestyle—even at company parties."
Here's an example of an affirmation that meets all eight criteria: "I am happily drinking sparkling mineral water at my daughter's wedding reception."
### Your Total Sobriety Affirmation
By now you probably recognize many of these guidelines from other solutions. We used affirmations on Day 2 with your 30-Day Vision Statement and on Day 4 with your forgiveness affirmation.
Today your first action step is to write your Total Sobriety Affirmation. This is one paragraph composed of several affirmations that represent your completed sobriety goals and your personal transformation from being a problem drinker to being a person thriving in sobriety. To do this, you will build on three of the past solutions. And don't worry about having to make it "perfect." Just think of this as a first draft. As you repeat the affirmations over time, the changes you need to make will become obvious, so all that matters now is that you begin writing.
Start by revisiting the 30-Day Vision Statement you wrote on Day 2 and then revised on Day 10 with your core values. If your vision statement doesn't follow these guidelines, take a moment to update it. See the example below.
Day 2 Example. Every day I wake up feeling excited, vibrant, and passionate about living a meaningful and fulfilling sober life.
Updated Affirmation. I am enjoying waking up every day feeling excited, vibrant, and passionate about living my meaningful and fulfilling sober life.
We simply added "I am" to the beginning of the sentence and adjusted the rest accordingly.
The next step is to write an affirmation for each of the SMART goals you committed to on Day 6, as in the following example:
Day 6 Example. I will have an amazing group of friends who are supportive of my sobriety, and regularly find creative, healthy, and fun activities to do with me that make thriving in sobriety a reality in my life by January 31, [year], at 9:00 a.m.
Updated Affirmation. I enjoy playing with my amazing group of friends who totally support my sobriety by finding creative, healthy, and fun things we can do together.
The next step is to review the list of the five limiting beliefs you identified and rewrote on Day 11 in the Lie Detector Solution (which we hope you have been reviewing regularly). Rewrite each of these as positive affirmations. For example:
Day 11 Updated Belief. I can create a more successful career when I am sober because I am more awake, clearheaded, and focused.
Updated Affirmation. I am being recognized at work for consistently exceeding expectations, which has led to exciting opportunities for promotion and new friends.
Feel free to add any more affirmation statements that you would like. You might decide there is nothing else to add, but before you decide that, go back and reread the first two pages of the "Getting Started" chapter, where we asked you to determine if this book was a fit for you. If any of these questions apply to you, make sure you have an affirmation to deal with each of them. For example:
Getting Started Question. Are you concerned with the effects of your drinking on your finances, family relationships, health, weight, and/or career?
Updated Affirmation. I am leaving the doctor's office feeling happy and relieved after hearing that my weight, blood pressure, and resting heart rate are perfect for my age and body type, and that all my blood work results are positive.
———
By combining these affirmations, you will have a long paragraph that is now your personal Total Sobriety Affirmation. This affirmation is very powerful. Even though it might not have taken very long to put together, you have spent a significant amount of time over the course of this program building the pieces that you are now combining in this personalized new statement. And as you work with your Total Sobriety Affirmation, these statements will become a reality in your life. To see more examples of creating effective affirmations and some other completed Total Sobriety Affirmations, be sure to visit the companion website. This can be an especially valuable resource if you feel stuck or need help with completing this solution.
### How to Use Your Affirmations
Written affirmations are . . . very effective. But I have found that repeating a mantra aloud has a wonderful effect on my spirit. When I need to feel motivated, I might repeat, "I am inspired, disciplined, and energized" out loud two or three hundred times. To maintain the supreme sense of self-confidence I have cultivated, I repeat, "I am strong, able, and calm." I even use mantras to keep me youthful and vital.
—ROBIN SHARMA
Author of The Monk Who Sold His Ferrari: A Fable About Fulfilling Your Dreams and Reaching Your Destiny
Now that you are empowered with your personal Total Sobriety Affirmation, you're probably wondering, How do I use it? The power comes from the repetition of reading it over and over until it becomes locked into your subconscious. Therefore, we want you to review it a minimum of three times a day, 30 days in a row. The best times are when you first wake up in the morning, in the middle of the day to refocus yourself, and at bedtime. Repeating your affirmation right before you go to sleep gives your subconscious mind six to eight hours to focus on it.
Because affirmations are one our of favorite tools, when we are focused on manifesting something that is really important to us—such as a new career or health goal—we will write an affirmation statement and repeat it out loud fifty, one hundred, or even "two or three hundred times," as Robin Sharma recommends. After a while it becomes a mantra, which we repeat out loud while driving or working out, or silently in a meeting or while waiting in line. Find what works best for you, but remember, more repetition creates faster results!
• Read it out loud. When appropriate, read your affirmations out loud in a firm, confident voice. This is not possible all the time, so it is just fine to read it silently to yourself when necessary. Both work. However, when you say your affirmation out loud, you can read it with more emotion.
• Record it. Record your affirmations and listen to them while you work, drive, exercise, or fall asleep. You can use your smartphone, an MP3 player, or an iPod or iPad.
• Post it. Write your affirmations on three-by-five-inch cards or sticky notes and carry them with you or post them where you will see them. You can also post them as the screen saver on your tablet or computer, as a note on your phone or tablet, or as a recurring meeting on your calendar. You can also use your phone to take a picture of your affirmations and store it in your photos. Make sure to protect your privacy where appropriate.
• Adjust it. Repeat your affirmations in the first person ("I am . . ."), second person ("You are . . ."), and third person ("He/she is . . ."). Or after you say "I," say your full name ("I, Jack Canfield, am . . .").
• Use it. When you catch yourself complaining, blaming, justifying bad behavior, or practicing any negative self-talk, replace that behavior by reviewing your affirmations.
• Ask questions. After reviewing each of your affirmations, ask a related question like you learned on Day 16 in the Quality Question Solution. For example, "How can I wake up every day excited and passionate about living a meaningful and fulfilling sober life?"
### Supercharge Your Affirmations
Habits of thinking need not be forever. One of the most significant findings in psychology in the last twenty years is that individuals can choose the way they think.
—MARTIN SELIGMAN
Psychologist, educator, author of Authentic Happiness: Using the New Positive Psychology to Realize Your Potential for Lasting Fulfillment
You can accelerate and deepen the impact of your affirmation using some or all of the following techniques.
• Visualization. After repeating the affirmation, close your eyes and visualize what you have just affirmed. See it as if you were looking out at the scene from inside of yourself. In other words, don't see yourself standing out there in the scene; see the scene as if you were looking through your own eyes while you experience what you are affirming.
• Use your other senses. Imagine what you would be feeling, tasting, smelling, and hearing when you successfully achieve what your affirmation describes—the sound of your voice as you casually decline the offer of an alcoholic beverage, the loving and nonjudgmental touch from your partner or family member, the taste of a delicious Starbucks Frappuccino, or the smell of your sober breath and the feeling of security you experience when you are pulled over at a sobriety checkpoint.
• Include people acknowledging you. Include the images and sounds of important people in your life congratulating you and telling you how pleased they are with your success at cutting back or quitting drinking for good.
• Add emotion. Feel the emotions that you will feel when you achieve that success. This is really important. The stronger the feelings, the more powerful the process.
• Use tapping. While saying your affirmation, tap on the eight acupressure points you learned on Day 13.
When you combine empowering affirmations with detailed visualizations and tapping, you have an unbeatable process to create massive change in a short amount of time.
### "I Am an Alcoholic"
Going to AA meetings actually made me want to drink . . . the focus seemed to be that you should always be scared because you were on the brink of drinking again. And I found it counterproductive to be constantly calling myself an alcoholic and saying that I was helpless. Overall, I know it has helped millions of people, and I respect that, but personally I found it to be negative in its approach and that the focus was always on "not drinking" instead of "thriving in sobriety."
—JAMES
30-Day Graduate from Istanbul, Turkey
Between the two of us, we have attended hundreds of Alcoholics Anonymous (AA) meetings. AA has helped Dave and three of Jack's family members get and stay sober.
As much as we are grateful for the existence of AA and the millions of people it has helped worldwide, we feel that the recommendation to attend AA meetings should come with some advice.
One of the oldest rituals in AA meetings is to introduce yourself at the start of the meeting by saying, "My name is Dave, and I'm an alcoholic." You are also supposed to repeat this phrase anytime before you speak at the meeting. And the reasoning behind this is clear—denial is a major issue with alcoholics. If you can't first accept that you have a problem, then overcoming it is impossible.
The problem, we believe, is that the phrase "I am an alcoholic" is also an affirmation. The process of personally repeating this affirmation and hearing it repeated dozens and dozens of times in a single meeting can be self-defeating—especially when you consider the impact of this constant repetition over the course of months and years of attending meetings.
This phrase also regularly affects your self-image. A large part of human behavior is influenced by how we see ourselves. When you have the self-image of an alcoholic, your subconscious will instinctively work to create the reality that matches that image. Whatever identity you reinforce and hold on to is the one that will eventually win out. By repeating the phrase "I am an alcoholic" over and over again, you are ultimately reinforcing this self-image, consciously and subconsciously.
AA meetings can be a fantastic resource. They can help you overcome your guilt and shame and start to believe it's possible to get sober. However, if you decide to use AA as a resource, we recommend that you silently repeat your 30-Day Vision Statement from Day 2 every time you hear the phrase "I am an alcoholic." You can even choose to just introduce yourself without labeling yourself as an alcoholic, since this is not a requirement for attending.
### Day 18 Action Steps
Napoleon Hill is widely credited with having influenced more people to create success than anyone in history. He concluded that affirmations were a critical part of the thirteen-step formula he published. That alone should convince you that if you are not using affirmations in your life, you need to start today.
• Write your Total Sobriety Affirmation. Using the eight guidelines for writing affirmations, update your 30-Day Vision Statement from Day 2 (if necessary). Also, rewrite your SMART goals from Day 6 as affirmations, rewrite your new beliefs from Day 11 as affirmations, and review the questions from the "Getting Started" chapter and write any additional affirmations for anything you feel is missing. This is your own personalized and incredibly powerful Total Sobriety Affirmation.
• Use your Total Sobriety Affirmation daily. Repeat your Total Sobriety Affirmation at least three times a day. And use the tips and supercharging recommendations that are provided in the Affirmation Solution.
• Listen to the thriving-in-sobriety guided affirmations. On the companion website, we have created some guided affirmations to help you reinforce, both consciously and subconsciously, what is most important to you over the long run. After listening to this recording of our favorite affirmations, you will feel more confident, inspired, and empowered.
On the companion website, we have posted additional Total Sobriety Affirmations, which are a great resource to help you write yours. We also include a list of some of our favorite affirmations that you might wish to add to your list. Visit the website at <http://Day18.Solutions>.
## Day 19
## The Attraction Solution
## Using the Law of Attraction to Accelerate Your Success
Every thought vibrates, every thought radiates a signal, and every thought attracts a matching signal back. We call that process the law of attraction. The law of attraction says: That which is like unto itself is drawn. And so, you might see the powerful law of attraction as a sort of Universal Manager that sees to it that all thoughts that match one another line up.
—ESTHER and JERRY HICKS
The law of attraction is known as the "universal law." Like attracts like. The core teachings of the law of attraction are found everywhere—from ancient texts, religious and spiritual teachings to modern-day philosophy, psychology, and self-help books. Whether you intentionally "use" the law or not, just like the law of gravity, it is always affecting you. It is critical that you learn how to leverage this incredibly powerful force in a positive way. In today's solution, we will teach you exactly how.
All of the principles and techniques covered in solutions 11 through 20 are related to harnessing and directing this powerful force. Visualization, affirmation, positive thinking, focusing on what you do want rather than what you don't want, releasing your limiting beliefs and emotional wounds through tapping, and practicing gratitude are all tools that will raise your level of vibration and activate this force to attract what you want into your life.
Today we will dive even deeper into how to make sure you are on the right side of this law as you create your sober and happy life.
### Ask, Believe, Receive
And whatever you ask in prayer, you will receive, if you have faith.
—MATTHEW 21:22
Ask. Believe. Receive. These are the three steps to manifesting what you want using the law of attraction. Let's look at this simple formula.
1. Ask for what you want. The first step is to get really clear about what you want. What does your ideal life thriving in sobriety look like? Think of it as if you are filling out a purchase order to the universe. You can have everything you want. All you have to do is add it to your online shopping cart. Take time to design your ideal life—including your inner experience, like how you want to feel, your attitude, your beliefs, and your physical sensations (relaxed, calm, pleasure), as well as the outer physical world. Write it all down. Also remember that every thought you think, every desire you have, every preference you have is sending out an "ask" to the universe. The old adage that "what you think about comes about" is true.
2. Believe it. Have unwavering faith that you will receive what you are asking for. The power of belief has been proven. The more you believe that you will get it, the more you will manifest it. Remember the placebo effect, which has been proven to cause resolution of symptoms (and real physiological change) in up to 80 percent of the patients in clinical trials who are treated with nothing more than sugar pills, saline injections, or fake surgeries.
3. Receive it. Act as if it is already yours. This means thinking like, talking like, dressing like, acting like, and feeling the feelings you would feel like the person who has already achieved your sobriety goal. This is called "being a vibrational match" for what you want. This includes keeping yourself in a state of love, joy, and appreciation. Think about this in regard to thriving in sobriety. Imagine you are an actor who has been cast in the role of being the sober you that you dream of. Start acting the part now. How would you act? What would your self-talk be? How would you show up at a social function? Think and feel the part now.
We're going to add a fourth step to this formula—what you do when you achieve or receive what you want—the practice of gratitude.
4. Be grateful for it. Be thankful for getting what you want. As we'll explore more fully in Day 20, gratitude is the healthiest of all human emotions, so whenever you receive or achieve what you want, take time and pause to experience your appreciation and gratitude—to God, the universe, and any people who helped contribute to your success.
If you repeat this process—ask, believe, receive, and be grateful—continually, you will find that health, wealth, fulfilling relationships, and lasting sobriety will come to you quickly and easily.
### A Lawyer's "Secret" to Sobriety
The solutions I learned from The 30-Day Sobriety Solution have been extremely effective in maintaining sobriety and thriving in it; they are the foundation upon which my sobriety is based.
—DAN
30-Day Graduate from Jackson, Wyoming
Dan's childhood had looked great from the outside. His dad was a successful doctor, his mother loving and supportive. His siblings were fun, smart, and frustrating in a "normal" kind of way. His family was full of high achievers, and even though Dan felt he had to work harder than many of his peers, he was more than willing to put in the time to live up to his parents' and his own expectations. His hard work paid off—he graduated from law school, passed the bar exam, and eventually started his own successful law firm. He fell in love, got married, and became a father to two beautiful, healthy children. It seemed like Dan had it all.
But all of these successes took a toll on Dan. Deep down he was always afraid of failing, of letting his parents down, of not being a great father, and of not being able to financially support his family. Over the years he found escape from these fears by drinking.
His drinking started socially, but by the time he was in his late twenties, it had become a problem and was getting worse. As his law firm became more successful, he drank alone more often. At first he mostly drank in the evening, but then began drinking over lunch, and eventually through the afternoon and evening. Dan tried quitting a dozen times over the years, but nothing worked. He told us:
I was a highly educated, practicing attorney with nearly eight years of running my own law firm, yet everything was on the brink of collapse. I could no longer work a normal workday. My lovely wife was on the verge of asking me to leave the house and separating me from my two young kids. My friends were wondering why I was acting so terrible and erratic. My binge drinking had finally spiraled completely out of control.
One day in his early forties, Dan found The 30-Day Sobriety Solution. Even though he was skeptical about his ability to get sober, let alone be happy sober, he was encouraged. As he worked through the program, he was excited to recognize the techniques from other books he had read, although he had not been able to "translate" them effectively into helping him to quit drinking until now. Dan had practiced the law of attraction and "ask, believe, and receive," but until The 30-Day Sobriety Solution, he had not known how to apply it to sobriety. Over the course of the program, Dan felt like he actually discovered the real secret—the secret of sobriety.
Today Dan has over three years of sobriety, something he had always hoped for but previously doubted would ever happen. Better yet, he is actually happy. He saved his marriage, is the father he always dreamed of being, and is flourishing in his career. Dan recently shared, "I continue to use the solutions I learned in The 30-Day Sobriety Solution to improve my connection to the person I want to be and know I can be. I move closer to that person every day."
For Dan, attending Alcoholics Anonymous meetings is a valuable ongoing support for his sobriety. When he sees new people attend meetings right after they hit rock bottom, their puffy faces, dejected attitude, and overwhelming feelings of fear and desperation continually remind Dan of the pain drinking once caused him. He enjoys being able to offer hope and inspiration to others that lasting change is possible.
### The "Daydreamer's Dilemma"
Financial success, or any other kind of success, does not require hard work or action, but it does require alignment of thought. You simply cannot offer negative thought about things that you desire and then make up for it with action or hard work.
—ESTHER and JERRY HICKS
Do you like to daydream? We do. It can be a fun escape. Maybe you put on some great music and let your imagination run wild. Sometimes the daydreams are just fun and really aren't important to you, but other times these daydreams are about goals that you believe hold the key to your ultimate happiness and fulfillment. And guess what? You are right.
Have you ever paid close attention to what happens after you seriously start thinking about achieving those goals? Usually some form of doubt sets in, which we call the "Daydreamer's Dilemma." For example, have you noticed that, when you dream about being sober, how proud everyone will be, and all the great changes you will make in your personal and professional life, almost immediately, the "what-ifs" start to kick in. What if I tell everyone and I fail again? What if I decide I don't want to change? What if I am not happy when I'm sober? What if this is just meant to be my life? What if I simply can't do it?
Do you do this in other areas of your life, too? You start thinking about a dream or goal, but then your thinking immediately shifts to how disappointed you, or others, will be when you fail? Unfortunately, this is an all too common phenomenon. Most people are great at wanting "more," but lousy at believing they can have it, or receive it. They are more accustomed to and comfortable with not getting what they want. And by "want," we don't mean getting the newest iPhone. We are talking about the life-changing "wants"—finding the love of your life, landing your dream job, having total financial freedom, and absolutely loving your new sober life.
However, getting what you really want often makes you uncomfortable because you are not used to it. You may have gotten used to following up your big "wants" with the expectation that you will not get them. Because of the law of attraction, this negative expectation virtually guarantees the opposite outcome of what you really want. In their book Money, and the Law of Attraction: Learning to Attract Wealth, Health, and Happiness, Esther and Jerry Hicks talk about this in relation to money:
Most of you are much closer to a financial fortune than you are even allowing yourself to purely desire, because, in the thought that it might come, you right away begin thinking of how disappointed you will be if it does not come in. And so, in your lackful thought, you do not allow yourself to desire or to expect anything magnificent in terms of money; and that is the reason why, for the most part, you are living rather mediocre financial experiences.
Your first action step for today is to pay attention to what thoughts and feelings come up the next time you are thinking—or daydreaming—about what you really want. If you catch yourself doubting your success, expecting failure, or thinking about why you can't accomplish your goal, acknowledge the thoughts and then go through the steps of the "ask, believe, receive" process with your goal.
### Input Equals Output
Psychologists have shown that the more television you watch, the lower are your levels of energy and self-esteem. At an unconscious level, you don't like or respect yourself as much if you sit there hour after hour watching television. People who watch too much television also gain weight and become physically unfit from sitting around too much.
—BRIAN TRACY
Dave's wife is a child therapist who knows that, in order to have a lasting positive impact on younger children, she has to work with their parents. One of the most basic concepts she teaches parents is that input equals output, or as it is often stated, "Garbage in, garbage out." In other words, don't expose young children to violent movies, books, video games, and TV shows, especially most nightly news programs, which primarily report murder, suicide, rape, deadly diseases, fires, and car accidents. Repeated exposure to these stories and images negatively affects children's personality, behavior, and how they interact with other kids. Some parents are surprised at how quickly their children's behavior changes for the better when they eliminate most exposure to these influences.
But the negative influence of negative news does not stop when you become an adult. If you are in the habit of watching the news before you go to bed, you are filling your head with negative, disturbing images and thoughts, which your subconscious focuses on all night. In his book 100 Ways to Motivate Yourself, Steve Chandler writes:
The news is not the news. It is the bad news. It is deliberate shock. The more you accept it as the news, the more you believe that "that's the way it is," and the more fearful and cynical you will become.
If we realized exactly how much vulgar, pessimistic, and manipulative negativity was deliberately packed into every daily newspaper and most television shows and Hollywood movies, we would resist the temptation to flood our brains with their garbage. Most of us are more particular about what we put in our automobile's gas tank than we are about what we put in our own brain every night. We passively feed ourselves with stories about serial killers and violent crime without any conscious awareness of the choice we are making.
However, the good news is that you can easily change this, and we have five key recommendations to help you with your second action step for today.
First, stop watching the news—at least the typical news programs that focus primarily on negative news. This doesn't mean you have to ignore all news—simply use news resources that allow you to pick and choose what you want to read. With all the online news aggregators available, you have virtually unlimited options. And if you want local news, visit your local affiliate's website, or see if they have an app for your phone. When you visit any of these websites, simply ignore the "bad news" unless you feel strongly that it is relevant.
Second, take a hard look at the TV shows and movies you watch, the books you read, and the video games you play. Be deliberate about your choices. We are not saying you should avoid all scary, violent, or negative content that makes you afraid and worried, but we are saying you should consciously limit it and actively choose other content that puts you in an inspired, positive, and uplifted state of mind. And if you do choose to watch TV before bed, pick something funny, inspiring, or educational.
Third, pay attention to your feelings. Ask yourself, Does this TV show, book, game, or movie add any real value to my life? If not, stop it.
Fourth, pay attention to any "inputs" that have a negative impact on you—not just broadcast media, but people, websites, social media sites, smartphone applications, specific locations, or even certain topics of discussion.
Last, revisit the Forgiveness Solution. Because you attract energy that matches the vibration of your feelings, being negative, angry, and unforgiving ensures that you'll attract more people and situations about which you'll be negative, angry, and unforgiving. If you feel that you haven't been able to fully embrace forgiveness, for others and for yourself, we encourage you to take yourself through the Total Truth Process again.
### Drunk-a-Log
One of the favorite questions to ask that I learned in The 30-Day Sobriety Solution is, "Am I moving closer to or farther away from my next drink?" It is a simple way for me to have awareness about my current state of mind, and make adjustments in my life when necessary.
—SUSAN
30-Day Graduate from Philadelphia, Pennsylvania
Yesterday we talked about the value of attending Alcoholics Anonymous meetings, and shared some advice on how to deal with the "I'm an alcoholic" affirmation. And today we shared Dan's story and the ongoing support that AA has given him. Because AA can be a great resource, and because you can find meetings almost anywhere, we want to touch on one other important component in AA meetings—the "drunk-a-log."
When people in recovery share their life stories, a lot of it focuses on their drinking escapades or their drunk-a-log. At an AA speaker meeting with an experienced speaker, it can be effective in connecting you to the pain associated with drinking, as you recall from Day 3 and the Pendulum Solution. But in meetings where one person after another stands up to share their drunken experiences, the law of attraction means that you get more of what you focus on. When you spend time sharing and listening to one drinking story after another, you are constantly focused on drinking, which is what you don't want—and not focused on sobriety, which is what you do want.
Our recommendation comes down to one of our common themes—awareness. Stay aware of how you feel after attending a meeting. Do you feel depressed and agitated or uplifted and inspired? When Dave attended AA meetings that were dominated by drunk-a-logs, he usually felt worse afterward. However, after Dave attended meetings where someone new to AA would share painful stories of alcohol abuse, he would relive his own pain all over again, feel grateful for his own sobriety, and leave with a renewed sense of purpose.
So, if you do decide to attend AA meetings (which we don't believe you need to do unless you feel they are helpful), pay close attention to how you feel. After attending a meeting, ask yourself, Am I moving closer to or farther away from my next drink? Also pay attention to who attends the meetings. AA meetings differ dramatically from one to the next, and each meeting tends to have its own "regulars," which will tell you a lot about the type of meeting and the people it attracts. Do attendees look healthy and have a positive attitude? Is there anyone whom you could look to as a role model? Or does the meeting seem to be full of unhealthy, negative people? Dave attended ten different AA meetings before he found one that felt like a fit—and to this day he still occasionally attends this same meeting because many of the people who attend are thriving in sobriety. If you choose to attend AA meetings, shop around until you find a meeting that is right for you.
### Your New Story
I had a thinking problem, not a drinking problem!
—CRAIG FERGUSON
It's important to create a new story for yourself and to leave your old story behind. One of the reasons this is true is because we keep repeating the same story—the story that is full of blaming, complaining, rationalizing, and justifying. Maybe you blame your parents for your drinking, or the lousy economy or your manager at work. Maybe you rationalize that you deserve to drink excessively on the weekends because of how hard your job is, or you justify your condition by thinking that everyone has health issues so your drinking is no big deal. You keep telling the same story, and you keep getting the same results, which leads to your third action step.
It is time for you to tell a new story. The story of the "new you"—the vibrant, passionate, sober you who is no longer held captive by the desire to drink. The "new you" has transformed—emotionally, physically, spiritually, and financially. Esther and Jerry Hicks say, "You have to begin to tell the story of your life as you now want it to be and discontinue the tales of how it has been or of how it is." When you spend more time focusing on, thinking about, and talking about how you want your new life to be, and less time thinking about and talking about how your old life was and current life is, your life will radically change for the better. Here are some important guidelines to follow as you write your new story. As you write it, don't worry about crafting the perfect story with perfect grammar. You are not writing a paper to be graded. The value is in the clarity you get from the process of writing it out.
• Start one year in the future. Write your new story as if it is one year from today, but write it in the present. For example, start by writing, "Today is September 3, [year], and I am . . ." Then describe what you are experiencing as if you were writing a letter to someone about your current experience and the journey that got you there.
• From the one-year-in-the-future frame of mind, reflect back. Briefly share some details about your life before you started The 30-Day Sobriety Solution (capturing whatever feels important to you as if you were looking back at this time from a year in the future), and then continue forward, working through the program and beyond—up to one year in the future. For example, after the sentence above, you might continue by writing: "When I purchased The 30-Day Sobriety Solution, I was struggling. My drinking had reached a point where it was affecting my health and relationships. I no longer felt like not drinking was a realistic option, and I knew there had to be more to life." Then your story might continue with your experience with the program to date—your challenges, your successes, and your breakthroughs.
• Write about what you want. Write about what you want your future life to look like as if you were already experiencing it. This is the fun part, and you can really embrace your creativity. Do not judge what you want. This is your chance to capture your dreams in writing, so take your time and enjoy it! What does your drinking look like? Do you abstain completely, or are you able to have a "take it or leave it" approach, having a drink or two when you want, but never feeling like you need to drink to be happy or relaxed? Then move into the really interesting part of the story—all the personal and professional changes you have experienced. Some resources you can use are the "new you" that you wrote on Day 2, your core values from Day 10, and the new beliefs you wrote on Day 11—and any other solutions you have done so far that have helped you get more clarity on what thriving in sobriety means to you. Consider including the following areas in this part of the story: your health, your job and career, what you are doing for fun and recreation, how you are growing personally and spiritually, what is happening with family and friends, your love life, what your physical environment looks like, your finances, and how you are contributing and giving back to others.
Although we encourage you to dream as big as you want, remember this is just one year from today, so go for what you want, but keep it believable. For example, it might not be likely for you to more than double your existing income or to move into a house worth four times your existing house's value in one year. But it is very possible to fall madly in love, get into the best shape of your life, find a new job or start your own business, pay off a substantial amount of debt, make new friends, start and excel at a new hobby, and find rewarding ways to give back to your community.
### Day 19 Action Steps
The positivity and enthusiasm of The 30-Day Sobriety Solution is infectious, and even though I am naturally a little cynical, the program effectively cut through that.
—THOMAS
30-Day Graduate from London, England
Like attracts like—it really is that simple. Whatever you have more of in your life today, you will naturally continue to attract: people (problem drinkers or role models), money (wealth or poverty), and happiness (fun or boredom). If you want to change it, then understanding how to leverage the law of attraction is one of the most powerful tools at your disposal. These action steps will help you do that.
• Use the "ask, believe, receive" process. Now that you have clarity about what you want, practice asking for it, believing it, receiving it, and appreciating it. Use this process when you catch yourself in the "Daydreamer's Dilemma," and use it with your new story. The real value comes from making the "new you" as real as possible, and the best way to accomplish this is through practice and repetition.
• Change your inputs. Stop watching the nightly news, or any news that primarily reports negative, fear-inducing, or manipulative stories, images, and videos. Use an online news aggregator instead, such as Google News, or search for one in your app store. Ask yourself if the TV and movies you watch, the books you read, and the video games you play leave you in a positive or negative frame of mind. Reduce your exposure to negative influences, especially right before bed. Let go of any resentments, anger, or thoughts of revenge that you may be holding on to—including those directed toward yourself—as these strong feelings will only attract more of that energy into your life.
• Write your new story. Write your new story of what you really want in the present tense as if it is one year from today. Get clear on what you want to accomplish over this next year, including what your drinking looks like, what has changed, and what is now happening in your health, career, finances, fun and recreation, personal growth, friends and family, romance, physical environment, and contribution/giving back. Keep this where you can read it at least once a week, and update it as you get more clarity.
On the companion website, we discuss the two "faces" of envy and how to really use it to your advantage. We also share an example of a completed new story, to help guide you in writing yours. Visit the companion website at <http://Day19.Solutions>.
## Day 20
## The Gratitude Solution
## Awakening the Power of Gratitude and Appreciation
Of all the "attitudes" we can acquire, surely the attitude of gratitude is the most important and by far the most life changing.
—ZIG ZIGLAR
By choosing to focus on what you have rather than what you don't have, you can reach a state of appreciation and gratitude. And as you learned yesterday in the Attraction Solution, you attract more of what you focus on. So when you focus on appreciating all that you have, you attract more to appreciate.
Cultivating the practice of gratitude in your daily life is one of the most transformative tools you can use to achieve a life of sobriety. Today the Gratitude Solution will teach you exactly how to easily integrate this life-changing attitude.
### Gratitude: The Secret of Sobriety
Develop an attitude of gratitude, and give thanks for everything that happens to you, knowing that every step forward is a step toward achieving something bigger and better than your current situation.
—BRIAN TRACY
What if you could be 25 percent happier, and it would take you only a few minutes a day to accomplish this? Robert Emmons, one of the world's leading experts on the science of gratitude and author of Thanks! How the New Science of Gratitude Can Make You Happier, proved exactly how to do this. His research discovered that participants who kept a daily journal and described five things for which they were grateful were 25 percent happier than other groups who did not keep a journal. The journaling group members felt better about their lives as a whole and were more optimistic about the future.
In many ways, when we think of "happy" we think of a state or emotion that can't really be measured. However, in the last decade, research on happiness shows that it actually can be measured and increased. Dr. Sonja Lyubomirsky writes in The How of Happiness: A Scientific Approach to Getting the Life You Want:
In becoming happier, we not only boost experiences of joy, contentment, love, pride, and awe but also improve other aspects of our lives: our energy levels, our immune systems, our engagement with work and with other people, and our physical and mental health. In becoming happier, we bolster as well our feelings of self-confidence and self-esteem; we come to believe that we are worthy human beings, deserving of respect. A final and perhaps least appreciated plus is that if we become happier, we benefit not only ourselves but also our partners, families, communities, and even society at large.
So practicing gratitude boosts your happiness. And when you are happier, you have more energy, better health, more confidence, and improved relationships with your family and friends. As we have discussed before, one of the most common myths that problem drinkers believe is that they cannot be happy and sober at the same time. Therefore, any solution that is proven to boost happiness by 25 percent that can be done without drinking is one you must use. The Gratitude Solution really is, in many ways, the secret to thriving in sobriety. When Dave started practicing gratitude in the early stage of his sobriety, he found that it had one of the most dramatic impacts of anything he did, and it took him only a few minutes to do before getting out of bed.
### An Attitude of Gratitude
When you are grateful, fear disappears and abundance appears.
—TONY ROBBINS
Consider this—the more grateful people are for the gifts you give them, the more inclined you are to give them gifts. Right? The appreciation and gratitude they express reinforces your giving. This same principle holds true on a universal and spiritual level. Like attracts like, so your gratitude will attract even more things into your life to be grateful for.
However, when you focus on what you don't have and haven't achieved, you will only attract more scarcity into your life. When you focus on the negative (what you don't have or don't want) and are overly judgmental of yourself (focusing on what you did wrong), then overcoming a challenge like cutting back or quitting drinking becomes much more difficult. If you focus on the times you "failed" when you tried to cut back or quit drinking, the shame and embarrassment you feel will only move you closer to your next drink.
The Gratitude Solution is best captured by a phrase you have probably heard in the 12-step and self-help worlds countless times—have an "attitude of gratitude." No matter what you have in your life today—even if your drinking has taken away a lot—you need to be grateful for it. Be grateful for your friends and family, for living in a country full of opportunity, for having a home, a car, a job, and anything else you can think of—including having found this book. It may help to remember that almost half the world's population—more than three billion people—lives on less than $2.50 a day.
An attitude of gratitude is not as much about "feeling" as it is about "being." It is easy to feel grateful when things are going your way—it is the natural response. But should you feel grateful if you lose your job or a loved one passes away? Catholic Benedictine monk Brother David Steindl-Rast, one of the world's leading teachers of gratitude and the founder of Gratefulness.org, writes: "Times that challenge us physically, emotionally, and spiritually may make it almost impossible for us to feel grateful. Yet, we can decide to live gratefully, courageously open to life in all its fullness. By living the gratefulness we don't feel, we begin to feel the gratefulness we live." The secret to gratitude is that it is a choice—a conscious, deliberate choice.
Being grateful makes you happier and healthier, attracts more fulfilling relationships and positive role models, and moves you more quickly down the path to thriving in sobriety, all without even realizing you are doing it. And, as your life improves, you find less need or desire to escape your reality through drinking.
### The Opposite of Gratitude
Today I am thrilled about how much my life has improved and how grateful I am that there is no temptation to drink whatsoever. And what is so exciting is that I get to focus on achieving my other goals in life, now that alcohol is no longer part of it.
—JAMES
30-Day Graduate from Istanbul, Turkey
Negativity is the opposite of gratitude. In our society it is so easy to get caught up in negative thoughts and emotions rather than gratitude. We commute to work in bad traffic or crowded mass transit. We hear daily news stories about terrorism, corruption, and a struggling economy. And by the age of twenty-one the average adult will have seen a million commercials—the core intention of which is to play on our fears that we are not enough and we need "more" to be happy. This results in an overall feeling of lack rather than a feeling of gratitude for who we are and what we already have.
### Susan's Attitude of Gratitude
The longer I am relieved of my symptom, the more I experience feelings of gratitude for my recovery. More frequently, the feelings arise from an overall sense of joy that I feel in my newfound life in sobriety. These feelings are enhanced by the certainty of the course my life would have taken had it not been for the saving grace of my Higher Power and discovering the life-altering techniques and solutions of The 30-Day Sobriety Solution.
—DESIREE
30-Day Graduate from Harare, Zimbabwe
Susan and her husband were eating dinner at a charming little pub they had frequented hundreds of times. Susan was drinking wine, as she did almost every night of the week, while socializing with her husband, the waitstaff, and other friends. But on this evening, Susan saw the rest of her life flash in front of her. She saw herself having the same meaningless conversations over and over again, watching the same meaningless TV shows, and the only thing that made it bearable was the wine. That night, she knew her life had to change—forever.
During the day Susan was a successful owner of two small businesses, a well-respected and liked member of the community, a great mother to four mostly grown-up children, and a loving and supportive wife. Because of these successes, Susan felt that at the end of the day she deserved to wind down by drinking wine. Sometimes she drank three "big glasses," and other times more, but rarely was it none.
What Susan found most hypocritical about her drinking was her love and passion for personal growth and physical health. Over the years she had gone to various personal development workshops, from Tony Robbins to a wide variety of spiritual retreats, and she even regularly practiced yoga and meditation. Yet, here she was, in her midforties, and still drinking almost every night.
As Susan shared, "I felt like a fake. Inside I felt horrible and sorry for myself, while everyone around me thought I was so happy and had it all together. I would attend all of these spiritual trainings, and spread words of encouragement to others to help them change and be happy, but I was failing at doing it in my own life."
When Susan found The 30-Day Sobriety Solution, she said, "I felt like I had discovered the missing numbers to my combination lock." Because of all the personal work she had done, she was familiar with a lot of the solutions and had used some of them to create successful businesses and relationships, but until she found The 30-Day Sobriety Solution, she hadn't thought to apply them to stopping her drinking.
Upon starting the program, she quickly realized, "My problem is not drinking; my problem is thinking I can solve or fill an emptiness within myself by drinking." As Susan started getting clear on what she really wanted in life, she was able to let go of her guilt and shame, and was finally able to imagine and believe she could thrive in sobriety.
The Gratitude Solution was one of Susan's favorites because, as she practiced daily gratitude, her decision to stay sober became easier and easier.
After three months of abstinence, in the midst of the holiday season, Susan decided to "test" drinking again and drank one or two glasses of wine on three different nights. Although she was encouraged by her newfound control, she realized that drinking no longer brought her any happiness, peace, or freedom. Today she has been sober for almost two years, is working to open a spiritual retreat center, and recently accomplished one of her lifelong goals of writing a book on meditation.
### Goals and Gratitude
I once heard a sober alcoholic say that drinking never made him happy, but it made him feel like he was going to be happy in about fifteen minutes. That was exactly it, and I couldn't understand why the happiness never came, couldn't see the flaw in my thinking, couldn't see that alcohol kept me trapped in a world of illusion, procrastination, paralysis. I lived always in the future, never in the present. Next time, next time! Next time I drank it would be different, next time it would make me feel good again. And all my efforts were doomed, because already drinking hadn't made me feel good in years.
—HEATHER KING
Author of Parched: A Memoir
People in general are obsessed with more—more money, more power, more recognition, and more alcohol. But this "more" that we are lusting for comes with the biggest price tag of all—it destroys our enjoyment of the present.
In the Outcome Solution, we explored how to create an outcome-focused, purpose-driven goal-setting strategy to make thriving in sobriety a reality in your life. Having dreams, setting goals, and desiring specific outcomes are key to thriving in sobriety, but focusing too intently on your future goals can make you feel incomplete or inadequate in the present.
You want to avoid creating more stress in your life by thinking that you are somehow not okay because you are not "there" yet. The everyday challenges of life are stressful enough without judging yourself as not okay because you haven't achieved one or all of your goals yet. You don't want to become so obsessed with getting to where you want to go that you are unable to enjoy the present. You must learn that all you have is the present moment—the here and the now—and to create the future of your dreams you must embrace and appreciate the present.
As Eckhart Tolle reminds us, "Are you stressed? Are you so busy getting to the future that the present is reduced to a means of getting there? Stress is caused by being 'here' but wanting to be 'there,' or being in the present but wanting to be in the future."
The secret to all success, as well as the secret to sobriety, is to appreciate everything you have and all that you are experiencing in the present while still actively pursuing the creation of what you want to have and what you want to experience in the future. When you choose to have an attitude of gratitude, you avoid falling into the state of "not enoughness." The key is to make the choice—and it is a choice—to fully enjoy everything you have today while you are working to create your ideal tomorrow.
There is one more thing we'd like to mention about the pursuit of goals. The achievement of your goals is not the most important thing. It's who you become in the process of achieving those goals that is most important. In order to achieve any worthwhile goal, you may need to learn new information, develop new skills, build new teams, forge new alliances, and develop or deepen important personal qualities and attributes like courage, commitment, patience, and perseverance. And the growth you experience—what you learn and who you become—is much more valuable than all the money, possessions, power, and prestige that you'll ever acquire.
### Day 20 Action Steps
After I completed the Gratitude Solution, I wrote letters of gratitude to four of my family members. Although it was a challenging and emotional process, the instant I put the letters in the mail I realized how uplifting and inspiring it was to express appreciation to others. At that moment, the power of gratitude was unquestionable and was only further reinforced when I talked to the recipients of the letters.
—BYRON
30-Day Graduate from Phoenix, Arizona
The Gratitude Solution is all about cultivating gratitude to increase happiness, which leads to more energy and confidence, better health, and improved relationships. We like to call the action steps for today the "Magic Three of Gratitude." When you do these three things, you will transform your life.
• In your journal, list twenty-five or more things you are grateful for. The main purpose is to start building your "gratitude muscle." It might surprise you that this is difficult at first. There are no rules about what to include—the list can range from gratitude for your family, friends, and pets to gratitude for refrigeration and indoor plumbing. The more challenging you find it is to make this list, the more important it is to implement this solution in your life. Here's one of Jack's recent gratitude lists.
I am so happy and grateful for:
1. How the sunlight comes into our bedroom in the morning
2. Inga, my wife, especially for how she makes me laugh
3. All my friends, especially everyone at TLC (Transformational Leadership Council)
4. My children and my grandson
5. Living in California—the weather, the ocean, the diversity
6. Joey, who is the cutest dog in the world, and my cats
7. Patty, my wonderful friend and incredible business partner
8. Chicken Soup for the Soul
9. All my Facebook fans
10. Television (especially The Voice and Dancing with the Stars)
11. Movies
12. Music, Pandora, SiriusXM radio, and Sonos
13. The internet, Amazon.com, Google, and Wikipedia
14. Monday Night Football
15. Comedians (especially Louis C. K., Chris Rock, Sebastian Maniscalco, Jim Gaffigan, Ron White, Paula Poundstone, Paul Rodriguez, and Russell Peters)
16. Steve Jobs, my Apple computer, iPhone, iPad, and all my apps
17. My health
18. My hair
19. My house
20. My car
21. My blender
22. My hair dryer
23. Erica's and Kristen's massages
24. Whole Foods
25. Veronica, my assistant, and all the rest of my staff
26. Having such good food in the refrigerator
27. All my Train the Trainer students and graduates
• When you wake up in the morning, think about five or more things that you are truly grateful for. The key to this action step is to not only think about what you are grateful for, but to close your eyes and spend a few minutes actually feeling grateful. Do this first thing in the morning—we find the best time is before you even get out of bed, but during your morning meditation or in the shower works fine, too. You can deepen the experience if you take the time to visualize an image of each thing as you think of it (or write it down in your journal) and feel the emotions of appreciation or gratitude in your body. We know we are really into feeling grateful when we feel our chest expand, a smile forming on our face, or tears welling up in our eyes. The more deeply you feel your feelings, the more powerful the impact will be. Let yourself really feel the love you have for your spouse or lover, the joy you experience when you play with your children, the excitement you feel about your work, the peace you feel when you are playing your guitar, or the freedom you experience when you are riding your motorcycle.
You can focus on the same five every morning, or focus on new ones every day. We like to see which ones spontaneously jump into our consciousness when we start the exercise.
The practice of beginning each day with this gratitude exercise will eventually lead you to naturally waking up happy and excited to start your day. This is because over time you are anchoring the experience of waking up to the positive experience of feeling deep gratitude. This simple practice can totally transform your life. On the companion website, you'll find a guided recording that will lead you through this morning gratitude process.
• Tell Someone how much you appreciate him or her, either face-to-face, with a phone call, in an email, or by writing a letter. This can have a huge impact on your relationships. After learning this simple technique, Dave wrote cards to both his young daughters and his wife, letting them know how grateful he was to have them in his life. Years later, his daughters shared with him how meaningful it was to actually have in writing how much their father appreciated them.
It's all too easy to forget the emotional wall that drinking can create between you and your loved ones, and this simple action step can start to reestablish critical connections. Writing only three letters of gratitude over a three-week period leads to increased happiness and life satisfaction, while also reducing symptoms of depression.
As always, be sure to visit the companion website for some additional information and material on today's solution, including a guided recording that will lead you through the morning gratitude process. Visit the companion website at <http://Day20.Solutions>.
## Day 21
## The Review Day and Bonus Solution
## Using the Secrets of Advertising to Create an Unshakable Belief in Yourself and Your Dreams
The thing is, if I don't have sobriety, I don't have anything.
—MATTHEW PERRY
Actor and addiction-awareness activist in recovery
Now that you have finished Phase III, "Creating an Unshakable Belief in Yourself and Your Dreams," you have learned some of the same techniques advertisers use to get you to buy their products, but instead you are using them to counteract that influence. In 2013, US advertisers spent more than $2 billion on advertising alcohol. When you think of taking a tropical vacation, is the first image that comes to your mind a bottle of Corona beer, glistening with water droplets, sitting on a small table on the sand next to your beach chair? And when you hear, "Great Taste, Less Filling," what do you see?
There is a reason why we have you constantly repeat and review the solutions that you learn, so you think of them as habitually as you think of an advertising jingle or slogan—repetition works! That's why you are repeating your affirmations over and over, and that's why you are visualizing every day. When you create and consistently focus on the mental images of the outcomes you want in your life and link them to a strong emotion, you are using the exact same technique as the makers of that Corona commercial. But instead of linking the feelings of relaxation, joy, and pleasure you experience when you are on vacation to a bottle of beer, you are linking the feelings of relaxation, joy, and pleasure to your experience of being sober.
Through constant repetition over time, these advertising jingles become embedded in your subconscious, leading you to make choices without your conscious awareness, just like the wine buyers whose purchases were influenced by the nationality of the music being played in the store that we mentioned in Day 12. And what about all the alcohol commercials linking socializing, laughing, and having fun with friends to always having a beer, a glass of wine, or a cocktail in your hand? The bottom line is that you are now empowered to use the same techniques that advertisers have spent billions on and thoroughly tested through their advertising campaigns to help you achieve your goal of thriving in sobriety.
In Phase III, you learned how the law of attraction affects your daily life, the importance of practicing gratitude and appreciation every day, and how the questions you ask can shape your future. And perhaps, most importantly, you now have a deeper understanding of your negative thinking patterns and how to release and replace them. On the companion website we review each of these key concepts further, and also share another special video from us.
You will also find this week's bonus solution, the Frequently Asked Sobriety Questions Solution, which includes answers to the most frequently asked questions we get from our sobriety coaching clients. You'll find answers to questions you did not even realize you wanted to ask, and without having to pay the thousands of dollars our coaching clients had to pay for these same answers. Make sure to visit the companion website at <http://Day21.Solutions> to get started right now with the Phase III review.
# PHASE IV
* * *
# Cultivating Courage and Positive Relationships to Thrive in Mind, Body, and Spirit
* * *
Every significant vital sign—body temperature, heart rate, oxygen consumption, hormone level, brain activity, and so on—alters the moment you decide to do anything . . . decisions are signals telling your body, mind, and environment to move in a certain direction.
—DEEPAK CHOPRA
Congratulations and welcome to Phase IV, "Cultivating Courage and Positive Relationships to Thrive in Mind, Body, and Spirit." This phase is often completed during the fourth week of The 30-Day Sobriety Solution, unless you have chosen the 60- or 90-day option. The end is in sight, and you are likely experiencing a wide range of emotions. Maybe you feel excited and empowered. Or possibly you feel scared and unsure. Or maybe you miss some of the secrecy and excitement you used to get from hiding alcohol or sneaking drinks. Or perhaps you are planning for Day 31—for what, how much, where, and with whom you are going to drink again. In fact, you might have started planning and thinking about that moment when you first decided to abstain for 30 days.
If so, that is okay—you are not alone. But we have to caution you that the more time you spend living in the future and planning the next time you will drink, the less time you have in the present to make positive lasting changes in your life. If you find yourself thinking about the next time you can drink, simply acknowledge that you feel this way and then review and choose to do one of the past solutions to change your thinking—such as asking yourself empowering questions, practicing visualization, reciting your affirmations, analyzing and changing your negative thinking, practicing gratitude, or using the "ask, believe, receive" process. Any one of these techniques can easily shift your focus, and these are only the tools you learned last week. Imagine what you can accomplish when you are able to leverage all of the tools and techniques in The 30-Day Sobriety Solution.
In Phase IV, you are going to add some new transformational tools to this toolkit. Today we are going to tackle one of the most important topics of all—fear. Let's get started.
## Day 22
## The Courage Solution
## Successfully Confronting Your Fears
Courage is resistance to fear, mastery of fear, not absence of fear.
—MARK TWAIN
As you move forward on your journey to thriving in sobriety, you are going to have to continue confronting fears that arise. Fear is natural. Whenever you start a new project, take on a new venture, or put yourself out there, as you have done with The 30-Day Sobriety Solution, fear is a normal reaction.
Unfortunately, many people let fear stop them from taking the necessary steps to achieve their dreams. Successful people, on the other hand, feel the fear along with the rest of us, but don't let it keep them from doing what they want to do—or have to do. They understand that fear is something to be acknowledged, experienced, and taken along for the ride. Today we'll cover how to let go of fear, so that living a courageous life thriving in sobriety comes naturally.
### The Courage Solution
You have to face your fear. And do the same with anger, do the same with jealousy, do the same with hatred. And a significant point to remember is: if you witness anything—fear, anger, hate—if you simply watch them as they arise, without any judgment or condemnation, they will disappear, leaving a tremendous amount of energy that you can use for creativity.
—OSHO
Author of The Book of Understanding: Creating Your Own Path to Freedom
You experience fear for many reasons. You fear that you are either not "enough"—pretty enough, smart enough, talented enough, or creative enough—or at some level you are afraid of what might happen if you become the person of your dreams. You may fear that if you do "shine" it will be at the expense of the people you love, and you might lose their love. You may be afraid of the unknown and afraid of change. And, of course, you are afraid to fail. However, your deepest fear may be of your own brilliance and power. Bestselling author and spiritual teacher Marianne Williamson captured this best when she wrote:
Our deepest fear is not that we are inadequate. Our deepest fear is that we are powerful beyond measure. It is our light, not our darkness, that most frightens us. We ask ourselves, who am I to be brilliant, gorgeous, talented and fabulous? Actually, who are you not to be? You are a child of God. Your playing small doesn't serve the world. There's nothing enlightened about shrinking so that other people won't feel insecure around you. We are all meant to shine, as children do. We are born to manifest the glory of God that is within us. It's not just in some of us, it's in everyone. And as we let our own light shine, we unconsciously give other people permission to do the same. As we are liberated from our own fear, our presence automatically liberates others.
Fear of your own brilliance and power leads you to complacency and comfort. So you trick yourself into believing that taking the "comfortable" approach serves you. On Day 2 you learned that change comes at the edge of your comfort zone. You may drink excessively because on some level you are afraid of letting your own light shine. But when you have the courage to face your fears, which you have demonstrated by making it this far in The 30-Day Sobriety Solution, not only is achieving your own dreams possible, but you give hope, inspiration, and permission to those around you to also reach for their dreams.
### Two Types of Fear
Fear is a chameleon that can be a wise guide in one moment and a terrible tyrant the next. Respect fear, but never let it be your master. If physical danger is involved, listen well; if psychological danger challenges you, then do what you most fear—live as a peaceful warrior.
—DAN MILLMAN
Author of Way of the Peaceful Warrior
There are two types of fear. There is the rational fear of mortal danger, where something threatens your survival, such as stumbling upon a rattlesnake in your path or seeing a car heading toward you weaving in and out of its lane. Recognizing these dangers puts you on alert so that you can protect yourself.
The other type of fear is psychological or irrational fear, which you experience more often, such as the fear of public speaking, the fear of asking out someone you like, or the fears that come up when you think of never drinking a drop of alcohol again. This type of fear is self-created and self-sabotaging. It creates stress, anger, resentment, and other negative emotions. Today is about facing your irrational fears—the ones that are really holding you back from getting what you want.
### Fear or Fantasy?
I personally believe this: We have only today; yesterday's gone and tomorrow is uncertain. That's why they call it the present. And sobriety really is a gift . . . for those who are willing to receive it.
—ACE FREHLEY
Guitarist, founding member of the rock band Kiss, and in recovery
Hopefully by today, your fears related to drinking have reduced in frequency and intensity. But recovery is an ongoing process, and fears can come and go like the tide. So what is fear? Fear is often explained as the anticipation of pain. We like to explain FEAR as the acronym for Fantasized Experiences Appearing Real. What this means is that you are the one who is creating your own experience of fear by imagining something negative in the future . . . you are the one creating the movie in your mind. And because your brain cannot tell the difference between a real event and a vividly imagined event, you actually experience the fear as real in your body. You want to remember that you are 100% responsible for creating the fear by imagining the negative future event. As Eckhart Tolle reminds us in his book The Power of Now, "Unease, anxiety, tension, stress, worry—all forms of fear—are caused by too much future, and not enough presence."
You are using the power of your creative imagination to scare yourself. But this fear is not real because you have no real way of knowing what the future will bring.
This type of fear is not rational. For years Dave was convinced that getting sober would negatively affect his career, his happiness, his friendships, and his social life. This irrational fear immobilized him from taking any serious steps to get sober. Even when he did take action, he really only had "one foot in" because deep down he was afraid of the pain he believed he would experience if he was sober. When he finally did get sober, he realized how misguided and irrational his fears had been. Today Dave's career and his social life are flourishing, and the real love he experiences in his relationships with his wife, children, family, friends, and clients was unimaginable during his drinking years. But think about this—if he had visualized sobriety as powerful and happy (as you learned to do on Day 15), he would have been using his mental power of visualization to motivate himself instead of to scare himself.
When you understand that almost all of your fears are self-created, then you have the power to change them. You can visualize a positive outcome by imagining a picture of what you do want rather than what you don't want. You can also stop and look at the actual facts, which show your fear is irrational. And you can simply bring yourself back to the present moment where you are safe and fine.
### Fear of Failing, Yet Again . . .
There's no such thing as failure. Mistakes happen in your life to bring into focus more clearly who you really are.
—OPRAH WINFREY
Failure is an emotionally charged word, loaded with negative connotations. This is especially true with problem drinkers. Most likely this isn't the first time you have tried to change or stop your drinking, and in the past you may not have succeeded or, as most would say, you "failed." And each of these failures probably led to more fear around your drinking, lower self-esteem, and reinforcement of the limiting belief that you couldn't stop.
You might remember that Dave was a high performer at work, yet for almost a decade his attempts to quit drinking all ended in failure. Even though he had many accomplishments in other areas of his life, Dave felt like a failure. He didn't understand why he couldn't stop drinking when he no longer even liked it. Dave reached the point where he was afraid to let anyone know he was going to try to quit drinking "yet again," because he fully expected to fail. However, when Dave finally redefined failure as feedback, everything changed.
### Failing Forward
I didn't fail, I found more than ten thousand ways that won't work. Every wrong attempt discarded was another step forward.
—THOMAS EDISON (1847–1931)
America's most successful inventor, on inventing the lightbulb
Many people fail to take action because they're afraid to fail. Yet, failure is an important part of the learning process. Failure is just a way we learn by trial and error. Success is the result of good judgment, and good judgment is the result of experience. And experience is frequently the result of bad judgment, which leads to failing. Therefore, failure is necessary to succeed.
In her highly acclaimed book Mindset: The New Psychology of Success, Dr. Carol Dweck breaks down the myth that we are either born with "natural" talent or not. She argues that a huge part of success is determined by how we have defined failure in our life. Those who have a "growth mindset" realize that failure is necessary to succeed. She writes:
Do you know that Darwin and Tolstoy were considered ordinary children? That Ben Hogan, one of the greatest golfers of all time, was completely uncoordinated and graceless as a child? That the photographer Cindy Sherman, who has been on virtually every list of the most important artists of the twentieth century, failed her first photography course? That Geraldine Page, one of our greatest actresses, was advised to give it up for lack of talent?
Another inspiring example of redefining failure is Esther Earl, the girl who died at the age of sixteen from thyroid cancer and inspired the book The Fault in Our Stars by John Green. Not only did this book become a bestseller, it also went on to be a hit movie, grossing more than $300 million. At the age of fourteen, two years after she had been diagnosed with cancer, Esther wrote a letter to her seventeen-year-old self and instructed her parents to read the letter if she died before she was able to open it. In the letter she wrote, "If you haven't done something amazing, don't forget to try. The worst that can happen is you fail, and then you can try again until you succeed." If a fourteen-year-old terminally ill child can redefine failure, you can, too.
You only really fail if you perceive or interpret your results as a failure. But when you redefine failure as just feedback, you "fail forward." When your past attempts to cut back or quit drinking didn't end with the results you wanted, that wasn't failing, it was just feedback. Rather than feeling embarrassed, guilty, or disappointed about "failing" again, and losing the opportunity to learn from it, instead acknowledge and recognize what worked and what didn't work.
There is only one way you can truly fail, and that is to give up.
Today's first action step is to redefine failure by writing in your journal about any past attempts you made to either cut back or quit drinking. Write down specifically what you did and what you learned each time. Maybe your only lesson was that your last approach didn't work; however, maybe you learned which times and in which situations you struggle the most to stay sober. Perhaps your past attempts came down to trying to use willpower alone because you never did any personal growth work. Or perhaps you discovered something that actually worked for a while.
For example, Dave tried to quit drinking by using what is commonly referred to as the "marijuana maintenance" program, which consisted of replacing alcohol with pot, which didn't work. He also used his strong willpower to quit for weeks, and even once for months, but throughout those times he would constantly be thinking about and planning when he could drink again. In each of these examples, Dave learned that unless he dealt with the root cause of his drinking, he would always come back to drinking or other addictive behaviors. He also learned that his willpower was a great asset he could use in early sobriety, but the key to thriving in sobriety was to do the personal growth work that dealt with the root cause.
After completing this action step, take a second to acknowledge what you learned and congratulate yourself for taking action and getting feedback.
### How Hannah Failed Forward
I don't like my sober life, I love it. Even though I have an occasional drink, The 30-Day Sobriety Solution has taught me how to never let alcohol be the negative and dominant force it was in my life for decades.
—HANNAH
30-Day Graduate from Sydney, Australia
When she was twelve years old, Hannah's parents divorced, and Hannah responded like most adolescents do—by becoming more independent. This included drinking alcohol for the first time, and from that moment on she loved alcohol and getting drunk. Hannah got drunk whenever she could throughout her teenage years, and one night while drinking she met her future husband. From a drinking perspective, they were a perfect match and started living together soon after graduating from high school. But by the time Hannah was thirty, she was a single mother of three young children and had a nightly drinking habit that almost always ended with her being drunk.
For the first time in her life, she was ready to face her drinking problem, so she attended Alcoholics Anonymous and managed to string together three months of sobriety. Even though she learned many valuable lessons over those three months, she struggled with the concept of "always focusing on not being drunk." Eventually she returned to drinking—slowly at first, but within months she was back to nightly drinking.
For the next several years, almost every month Hannah tried a new way to stop or cut back her drinking. In her midforties, even though she had created a good life in many ways, she just couldn't stop drinking. She owned a successful hairdressing salon; she had become a certified neurolinguistic programming practitioner (an alternative type of therapy to understand and change human behavior) and ran a small life-coaching business; and she had an open and honest relationship with her children, acknowledging her drinking problem with them and sharing her desire and attempts to change. But every night she returned home with one thing on her mind—alcohol. And almost every night she would drink either two bottles of wine or half a liter of vodka. Then one day she came across The 30-Day Sobriety Solution. Hannah recalls:
I felt like The 30-Day Sobriety Solution was breathing life back into me. Every day I learned new tools and techniques that actually worked. I was finally able to imagine a happy life without alcohol, something that had always escaped me. And one of the surprising results was that for the first time in my life, I felt like I was not alone, even though I was doing the program alone at home.
Hannah believed she had found the solution to her lifelong drinking problem, but she still found herself struggling with the two "people" battling it out inside of her—the person who depended on alcohol to live and cope with life, and the new person who was sober and happy but had never been given a chance to really exist since she was twelve. Hannah said, "I was scared about who I was without alcohol, and now that I really saw sobriety as a possibility, it became even more scary. And so I let that fear lead me back to where I felt safe—drinking."
The first two times Hannah began The 30-Day Sobriety Solution, she let her fear take over and gave up before she finished. But Hannah knew that she had to be persistent. She was not the same person she had been before she started the program, and so when she started The 30-Day Sobriety Solution once again, she discovered that the saying "third time's a charm" was true for her.
The third time through the program was amazing. This time I was able to finish it, and on the other side I found the happiness I had been searching for my whole life. My new story is exciting and full of unlimited potential. I have rediscovered my passion for music, dancing, and laughing, and I finally know what it feels like to be truly in love. I met a wonderful, supportive, and loving man, one that alcohol would never have let into my life, and we recently became engaged.
After far surpassing her longest time sober as an adult, today Hannah has found she can occasionally have a drink without the risk of returning back to her previous levels. She knows the part of her that was addicted to excessive drinking is long gone, and the part that now replaced her is stronger, healthier, and happier, and, most importantly, will never rely on alcohol again.
### Thriving
Inaction breeds doubt and fear. Action breeds confidence and courage. If you want to conquer fear, do not sit home and think about it. Go out and get busy.
—DALE CARNEGIE (1888–1955)
Author of How to Win Friends and Influence People
Think back to one of your greatest accomplishments. Most likely you had to push yourself in some way to overcome some fear. In fact, right before you have done most of the amazing things in your life, you likely felt scared.
Our goal with The 30-Day Sobriety Solution is for you to thrive. And yes, that means thriving in sobriety, but it goes way beyond just cutting back or quitting drinking. The key to thriving in sobriety is thriving in life—living to the highest potential both personally and professionally. To thrive, you must grow. And not just for these 30 days. Growth is a lifelong process if you want to be happy and fulfilled. And what is necessary to keep growing? Action—but not just any action. When you act to confront your biggest fears, you grow the most. The presence of fear is a signal that you have an opportunity to grow.
To sum this up: Thriving requires growth. To grow requires action. And this action must be directed toward overcoming your fears. Or, in short:
Thriving = Overcoming Your Fears
Facing irrational fears can be challenging, but the reality is that you must overcome them in order to thrive. In The Magic of Thinking Big, David J. Schwartz writes, "Action cures fear. Indecision, postponement, on the other hand, fertilize fear. . . . When we face tough problems, we stay mired in the mud until we take action." Many people fear that taking action will be more painful than not taking action, so they procrastinate. And this procrastination feeds the fear. The solution is to just get going. Take action. Even the smallest step can break this cycle.
Let's look at this equation in relation to problem drinking. Every problem drinker fears cutting back or quitting drinking for one reason or another. Overcoming this fear is one of the greatest demonstrations of courage. When you have successfully dealt with many of the driving factors that led you to drinking in the first place, as The 30-Day Sobriety Solution helps you do, you will no longer be holding yourself back from all your other goals. The time you spent drinking, recovering from your drinking, or planning your next time drinking will be restored to you, as well as your confidence, self-worth, and pride, which will accelerate your success in other areas.
### Fear Is Your Compass
A compass is "something that helps a person make choices about what is right, effective, etc." To us, fear also serves as a compass, telling us if we're on or off course. Tony Robbins says, "If you can't, you must, and if you must, you can." We agree. Those very things you are most afraid of will actually provide you with the greatest insights and growth when you do something about them. You have started with what may be one of your greatest fears—cutting back or quitting drinking. The question to ask yourself now is, What's next?
The second action step for today is to write a list of the fears you have not addressed due to your drinking. Then write down the "benefit" you experience from letting this fear hold you back—yes, there is always some benefit you believe you are getting from letting this fear stop you. Last, write down how you will specifically be able to overcome these fears during the rest of, or after, the program. Use the following set of questions to guide you.
What would I do if I wasn't afraid? (Start with the words "Up until now.")
• Fear. Up until now, I have been afraid to explore new career opportunities.
What benefit have I been getting from letting this fear stop me?
• Benefit. The benefit of letting this fear control me is that I don't have to update my resume or risk being rejected for a new position.
What would I do if I had no fear?
• Overcoming. I am excited to explore new career opportunities because now that I am sober, I have more time and more energy, and I am performing at a higher level. I also have a deeper understanding of my strengths and what I really want in life, and I can now use some powerful techniques I'm learning to help me succeed in an interview and in a new career.
What would I feel and experience if I took that action?
• Feelings. Exploring different career opportunities makes me feel happy, successful, excited, and alive.
Remember, your problem drinking has probably held you back more than you realize. Dave always knew deep down he was meant to help motivate and inspire others, but the idea of it scared him, not only because his existing job felt so safe, but because he also knew he couldn't do it while drinking. Dave also had always wanted to be fit and healthy, but again his fear of having to stop drinking stopped him from committing to it. He also wanted to be more active in his children's lives and coach their sports teams, but he was afraid the time commitment would interfere with his drinking.
But once Dave removed drinking from his life, and addressed the underlying causes of his drinking, he was able to accomplish all of these goals and many others that he had "buried" beneath his drinking. Within a year he lost sixty-six pounds, ran seventy-five miles in one weekend—including two marathons—and completed the challenging P90X program. Within months he was coaching his oldest daughter's basketball team, and he started taking the necessary steps to build a new career, including developing the program that became this book.
Your fears signal your opportunities, and when you conquer your fear of significantly cutting back or quitting drinking, you will discover how easily and quickly you can overcome other fears that have held you back.
### Just Say Yes!
Without fear there cannot be courage.
—CHRISTOPHER PAOLINI
Author of Eragon
Before you can face your fears, you first have to be aware of them. You may have accommodated a fear for so long that you just assume the way you are acting is natural and not recognize it as fear. For example, if you have a fear of rejection, you may automatically avoid social situations where you know you won't be able to drink to lessen your anxiety. Perhaps you rationalize this as a personality trait, saying you are "introverted." But if you were to honestly explore this, you might discover that you have just become so accustomed to letting your fear run the show that you don't even notice that you are on autopilot when making decisions that keep you from experiencing and facing your fears.
You probably have friends or family members who are so firmly rooted in their ways that anytime you ask them to do something new or different, they promptly turn you down. They would never acknowledge any fear and there is no option of convincing them otherwise. You can look at this as a subconscious response in reaction to the idea of doing something outside their normal behavior. This is because they have become "stuck" in their comfort zone. And the longer they stay "stuck," the harder it is to break free and be aware that it is occurring.
You can probably relate to being like this at times. Problem drinkers are masters at getting "stuck" in drinking rituals and building their lives around being able to drink the way they want to. And underneath all of this, feeding this continued behavior, is fear. The challenge is breaking free from it.
In the movie Yes Man, the lead character, played by Jim Carrey, is "stuck" until he attends a personal growth seminar and agrees to say "yes" to anything he is asked. His life improves dramatically with this simple change. He gets a promotion at work, falls in love, and improves his relationships with his friends and coworkers. Yes, we know this is just a movie, but it conveys a deep message about the power of saying yes. Having the courage to say yes to things you usually say no to—assuming they are not dangerous—and breaking out of your comfort zone and your routine behaviors are essential to creating a fulfilling life.
Your third action step for today is to write in your journal about the times you have turned down opportunities or invitations to try something new and how this has affected you. This can include pursuing a new career, developing new friendships, going dancing, traveling to a new destination, attending a family reunion, personal growth training, meditation, couples counseling, joining a health club, going to an AA meeting, going back to school, hiring a coach, taking piano lessons, or simply accepting an invitation to go out to lunch.
Many times, turning down these opportunities will be related to your drinking, but some may not be. Regardless, your responses to new opportunities are likely to be so automatic that you don't even realize you're saying no or when fear is guiding you. So we encourage you to be courageous and ask your friends and your family members when they have seen you turn down invitations and opportunities in order to stay in your comfort zone.
Most importantly, just pay attention. Make a conscious decision right now that you are going to stop and listen when someone asks you do to something. This declaration will shift your awareness enough to notice it in the future. Then say yes! If it really scares you, it might be exactly what you need to do to have a breakthrough. One of the mantras we teach our students and coaching clients when we are discussing overcoming your fears is "Oh, what the heck, go for it anyway!"
However, when you are stretching into saying yes more often, remember to use common sense. Saying yes to a weekend bachelor party in Las Vegas or a wine-tasting tour in Napa Valley with your own private limousine service when you have just decided to not drink would not be a good idea.
One more thing. If you are still struggling to say yes to a new opportunity, silently ask yourself, What if I said yes to this offer? Then pay attention to the feelings that come up—sometimes just asking this question is enough for you to recognize fear and not let it take over.
### Your Personal Barometer for Measuring Fear
The danger lies in refusing to face the fear, in not daring to come to grips with it. If you fail anywhere along the line, it will take away your confidence. You must make yourself succeed every time. You must do the thing you think you cannot do.
—ELEANOR ROOSEVELT (1884–1962)
US First Lady and humanitarian
Do you remember the first time you drove a car? What about your first date or first kiss? Or when you first took the stage in a play, or stepped onto the court or field for your first playoff game? You probably felt at least some fear in each of these experiences, which included a physical response. Your body physically reacts by pumping adrenaline into your muscles. Your breathing and heart rate increase, pumping more blood throughout your body.
For example, if you think about a future speaking engagement where you have to get up in front of thousands of people, you may experience fear. Psychologically, you'll have negative "what-if" thoughts. What if I completely freeze on the stage? What if the presentation doesn't work? What if I mess up and my manager wants to fire me? Physically, you'll have "fear spots." You might feel a sunken pit in the bottom of your stomach, or tension in your jaw, shoulders, arms, feet, neck, or even your mouth and lips. You might fidget, bounce your leg up and down, or rub your fingers against the palms of your hands. You might sweat, even profusely, or your mouth might dry up so that it is hard to speak.
In order to acknowledge and respond to your fears, you must be aware of them. Your body is a barometer for emotions, and as you get better at "reading" your barometer, you will get better at responding to fear.
The fourth action step for today is to take some "measurements." First, think about anything that scares you about your drinking, such as its effect on your health, relationships, career, and finances. Take a minute to feel that fear. For example, imagine getting a call from your doctor asking you to come in for more testing on your liver. Notice how and where your fears show up physically. Repeat this process for other fears, making note each time of your physical reaction. We are aware that imagining what you don't want to happen goes against our past advice, especially at this stage of the program, but the value you will get from becoming aware of the physical sensations you experience when you are afraid will far outweigh any negative impact.
Now, think of other fears you might have, such as public speaking, flying, talking to your boss about a promotion, your spouse glumly asking you, "Can we talk?" or whatever else comes to mind. Some fears will elicit different physical responses and different levels of intensity. Make note of how each fear manifests itself physically.
The goal with this exercise is to simply identify how your body reacts to fear. When you know what physical symptoms to watch out for, the presence of fear becomes far easier to identify. You will most likely discover that fear shows up at surprising times and places.
### Day 22 Action Steps
We're miserable because we think that we are mere individuals, alone with our fears and flaws and resentment and mortality.
—ELIZABETH GILBERT
Author of Eat, Pray, Love
You are not alone. The experience of fear is universal. But how you respond to fear is individual. When you face your fears and use the tools we have been teaching you, you develop courage and confidence, and thriving in sobriety will become your reality. Be sure to review the text above for additional details on these action steps.
• Write down your past attempts to cut back or quit drinking. Brainstorm, in writing, as many of your past attempts to change your drinking as you can recall. What did you do and what did you learn? How did you fail forward?
• Write down your "drinking" fears, how you will overcome them, and how that will feel. Write down each fear you have related to your drinking that you have yet to overcome. Then write down the benefits you have experienced by letting that fear run you. For instance, if you are afraid that you won't be able to deal with stress without drinking, the benefit you have by letting this fear run you is that you probably do give yourself permission to temporarily forget the stress in your life when drinking. Last, write down how you will overcome those fears now and how it will feel when you do that. Be sure to refer back to the text for the questions to ask yourself.
• Say yes. Think back to the times you have turned down offers, invitations, and opportunities related to your career, health, family, or friends. Were they related to drinking or automatic responses to avoid change? Consider new opportunities that come up and ask yourself, What if I said yes to this? Notice how that feels, and see if irrational fear is driving your decisions.
• Recognize, acknowledge, and embrace the presence of fear. Write down how your body reacts to fear, including fears specific to your drinking and other general fears. Remember, fear is your compass, so follow it. When you feel fear, acknowledge it, be thankful for it showing up, and then ask yourself, What would I do if I wasn't afraid? And do exactly that. To help neutralize fears, shift your focus every fifteen seconds between the physical sensations you are feeling and the feelings you want to feel instead (courage, confidence, peace).
On the companion website, you'll find a famous and entertaining video on the fear of failure. Be sure to visit it at <http://Day22.Solutions>.
## Day 23
## The Emotional Sobriety Solution
## Successfully Handling Your Emotions
Even though The 30-Day Sobriety Solution is about quitting or cutting back on alcohol, so many of the techniques are easily applied to other areas of life. My life has changed in amazing ways after only seventy-five days of sobriety. I am sleeping better. I am eating better. I even go running, which is the first regular exercise I have done in over ten years. And one of the most significant changes has been in the emotional realm. My newfound awareness of my thoughts and feelings, and my ability to be more emotionally present with others, has changed my life.
—THOMAS
30-Day Graduate from London, England
One of the keys to thriving in sobriety, and life, is learning to maximize your positive emotions and minimize the negative. When you started drinking, it was most likely to minimize your negative experiences, have more fun and laughter, feel the joy of connecting with others, and heighten the celebration of special occasions. But over time, your drinking most likely changed into a behavior for dealing with stress, anger, disappointment, and sadness. Over many years, drinking became your automatic response to any intense and uncomfortable emotion. Whether you were bored, coping with feelings of social awkwardness or unexpressed feelings in your relationship, or avoiding fears about money, your solution became alcohol.
But as you know, alcohol isn't a solution. It can numb out your feelings temporarily, but in the long run it only makes everything worse, until your solution has now become your problem.
### Emotional Sobriety
If you want to improve your life, you have to learn how to consciously manage your emotions. This is called emotional intelligence, or as psychologists and addiction specialists refer to it, "emotional sobriety." Today's solution will teach you how to achieve emotional sobriety so that the stress of negative emotions will not lead you back to drinking.
According to psychologists like Tian Dayton, author of Emotional Sobriety: From Relationship Trauma to Resilience and Balance, emotional sobriety means being able to experience and regulate strong emotions rather than repress or run away from them. It means that you have the skills to live in the present rather than being caught in the past or being obsessed with the future. When you're emotionally sober, you can tolerate and express strong emotions, and you are able to create deep and intimate connections with other people. Your mind-set allows you to be resilient in the face of unexpected difficulties.
Many problem drinkers (96 percent, according to many experts) grew up in a dysfunctional family,,, meaning that the odds are overwhelmingly high that you didn't learn the skills of emotional sobriety. Had your parents not also been "emotionally ignorant," you would have learned how to always bring yourself back into emotional balance when you were frightened or hurt. You would have learned how to soothe yourself. But because you didn't learn the tools for doing that, you turned to alcohol to calm yourself.
Today is about learning two more effective tools for dealing with your negative emotions so that you can achieve a greater state of emotional sobriety.
### Emotion or Feeling?
Emotions that spontaneously occur all day long, such as those you experience when someone cuts you off in traffic, when you learn that the dog jumped up on the table and ate your dinner, or when someone puts you down in front of others at work. Emotions also seem to come up out of nowhere—like when you wake up in a bad mood or are suddenly overcome by a feeling you can't explain.
The truth is that we actually create most of our emotions that seem to occur spontaneously and seemingly out of our control, by how we think about people and events, by the meaning we ascribe to them, and by the stories we tell ourselves.
Simply put, all events are meaningless until we assign some meaning to them. What is just is, until we interpret it as good, bad, or neutral. For example, if you are sitting in a movie theater and a man steps on your foot while attempting to get into his seat, your immediate reaction might be one of irritation or anger. However, if you look up and see he is carrying a white cane and realize he is blind, you may feel understanding, compassion, or concern. The event was the same, but the thought that it was not intentional changes your experience. Changing your thought changes your experience.
The words emotion and feeling are usually used interchangeably, but psychologists make an important distinction between them. Emotions are instinctual responses to your outer environment that you feel as physical sensations. They are usually intense, brief, and accompanied by a physical reaction. For example, in the case of the blind man stepping on your foot, you might quickly feel irritation or anger as well as a physical contracting of muscles in your face, chest, stomach, and arms.
In other situations, you might feel a positive emotional reaction as a sense of expansion or a wave of relaxation in your body. Emotions such as joy, fear, and sadness occur all day long, mostly without your conscious control and often outside your awareness. So your emotions are the result of outside stimuli and they give you information that something is going on.
On the other hand, feelings are the result of your conscious reaction to an emotion. These are usually less intense, but last longer and are affected by your beliefs, attitude, and views on "right" and "wrong." For example, when a driver runs a red light and narrowly misses hitting your car, your initial emotional reaction might be one of fear or anger, but after a second, you might suddenly feel grateful that you were not hit. Or you might begin to wonder why the person was in such a hurry and think maybe they were rushing to the hospital. Your thoughts after you experience an emotion determine your longer-term feelings, for example, how you feel the rest of the day (in a bad mood because "everyone's driving is crazy" or in a state of constant anxiety because you dwell on the thought that you might die in an automobile accident). The quality of your feelings depends on the quality of your thoughts and beliefs after you experience a burst of emotion, whether you are consciously aware of them or not.
So why does this matter? Emotions, or more specifically your initial emotional reactions, are your natural, temporary, intense, and instinctual reactions to a situation. However, how you respond to those initial emotions determines the quality of your happiness. And how you respond can be changed over time by the techniques you are learning in this program.
In order to experience an emotionally balanced life, you first need to be aware of your emotions. Many people who struggle with alcohol have lost touch with their emotions, for fear of not being able to handle the consequences of feeling or expressing them. In your effort to escape feeling or expressing those emotions, you shut down. The first step in healing is to have the courage to feel emotions with the confidence that you can handle them.
### Your Emotional Sobriety Filter
Consider your emotional reaction to the following scenarios: (1) You are hiking in the woods, and a bear comes crashing out from the trees ahead of you; (2) You are at a zoo, and you walk up to a glass wall, and suddenly a bear runs out from behind some trees in the enclosed cage and charges at you. You would probably feel an immediate automatic response of fear in both situations because a bear was running toward you; but your fear would be more intense in the woods than at the zoo, where your conscious mind would kick in and remind you that the glass wall will protect you from being attacked. This is just one more example that illustrates that you can change your emotional reaction to an event by expanding your awareness (there is a glass wall) and changing how you think about it (this wall will protect me from the bear). This is why the work of examining and changing your limiting beliefs that we explored in Day 11 is so important.
Now consider this with regard to your drinking. You walk into a bar (not a bear!) and see your favorite bartender making your favorite drink, or you hear that subtle pop as the cork is removed from a bottle of wine, or you feel a light spray envelop your face when a can of beer is opened. Today one of these situations might instantly create an intense desire to drink with a very real physical reaction before you are able to stop it—such as your mouth watering, a tingling anticipation in your stomach, or the automatic clasping of your hand as if you were picking up a cold bottle of beer. And that reaction could lead you to drink.
However, you can learn to consciously and intentionally override these automatic emotional and physical reactions. The key is learning how to skillfully manage the process that occurs as an emotion becomes a feeling. Your ability to do this will influence how happy or unhappy you'll be.
This brings us to the "Mental Makeover" process, which will help you trace a triggering emotion back to its source so you can resolve and release it. The "Mental Makeover" consists of four stages: awareness, acceptance, analyzing, and assigning.
### Awareness
In order to work with an emotion, you have to first become aware that you are experiencing it, so you want to notice the physical sensation that accompanies it in your body. For instance, you might notice a tightness around your eyes, a clenching of your jaw, a tension in your neck and across the back of your shoulders, a slight pain in your stomach and lower back, a cramping in your buttocks, or tightening in your thighs.
For example, several years ago, when Dave was driving by a school, he noticed a school zone speed limit sign, which reminded him of the time his wife got a speeding ticket there. He then remembered that his wife had attended a party a year later where she met the same police officer who had given her the speeding ticket. He then remembered that the party had been hosted by a mutual friend we'll call Mary, who had once asked Dave for some very specific information, which he had then spent hours compiling and providing to her. Although it had been over a year since he had helped her out with the information, she had never acknowledged or thanked him for it, even though Dave had heard from his wife that she had received it. That whole train of thought took place in a matter of seconds, without Dave's conscious awareness of it, and it triggered an emotional response that resulted in a feeling of tension throughout his entire body. And here's the point of all of this—in a matter of seconds Dave's mood had significantly changed for the worse.
But because Dave was consciously practicing the stages of the "Mental Makeover" at the time, he quickly noticed the sensation of his body tensing up. Without this "awareness" he could have never moved on to the second stage of the "Mental Makeover"—acceptance.
### Acceptance
"Acceptance" is allowing yourself to fully accept and experience whatever emotion is happening. One of the ways you can get stuck is by trying to push away sensations and emotions that you don't want to feel (loneliness, sadness, hurt, pain, and fear). You may ignore them (distracting yourself by staying busy or having the radio on all the time), repress them by tightening up against the feeling (resulting in neck and lower back pain, a spastic colon, and other diseases), or cover them up with drugs and alcohol.
In order to heal yourself and feel alive again, you need to allow yourself to simply experience and accept the emotion, knowing that whatever you fully experience will subside as it passes on through. It is just energy in motion, e in motion, or e-motion. When you don't resist the emotion, it will resolve itself. Many teachers of meditation, which we will discuss in more depth tomorrow, would say that these first two stages alone are enough for healing and transformation to occur. However, we think there are two other stages that can be extremely useful.
### Analyzing
Once you have allowed yourself to experience the emotion, you "Analyze" it. What stimulated the emotion in the first place? Where did it come from?
Sometimes figuring out what triggered your emotional reaction is easy; other times it can be extremely challenging, like trying to remember a dream. If you focus on it quickly enough, you might figure out the trigger, but sometimes it can take a little longer to emerge from your subconscious so that you can figure it out.
Let's look at Dave's story again. When he drove by that stop sign, he noticed his body tense, which led him to the awareness that something had just triggered a negative emotional reaction. By accepting this awareness instead of ignoring or fighting it, he was able to trace it back to its source. Because he was able to quickly analyze what happened, he could follow his train of associations back to the trigger: speed limit sign —> wife getting a speeding ticket —> party his wife went to that the police officer was at —> party was thrown by a friend —> that friend had asked for help, which Dave provided, and she had never thanked him.
This had bothered Dave for some time, so this memory could have been triggered in countless ways. Even though your first reaction might be How will I ever be able to analyze it effectively enough to determine the source? the reality is your brain will keep taking you back to your unresolved emotions in one way or another.
To help you think about what triggers your emotional reactions, here are some common emotional triggers that problem drinkers experience. Take a minute to review this list and note in your journal if any of these affect you.
• Early sobriety triggers. You are grumpy or short-tempered at certain times of the day or on specific days. This often relates to the time of day when you used to start drinking, or when you started to look forward to or started to plan your drinking. When you remove drinking as a coping mechanism, you will have an adjustment phase while you discover and implement new ways to cope.
• People triggers and drinking triggers. Certain people trigger negative reactions in you. Be careful not to immediately assume it is directly related to them. The way they look, the way they talk, their tone of voice, or even their body language may be the same as someone in the past who has hurt you in some way, which may trigger an unconscious emotional response. When you are no longer drinking, you may now feel much more intensely anything that used to trigger your drinking, because you are not numbing out those feelings with alcohol.
• Pet peeves. These might include foot tappers, obnoxious laughers, overly disorganized or overly organized people, people talking too fast or too slow, constant interrupters, sloppy dressers, people sharing too much or too little, or people texting or talking on their cell phones while driving or on the bus or train.
Sometimes, no matter how hard you look, you won't be able to immediately analyze and determine what stimulated the emotion. That is okay. It will keep coming up in one form or another until you eventually recognize and deal with the emotion. As you work with this process, you will eventually figure out the source. That said, give yourself permission to experience the emotion rather than resist it.
### Assigning
The last stage of the "Mental Makeover," "Assigning" is where the real magic can happen. You specifically assign a new meaning to the thought, belief, or rule that is creating the negative feeling you wish to release. By embracing the power of questions, you can actually change a feeling and replace it with one that leaves you feeling better—which some people refer to as a "better-feeling thought."
For example, imagine that you get in your car and head off to work tomorrow. There is a bit more traffic than usual and you start to get agitated. When another driver cuts you off, coming dangerously close to hitting you, you immediately yell and bang your hands on the steering wheel. However, this time instead of letting that emotion shift into an overall feeling of lasting frustration that sticks with you all morning, you change your frame of reference by asking yourself some questions.
You ask yourself, How would I react if that was my grandmother driving the other car? Or, What would my reaction be if I knew that person had just found out their child was being rushed to the emergency room? Or, Are these opportunities I'm being given to develop and test my awareness, like some kind of freeway samurai training? Suddenly you notice that your feelings shift. You realize that your initial anger quickly dissipates, and you feel back in control of your feelings.
What would happen if every time you are cut off in traffic you choose to think a better-feeling thought? With continued practice over time, your automatic emotional reaction will shift from one of instant anger to something more positive.
Inevitably, life is going to hand you situations that you don't have any control over—bad drivers, the weather, airline delays, power outages, computer crashes, the economy, and deaths of people you care about. You also don't have any control over coworkers who obsessively look at their phones, laugh obnoxiously, slurp their coffee, chew with their mouths open, or wear too much makeup. But you ultimately do have complete control over how you let these experiences make you feel—only you can decide that.
Consider Dave's example again, and his awareness of his unresolved resentment. Because Dave was able to identify the source of this trigger, he had a breakthrough. Dave started by asking himself this empowering question: How am I responsible for the feeling I created? He understood that if he did help create it, he could avoid creating it again in the future. As he explored this question, Dave realized this was a recurring theme in his life. Someone would ask for his help, and he would then provide far more than they even asked for and then expect them to be overly appreciative of his extra effort. When they were not, he would feel resentful.
As Dave asked himself how else this showed up in his life, he realized that at times he wanted to help someone so much that he would offer unsolicited feedback and advice. Some of these people then felt obligated to accept his offer, but because they hadn't asked for it in the first place, they wouldn't act on it or later express any appreciation for it, and Dave would feel unappreciated and resentful once again. However, after this one simple insight, Dave realized he had no right to resent Mary. He also forgave himself for wanting to feel needed and useful, and, most importantly, he decided he needed to change his standards, which we will talk more about in the next section.
As you analyze the source of your emotional reactions, you might discover that your negative emotional response is the result of your actions being incongruent with your core values. For example, you might notice that the morning after you drink you tend to wake up in a negative emotional state. You may just write this off as part of a hangover, but it is also likely that you intuitively realize your decision to drink heavily was out of alignment with your core values. If love and family are two of your core values, and you choose to go out and drink instead of spending time with your spouse and your kids, when you sober up in the morning it is normal to experience a negative emotional reaction. So when you explore the source of your negative emotions, always be sure to ask yourself if your actions are aligned or out of alignment with your core values.
Let's go over some questions that can help you in this stage, which are related to some of the examples we gave in the first stage, "Awareness."
• Someone slurping coffee. What affirmation can I silently repeat and visualize when I hear this sound to create a positive association? Is it possible that I have some annoying bad habits that I might not notice? Does my coworker have a physical limitation that he or she is unable to change that causes this?
• Positive/successful/fit/rich/sober people. Am I jealous? How would my perception of them change if I stopped looking for their faults and focused on their positive qualities? If I appreciated their positive qualities, would that help attract more positive qualities into my life? Is it possible I am unfairly judging them based on past experiences with other people I have met?
• Negative/mean/unfriendly/overweight people. If I knew all the "bad stuff" that happened to them in their life, is it possible I would understand their perspective? What are they like with their family and friends? Is there something I am doing that keeps attracting this type of response from them? Do I feel this way simply because they are different from people I usually spend time with? Does something about them remind me of something I don't like about myself?
• Afraid/sad/angry/bitter about not drinking or missing a drinking event. What am I missing? What "price" will I pay if I did drink? How will drinking affect my dreams, my health, my family, and my finances? Is it time to try a new approach to life, knowing I can always go back to my old life if I choose to? How will I feel in the morning if I decide to drink? Do I know or have I read about someone who is thriving in sobriety? What can I learn from them?
• Drinking triggers. What does the smell of beer, wine, or liquor really mean to me? Does it mean that I am letting a poison control my life? That I am not free to make healthy decisions? Does it mean long-term failure? What does the look, feel, and sight of my favorite alcoholic beverage represent? Being unhealthy? Wasting money? That I'm ruining my relationships?
These are just a few of the questions you can ask yourself. The key is to focus on questions that change the perception or the meaning of the event that triggers the negative emotion.
You also might notice another recurring theme emerging here—practicing forgiveness for yourself and for others. You can't change what happened in the past, but you can change the meaning you ascribe to the past. Many people tend to revisit past mistakes, regrets, and resentments. If you find that you keep getting drawn back to negative past events, go back and use the action steps on Day 4 in the Forgiveness Solution to finally let them go.
### Change Your Standards of Success
Asking the right questions can often lead to a breakthrough, but examining "standards" or "rules" that you judge yourself by is also important to completing this "Mental Makeover." Your standards might include your physical (or intellectual) weight, how much alcohol you drink every week, your level of income, how hard you work, or how much time you devote to helping others.
Going back to Dave's story, when he realized that he was responsible for creating many of his own past resentments, he consciously created a new standard for helping others. Before, his standard included helping everybody, sometimes even including those who didn't ask for it. He was still committed to making a difference by helping others, but he decided that his new standard would be to help someone once they proved they really "wanted" his help. He decided to test their commitment by having them read a specific book or complete a detailed questionnaire. If they followed through in a timely manner, he would then gladly invest more time with them.
Dave was shocked by the overall impact this made in his life. He found that most people loved to ask for help, but when it required work and follow-through to get it, they no longer wanted it. Instead of initially spending hours with these people, he spent only minutes, and if they didn't follow through, he didn't feel any resentment. Dave now had plenty of time to help the people who did follow through, and he found that he was actually excited about working with them. It was clear these people were action-oriented, which he knew would lead to their success. Dave loved the rewarding feeling that came from helping someone create new success, and over time many of these people became trusted friends and colleagues.
When Dave explored the source of an unexpected mood change, he experienced a major shift from an underlying, long-standing feeling of disappointment and lack of appreciation into an experience of fulfillment and joy. This simple awareness led him to create a new standard, saved him countless hours of unhappiness, and removed a self-destructive behavior.
One more thing to be aware of is to not set your standards so high that they are impossible to live up to. For example, when some people decide to quit drinking, they also decide they are going to quit smoking, start working out five days a week, and completely change their diet. We entirely understand and appreciate this enthusiasm, but we also know that most people who set their standards of success too high end up having a major setback that leads back to drinking.
Having standards that motivate you to create more personal and professional success is great, but if you set too many standards at too high a level, you set yourself up for failure. Cutting back or quitting drinking sets a major new standard for your life, so initially focus all your efforts on that one change so that you succeed in it.
Ask yourself what unconscious rules or unrealistic standards of success you are holding to that you might need to change in order to eliminate some negative emotions and make yourself happier and make your goals easier to achieve. We are not saying to give up goal setting or to stop confronting and addressing any fears that might be blocking your success. We are saying that there are most likely standards that you are holding yourself to that you can never live up to, so you are in a constant state of letting yourself down.
Before reading any further, take time to write down in your journal any self-imposed or unconsciously adopted standards that might be holding you back right now, and then rewrite them so it is easier for yourself to "win," like in the examples below.
Old Standard. If I don't accomplish my goals as I have written them, I have failed.
New Standard. The only way I can fail is by not learning from the experience and no longer continuing to try.
Old Standard. Everything I do has to be perfect.
New Standard. I do everything well enough to meet the needs of the task, leaving myself enough time to lead a balanced and healthy life with my friends and my family.
We know that this "Mental Makeover" process can initially seem a little intimidating, but you might be surprised at how easy and intuitive it really is once you try it. When you have the initial "Awareness" of an uncomfortable or negative feeling or mood, simply "Accept" it. Then, ask questions to "Analyze," and "Assign" new meanings to it. When necessary, change any unrealistic standards or rules you have related to it.
Now we want to teach you another incredibly powerful process that is a perfect complement to the one you just learned.
### The Work
I discovered that when I believed my thoughts, I suffered, but that when I didn't believe them, I didn't suffer, and that this is true for every human being. Freedom is as simple as that. I found that suffering is optional. I found a joy within me that has never disappeared, not for a single moment. That joy is in everyone, always.
—BYRON KATIE
Author of Loving What Is: Four Questions That Can Change Your Life
Let's look at one other simple and effective inquiry process that you can use to facilitate your emotional sobriety. This method, called The Work, was developed by Byron Katie and helps you question the thoughts that create your emotional suffering.
This simple five-step process can help you live with less anxiety and fear; create deeper connection and intimacy with your partner, parents, and children; understand what makes you angry and resentful; become less reactive less often and with less intensity; and feel a new sense of ongoing vigor and well-being.
In its most basic form, The Work consists of four questions and three turnaround statements. You start by choosing a behavior or event that is triggering your negative feeling, usually something that you think shouldn't be that way. It might be that your spouse doesn't listen to you, your boss doesn't respect you, rush hour traffic is too congested, your parents should have loved you more, your brother shouldn't have made fun of you at the wedding, the people on Wall Street should act more responsibly, and so on.
Then ask yourself, What is the underlying thought or belief I have about that person or situation? The answer is the statement you will use for the exercise. For example, your statement could be as simple as "My mother should pay more attention to me." The next step is to take that statement and put it up against the four questions and turnarounds of The Work as follows.
The 4 Questions
1. Is it true? (Yes or no. If no, move to 3.) Can you absolutely know that what you are thinking is true? Be still and wait for your heart's response.
2. Can you absolutely know that it's true? (Yes or no.) Ultimately, can you really know what anyone else should or shouldn't do? Can you absolutely know what is in their best interest to do or not do? Or what they should think or not think?
3. How do you react (what happens) when you believe that thought? Do you experience anger, hurt, stress, or frustration? How do you treat the other person? Do you punish them in some way? Do you try to change them in any way? How do these reactions feel? How do you treat yourself? Does that thought bring stress or peace into your life? Be still as you listen.
4. Who would you be without that thought? Close your eyes. Picture yourself in the presence of this situation. Now imagine being there without the thought. What do you see? What would your life look like without that thought?
Then turn the thought around. Find at least three specific, genuine examples of how each turnaround is true for you in this situation. Here's our statement again: "My mother should pay more attention to me."
1. Turn the thought around first to yourself. (I should pay more attention to me.)
2. Next, turn the thought around to the other. (I should pay more attention to my mother.)
3. Third, turn the thought around to the opposite. (My mother does pay attention to me, or I don't need my mother to pay attention to me.)
The turnaround sentences get you to focus your attention back on what you can change in yourself, which is the real source of your liberation—not trying to change the other person or the world, which is the source of your pain and suffering.
Let's take Dave's experience of being upset with Mary, who had not expressed appreciation for all the work he did to help her out.
Using the four questions, Dave will investigate his statement Mary should have taken the time to personally appreciate me for helping her.
1. Is it true? Is it true that she should have appreciated you? Be still, and wait for your heart to respond.
I'm not sure.
2. Can you absolutely know that it's true? Ultimately, can you really know what Mary should or shouldn't do? Can you absolutely know what is in her best interest to do or not do? Can you absolutely know for sure?
No. I can't know for sure what anyone should do. I don't know what else was going on in her life.
3. How do you react (what happens) when you believe that thought? What happens when you believe "Mary should have appreciated me," and she didn't? Do you experience anger, hurt, stress, or frustration? How do you treat Mary? Do you avoid her at a party? Do you try to change her in any way? How do these reactions feel? How do you treat yourself? Does that thought bring stress or peace into your life? Be still as you listen.
Angry, hurt, unappreciated. And cut off from connecting to Mary. Then I feel isolated and shut down.
4. Who would you be without that thought? Close your eyes. Picture yourself in the presence of Mary in this situation. Now imagine looking at Mary, just for a moment, without the thought I want her to express her appreciation to me. What do you see? What would your life look like without that thought?
I'd be relaxed, calm, and at peace. I wouldn't need anything from her. I would just be present with her. I could just experience the joy of me being myself without needing anything from her.
The Turnarounds. Find at least three specific, genuine examples of how each turnaround is true for you in this situation. For example:
1. To yourself. (I don't appreciate myself enough.)
2. To the other. (I don't appreciate Mary.)
3. To the opposite. (Mary does appreciate my help, or I don't need Mary's appreciation.)
Finally, stop and notice how you feel after you take yourself through this process.
———
Once you have learned the four questions and turnaround statement format, you can take yourself through it in your journal—and eventually just in your mind—whenever you are upset, or at night as a way to simply clear out any negativity that you may have built up over the course of the day. The Work will leave you in a state of natural peace and joy, where the desire for alcohol doesn't exist.
You can also learn how to use this process by watching a few short videos of Byron Katie actually guiding someone through the four questions and the turnarounds, which you'll find on today's companion website.
### Day 23 Action Steps
Not only does the Emotional Sobriety Solution allow you to recognize and change the negative emotions you experience daily, it also teaches you emotional resilience. Just as regular workouts result in a quicker recovery from intense exercise, today's solution teaches you how to quickly recognize and break free from your negative emotional states.
• Practice the "Mental Makeover" when you experience negative emotions. You can do this process in your head, although we highly recommend that you do it in writing when you can. Make sure to record any breakthroughs or insights you have during the process in your journal. You can find a detailed example on the companion website. The steps below are a brief review:
• Awareness. Notice when and where negative emotions show up, as well as some of the most common negative emotional triggers and track down the source of these emotions.
• Acceptance. Allow yourself to experience the emotion—it is there for a reason, and fighting it will only guarantee that it will keep coming back.
• Analyzing. Determine what triggered or stimulated the emotion in the first place by reviewing the list of common problem drinker triggers, and make note in your journal of which ones are currently holding you back.
• Assigning. Ask questions in order to free yourself from being triggered again by this particular emotion. Write down in your journal any self-imposed or unconsciously adopted standards that might be holding you back, and rewrite them to allow yourself to succeed. Refer to examples in today's solution.
• Practice The Work. Pick a behavior or a situation that upsets you, and take yourself through the process of The Work described above. Write down your insights in your journal.
The companion website includes a detailed example of the "Mental Makeover" process, some links to several videos of Byron Katie demonstrating The Work, and an introduction to The Sedona Method—another simple and powerful technique to help you effectively let go of painful and unwanted feelings. Be sure to visit the companion website at: <http://Day23.Solutions>.
## Day 24
## The Meditation Solution
## Meditate to Release Stress and Develop Inner Peace
Whatever our past, whatever our present, all of us have the capacity to change ourselves completely through the practice of meditation.
—EKNATH EASWARAN (1910–1999)
Meditation teacher and author
Would you like to have a healthier heart, a stronger immune system, and be less susceptible to bouts of depression and anger? What about reducing stress while increasing your productivity and creativity? Hundreds of studies have proven that these are just some of the benefits you can expect from the practice of meditation.
Meditation is not new. It has stood the test of time, dating back over five thousand years. By adding the practice of meditation to your new life of thriving in sobriety, you dramatically improve every aspect of your life. Whether you want better health, more financial freedom, or just to be happier without feeling the desire to drink, today will show you how to accomplish this.
### The Benefits of Meditation
Have you ever felt winded after climbing a short flight of stairs? If you have, it is probably the result of not exercising regularly. Have you ever felt short-tempered, easily distracted, or just unhappy? Although it is human nature to occasionally experience these feelings, those who don't meditate regularly feel them more often. Meditation is to the mind what exercise is to the body.
The National Institutes of Health (NIH) reviewed 813 scientific studies of subjects who meditated for at least two weeks. In his book Transformation, bestselling author Bill Phillips explains that the people in these studies "often experienced lower blood pressure, a healthier heart rate, strengthened immune systems and improved sleep (reduced insomnia). People also reported a reduction in muscle tension, backaches and pain, improved memory, and better cognitive performance."
That alone is reason enough to practice meditation, but the benefits are even greater for problem drinkers. Meditation has been found to be an effective technique to prevent relapse in recovery from addictive behaviors, such as alcoholism. Phillips recounts: "In longer-term scientific studies, a significant reduction in relapse rates among those in recovery from addictive habits has also been documented."
### The Myths of Meditation
Meditation suffers from a towering PR problem, largely because its most prominent proponents talk as if they have a perpetual pan flute accompaniment. If you can get past the cultural baggage, though, what you'll find is that meditation is simply exercise for your brain.
—DAN HARRIS
Author of 10% Happier: How I Tamed the Voice in My Head, Reduced Stress Without Losing My Edge, and Found Self-Help That Actually Works—A True Story
Meditation sometimes gets a bad rap. That it is only for new agers or hippies. That it is a spiritual or religious practice. That it is difficult, or takes years of dedicated practice to benefit from it. Or that it is only for saints and holy men. These are all meditation myths! If you don't believe us—just ask the United States Marines or the Super Bowl XLVIII champions.
The Seattle Seahawks used meditation in their training to help them become one of the best teams in football. Russell Okung, a sixth-overall NFL draft pick who signed a $48 million contract, said to ESPN, "Meditation is as important as lifting weights and being out here on the field for practice. It's about quieting your mind and getting into certain states where everything outside of you doesn't matter in that moment. There are so many things telling you that you can't do something, but you take those thoughts captive, take power over them, and change them."
Psychologist Amishi Jha, director of the University of Miami's Contemplative Neuroscience, Mindfulness Research and Practice Initiative, teaches US Marines meditation to achieve mental resilience in a war zone. Jha says, "We found that getting as little as twelve minutes of meditation practice a day helped the Marines to keep their attention and working memory."
### What Is Meditation?
Meditation is a technique for quieting the mind and achieving a clear, relaxed, and peaceful state of consciousness. You are fully awake and alert, but not focused on your thoughts or feelings. Meditation is an opportunity to slow down—to create an inner state of connectedness and peacefulness that allows you to get in touch with your higher self and whatever gives your life purpose and meaning. The ideal state when meditating is one of focused awareness, where you are no longer distracted by your thoughts; however, if and when thoughts arise, you simply notice them, without judgment, and let them pass by as if they were a ship passing in the distant horizon.
In his TED Talk (a talk designed to spread powerful ideas, usually in eighteen minutes or less), "All It Takes Is 10 Mindful Minutes," Andy Puddicombe, who is considered a leader in the modern mindfulness movement, said, "Most people assume that meditation is all about stopping thoughts, getting rid of emotions, somehow controlling the mind, but actually it's much different than that. It's more about stepping back, seeing the thought clearly—witnessing it coming and going—without judgment, but with a relaxed, focused mind."
### Meditation, Mindfulness, and Bad Habits
Yesterday we looked at how negative emotions can unconsciously control how you feel and what you do. The first step in changing this is making the unconscious conscious, which starts with being conscious of the present moment, including your thoughts, feelings, and physical sensations. And one of the best ways to cultivate mindfulness is through meditation.
The practice of meditation develops your ability to observe your thoughts and feelings without judgment. With continued practice, you can bring this mindfulness into your daily life. As David Sheff writes in his book Clean, "Research has shown that mindfulness meditation, as one version of therapy is called, effectively interrupts cues. Addicts are taught to recognize and sit with their feelings—to experience them with curiosity and acceptance rather than react impulsively to them. This makes them better able to defuse their triggers."
As we have discussed, problem drinkers love to fulfill their short-term desires. They tend to be more impulse driven and believe that drinking is an effective solution for dealing with stress, frustration, anger, fear, disappointment, and grief. They also often believe that they need to drink to experience pleasure and happiness. And most of these beliefs are unconsciously driven.
When you meditate, you can stop reacting to the constant mental chatter of your thoughts and beliefs, and simply observe and accept them instead. Problem drinkers often report that meditating is like being an impartial observer, seeing their true self for the first time and finally understanding the root cause(s) of their desire to drink. Meditation also allows you to observe and eventually silence the inner "voice" that might be constantly judging or critiquing you. Over time it allows you to experience inner peace and a true sense of freedom—feelings most problem drinkers once believed only came from drinking.
### Cleaning Up Your Mental Clutter
Think about all the things that cause you stress—a looming deadline at work, a disturbing call from your doctor, having an argument, getting stuck in traffic, preparing for a presentation, losing a sale, an unexpected auto repair bill, or losing your cell phone. All of these can create stress, and in many ways the quality of your life is determined by the amount of stress you do or don't experience.
Stress is the underlying cause of more than 60 percent of all human illness and disease. In a New York Times article, Sandra Blakeslee writes, "Chronic stress sets into motion a cascade of biological events involving scores of chemicals in the body—serotonin, cortisol, cytokines, interleukins, tumor necrosis factor and so on. Such stress lowers resistance to disease and alters gene expression. When people are under stress, wounds tend to heal more slowly, latent viruses like herpes erupt and brain cells involved in memory formation die off. The precise molecular steps underlying all of these changes have been mapped out."
When you experience stress your body releases cortisol, which is often referred to as the "stress hormone." In The Biology of Belief, Bruce Lipton notes that this hormone is given to patients who are receiving organ transplants. Why? Because cortisol is so effective at weakening the body's immune system that it cannot fight the newly transplanted organ as effectively.
Stress also causes "cortical inhibition," which means the smart part of your brain can't function as well, often resulting in poor decision making, lack of focus, and even the inability to make decisions. Simply put, stress makes you dumber.
Enoch Gordis, MD, the former director of the National Institute on Alcohol Abuse and Alcoholism, writes, "Drinking alcohol produces physiological stress, that is, some of the body's responses to alcohol are similar to its responses to other stressors. Yet, individuals also drink to relieve stress. Why people should engage in an activity that produces effects similar to those they are trying to relieve is a paradox that we do not yet understand." So not only does problem drinking often lead to negative consequences, and therefore stress, but also the actual consumption of alcohol creates physiological stress.
Another reason problem drinkers frequently experience more stress than others is because excessive drinking often creates added strain on finances, career, health, and family. In addition, when problem drinkers are finally able to quit or cut back drinking, they lose their primary coping mechanism for stress—alcohol. So the ultimate irony for a problem drinker is that drinking often leads to increased stress, but in the beginning not drinking can also cause stress and increase the odds of relapse.
No other technique in this program is more effective or more proven to relieve stress than meditation. When your mind is "cluttered" with stressful thoughts and feelings, fear and anxiety, shame and guilt, you become physically and mentally impaired. Meditation can help you overcome this. Just as cleaning your home or office can help you feel less stress, meditation helps you to "declutter" your mind—eventually freeing you from negative patterns of thinking and emotions and unconscious self-defeating behaviors. However, the benefits of meditation for problem drinkers don't stop there—meditation provides another ssignificant benefit.
### Meditating Your Way to Happiness
On Day 7, we first introduced you to the importance of serotonin and dopamine. Serotonin helps regulate your mood, prevents depression, and makes you feel happy. Dopamine also affects your mood and your, ability to focus and feel pleasure. Alcohol naturally stimulates the release of these neurotransmitters, which is one of the reasons it is addictive, and when you stop drinking it takes time before your brain will start producing these again at normal levels. Besides the food and supplements we recommended that naturally stimulate the brain's production of serotonin and dopamine, meditation also increases the production of serotonin and dopamine.
### Breathing Away Cravings and Anxiety
The single most effective relaxation technique I know is conscious regulation of breath.
—ANDREW WEIL, MD
Author of 8 Weeks to Optimum Health: A Proven Program for Taking Full Advantage of Your Body's Natural Healing Power
Take ten seconds now to notice your breathing—do not try to change it. Now take thirty seconds and breathe deeply—intentionally breathing in slowly, feeling the air fill and extend your stomach, holding it in for a few seconds, then slowly exhaling completely. What changes did you notice? Most likely you experienced a physical response, such as your shoulders dropping or your heart rate slowing, as well as an emotional response, such as feeling calmer or more centered.
Proper breathing is critical to effective meditation and to your health and wellness, yet it is one of the most overlooked practices taught to achieve optimum health. Breathing serves two primary purposes. It supplies your body with oxygen and rids your body of waste and toxins. When you practice breathing exercises, not only do you more effectively oxygenate your body and free it from toxins, you also reduce stress, calm your mood, and feel more energized.
There are many different breathing exercises you can learn, but we especially like the 4-7-8 Relaxing Breath Exercise taught by Dr. Andrew Weil. It consists of five simple steps you can do anywhere and anytime. Place the tip of your tongue against the ridge of tissue just behind your upper front teeth, and keep it there throughout the entire exercise. You're going to be exhaling through your mouth and inhaling through your nose.
1. Exhale completely through your mouth, making a "whoosh" sound.
2. Close your mouth and inhale quietly through your nose to a mental count of four.
3. Hold your breath for a count of seven.
4. Exhale completely through your mouth, making a "whoosh" sound while mentally counting to eight.
5. This counts as one breath. Now repeat steps 2 through 4 three more times—for a total of four breaths.
You can watch a video of Dr. Weil demonstrating this technique at www.drweil.com. (Once you get there, type "The 4-7-8 Breath" into the search window.) Dr. Weil says, "You must do this at least two times a day," but he also says that you can do it as many times as you wish. However, in the first month, you should not do more than four consecutive breaths each time. Dr. Weil says it is a very useful tool to fight any craving and "the most powerful antianxiety measure" he has ever found. Your first action step today is to practice this method and then continue to do it at least twice a day. The best time to do it is right before you meditate.
### How to Practice Meditation
The ultimate reason for meditating is to transform ourselves in order to be better able to transform the world. To put it another way, we transform ourselves so that we can become better human beings and serve others in a wiser and more effective way. Meditation thus gives our life the noblest possible meaning.
—MATTHIEU RICARD
Author of Why Meditate: Working with Thoughts and Emotions
Meditation is often described as "simple but not easy." It is simple because the steps are not complex. But it can take practice to actually silence your mind and effectively let go of all the nonstop chatter and thoughts that barrage your mind.
There are many effective ways to practice meditation. We have outlined the key steps to meditating common to most practices, but we encourage you to explore other techniques after completing this program. The second action step for today is to listen to the guided meditation on the companion website that leads you through the steps below.
• Start with ten minutes, but build a habit. When you are not using the guided meditation, we recommend starting with ten minutes of meditation a day. Studies say this is the best way to get the most value. However, you can leverage the power of creating "tiny habits," as we covered on Day 9 in the Action Solution and begin with as little as two minutes and build from there.
• Pick a comfortable, quiet place. Ideally, find a time and location free from noise and potential interruptions. Pay attention to your posture. In his book Wherever You Go, There You Are, Jon Kabat-Zinn captures this best by saying, "Sit in a way that embodies dignity."
• Deep breathing. Focusing on your breathing, let go of everything else. Breathe in through your nose, down to your stomach, and back out through your mouth. Find a relaxing rhythm, such as breathing in for four seconds, holding for two, and breathing out for six. Or use the 4-7-8 method described above. Do either one of these for four repetitions. You do not need to focus on your breathing throughout the meditation, but bringing your focus back to breathing helps to silence your mind. You can keep your eyes open, gazing at a space on the floor in front of you with a soft focus, or you can close your eyes, as most people generally prefer to do.
• Release all tension. Imagine a ball of soft golden light, roughly the size of a tennis ball, radiating healing energy. Scan your body for any areas that might be holding tension and imagine this ball moving to those areas. Picture the healing energy from the ball dissolving the tension, and as you breathe out, the tension is released from your body.
• Meditate. The ideal state is to ultimately silence all of your internal thoughts and dialogue. Here are two effective techniques. One is to simply focus on your breathing and direct your attention to the sensation of air passing through the tip of your nose as you inhale and exhale or the expansion and contraction of your belly. When you notice any thoughts coming up, just accept them and let them go, and come back to concentrating on the sensation of your breathing. Another technique is to use a mantra. One that we like is to repeat "I Am" over and over again. Say "I" as you slowly breathe in, and "Am" as you slowly breathe out. If and when thoughts come up, you can picture the thought in a bubble and just let it float away, without judgment or contemplation. With either technique, when a thought comes up (and in the beginning you'll have lots of them) and you find yourself caught up in the thought, once again just let it go and return your attention back to your breath or the mantra.
As you meditate, the best approach is one of overall acceptance—accept your breath, accept your active mind, accept your rhythm, accept all parts of yourself, accept any thoughts and feelings, and accept the flow of the meditation. Don't get discouraged or beat yourself up if you find it challenging to silence your mind—even people who have practiced meditation for years still experience this challenge. This is why meditation is called a practice. Even if you feel like you are struggling, you are still benefiting from the practice.
Another way to help focus your attention is to count while breathing. Start with "one" on your first exhale, and then count "two" silently to yourself on the next exhale, and then "three" on the next exhale, all the way to "ten." When you reach ten, just start over again at one. It is perfectly normal to become distracted by a thought and lose count. Just accept it and gently bring your attention back to the breath, and start again at one.
You can vary your practice—by adding music, meditating in nature, and using different mantras and breathing techniques. We have provided a list of some of our favorite meditation music on the companion website.
### Powerful Meditation Variations
At the root of addiction is a natural impulse to satisfy our human needs for security, comfort, self-esteem, sensory gratification, and power. But at a deeper level, we know that that our addictions cannot fill the emptiness inside ourselves and will not lead to lasting peace and inner satisfaction. Identifying the void you have been trying to fill and replacing life-damaging beliefs and behaviors with those that are life-supporting—including meditation and other practices for higher consciousness—will serve you immeasurably on your journey to healing and transformation.
—DAVID SIMON
Coauthor of Freedom from Addiction: The Chopra Center Method for Overcoming Destructive Habits
Once you begin to see the power of meditation in your life, you may want to expand on the techniques we've given. Here are three variations using other solutions you've learned that can complement your meditation practice. When you have time, we recommend that you integrate these into your daily routine.
• The 4-Minute-Mile Solution. After you have released the tension in your body with the golden ball of light and completed your deep breathing exercise, but before you drop into meditation, is also a great time to practice your visualizations from Day 15 in the 4-Minute-Mile Solution. Meditation quiets the mind and powerfully connects you to the universal source, from which all things manifest. Attach positive emotions and feelings to your detailed images in order to make them more powerful. You can also visualize at the end of your meditation, when your relaxed state will deepen the impact of your visualizations.
• The Quality Question Solution. When you meditate you are essentially tapping into a deeper and higher part of your own subconscious mind and into a higher energy outside of yourself, which can be referred to as Source, God, Higher Power, Universal Intelligence, or the Quantum Field. Whatever you choose to call it is unimportant. However, meditating is incredibly powerful in revealing answers to your questions that align with your life purpose. Diana Robinson says, "Prayer is when you talk to God; meditation is when you listen to God." The practice of meditation allows you to accept and quiet all the incessant thoughts and chatter in your mind so you can actually "listen" to the answer. We often find that when we come out of a meditation, we are reconnected with what is really important to us. This enables us to let go of the worries, regrets, fears, and resentments that were holding us back.
After you have released the tension from your body, simply ask the question you want answered, being sure to use the format you learned on Day 16 in the Quality Question Solution. Then let it go and begin meditating. During, or after your meditation, you might find you have connected with the answer, or it might come to you in future meditations.
When Jack was searching for a title to his collection of inspirational stories, he asked for a title in meditation. Eventually he saw a picture of a hand come out and write the words Chicken Soup on a green chalkboard. Within minutes, it evolved into Chicken Soup for the Soul, which became a bestselling book and book series and evolved into a multimillion-dollar brand recognized around the world.
• The Gratitude Solution. A perfect time to practice gratitude is when you are coming out of your meditation, when you have heightened clarity about what is truly important. So take a minute and silently give thanks for some of the things you are most grateful for.
A guided meditation for each of these variations is on the companion website.
### Day 24 Action Steps
I can't tell you how much I'm enjoying being back in school, having the chance to work on my writing, including my second novel, with some big-name authors; it's life changing. Also, I am still happily sober. I go to the gym regularly, I moved in with my girlfriend, and I meditate every day—all things I never would've imagined myself doing before.
—THOMAS
30-Day Graduate from London, England
The practice of meditation is truly transformational. It will help you become happier, healthier, more relaxed, and more creative.
• Practice breathing. Inhale through your nose to a count of four, hold your breath to a count of seven, and exhale to a count of eight out your mouth. Repeat four times. Complete this two or more times a day.
• Listen to the guided meditation and start meditating ten minutes or more a day. Use the following guidelines; however, feel free to add meditation music. We list some good options on the companion website. You can also use different mantras or experiment with different meditation practices.
• Location. Find a comfortable and quiet location and sit upright "in a way that embodies dignity."
• Breathing. Focus on deep breathing, in through your nose, down to your stomach, and back out through your mouth. Your eyes can be open, gazing at a space on the floor in front of you, or as most people prefer, closed.
• Tension. Imagine a ball of soft golden light radiating healing energy and move it toward any areas of tension in your body. As you exhale, picture the ball dissolving the tension.
• Meditate. Silence your thoughts and internal dialogue. You can repeat a mantra, like "I Am," as you breathe in and out, or focus on the sensation of your breathing. If you find it challenging to silence the thoughts that come up, simply notice them without judgment and gently repeat your mantra or focus on your breathing.
• Integrate the meditation variations. Over the next few weeks, practice each one of these variations, either on your own or using the guided meditations on the companion website.
• The 4-Minute-Mile Solution. Right before or after you meditate, practice your visualizations. As best you can, be sure to experience the feelings of achieving your goal.
• The Quality Question Solution. Release your tension with the golden ball of light, ask a question that you want answered, and then meditate, allowing for the answer to emerge.
• The Gratitude Solution. Finish your meditation by focusing on five or more things you are grateful for, remembering to really work at feeling the gratitude, not just thinking about it.
All the guided meditations are on the companion website, as is information on the topic of drinking and stress, and some additional resources and techniques on breathing. Be sure to visit the companion website at <http://Day24.Solutions>.
## Day 25
## The Mind and Body Solution
## Thriving in Your Mind and Body Through Nutrition
When health is absent, wisdom cannot reveal itself, art cannot become manifest, strength cannot be exerted, wealth is useless, and reason is powerless.
—HEROPHILUS (335–280 BC)
Greek physician
Imagine yourself one year from today. You are thriving in sobriety. You are in love, have great relationships with friends and family, and work with passion. You have discovered your life purpose and are living it every day. You have found balance in your life, and have time for work, friends, family, and hobbies. You are financially free, and maybe you are even regularly volunteering at a local nonprofit organization. You have found a deep sense of peace and spirituality in life, fueled by personal-growth work you love doing.
This probably sounds fantastic, if you make one assumption—you are physically healthy. Your quality of life starts with your body, and to thrive in sobriety, you want to be physically healthy. The Mind and Body Solution will start you down the path to thriving physically, so you can have the health, energy, and vitality you need to create success throughout your life.
### The Mind-Body Connection
Seventy percent of all patients who come to physicians could cure themselves if they got rid of their fears and worries.
—O. F. GOBER, MD
Chief physician of the Gulf, Colorado and Santa Fe Hospital Association in the 1940s
Each of the last three days touched on a common theme for Week 4—your body. Your strong emotions—fear, sadness, excitement, and joy—elicit a physical response. When you meditate, you balance your body's systems, bringing your breath, posture, heart rate, and brain into a relaxed and aligned state. Today we continue with this theme.
Your mind, your thoughts and beliefs, directly affect your body by influencing what, when, and how much you choose to eat. The reverse is also true. The food you put in your body affects what you think and believe and how you feel. The Mind and Body Solution is about what to feed your body for lasting recovery, energy, and health, and it is about the importance of the mind-body connection and how to successfully approach changing your diet.
Plato wrote, "The greatest mistake physicians make is that they attempt to cure the body without attempting to cure the mind; yet the mind and the body are one and should not be treated separately!" Even though many of the solutions up until this week have focused on your mind, much of what you have done also applies directly to successfully changing your body.
Graduates of The 30-Day Sobriety Solution often say that changing their diet was easy compared with cutting back or quitting drinking. In part, because the work they did in this program, such as visualizing themselves thriving in sobriety, healthy and fit, helped them eat and exercise better. And once they learned how to recognize and change their limiting beliefs related to drinking, it was much easier to recognize other limiting beliefs that were holding them back from thriving physically.
Most problem drinkers also find that their poor eating habits, such as eating late at night, eating greasy and unhealthy food, or consuming too many calories, are directly related to their drinking. Once you remove alcohol, eating healthy becomes much easier, and you instantly eliminate a huge source of empty calories. You feel emotionally healthy, happier, and more stable than when you were drinking. So now, even when you have a bad day, or just get down, you know how to cope and change that state, whereas in the past you might have dealt with stress, fear, worry, anxiety, or self-esteem issues by drinking beer, wine, or cocktails, and eating pizza, candy bars, or nachos.
### New Standards for Your New Body
One of the most exciting things we get to see, literally, are the physical changes our clients go through when they get sober. Sometimes these changes are obvious, such as weight loss, less puffiness in the face, a healthy skin color and glow, and clearer, more alive eyes. Many of these changes happen even if your eating is still somewhat unhealthy while you are getting sober. However, in the long run, it is critical that you embrace an overall healthy diet to thrive physically.
As we mentioned on Day 1 in the 100% Solution, there is a reason why we have waited to include this topic, which is that if you try to accomplish too many big goals at once, you may fail at all of them. Remember, not only do you have a dependency on alcohol, you also have a dependency on sugar because alcohol is essentially fermented sugar. So, for most people, quitting drinking while also changing your diet and dramatically cutting back on sugar is a recipe for failure. You may find by today that your cravings have already reduced dramatically, but some changes in your diet may curb your alcohol cravings further.
Nutrition and exercise are crucial in recovery. We have attended plenty of Alcoholics Anonymous meetings where we were overwhelmed by cigarette smoke, donuts, junk food, coffee, and empty sugar packets spread around the room. Too many attendees were overweight and unhappy. This is not what we consider thriving in sobriety. Not all AA meetings are like this, but these types of meetings remind us of the importance of not trading your dependency on alcohol for one on cigarettes, sweets, or overeating.
When your mind and body are healthy, there is no limit to what you can achieve. The first step toward this is to establish a new rule, or standard, for nutrition and exercise. Any progress, no matter how small, in your diet and exercise is positive—even if you just read a good article on nutrition, do one push-up, or eat one less serving at dinner.
We want you to be flexible when you make any nutritional changes or take on any intense new workout regimens. If a strict all-or-nothing approach has worked for you in the past, go ahead and try it; however, not until after you have finished the program. And better yet, after at least three months of sobriety.
The challenge of starting a strict diet now is that, if you slip, it can lead to feelings of guilt, frustration, and failure. Your self-esteem may take a hit because anytime you make an agreement with yourself and break it, you tend to feel worse about yourself. So approach today's solution as a learning opportunity—one where you can embrace small changes in your diet. As you continue to practice and apply these solutions, thriving physically will come naturally.
### Reclaiming Your Body from Alcohol
Freeing your body and mind from being a "prisoner" of alcohol can be one of the most rewarding experiences of your life. Dave always dreamed of getting fit and healthy, but couldn't do it while drinking. Here is his journey to thriving physically:
In 2004 I was drinking almost nightly. I rarely exercised and I certainly didn't pay attention to what I was eating. I weighed an all-time high of 252 pounds. My drinking, weight, and lack of exercise were having a profoundly negative impact on my overall health.
I had two visits to the emergency room, one for alcohol poisoning and one for a heart attack scare. My doctor discovered that I had an enlarged heart. Another doctor was concerned because my liver appeared enlarged and I might need a biopsy. I had incredibly high counts in my blood work, including cholesterol, triglycerides, and the tests related to my liver. I also was frequently sick and even experienced strange, unidentifiable discomfort and pain in various areas of my body at random times.
Finally, in 2007, I got sober, and even though I still wasn't thriving in sobriety, I had managed to put together ten consecutive sober months for the first time in my adult life. As I contemplated my life in sobriety and my friend Bryan taking his life, I knew things had to change. Fortunately, my recent blood work revealed improvements in every area, but a recent photo of me and my daughter told me otherwise. I felt lousy—overweight, unhappy, and unhealthy.
Over the next year, I became dedicated to my health, and it ended up being a year that changed my life—especially my body and mind. I did programs like P90X, Bill Phillips's Body for Life and Transformation, and I incorporated ideas from one of my favorite health/fitness/nutrition books by trainer-bodybuilder Tom Venuto called The Body Fat Solution: Five Principles for Burning Fat, Building Lean Muscles, Ending Emotional Eating, and Maintaining Your Perfect Weight. I also read at least forty books on fitness, nutrition, strength training, and running.
Roughly one year after I looked at that photo, I ran seventy-five miles in a weekend, completing two marathons, a half marathon, and a nine-mile run. This was a way of challenging myself and celebrating the transformation I was able to make. My weight reached an all-time low of 169 pounds (83 pounds less than my heaviest weight), and I was stronger than I had ever been in my life. Since I regularly get requests to see some before and after photos, we have included some on the companion website.
Most exciting, and ironic, was that these improvements weren't that hard. But when I was drinking, they seemed impossible—I had started countless diets and workout programs over a ten-year span, but all of them ended with very little results because the drinking was always there. Going from drinking almost every night to being sober, and practicing the solutions we teach in this program, not only freed up an abundance of time and hangover-free energy but also led to a thriving-in-sobriety mind-set. As a result, adding in exercise and sticking to a healthy diet were easy.
You, too, will find that starting new healthy habits comes much more easily now, because you are not the same person who started this program.
### The Real "Cost" of Alcohol and Your Health
Which intoxicating substance is associated with the most lethal violence? The correct answer, by far, is alcohol. It's involved in more homicides than pretty much every other substance combined. Alcohol's relative importance has grown over the last fifteen years, as aging populations of cocaine users account for a declining proportion of violent crime.
—HAROLD POLLACK
University of Chicago professor and frequent contributor to the Washington Post blogs
One of the most common fears we hear from our clients is that their drinking has caused irreversible health issues. Although these fears are justified, remember that your body has amazing restorative capabilities. And when you start integrating healthy nutrition and exercise into your life, you can completely change your body's overall health and reverse decades of drinking abuse.
As common as it is to have concerns about your health because of your drinking, it is also common to rationalize away the various issues with your health and say that they are unrelated to your drinking. But let's be absolutely clear here—alcohol is a poison. And when you continuously put poison in your body, every system in your body can be negatively affected. Where in your body these issues show up will vary depending on your hereditary and environmental conditions, as well as your age, diet, and exercise habits. Health issues that you quickly disregard as unrelated to your drinking might not be as unrelated as you think.
Problem drinkers tend to live in denial, and even when they accept that they have to cut back or quit their drinking, they don't always fully acknowledge the potential consequences of continued drinking. Here are the health problems that heavy drinking, and in some cases even moderate drinking, can cause:
• Liver disease and/or cirrhosis of the liver
• Brain damage or dementia
• High blood pressure and irregular heartbeat
• Stomach ulcers, esophageal ulcers, and gastritis
• Cancer of the breast, head and neck, colon, and liver
• Slower healing/recovery from illness or injury
• Damage to retrospective memory (learning, retention, and retrieval)
• Higher risk of more than two hundred diseases, including tuberculosis and pneumonia
Not only does heavy drinking directly affect the health of your body, it can also lead to other very serious consequences. Alcohol is a factor in:
• 40 to 50 percent of traffic fatalities
• 40 percent of suicides and fatal falls
• 50 percent of sexual assaults and trauma injuries
• 60 percent of all fatal fires, drownings, and homicides
• 48 percent of hypothermia and frostbite cases
The negative consequences of drinking on the female body can be even more severe. One study showed that women who had two to four drinks a day increased their breast cancer risk by 41 percent; another study showed that women who drank three or more drinks a day on average had a 69 percent higher risk of getting breast cancer. Women are also at a 40 percent higher risk than men of developing high blood pressure from excessive drinking.
Last, and to us the most shocking, is a recent report from the World Health Organization that disclosed that every ten seconds someone dies from problems related to alcohol use. Although we don't want you to dwell on the potential negative health consequences from excessive drinking, it is crucial that you are not in denial about what drinking alcohol can "cost" you.
Remember, it doesn't have to be this way, just as one 30-Day Graduate shared:
The 30-Day Sobriety Solution has given me back time. I no longer have a daily time constraint at night to start drinking. My goals are no longer determined by the massive amount of time my drinking took from me. The overall freedom I experience today is incredible. Every morning I look in the mirror and see a clear-eyed and healthy reflection and I get to live a happy and fulfilling life that is free from the constant worries and fears that my drinking might tragically take my life and leave my children without a mother.
### Your Body's Incredible Restorative Powers
The best way to detoxify is to stop putting toxic things into the body and depend upon its own mechanisms.
—ANDREW WEIL, MD
Your body has a remarkable ability to heal itself. When you stop drinking and start eating right, your body can begin healing and reverse years or even decades of abuse.
For example, in a common living-donor transplant, a donor gives roughly 50 percent of his liver to a recipient. Not only is this enough to cure the recipient, but the donor's liver grows back to its original size in six to eight weeks., Your whole body is constantly regenerating, eliminating old cell matter and processing vitamins, minerals, and protein to create new cell matter:
• Every 120 days—new red blood cells
• Every 90 days—new skeleton
• Every 60 days—new brain cells, tissue
• Every 49 days—new bladder
• Every 45 days—new liver and new DNA cell material
• Every 30 days—new hair and new skin
• Every 5 days—new stomach lining
Roughly six billion cells are turned over every day by your body. Once you remove alcohol from your body, this regenerative process really starts to benefit you. As you provide your body with the proper nutrition, the healing is even more rapid.
### It Was Just One Pound . . .
Primary food is more than what is on your plate. Healthy relationships, regular physical activity, a fulfilling career and a spiritual practice can fill your soul and satisfy your hunger for life. When primary food is balanced and satiating, your life feeds you, making what you eat secondary.
—JOSHUA ROSENTHAL
Founder and president of the Institute for Integrative Nutrition
Our goal for today is to provide you with some basic nutritional advice from several nutritional experts we consulted to make sure the information we are providing is accurate and appropriate for the problem drinker. As a reminder, on Day 7 we addressed some of the specific nutritional issues excessive drinking can lead to, such as serotonin and dopamine deficiencies and sugar addiction. We are not going to repeat most of that information today, so we recommend you take a few minutes to review it.
Not only is the topic of nutrition complex, in recent years it also has become much more specific to each individual. What might work great for one person might not for another, in part because of food sensitivities, intolerances, and allergies. Therefore, on the companion website we have included some of our favorite books, experts, and resources regarding diet and nutrition; but we recommend you explore these in greater depth only after you complete The 30-Day Sobriety Solution.
The effects of a healthy diet that is right for your body can be life changing. You will lose weight, have more energy, experience less stress, feel happier, get sick less frequently, and your cravings for foods high in fat, salt, and sugar will diminish greatly. And if you combine this with a healthy exercise routine, you will get stronger faster.
We have used the word diet a lot today, so we want to be clear. Diet essentially just means the food you put in your body, not a weight-loss regimen. So when we say diet, we mean what you choose to eat and drink as part of your normal routine or lifestyle. The best diet is one you can sustain for the rest of your life.
Weight is usually gained and lost slowly. If you are overweight, most likely it came from putting on one pound a month. Gaining one pound a month reflects a surplus of roughly 100 calories a day, so if you give up a few candy bars, sugary sodas, or bags of chips each week, you could lose one pound a month or twelve pounds in a year. Just as we have said in the other solutions, a long-term strategy for your nutrition is far more effective than a short-term extreme diet.
### Key Nutrients for a Healthy Body
To eat healthy, you should try to get the right balance of water, protein, carbohydrates, essential fats, vitamins, minerals, and phytonutrients into your diet. On the companion website we provide more information about each of these, but there is one that is so critical, and so relevant to you as a problem drinker, it is essential we address it first—water.
Water is an essential nutrient, and the basis for all life, including your body. Your muscles are 75 percent water, your blood is 82 percent water, your lungs are 90 percent water, your bones are 25 percent water, and your brain is 76 percent water.
Most of us go through life dehydrated. In Your Body's Many Cries for Water, Dr. F. Batmanghelidj writes, "We have forgotten how to respond to our numerous thirst signals. But if, instead of taking painkillers and medication, we just drank lots of ordinary tap water, we would probably find that not only the pain but also the condition would go away forever."
This is even more relevant to heavy drinkers than to other people, because drinkers often live in a dehydrated state. Don't wait to drink water until you are thirsty or you are already dehydrated. The general rule of thumb is to drink one ounce of water for every two pounds of body weight every day (one-third liter of water for every 10 kilograms). So, if you weigh 200 pounds, you should drink one hundred ounces of water each day. That's roughly twelve 8-ounce glasses of water a day (or if you weigh 90 kilograms that would be just under three liters of water a day). If you're 140 pounds, that's roughly nine 8-ounce glasses of water every day. Also, you need to add another six to eight ounces of water for every fifteen minutes you work out. And please note that caffeinated drinks, sodas, and alcoholic beverages do not count as water.
For most people it takes some time to get used to drinking this much water, but we find one effective method is to start the day with two large glasses of water, especially since your body becomes dehydrated throughout the night. Another rule of thumb that's even easier to follow is always drink eight ounces of water for every two waking hours. Even if you weigh over 150 pounds, this will end up being a little below what is recommended, but it is very likely a significant improvement to what you are doing now.
Your first action step for today—assuming you don't drink this much water already—is to start doing so right now. One expert we consulted with also recommends that you drink alkaline water, which can be purchased at various health food stores, or start your day by drinking a warm cup of water with freshly squeezed lemon juice—both of which can help you flush out accumulated toxins.
### Hardwired for Fats, Sugars, and Salts
Just as it is important to know what nutrients your body needs to be healthy, it is equally important to know what foods you should avoid. In general these include processed foods containing fat, sugar, and salt. It can be challenging at first to limit these, because not only does consuming them trigger a release of opioids and dopamine (two chemicals in the brain that produce pleasure), humans are also genetically wired to prefer calorie-dense foods. And the most calorie-dense food you can find is fat, which has significantly more calories per gram than any other food. In addition, many food manufacturers produce and market foods high in sugar, fat, and salt (in part because they know how addictive they are), which has helped result in the World Health Organization estimating that more than 1.4 billion people in the world are overweight.
However, not all fat, sugar, and salt are bad. You need salt and essential fats, but not at the level that most industrialized countries consume. If you can eliminate other forms of sugar from your diet, such as candy, sweets, refined sugar found in white pasta, and anything with high-fructose corn syrup, you will dramatically curb other food cravings and also curb alcohol cravings. As we recommended in Day 7, you can get your sugar "fix" instead from eating fruit or drinking fruit smoothies.
### Strategies for Healthy Eating
Within two months of starting The 30-Day Sobriety Solution, I was closer to my family, performing better at work, coping with stress much more easily, had lost thirty pounds, was training for a marathon, and my social life actually improved.
—ROBERT
30-Day Graduate from Vienna, Austria
There are several strategies that have worked well for us and our clients and allow you to still be healthy while occasionally enjoying some "bad" food. For example, Bill Phillips's bestselling programs recommend you eat healthy six days a week, and eat whatever you want one day a week. This works well because each week you can plan out which day fits your schedule best. So if you have a party or work event on a particular day, you can make that your free day and eat whatever you want. What you often find is that the free day is enjoyable and allows you to eat some of your favorite unhealthy foods, but by the end of the day you don't feel all that great and are ready to return to eating healthy the following morning.
Tom Venuto recommends another approach we like, which is to eat healthy 90 percent of the time. The other 10 percent, you can eat whatever you want. This approach works well when you know you have several things going on that week and want to have some freedom at those events. However, when you use either of these two approaches, it is difficult to turn off the cravings. When you eat the fatty, sugary, and salty foods, you reactivate your cravings for more. If you take a "free" meal or eat whatever you want at lunch, it can be very challenging to go back to eating healthy again for dinner. So if you do use this approach, we find it works best if you plan most of your free meals for the end of your day.
Ultimately, it may be better to cut out processed sugar completely. Research shows that for most people, after a week of no sugar the desire for it basically disappears. Jack discovered that when he cut all processed sugar out of his diet, after a week he could watch others eating ice cream and chocolate cake, with no desire for it at all. If he ever does order dessert at a restaurant, he just orders a bowl of fresh seasonal berries. But if you feel this is too challenging, at least now, just start one of these two options so that you still limit the amount of sugar you consume.
With either the free day or 90 percent plan, you want to free yourself from any guilt around these meals or days. The idea behind a free day or meal is that you grant yourself permission to eat what you want. If you end up regretting or feeling guilty about it, you defeat the purpose.
Another successful strategy is replacing meals or snacks with a healthy smoothie. As we mentioned in Day 7, you should not skip meals (eat at least three a day), always eat breakfast, eat at least every five hours, and ideally get your vitamins and nutrients from food and your sugar "fix" from fruit. A smoothie, often referred to as a protein drink, can accomplish all of this. Remember to check out the alcohol detox smoothie recipe we posted on the companion website for Day 7.
You can buy different smoothie/protein mixes and powders, and mix in fresh or frozen fruits or vegetables. One expert we consulted recommended using whole fruit (not fruit juice—which contains too high a concentration of sugar) or adding chia seeds, as both of these increase the amount of fiber in the smoothie, which reduces sugar shock (large fluctuations of blood sugar levels in a short amount of time) and therefore also reduces the likelihood of alcohol cravings.
### What Works for One Might Not for Another . . .
According to a study by the US Centers for Disease Control and Prevention (CDC), food allergies among children increased approximately 50 percent between 1997 and 2011. Food allergies now affect fifteen million Americans, and all indications point to this trend continuing. Food allergies, sensitivities, and intolerances force you to change how you approach your diet, so it is absolutely critical you learn what works best for you. Dave's daughters, for instance, have had significant food allergies. When they were eight and five, they already had a long list of health issues. They would get sick constantly and were on antibiotics almost monthly. They took prescription medication for severe reflux, and had to increase the dosage many times. Finally, a new food intolerance blood test became available, which revealed that both daughters had a severe gluten intolerance, and one also had a severe soy intolerance. By removing these foods from their diet, their health issues disappeared. They were off medication within a couple of weeks and have been healthy ever since.
After seeing the profound impact of changing their children's diets, Dave and his wife, Anya, also took the blood test and discovered that they, too, were regularly eating foods to which they had moderate to severe intolerances. Anya was having severe migraines regularly and Dave was occasionally experiencing stomach pain and digestion issues. Once they removed these foods from their diet their health dramatically improved.
In these cases, the health implications of food sensitivities and intolerances are obvious, but since the body can build up some resistance to foods you eat regularly, other types of allergies might not be as apparent. The continued exposure to foods that cause allergies, sensitivities, or intolerances can worsen as you get older, and result in a wide variety of health issues, some that might not seem food-related at all. And one of the most aggravating consequences can be an inability to lose weight despite following a healthy nutrition plan and exercise routine.
Lyn-Genet Recitas's bestselling book The Plan: Eliminate the Surprising "Healthy" Foods That Are Making You Fat—and Lose Weight Fast has brought mainstream attention to this problem. The core premise of the book is this: "Foods that are revered by traditional weight loss programs, such as turkey, eggs, cauliflower, beans, and tomatoes, may be healthy in a vacuum, but when combined with each person's unique chemistry, they can cause a toxic reaction that triggers weight gain, premature aging, inflammation, and a host of health problems including constipation, migraines, joint pain, and depression."
Because this topic is so important to your individual health, we couldn't overlook it; however, there is a lot of confusion and misinformation in the world regarding food allergies, sensitivities, and intolerances, including what the best approach is for diagnosing them, and determining their overall impact on your health. Therefore, we highly recommend you talk to a qualified doctor, nutritionist, or health care professional if you believe this is something affecting you.
### Day 25 Action Steps
I think, at a certain point, it's better for women not to have any alcohol, because it can make your face, breasts, and midsection get very bloated.
—SHARON STONE
Actor
By cutting back or quitting drinking you have taken the most important step to reclaiming your health, and today's focus is all about how to accelerate that process.
If you feel overwhelmed by this topic, please feel free to come back to it at a later date. The main goal of today was to introduce you to some basic nutritional concepts, share facts that remind you of the ultimate "cost" to your health if you return to excessive drinking, and provide you with resources here and on the companion website, to which you can refer when ready.
• Drink lots of water. Drink one ounce of water for every two pounds of weight, and more if you exercise. Or drink at least eight ounces of water every two hours you are awake. This change alone can have a profound impact on your health and energy.
• Keep a food journal. Write down everything you eat and drink over a twenty-four-hour period (you can even make a photo collage or use a smartphone app to track it). This can be done after you finish the program, and your goal is simple—awareness. Many eating habits are unconscious, and until you consciously decide to record what you eat and drink, what and how much you think you eat and drink often differs from the truth.
• Make small changes to your diet. Every week add a new positive change to your diet. The first one can be to drink the proper amount of water. In another week add a new one—such as cutting back on a specific sugary or fatty treat you enjoy, not taking second servings at dinner, or eating fast food one less time a week. To make sure you remember to do this, stop now and put reminders on your calendar.
On today's companion website, you will find the list of the top recovery foods, the key nutrients your body needs to thrive physically, a list of foods that promote good moods, and a list of foods that promote bad moods. You'll also find a list of some of our favorite books, experts, and resources on diet, nutrition, food allergies, and detoxes and cleanses. Be sure to visit <http://Day25.Solutions>.
## Day 26
## The Positive Addiction Solution
## Adding Fun, Healthy, and Confidence-Building Activities to Your Life
It is the spinning-free, mentally relaxed Positive Addiction state that provides an extremely optimal condition for our brains to grow.
—WILLIAM GLASSER, MD (1925–2013)
If you had ten to twenty extra hours a week, what would you do with that time? To thrive in sobriety, not only do you need to answer this question, but also how you answer it will directly impact the quality of your life, and likely determine whether or not you return to your previous level of drinking.
Cutting back or quitting drinking will give you extra time, even if you previously drank while multitasking—taking care of your kids, watching TV, paying bills, cleaning your house, or networking with peers. The reality is that your drinking affected your decision making, and as you change your drinking, your energy level, interests, and daily decisions will also change.
The Positive Addiction Solution prepares you for your new life of thriving in sobriety, and tells you how to avoid a major sobriety killer—boredom. By learning the "what and why" of exercise, you will discover how you can get more fit and actually enjoy it. You will also learn how an apparent "weakness" can actually lead you to being stronger and happier, as well as help you discover and embrace new fun activities in your new life.
### The Top Five Factors Affecting Your Health
The way you think, the way you behave, the way you eat, can influence your life by thirty to fifty years.
—DEEPAK CHOPRA
Dr. Deepak Chopra has stated that the top five influencing factors for health are "food, water, breathing, exercise, and sleep." In yesterday's solution, we discussed the importance of feeding your body the right foods at the right times, and in the right quantities, as well as how critical drinking enough water is to maintaining your optimum health. Two days ago, we discussed the importance of proper breathing, and you learned to breathe as an effective technique for ridding your body of toxins, reducing stress, and feeling more energized. And today we will address exercise and sleep.
Imagine how much your overall energy, self-confidence, and physical health will be transformed by embracing the top five influencing factors for your health. Even if you only start with small changes in each of these areas and combine that with cutting back or quitting drinking, you will be able to experience remarkable positive results in a relatively short amount of time.
### The Magic Pill
What if there was a pill that would keep you fit and lean as you aged, while protecting your heart and bones? What if it was as good for your brain as for your body, if it made you stronger, more confident, and less susceptible to depression? What if it improved your sleep, mood, and memory and reduced your risk of cancer, all while adding life to your years and years to your life? A great number of studies have found that exercise can provide all these benefits and more, even for people who begin late in life. We are learning that much of the physical decline that older people suffer stems not from age but from simple disuse.
—JOHN ROBBINS
Author of Diet for a New America: How Your Food Choices Affect Your Health, Your Happiness, and the Future of Life on Earth
If you want to change how you feel, get moving. This is true for everyone, but it is even more so for problem drinkers. Not only do you get all the benefits that John Robbins mentions, but you are also less likely to drink again. The Research Society on Alcoholism recently published a study that found that "alcohol consumption and loss of control over drinking are greater among individuals who do not exercise regularly."
We see this as common sense. After exercising, do you usually want to drink alcohol or eat fatty or sugary foods? As long as the exercise is fairly strenuous, the answer is most likely no. If you were feeling "down" before you exercised, you usually find that your mood has improved. If you get your body excited, your mind will follow. We encourage you to test this the next time you are feeling unhappy—get up and do some jumping jacks or push-ups, take a short jog, power walk around your neighborhood, or do some deep breathing exercises combined with yoga poses. Then notice how you feel afterward.
### The Science of Exercise
A strong body makes the mind strong.
—THOMAS JEFFERSON (1743–1826)
Third president of the United States
Shawn Achor spent over a decade at Harvard University researching and lecturing on what makes people happy, and he published his findings in The Happiness Advantage: The Seven Principles of Positive Psychology That Fuel Success and Performance at Work. His research included a study of three groups of patients who treated their depression with medication, exercise, or a combination of the two. Over the course of six months, 38 percent of those who only used medication slipped back into depression and 31 percent who used a combination of medication and exercise relapsed. However, the relapse rate of the test group that only exercised was a scant 9 percent, once again confirming that exercise really is the "magic pill."
Like meditation, exercise has also been proven to increase the production of serotonin, addressing an important deficit many people in early sobriety experience. Furthermore, exercise stimulates the release of endorphins within thirty minutes from the start of activity, which results in minimizing pain and discomfort and creating feelings of euphoria. When you consider this along with some of the other obvious benefits, such as helping you relax and sleep—and improving your body image and self-confidence—exercise is a perfect example of a positive addiction.
### Dave's New Habits
Dave realized that embracing new fun and healthy activities was a critical component to thriving in sobriety:
Growing up, I was extremely active, always learning and playing a wide range of sports; however, once I discovered drinking in college, I found myself watching more sports, and participating less and less. When I got sober I realized two important things: My apparent "love" for watching sports was much more about using it as an excuse to drink. And I mostly avoided playing sports, and learning new ones, because they often conflicted with my desire to drink.
Once I was free from alcohol, embracing new physical activities gave me a lot of enjoyment. The first thing I did was start coaching my oldest daughter's basketball team, which not only helped me become more engaged in my children's lives but also helped me become more active.
Soon after, I started playing racquetball at lunch. Our company had two racquetball courts, but finding other players at my skill level was challenging. I ended up starting a racquetball ladder, and more than fifty-five people signed up. Over the next year and a half, I met lots of new coworkers through the ladder and advanced my game. I also played in leagues at a local recreation center, took lessons, and played in a variety of tournaments. One simple idea dramatically improved my physical fitness and created more positive relationships at work and in my personal life.
Although racquetball was enjoyable, I realized that I love variety, and since I was now coaching both of my daughters' basketball teams, I also wanted to play. However, I had never played organized basketball and was not very good, despite having learned a lot about technique and drills from coaching. I checked with the local recreation center and found out that I could start a team in the league, so I reached out to some coworkers. A few were interested, but I still needed four more players. I also belonged to 24 Hour Fitness, and decided to play in the pickup games to see if I could find anyone there. In order to do this, I had to overcome some fear because I wasn't nearly as skilled as everyone else on the court. Even though I wasn't very good, I ended up meeting some great people (and some really good players) who were interested in joining my team because I was organizing the league. That filled the last two spots, and helped to make our team somewhat competitive.
This experience taught me some critical lessons: First, if you are willing to organize, people will follow (even if they have a lot more experience and skill than you). Second, the lessons I learned in the league helped me become a far better coach for my daughters. And last, my family came to watch some of my games, just as they'd watched some of the racquetball tournaments, and this taught my daughters that sports activities can be great at any age or skill level.
I have continued to exercise in a variety of ways, practicing yoga, taking martial arts classes, skiing (and teaching my daughters), joining five different boot camp programs over a three-year period, hiking, completing obstacle races (like the Tough Mudder, a ten-to-twelve-mile obstacle course designed to test physical strength), and bicycling with my wife and kids.
The reason I share this with you is because I had always wanted to do these things, but I had unconsciously made my drinking a higher priority. However, once I began all these physical activities, my health and energy improved dramatically. It also increased my self-confidence, strengthened my relationship with my wife and kids, and helped me create new healthy relationships.
### Exercising Is Easy
The market is inundated with bestselling books, blogs, and programs on fitness and exercise that all claim to have the answer you have been searching for—whether you want to lose weight, get six-pack abs, drop two dress sizes, or just have more energy. As great as many of them are, they can sometimes lead you to believe that implementing an exercise program must be complicated or difficult. And with so many options, it can be overwhelming, resulting in no action being taken at all.
The truth is that exercising is easy, and all that matters is that you start. We both have done numerous different workouts and fitness programs and have read hundreds of books and articles, and most of them have the exact same common goals: increase your breathing and heart rate (endurance), build muscle, increase flexibility, and improve your balance and core strength.
This doesn't mean you shouldn't try different approaches. We certainly have—and not because we are searching for "the answer," but because we appreciate variety and also because our fitness goals change over time. But some of the healthiest, strongest, most vigorous people we know have been doing the exact same exercises for decades. They know what works, have an established routine, and find peace of mind by not mixing it up. Others, like us, get bored with the same routine and need to try new things to stay engaged. Either approach can be equally effective.
If you have always embraced a healthy exercise routine and feel you are knowledgeable on the topic, feel free to skim through the next few sections.
### Getting Started
Physical fitness is not only one of the most important keys to a healthy body, it is the basis of dynamic and creative intellectual activity.
—JOHN F. KENNEDY (1917–1963)
Thirty-fifth president of the United States
Here are a few simple recommendations to help you get started. First, if you haven't been working out, get approval from your doctor or health care professional. Going from a sedentary lifestyle to exercising can be dangerous if you have certain existing health conditions, especially heart disease.
Second, if you are just beginning, start small. This advice should be familiar by now. If you push yourself too hard right away, the initial soreness you will likely experience in the first week or two may deter you from continuing. However, if you do experience intense soreness, which can be very common when doing new exercises that are engaging new muscles, it only lasts one to two weeks at the most.
Third, you don't need a lot of time to dramatically improve your fitness. A lot of research has been done in the last few years on high-intensity interval training (HIIT) and high-intensity circuit training (HICT). This research has proven that as little as a seven-minute workout using just your body weight is enough to provide many of the fitness benefits that prolonged endurance training provides, as well as build muscle. One of these workouts was published recently in the New York Times Magazine, which we provide a link to on the companion website.
Last, don't be afraid to start by taking brisk walks outside. Not only is this good exercise, according to Richard Ryan, professor of psychology, psychiatry, and education at the University of Rochester, but research demonstrates that "being outside in nature for just twenty minutes in a day was enough to significantly boost vitality levels." By exercising outdoors in nature, you can noticeably shift your state of mind.
There are two core components of a balanced fitness plan that will provide you the greatest health benefits: aerobic training and strength training. Although flexibility and balance can be extremely beneficial to your overall health, aerobic and strength training often incorporate exercises that improve flexibility and balance as well.
### Aerobic Training
Ninety percent of the stimulation and nutrition to the brain is generated by the movement of the spine.
—DR. ROGER SPERRY (1913–1994)
Nobel Prize–winning brain scientist
Aerobic exercise is simply getting your heart rate up and maintaining it, but at a level of intensity where your breathing is still relatively comfortable. The benefits of aerobic exercise include strengthening your heart and lungs, reducing stress, burning calories, gaining energy, and improving your thinking. This can include just about any type of exercise, whether it is running, power walking, weight lifting, or even yoga, as long as you are exercising at a pace that keeps your heart rate elevated. However, if your workout becomes too intense—meaning when you talk out loud you can't finish a sentence without gasping for air—you are exercising anaerobically. In this state you often become uncomfortable. You might want to consider purchasing a heart rate monitor when starting a new exercise plan, as it will help you to know your limits so you can "train, not strain" your heart. Plus, you can use it to measure your progress. Just visit your local sporting goods store or Amazon.com.
Although there is nothing wrong with anaerobic exercise, and inevitably you will transition between both modes at times during your exercising, anaerobic exercise is generally only important for those who compete. If you are only concerned with the health benefits of exercise, then you should focus on exercising aerobically, which is great news because this is much easier. The main reason you might want to exercise anaerobically, or simply be forced to, is if you are doing activities or sports such as basketball, football, soccer, tennis, or swimming that require intense bursts of energy.
### Strength Training
After the age of thirty-five, you lose roughly a half pound of muscle each year. That means if you don't do any strength training, every year you will lose muscle and gain weight in the form of fat unless you consume fewer calories. In addition, even if you maintain your weight, you will basically be replacing muscle with fat. And as this happens, you will look bigger. Over the course of a year, the impact is minimal; however, the cumulative impact over years or decades can be enormous, which is why strength training should be an integral part of your exercise routine.
There are countless ways to build muscle, so we will only touch on a few key concepts. However, there are additional resources on the companion website, including some of our favorite strength training programs. Strength training is not just for men. Women also greatly benefit from integrating this into their exercise routine because muscle is 18 percent more dense than fat and burns more calories at a resting rate than fat. There is little risk of women becoming overly muscular—this typically only happens if you are specifically training for that goal.
Even if you do strength training just once a week, you can still see results. One of the most common ways to build muscle is to work with weights. One key to working with weights is to pay attention to when you reach "failure." This is the point where your arms or legs start to shake and you can barely bring the weight back up. Reaching failure is a significant way to accelerate muscle growth. Just be careful that you don't switch to poor form as you do your last few repetitions, as that is how injuries happen. Working with a trainer and having a spotter are highly recommended for when you first begin in order to learn correct form.
Although using weights is a very common method to build muscle, there is a growing trend that uses just your body weight for resistance. These workouts often include variations of push-ups, pull-ups, lunges, squats, and various abdominal exercises to build core strength. The great thing about these types of workouts is that they don't require special equipment and are usually done at a pace that gives you an aerobic workout as well.
Last, we have primarily focused on exercise outside of specific sports and activities. By integrating various active sports and activities in your life you can easily, and often more enjoyably, leverage the benefits of exercise. Depending on the sport, likely results include building specific muscle groups, improving balance and flexibility, and getting a mixture of aerobic and anaerobic exercise.
### Ten Tips to Start Exercising and Never Stop
For me, the temptation to drink often surfaces with boredom, long business trips, and when working on really large projects, so now I know when and how to prepare.
—JAMES
30-Day Graduate from Istanbul, Turkey
When is the last time you worked out and regretted it? What is wonderful about exercise is that it is one of the few things you can do in life that you won't regret. The only possible exception to this is if you injure yourself by pushing too hard. Here are some tips to help make integrating exercise in your life easy:
• Work out in the morning. Your willpower diminishes as the day goes on, so it is best to start your day with the things you are most likely to skip. Also, working out in the morning carries over to the rest of your day. You more often feel naturally motivated to get important tasks done, and your desire to eat poorly is lessened.
• Reward yourself. Treat yourself to something special for working out that day, such as fifteen minutes of watching funny videos on YouTube, or give yourself a bigger reward for working out a certain number of days in the month, such as scheduling a massage or buying yourself a new piece of clothing.
• Use accountability. Find a workout partner. Or use one of the many free apps available for your iPhone or Android that tracks and shares your workout with friends. To increase your accountability, make an agreement that if you don't follow through with your workout, you will pay your workout partner some amount of money (enough that it will bother you), or some other consequence that you prefer to avoid.
• Stop setting goals. This might sound counterintuitive, but it can be easy to get discouraged if you have a lot of weight goals and other benchmarks with which you measure your success. If you do set a goal, make it easy to accomplish, such as just exercising for twenty minutes four times a week. Feel great about showing up, and focus on effort, not results.
• Join a team or group. Find a sport or activity that requires exercise and join a team or group, or if necessary, start your own team.
• Combine exercise with errands or commuting. If you can, walk or ride your bike when you run errands, commute to work, or go to lunch. Find ways to exercise as you go about your day, like taking the stairs instead of the elevator, or parking in the furthest spot in the parking lot. Jack has a rule that he always walks up two flights of stairs or down three instead of taking the elevator.
• Enter a race or other athletic competition. You are more likely to follow through when you know you have an event to prepare for.
• Make a playlist of your favorite music and listen to it while working out. Not only does music release endorphins that increase tolerance for pain, it can also evoke a positive emotional response, making your workout more enjoyable. Jack has several playlists of upbeat music on his iPod, including a set of tracks of Marine Corps cadence tapes from drill instructors at Parris Island that he uses to keep him motivated and on a steady pace when he is running.
• Don't take more than one day off. Better yet, don't take any days off from exercise. The more you integrate exercise into your daily life, the easier it is to continue.
• Put your gym bag or workout clothes on the floor near your bedroom door, in your car, or somewhere else where you can't miss them. When you see your bag or clothes, or better yet have to step over them in the morning, it will remind you to work out.
### But I Need a Drink to Get a Good Night's Sleep
If food, water, breathing, exercise, and sleep are the five most important things for your health as Dr. Deepak Chopra claims, then imagine how much more important these are to the problem drinker. Excessive drinking poisons your body, increases your cravings for unhealthy foods, dehydrates you, can reduce your capacity to absorb nutrients, is detrimental to exercise, and, based on a review of twenty-seven studies, is disruptive to your sleep.
According to the director of the Edinburgh Sleep Centre, "Alcohol on the whole is not useful for improving a whole night's sleep. Sleep may be deeper to start with, but then becomes disrupted. Additionally, that deeper sleep will probably promote snoring and poorer breathing. So, one shouldn't expect better sleep with alcohol." Researchers also found that alcohol decreases sleep duration and increases wakefulness, especially for women.
We all need regular sleep. Even though everyone is a bit different, the average person needs between 6.5 to 7.5 hours. (It is estimated that only about 3 to 5 percent of the population needs less than 6.5 hours of sleep to function normally.) In an interview, Daniel Kripke, an acclaimed researcher on sleep, explains, "People who sleep between six and a half hours and seven and a half hours a night live the longest, are happier, and most productive." Sleeping either less or more than this range strongly correlates to a significant decline in your productivity and ability to focus, in addition to being more irritable and having impaired judgment—all of which can negatively affect your overall happiness.
Studies have also validated that exercise can significantly improve sleep, including sleep duration and sleep quality, even in those that have struggled with insomnia. Sleep is also critical for rejuvenation and body repair from intense exercise. However, exercise does not necessarily result in sleep improvement right away. Rather, it can take up to two months before this benefit is experienced. Although exercise improves sleep, you should not exercise within a few hours of your bedtime.
Along with exercise, there are a few other things you can do to improve your sleep. First, take naps between twenty and forty minutes—anything over forty minutes may cause you to go into REM sleep, which will make you more tired when you wake. John D. Rockefeller, Winston Churchill, and Albert Einstein are just three examples of well-known people who were known to take short naps.
Second, disengage from your day the last twenty minutes of the night, either by reading (or listening to) fiction, meditating, or even practicing gratitude. If you are still having issues with sleep, try to maintain a regular schedule for going to bed and waking, keep your bedroom at a cool temperature, stay away from caffeine in the evening, and use the bed only for sleeping, sex, and possibly reading.
Drinking alcohol negatively affects at least four of the five healthiest things you can do for your body: food, water, exercise, and sleep. So just removing alcohol from your life can dramatically improve your health. Now imagine if you start making other small changes in these areas, such as eating a little healthier, drinking more water, exercising for five minutes a day, focusing on your breathing, and sleeping at least six and a half hours a night. Your body's capacity to heal itself, as well as the added benefits to your overall happiness, productivity, and vitality that come with improvements in these areas, will make thriving in sobriety a reality.
Your first action step for today is to start exercising (if you are not already). This can be as simple as taking a brisk seven-minute walk or a five-minute jog. The key is to get started right away by building your exercise "muscle." Seriously, you might even want to put this book down and go for a seven-minute walk right now.
### The Positive Addict
On Day 3 in the Pendulum Solution, we introduced you to the idea of positive addiction: If you become positively addicted to things that have a beneficial effect on your mind or body, such as meditating or running, you will live a longer, happier, and more fulfilling life.
If you have struggled with addiction in the past, you have more options and more advantages than your nonaddictive counterparts, as long as you are able to channel that all-or-nothing behavior toward positive addictions instead of negative addictions, like drinking. And this advantage, when your energy is properly focused, will actually make you stronger and happier than others who haven't had the same challenges with addiction. We are not saying that you should simply replace your drinking with another activity that you become compulsive and obsessed with, rather that you leverage the inherent positive traits that addictive personalities have to excel at a healthy activity, while still embracing variety and balance.
When you become positively addicted in sobriety, you often experience exciting and surprising success, which, in turn, is very fulfilling both personally and professionally. This phenomenon feeds into the "Why is your drinking your greatest gift?" concept from Day 3. When you remove the negative addiction and replace it with its opposite, positive addiction, you are able to finally experience great success and pleasure in your life.
### Laughing Your Way to Sobriety
Laughter is the tonic, the relief, the surcease for pain.
—CHARLIE CHAPLIN (1889–1977)
Comic actor-director
Did you know that children laugh up to three hundred times in a single day, but adults laugh only roughly fifteen times a day? A new exercise routine, which set out to rectify this discrepancy, is gaining worldwide recognition and acceptance and is now in seventy-two countries and in more than six thousand clubs. Deemed a "complete well-being workout," Laughter Yoga combines unconditional laughter with yogic breathing, and the driving reason behind its success is simple—laughing is loaded with positive benefits.
It is estimated that 60 to 90 percent of all doctor visits are stress-related. Numerous studies have demonstrated that laughter has physical benefits on the body, such as lowering blood pressure, improving blood circulation, and helping boost the immune system. And one of laughter's biggest benefits is stress reduction. In a study on heart disease, cardiologist Michael Miller, director of the Center for Preventive Cardiology at the University of Maryland Medical Center, says, "The old saying that 'laughter is the best medicine' definitely appears to be true when it comes to protecting your heart health."
And the emotional benefits are just as significant. Have you ever been in a heated argument, and then someone says something funny (usually accidentally), or something happens, like one of you farts, and instantly you both start laughing? What happened to the negative emotions that you were experiencing? Most likely they vanished or significantly diminished. In fact, it is often hard to return to that same level of emotional intensity. Laughter releases "feel-good" hormones like dopamine and endorphins, which relieve physical tension and emotional stress, and help to rejuvenate your body and mind. And there is nothing quite like connecting a group of people through sharing a good laugh together, as long as the source of the humor does not belittle or hurt another person or group.
As you explore new activities, look for some that make you laugh. For example, we have both taken improvisation workshops. Not only did we laugh a lot during the workshops, but they also helped us bring more humor and lightheartedness to our personal and professional lives. Jack also listens only to the comedy channels on SiriusXM radio when he is driving.
### Adding Variety to Your Sobriety
The 30-Day Sobriety Solution attracts a lot of high-functioning problem drinkers—people who have had successful careers, and from the outside, you would not expect that they have a drinking problem. When anyone gets sober, but especially when high-functioning problem drinkers do, they tend to replace the time they spent drinking with work, essentially replacing one compulsive behavior with another one. This might work in the short term, but it doesn't in the long term. Eventually an out-of-balance life leads back to drinking.
Lasting sobriety, and thriving in sobriety, can only be attained and sustained by balancing your life with some fun activities and enjoyable hobbies—maybe things from the past that you stopped doing, or new things you have always wanted to do. We know you might be thinking, I don't have time, and our response is always the same: if you don't have time, then how did you have time to drink?
Contrary to what you might think, engaging in activities that are fun not only make you a better spouse, friend, and parent, as well as healthier and happier, they also make you a better and more productive person at work.
Your second action step for today is to go through the list of "101 New Activities for Your New Life of Thriving in Sobriety" and see what interests you. You will notice that some of these are things you might do just once, or once in a while, where others might become daily or weekly activities. As you read the list, trust your intuition. Don't worry about the "how" right now, just your desire or interest in doing them. Also, it is very likely you already have a good idea of the activities you have enjoyed in the past and stopped doing, and the "one of these days" or "someday, I'll" activities you have always wanted to start. Write all of these down, either in your journal or somewhere else you can easily review. If there are activities you think of that are not on the 101 New Activities list, write those down as well.
Once you have completed your list, pick one of the activities to do. Ideally, pick one that's easy to do, since starting small and building momentum is the most important thing; however, if there is another one you are really excited about, you can pick that one as well. If you are having a hard time deciding which activity to start with, consider the topics we discussed today. If it is an aerobic exercise, strength training, or it will make you laugh, then you will likely get doubly high value from doing that activity. You can even combine today's first action step of starting to exercise with this one. For example, if you have always wanted to learn a martial art, sign up for classes. Just remember, your goal is balance and variety. We wouldn't recommend you pick an activity, such as "learning the guitar," and become compulsive about practicing, playing, and studying.
Once you have picked your activity, do something right now to move it forward. Register for a class, call a friend for advice, do internet research, schedule times on your calendar, or actually begin the activity right now, if you can. The sooner you get started, the more likely you will follow through.
When Jack was participating in a twelve-week teleseminar called the "Happy, Healthy, Wealthy Game," he was asked what his major goal for the seminar was. Jack responded, "To really get in shape." At that point, the trainer said, "Great! Put down the phone and do ten push-ups right now." Jack said, "No, you don't understand. I mean, like I need to join a gym or get a personal trainer to work out with." The trainer responded, "No, I mean right now! Ten push-ups." This dialogue went back and forth about five times until Jack finally put down the phone and did ten push-ups, which resulted in him then setting and reaching his goal of eighty push-ups in a row. This is an illustration of what we mean by "Start now!"
The last part of this action step is to make sure you don't forget the rest of the activities on your list. We recommend that you create a recurring appointment in your online calendar for the first Saturday of every month, and in the details of that appointment include your list of activities. If you use a physical calendar, write down a monthly appointment to review your list. Then every month you will be reminded to look over your list of activities and see if there are any you want to start during the next month. Sometimes you might want to do a certain activity during a certain time of the year, like skiing or surfing, in which case you would make a separate calendar entry to remind you to do those activities. Regardless, creating and using a personal reminder system is key to your success, just like it is at your job. If you don't schedule the activities, the force of your old habits can take over. Adding new activities into your life takes conscious intention and effort.
The third action step for today is a powerful guided process called Rediscovering Your Joy, which you will find on the companion website, that takes you back through your life to explore and discover what brings you true happiness and fulfillment without alcohol. If you are having any challenges choosing activities, this process will help you get more clarity.
One 30-Day Graduate shared the value of:
One of the most powerful solutions while doing The 30-Day Sobriety Solution was the breakthrough experience I had with one of the guided meditations. This one in particular took me back to a time in my life where I could actually see the younger version of myself that was happy without drinking. This was a wake-up call—I remembered and saw that I had been sober and happy before in my life, so there was no reason I couldn't do it again. I even realized, and believed, that my sober future was full of new adventures and "highs," which finally got me excited about not drinking.
So get started now picking new activities!
### 101 New Activities for Your New Life of Thriving in Sobriety
After I got back to LA, I tried to keep all these things in mind. But what really helped me get back on track was starting to pursue a new dream. I had wanted to be a pilot all my life, and I decided to start taking flying lessons.
—PATRICK SWAYZE
1. Go for a brisk walk.
2. Listen to audiobooks or self-help content while driving.
3. Make a playlist of your favorite music and listen to it while exercising.
4. Practice smiling—yes, this is actually proven to make you feel better.
5. Learn to play a new instrument or practice the instrument you already know.
6. Read books, especially memoirs of people in recovery.
7. Take a dancing class (ballroom, hip-hop, swing, jazz, two-step, or salsa).
8. Take a day off from work and use it just for you. (Call in "well.")
9. Go for a hike and take a picnic.
10. Research cities and countries you want to travel to, and even plan your trip—whether you are serious about going or not.
11. Sign up for local-deal emails (such as Groupon and LivingSocial), and when you see an activity you have wanted to try, buy it.
12. Watch funny YouTube videos (such as funny animal videos or stand-up comics).
13. Take a class at a local college, recreation center, YMCA, and so on.
14. Get into nature, or even a local park, for twenty minutes a day.
15. Join a men's group or a women's group.
16. Take a yoga or Pilates class.
17. Spend more time with inspiring and positive family members and friends.
18. Go camping.
19. Reorganize a room in your house.
20. Visit the Meetup website (www.meetup.com) to find a group or get-together that interests you.
21. Paint a room or a wall.
22. Give a back rub or a massage.
23. Do a random act of kindness and don't wait for or expect a thank-you or any kind of recognition.
24. Start a home improvement project.
25. Join a creative writing group.
26. Cuddle your spouse or partner.
27. Take an improv or comedy workshop, or join an improv group.
28. Create a family website, online photo, or video album.
29. Join a local boot camp, CrossFit gym, or other specialized local gym.
30. Go to a play, a musical, an opera, or a concert.
31. Attend a sporting event.
32. Play a board game or card game, especially with loved ones and friends. (Amazon.com reviews can be a perfect resource to find the right game.)
33. Join a book club.
34. Reach out to a friend from your past with whom you want to reconnect.
35. Become a coach for your children's teams, or volunteer as a coach for any team.
36. Find and attend free speaking events in your area.
37. Join a local public speaking group (such as Toastmasters International).
38. Take singing lessons.
39. Have a party or get-together.
40. Go to AA meetings or other recovery program meetings such as Rational Recovery (RR), SMART Recovery, Women for Sobriety (WFS), or Harm Reduction Abstinence and Moderation Support (HAMS).
41. Join a cooking class or try cooking new recipes.
42. Make a vision board or vision book.
43. Write down all of your goals for every area of your life.
44. Start or join a mastermind group, a group of like-minded people who meet regularly to brainstorm ideas and tackle challenges together.
45. Watch funny TV shows or search the internet for the funniest or most inspiring movies and watch one per week.
46. Go to a comedy club or an improv club.
47. Do something artistic such as drawing, sculpting, or painting.
48. Pamper yourself at a spa, or simply schedule a massage.
49. Randomly stop what you are doing and do ten push-ups, jumping jacks, sit-ups, squats, or pull-ups.
50. Start a blog on a topic you are passionate about.
51. Start or join a team in a local recreation league.
52. Play fantasy sports or start a fantasy sports league.
53. Get involved with a nonprofit organization, whether it is through donating, volunteering, or even starting your own.
54. Give yourself permission to be silly sometimes.
55. Sign up for a seminar or a conference.
56. Go on a road trip.
57. Do something fun with your children, or just engage them by asking them interesting questions. (Search online for "great questions to engage your children in conversation.")
58. Take up sewing, knitting, or needlework.
59. Start martial arts training.
60. Research getting a pet, and get one if you are ready for the commitment.
61. Write a bucket list (everything you want to do before you die).
62. Go to church or engage in religious or spiritual events in your community.
63. Sell some of your stuff and use the money to start a new hobby.
64. Write down all your important dates, such as anniversaries and birthdays, and set up a system so that you never forget them.
65. Create a document with all of your favorite quotes and continue to update it.
66. Organize your life, office area, kitchen, basement, or garage.
67. Take up a new activity with your spouse, girlfriend/boyfriend, or friend.
68. Learn how to type.
69. Hire a life coach.
70. Try a new aerobic exercise class or do one at home.
71. Do a yard project, like planting flowers, making a rock garden, or building a patio.
72. Take up photography or videography.
73. Make jewelry.
74. Learn how to use a new software program on your computer.
75. Get a new degree or certification.
76. Visit a museum, art gallery, zoo, or botanical garden.
77. Donate blood.
78. Let someone go ahead of you in line who appears to be in a rush.
79. Take a friend out to lunch, dinner, or coffee.
80. Brainstorm rewards you can give yourself for sobriety milestones (30 days, 60 days, and so on).
81. Sign up for a 10K, marathon, triathlon, or some other physically challenging event.
82. Collect something, like baseball cards, basketball cards, coins, stuffed animals, records, or theater posters.
83. Go mountain biking or cycling.
84. Take a chance on a new hairstyle.
85. Clean and organize your car.
86. Teach someone something that you have learned.
87. Become a Boy Scout or Girl Scout leader or a Big Brother/Big Sister.
88. Write a thank-you letter or email to someone who has had a positive impact on your life, whether it is a family member, a friend, or even a teacher from high school.
89. Buy yourself a new wardrobe and/or workout clothes.
90. Plan a surprise night for a loved one.
91. Make a special meal for your family or friends.
92. Take up woodworking, cabinetmaking, or metalworking.
93. Learn a new language. (Check out Rosetta Stone or a Berlitz class.)
94. Find an inspiring place outside your house to read, meditate, study, or do work, such as a library, park, or nice coffee shop.
95. Write down what you would tell a tourist to see or do when visiting your city or state, and then do these things yourself.
96. Do The 30-Day Sobriety Solution again, or redo your favorite days and exercises.
97. Learn to play chess, bridge, Go, Scrabble, or backgammon.
98. Play an interactive video game where you actually exercise while playing, such as Wii Sports, which includes tennis, baseball, golf, bowling, and boxing.
99. Try out different restaurants around town.
100. Go to the beach, lake, or river.
101. Perform karaoke.
We act as though comfort and luxury were the chief requirements of life, when all that we need to make us happy is something to be enthusiastic about.
—ALBERT EINSTEIN
### The "Permission Slip" for Fun!
I had my first vacation without drinking, and it was thrilling. On occasion I found myself romanticizing drinking, but what surprised me was that the people who were drinking to excess, like I always did on vacation, seemed to be having fun, but often were annoying many of the people around them.
—SUSAN
30-Day Graduate from Philadelphia, Pennsylvania
Would you consider yourself a high-functioning alcoholic? Do you lead what appears to be a successful life, at least from the outside, but know that drinking is still an issue in your life? If you can relate to this, then we have one last suggestion for you today. And it's important!
Dave and our many graduates share how alcohol was the one, and often only, way they could let themselves "turn off" for the day. They would work hard all day or all week, and then drink to relax. This behavior became so ingrained over time that they didn't give themselves permission to stop "doing" until they started drinking. Drinking was essentially the trigger, or the "off switch," that allowed them to relax. This created a major challenge when they chose to become sober. They felt like they had to be productively working every waking hour because they had forgotten how to give themselves permission to stop and have fun without drinking.
If this sounds like you, it's critical that you consciously give yourself permission to start a new hobby or practice an existing one, join an activity like a book club or a cooking class, or just relax. To give yourself conscious permission, set a goal before the activity. For example, when Dave goes to a movie with friends, on a date with his wife, or does something fun with his kids, but feels a little stressed about his work or home responsibilities, he asks himself one simple question, What is the outcome I most want from this activity? What is my goal? and then answers it with a goal statement: My goal is to have a fun time with my friends, or My goal on this date is to be a supportive and loving husband, really listen to my wife, and have fun.
If you find that it's hard to relax without alcohol, this process can be very powerful. Once Dave integrated this into his life, he was finally able to let go of all his responsibilities and actually have fun and be present for the fun and relaxing activities—all because that was his goal. And Dave loves to accomplish his goals. Your fourth action step is to start asking yourself the question, "What is the outcome I want from this activity?" right before you do anything to relax and have fun.
### Day 26 Action Steps
Up until I found The 30-Day Sobriety Solution, it always seemed like to conquer alcohol I needed to have a boring and somewhat painful life that would not involve much with social activities. And that I probably would be committing myself to a life with not much fun. But The 30-Day Sobriety Solution got me excited about being sober.
—ANN
30-Day Graduate from New York City
Your state of mind is shaped by your habits. If you go through life doing the same things over and over again, you will continue to get the same results over and over. Today is about discovering and adding new positive habits or activities to your new life.
• Start exercising. If you are not already exercising, start today. It can be as simple as taking a brisk walk. Use the "Ten Tips to Start Exercising and Never Stop" to make certain this new habit sticks.
• Review the 101 new activities list. Write down all the activities that interest you, and add any others you can think of. Pick one and do something right now to get started. Take the rest of the list and set a monthly recurring appointment so you are consistently reminded to add new activities to your life. You may want to type up and print this list, or your edited version of it, and put it on your refrigerator or your wall.
• Listen to "Rediscovering Your Joy," the guided meditation on today's companion website. After reviewing the activities, listen to this guided process and write down any observations and breakthroughs you have right after completing it.
• Set relaxation and entertainment goals. Start consciously setting goals (in your mind) and ask yourself, "What is the outcome I want from this activity?" before doing any activity. Whether the goal is to have fun, let go of any stress, socialize, or just learn a new activity without judging yourself, this simple internal "permission slip" process works!
The companion website at <http://Day26.Solutions> includes some of our favorite exercise books and programs and the "Rediscovering Your Joy" guided process.
## Day 27
## The Love and Relationship Solution
## Surrounding Yourself with Positive and Supportive Relationships
Personal relationships are the fertile soil from which all advancement, all success, all achievement in real life grows.
—BEN STEIN
Writer and actor
Relationships are a requirement for everything in life because you cannot achieve anything without them. Think about all the relationships you have (including relatives, friends, clients, associates, coworkers, staff, retailers, customers, students, teachers, fans, colleagues, audience members, coaches, bosses, board members, or mentors) and how each of those relationships somehow helped you accomplish something in your life. The irony is that in the twilight years of your life, all those things you thought you always "wanted" won't matter very much. What will matter are the relationships themselves—especially with your family and closest friends.
To cut back or quit drinking, and to thrive in sobriety, you need to develop and maintain relationships with your friends and family that are positive and nurturing, or you will eventually return to drinking. The Love and Relationship Solution will show you how to heal any damaged relationships from the past, how to avoid another sobriety killer—loneliness—and finally, how to free yourself from what is potentially the most damaging relationship in your life—your relationship with alcohol.
### What Will Your Greatest Regrets Be?
We are happy when we have family, we are happy when we have friends, and almost all the other things we think make us happy are actually just ways of getting more family and friends.
—DANIEL GILBERT
Psychologist and author of Stumbling on Happiness
Bronnie Ware, a palliative care nurse, spent years caring for patients in the last twelve weeks of their lives and recorded their dying epiphanies. She recognized that there were five regrets that burdened most of her patients, two of which were directly related to relationships: not spending enough time with family, and letting important friendships fade away. "It all comes down to love and relationships in the end," she concluded.
Most of us can relate to these regrets. The "We really should get together" comments that never get followed up on, or the "I have a big work deadline" that keeps you from attending your kid's sporting event or family get-together. Think back to some of the most fulfilling, meaningful, and happy memories of your life. Were you alone? If not, who were you with? Most likely the memories that stand out include being with your family or your friends.
So what are friends? The best definition we've heard is that friends are the family you have chosen for yourself. And to thrive in sobriety, you must look carefully at the family you have chosen—the people you spend time with, and maybe more importantly, the people you decide not to spend time with.
### Drinking Is Just a Substitute for Love
If you have love in your life, it can make up for a great many things that you lack. If you don't have it, no matter what else is there, it isn't enough.
—ANN LANDERS (1918–2002)
Author of a syndicated advice column
For most people, problem drinking doesn't happen overnight. It starts off innocently enough with parties, hanging out with some close friends, and celebrating special events. Over time it consumes a little more of your free time, and without even realizing it, drinking becomes a central aspect of your decision making. It affects the activities you do and the places you go, but most importantly it affects the people you spend time with. What starts out as a social habit eventually leads to something you prefer to do in isolation—where drinking alone becomes a normal part of life. Some of you reading this may have reached this stage before starting The 30-Day Sobriety Solution, and some of you may not have.
But regardless of what stage you are at, one thing is true for all problem drinkers—excessive drinking, and all addiction, is at some level a substitute for love. As Deepak Chopra and David Simon explain, "Addictive behaviors and substances are poor substitutions for the love that flows in nourishing relationships. Learning to heal our core relationships and cultivate skills in conscious communication can provide the inner peace that eliminates the need for self-medication." Your excessive drinking is trying to fill a void in your life, and a big part of that void is love. And without love, you can become addicted to your guilt, shame, and suffering.
Not only is your drinking a substitute for love, it also acts as a substitute for any authentic and meaningful connection. The ultimate irony is that the family and friends who can help you the most, end up being the exact people you push away the most. And like we discussed on Day 4 in the Forgiveness Solution, you also end up not loving or even liking yourself, and in the end, alcohol becomes your best and only "friend."
Deep down we all want to be loved, and yet our deepest fear is that we won't be. Tony Robbins says that all our fears, regardless of our age, gender, culture, or country, can be reduced down to two primary fears: the fear of not being enough, and the fear of not being loved. And it is the feeling of not being enough and the pain of not being loved that ultimately leads many people to drink. But sadly, the effects of excessive drinking usually just make you even less capable and less lovable.
To avoid this downward spiral and create the sober life you want, it's critical that you learn how to heal, rebuild your broken relationships, and also create new healthy relationships.
Your first action step for today is to write in your journal about how drinking has negatively affected your relationships and/or led to isolation and loneliness. Have you pushed away family or friends because they don't drink or are critical of your drinking? Have you had outbursts of self-pity or anger that have pushed people out of your life, or maybe even cost you your job? Have you made or kept friends, or spent more time with certain family members, in part because they drink or were supportive of your drinking? Have you spent money on alcohol that required sacrifices elsewhere in the family budget? Have you done things when you were drunk, like getting caught having inappropriate sex with someone, that cost you an important relationship? Do your peers see you as a leader, someone deserving of a promotion, or as the "fun guy or gal" that is always willing to go out and party? Would they want you representing them at an important business meeting over dinner and drinks? Would you rather drink alone? When you drink, do you sometimes feel all alone, even when you are with others?
### Merging the Two Yous
It was to the point where I felt it was negatively affecting my relationships and getting in the way of things I wanted to accomplish in life. So I quit [drinking].
—TIM MCGRAW
Country music recording artist in recovery
There are essentially two people living inside of you. Think of it like a split personality, although these two identities are aware of each other, and each of them desperately wants to be expressed.
Who are these two identities? They are the "sober you," who knows alcohol is holding you back and wants more from life, and the "problem-drinker you," who is fully committed to your destructive relationship with alcohol. These two identities are at odds with each other, resulting in an internal struggle for control of your thoughts, beliefs, emotions, feelings, and actions. And because the rules and beliefs of each are so different, they are continuously sabotaging each other's efforts.
Before starting The 30-Day Sobriety Solution, the "sober you" was losing this battle most of the time, but was able to take control long enough to start the program. And since Day 1, you have been strengthening and empowering this part of yourself—learning and applying powerful tools and techniques for it to thrive—with the goal of eventually resolving this internal conflict, and consequently removing your overwhelming desire to drink. The challenge is that the "problem drinker you" will not go away quietly. It has been in control for a long time, and it's now scared. It can see things are changing, and eventually it will become desperate to regain control.
Let's revisit Hannah's story from Day 22. Hannah found herself struggling with two "people" battling inside of her: the person who depended on alcohol to live and cope, and the new person who was sober and happy. Hannah said, "I was scared about who I was without alcohol, and now that I really saw sobriety as a possibility, it became even more scary. I let that fear lead me back to where I felt safe—drinking."
As you finally get close to letting go of the "problem drinker you" for good, it is very common for that part of you to make one last stand. And it is in this moment that you will face what perhaps will be your greatest challenge, or your greatest desire to give in to your urge to drink. You can concede control back to the "problem drinker you" like Hannah did for almost a year and return to your old drinking habits, or you can essentially recruit the "problem drinker you" to the "sober you" team.
What do we mean by this? The key to resolving this once and for all is to acknowledge that this "problem drinker you" actually had a positive intention at first. It wasn't out to turn you into an alcoholic or lead you down the path of being an unhealthy problem drinker, it just wanted to feel good. And maybe it even wanted to help protect you from pain you were feeling over a past trauma. Regardless, this desire to feel good initially had an honorable intention, even though it didn't serve you in the long term. The goal is to retrain this part of you, or to essentially make you whole again. Your second action step for today is to listen to a guided meditation called the Merge Meditation, which will release you from this internal conflict by merging your two identities, finally freeing the "sober you" to forge ahead unburdened.
### Cleaning Up Your Messes
At the time, Lisa [ his wife] wasn't sure how to deal with what was happening to me, and to us. She was trying to change my behavior, without realizing that the only person who could change it was me. Negotiating and arguing and threatening don't work, though those are natural responses. But her actions had only been making things worse for both of us, to her frustration.
—PATRICK SWAYZE
Being human means making mistakes. And some of your greatest lessons come from some of your biggest mistakes. These mistakes often involve other people whom you care about and end up hurting. It might be related to your drinking, and it might not. But what it definitely relates to is your ability to thrive.
Leading up to today, you have learned an incredible amount—the importance of optimism and gratitude, your beliefs about emotional sobriety, and the power of your subconscious. Not only do all of these affect your life and the choices you make, but they are also directly affected by the "messes" in your past, especially the ones you haven't cleaned up. If you have hurt others or made mistakes and still feel guilty and ashamed about it, this affects your level of optimism, how you see yourself, your beliefs, your emotional sobriety, your feelings of gratitude, and ultimately your decision to drink or not.
Cleaning up your messes, or making amends, is critical to your happiness. Making amends has been popularized by Alcoholics Anonymous, but it is a practice that everyone who is happy and fulfilled in life embraces. You might notice this is very similar to something we asked you to do in Day 4; however, today we are asking you to explore all of your relationships and how they have been impacted by your drinking, which may lead to some new realizations.
The third action step for today is to look at your list from the first action step of relationships that drinking negatively affected and make note of any that need to be addressed. Who are the people you care about that you have hurt and whom you need to apologize to? And what do you feel embarrassed, guilty, or ashamed about that you need to forgive yourself for? You need to both clean up your relationship messes with others and forgive yourself for your past actions in order to get totally free.
It is important for you to put this list in a location that you can easily refer back to, and set a target date to clean it up by. It is not usually practical or wise to try to clear all of these up right away. You might be ready to address some now, and you might not be ready to address others for quite some time. Regardless, you want to be consciously aware of this list so if an unexpected opportunity presents itself, you can address it instead of bury it. On the companion website we provide you with a framework to help you complete your list, as well as some valuable conversation guidelines you can follow to help ensure the conversations go smoothly.
Because we know how difficult making amends can be, we highly recommend you pick the easiest relationship first and make a plan to clean it up now. Many of our clients have put this off again and again, until they finally do it and then realize that not only was it easier than they thought, but it turned out to be one of the most meaningful, fulfilling, and freeing experiences in their life.
### The Myth Behind Your Messes
My first reaction to it [a diagnosis of Parkinson's disease] was to start drinking heavily. I used to drink to party, but now I was drinking alone and . . . every day. Once I did that, it was then about a year of like a knife fight in a closet, where I just didn't have my tools to deal with it.
MICHAEL J. FOX
Actor and author of Lucky Man: A Memoir
One thing more than anything else holds people back from effectively cleaning up their messes—the fear of being vulnerable. We live in a world that celebrates strength, perseverance, knowledge, leadership, individualism, and competitiveness. But when it comes to being vulnerable, most people consider this a sign of weakness. This couldn't be more false.
Being open and vulnerable is one of the most effective ways to connect with another person. The irony is that your fear of being vulnerable is often due to a fear of being judged and not accepted, but the exact opposite is what usually happens. When you openly share your true feelings and concerns—whether it is your challenges with drinking, concerns about inadequacy, or social anxiety—these feelings create an honest, authentic, and compassionate connection. In an article in Forbes magazine, Lawton Ursrey writes, "Vulnerability is where we all can: find great strength, realize substantial and meaningful growth through the lens of hindsight reflection, and generate deeper human connections with ourselves and others."
Sharing your story, your faults, and your challenges is what makes you normal, and because we all feel vulnerable at times, you will discover that as you clean up your messes you create a level of intimacy and honesty with the other person that perhaps you have never experienced before.
### Keep Your Agreements
Your life works to the degree you keep your agreements.
—WERNER ERHARD
Founder of est (Erhard Seminars Training) and The Landmark Forum
Many of your messes might exist because of broken agreements. Agreements are an integral part of any relationship. You are constantly making agreements with your coworkers, spouse, children, roommates, family, friends, and neighbors, and how you handle those agreements impacts the quality of your relationships. Unfortunately, many people go through life not realizing how often they make and break their agreements, especially in their personal lives. In work, we understand that if we commit to do something by a certain time and we don't do it, there is usually a consequence. We lose the trust of our managers and our peers. We might end up being micromanaged on future projects or it might cost us a promotion or a raise. However, once you move into the personal realm, most people tend not to take their agreements as seriously.
You might make agreements to help a friend move, bring cookies for the PTA meeting, mow the lawn, clean the garage, spend more time with the kids, do the dishes, pick up the laundry, feed the cats, walk the dog, keep your house or apartment clean, return the book you borrowed, not mess up the living room, put away the tools, and the list goes on. Most times we agree to things without thinking if we really have the time for them; we don't write our agreements down, and if we do, we fail to read our lists.
As you read this you may be thinking to yourself, I am not one of those people. But be aware that most of us are oblivious to all of the agreements that we make and never follow through on.
The fourth action step for today is to write down how not keeping agreements shows up in your life. Think about how many times in the past you have told others you were cutting back or quitting drinking and did not. Write down all the broken agreements you think you have and everyone you can think of that you might have a broken agreement with. Consider the agreements you may have made at home with your family and also ones with your friends. Did you agree to save money, help a friend on a special project, or schedule a lunch or some other get-together? Did you tell your spouse or your child that you would attend a specific event, help them with a project or homework, or work fewer hours? How often did you not follow through with your agreements? Or maybe you eventually followed through, but a lot later than you promised.
When you are able to honestly notice and review the agreements you make, you will be surprised at how many you have broken, or completed much later than you agreed to. Stop for a minute and think about all the times someone made an agreement with you and didn't follow through. How did it make you feel? Have you ever been stood up by a friend? Or when you were a child, did a parent or loved one not keep a promise that was important to you? If so, you might find just thinking about it brings back a little of that pain.
The truth is that broken agreements dramatically affect your life. They cause you to lose the trust of others, damage relationships, lower your self-confidence and self-esteem, and even negatively affect your energy level. But when you keep your agreements, you gain trust, build self-confidence and self-esteem, and have greater clarity, focus, and energy. In fact, your self-confidence rises or falls in direct proportion to how diligently you keep your agreements.
Contrary to what many think, there is no such thing as unimportant broken agreements. Some broken agreements might have a greater external consequence, but each has a price. For example, if you agree to not drink and drive, but decide to drive after having only "a few drinks" and get in an accident, the consequence could be life changing. If you agree you will start coming home from work on time and don't, it might not seem like much of a consequence, but the truth is that you are slowly eroding the other person's trust in you. And over time, if you add one "small" broken agreement on top of another, the end result is the same—a damaged relationship. In fact, many divorces are the result of years of small broken agreements that add up to a total loss of trust.
As significant as broken agreements are to your relationships, there is one relationship they affect more than any other.
### Every Agreement Is with Yourself
Every agreement has one thing in common—you are also making an agreement with yourself. When you tell someone else you will do something, your brain also registers this as a commitment to yourself. And if you don't follow through, you are also learning not to trust yourself.
Think about all the personal agreements you only make with yourself, whether they are related to your drinking, what time you are going to get up in the morning, or when you are going to work out. Unfortunately, the agreements you break the most are the ones you make exclusively with yourself. Why? If you have only agreed with yourself to do something, you might feel like it is no big deal if you don't follow through. But it is a big deal! When you don't do what you say you will, you create a state of self-doubt and confusion in your mind that ultimately undermines your ability to take action.
So stop reading now and add to your list all the agreements that you make and break with yourself and then write down how this impacts your life.
### Whom Do You Spend Time With?
As I worked through The 30-Day Sobriety Solution, I occasionally found myself surprised at how obvious some of the solutions were, but my drinking was blinding me from seeing them. For example, in the Love and Relationship Solution, when "ranking" the people I surrounded myself with, it was clear how two specific friendships were continuing to hold me back. And because of how much I had already changed at this stage in the program, I found that not only was it relatively easy to let go of these relationships, but it was a critical step to freeing myself from drinking.
—BRIAN
30-Day Graduate from Trenton, New York
We all know there are people that hold you back. Maybe they are always complaining and blaming, or getting drunk and acting like an idiot, or doubting and making fun of you, or putting others down. People like this are toxic. And if they also drink excessively, they will make it impossible for you to thrive in sobriety if you actively keep them in your life.
One of the easiest ways to change who you are is to change whom you spend time with. It really is that simple. And once you have cleaned up your messes, this becomes easier to change because it is very possible that the best role models in your life are the people that you have avoided or hurt the most because of your drinking.
And if you are going to be successful, you have to start hanging out with successful people. And by "successful," we do not mean someone who necessarily makes a lot of money—the world is full of wealthy people who are unhappy. Being really successful means having healthy relationships with your family and friends, working in a career that you enjoy (or at least grants you the freedom to do the other things you love), being physically and emotionally healthy, and contributing to others in a positive way.
The fifth action step for today is to write down a list of everyone you spend any time with—whether they are coworkers, neighbors, family, or people at the bar. Also write down anyone that you would like to spend time with, but due to your drinking maybe you have avoided, such as a positive role model in your family. Then next to each name write a number from 1 to 5 in relation to how much they drink. The more they drink, the lower the number. For example, a 1 is someone who drinks excessively, and a 5 is someone who doesn't drink much, or at all. If you are not sure, then make an educated guess or rate that person a 3.
Next, write down a second number related to the person's overall influence in your life. If she is an extremely positive influence, she is a 5, and if she is exceedingly negative, she is a 1. Whether or not the person drinks will also affect this rating. For example, you might have a friend who seems happy and successful—he has a great job, is physically fit, and is in a happy marriage—but you know that he drinks excessively. That person would not be a 5, but possibly a 3 or a 4.
Then add these two numbers together. You will notice that this "ranking system" is heavily weighted against drinkers—if they drink a lot, the odds of them getting an overall 5 or better is unlikely. As much as possible, you should avoid spending time with anyone who has a total score of 6 or less, because he or she will eventually pull you down.
An old fisherman's technique says that if you put a crab in a bucket, you have to put a lid on it, or the crab will climb out. But if you put a bunch of crabs in a bucket, you don't need a lid. Why? Because if one crab tries to escape, the other crabs end up grabbing the legs of the escaping crab and pull it back down. This is exactly what a 6 or less does to you—the person pulls you right back down to his or her level no matter how hard you try or how much you want to change.
On the other hand, anyone on your list with an 8, 9, or 10, you would want to spend more time with. When you identify those that are a great influence in your life, make an effort to be with them. And when you are with them, be curious. Ask them about their philosophy of life and what some of their "secrets of success" are, and then try some of them out for yourself. These new "success secrets" might include reading what they read, attending a specific workshop they have attended, or trying out a new morning or evening ritual that has been successful for them.
You might even discover they are great role models in helping you accomplish a specific goal, such as running a marathon, exploring your spirituality, or having a healthier relationship with your spouse. Or he or she may even be a role model for life—someone who embodies the values and character traits you most want in your life, and exemplifies real success to you.
### I'm Not Being Fair!
Free of alcohol, I learn that while I do love people, I hate small talk, am bored by the idle banter, and am wildly uncomfortable in big rooms with people I don't know. I want a real connection, not a surface one, and in its absence, I will medicate my discomfort and boredom.
—ROB LOWE
You might be asking yourself, Isn't it hypocritical for me to avoid others who act exactly like I used to? No, it isn't. You can let them know that you are making some changes in your life that require you to allocate your free time differently. You are not helping them, yourself, or the people you do want to spend time with by letting the people who are ranked a 6 or less play an active role in your life. The best thing you can do is make positive changes and hope that it will inspire them to do the same.
Another question might be What if that person is my coworker or my mother? If it is someone you don't live with, the answer is simple—you must do everything you can to minimize the time and impact they have in your life. If it is a coworker and you socialize with them, stop it. And when you are at work, make sure the time you spend with them is only work related. Don't go on breaks or out to lunch with them. If you sit nearby, find creative solutions, such as wearing noise-reduction headphones if they are allowed.
If it is a close family member, like your mother who lives nearby, you still have to prioritize what is best for you. That might mean hiring someone to help take care of her, or just telling your mother that you are working on a personal or professional project that requires most of your free time right now. Remember, it is critical to put yourself first.
### I'm Married to a Bad Influence!
You are the average of the five people you spend the most time with.
—JIM ROHN
One of the most challenging situations is having a spouse or partner who is currently struggling with drinking or is just very toxic and negative. The best thing you can do is to work on yourself, love the person as best you can, and lead by example, showing the possibilities of change. Over time partners will often follow in your footsteps, especially when it's clear you have changed for good. Not only do they want what you now have in your life, they also know that if they don't change they will probably lose you.
On the other hand, if you are living with someone who is violent and abusive, you may need to consider getting totally out of the relationship. As you progress in your sobriety, your willingness to put up with abusive behavior will lessen. And when you escape an abusive relationship and build nurturing relationships in your life, your need to numb out your pain will also diminish.
Regardless of your current situation, whether you are with someone who is just constantly negative and cynical or someone who is intentionally emotionally or physically abusive, we recommend that you set certain boundaries for yourself. The most important boundary is to make and communicate the decision to not spend time with your spouse or partner when they are drunk. Ultimately if they don't change, they are going to want you to drink again, so spending time with them while they are intoxicated can be very risky. Without coming across as judgmental or resentful of their drinking or attitude, explain that you love them, but you need to make this change because you are concerned for your own well-being.
The second boundary you can set for yourself is to ask them to see a counselor, work with a therapist, or attend a personal growth workshop—either with you or without you. On the companion website for Day 30 we have listed some of our favorite personal growth workshops. This can be particularly useful if their challenge has more to do with being overly negative than with drinking. Just because you have decided to make this change in your life, your spouse or partner might need some time to accept that he or she may have to change as well. It is important you give them the space to reach this realization on their own.
### I'm Being Selfish!
My family and my friends have helped. I don't like yes-people. I don't want yes-people around me; I think they're extremely dangerous. I like people who are honest with me and tell me the truth. I can take it. I have much more respect for someone who tells me the truth. My real friends tell it to me like it is; I don't need "enablers." I need people who tell me what's what.
—NAOMI CAMPBELL
When you make changes like those we recommend, you may feel as if you are being selfish—selfish for not spending time with certain people, selfish for focusing on your own needs and personal growth, and selfish because you know how those changes will affect your family and friends.
Yet the exact opposite is true! It's less selfish! One of the most courageous and unselfish things you can do is to cut back or quit an addictive behavior, like drinking.
When you successfully cut back or quit drinking and are thriving in life, you are actually able to finally live a more unselfish life. Not only will your newfound health and happiness naturally inspire others, you'll also have more time and money to volunteer in service of others, whether it is volunteering for a nonprofit group, helping out at your kids' school, or just teaching someone in the neighborhood how to play the guitar, bake a pie, or fix their car. And over time you'll find that you are mostly surrounded by loving, supportive, and positive friends and family.
### Day 27 Action Steps
After completing The 30-Day Sobriety Solution and finally quitting drinking, one of the eye-opening experiences was how many of my drinking "friends" were no longer interested in spending time with me. At first I felt a little hurt, but I quickly realized they did me a favor. They were standing in my way, preventing me from becoming the person I really desired to be.
—NATHALIE
30-Day Graduate from Winnipeg, Canada
The Love and Relationship Solution can be summarized best by one of Tony Robbins's well-known quotes—"The quality of your life is in direct proportion to the quality of your relationships."
• Write down all the negative impacts drinking has had on your relationships. Use the questions in the text (and additional ones on the companion website) and write in your journal about how drinking has hurt your relationships.
• Listen to the Merge Meditation. Listen to the guided meditation on the companion website to finally merge the identities of "problem drinker you" and "sober you" so you can release any internal conflict that might lead you back to drinking.
• Create a list of relationships you need to clean up. Using your notes about how drinking has negatively affected relationships in your life, make a list of any relationships that you feel need to be cleaned up—whether this means you need to forgive yourself, apologize to a friend or family member, or both. Use the framework on today's companion website to help you complete this list and review the conversation guidelines to help you create a positive outcome from your discussion.
• Write down your broken agreements. Most likely many of the relationships you listed in the previous step are messes in part because of broken agreements. Write down all the broken agreements you have made to others—big or small. Be sure to add all the agreements you make and break with yourself and the overall impact on your life.
• Make a list of everyone you spend time with, and then "rank" those relationships in your life. Your list should include personal and professional relationships, as well as people you might not spend much time with currently, but would like to. For example, maybe you have a family member that you consider a positive influence, but because you drink you avoid them. After creating this list use the ranking system we discussed above and assign them a final "ranking." As a guide, avoid spending time with anyone with a final ranking of 6 or below.
You'll find some new ideas that will help you build stronger relationships in your life on today's companion website, including tips on how to be a better listener, some advice regarding what you say verses how you say it, and, of course, the Merge Meditation. Go to <http://Day27.Solutions>.
## Day 28
## The Review Day and Bonus Solution
## Nurturing Your Body, Mind, and Spirit
Energy of the body has to be kept in balance through the use of other energies that come in the form of breath, food, water, sunshine, exercise, and sleep.
—DEEPAK CHOPRA
Wow, can you believe you only have two days left after today? As we mentioned at the beginning of Phase IV, you might be surprised to realize you have mixed feelings. You might feel excited and proud of your dedication and achievement, or you might feel, as one of our recent graduates shared, "sad to say good-bye to my companion." Remember, even though you are about to become a 30-Day Graduate, you can still revisit your favorite solutions, continue to expand your knowledge by reviewing all the content on the companion website, work through The 30-Day Sobriety Solution again, or perhaps most importantly, support others who are trying to overcome their problem drinking.
Phase IV, "Cultivating Courage and Positive Relationships to Thrive in Mind, Body, and Spirit," introduced you to several ways you can maintain balance in your life. In the last six days you learned a simple but powerful breathing technique that can reduce stress, regulate your mood, create more energy, and release toxins from your body. You discovered the real "cost" of alcohol to your body and why drinking enough water is essential to your health and wellness. You also explored how exercise can improve your body image and confidence, help you sleep better, reduce your risk of cancer, and add years to your life. Finally, you learned that alcohol actually deprives you of sleep, and that getting the right amount of sleep will not only increase your productivity and ability to focus, but will help you live longer and be happier.
In addition, you uncovered the many benefits of meditation, which makes you happier, healthier, less stressed, and more creative. You learned how to identify and overcome fear, and how to live a life that is not controlled by your negative emotions. And yesterday, in the last solution of Phase IV, you explored how to heal your damaged relationships and make your family and friends the most satisfying part of your life.
Visit today's companion website for a review of all of this week's key concepts in addition to your fourth and final bonus solution, the Sobernomics Solution, which teaches you the basics of sobernomics and outlines a path for creating financial wealth and security with your newfound sobriety. Go to <http://Day28.Solutions> to get started now.
Also, check out the last special video from us and be sure to complete the Phase IV review.
# PHASE V
* * *
# Creating Your Personalized Plan to Thrive in Life
* * *
The most effective way I know to begin with the end in mind is to develop a personal mission statement or philosophy or creed. It focuses on what you want to be (character) and to do (contributions and achievements) and on the values or principles upon which being and doing are based.
—STEPHEN COVEY (1932–2012)
Author of The 7 Habits of Highly Effective People
You finally made it—Phase V, the last phase of The 30-Day Sobriety Solution. We are excited to close out your journey with two powerful solutions, specifically designed to empower you with a purpose and plan to move beyond these 30 days. However, before we get started we want to take a minute and review the ongoing action steps we asked you to do during the last two weeks, or Phases III and IV of the program. Now don't get us wrong, this does not mean you are off the hook for the ongoing action steps from the first two weeks, or Phases I and II. We recommend you also go back and review those, which you can find at the beginning of week 3, or Phase III.
Once again, we know how much we are asking of you during the course of this program. But we also know that if you complete all the solutions in 30 days, as well as all the "required" action steps, it would still take less time than your drinking would have taken from your life in 30 days. One night a week of drinking is about the same amount of time this program takes every week, especially if you sleep in or are less productive during the mornings after you drink.
So let's take a look at these ongoing action steps that will help you thrive in sobriety and thrive in life.
#### The Top Fourteen Ongoing Action Steps (in Order of Importance)
1. Journaling. No, this isn't new, but it bears repeating given its importance (Day 1).
2. Meditate daily. Yes, we consider meditation powerful enough to rank it higher than the following action steps (Day 24).
3. Visualize daily the images and short movies that focus on what you want (Day 15).
4. Practice gratitude every morning by thinking about five things you appreciate (making sure to feel the emotion of it as well). Pick one or more people a day to actively appreciate by telling them in person, by phone, or in a letter or email (Day 20).
5. Clean up any past relationships and spend time with people who are good role models. Surrounding yourself with people who are positive role models and who embody the kind of person you want to be is one of the easiest ways to sustain change in your life (Day 27 and Day 4).
6. Review your Total Sobriety Affirmation (Day 18) and ask your 30-Day Vision question (Day 16).
7. Exercise and add some new activities to your life (Day 26).
8. Use the "ask, believe, receive" process and change your negative inputs, such as watching nightly news (Day 19).
9. Feel your fear and take action anyway (Day 22).
10. Take control of your emotions, change your self-talk, and discover the source of your negative emotions and change them (Day 17 and Day 23).
11. Drink enough water and make small healthy changes in your diet (Day 25).
12. Say "yes" more often, and be sure your answer isn't guided by fear (Day 22).
13. Practice the 4-7-8 breathing exercise twice a day (Day 24).
14. Create a vision board, which we asked you to complete within a month, and spend a few minutes looking at it every day (Day 15).
Okay, are you feeling overwhelmed after reading this? Don't be! Many of these won't take more than an extra minute or two and can be done as you go about your normal day. And you can remind yourself by printing and posting your own prioritized list or setting up a daily recurring calendar entry. For example, thinking about five things you are grateful for when you wake up in the morning can be done while you are in the shower or while you are brushing your teeth, and visualizing can be done almost anywhere and anytime. And many of these just take a little bit of extra awareness as you go through your day, such as recognizing and overcoming your fear, discovering the source of your negative emotions, changing your self-talk, and using the "ask, believe, receive" process. And while drinking more water means that you might have to go to the bathroom a little more often, you could review your affirmation statement and ask your 30-day Vision question at the same time.
We don't expect you to do everything on this list every day; however, it is most beneficial for you to do most of them as often as possible if you want to continue to thrive in sobriety after you finish this program.
So, let's get started on the Vision Solution.
## Day 29
## The Vision Solution
## Discovering Your Life Purpose and Vision
When I chased after money, I never had enough. When I got my life on purpose and focused on giving of myself and everything that arrived into my life, then I was prosperous.
—WAYNE DYER
We believe that each of us is born with a life purpose. Identifying, acknowledging, and honoring this purpose is perhaps the most important action you will take after completing The 30-Day Sobriety Solution.
When you take the time to understand what you are here to do—and then pursue it with passion and enthusiasm—you will find that cutting back or quitting drinking will come more easily. The Vision Solution will show you how to finally discover what you are meant to do with your life, and how to create a vision that is perfectly suited to your unique gifts.
### What Were You Put on This Earth to Do?
If you don't build your dream, someone else will hire you to help them build theirs.
—DHIRUBHAI AMBANI (1932–2002)
Indian business leader
If you are like most people, the idea of finding your life purpose is scary. What if you think you know what your life purpose is, but are wrong? What if you can't figure it out? What if you discover that what you are "supposed" to be doing is completely different from what you are doing today?
We want to start by dispelling a few misconceptions about a life purpose. You do not have to know your life purpose to be successful. You do not have to know your life purpose to be happy. And your "day job" does not have to focus on your life purpose in order for you to be fulfilled. Wherever you are today and whatever you have come through to get here—regardless of your income, age, or status—are perfect. We believe there is a reason and a purpose for your past and a purpose for everything that has brought you to this point in your life. We all have different lessons to learn and paths we have to take.
For example, Jack discovered what he was put on this earth to do early in life. He determined his true purpose and discovered how to inject passion and determination into most of his activities. And he learned how knowing his purpose allowed him to bring an aspect of fun and fulfillment to virtually everything he does.
On the other hand, Dave struggled to discover his life purpose early on. While he always felt a strong connection to helping others and believed he was meant to inspire and teach, his drinking was always a major distraction. It wasn't until he got sober, and started thriving in sobriety, that he could finally clearly see and start to believe in his purpose.
However, Dave realized later that his years of struggling with drinking were a necessary part of his path, and even though he felt like he had wasted almost eighteen years of his life drinking, this was the journey he had to take in order to do the fulfilling work that he now does. He eventually came to understand that what he used to consider his "mess" was actually the foundation of his message. And now he can help people with getting sober because of his past, not in spite of it. You might recall from the Lie Detector Solution that sometimes all you need to do to empower yourself in the present and future is to assign a new meaning to something in your past.
Now let's begin to uncover your life purpose!
### Discovering Your Life Purpose
Your work is to find out what your work should be. Clearly discover your work and attend to it with all your heart.
—THE BUDDHA
When you don't have purpose, you can lose focus on what you are supposed to be doing and become sidetracked. When you are aware of your purpose and consciously align your activities with it, things seem to take shape and easily fall into place. You naturally attract the resources, people, and opportunities you need.
When you know your life purpose, it becomes a compass that guides you and helps you coordinate and organize all of your actions and activities. To live with purpose means that everything you do is an expression of that purpose. If not, your action plan and goals may not be fulfilling. As Stephen Covey aptly states in The 7 Habits of Highly Effective People, if you don't figure out your purpose, you might find you're "climbing the ladder of success only to realize, when you get to the top, you're on the wrong building."
Or as another 30-Day Graduate shared, "It [The 30-Day Sobriety Solution] allowed me to live a life that was congruent with my values and my desire to lead by example. Today I finally get to fulfill my life purpose, instead of always knowing my drinking would deny me of it." There are countless examples of what can happen when you get clarity and focus on your purpose. There are many ways to define your life purpose; however, we are going to introduce you to a simple four-step process that we have found to be incredibly effective. As you work through the next few sections, have fun. There are no right or wrong answers. The goal is to begin to identify and acknowledge what really ignites your passion and makes you come alive.
### The Life Purpose Exercise
The positive format of The 30-Day Sobriety Solution, combined with all of the life-changing tools and techniques, has done what years of therapy and AA meetings never could—it helped me discover my life purpose, which finally made achieving sobriety a reality in my life for the first time since my husband passed away eight years ago.
—MISSY
30-Day Graduate from Grand Rapids, Michigan
Up until today it is possible that your life purpose was based on misguided beliefs and experiences. Maybe your parents always told you what you should do when you grew up, or maybe someone convinced you that you were not smart enough or talented enough to do what you wanted to do. Or maybe you let your habit of drinking act as the guiding force instead of your purpose.
The first action step for today is to complete a four-step process we call the Life Purpose Exercise. The questions are simple, but the answers won't always come easily. As you do this exercise, accept whatever answers come to mind. Don't judge what comes up, and don't worry about how you would accomplish it, or even if it is possible. And don't think about how anyone else might react. Just answer the questions in writing as honestly as you can. If you would like to be guided through this process, visit the companion website and listen to the Life Purpose Exercise audio.
#### 1. Your Passion
• What excites you? What are you passionate about?
• Think about some of your happiest memories, from childhood to your most recent. What was it about those experiences that made you feel the most alive? What emotions did you experience? Did you feel joy, happiness, fulfillment, freedom, love, or an authentic connection? Who was there?
• What are you doing when you lose all sense of time?
• If money wasn't an issue, what would you do?
• What are your biggest accomplishments, and what made them significant? Was it how the accomplishment made you feel, the difference you made, or the challenges you had to overcome?
• Have you had to overcome specific challenges, like drinking, dyslexia, depression, racism, abuse, or divorce, and through that process realized you can help others do the same?
As you read through your responses, look for any common threads such as emotions, people, or experiences. For example, maybe you remember a variety of events where you felt important, helpful, and energized, and in each of them you were connecting and helping people in a specific way. Maybe you helped a friend handle something he or she was struggling with, or listened compassionately to a loved one share a problem with you, or simply did a favor for a stranger. You may have a passion for helping others, and as you compare those moments you might realize that you felt the most joy when working with a specific group of people, whether it was kids, young adults, elders, or a group of people struggling with addictive behaviors.
Or maybe you felt most alive when you expressed your creativity in specific ways such as painting, creating a website, or writing. Or maybe you felt most alive when you were using your body teaching yoga, building a house, or working in the garden. Whatever you realize ignites your passion and brings you joy, write it down. There are probably many things that make you feel alive, so write them all down.
#### 2. Your Talents and Strengths
• What are you good at?
• What do you think others would say you are good at? Better yet, over the next few weeks, actually ask coworkers, friends, and loved ones what they think you are good at. Sometimes it is hard to be objective about what your unique talents are; however, your friends and family can often see them more clearly than you.
• How do your strengths and talents relate to your passions?
• Do you believe you have a specific talent or strength that you haven't taken the time to develop yet? For example, you might recall the story of "The Alcoholic King" from Day 2, the Purpose Solution, which illustrates how you might have been dreaming about all the great stuff you were going to do in your life while you drank.
• Think about your happiest moments again—what strengths or talents were you using to create them?
Be sure to write down at least three or more of your top strengths and talents before moving forward.
#### 3. Your Legacy
• What lasting difference or contribution would you like to make in your life? Let the answer come from your heart.
• What, if anything, are you doing to create that today?
• Are you making a difference in your current job? In any other way?
• If so, is there a way you can do more of that?
Don't worry about thinking you need to make a big impact. You do not have to affect thousands of lives to make a difference, in fact, one of the most meaningful ways to give back is to start with your loved ones, especially if your drinking has previously affected your ability to spend quality time with them. Write down whatever comes to mind.
#### 4. Your Life Purpose
When you combine your passions and your unique strengths and abilities, and use these to consistently make a difference in the world, it is life changing. You will no longer look to external things (like material possessions) to feel happy or impress your family and friends. Instead, you will wake up in the morning feeling the inner sense of peace and joy that in the past you tried to create by drinking.
As you start to write out your life purpose, remember it is only a first draft—nobody gets it perfect the first time. Ideally you want your life purpose statement to be no more than two sentences that describe using some of your passions and strengths in a way that contributes to others in some way.
If you are fortunate enough to already have a career that allows you to express your purpose, that is fantastic. However, this may not be the case. As you become clearer about your true purpose, you may decide that you want to change your career to one in which you can more fully express your purpose, but you might also find that the income generated by your current job gives you the freedom to express your life purpose outside of your work. However, if you can find or create a job that is aligned with your purpose, it makes thriving in sobriety a lot easier.
Your life purpose is about giving, not getting. True happiness and lasting fulfillment come from making a difference in the world. But "making a difference" means something different for everyone. For some, that might mean being an honest and talented auto mechanic or the best barista at the local coffee shop. And for others that might mean starting a nonprofit organization. The key here is to remember that whatever makes you come alive will automatically be of service to others. That's part of how we are all wired.
Here are the life purpose statements we created for ourselves using this process. Even though they are both brief, notice how they give insight into our passions, our talents, and the contribution we want to make.
• Jack's Life Purpose: Using my unique abilities to speak and write, I inspire and empower people in a context of love and joy to live their highest vision in harmony with the highest good of all concerned.
• Dave's Life Purpose: Using my passion and my sense of humor, I inspire and teach people how to thrive in sobriety by applying the principles and techniques taught in The 30-Day Sobriety Solution.
This exercise is not about writing the "perfect" life purpose statement. Rather, it's about creating awareness about what your unique abilities are, what really makes you come alive, and how you want to express that in a way that contributes to others. As your awareness expands and you proactively choose activities that better express your unique qualities and desires, you will feel happier and more fulfilled, making thriving in sobriety your everyday experience.
### How Thomas Found His Life Purpose
Sobriety has become second nature. I can't really explain it, other than soon after completing The 30-Day Sobriety Solution I just stopped thinking about drinking, even though I still go to the pub with friends.
—THOMAS
30-Day Graduate from London, England
Thomas was in his midthirties when he realized his life had not turned out like his childhood dreams. Not that this surprised him, as he had always been a little cynical. Thomas grew up in England, which is known for its strong drinking culture, and like most of his friends he had his first drink at the age of fourteen.
When Thomas started college, drinking was not a big part of his life, but in college he drank a lot, and even though he was surrounded by heavy drinkers, he realized that his drinking was different. He was never satisfied drinking just on the weekends, and the rare nights he didn't drink he would spend thinking about his next chance to drink. By the time he left college, drinking had become an essential part of his life.
Thomas found a variety of jobs out of college, none of which he was passionate about, but all of which funded his drinking habit. But now that he wasn't immersed in college life, he couldn't hide from the reality of how bad his drinking had actually become. He drank almost every night, usually staying out later than his friends and colleagues, and almost always drinking more than they did. Bad hangovers were now a normal part of his life.
Eventually he got a job teaching English, which wasn't his dream job, but it did reignite his passion for literature. Regardless, Thomas continued drinking excessively and rarely was sober for two consecutive days. He could see forty on the horizon. He tried a variety of online programs and self-help books, and even attended a live quit-drinking seminar, but nothing worked until he came across The 30-Day Sobriety Solution.
Today Thomas has over two and a half years of sobriety, and he realized that cutting back was not an option for him. Like many graduates, he found that The 30-Day Sobriety Solution and his continued sobriety helped him get in touch with his life purpose. He realized that his love for literature was not just limited to reading—his real passion and calling was to write. Ironically, this led him back to the same place where his heavy drinking had begun—college. Thomas shared recently, "I can't tell you how much I'm enjoying being back in school, having the chance to work on my writing, including my second novel, with some big-name authors; it's life changing. Also, I am still happily sober. I go to the gym regularly, I moved in with my girlfriend, and I meditate every day—all things I never would've imagined myself doing."
### The Corporate Vision/Mission
Most successful companies, whether they are small businesses or the largest corporations, have clear vision and mission statements.
Having a clear vision and mission statement helps ensure that the company does not stray from its core values and objectives. They keep the company in check and on track, and when someone says, "Let's create this product or service," the company can refer to the vision and mission statements and say, "Wait, this new product or service does not help our end mission; therefore, we need to either rethink our vision and mission or not go this route."
Numerous companies have failed because they strayed from their core mission. Your vision and mission statements will keep you from letting anything—including alcohol—pull you away from fulfilling your life purpose.
Even though having a vision and mission is so critical for your success in life, most of us only have a general idea of what we want to have, do, and be in our life, and almost no one has a written vision statement for their life. Without a vision for your ideal life, you don't know what you are aiming for, and you don't have a way of knowing if you are moving closer to or farther away from the life that will bring you the happiness, meaning, and fulfillment that you want.
### Clarify Your Vision of Your Ideal Life
We know that one of the keys to thriving in sobriety is to have a clear and compelling vision of your ideal life. That vision directly affects the actions you take today. As you become clearer about what your ideal life looks like, your daily decisions naturally support that ideal.
In the first two days of this program you started to uncover what the "new you" might look like when you finally removed the destructive force of alcohol from your life. Since that time you have been adding to that awareness by rediscovering your core values, by writing goals, and by completing today's Life Purpose Exercise. Now it's time to use all of this new knowledge to write your vision.
Your vision will describe in detail what your ideal life looks and feels like. To create a balanced and successful life, your vision needs to include the following seven areas: work and career, finances, free time and recreation, health and fitness, relationships, personal goals including sobriety, and contribution to the larger community. In the diagram of the Vision Compass, which appears below, notice what sits in the middle of all these areas—your life purpose. If you keep your life purpose in mind as you write your ideal vision, thriving in sobriety will be a natural by-product of successfully accomplishing your goals in the seven main areas of your life.
### The Vision Compass
When you honestly examine your life, you may realize that as a problem drinker, your obsession with alcohol replaced your life purpose. Alcohol can become such a central and often overbearing part of your life that—over time—it simply "drowns" any hope of living a life of purpose and meaning because each of the seven critical areas of life is negatively impacted by your drinking.
### The Vision Compass
Yes, gymnastics had been my dream—and it stung like hell to know I'd missed my chance to achieve it. But I somehow knew instinctively that when one dream dies, you have to move on to a new one. The unhappiest people in this world are those who can't recover from losing a dream—whose lives cease to have meaning. I wasn't going to let that happen to me. It was a revelation that would later save my life.
—PATRICK SWAYZE
The second action step today is designed to help you clarify your vision. Start by putting on some relaxing music and sit quietly in a comfortable environment where you won't be disturbed. Then close your eyes and ask your subconscious mind to give you images of what your ideal life would look like if you could have it exactly the way you want it. (If you would rather be guided through this process, listen to the Vision Compass Creator on the companion website.)
Remember, at this stage in the journey, it is not necessary to know exactly how you are going to get there. All that is important is that you figure out where there is. If you get clear on the what, the how will become apparent over time.
• First, visualize your ideal job or career. Where are you working? What are you doing? With whom are you working? What kind of clients, customers, or job do you have? What does your ideal day at work look like? Is it your own business? Are you able to use your unique abilities and your passions? How does your career make you feel—alive and passionate, grateful and successful, fulfilled and creative? How have your productivity, attitude, and energy improved at work now that you are clearheaded?
• Now focus on the financial area of your life. What is your annual income? How much money do you have in savings and investments? What is your total net worth? How much money have you saved from cutting back or quitting drinking and your drinking related activities? Next: What does your ideal home look like? Where is it located? Walk through your perfect house, filling in all of the details. Now picture any other important possessions your finances have provided, such as your ideal car, jewelry, art, clothes, musical instruments, electronics, tools, boats, and so on.
• Now focus on your free time and recreation. What are you doing with your family and friends in the free time you've created for yourself? Are you pursuing new hobbies, perhaps implementing ideas from the 101 New Activities list you created? What kinds of vacations are you taking? What do you do for fun? Are you totally abstaining from alcohol or only having a drink or two on occasion?
• Next, what is your ideal vision of your body and your physical health? Are you open, relaxed, and feeling happy all day long? Are you full of vitality? Are you physically thriving? Are you flexible as well as strong? Do you exercise, eat good food, and drink lots of water? Have you reached an ideal, healthy weight? Is your blood work healthier? Are you disease free with all of your organs functioning at their optimum level?
• Now move on to your ideal vision of your relationships. What is your relationship with your family like? Who are your friends? What is the quality of your relationships with your friends and family, and how have those relationships changed? Are they loving, supportive, empowering? What kinds of things do you do together? Are you the role model to your children that you always dreamed of being, or are you a new parent? Have you rekindled the passion in your marriage, or met and fallen in love with your soul mate? Or are you enjoying the freedom of being single?
• Now focus on your personal goals. Do you see yourself going back to school, getting more training, attending workshops, working with a coach, seeking therapy for a past hurt, or growing spiritually? Do you meditate, go on spiritual retreats with your church or synagogue, or belong to a support group? Are you learning to play an instrument or writing your autobiography? Are you running a marathon, learning to surf, or taking an art class? Are you continuing to use the tools and techniques you learned in The 30-Day Sobriety Solution? Are you easily accomplishing personal goals that eluded you during your drinking days?
• Finally, focus on the community you live in and the community of people with whom you spend the most time. What does your ideal community look like? How do people interact with each other? Are they friendly, peaceful, supportive, interesting, and fun? What kinds of community activities do you participate in? What about your charitable or volunteer work? What do you do to help others and make a difference? How often do you participate in these activities? Who are you helping? How do you feel?
You can write down your answers as you go, or you can do the whole visualization exercise first and then open your eyes and write down your answers. In either case, make sure you capture everything in writing before you move on to the final step.
### Aligning Your Vision Compass
Substance-abusing writers are just substance abusers—common garden-variety drunks and druggies, in other words. Any claims that the drugs and alcohol are necessary to dull a finer sensibility are just the usual self-serving bullshit.
—STEPHEN KING
Now that you have directed your Vision Compass toward what you want in each area of your life, it's time for your third action step—to write out a powerful vision statement that is in alignment with your values, purpose, strengths, talents, and passions. Although you might now have a lot of details written down for each area, start by capturing the essence of your vision for each area in only one or two sentences. As you write them, follow these three guidelines.
1. Write them as an affirmation. Use the same guidelines for writing an affirmation that you learned on Day 18 in the Affirmation Solution. Start with the words "I am . . ." Use the present tense. State it in the positive. Be brief. Be specific. Include an -ing action word. Include emotion/feeling words. Describe your own behavior, not others'.
2. Include your core values. Include some of your core values that you identified on Day 10 in your vision.
3. Include your unique abilities, strengths, talents, and passions. Where applicable, include your purpose, and add all your strengths, talents, and passions to each area.
To help you get started with this process, we have included examples from Dave's vision statement. When you read these, Dave's values, passions, strengths, and life purpose should all become clear.
• Work and career. I am drawing on my passion, love of learning, and sense of humor to courageously inspire and teach people how to overcome their addictive behaviors by implementing the techniques taught in The 30-Day Sobriety Solution.
• Finances. I am thrilled and proud that every year my wife and I have a positive net income across our businesses and are able to save 20 percent of our annual gross income for traveling, retirement, and emergencies.
• Free time and recreation. I am passionate, excited, and full of love from spending high-quality time with my family and friends, including participating in fun activities, playing sports, going on dates with my wife, playing with our animals, going to movies, watching funny TV shows, and taking wonderful family vacations.
• Health and fitness. I am full of energy, vitality, and strength from fueling my body with nutritious whole foods 90 percent of the time, drinking ninety ounces of water every day, and vigorously exercising for at least twenty minutes five days a week.
• Relationships. I am thoroughly enjoying a strong sense of connectedness, love, and support through my relationships and different roles in life as a parent, spouse, coach, friend, peer, nonprofit board member, speaker, author, CEO, and leader.
• Personal goals. I am feeling confident, focused, and at peace from daily practicing meditation and visualization and regularly attending personal-growth-related seminars and workshops.
• Contribution to the larger community. I am experiencing a deep sense of purpose, fulfillment, and happiness from dedicating at least two hours a week to give back to recovery organizations and individuals who need help overcoming their addictive behaviors.
When you complete this exercise, you will have an incredibly powerful vision that will actually get you excited to get out of bed in the morning. If not, it simply means that you haven't yet dared to write down what you truly want. Keep at it until you do. We'll remind you again not to let not knowing how to go about creating it stop you from writing it down. As we stated before, the how will show up once you commit to what you want. There is unbelievable power in having clarity about what you want in life! As you complete the first draft of your vision statement, acknowledge yourself for the significance of this accomplishment. Only a very small percentage of people ever take the time to create a clear and compelling vision for what they want in life.
We recommend you read your vision statement every day—perhaps first thing in the morning. It will take you only one or two minutes at the most. And as you review your statement, you will get additional clarity about what is authentic in your statement and what isn't. When you have these insights, just make a note of them. Over time your small updates will result in an amazingly accurate vision statement that you will love reviewing.
### Using Your Vision Compass to Thrive in Sobriety
I got into trouble when I didn't have baseball. It was the catch-22 of my problem: without baseball, I had little reason to stop using; while I was using, I would never be allowed to return to baseball.
—JOSH HAMILTON
Once you have identified what you want in the seven main areas of your life and integrated your core values and life purpose to create a compelling and inspiring vision statement, it's time to bring this vision to life. To help you manifest all the different aspects of your vision, here are our top nine tips to avoid getting "lost" along your journey to thriving in sobriety and life.
1. Review your vision daily. When you review your vision statement, you keep your conscious and subconscious minds focused on what you want. For example, Dave keeps his posted on his medicine cabinet mirror and reads it out loud every morning. Jack keeps his on his iPad and reads it every morning and visualizes each part of it as if it were already accomplished.
2. Share your vision for maximum impact. You'll find that when you share your vision with people who are positive and supportive, not only do they often want many of the same things, they often will offer advice, contacts, time, and resources to help you achieve it. You'll also find that each time you share your vision, it will feel more real and attainable to you. And most importantly, sharing it strengthens your own subconscious belief that you can achieve it.
3. Follow your heart. Whenever you feel discouraged, come back to your life purpose and what really makes you feel good, regardless of the potential reward. Jim Loehr and Tony Schwartz, authors of the New York Times bestseller The Power of Full Engagement: Managing Energy, Not Time, Is the Key to High Performance and Personal Renewal, write: "Purpose also becomes a more powerful source of energy when it moves from being externally to internally motivated. Extrinsic motivation reflects the desire to get more of something that we don't feel we have enough of: money, approval, social standing, power or even love. 'Intrinsic' motivation grows out of the desire to engage in an activity because we value it for the inherent satisfaction it provides." So focus on doing what brings you the greatest satisfaction.
4. Write out your goals. Go back to Day 6, the Outcome Solution, and use the SMART guidelines to write specific, measurable, attainable, realistic, and time-bound goals for each of the seven areas of your new vision statement. Put your list of goals where you'll see it every day.
5. Embrace high intention . . . and low attachment. Do what you can to create your desired outcomes, and then let it go. Sometimes you will get the intended result by the date you want and other times you won't. Whatever happens, just keep moving in the direction of your vision and your goals. It's also important to remember that sometimes the universe has other plans for you that are better than the ones you had in mind. Remember, it's not the destination that matters nearly as much as the personal transformation you experience along the journey to that destination.
6. Your joy is your inner guidance system. Smartphones and cars now have GPS technology that helps you find your destination and gives you feedback when you get off course. What you may not know is that you also have an internal guidance system that you were born with, and that gives you feedback about whether or not you are on course. And that feedback is simply the amount of joy you are experiencing. When you are experiencing joy, whatever you are doing is aligned with your purpose. It's a feedback system that you've always had, but many of us were taught to ignore or not trust it. From now on, pay attention to your experience of joy. Follow your heart and do what makes you feel most alive.
7. Be patient and practice persistence. Think about the saying, "It takes ten years to become an overnight success." Overnight successes are an exception and actually come from years of work, being incredibly resilient in the face of setbacks, and persisting when many would be inclined to give up. Then a sudden major breakthrough changes everything. Maybe it was being cast in the right role in a hit movie, having a blog post or YouTube video go viral, or gaining the attention of one of the leaders in your industry. Whatever the success, it came from years of work—developing one's craft while being turned down for countless roles, writing a thousand blog posts before one took off, or working in an industry for a decade before gaining attention and recognition. So keep following your purpose and doing what you love, knowing that your success will eventually come.
8. Take action. Keep taking steps, no matter how small, toward the achievement of your vision. When you encounter the inevitable roadblocks and setbacks along the way, the momentum you have created will carry you through.
9. Surround yourself with supportive people. Whether you spend time with role models that have accomplished parts of your vision, learn from leading experts in your field, work with a coach, or belong to a support group, remember that the people you spend time with will dramatically shape the results you experience. So choose wisely.
If your progress in transforming your vision into reality doesn't match your expectations, come back to these tips. Schedule a time in your calendar to review them once a month, and evaluate whether or not you are applying them in your life. The bottom line—you have to use these principles and techniques to manifest your vision.
### Always Come Back to Your "Why"
I knew very well right then that this [going to rehab] is actually going to be the best, strongest road to get me back to the two things I love, which are my home life and my career, and finding the balance in those two. I need them both. I've got to play [music], and I need to be a husband. I love it.
—KEITH URBAN
Singer-songwriter
Dave had to overcome countless hurdles to bring The 30-Day Sobriety Solution into reality. On many occasions, he seriously considered giving up on his dream, but he always came back to one thing—his "why."
Dave felt he needlessly wasted years of his life suffering with problem drinking, so early in his sobriety he realized that his "why" was to help reduce the amount of time others needlessly suffered. When he felt like quitting, he reminded himself that there might be other people just like him who needed help. And if he could reach them sooner than he was able to be reached, then maybe he could help them save years of their life, their relationships, their health, or their career.
When you discover your life purpose and remind yourself that your unique talents, strengths, and passions make you the only person in the world that can fulfill that purpose, then you will discover that nothing can hold you back. Your "why" will make sure you push through and persevere no matter what setbacks you experience. So your fourth action step for today is write down your "why" statement—the deep-down drive that motivates you to keep going. Most likely this is very similar to your life purpose statement, like Dave's is, but is just coming at it from a slightly different perspective.
### Day 29 Action Steps
Over the years I have become a fan of self-help, but it wasn't until I did The 30-Day Sobriety Solution that I was able to really apply self-help material in my life to facilitate a major breakthrough. One of the most important discoveries came from the Vision Solution, which allowed me to finally get clarity around my purpose and vision.
—LENORE
30-Day Graduate from Dallas, Texas
When you discover and commit to living your life purpose, and you create a vision for the key areas of your life around this purpose, you'll find that your life will actually unfold much more effortlessly than you ever imagined possible. The most important thing now is to stop and do the exercises we have just outlined. Be sure to review the detailed instructions in this chapter, or use the guided recordings on the companion website to complete today's action steps.
• Write a life purpose statement. Use the four-step Life Purpose Exercise to (1) identify your passions, (2) recognize your talents and strengths, (3) discover the legacy/contribution you want to make in your life, and (4) integrate these three steps to write your one- to two-sentence life purpose statement.
• The Vision Compass. Get clear about what you want by visualizing what your ideal life looks like in these seven areas: work and career, finances, free time and recreation, health and fitness, relationships, personal goals, and contribution to the larger community. We recommend that you listen to the Vision Compass Creator audio on the companion website to guide you through this essential process.
• Write your vision statement. Sum up each of the seven areas by writing one or two sentences in the form of an affirmation. Integrate your core values, unique abilities, strengths, talents, and passions where possible. Review your vision statement daily.
• Write down your "why." What is your "why"? Write a paragraph about what deep in your soul motivates and drives you to keep going in life in spite of obstacles and setbacks.
On the companion website at <http://Day29.Solutions>, you can access the guided recordings for the Life Purpose Exercise and the Vision Compass Creator. We also include some additional methods for discovering your life purpose, more examples of people's life purpose and vision statements, more information on how to turn your vision and life purpose into actionable goals, and some inspirational stories.
## Day 30
## The Sobriety for Life Solution
## Wrapping Up The 30-Day Sobriety Solution
As you transcend your own limitations and tendencies, you will naturally show loving-kindness to others. As your own light shines more brightly, you illuminate the world.
—DAN MILLMAN
Author of Everyday Enlightenment
Day 30! Congratulations! We know the level of commitment it takes to complete The 30-Day Sobriety Solution, and we applaud your dedication. More importantly, we applaud your willingness to get out of your comfort zone: abstaining from alcohol, working through emotionally challenging exercises, and getting through all the various solutions and resources. As you worked through these challenges, it is likely you found yourself in unfamiliar territory at times. In those moments you had two choices—resorting to your familiar coping mechanism by drinking, or embracing your discomfort knowing it is living on the edge of your comfort zone that facilitates the greatest growth and progress toward thriving in sobriety and thriving in life.
Before starting The 30-Day Sobriety Solution, you had unknowingly put in place numerous self-imposed limits, specifically limits on your ability to successfully cut back or quit drinking and thrive in sobriety. Today it is likely you have freed yourself from those limits. You have broken your past conditioning and opened up a whole new world of opportunity. How much success, happiness, and fulfillment you experience beyond this program is up to you. You can choose to slowly let your old conditioning take back over, or you can choose to continue down the path of personal development beyond these 30 days by applying what you have learned.
The Sobriety for Life Solution will show you how to make sure your self-imposed limits are gone forever, so that thriving in sobriety is a lasting reality for you.
### Can You Become a "Normal" Drinker?
We believe that anything is possible, at least within reason. There is no question that some people can go from being an alcoholic to having the coveted "take it or leave it" attitude of a "normal drinker." And there are numerous studies that validate this fact, but that doesn't mean we recommend it. And in fact, for most of you, we don't.
The obvious reason that you want to be a "normal drinker" is that the opposite of normal is "abnormal." And who wants to be abnormal? "Normal drinker" is one of those phrases used commonly by our clients, which is why we reference it. However, the first thing you need to drop is this label from your vocabulary. The act of using it, or thinking about being a "normal drinker," actually holds you back. It creates a belief that abstinence is not normal—and by now you have enough information to know that isn't true.
In Day 1, the first guideline was to abstain for at least 30 days (the 30-Day Reboot), but we also said you could wait until Day 8. So if your goal is to cut back, the requirement to abstain for 30 days still stands. We also mentioned that this program reaches those of you who are "all along the continuum of problem drinking, which means that no cookie-cutter, one-size-fits-all solution exists." So to answer the question "Can I have a healthy relationship with alcohol—where I only drink on occasion and rarely more than one or two drinks?" we need to explore some additional topics, and then return to it. Even if you already know that complete abstinence is your path, read these next four sections carefully, as they will still be of great value.
Last, we want to remind you that we are using this definition of sobriety: "moderation in or abstinence from consumption of alcoholic liquor or use of drugs." So when we say "sobriety," we do not necessarily mean abstinence only.
### Are You Depriving Yourself?
I now set off on a path of attempting controlled social drinking in the way I saw other people do it. I studied them, and for a while my life consisted of going up to the Windmill for lunch and having one or two lagers, and then in the evening maybe a glass of wine with dinner or a scotch after eating. The reality was, as much as I may have been trying to establish some kind of normal day like other people, what it really amounted to was these two drinking sessions with me desperately trying to kill the time in between them, often by sleeping all through the afternoon. This schedule was purely alcoholic in its development and focus, and our life just crumbled as a result.
—ERIC CLAPTON
Honestly ask yourself the following questions: What do you really want when you think about drinking? What are the first thoughts that enter your mind? Do you still think about getting drunk? Who comes to mind when you think about drinking? Do they have issues with alcohol? What future events do you think about when you consider drinking again? Are these occasions where you would usually drink a lot?
One of the greatest challenges of transitioning from being a problem drinker to someone who has a healthy relationship with alcohol is that your history with drinking is dominated by memories and experiences of drinking to excess. The idea of having only one or two drinks is a foreign concept, and in the past you would have thought you were depriving yourself.
Many of our clients share how annoying it is when they could only have a couple of drinks the entire night. In fact, most considered it such an annoyance they wouldn't even bother drinking at all. Does drinking one or two drinks make you feel like you are making a sacrifice? If the answer is yes, then we can virtually guarantee you will not be successful cutting back.
A true "take it or leave it" attitude means it simply doesn't matter to you. For example, can you imagine walking into a casino and not gambling at all? Or gambling for just a few minutes? Assuming you do not have a gambling addiction, the answer is probably yes. You are able to play a few hands of blackjack, get a call from a friend who needs help, and leave the table without thinking twice. This is exactly how you should feel about drinking. If not, it is likely you have not done the work you need to do in order to return to a healthy relationship with alcohol.
If you find that the questions above still trigger thoughts and desires of excessive drinking, then it is likely that beginning to drink again will eventually lead you back to where you started. You might be able to successfully "control" your drinking in the beginning, but if you don't have a true "take it or leave it" attitude, you will become obsessed with planning and managing it. And this is not healthy or sustainable.
### "Testing the Water"
In AA, people feel that if they slip and have a drink they're lost entirely, back to day one. That attitude in itself can sometimes be enough to turn a slip into a full relapse, since it can lead to the attitude that if you've had one drink, you're off the wagon, so you may as well keep drinking.
—DR. HOWARD J. SHAFFER
Psychologist at the Center of Addiction Studies at Harvard Medical School
At some point, you might decide that you are going to drink again. But rather than this being deliberate and planned, it might be a spontaneous decision. You may find yourself at a party or have a lousy day, and decide to drink. This is okay, and more common than you think; however, what you do after this can change everything.
In part, this is related to an abstinence-only approach. There tends to be a collective belief around this topic that can be highly destructive. Alcoholics Anonymous has popularized the concept of counting days since your last drink as a way of celebrating your success. Although we love the idea of celebrating your successes, this approach sometimes has an unintended side effect.
It feeds into the all-or-nothing attitude that many problem drinkers have, and when you have one drink, you experience a major letdown. Instead of chalking it up as valuable feedback, you feel like you've lost all of your previous "days" or "years" of continuous abstinence and have to start all over. Now you are back to Day 1. And if you attend AA, this letdown can be even more pronounced.
For example, many AA meeting formats include a question such as, "Is there anyone present who is at his first AA meeting, or is in his first 30 days of sobriety?" If you have to answer yes to this question after all the work and progress you have made, then you can end up feeling like a failure. And this can lead to an attitude of "Oh, well, I am starting over, so I might as well go party for a few more days and get it out of my system." Before you know it, one weekend turns into one week, and then one month, and it could be years before you can turn things around again.
Some of our graduates had over a year of sobriety, and then decided to "test" drinking again, sometimes with just two or three drinks. After this experience, they realized that drinking wasn't a positive influence and returned to abstinence. If they were to follow standard AA guidelines, they would have to start over counting days, but we believe this isn't a fair representation of the changes they have made in their lives. It is critical that you don't judge your "testing the water" as an all-or-nothing event that somehow redefines the work you have done in the past as no longer applicable. If these 30-Day Graduates had treated their return to drinking as a complete failure requiring them to start all over, who knows if and when they would have become sober again.
Sometimes the information you get from "going back out there" can be invaluable. We are not saying you should drink again just to get that information, but if you decide to, then make sure you learn from the experience. As long as you practice some basic self-awareness and are honest with your feelings around the experience, it will be obvious whether or not you can maintain a healthy relationship with alcohol.
### Thriving in Sobriety Through Abstinence
For most of you, abstinence is going to be the path that best serves you. And you are not alone. Conservative estimates show that at least 23.5 million American adults are living in recovery from alcohol or drug abuse, and this doesn't include all the teetotalers who just choose to not drink or use drugs in the first place.
Sometimes the real magic of thriving in sobriety comes when you actually decide you are done with drinking for good. When you know that door will never be opened again, you start to really understand your relationship to alcohol. The back and forth can be emotionally exhausting, and can take you away from doing the work you need to do. It goes back to the 100% Solution from Day 1—when you are not 100% committed to abstaining, you let the ongoing debate continue in your head.
However, when you decide you are never going back, the real you shows up. You cannot hide behind the hope that you will drink again, which frees you to deal with the emotions and fears that often accompany the plan to never drink again. And once you have overcome those, you truly are free to live a thriving life in sobriety.
### Thriving in Sobriety Through Cutting Back
In 1995 Audrey Kishline knew her drinking was a problem, and even though she had practiced abstinence at times, her goal was to cut back. After doing a lot of research, not only did she believe she could successfully do this, she founded Moderation Management, a group dedicated to helping teach others how to manage their drinking. Although the program grew quickly, she failed to apply the principles to her own life and drank more than she was "allowed." Eventually she drove while intoxicated and took the lives of Danny Davis and his twelve-year-old daughter.
Yes, you can successfully cut back your drinking for the rest of your life, but if that is your goal, we have some recommendations so your story doesn't end up mirroring that of Audrey, who went to prison, continued drinking (often heavily) throughout the rest of her life, and committed suicide in December 2014. First, you need to journal—specifically and honestly—about your experience with drinking. The nature of addiction is to trick you into thinking you are under control when you are not, which is why moderation doesn't work for so many people. If you decide to drink again, then take an analytical approach. Write down your experience—when you drink, how much you drink, and with whom. As long as you are honest, it will be clear whether you can successfully maintain a cutting-back approach.
Second, never drink alone. No exceptions. This is not healthy. And ideally don't drink at home either. Keep your home environment healthy and completely free from alcohol, if possible. When you limit your drinking to social situations outside of the home, it dramatically improves your ability to be successful in cutting back.
Third, pay attention to the quantity and alcohol content of what you drink, especially in relation to your new tolerance. Remember, when you stopped drinking for a while, you changed your tolerance. If you decide to drink the same amount of alcohol you did in the past, it can be very dangerous. Two drinks today, after a period of abstinence, might make you feel buzzed or even drunk. Pay special attention to serving sizes or measurements, because a bar might serve you a glass of wine that is between five and six ounces, but if you go to a party, you might be served a glass with ten to twelve ounces.
Fourth, avoid binge drinking situations and drinking practices that often accompany binge drinking. Don't do shots or put yourself with groups of people where most are going to be drinking excessively. It isn't fun, and you might even discover how dumb people are (and you were) when drinking excessively. It can easily trigger you to excessively drink. If you find yourself in these situations, don't drink at all—that way it is far less likely that you will "give in" and decide to go from two drinks to too many.
If you choose to drink, drink slowly. Take your time, and don't be afraid to not even finish your drink. If you are drinking something at room temperature such as red wine, sip it instead of going through drinks quickly like you did in the past. Your new approach should be very different from your old approach, and the best way to make sure you don't fall back to your old habits is to replace them with new healthy habits.
Last, notice if you seem to be craving alcohol. Cravings give you fantastic feedback because they let you know that you do not have a healthy relationship with alcohol. If you have cravings, it is time to abstain—you can always revisit cutting back as an option later on.
When you are really ready to have a healthy relationship with alcohol, the ultimate irony is that you won't care. The "take it or leave it" attitude will be fully entrenched, and it simply won't matter. Dave always felt very confident that he could have a drink on occasion and be completely fine, but he realized that he just doesn't care. However, he knows the people who love him care and would understandably be concerned, so he chooses to not drink. This choice is made even easier because alcohol no longer holds any power over his life.
### Deciding Your Approach
I continue to use the solutions I learned in The 30-Day Sobriety Solution to improve my connection to the person I want to be and know I can be. I move closer to that person every day.
—DAN
30-Day Graduate from Jackson, Wyoming
Think back to a serious past relationship that ended in a breakup, possibly after a lot of tough conversations and struggling back and forth. Maybe you were even engaged or living together at the time. After you broke up, how often did you see each other? Was it easier if you didn't see the other person at all, at least for a while? You would probably agree that seeing someone after a breakup isn't ideal.
The process of cutting back or quitting drinking is much like ending a serious relationship. In fact, it is sometimes much harder, as you try to integrate two identities that have been "battling" each other—the "sober you" and the "problem drinker you." Just like when ending a human relationship, if you keep feeding alcohol and hope to the "problem drinker you," you make moving on very hard.
However, if you don't see the other person again until years later, it is often much easier. Similarly, for cutting back to really be a successful option, you need a lot more than 30 days of abstinence. We recommend a minimum of six months. And most of our cutting-back success stories came after a year or more of no drinking. The best approach is to not worry about it. If you know you are not ready today, then decide now that you will revisit this question in one month, six months, or whatever amount of time feels right to you. But whatever time frame you decide on, stick to it.
So, your first action step after reading today's solution is to make this decision: Are you going to move forward with abstinence (at least for the near term) and revisit the question later? Are you going to move forward with abstinence as your long-term approach? Or are you going to see if cutting back is a long-term option for you—making sure to follow our recommendations?
### The Gift of Giving Back
This is the only perfection there is, the perfection of helping others. This is the only thing we can do that has any lasting value or meaning. This is why we are here. To make each other feel safe.
—ANDRE AGASSI
One of the most surefire ways to ensure your success and happiness in sobriety is to find a way to give back—especially to those who are struggling with some of the same challenges you have overcome, as well as to any of the many other worthy causes and individuals in need of support.
The Corporation for National and Community Service (CNCS) released a report indicating that "volunteering provides individual health benefits in addition to social benefits. This research has established a strong relationship between volunteering and health: those who volunteer have lower mortality rates, greater functional ability, and lower rates of depression later in life than those who do not volunteer."
When you offer to help others with no expectation for them to reciprocate, it has an incredibly powerful and positive impact in your life. All human beings—including you—have a core need to connect with others, and a great way to connect is by lending an unselfish hand. Dan Millman writes, "Find a form of service that calls to you, that suits your abilities, aptitudes, qualities, and interests, that makes time fly, that draws forth your best, that tells you you've arrived home and found yourself."
Your second action step for today is to decide how and where you want to give back. Use your list from the Positive Addiction Solution on Day 26 to see if any of the activities you have chosen involve giving back, or if you can choose to do them in a way that gives back. Take a minute and write down some things you would like to do over the next six months to contribute to the lives of others.
Giving back and being of service to others addresses another important need we have discussed—your serotonin deficiency in early sobriety. In The Power of Intention, Wayne Dyer writes, "Research has shown that a simple act of kindness directed toward another improves the functioning of the immune system and stimulates the production of serotonin in both the recipient of the kindness and the person extending the kindness. Even more amazing is that persons observing the act of kindness have similar beneficial results. Imagine this! Kindness extended, received, or observed beneficially impacts the physical health and feelings of everyone involved!"
Remember, you make a difference whether you want to or not. It just depends on whether you are going to make a positive or negative difference.
### Are You Moving Closer to or Farther from Your Next Drink?
It's easy to make things more complicated than you need to, when in fact the answer is right there. In the Attraction Solution on Day 19, we introduced you to the question "Am I moving closer to or farther from my next drink?" We recommend that you ask yourself this question at least once a week. When you consciously pay attention to where you are, especially in regard to the direction you are headed, it becomes surprisingly easy to catch yourself before it's too late. You might want to post this question on your bathroom mirror so you are sure to see it every day—especially when you are shaving or putting on your makeup before going out to a social event.
You can also ask yourself variations of this question in relation to each of your goals, relationships, and any other area of your life where you want to ensure that you are making progress. Am I moving closer to or farther from having the relationship I desire with my spouse/partner/child/parent? When your answers continue to show that you are moving away from your desired goal, you need to adjust your behavior.
If you are unsure, ask yourself this follow-up question: On a scale of 1 to 10, with 10 being high, how convinced am I that I will stay sober? To get even more clarity you can add a time frame to the end of the question, such as for the next day, the next week, or the next month. If your answer is less than an 8, there is reason for concern; however, not all 8s are created equal. For some of you an 8 might mean "very convinced," and for some of you anything below a 10 is a risk—so once again make sure you tailor this to your own unique rating system.
### Do You Miss Happy Hour?
My new drug is golf. It's my drug of choice. I also think that if I go back to using, all of this will go away. I'd rather have my big trailer.
—SAMUEL L. JACKSON
Some of the most successful and happy people we know allocate an hour of their day to themselves. Motivational speaker Tony Robbins refers to this as the "Hour of Power," where you integrate some of the most beneficial personal growth practices to help you gain clarity, appreciate the present moment, become more physically fit and vibrant, and get mentally prepared to take on your greatest challenges.
Now that you are almost done with The 30-Day Sobriety Solution, we highly recommend you implement a new kind of "Happy Hour" for your new life thriving in sobriety. And you can even start this hour at the same time you used to start drinking; however, many people also find doing this in the first hour of the day sets them up for success the whole day. We recommend you test both approaches and see what works best for you.
This hour can include a variety of different solutions you have done, or are already doing daily. For example, you may start with an integrated meditation practice for fifteen minutes, which includes meditation, visualization, gratitude, and sometimes asking yourself an important question. Then exercise for fifteen minutes, combining aerobic and strength training, while occasionally repeating one of your favorite empowering affirmations. And finish off the hour by making a simple and healthy breakfast, and—instead of watching the news, which is mostly negative—reading an inspiring book during or after eating.
Your third action step for today is to take a few minutes and design your new "Happy Hour." However, if this seems like a big-time commitment, start small. You can even start with just five minutes, five days a week, and then increase your time by five minutes every week. For example, the first week you might do a five-minute meditation, then the second week you add five minutes of exercise after your meditation, and the third week you add an additional five minutes to exercising. There is no right or wrong way; just get started.
### The Defining Characteristic of Thriving People
One defining characteristic of successful people is that they never stop growing and learning. They are continuously looking for ways to improve themselves both personally and professionally. In many ways the opposite of growth is stagnation and boredom, and when boredom lasts for too long, you are likely to seek out unhealthy ways to break free from it such as drinking, using drugs, overeating, gambling, inappropriate sex, and high-risk behavior like driving too fast. Successful people are rarely bored because they are constantly developing themselves physically, emotionally, and spiritually by reading, exercising, playing sports, playing an instrument, spending time in nature (which is rarely boring), traveling, attending workshops, and constantly working on the fulfillment of their most meaningful and heartfelt dreams. Most importantly for you, in relation to The 30-Day Sobriety Solution, we recommend you keep revisiting and working the solutions on a regular basis.
This doesn't mean that you have to engage with the same level of time and effort you have for these last 30 days, but it does mean that continual personal growth has to be part of your life moving forward. The great news is that there are countless fun ways to continue to bring personal growth into your life. Here are some suggestions.
• Repeat The 30-Day Sobriety Solution. We regularly hear comments like this one, "The third time through the program was amazing." Doing the program again will help you better integrate the tools and techniques into your life, overcome other addictive behaviors (smoking, overeating, gambling, prescription medications, and so forth), and more importantly, result in additional breakthroughs. We know some people who have done the complete program four times, and others who have repeated the same day ten times. Repetition adds value!
• Read memoirs of people in recovery. Many of the high-profile quotes in this book come from memoirs. When you read other stories of recovery and success, you will have insight into your own story. To make best use of these books, take notes, and spend some time journaling about a particular person's story and what really affected you and why. We have included a list of our favorites on today's companion website.
• Read self-help books and books about the lives of people you admire. We have referenced a lot of our favorite books throughout this program that can add incredible value to your life. You can also read autobiographies of the people you most admire and respect. Take notes, and apply at least some of what you learn. There is also a list of our recommended self-help books on the companion website.
• Attend conferences, workshops, retreats, and seminars. A live training facilitated by experienced instructors can be one of the best investments you ever make. When you are able to learn and apply great content in a group setting, it can lead to incredible growth, inspiration, and also new friends for life. Some of our best friends today are people we met in training seminars we attended. A list of our favorite conferences, workshops, retreats, and seminars is included on today's companion website.
• Remain teachable and open. In life, you will sometimes be a teacher, but you always need to be a student. If you are not willing to learn from others and to look at things from a different perspective, you will stop growing. On the companion website we have included a list of other ways you can continue to grow.
• Make your car your college. If you spend more than ten minutes commuting a day, use some of this time to listen to inspirational and educational CDs, podcasts, or audiobooks. Some of our favorites are listed on today's companion website.
• Don't let the top two "sobriety killers" creep into your life. Although we have mentioned various "sobriety killers" throughout the program, there are two that we regularly see lead people back to excessive drinking—boredom and loneliness (or isolation). Revisit the 101 New Activities list and pick something new to do every day or week. And we have some information on how to join or start up your own mastermind group on the companion website.
### Day 30 Action Steps
Before success comes in any man's life, he is sure to meet with much temporary defeat, and, perhaps, some failure. When defeat overtakes a man, the easiest and most logical thing to do is to quit. That is exactly what the majority of men do. More than five hundred of the most successful men this country has ever known told the author their greatest success came just one step beyond the point at which defeat had overtaken them.
—NAPOLEON HILL
• Decide on your plan. Write down what your strategy is for the next 30 days regarding drinking—specifically stating whether you are going to cut back or abstain. If you have decided to abstain for the short term (instead of the long term), how long will you "test" this approach out before revisiting? If you decide cutting back is your plan, make sure you review and use the guidelines we covered for this approach.
• Write down how and where you want to give back. Pay attention to what type of activities fit your strengths, qualities, passions, and interests, and pick one or more ways that you would like to contribute and give back over the next six months.
• Design your new "Happy Hour." Start a daily ritual dedicated to your overall health, wellness, and vitality that includes the solutions we have covered in this book—such as meditation, visualization, exercise, practicing gratitude, and eating healthy. This is best done at the start of the day. Begin with just five minutes a day, five days a week, and add additional time each week until you have built up to a full hour. Consider starting this new routine the same time you used to start drinking.
• Review your "before you" and your before photo, and keep journaling. Take a minute and acknowledge how far you have come since you started the program. It is human nature to focus on the gap between your ideal vision and your actual results and overlook what you have accomplished and how far you have actually come, so go back in your journal and read the "before you" exercise that you did on Day 2. Also look at the photo you took of yourself from Day 1, and consider taking a picture of yourself today and see if you notice any positive differences (less bloating, clearer eyes, healthy skin). Last, but not least, we want to remind you to keep journaling, at least every few days. It doesn't have to be a lot, but a life worth living is a life worth recording. Journaling provides constant insights and is a way for you to see who you are today and how far you've come on your journey of thriving in sobriety.
As you finish the final sections for today be sure to celebrate your successful completion—it takes an extraordinary amount of dedication and perseverance to work through all the content and action steps, and you should be incredibly proud. So right now take a moment, shut your eyes, take a deep breath, and really acknowledge and appreciate yourself for all that you have accomplished over the course of this program. As always, you can find the companion website for today at <http://Day30.Solutions>, where we list some of our favorite books, CDs, and trainings. In addition, we have included our favorite solutions, tools, and resources from The 30-Day Sobriety Solution that you can use to easily continue moving forward.
## WRAPPING UP THE 30-DAY SOBRIETY SOLUTION—NOW WHAT?
The 30-Day Sobriety Solution helped me accomplish so many goals and "firsts" in my life, such as my first sober birthday as an adult. This success helped me believe that I don't need alcohol to celebrate special occasions, even New Year's Eve and the Fourth of July—two holidays I was certain I needed to drink to enjoy.
—BYRON
30-Day Graduate from Phoenix, Arizona
You are about to embark on an amazing year, one that will surely include some memorable and exciting moments, as well as some challenging and tough ones. And mixed within these moments will be a year full of firsts. This might include your first birthday as an adult without drinking, or the first Christmas, Fourth of July, Thanksgiving, or wedding anniversary where you are not drunk. Each first brings you one step closer to becoming the person you want to be and are meant to be. Each first brings you closer to the life you always knew, deep down, you could live.
By today, you know how far you have come; you, and others around you, can see the transformation you have made in just 30 days. Or perhaps you may not be so sure. You might feel a little different and notice you are thinking somewhat differently, but you are not sure if you have really changed that much. Our experience is that the transformation does happen—almost without fail—as long as you do the work we have outlined. However, for some people it works more quickly, maybe because they have already done a lot of personal growth work or have a less challenging history to deal with. And for others, it just takes a little longer to get the level of honest self-awareness necessary to really break through and overcome some of the limiting patterns that have been in place for decades.
One day in the near future, you will look back and surprise yourself. You will think back to the person you were in the past, and you won't recognize that person. You will realize that all your work and faith paid off, and that each little change you made added up over time to completely transform who you are for the better.
The only thing that can hold you back from experiencing this transformation is giving up. Remember, our greatest triumphs often come after our darkest and most challenging moments—as if the universe is saying, "I am going to give them one last huge test to make sure they are really serious." And when you pass that test, all of a sudden you go from feeling like a fish out of water to swimming with the current.
You find that a sense of natural congruency exists—starting with your core values and continuing through your thoughts, beliefs, feelings, and actions—that leads to the outcomes you want and expect. You discover that you can actually listen to and trust your intuition, and you no longer struggle with erratic emotions, negative thinking, and the overwhelming bouts of sadness and disappointment you experienced when drinking.
Instead you are able to quickly notice and identify when you have a setback, what the root cause is, appreciate it for the lesson it teaches you, and then overcome it. You find that so many of the tools and techniques you learned have not only helped you to thrive in sobriety, but have led to better relationships with your loved ones, better finances, more career opportunities, new friendships, and on top of that, you are the healthiest you have been in many years.
As you move forward beyond today, know that your future will take care of itself as long as you take care of the present. Achieving success and thriving in sobriety is an exciting journey—enjoy every moment of it! It has been an honor and a privilege to be your guides up to this point, and we eagerly look forward to the day where our paths cross and we have the opportunity to get to know one another. Here's to your new life thriving in sobriety!
Jack Canfield and Dave Andrews
## THE 30-DAY GRADUATES
#### Share Your Story
Once you have successfully completed The 30-Day Sobriety Solution, we would love to hear from you—not only your stories of success, but also your challenges and anything that was difficult for you. Let us know how you are doing, what solutions were the most valuable for you and why, what was the most difficult for you and why, as well as anything else you would like us to know.
Nothing is more powerful than a true story—your story—to inspire others. When people read about others like themselves who have successfully faced and overcome the same challenges and obstacles they are faced with, they become inspired and they start to believe—not only that it is possible to change, but that they can change. But this can only happen if people like you share their stories, just like the courageous people whose stories we included in this book. In fact, you might have even decided to buy this book because you read one of the testimonials we included in the front of the book or one of the stories in the book itself.
Whatever "your" story is, it might be exactly what someone else needs to hear in order to inspire him or her to take that first step.
To share your story of hope, courage, and recovery—please go to the companion website at <http://30DaySuccessStories.com> or simply email your story to SuccessStories@The30DaySolution.com. Please be assured that by sharing your story you are not giving us permission to publish it. Our staff will review it and, if we are interested in publishing it, we will contact you for approval, including the option to share your story anonymously.
Website: http://30DaySuccessStories.com
Email: SuccessStories@The30DaySolution.com
## ACKNOWLEDGMENTS
#### Our Mutual Acknowledgments
Stephen Hanselman, our literary agent at LevelFiveMedia, who believed in this book when many others didn't. Steve has been described as "the agent every writer dreams of having." We agree. Your friendship, faith, expertise, and guidance are so appreciated.
Julia Serebrinsky, who helped edit the original book proposal.
Judith Curr, president and publisher of Atria Books, who immediately caught the vision of what we were doing and championed the book.
Leslie Meredith, our editor at Atria, for your honest and thoughtful feedback and your commitment to delivering excellence. Your contribution and insight were indispensable.
Jennifer Phelps, for your incredible dedication and commitment to this project. You did it all: editing, fact-checking, rewrites, and even helping us maintain the woman's perspective throughout. Your excellent writing ability and being willing to go the extra mile no matter what are what kept us sane, especially during the last couple of weeks of the editing process.
Tehsin Gul, from Pakistan, who designed the original cover concept for the book, and all the other great designers who submitted their cover designs on 99designs.com.
Steve Harrison, co-owner of Bradley Communications, for introducing us to each other.
Anoop, Anya, Brad, Brian, Cheryl, Christina, Christopher, Forrest, Jerry, Karla, Lenore, Liz, Meg, Nathalie, Pat, Sheira, Tamara, and Teresa—the wonderful group of eighteen people who read the first draft of the book, completed all the exercises, validated that the program worked in the form of a book, and gave us valuable feedback for improving it. Thank you all for your time, your courage, and your commitment.
Ann, Byron, Chris, Dan, Desiree, Diane, Hannah, James, Jessica, John, Matthew, Mike, Robert, Susan, and Thomas—for so courageously sharing your stories of success in quitting and cutting back drinking with us. Even though your names have been changed, you know who you are. Your willingness to openly and honestly share your experience with The 30-Day Sobriety Solution has been invaluable in assisting us to reach and help others, and we are forever grateful for you agreeing to be part of this book.
#### Jack Canfield's Acknowledgments
Dave Andrews, for originally creating "The 30-Day Sobriety Solution" online coaching program, on which this book is based. Your decision to integrate the best ideas and techniques from the human potential movement with the best from the recovery movement was a needed breakthrough whose time had come. I have enjoyed the process of writing this book with you—all of it, from the late night conversations to the silly humor that kept us sane. You have been great to work with.
My wife, Inga, who bravely put up with the long hours and several lost weekends, especially between Thanksgiving and Christmas, when the final push was on to finish the book. I appreciate how you not only didn't complain (too much!), but you also went out of your way to lovingly support me by scheduling massages, doing all the shopping, and doing more than your fair share of cooking and cleaning up.
Patty Aubery, my partner and co-CEO of the Canfield Training Group, for running the company virtually by herself for the months I was completing the book, and for always being there to encourage me to keep going when I feel tired or overwhelmed. Thanks for always believing in me and demanding my best even when I can't yet see it.
Veronica Romero, my personal assistant and office manager for the Canfield Training Group, who took care of virtually everything else for months, in addition to helping with typing, photocopying, scanning, faxing, and emailing chapters back and forth between Dave and me, and who oversaw getting all the permissions for the cartoons that appear in the book.
Lisa Williams, our director of marketing, and Lexi Wagner, who are responsible for all the marketing, PR, and social media (Facebook, Twitter, Pinterest, and YouTube) as well as publishing our biweekly Success Strategies ezine, which keeps everyone informed and excited about all our projects, including this book.
Russ Kamalski, our COO, who worked tirelessly with Patty to create our Train the Trainer Home Study Program while I was writing this book. Your ability to pull this off with minimal input from me during the video editing process is what allowed me to focus on this book.
Jesse Ianniello, Donna Bailey, Teresa Collett, Alice Doughty Refauvelet, Andrea Haefele, Kajsa Garrett, Jody Schwartz, and Dwain Jeworski—the rest of my staff, who kept the ship running while I was buried in this project.
Janet Switzer, for doing a great deal of the final editing and proofreading of the Tenth Anniversary Revised Edition of The Success Principles: How to Get from Where You Are to Where You Want to Be, which allowed me to finish writing this book.
Kathleen Seeley, our senior associate trainer, whose commitment and creativity in helping Patty Aubery redesign our live Train the Trainer Program and helping with the online Train the Trainer Program allowed me to focus on The 30-Day Sobriety Solution.
Kim Kirberger, my sister and the coauthor of most of the Chicken Soup for the Teenage Soul books, who read a lot of the manuscript and provided valuable feedback.
Oran, Christopher, and Riley, who have all had to deal with their own battles with drugs and alcohol, and have emerged victorious. I have learned a lot about courage, commitment, and perseverance from you. I appreciate having shared parts of the journey with you.
#### Dave Andrews's Acknowledgments
In the summer of 2008, as I was listening to Tony Robbins's Personal Power II while driving to a class for my master's degree, I asked myself a question that changed my life—Why don't they teach this to people in recovery? With the recent passing of a friend of mine who took his life while in recovery, I knew there had to be a better answer. At that moment I decided to create the program that came to be called "The 30-Day Sobriety Solution," and ultimately this book. I called my wife, Anya, and shared the idea with her, and she loved it. I want to thank the following:
Anya, who believed in me when I no longer believed in myself. You stood by me when most would not. Without you not only would this program not exist, but I am not even sure I would be alive. Thank you for being able to see the "real me" hiding behind my addiction. You are my best friend and my soul mate, and I am the luckiest person in the world to get to spend the rest of my life loving you.
Briana and Ella, my two amazing daughters, who have brought more joy, pride, and love to my life than I ever dreamed possible. You have taught me more than I can ever teach you, and I am in awe that I get to be your father. Briana, your courage and intuitiveness at the young age of five to tell me you thought I was going to die finally woke me up to the ultimate cost of my drinking. Ella, your spirit and energy remind me of myself as a child, and your enthusiasm, talent, and generosity are an inspiration to me every day.
Bryan Duke, who is one of the most charismatic people I have ever met. Without you I would never have had the insight and dedication to search for answers like the ones included in this program. Your memory will never be forgotten, and I only hope your family, and your two children, can find some peace that your passing helped inspire The 30-Day Sobriety Solution.
Jack Canfield, who courageously agreed to partner with a first-time author because he believed in me and my vision. Wow, working with you has been a dream come true. Your passion and commitment to making a difference in this world are unmatched. The last few weeks of this project were awe inspiring, as I watched you work "magic" on the final edits, all while putting in sixteen-plus-hour days. Even though the final push was exhausting and intense, it was incredibly rewarding, and your sense of humor helped keep us sane.
Chris, who was the first person to complete "The 30-Day Sobriety Solution." You were my "light" when I lost my way. Every time I doubted myself, or the program, you were always there reminding me of the impact it had in your life. I will always be grateful for you finding my website that one day many years ago, and forever changing both of our lives.
All the people whom I have coached, everyone who has worked their way through "The 30-Day Sobriety Solution," and everyone who has listened to my interviews, read my blog posts, and watched my videos. Your transformational stories, many of which are in this book, have been my sustaining inspiration. You have all played a role in this book being published, and your invaluable feedback has allowed me to make this program much more effective and even better than I thought possible.
Advocates for Recovery (AFR) and executive director Tonya Wheeler, whom I consider it an honor to know and serve on the AFR Board with, as well as the great team, including Heidi Williams and Suquana Charley. And to the rest of the AFR Board, who are my friends and role models: Merlyn Karst, Sarah Roisman, Juli Edwards, Bert Singleton, and Megan Marx. You all are such a positive force in the world of recovery.
Young People in Recovery (YPR) and president and CEO Justin Luke Riley, whose commitment and leadership skills are an inspiration. It has been an honor and privilege to get to know you and serve on the Board of YPR. You are truly the voice of your generation's recovery movement. And to Doug Rudolph and AJ Senerchia at YPR, who are leading the way by changing the youth recovery landscape.
Tony Robbins, whom I started listening to in my late teenage years. Your passion and life-changing content breathed life into the idea to create this program, and ultimately this book. I am forever indebted to you, and to so many other amazing teachers we quote from and mention in The 30-Day Sobriety Solution, for providing me the information, tools, and techniques I needed to not just change my life, but to help facilitate change in others.
Alcoholics Anonymous (AA), which helped me finally overcome the incredible guilt and shame I felt about my drinking and started me down the path to actually believing I could be happy sober. You have ensured that anyone who is suffering from alcoholism can find free support in almost any decent-sized city around the world. Thank you.
Art and Mike, my first two sponsors in AA, who helped me embrace the power of journaling and are amazing sober role models, and Jim for helping me find my way to them. And every other sponsor in AA who so unselfishly gives their time, compassion, shared personal experience, and wisdom to help others find a way to the other side of addiction.
Oran Canfield, who encouraged me one last time to reach out to Jack regarding this book, after I had all but moved on from the possibility.
Judy, my mom, who has always been there for me no matter what. Your lifelong commitment to helping others has always served as a positive example for me to follow. My childhood is full of wonderful, loving memories with you, and you instilled in me a lifelong desire to grow and learn that eventually helped carry me to the other side of my alcoholism. Your encouragement and support have never faded, and your detailed feedback on virtually every solution in The 30-Day Sobriety Solution is something I will never forget. And to your husband, Norm, my stepdad, who always taught me to do what is right, regardless of what others around me are doing.
Peter, my dad, who taught me one of my most important life lessons. When I was a young child, you came out in a society that discriminates and modeled to me what real courage is. You taught me how important it is to never be afraid to be true to who you are. And to Ron, for being such a loving life partner to my dad. It has truly been a gift to watch your love and commitment to each other grow deeper every year.
Mike, my brother, who has been a positive role model to me my whole life. You, more than anyone, have taught me how to live a life in alignment with my core values. Your passion for fighting for just and equal rights is a gift to this world. I am incredibly lucky to have you and your amazing life partner, Carol, as family. You both serve as moral and ethical compasses in my life.
Anne, my aunt, who I know is watching over our family. I will always remember your infectious laugh and your smile that could light up a room.
Ernie, Ruth, Leo, Lorraine, and Jan, my grandparents, who each helped make this book a possibility in one way or another. In particular, at Ernie's funeral service, I had the important realization and clarity that no matter what challenges I faced, I had to publish "The 30-Day Sobriety Solution" as a book so that I could reach more people who were searching for alternative answers for a way to thrive in sobriety.
Al and Donna, my in-laws, who embraced me as their daughter's boyfriend right from the start. You introduced me to so many of the amazing authors, such as Og Mandino, that we included in this book. And you have always been so supportive and loving. Thank you. I could never have asked for better in-laws.
Ryan, my brother-in-law, who is the younger brother I never had. It amazes me that I have known you since before you were even in high school. You are an amazing man and I feel lucky to have you in my life!
Jillian and Ana Lucia, my two nieces, who inspire me with their love for life. I love you both and only hope that your generation struggles less from addiction than mine.
My wonderful dogs and cats, past and present. I especially have to thank my dogs, because every time I had writer's block, had too much pent-up energy, or just needed to let off some steam, my dogs were always there for me, even if they were sometimes annoyed by the attention.
Starz, which created a wonderful culture and work environment, with so many great people. You provided a positive time and place where I was able to finally turn my life around. Leaving Starz to follow my passion with the work I do full-time today was one of the hardest decisions I have ever had to make.
Jon Seashore, Chris Yonker, Denise Winston, Adam Carroll, Tracy Cook, James Ross, Chris Winters, Josh Kauffman, Dan Markel, Gabriel Dicristofaro, Sean Marshall, Nancy McCaughey, Brian Gretz, Michael Casey, Ryan Judd, and Jeff Hill, who are some of my mastermind group members, past and present. You made sure that I could imagine persevering past another obstacle when I couldn't imagine doing so. And so many others, including the wonderful PSI community in Colorado that Dan Gibbons helped create and foster for decades. Your role in the publishing of this book will never be forgotten.
## 30-DAY RESOURCES
We know that cutting back or quitting drinking can be a challenging, lonely, and scary process. The following resources are available to help you succeed. To get the most up-to-date information on current 30-Day Resources, visit <http://30DayResources.com> or call us toll free at 1-844-My30Day (1-844-693-0329).
#### Private Coaching
When it comes to successfully cutting back or quitting drinking, and creating the results you desire in every area of your life, having your own personal coach will help you produce extraordinary results far more quickly than doing it on your own. That's why we developed an exclusive coaching program centered on The 30-Day Sobriety Solution, specifically designed to help you overcome sobriety-related challenges, and lead you to a life thriving in sobriety—one where you can finally achieve breakthrough success in accomplishing all your dreams, including attaining greater financial wealth, greater health and fitness, greater passion and joy in your relationships, or overall greater happiness and fulfillment.
To learn more, see: <http://30DayResources.com/Coaching> or call us toll free at 1-844-My30Day (1-844-693-0329).
#### Live Trainings and Workshops
If you could wave a wand and magically transform one thing in your life, what would it be? Would you remove the desire to drink? Wake up excited for the day ahead and full of gratitude for the joy and abundance in your life? Lead a life of service, helping others overcome some of the same challenges you have faced, while still making enough money to support your dreams? Enjoy more loving and intimate relationships with your spouse, family, and friends—that don't include drinking?
All of these things are possible, and much more. However, there is no magic wand. To create your ideal life requires time, effort, and energy. The good news is, there's a simple way for you to dramatically accelerate your journey and get big results fast. It is a live training called Breakthrough to Sobriety.
By delivering the most effective and life-changing teachings and techniques from The 30-Day Sobriety Solution in a positive, inspiring, and private environment with other enthusiastic, growth-focused individuals, the Breakthrough to Sobriety training will help you finally achieve the lasting results you desire.
To learn more, see: <http://30DayResources.com/Training> or call us toll free at 1-844-My30Day (1-844-693-0329).
#### Online Training
Are you looking for additional support, resources, and accountability to help you learn and apply the 30-Day sobriety solutions in your life? Do you want to take your sobriety, and your success, to the next level? By leveraging the flexibility, privacy, and power of the internet, we have created several online trainings that perfectly complement The 30-Day Sobriety Solution and your goal to cut back or quit drinking, or to get reinspired in recovery.
To learn more about these online trainings, see: <http://30DayResources.com/OnlineTraining> or call us toll free at 1-844-My30Day (1-844-693-0329).
#### Hire Jack or Dave to Speak
Whether you are looking for an inspiring, fun, and thought-provoking keynote speaker for your conference or organization, or you are seeking a more interactive experience, with customized exercises and activities that meet your needs, Jack and Dave are both able to deliver this to your audience.
To learn more about the presentation formats, including keynote, training, and group facilitation options, see:
<http://the30daysolution.com/speaking>
or
www.JackCanfield.com/book-jack
#### Employee Assistance Programs
The cost of excessive alcohol consumption in the United States has reached a staggering $223.5 billion, which largely comes from losses in workplace productivity (approximately $160 billion) and health care expenses for problems caused by excessive drinking (approximately $24 billion). With numbers like these, it is critical that employers offer a variety of solutions to employees to help them overcome problem drinking, especially cost-effective solutions like The 30-Day Sobriety Solution.
To learn more about The 30-Day Sobriety Solution Employee Assistance Program, and how you can bring it to your company, see: <http://30DayResources.com/eap> or call us toll free at 1-844-My30Day (1-844-693-0329).
## ABOUT THE AUTHORS
JACK CANFIELD, known as America's #1 Success Coach, is a bestselling author, professional speaker, trainer, and entrepreneur. He is the founder and CEO of the Canfield Training Group, which provides training and multimedia programs on personal transformation, leadership, motivation, self-esteem, and peak performance, and how to accelerate the achievement of one's personal and professional goals. He has conducted live training for more than a million people in more than forty countries around the world. He holds two Guinness World Record titles and is a member of the National Speakers Association Speaker Hall of Fame.
Jack is the coauthor and editor of more than two hundred books, including The Success Principles: How to Get from Where You Are to Where You Want to Be, The Success Principles for Teens, Tapping into Ultimate Success, Coaching for Breakthrough Success, The Success Secret, The Power of Focus, The Aladdin Factor, Jack Canfield's Key to Living the Law of Attraction, and the Chicken Soup for the Soul® series, which includes forty New York Times bestsellers and has sold more than five hundred million copies in forty-seven languages around the world.
Jack is a featured teacher in the movie The Secret, and has appeared on more than a thousand radio and television shows, including The Oprah Winfrey Show, the Today show, Fox & Friends, Larry King Live, and the NBC Nightly News and the CBS Evening News.
Jack's coaches at Jack Canfield Coaching (www.canfieldcoaching.com) have provided one-on-one breakthrough success coaching to more than four thousand people in eighty countries.
Jack is the founder and chairman of the board of the Transformational Leadership Council, a professional association for owners of transformational training and coaching companies and thought leaders in the field of personal and organizational transformation.
To find out more about Jack's other books, audio programs, and live training, including his flagship Breakthrough to Success training and his Train the Trainer program, contact his office at:
The Canfield Training Group
PO Box 30880
Santa Barbara, CA 93130
www.jackcanfield.com
Phone: 805-563-2935
Email: info@jackcanfield.com
www.facebook.com/JackCanfieldFan
<https://twitter.com/jackcanfield>
DAVE ANDREWS is an author, speaker, and sobriety coach who has been a featured "sobriety expert" on more than fifty national and international talk shows. After suffering for over a decade as an alcoholic, putting his work, his marriage, his hopes and dreams, and his life at risk, he was finally able to triumph over addiction. He is one of the world's leading experts in helping others recover, reclaim, and reinvent their lives without alcohol, freeing them to live a thriving life in sobriety.
As "America's #1 Sobriety Coach," Dave specializes in coaching people in early sobriety. With over six years of experience as a sobriety and life coach, Dave focuses on eliminating addictive behaviors and paving the way for positive change. He gets to the underlying causes of what holds people back, providing them with a road map for creating permanent breakthroughs.
Dave is a certified comprehensive positive psychology coach, a certified neurolinguistic programming (NLP) private practitioner Level 1, and a certified strategic intervention coach and marriage educator by the Robbins-Madanes Center for Strategic Intervention.
Dave is the CEO of The 30-Day Solution, LLC, and serves on the board of directors of the nonprofit organizations Young People in Recovery and Advocates for Recovery. He currently resides outside of Denver with his wife and two daughters, and has been sober for more than eight years.
To find out more about Dave's recovery resource offerings, including live training and speaking engagements, or to hire Dave as your personal sobriety coach, contact his office below.
To learn more about how you can help expand the reach of The 30-Day Sobriety Solution, including bringing The 30-Day Sobriety Solution Employee Assistance Program to your company, contact info@the30daysolution.com or see more at <http://30DayResources.com/eap>.
The 30-Day Solution, LLC
6590 South Vine Street, Suite 112
Centennial, CO 80121
www.TheSobrietySolution.com
Phone: 1-844-My30Day (1-844-693-0329)
Email: info@thesobrietysolution.com
<https://twitter.com/30daysolution>
<https://www.facebook.com/The-30-Day-Sobriety-Solution-560365707446211/>
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## PERMISSIONS
© Mike Baldwin/Cornered
© 2011 by Randy Glasbergen. www.glasbergen.com
© Stock photo sellingpix
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Reprinted with Permission
David Ian Babb
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Phil Selby
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## NOTES
Getting Started
1. From an interview on the Today show, September 2010.
2. Marissa B. Esser et al., "Prevalence of Alcohol Dependence Among US Adult Drinkers, 2009–2011," Preventing Chronic Disease 11, no. E206 (November 11, 2014): 1–11, doi:<http://dx.doi.org/10.5888/pcd11.140329>.
3. Dotson Rader, "He Found His Voice," Parade, January 9, 2005.
4. For a list of various books, studies, articles, and other programs that advocate cutting back on drinking, see <http://the30daysolution.com/cuttingbackfootnote>.
5. Demi Lovato, "Sober Is Sexy!" Seventeen, August 6, 2011, www.seventeen.com/health/tips/demi-lovato-sober-is-sexy.
PHASE I: MASTERING THE ABSOLUTE BASICS TO GET FROM WHERE YOU ARE TO WHERE YOU WANT TO BE
Day 1: The 100% Solution
1. Manning Marable, Leith Mullings, et al., Let Nobody Turn Us Around: Voices on Resistance, Reform, and Renewal: An African American Anthology (Lanham: Rowman & Littlefield Publishers, 1999) or also see www.goodreads.com/quotes/199214-take-the-first-step-in-faith-you-don't-have-to.
2. Jack Canfield and Mark Victor Hansen, Chicken Soup for the Soul (Deerfield Beach, FL: Health Communications, 1993).
3. Stephen King, On Writing (New York: Scribner, 2000).
4. See Dr. Gail Matthews's research on the factors that accelerate goal setting achievement at www.dominican.edu/academics/ahss/undergraduate-programs-1/psych/faculty/fulltime/gailmatthews/researchsummary2.pdf.
5. See www.glamourmagazine.co.uk/celebrity/celebrity-galleries/2011/01/teetotal-celebrities#!image-number=8.
6. For a list of various books, studies, articles, and other programs that advocate cutting back on drinking, see <http://the30daysolution.com/cuttingbackfootnote>.
7. For the full definition, see www.thefreedictionary.com, s.v. "sobriety."
8. John Assaraf and Murray Smith, The Answer: Your Guide to Achieving Financial Freedom and Living an Extraordinary Life (New York: Simon & Schuster, 2008).
9. Jack Canfield and Janet Switzer, The Success Principles (New York: HarperCollins, 2015).
10. Josh Hamilton, Beyond Belief: Finding the Strength to Come Back (New York: Faith Words, 2008).
11. Patrick Swayze and Lisa Niemi, The Time of My Life (New York: Atria Books, 2009).
12. David Hinckley, "Average American Watches 5 Hours of TV per Day, Report Shows," New York Daily News, March 5, 2014, www.nydailynews.com/life-style/average-american-watches-5-hours-tv-day-article-1.1711954.
13. You can easily access the companion website for The 30-Day Sobriety Solution for any day by following the easy-to-remember format: http://Day##.Solutions. For example, today is <http://Day1.Solutions> and tomorrow is <http://Day2.Solutions>. These are not case sensitive, so uppercase or lowercase is fine. The companion website is a great way to access the most up-to-date resources, exercises, and audio recordings to help you thrive in sobriety.
Day 2: The Purpose Solution
1. Tony Robbins, Money: Master the Game—7 Simple Steps to Financial Freedom (New York: Simon & Schuster, 2014).
2. Ayn Rand, The Fountainhead (New York: Penguin Books, 1943).
3. For more information on how the subconscious mind works, see Irene Colville, "Does the Unconscious Mind Hear Negatives?" Center for Counseling and Hypnosis, www.hypnocenter.com/articles/does-the-unconscious-mind-hear-negatives-.
4. See www.goodreads.com/author/quotes/38285.C_G_Jung.
5. T. Harv Eker, Secrets of the Millionaire Mind: Mastering the Inner Game of Wealth (New York: HarperCollins, 2005).
6. Paulo Cohelo, The Alchemist (New York: HarperCollins, 1993).
7. To read more about Naomi Campbell, see www.bangshowbiz.com/products/showbiz/index.html?id=2010244175518187104&ch=Showbiz.
Day 3: The Pendulum Solution
1. Lao Tzu, Tao Te Ching, translated by Jonathan Star (New York: Penguin, 2001).
2. See www.imdb.com/title/tt0416449/news?year=2012.
3. Andre Agassi, Open (New York: Random House, 2009).
4. Brené Brown, I Thought It Was Just Me (New York: Penguin Group, 2007).
5. See <http://thinkexist.com/quotation/character_cannot_be_developed_in_ease_and_quiet/13579.html>.
6. See www.goodreads.com/author/quotes/399.Napoleon_Hill.
7. Sigmund Freud, Beyond the Pleasure Principle translated by James Strachey (Seattle: Pacific Publishing Studio, 2010).
8. William Glasser, MD, Positive Addiction (New York: Harper & Row, 1976).
9. See www.goodreads.com/author/quotes/33117.Drew_Barrymore.
10. E. Tory Higgins, "Beyond Pleasure and Pain," American Psychologist, December 2007.
11. Charles Duhigg, The Power of Habit: Why We Do What We Do in Life and Business (New York: Random House, 2012).
12. Eric Clapton, Clapton: The Autobiography (New York: Broadway Books, 2007).
Day 4: The Forgiveness Solution
1. Lewis B. Smedes, The Art of Forgiving: When You Need to Forgive and Don't Know How (Nashville: Moorings, 1996).
2. Stephanie Sarkis, "30 Quotes on Making Mistakes," Psychology Today, September 30, 2011, www.psychologytoday.com/blog/here-there-and-everywhere/201109/30-quotes-making-mistakes.
3. To read more about how guilt and shame lead to relapse, see Maia Szalavitz, "Being Ashamed of Drinking Prompts Relapse, Not Recovery," Time.com, last modified February 7, 2013, <http://healthland.time.com/2013/02/07/being-ashamed-of-drinking-prompts-relapse-not-recovery>.
4. Thanks to John Gray and Barbara DeAngelis, who first taught us this process.
5. Stephen M. Silverman, "Ewan McGregor Reveals Battle with Alcohol," People, July 5, 2005, www.people.com/people/article/0,,1079768,00.html.
6. See Stephanie Sarkis, "30 Quotes on Forgiveness: Ponder These Words of Wisdom," Psychology Today, February 1, 2011, www.psychologytoday.com/blog/here-there-and-everywhere/201102/30-quotes-forgiveness.
7. John Green, The Fault in Our Stars (New York: Dutton Books, 2012).
8. See <http://thedailylove.com/todays-quotes-forgive-them-and-let-it-go>.
9. Tony Robbins, "Stop Your Limiting Beliefs: 10 Empowering Beliefs That Will Change Your Life," The Anthony Robbins Blog, August 1, 2013, <http://training.tonyrobbins.com/stop-your-limiting-beliefs-10-empowering-beliefs-that-will-change-your-life/>.
10. Kristen Johnston, "Guest Post," Veronicavalli.com, February 5, 2014, <http://veronicavalli.com/2014/02/guest-post-by-kristen-johnston/>.
11. See <http://thedailylove.com/are-you-trying-to-change-someone-2/>.
12. Kamal Ravikant, Love Yourself Like Your Life Depends on It (CreateSpace Independent Publishing Platform, 2012).
13. The Anonymous People is a film by director Greg Williams about the 23.5 million Americans living in long-term recovery from addiction to alcohol and drugs. You can also rent it and watch it online at Amazon.com, Netflix, iTunes, and Vudu.
Day 5: The Believe-in-Yourself Solution
1. See www.goodreads.com/author/quotes/69188.Frank_Lloyd_Wright.
2. To read more about expectancy theory, see <https://wikispaces.psu.edu/display/PSYCH484/4.+Expectancy+Theory>.
3. Brooke Hauser, "Blake Lively: Her Allure Photo Shoot," Allure, October 2012, <http://www.allure.com/celebrity-trends/cover-shoot/2012/blake-lively>.
4. See "Powerful Placebos," The Wellness Chronicle 2, no. 2 (December 15, 1998), <http://medicine.creighton.edu/wellness/V2N2/V2N2.htm>.
5. See Sandra Blakeslee, "Placebos Prove So Powerful Even Experts Are Surprised: New Studies Explore the Brain's Triumph over Reality," New York Times, October 13, 1998, www.nytimes.com/1998/10/13/science/placebos-prove-so-powerful-even-experts-are-surprised-new-studies-explore-brain.html.
6. See J. Bruce Mosely et al., "A Controlled Trial of Arthroscopic Surgery for Osteoarthritis of the Knee," New England Journal of Medicine 347 (July 11, 2002): 81–88, www.nejm.org/doi/full/10.1056/NEJMoa013259#t=article.
7. Steven Locke and Douglas Colligan, The Healer Within: The New Medicine of Mind and Body (New York: Plume, 1997).
8. King, On Writing.
9. Aly Weisman, "14 People Who Failed Before Becoming Famous," Business Insider, February 20, 2014, www.businessinsider.com/people-who-failed-before-becoming-famous-2014-2?op=1.
Day 6: The Outcome Solution
1. Canfield and Janet Switzer, Success Principles.
2. To read more about Kristin Davis, see Barbara Ellen, "Charlotte's Web," Observer, February 10, 2002, www.theguardian.com/theobserver/2002/feb/10/features.magazine27.
3. Mihaly Csikszentmihalyi, Flow: The Psychology of Optimal Experience (New York: Harper & Row, 1990).
4. Brian Tracy, Eat That Frog!: 21 Great Ways to Stop Procrastinating and Get More Done in Less Time (San Francisco: Berrett-Koehler Publishers, 2007).
5. For more general information on the positive effects of goal setting, see Daniel Wong, "Reflections of a Compulsive Goal-setter," The Duke Chronicle, April 5, 2011, www.dukechronicle.com/articles/2011/04/06/reflections-compulsive-goal-setter.
6. See www.notable-quotes.com/z/ziglar_zig.html.
7. To learn more about SMART criteria, see <http://en.wikipedia.org/wiki/SMART_criteria#cite_note-Doran-1981-2>.
8. To learn more about structural tension, see Robert Fritz, The Path of Least Resistance: Learning to Be the Creative Force in Your Own Life (New York: Random House, 1984).
Day 7: The Review Day and Bonus Solution
1. See www.glamourmagazine.co.uk/celebrity/celebrity-galleries/2011/01/teetotal-celebrities#!image-number=14.
2. To read more about hormones that can make you happy, see M. Farouk Radwan, "Hormones That Make You Happy," www.2knowmyself.com/Hormones_that_make_you_happy.
3. To read the entire article, see "Alcohol Use Disorder," New York Times Health Guide, March 8, 2013, www.nytimes.com/health/guides/disease/alcoholism/causes.html.
4. To learn more about this 90-day period, see Tony O'Neill, "The 100-Day Hangover," The Fix, April 19, 2011, www.thefix.com/content/one-big-pain-brain.
5. We wish to thank Dr. Tony O'Donnell and Michael McCarthy for their guidance on nutrition and quitting drinking. We'll have more from them on Day 25's companion website.
PHASE II: REMOVING THE MENTAL AND EMOTIONAL BLOCKS THAT PREVENT YOU FROM THRIVING IN SOBRIETY
1. For more on the drunk dream and overcoming addiction, see "Elton John Opens Up About Overcoming Addiction in New Memoir," Huffpost Celebrity, July 17, 2012, www.huffingtonpost.com/2012/07/17/elton-john-talks-overcoming-addiction-memoir_n_1680055.html.
Day 8: The "Why Can't You Just Quit?" Solution
1. For more thoughts on willpower, see Rick Warren, "Healing Choices: A Mind for Repentance," Daily Hope with Rick Warren, May 21, 2014, <http://rickwarren.org/devotional/english/healing-choices-a-mind-for-repentance>.
2. For the full definition, see www.merriam-webster.com, s.v. "willpower."
3. John Ortberg, The Life You've Always Wanted (Grand Rapids, MI: Zondervan, 1997).
4. To read more about willpower, see Kirsten Weir, "What You Need to Know About Willpower: The Psychological Science of Self-Control," American Psychological Association's Mind/Body Health Campaign Report, 2012, www.apa.org/helpcenter/willpower.aspx.
5. Rick Warren, The Purpose Driven Life: What on Earth Am I Here For? (Grand Rapids, MI: Zondervan, 2012).
6. To find out more about decision making and willpower, see Drake Baer, "14 Surprising Things That Affect Your Willpower and Decision Making," Business Insider, April 15, 2014, www.businessinsider.com/surprising-things-that-affect-your-willpower-and-decision-making-2014-4.
7. For more on decision fatigue, see John Tierney, "Do You Suffer From Decision Fatigue?" New York Times Magazine, August 17, 2011, www.nytimes.com/2011/08/21/magazine/do-you-suffer-from-decision-fatigue.html?pagewanted=1&%2334&sq&st=cse&%2359;&scp=1&%2359;decision%20making%20fatigue.
8. David Sheff, Clean: Overcoming Addiction and Ending America's Greatest Tragedy (New York: Houghton Mifflin Harcourt, 2013).
9. See www.goodreads.com/author/quotes/102037.James_Gordon.
Day 9: The Action Solution
1. Caroline Knapp, Drinking: A Love Story (New York: Random House, 1996).
2. From an interview on The Conversation with Amanda de Cadenet, May 2012.
3. Brian Tracy, No Excuses!: The Power of Self-Discipline (New York: Vanguard Press, 2010).
4. See Diane M. Tice and Roy F. Baumeister, "Longitudinal Study of Procrastination, Performance, Stress, and Health: The Costs and Benefits of Dawdling," Psychological Science 8 (1997): 454–58.
5. For more information about procrastination, see Eric Jaffe, "Why Wait? The Science Behind Procrastination," Observer 26, no. 4 (April 2013): www.psychologicalscience.org/index.php/publications/observer/2013/april-13/why-wait-the-science-behind-procrastination.html.
6. Steve Chandler, 100 Ways to Motivate Yourself: Change Your Life Forever (Franklin Lakes, NJ: Career Press, 2004).
7. David K. Reynolds, Constructive Living (Honolulu: University of Hawaii Press, 1984).
8. This concept is based on Canfield and Switzer, Success Principles.
9. Stephen M. Silverman, "Ewan McGregor Reveals Battle with Alcohol," People, July 5, 2005, www.people.com/people/article/0,,1079768,00.html.
10. William Harris, "How Newton's Laws of Motion Work," HowStuffWorks.com. July 29, 2008, <http://science.howstuffworks.com/innovation/scientific-experiments/newton-law-of-motion.htm>.
11. Maxwell Maltz, Psycho-Cybernetics: A New Way to Get More Living out of Life (New York: Prentice-Hall, 1960).
12. To read more about why things catch on, see Kare Anderson, "The Secret Behind Why Things Catch On," Forbes, February 18, 2013, www.forbes.com/sites/kareanderson/2013/02/18/the-secret-behind-why-things-catch-on.
13. Jennifer Chang, "Tiny Habits: Behavior Scientist BJ Fogg Explains a Painless Strategy to Personal Growth," Success, October 8, 2013, www.success.com/videos/youtube/bj-fogg-for-lasting-change-think-small.
14. Steve Chandler, Time Warrior: How to Defeat Procrastination, People-Pleasing, Self-Doubt, Overcommitment, Broken Promises and Chaos (Anna Maria, FL: Maurice Bassett, 2011).
Day 10: The Core Values Solution
1. Henry Kimsey-House et al., Co-Active Coaching: Changing Business, Transforming Lives, 3rd ed. (Boston: Nicholas Brealey Publishing, 2011).
2. Dotson Rader, "Interview with Robert Downey Jr.," Parade, February 4, 2008.
3. See www.brainyquote.com/quotes/quotes/m/martinluth135188.html.
4. See www.goodreads.com/author/quotes/50316.Zig_Ziglar.
5. Stephen R. Covey, The 7 Habits of Highly Effective People: Powerful Lessons in Personal Change (New York: Free Press, 1989).
Day 11: The Lie Detector Solution
1. See www.brainyquote.com/quotes/authors/d/deepak_chopra.html.
2. Maltz, Psycho-Cybernetics.
3. To read more about how alcohol can affect your sex life, see Chris Iliades, "Why Boozing Can Be Bad for Your Sex Life," Everydayhealth.com, last modified January 4, 2012, www.everydayhealth.com/erectile-dysfunction/why-boozing-can-be-bad-for-your-sex-life.aspx.
4. Esser at al., "Prevalence of Alcohol Dependence Among US Adult Drinkers."
5. See <http://en.wikipedia.org/wiki/Harvard_Law_School>.
6. Melissa Healy, "Resveratrol in the Diet Is No Help at All, Study Says," Los Angeles Times, May 12, 2014. Also, see www.medpagetoday.com/Endocrinology/GeneralEndocrinology/45738.
7. For the full definition, see www.merriam-webster.com, s.v. "intoxicate."
8. Stanton Peele and Archie Brodsky with Mary Arnold, The Truth About Addiction and Recovery (New York: Simon & Schuster, 1992). To read a chapter online, see <http://lifeprocessprogram.com/the-truth-about-addiction-and-recovery-are-people-born-alcoholics>.
9. For the most current list of the top-grossing actors of all time, see www.boxofficemojo.com/people/?view=Actor&sort=sumgross&p=.htm.
10. For a complete list of teetotalers, see <http://en.wikipedia.org/wiki/List_of_teetotalers>.
11. King, On Writing.
12. Alan H. Cohen, Why Your Life Sucks . . . and What You Can Do About It (New York: Bantam, 2005).
13. To read Christina Ricci's full interview with BlackBook, see "Drive, She Said," bbook.com, April 21, 2008, www.bbook.com/drive-she-said/.
Day 12: The Subconscious Mind Solution
1. To read Bruce Lipton's interview "Mind, Growth, and Matter" from Succeed Magazine, June 7, 2012, see www.brucelipton.com/resource/interview/mind-growth-and-matter.
2. For the full definition, see www.merriam-webster.com, s.v. "subconscious."
3. Joseph Murphy, The Power of Your Subconscious Mind (Englewood Cliffs, NJ: Prentice-Hall, 1963).
4. To read more about how the subconscious mind records life events, see Dietrich Klinghardt, "Applied Psycho-Neurobiology," mercola.com, www.mercola.com/article/applied_psycho_neurobiology/apn.htm.
5. John A. Bargh and Ezequiel Morsella, "The Unconscious Mind," Perspectives on Psychological Science 3, no. 1 (January 2008): 73–79. To read the full paper, see www.ncbi.nlm.nih.gov/pmc/articles/PMC2440575.
6. Bruce H. Lipton, The Biology of Belief: Unleashing the Power of Consciousness, Matter & Miracles (Carlsbad, CA: Hay House, 2008).
7. Steven Kotler, "Learning to Learn Faster Part II: How to Read Faster and Solve Problems Like MacGyver," Forbes, July 3, 2013, www.forbes.com/sites/stevenkotler/2013/07/03/learning-to-learn-faster-part-ii/2.
8. Dr. Drew Pinsky, "Keynote Address by Dr. Drew Pinsky" (presented at the Fifth Annual Luncheon for the Arapahoe House, Denver, September 18, 2014).
9. To read more about the lottery and bankruptcy study, see Amy Wolf, "Lotteries: From Big Bucks to Bankruptcy," Research News at Vanderbilt, July 7, 2009, <http://news.vanderbilt.edu/2009/07/lotteries-from-big-bucks-to-bankruptcy-83864>.
10. Leonard Mlodinow, Subliminal: How Your Unconscious Mind Rules Your Behavior (New York: Vintage Books, 2012).
11. Debra Ollivier, "Leonard Mlodinow on Subliminal: How Your Unconscious Mind Rules Your Behavior," Huffingtonpost.com, last modified August 7, 2012, www.huffingtonpost.com/debra-ollivier/leonard-mlodinow-on-subliminal-how-your-unconscious-mind-rules-your-behavior_b_1575795.html.
12. Bill Wilson, "The Next Frontier: Emotional Sobriety," Grapevine, January 1958.
13. For more studies on the development of the personality in early childhood, see Linda Carroll, "Personality May Be Set by Preschool," Msnbc.com, last modified January 15, 2008, <http://www.nbcnews.com/id/22554554/ns/health-childrens_health/t/personality-may-be-set-preschool/#.VQdRxI7F-Sq>.
14. For more information on how the brain develops in early childhood, see Judith Graham, "Children and Brain Development: What We Know About How Children Learn," Bulletin #4356, Cooperative Extension Publications, The University of Maine, <http://umaine.edu/publications/4356e>.
15. For studies on thought suppression, see Jeremy Dean, "Why Thought Suppression Is Counter-Productive," PsyBlog, May 22, 2009, www.spring.org.uk/2009/05/why-thought-suppression-is-counter-productive.php.
16. For more about the subconscious mind and negatives, see Abdallah Nacereddine, "How the Subconscious Mind Functions," Unspecial.org, www.unspecial.org/2011/12/how-the-subconscious-mind-functions.
Day 13: The Tapping Solution
1. Roger Callahan, PhD, The Five Minute Phobia Cure: Dr. Callahan's Treatment for Fears, Phobias and Self-Sabotage (Wilmington, DE: Enterprise Publishing, 1985).
2. You can get a quick overview of the technique at www.EFTuniverse.com and in Nick Ortner, The Tapping Solution (Carlsbad, CA: Hay House, 2013). Also see Dawson Church, The EFT Manual (Fulton, CA: Energy Psychology Press, 2014), which is a new and completely revised edition of the original EFT manual written by Gary Craig. Both of these books are eminently practical and easy to read and apply. Also see Jack Canfield and Pamela Bruner, Tapping into Ultimate Success: How to Overcome Any Obstacle and Skyrocket Your Success (Carlsbad, CA: Hay House, 2012). This book also contains a ninety-minute DVD that teaches and demonstrates the various EFT tapping protocols. You can also watch free videos on YouTube that demonstrate the basic EFT tapping procedure. Finally, if you would like further help in applying tapping to your recovery, you can locate a local practitioner by going to <http://Practitioners.EFTuniverse.com>.
3. Kari Reed, "Battling a Giant with Really Small, Surprisingly Effective Rocks," in The EFT Manual, by Dawson Church (Fulton, CA: Energy Psychology Press, 2014), 31–32.
4. Mair Llewellyn-Edwards, "Using EFT for a Headache Leads to Recovery in Alcohol Addiction," Eftuniverse.com, www.eftuniverse.com/addictions/using-eft-for-a-headache-leads-to-recovery-in-alcohol-addiction.
5. Church and Brooks also performed a randomized, controlled trial demonstrating that cortisol levels drop quickly after a brief EFT treatment, in tandem with reductions in psychological stress. See D. Church, G. Yount, and A. J. Brooks, "The Effect of Emotional Freedom Techniques (EFT) on Stress Biochemistry: A Randomized Controlled Trial," Journal of Nervous and Mental Disease 200, no. 10 (2012): 891–96, doi:10.1097/NMD.0b013e 31826b9fc1.
6. Gloria Arenson, EFT for Procrastination (Santa Rosa, CA: Energy Psychology Press, 2009).
7. Dawson Church and Audrey J. Brooks, "The Effect of a Brief EFT (Emotional Freedom Techniques) Self-Intervention on Anxiety, Depression, Pain and Cravings in Healthcare Workers," Integrative Medicine: A Clinician's Journal (October/November 2010): 40–44.
8. We wish to acknowledge Robert Elias Najemy, the founder and director of the Center for Harmonious Living in Athens, Greece, for his work on tapping and addiction, from which we have drawn upon extensively for this solution.
9. We want to remind you again that if you have developed a strong dependency on alcohol, or if you have detoxed from alcohol several times in the past, you run the risk of more serious side effects such as tremors, seizures, DTs, and visual, auditory, and tactile hallucinations—even death. So once again we advise you to work with a doctor to determine if you need medication and monitoring.
10. Javier Gomez, "EFT Tapping for Unresolved Grief Curbs Beer Craving," Eftuniverse.com, www.eftuniverse.com/addictions/using-eft-for-unresolved-grief-aids-an-alcohol-problem-as-a-side-benefit.
PHASE III: CREATING AN UNSHAKABLE BELIEF IN YOURSELF AND YOUR DREAMS
1. Eckhart Tolle, The Power of Now: A Guide to Spiritual Enlightenment (Novato, CA: New World Library, 1999).
Day 15: The 4-Minute-Mile Solution
1. Charles A. Garfield, Peak Performance: Mental Training Techniques of the World's Greatest Athletes (New York: Warner Books, 1989).
2. For studies on how visualization is just as powerful as doing, see Frank C. Bakker et al., "Changes in Muscular Activity While Imagining Weight Lifting Using Stimulus or Response Propositions," Journal of Sport & Exercise Psychology (1996), <http://journals.humankinetics.com/AcuCustom/Sitename/Documents/DocumentItem/8962.pdf>.
3. Maltz, Psycho-Cybernetics.
4. To read about Roger Bannister's historic moment, see "On This Date 1950–2005," BBC.com, <http://news.bbc.co.uk/onthisday/hi/dates/stories/may/6/newsid_2511000/2511575.stm>.
5. See Bruce Lowitt, "Bannister Stuns World with 4-Minute Mile," St. Petersburg Times, December 17, 1999, www.sptimes.com/News/121799/Sports/Bannister_stuns_world.shtml.
6. From an interview on the Oprah Winfrey Show, 1997.
7. For the full definition, see www.thefreedictionary.com, s.v. "reticular activating system."
8. For more information about the brain's processing speed, see Steven Kotler, "Learning to Learn Faster Part II: How to Read Faster and Solve Problems Like MacGyver." Forbes, July 3, 2013, www.forbes.com/sites/stevenkotler/2013/07/03/learning-to-learn-faster-part-ii/2. This source references a study that found Lipton's figures conservative, calculating that the subconscious is as much as two million times faster than the conscious.
9. For more information on goal setting and the RAS, see Ruben Gonzalez, "The Neuroscience of Success," Ruben Gonzalez the Luge Man Blog, www.thelugeman.com/motivational_speaker_the_neuroscience_of_success.htm.
10. For more information about the brain's RAS filter, see Sheila Kloefkorn, "How to Train Your Brain for Success," Phoenix Business Journal, May 23, 2014, www.bizjournals.com/phoenix/blog/business/2014/05/how-to-train-your-brain-for-success.html?page=all.
11. See Angie LeVan, "Seeing Is Believing: The Power of Visualization," Psychology Today, December 2, 2009, www.psychologytoday.com/blog/flourish/200912/seeing-is-believing-the-power-visualization.
12. See www.goodreads.com/author/quotes/8435.Norman_Vincent_Peale.
13. To learn more about adding all the senses to your visualization practice, see JoAnn Dahlkoetter, "Sochi Olympics and Sports Psychology for Athletes," Huffingtonpost.com, last modified April 12, 2014, www.huffingtonpost.com/dr-joann-dahlkoetter/sochi-olympics_b_4582950.html.
14. See Mary C. Lamia, "Emotional Memories: When People and Events Remain with You," Psychology Today, March 5, 2012, www.psychologytoday.com/blog/intense-emotions-and-strong-feelings/201203/emotional-memories-when-people-and-events-remain.
15. Greg Miller, "How Our Brains Make Memories: Surprising New Research About the Act of Remembering May Help People with Post-traumatic Stress Disorder," Smithsonian Magazine, May 2010, www.smithsonianmag.com/science-nature/how-our-brains-make-memories-14466850/?no-ist.
16. See Mike Bundrant, "Success or Stress: The Impact of Your Subconscious Self-Questioning," Living Green Magazine, December 11, 2013, http://livinggreenmag.com/2013/12/11/people-solutions/success-stress-impact-subconscious-self-questioning.
Day 16: The Quality Question Solution
1. Brian Tracy, "How to Trigger Great Ideas," Brian Tracy's Blog, www.briantracy.com/blog/business-success/how-to-trigger-great-ideas.
2. See www.pbs.org/wgbh/nova/einstein/wisd-nf.html.
3. For more tips on working with the subconscious mind, see "How to Reprogram Your Subconscious Mind," Hubpages.com, March 20, 2013, <http://thegoalsettingg.hubpages.com/hub/subconscious_mind>.
4. Michael J. Gelb, How to Think Like Leonardo da Vinci: Seven Steps to Genius Every Day (New York: Dell Publishing, 2000).
5. Niurka, Supreme Influence: Change Your Life with the Power of the Language You Use (New York: Harmony Books, 2013).
6. See www.woopidoo.com/business_quotes/authors/amory-lovins/index.htm.
7. Dotson Rader, "Interview with Robert Downey Jr.," Parade, February 4, 2008.
8. Gelb, How to Think Like Leonardo da Vinci.
Day 17: The Eternal Optimist Solution
1. Norman Vincent Peale, The Power of Positive Thinking (New York: Prentice-Hall, 1952).
2. For more information about how our thoughts can determine our emotional states, see Ben Martin, "Stress and Personality," Psych Central, 2006, <http://psychcentral.com/lib/stress-and-personality/000106>.
3. Tolle, The Power of Now.
4. For more stories about how small choices saved lives on 9/11, see Madison Park, "Small Choices, Saved Lives: Near Misses of 9/11," CNN.com, September 5, 2011, www.cnn.com/2011/US/09/03/near.death.decisions.
5. See www.goodreads.com/author/quotes/7275.Helen_Keller.
6. Fred R. Shapiro, ed., The Yale Book of Quotations (New Haven, CT: Yale University Press, 2006).
7. Esther and Jerry Hicks, Ask and It Is Given: Learning to Manifest Your Desires (Carlsbad, CA: Hay House, 2004).
8. Vernon Howard, The Power of Your Supermind (Pine, AZ: New Life, 2011).
9. Robbins, Money: Master the Game.
10. Erik Sherman, "This Easy 'Mental Contrasting' Technique Can Help You Achieve Your Goals," Business Insider, October 29, 2014, www.businessinsider.com/this-easy-mental-contrasting-technique-can-help-you-achieve-your-goals-2014-10?nr_email_referer=1&utm_source=Sailthru&utm_medium=email&utm_term=Business Insider Select&utm_campaign=BI Select %28Wednesday Friday%29 2014-10-29&utm_content=BISelect.
Day 18: The Affirmation Solution
1. From an interview in Movieline, July 1994.
2. See JM Emmert, "Rich Man, Poor Man: The Success of Napoleon Hill," Success, January 5, 2009, www.success.com/article/rich-man-poor-man.
3. Hans Villarica, "How the Power of Positive Thinking Won Scientific Credibility," The Atlantic, April 23, 2012, www.theatlantic.com/health/archive/2012/04/how-the-power-of-positive-thinking-won-scientific-credibility/256223, and <http://exploringthemind.com/the-mind/the-truth-about-affirmations>.
4. Napoleon Hill, Think and Grow Rich: The Original 1937 Unedited Edition, reprint. (Wise, VA: Napoleon Hill Foundation, 2012).
5. For more information about the differences between the conscious mind and the subconscious mind, see Michael Carroll, "Understanding Your Mind; Conscious and Unconscious Processing: How to Utilise the Recourses of Your Unconscious Mind," Nlpacademy.co.uk, July 2008, www.nlpacademy.co.uk/articles/view/understanding_your_mind_conscious_and_unconscious_processing.
6. Claude M. Bristol, The Magic of Believing: The Science of Setting Your Goal and Then Reaching It (New York: Fireside, 1985).
7. Robin S. Sharma, The Monk Who Sold His Ferrari: A Fable About Fulfilling Your Dreams and Reaching Your Destiny (New York: HarperCollins, 1997).
8. Martin E. P. Seligman, Learned Optimism: How to Change Your Mind and Your Life (New York: Random House, 1991).
9. Paul J. Brouwer, "The Power to See Ourselves," Harvard Business Review, November 1964, <https://hbr.org/1964/11/the-power-to-see-ourselves>.
Day 19: The Attraction Solution
1. Hicks, Ask and It Is Given.
2. For more about how the law of attraction actually works, see Srinivasan Pillay, "Is There Scientific Evidence for the 'Law of Attraction'?" Huffingtonpost.com, last modified November 17, 2011, www.huffingtonpost.com/srinivasan-pillay/is-there-scientific-evide_b_175189.html.
3. To read an interview with Dr. Lissa Rankin, author of Mind over Medicine: Scientific Proof That You Can Heal Yourself, see www.drfranklipman.com/interview-with-dr-lissa-rankin.
4. Esther and Jerry Hicks, Money, and the Law of Attraction: Learning to Attract Wealth, Health, and Happiness (Carlsbad, CA: Hay House, 2008).
5. Ibid.
6. Brian Tracy, No Excuses! The Power of Self-Discipline (Boston: Da Capo Press, 2010).
7. Chandler, 100 Ways to Motivate Yourself.
8. "Craig Ferguson Speaks from the Heart." See www.youtube.com/watch?v=7ZVWIELHQQY.
9. Esther and Jerry Hicks, Money, and the Law of Attraction.
Day 20: The Gratitude Solution
1. Robert A. Emmons, Thanks! How the New Science of Gratitude Can Make You Happier (New York: Houghton Mifflin Company, 2007). Also, to read more about the power of gratitude, and see what some critics of Emmons's study are saying, see <http://greatergood.berkeley.edu/article/item/gratitude_research_why_bother>.
2. Sara Rimer and Madeline Drexler, "Happiness and Health," Harvard Public Health, Winter 2011, www.hsph.harvard.edu/news/magazine/happiness-stress-heart-disease.
3. Sonja Lyubomirsky, The How of Happiness: A Scientific Approach to Getting the Life You Want (New York: Penguin Press, 2008).
4. Anup Shah, "Poverty Facts and Stats," Globalissues.org, last modified January 7, 2013, www.globalissues.org/article/26/poverty-facts-and-stats.
5. For more about Brother David Steindl-Rast and to read more about his ideas on gratitude, see www.gratefulness.org/qbox/item.cfm?qbox_id=32.
6. Emmons, Thanks!
7. Heather King, Parched: A Memoir (New York: Chamberlain Bros., 2005).
8. Tolle, The Power of Now.
9. Steven M. Toepher, Kelly Cichy, and Patti Peters, "Letters of Gratitude: Further Evidence for Author Benefits," Journal of Happiness Studies 13, no. 1 (January 2012): 187–201, doi:10.1007/s10902-011-9257-7.
Day 21: The Review Day and Bonus Solution
1. From an interview on Larry King Live, August 2002. To read the full interview with Matthew Perry, see <http://transcripts.cnn.com/TRANSCRIPTS/0208/22/lkl.00.html>.
2. WikiHow contributors, "How to Identify Persuasive Techniques in Advertising," WikiHow, The Free How-to Guide, www.wikihow.com/Identify-Persuasive-Techniques-in-Advertising (accessed December 16, 2014).
3. See www.statista.com/statistics/245318/advertising-spending-of-the-alcohol-industry-in-the-us-by-medium/.
PHASE IV: CULTIVATING COURAGE AND POSITIVE RELATIONSHIPS TO THRIVE IN MIND, BODY, AND SPIRIT
1. Deepak Chopra, The Book of Secrets: Unlocking the Hidden Dimensions (New York: Random House, 2004).
Day 22: The Courage Solution
1. Osho, The Book of Understanding: Creating Your Own Path to Freedom (New York: Harmony Books, 2006).
2. Marianne Williamson, A Return to Love: Reflections on the Principles of A Course in Miracles (New York: HarperCollins, 1992).
3. Dan Millman, Everyday Enlightenment (New York: Warner Books, 1998).
4. To read more about fear, see Dean Burnett, "Phobias: The Rationale Behind Irrational Fears," The Guardian, June 28, 2013, www.theguardian.com/science/brain-flapping/2013/jun/28/phobias-rationale-irrational-fears, and Joseph Ledoux, "Searching the Brain for the Roots of Fear," New York Times, January 22, 2012, <http://opinionator.blogs.nytimes.com/2012/01/22/anatomy-of-fear/?_r=0>.
5. Ace Frehley, Joe Layden, and John Ostrosky, No Regrets (New York: Gallery Books, 2011).
6. For more information on how an imagined event can seem real, see Sandra Blakeslee, "Tracing the Brain's Pathways for Linking Emotion and Reason," New York Times, December 6, 1994, www.nytimes.com/1994/12/06/science/tracing-the-brain-s-pathways-for-linking-emotion-and-reason.html.
7. Carol S. Dweck, Mindset: The New Psychology of Success (New York: Ballantine Books, 2008).
8. To read more about Esther Earl, see Zakiya Jamal, "Meet Esther Earl, the Brave Girl Who Inspired The Fault in Our Stars," People, June 7, 2014, www.people.com/article/esther-earl-john-green-inspiration-fault-in-our-stars-book-movie and This Star Won't Go Out, "Esther's Story," http://tswgo.org/esthers-story.html.
9. See www.boxofficemojo.com/movies/?id=faultinourstars.htm.
10. Esther Earl, Lori Earl, and Wayne Earl, This Star Won't Go Out: The Life and Words of Esther Grace Earl (New York: Dutton Books, 2014).
11. David J. Schwartz, The Magic of Thinking Big (New York: Fireside, 1987).
12. For the full definition, see www.merriam-webster.com, s.v. "compass."
13. See www.goodreads.com/author/quotes/5627.Anthony_Robbins.
14. Eleanor Roosevelt, You Learn by Living (Louisville: Westminster John Knox Press, 1960).
15. For more information on how your body responds to fear, see Susanne Babbel, "Fear of Success," Psychology Today, January 3, 2011, www.psychologytoday.com/blog/somatic-psychology/201101/fear-success.
16. Elizabeth Gilbert, Eat, Pray, Love: One Woman's Search for Everything Across Italy, India and Indonesia (New York: Penguin Books, 2006).
Day 23: The Emotional Sobriety Solution
1. The term "emotional intelligence" was first coined by Peter Salovey but popularized by Daniel Goleman. See www.psychologytoday.com/articles/199709/the-unconventional-wisdom-emotional-intelligence.
2. Tian Dayton, "Signs of Emotional Sobriety," Tiandayton.com, October 15, 2013, www.tiandayton.com/signs-of-emotional-sobriety.
3. Victoria Balfour, "John Bradshaw," People, May 28, 1990, www.people.com/people/archive/article/0,,20117761,00.html. This source quotes recovery specialist John Bradshaw.
4. Only 47 percent of children reach the age of seven in an intact family. Patrick F. Fagan and Nicholas Zill, The Second Annual Index of Family Belonging and Rejection (Washington, DC: Marriage and Religion Research Institute, Family Research Council, November 17, 2011), <http://downloads.frc.org/EF/EF11K28.pdf>.
5. According to the American Medical Association, 72 percent of American homes harbor someone with an addiction. www.theonion.com/articles/dysfunctional-family-statistically-average,4699.
6. www.thework.com.
7. Ibid.
8. You can find a more detailed description of the steps of the process and a set of free downloadable worksheets to guide you in the process at www.thework.com. When you have time, after you complete the 30-day program, you might want to read Katie Byron, Loving What Is: Four Questions That Can Change Your Life (New York: Random House, 2002).
Day 24: The Meditation Solution
1. Eknath Easwaran, Conquest of Mind: Take Charge of Your Thoughts & Reshape Your Life Through Meditation (Tomales, CA: Nilgiri Press, 1988).
2. To read about some studies that talk about the benefits of meditation, see Robert Schneider, "Does Meditation Have Benefits for Mind and Body?" Medicalnewstoday.com, last modified February 26, 2014, www.medicalnewstoday.com/articles/272833.php.
3. To learn more about the history of meditation, see Robert Puff, "An Overview of Meditation: Its Origins and Traditions," Psychology Today, July 7, 2013, www.psychologytoday.com/blog/meditation-modern-life/201307/overview-meditation-its-origins-and-traditions.
4. For an overall description of the study see M. B. Ospina, K. Bond, M. Karkhaneh, L. Tjosvold, B. Vandermeer, Y. Liang, L. Bialy, N. Hooton, N. Buscemi, D. M. Dryden, and T. P. Klassen, "Meditation Practices for Health: State of the Research," Evidence Report/Technology Assessment 155 (June 2007): 1–263, www.ncbi.nlm.nih.gov/pubmed/17764203.
5. Bill Phillips, Transformation: The Mindset You Need, the Body You Want, the Life You Deserve (Los Angeles: T-Media, 2010).
6. For more information on how meditation is an effective technique for those recovering from addiction, see "Meditation for Alcoholism and Drug Addiction Recovery," Elementsbehavioralhealth.com, July 6, 2014, www.elementsbehavioralhealth.com/featured/meditation-for-alcoholism-and-drug-addiction-recovery.
7. Phillips, Transformation.
8. To read about Dan Harris's experience and suggestions to make you happier, see Eric Barker, "Why You Should Meditate—and How to Do It," Business Insider, September 3, 2014, www.businessinsider.com/3-simple-things-that-will-make-you-10-happier-2014-8?nr_email_referer=1&utm_source=Triggermail&utm_medium=email&utm_term=Business%20Insider%20Select&utm_campaign=BI%20Select%20%2528Wednesday%20Friday%2529%202014-09-03&utm_content=emailshare.
9. To read the full article about the Seattle Seahawks and meditation, see Alyssa Roenigk, "Lotus Pose on Two," ESPN the Magazine, August 21, 2013, <http://espn.go.com/nfl/story/_/id/9581925/seattle-seahawks-use-unusual-techniques-practice-espn-magazine%22%20%5Ct%20%22_blank>.
10. To read more about the benefits of mindfulness and meditation, see Dan Hurley, "Breathing In vs. Spacing Out," New York Times Magazine, January 14, 2014, www.nytimes.com/2014/01/19/magazine/breathing-in-vs-spacing-out.html.
11. To view Andy Puddicombe's TED Talk or to read the interactive transcript, see "Andy Puddicombe: All It Takes is 10 Mindful Minutes," Fall 2012, www.ted.com/talks/andy_puddicombe_all_it_takes_is_10_mindful_minutes.
12. Sheff, Clean.
13. For more about ways that stress can affect your body, see "How Stress Affects the Body," Heartmath.com, 2010, www.heartmath.com/infographics/how-stress-effects-the-body.
14. To read more about the impacts of stress, see Laura Garnett, "10 Signs Stress Is Ruining Your Performance," Business Insider, March 26, 2014, www.businessinsider.com/10-signs-stress-is-ruining-your-performance-2014-3?nr_email_referer=1&utm_source=Triggermail&utm_medium=email&utm_term=Business%20Insider%20Select&utm_campaign=BI%20Select%20%28Wednesday%20Friday%29%202014-03-26&utm_content=emailshare.
15. Blakeslee, "Placebos Prove So Powerful Even Experts Are Surprised."
16. To read more about stress hormones, see Sarah Klein, "Adrenaline, Cortisol, Norepinephrine: The Three Major Stress Hormones, Explained," Huffingtonpost.com, last modified April 19, 2013, www.huffingtonpost.com/2013/04/19/adrenaline-cortisol-stress-hormones_n_3112800.html.
17. Lipton, Biology of Belief.
18. For more uncommonly known facts about stress, see "What You Need to Know About Stress," Heartmath.com, March 25, 2014, www.heartmath.com/blog/health-well-being/what-you-need-to-know-about-stress.
19. To read more about alcohol and stress, see <http://alcoholism.about.com/cs/alerts/l/blnaa32.htm>.
20. To read more about hormones that can make you happy, see M. Farouk Radwan, "Hormones That Make You Happy," www.2knowmyself.com/Hormones_that_make_you_happy.
21. To read about other natural ways to increase serotonin in the brain, see Simon N. Young, "How to Increase Serotonin in the Human Brain Without Drugs," Journal of Psychiatry & Neuroscience 32, no. 6 (2007): 394–99, www.ncbi.nlm.nih.gov/pmc/articles/PMC2077351.
22. To read more about Dr. Andrew Weil's thoughts on breathing, see "Breathing: An Introduction," www.drweil.com/drw/u/ART00519/An-Introduction-to-Breathing.html.
23. To learn more about the 4-7-8 breath exercise, as well as other breathing exercises, see "Breathing: Three Exercises," www.drweil.com/drw/u/ART00521/three-breathing-exercises.html.
24. Matthieu Ricard, Why Meditate? Working with Thoughts and Emotions (Carlsbad, CA: Hay House, 2010).
25. Jon Kabat-Zinn, Wherever You Go, There You Are (New York: Hyperion, 1994).
26. See "Overcoming Addiction," www.chopra.com/overcoming-addiction.
27. See <http://thinkexist.com/quotes/diana_robinson/>.
Day 25: The Mind and Body Solution
1. See www.entheos.com/quotes/by_teacher/plato.
2. Harold Pollack, "Alcohol Is Still the Deadliest Drug in the United States, and It's Not Even Close," Washington Post Wonkblog, August 19, 2014, www.washingtonpost.com/blogs/wonkblog/wp/2014/08/19/alcohol-is-still-the-deadliest-drug-in-the-united-states-and-its-not-even-close.
3. To read more articles about alcohol and liver disease, see <http://alcoholism.about.com/od/liver>.
4. To read more articles about alcohol and cirrhosis of the liver, see <http://alcoholism.about.com/od/cirrhosis>.
5. To read more articles about alcohol and damage to the brain, see <http://alcoholism.about.com/od/brain>.
6. To read more articles about alcohol and dementia, see <http://alcoholism.about.com/od/dementia>.
7. To read more about alcohol and blood pressure, see <http://alcoholism.about.com/cs/heal/a/aa020722a.htm>.
8. To read more about alcohol and an irregular heartbeat, see <http://alcoholism.about.com/od/health/a/bljama041011.htm>.
9. To watch a video about how alcohol affects the body, see Samuel Ball, "Here's What Alcohol Does to Your Brain and Body," produced by Will Wei, Business Insider, May 28, 2014, www.businessinsider.com/alcohol-effects-brain-body-2014-5?nr_email_referer=1&utm_source=Triggermail&utm_medium=email&utm_term=Business%20Insider%20Select&utm_campaign=BI%20Select%20%28Wednesday%20Friday%29%202014-05-28&utm_content=emailshare.
10. To read more articles on alcohol and cancer, see <http://alcoholism.about.com/od/cancer>.
11. To read more about how alcohol slows healing, see S. Guo and L. A. DiPietro, "Factors Affecting Wound Healing," Journal of Dental Research 89, no. 3 (2010): 219–29, doi:10.1177/0022034509359125.
12. US Department of Health and Human Services, National Institutes of Health, and National Institute on Alcohol Abuse and Alcoholism, "Alcohol's Damaging Effects on the Brain," Alcohol Alert, no. 63 (October 2004), <http://pubs.niaaa.nih.gov/publications/aa63/aa63.htm>.
13. For more information on alcohol related deaths, see Glenn Thomas and Tarik Jasarevic, "WHO Calls on Governments to Do More to Prevent Alcohol-Related Deaths and Diseases," World Health Organization News Release, May 12, 2014, www.who.int/mediacentre/news/releases/2014/alcohol-related-deaths-prevention/en.
14. For more statistics on the consequences of alcohol use, see the following websites: www.niaaa.nih.gov/alcohol-health/overview-alcohol-consumption/alcohol-facts-and-statistics, www.alcoholism-and-drug-addiction-help.com/statistics-on-alcoholism.html, and <http://alcoholism.about.com/od/effect/a/alcohol_harm.htm?nl=1>.
15. Cynthia Kuhn, Scott Swartzwelder, and Wilkie Wilson, Buzzed: The Straight Facts About the Most Used & Abused Drugs (New York: W. W. Norton, 2008).
16. To read more about this shocking statistic, see Alexandra Sifferlin, "Alcohol Kills 1 Person Every 10 Seconds, Report Says," Time.com, May 12, 2014, <http://time.com/96082/alcohol-consumption-who>.
17. For more information on the body's restorative capabilities, see Alan Goldhamer, "How Your Body Heals Itself," T. Colin Campbell Center for Nutrition Studies Newsletter, October 15, 1997, <http://nutritionstudies.org/body-heals>.
18. For more information about liver transplants and how the liver grows back, see <http://uvahealth.com/services/digestive-health/digestive-conditions>.
19. To read more about how old some body parts really are, see Angela Epstein, "Believe It or Not, Your Lungs Are Six Weeks Old—and Your Taste Buds Just Ten Days! So How Old Is the Rest of Your Body?" Dailymail.com, last modified October 13, 2009, www.dailymail.co.uk/health/article-1219995/Believe-lungs-weeks-old—taste-buds-just-days-So-old-rest-body.html.
20. To read more about how the body regenerates, see Brent Atwater, "Time Schedule of Your Body's Cellular Regeneration," Positive Attitudes for Health Challenges Blog, July 28, 2012, <http://positiveattitudesforhealthchallenges.blogspot.com/2012/07/time-schedule-of-your-bodys-cellular.html>.
21. Karen Fischer, The Healthy Skin Diet: Your Complete Guide to Beautiful Skin in Just 8 Weeks (London: Rodale, 2009).
22. Joshua Rosenthal, Integrative Nutrition (New York: Integrative Nutrition Publishing, 2008).
23. We wish to thank Dr. Tony O'Donnell and Michael McCarthy for their guidance on nutrition and quitting drinking. We'll have more from them on the companion website for Day 25.
24. For more information about food allergies or intolerances, see Erik Ofgang, "Healthy Living: Allergy or Intolerance," Connecticut Magazine, May 2014, www.connecticutmag.com/Connecticut-Magazine/May-2014/Healthy-Living-Allergy-or-Intolerance.
25. For more information about these nutrition basics, see "Nutrition Basics," www.cafebonappetit.com/wellness/nutrition-basics.
26. For more information about water, see F. Batmanghelidj, "You're Not Sick; You're Thirsty. Don't Treat Thirst with Medication," <http://watercure.com>.
27. F. Batmanghelidj, Your Body's Many Cries for Water (Falls Church, VA: Global Health Solutions, 1997).
28. For more information about why we prefer calorie-dense foods, see Katherine Harmon, "Addicted to Fat: Overeating May Alter the Brain as Much as Hard Drugs," Scientific American, March 28, 2010, www.scientificamerican.com/article/addicted-to-fat-eating.
29. For more statistics on obesity, see "Obesity and Overweight," World Health Organization Fact Sheet, No. 311, January 2015, www.who.int/mediacentre/factsheets/fs311/en.
30. Wendy C. Fries, "13 Ways to Fight Sugar Cravings," Webmd.com, June 22, 2011, www.webmd.com/diet/features/13-ways-to-fight-sugar-cravings.
31. Food Allergy Research and Education (FARE), "Facts and Statistics," www.foodallergy.org/facts-and-stats.
32. Nutritionist and fitness expert JJ Virgin has found that the seven most common allergies are to soy, corn, gluten (found in wheat, barley, and rye), dairy, sugar, artificial sweeteners (and alcohol!), eggs, and peanuts. For more information, see her book The Virgin Diet: Drop 7 Foods, Lose 7 Pounds, Just 7 Days (New York: Harlequin, 2012).
33. Lyn-Genet Recitas, The Plan: Eliminate the Surprising "Healthy" Foods That Are Making You Fat—and Lose Weight Fast (London: Orion, 2013).
Day 26: The Positive Addiction Solution
1. Glasser, Positive Addiction.
2. Veronica M. Hay and Deepak Chopra, "An Exclusive Interview by Veronica M. Hay with Deepak Chopra," A Magazine of People and Possibilities, www.peopleandpossibilities.com/chopra.html.
3. John Robbins, Healthy at 100 (New York: Ballantine Books, 2007).
4. To learn more about the Research Society on Alcoholism (RSA), see www.rsoa.org.
5. To learn more about and read the RSA's study, see H. C. Karoly, C. J. Stevens, R. E. Thayer, R. E. Magnan, A. D. Bryan, and K. E. Hutchison, "Aerobic Exercise Moderates the Effect of Heavy Alcohol Consumption on White Matter Damage," Alcoholism: Clinical and Experimental Research 39, no. 9 (September 2013): 1508–515, doi:10.1111/acer.12135.
6. Shawn Achor, The Happiness Advantage: The Seven Principles of Positive Psychology That Fuel Success and Performance at Work (New York: Crown Business, 2010).
7. To read more about the release of endorphins and serotonin during exercise, see Jacqueline Stenson, "Getting High on Exercise: How Much Does It Take to Boost Mood?" MSNBC.com, September 18, 2007, www.nbcnews.com/id/18043835/ns/health-fitness/t/getting-high-exercise/#.VGzti_nF-So.
8. To read about other hidden benefits of exercise, see Mark Stibich, "The Hidden Benefits of Exercise," About.com, June 18, 2013, <http://longevity.about.com/od/lifelongfitness/tp/Hidden-Benefits-of-Exercise.htm>.
9. Brett Klinka and Chris Jordan, "High-Intensity Circuit Training Using Body Weight: Maximum Results with Minimal Investment," ACSM'S Health & Fitness Journal 17, no. 3 (May/June 2013): pp. 8–13, doi:10.1249/FIT.0b013e31828cb1e8.
10. For more information about the 7-minute workout, see Gretchen Reynolds, "The Scientific 7-Minute Workout," New York Times, May 9, 2013, http://well.blogs.nytimes.com/2013/05/09/the-scientific-7-minute-workout/?_php=true&_type=blogs&_r=1.
11. To learn more about the benefits of being outside in nature, see Jessey Bernstein, Kirk Warren Brown, Louis Mastella, and Marylène Gagné, "Spending Time in Nature Makes People Feel More Alive, Study Shows," Rochester.edu, June 3, 2010, www.rochester.edu/news/show.php?id=3639.
12. To learn more about beginning an exercise plan and the different types of exercise, see Brian D. Johnston, "Starting an Exercise Program," Merckmanuals.com, September 2014, www.merckmanuals.com/home/fundamentals/exercise_and_fitness/starting_an_exercise_program.html.
13. See <http://events.stanford.edu/events/324/32425>.
14. To read more about the differences between aerobic and anaerobic exercise, see Sharon E. Griffin, "Aerobic vs. Anaerobic: What Is the Difference?" www.myfooddiary.com/resources/ask_the_expert/aerobic_vs_anaerobic.asp.
15. For more information on preventing the loss of muscle mass, see Laura Skladzinki, "How to Stay Strong and Prevent Muscle Loss," Greatist.com, May 24, 2012, <http://greatist.com/fitness/how-stay-strong-and-prevent-muscle-loss>.
16. To read more about muscle and fat, see Jennifer M. Regan, "One Pound of Fat Versus One Pound of Muscle: Clearing up the Misconceptions," Bamboo Core Fitness Blog, <http://bamboocorefitness.com/one-pound-of-fat-versus-one-pound-of-muscle-clearing-up-the-misconception>.
17. When starting to exercise after taking time off to recover from an injury, Jack found that Tony Horton's 10-Minute Trainer DVDs provided him with a total body workout in just ten minutes first thing in the morning. You can learn more about it and order it at www.beachbody.com.
18. To read more about music releasing endorphins and increasing tolerance for pain, see Robin Dunbar, Kostas Kaskatis, Ian MacDonald, and Vinnie Barra, "Performance of Music Elevates Pain Threshold and Positive Affect: Implications for the Evolutionary Function of Music," Evolutionary Psychology 10, no. 4, www.epjournal.net/articles/performance-of-music-elevates-pain-threshold-and-positive-affect-implications-for-the-evolutionary-function-of-music.
19. The US Marine Corps, Run to Cadence with the US Marines, vols. 1–3 (Documentary Recordings, 2002).
20. For more information on alcohol and sleep disorders, see Denise Mann, "Alcohol and a Good Night's Sleep Don't Mix," WebMD.com, January 22, 2013, www.webmd.com/sleep-disorders/news/20130118/alcohol-sleep.
21. To read more about alcohol's effect on sleep, see "Reviewing Alcohol's Effects on Normal Sleep," Alcoholism: Clinical & Experimental Research, January 22, 2013, www.sciencedaily.com/releases/2013/01/130122162236.htm.
22. To read more about the effects of alcohol on the body, especially when exercising, see Selene Yeager, "Drinking and Exercise: How Alcohol Affects Your Body: Do Drinking and Exercise Mix?" Women's Health, February 17, 2012, www.womenshealthmag.com/health/drinking-and-exercise.
23. Laura Entis, "How Much Sleep Do You Really Need?" Entrepreneur, April 4, 2014, www.entrepreneur.com/article/232784.
24. To read more about the ideal amount of sleep, see Laura Blue, "How Much Sleep Do You Really Need?" Time.com, June 6, 2008, <http://content.time.com/time/health/article/0,8599,1812420,00.html>.
25. To read more about the benefits of exercise and a good night's sleep, see "Exercise Helps Ready the Body for a Good Night's Sleep," Premierhealth.com, February 17, 2014, www.premierhealthnet.com/phndefault.aspx?id=78284.
26. To learn more about how naps can improve your performance, see Diana Rodriguez, "Why You Should Still Nap," Everydayhealth.com, February 14, 2011, www.everydayhealth.com/health-report/healthy-sleep/why-nap.aspx.
27. For a slideshow of some of these famous nappers, see "Famous Nappers: Historical Figures Known for Napping," Huffingtonpost.com, last modified November 17, 2011, www.huffingtonpost.com/2010/01/14/famous-nappers-historical_n_423279.html.
28. To read more about the health benefits of exercising for just five minutes, see Kevin Loria, "Running Just 5 Minutes a Day Could Add Years to Your Life," Business Insider, July 31, 2014, www.businessinsider.com/running-just-5-minutes-a-day-could-add-years-to-your-life-2014-7.
29. Glasser, Positive Addiction.
30. To read more about the frequency of daily laughter of children and adults, see Pamela Gerloff, "You're Not Laughing Enough, and That's No Joke," Psychology Today, June 21, 2011, www.psychologytoday.com/blog/the-possibility-paradigm/201106/youre-not-laughing-enough-and-thats-no-joke.
31. To learn more about laughter yoga, see www.laughteryoga.org/english/news/news_details/405.
32. To read more about the life-threatening dangers of stress, see Dr. Mercola, "Documentary Examines How Stress Kills," Mercola.com, July 5, 2014, <http://articles.mercola.com/sites/articles/archive/2014/07/05/stress-effects.aspx>, and "America's #1 Health Problem," The American Institute of Stress, www.stress.org/americas-1-health-problem.
33. For more information on the healing benefits of laughter, see Melinda Smith and Jeanne Segal, "Laughter Is the Best Medicine: The Health Benefits of Humor and Laughter," Helpguide.org, last modified February 2015, www.helpguide.org/articles/emotional-health/laughter-is-the-best-medicine.htm.
34. For more information about laughter and heart health, see Michelle Murray, "Laughter Is the Best Medicine for Your Heart," University of Maryland Medical Center News Release, July 2, 2013, <http://umm.edu/news-and-events/news-releases/2009/laughter-is-the-best-medicine-for-your-heart>.
35. Swayze and Niemi, Time of My Life.
Day 27: The Love and Relationship Solution
1. To read more about Bronnie Ware's experience and the top five regrets of the dying, see www.ariseindiaforum.org/nurse-reveals-the-top-5-regrets-people-make-on-their-deathbed.
2. See Deepak Chopra and David Simon, Freedom from Addiction: The Chopra Center Method for Overcoming Destructive Habits (Deerfield Beach, FL: Health Communications, 2007).
3. Glenn Plaskin, "Playboy Interview: Anthony (Tony) Robbins," Awaken.com, August 17, 2013, www.awaken.com/2013/08/playboy-interview-anthony-tony-robbins.
4. Alicia Dennis, "Tim McGraw: 'I Feel Better Than Ever,' " People, February 11, 2013, www.people.com/people/archive/article/0,,20674394,00.html.
5. Swayze and Niemi, Time of My Life.
6. Kathy Ehrich Dowd, "Michael J. Fox: I Was 'Drinking Heavily' Following Parkinson's Diagnosis," People, September 26, 2013, www.people.com/people/article/0,,20739261,00.html.
7. Lawton Ursrey, "The Fastest Way to Life Success: Vulnerability," Forbes, July 20, 2014, www.forbes.com/sites/lawtonursrey/2014/07/20/the-fastest-way-to-life-success-vulnerability.
8. To read more quotes from Werner Erhard, see <https://wernererhardquotes.wordpress.com/tag/erhard-seminars-training>.
9. Rob Lowe, Stories I Only Tell My Friends (New York: Henry Holt, 2011).
10. To read more about Naomi Campbell, see Louise Gannon, " 'I Didn't Think I Would Make It to 40. I'm Not Proud of What I've Done,' Naomi Campbell on Her Regrets," Mail Online, last modified March 21, 2010, www.dailymail.co.uk/home/moslive/article-1258631/Naomi-Campbell-I-didnt-think-I-make-40-Im-proud-Ive-done.html.
11. For more quotes by Anthony Robbins, see www.goodreads.com/author/quotes/5627.Anthony_Robbins.
Day 28: The Review Day and Bonus Solution
1. Deepak Chopra, A Deepak Chopra Companion: Illuminations on Health and Human Consciousness (New York: Three Rivers Press, 1999).
PHASE V: CREATING YOUR PERSONALIZED PLAN TO THRIVE IN LIFE
1. Covey, 7 Habits of Highly Effective People.
Day 29: The Vision Solution
1. See <http://yourstory.com/2014/05/dhirubhai-ambani-quotes>.
2. Soren Gordhamer, "If the Buddha Used Twitter," Huffington Post, August 6, 2009, www.huffingtonpost.com/soren-gordhamer/if-the-buddha-used-twitte_b_224963.html.
3. Covey, 7 Habits of Highly Effective People.
4. Swayze and Niemi, Time of My Life.
5. To read an article on finding your dream job and how to get it, see Laura Garnett, "5 Steps to Discover Your Dream Job," Business Insider, February 24, 2014, www.businessinsider.com/how-to-find-your-dream-job-2014-2?nr_email_referer=1&utm_source=Triggermail&utm_medium=email&utm_term=Business%20Insider%20Select&utm_campaign=BI%20Select%20Mondays%202014-02-24&utm_content=emailshare.
6. King, On Writing.
7. Hamilton, Beyond Belief.
8. Jim Loehr and Tony Schwartz, The Power of Full Engagement: Managing Energy, Not Time, Is the Key to High Performance and Personal Renewal (New York: Free Press, 2003).
9. See www.people.com/people/archive/article/0,,20160692,00.html.
Day 30: The Sobriety for Life Solution
1. Millman, Everyday Enlightenment.
2. To read more about alternatives to abstinence and various studies, see Adi Jaffe, "Helping Addicts Get Their Lives Back," Psychology Today, www.psychologytoday.com/blog/all-about-addiction/201103/abstinence-is-not-the-only-option, and www.astrocyte-design.com/pseudoscience/alcoholism.html.
3. For the full definition, see www.thefreedictionary.com, s.v. "sobriety."
4. Clapton, Clapton.
5. Daniel Goleman, "Breaking Bad Habits: New Therapy Focuses on the Relapse," New York Times, December 27, 1988, www.nytimes.com/1988/12/27/science/breaking-bad-habits-new-therapy-focuses-on-the-relapse.html.
6. To read more about how abstinence is the best path for some people, see William J. Cromie, "Five Years Is Magic Number for Recovering Alcoholics: Attempts at Social Drinking Frequently Lead to Relapse," Harvard University Gazette Archives, March 14, 1996, <http://news.harvard.edu/gazette/1996/03.14/FiveYearsIsMagi.html>.
7. To read more about a survey that asked, "Did you once have a problem with drugs or alcohol, but no longer do?" see Josie Feliz, "Survey: Ten Percent of American Adults Report Being in Recovery from Substance Abuse or Addiction," Drugfree.org, March 6, 2012, www.drugfree.org/newsroom/survey-ten-percent-of-american-adults-report-being-in-recovery-from-substance-abuse-or-addiction.
8. To read and watch an interview with Audrey Kishline, see Dennis Murphy, "Road to Recovery," Dateline, Nbcnews.com, www.nbcnews.com/id/14627442/ns/dateline_nbc/t/road-recovery/#.VG6NJ_nF-Sp.
9. Agassi, Open.
10. The Health Benefits of Volunteering: A Review of Recent Research (Washington, DC: Corporation for National and Community Service, Office of Research and Policy Development, 2007), www.nationalservice.gov/sites/default/files/documents/07_0506_hbr.pdf?tbl_pr_id=687.
11. Millman, Everyday Enlightenment.
12. Wayne W. Dyer, The Power of Intention (Carlsbad, CA: Hay House, 2010).
13. "Samuel L. Jackson with 64 Movies to His Credit, Is Featured in 'Star Wars the Phantom Menace,' " Jet, June 7, 1999.
14. After a period of not being able to exercise for several months due to a back injury, Jack started back into exercise by using Tony Horton's 10-Minute Trainer DVDs, produced and distributed by Beachbody. You can order the videos from amazon.com or beachbody.com. This is an easy way to get started. You just turn on the DVD and follow along.
15. See www.goodreads.com/author/quotes/399.Napoleon_Hill.
## Index
A note about the index: The pages referenced in this index refer to the page numbers in the print edition. Clicking on a page number will take you to the ebook location that corresponds to the beginning of that page in the print edition. For a comprehensive list of locations of any word or phrase, use your reading system's search function.
A
Abstinence, . See also Sobriety; Teetotalism; 30-Day Reboot
AA view of,
making the decision, –82,
prior to cutting back,
thriving in sobriety through, –79
Acceptance
meditation and,
in "Mental Makeover," , ,
Achievement
The Affirmation Solution and,
The Believe-in-Yourself Solution and, –4
Achor, Shawn,
Action
growth and,
as the heart of the program,
the Sobriety System and,
toward vision achievement,
The Action Solution, –67,
avoiding distraction in,
as a bridge to thriving in sobriety,
heroism in, –59
overcoming resistance in, –63
ready-fire-aim approach in, –64
sobriety anxiety as an obstacle to, –61
tiny habits in (see tiny habits)
Action steps
the Action Solution, , –67
the Affirmation Solution, , –95
the Attraction Solution, , , , –9
the Believe-in-Yourself Solution, , , , –16
the Core Values Solution, –80
the Courage Solution, , , , , –44
the Emotional Sobriety Solution, –64
the Eternal Optimist Solution, , –82
the Forgiveness Solution, , , –2
the 4-Minute-Mile Solution, –53
the Gratitude Solution, –21
importance of completing,
the Lie Detector Solution, , , , –201
the Love and Relationship Solution, , , , , , –43
the Meditation Solution, , , –79
the Mind and Body Solution, , –97
the 100% Solution, –45, –50,
the Outcome Solution, , , –32
the Pendulum Solution, , , , –84
the Positive Addiction Solution, , , , –24
the Purpose Solution, , , , , –70
the Quality Question Solution, –64
reviewing, –35
the Sobriety for Life Solution, , , , –89
the Subconscious Mind Solution, –11
the Tapping Solution, , ,
top fourteen, –49
the Vision Solution, , , , –72
the "Why Can't You Just Quit?" Solution, , , –53, –55
Acupuncture points, –13
Addiction. See also Alcohol abuse
explained, –80
loving your, –100
number of Americans in recovery from,
positive (see The Positive Addiction Solution)
"Addictive personalities," –88
Adrenaline,
Advertising, secrets of, –23
Aerobic training, –6
Affirmations, –95,
defined,
effectiveness of,
forgiveness, , , ,
guidelines for creating, –87
how to use, –91
the magic of, –86
personal achievement and,
supercharging, –92
Total Sobriety, –89, , –95,
vision statements as,
visualization and, ,
The Affirmation Solution, –95, . See also Affirmations
Agassi, Andre, ,
Agreements, keeping, –36, –43
The Alchemist (Coelho), ,
Alcohol
advertising of, –23
as poison, , ,
as stupid juice, –28
Alcohol abuse. See also Addiction; Drinking
disease model of,
dysfunctional family background and,
genetic predisposition in, ,
number of children affected by,
percentage of population involved in, ,
reclaiming your body from, –85
Alcohol detox smoothie, ,
"The Alcoholic King," –56,
Alcoholics Anonymous (AA), , , , , , , , , ,
attitude toward slips in, –77
the drunk-a-log in, –5
introduction ritual in, –94
Alcoholism/alcoholic (avoiding use of terms),
Ali, Muhammad, , , ,
Alkaline water,
Allergies. See Food allergies, sensitivities, and intolerances
"All It Takes Is 10 Mindful Minutes" (TED Talk),
All-or-nothing mentality, –73, , –71,
nutritional changes and,
positive addiction and,
Ambani, Dhirubhai,
American on Purpose (Ferguson),
Amygdala,
Anaerobic exercise,
Analyzing, –53, , –64
Anchors, ,
Andrews, Dave
AA meetings attended by,
affirmations used by,
as America's #1 Sobriety Coach,
before-and-after photos of,
"before" story of, –65
Bryan's influence on, –98
childhood drinking by,
congratulatory letter from his daughter, –78
core values of, –70
dietary changes made by, –95
exercise habits of, –3
fears of, –32,
first meeting with Jack, , –8
gratitude practiced by,
health improvements and, –85
health problems caused by drinking, –45, –96, –13
letters of gratitude written by,
life purpose of, –53, , –71
limiting beliefs and, –95, –98
"Mental Makeover" and, –51, , –55
negative thinking and,
"new you" exercise and,
"normal drinking" and, –81
the 100% Solution and, –39
personal struggle with drinking, , , –34
questions asked by, ,
reasons for drinking,
success standards of, –58
tapping and,
Thriving-in-Sobriety Vision of,
vision board created by,
vision statement of, –66,
willpower limitations and, , ,
The Work and, –62
The Anonymous People (film), , n13
The Answer: Your Guide to Achieving Financial Freedom and Living an Extraordinary Life (Assaraf and Smith), –30
Antabuse,
Anxiety
meditation and, –73
sobriety, –61
Arenson, Gloria, –16
Aristotle, ,
The Art of Exceptional Living (Rohn),
Ask, believe, receive process, –98, , , –9,
Ask and It Is Given: Learning to Manifest Your Desires (Hicks and Hicks),
Assaraf, John, –30
Assigning, –56, ,
Attitude of gratitude
cultivating, –13
Susan's, –15
The Attraction Solution, –309,
ask, believe, receive process in, –98, , , –9,
Dan's story, –300
the Daydreamer's Dilemma and, –302,
the Gratitude Solution and, ,
input = output equation in, –4,
your new story and, –8,
Audio version of book/program, , ,
Authentic Happiness (Seligman),
Awaken the Giant Within (Robbins),
Awareness, , –49
in "Mental Makeover," –51, , ,
the power of, –74
B
Bannister, Roger,
Barrymore, Drew,
Batmanghelidj, F.,
Baumeister, Roy,
Beatles,
"Before you," ,
guidelines for capturing, –66
reviewing notes on, –82, ,
Beliefs, –201. See also The Believe-in-Yourself Solution
affirmations and, –89
the Attraction Solution and,
changing limiting, –85,
creating new, –200
the cross-examination, –98,
influence of, –83
lies that limit, –90
the Sobriety System and, , ,
sources of limiting, –96
tapping for release of limiting,
The Believe-in-Yourself Solution, –16, , –84. See also Beliefs
achievement and, –4
choice in, –11
as essential for sobriety, –6
opinions of others and, –12
the placebo effect and, –10
sober vacations and, –7
summing up,
teetotalism and, –8
visualization and,
Bell, Alexander Graham,
Beyond Belief: Finding the Strength to Come Back (Hamilton),
The Biggest Loser (television program),
Binge drinking,
The Biology of Belief (Lipton), , ,
Blakeslee, Sandra,
Blaming, giving up, –35
Blanchard, Ken,
Blood pressure
high, ,
laughter and,
The Body Fat Solution (Venuto),
Body for Life: Weeks to Mental and Physical Strength (Phillips), ,
Bono,
Bonus solutions
the Frequently Asked Sobriety Questions Solution, , ,
the Relapse Solution, , , ,
the Sobernomics Solution, ,
the Social Solution, , , ,
The Book of Understanding: Creating Your Own Path to Freedom (Osho),
Boredom, , –86,
"Breakthrough to Success" (seminar),
Breast cancer, ,
Breathing, , –73, , , ,
Bristol, Claude M.,
Brooks, Audrey,
Brown, Brené,
Bruner, Pamela,
Buddha, –25, ,
Buffett, Warren, ,
Butler, Gerard,
C
Callahan, Roger,
Campbell, Naomi, ,
Cancer, ,
Canfield, Jack
addictions in family of, –2, ,
affirmations used by,
as America's #1 Success Coach,
dietary changes made by,
exercise habits of, ,
first meeting with Dave, , –8
goal setting and,
life purpose of, ,
meditation practice of,
tapping and, –14
vision statement of,
Career/job
drinking impact on,
ideal vision of, , –66
Carnegie, Andrew, ,
Carnegie, Dale,
Carrey, Jim, , , , ,
Celebrity Rehab (television program),
Center for Mind-Body Medicine,
Center for Preventive Cardiology,
Center for Progressive Recovery,
Center of Addiction Studies,
Centers for Disease Control and Prevention (CDC),
Chandler, Steve, , ,
Chaplin, Charlie,
Chbosky, Stephen,
Chia seeds,
Chicken Soup for the Soul (Canfield and Hansen), , ,
Childhood trauma, , , ,
Chopra, Deepak, –82, , , ,
Church, Dawson, , ,
Churchill, Winston, ,
Cirrhosis,
Clapton, Eric, ,
Clapton: The Autobiography (Clapton),
Clean: Overcoming Addiction and Ending America's Greatest Tragedy (Sheff), , ,
Co-Active Coaching: Changing Business, Transforming Lives (Kimsey-Housen et al.),
Coelho, Paulo, ,
Cognitive therapy, ,
Cohen, Alan,
Colon cancer,
Comfort zone, , ,
change at the edge of, –54,
the subconscious mind and,
Community, ideal vision of, ,
Companion website
accessing, –13
affirmations on,
alcohol detox smoothie recipe on, ,
"before you" exercise on,
benefits of using, ,
cognitive therapy resources on,
documentary film on,
on envy,
on exercise, ,
the Frequently Asked Sobriety Questions Solution on,
gratitude process on,
on hypnotism,
imagery exercises on,
journaling solutions on,
Life Purpose Exercise on, ,
list of core values on,
list of famous teetotalers on, ,
list of memoirs on,
list of workshops, retreats, and seminars on,
material and features of, –17
meditation music on, ,
meditations on, , , , , ,
the "Mental Makeover" on,
Movie Moment (guided version) on,
personal growth resources on,
on the placebo effect,
the Relapse Solution on, ,
the Sedona Method on,
the Sobernomics Solution on,
the Sobriety System on,
the Social Solution on,
success stories on, –96
tapping video on, ,
on the two most self-destructive words,
Vision Compass Creator on, ,
visualizations on,
on The Work, ,
Comparison game, –53,
Complaining, giving up, –36
Cone of Learning, –48
Confirmation bias, –13, –16
Conscious Living: Finding Joy in the Real World (Hendricks),
Constructive Living (Reynolds),
Consumer Lab,
Contemplative Neuroscience, Mindfulness Research and Practice Initiative,
Core values, –80,
contradictions to, –70
defining,
discovery process, –79
integrating, –80
mission statements reflecting,
questions and,
Robert's story, –75
the Sobriety System and (see The Sobriety System)
in vision statement,
The Core Values Solution, –80, . See also Core values
Corporate vision/mission,
Corporation for National and Community Service (CNCS),
Cortical inhibition,
Cortisol, ,
The Courage Solution, –44. See also Failure; Fear
Covey, Stephen, , , ,
"Crabs in a bucket" analogy, –38
Craig, Gary, , ,
Cravings
diet and, , , ,
meditation and, –73
"normal drinking" and,
tapping for relief from, , –25
Cross-examination (of limiting beliefs), –98,
Crossroads Centre Antigua,
Cruise, Tom,
Csikszentmihalyi, Mihaly,
Curtis, Jamie Lee,
D
TheDailyLove.com,
Dale, Edgar,
Darwin, Charles,
Davis, Danny,
Davis, Kristin,
Daydreamer's Dilemma, –302,
Daydreaming, –56
Dayton, Tian,
DeAngelis, Barbara,
Deaths, alcohol-related,
Decision fatigue, –52,
Decisions, destiny as the consequence of, –32,
Dehydration,
Deletion, , –79
Dementia,
Denial, , ,
the comparison game and, –53,
the Movie Moment and, –51, –55
Depp, Johnny,
Depression,
Destiny, decisions and, –32,
Diet. See Nutrition/diet
Diet for a New America (Robbins),
Disease model of alcoholism,
Disney, Walt,
Divorce,
Docosahexaenoic acid (DHA),
Doctors/health care professionals
advice on supplements from,
approval for exercise from,
consulting before quitting drinking, , , n9
getting a physical exam from, –45
guidance on nutrition from,
Dopamine, –37,
diet and,
drinking impact on, –36
laughter and,
meditation and,
superstress and,
supplements for stimulating, –37
Downey, Robert, Jr., , , ,
Dreams, drunk,
Drinking. See also Alcohol abuse; "Normal drinking"
alleged health benefits of,
binge,
choosing the time to quit,
dangers of quitting abruptly, , n9
daydreams during, –56
dealing with temptation, , –19,
health problems caused by, –45, –87
as a substitute for love, –28
triggers for, –53,
underlying causes of, –42, , –49, ,
as your greatest gift, –78,
Drinking: A Love Story (Knapp),
Drinking thinking, –69
Drownings, alcohol-related,
Drucker, Peter,
Drunk-a-log, –5
Drunk dreams,
Drweil.com,
Duality, law of,
Duhigg, Charles,
Dweck, Carol,
Dyer, Wayne, , ,
E
Earl, Esther, –33
Easwaran, Eknath,
Eat, Pray, Love (Gilbert),
Eat That Frog! 21 Great Ways to Stop Procrastinating and Get More Done in Less Time (Tracy),
Edinburgh Sleep Centre,
Edison, Thomas, ,
EFT (Emotional Freedom Techniques), . See also The Tapping Solution
EFT for Procrastination (Arenson),
The EFT Manual (Church),
The EFT Manual (Craig), ,
Eicosapentaenoic acid (EPA),
8 Weeks to Optimum Health (Weil),
Einstein, Albert, , , ,
The Einstein Solution, –58
Eker, T. Harv,
Elance,
"The 11 Forgotten Laws" (program),
Email support system, ,
Emmons, Robert,
Emotional intelligence, , n1
Emotional reasoning, , ,
Emotional Sobriety: From Relationship Trauma to Resilience and Balance (Dayton),
The Emotional Sobriety Solution, –64
awareness in, –49, –51
definition of concept,
emotional sobriety filter in, –50
emotion-feeling distinction in, –48
"Mental Makeover" in (see "Mental Makeover" process)
success standards in, –59
The Work in, –63,
Emotions,
affirmations and, ,
awareness of, –49, –51
feelings distinguished from, –48
highs and lows in, –56
the Quality Question Solution and,
the Sobriety System and,
the Tapping Solution and,
visualization and, –44
Endorphins, , ,
Eragon (Paolini),
Erhard, Werner,
E (Event) + R (Response) = O (Outcome) equation, –34,
Esophageal ulcers,
est Training,
The Eternal Optimist Solution, –82
awareness in, –74
on negative drinking thinking, –69
on negative thinking traps (see Negative thinking traps)
on negativity, –67
positive-focus approach in, –78
on the positive thinking trap, –81
Euphoric recall, , ,
Everyday Enlightenment (Millman),
Exaggeration, –72, ,
Exercise, , , –411, , , ,
aerobic, –6
alcohol consumption reduced by,
anaerobic,
easy, –4
getting started, –5
injury avoidance, ,
as a "magic pill," –400
the science of, –401
sleep improvement and, –11
strength training, , –7
ten tips to start and never stop, –9
Exploding-through visualization, ,
F
Failure
failing forward, –36
fear of, –32
Fats, –92
The Fault in Our Stars (Green), ,
Favre, Brett, ,
Fear, –32,
acknowledging and accepting,
as a compass, –39
of failure, –32
fantasy role in, –31
of leaving the comfort zone, –54
measuring, –43
reasons for,
saying "yes" in spite of, –41
thriving through overcoming, –37
two primary,
two types of,
of vulnerability, –33
Feelings
emotions distinguished from, –48
The Quality Question Solution and, –60
the Sobriety System and, ,
Ferguson, Craig, ,
Finances, ideal vision of, ,
Fires, alcohol-related,
Five Minute Phobia Cure,
Fiverr,
Flow: The Psychology of Optimal Experience (Csikszentmihalyi),
Fogg, B. J.,
Foggy brain, –35
Food allergies, sensitivities, and intolerances, , –95, n32
Forbes (magazine),
Ford, Henry,
Forgive and Forget: Healing the Hurts We Don't Deserve (Smedes),
The Forgiveness Solution, –102, , , , ,
accepting sobriety as deserved in, –87
affirmation for, , , ,
Bryan's story, –98
Desiree's story, –94
loving your addiction in, –101
moving on in,
self-forgiveness in, , –92
self-love in, –101
tapping and, ,
the Total Truth Process in (see The Total Truth Process)
visualization and,
The 4-Minute-Mile Solution, –53, , . See also Visualization
4-7-8 Relaxing Breath Exercise, –73, ,
Fox, Michael J.,
Freedom from Addiction: The Chopra Center Method for Overcoming Destructive Habits (Chopra and Simon), ,
Freeman, Morgan,
Frehley, Ace,
French, Jemima,
The Frequently Asked Sobriety Questions Solution, , ,
Freud, Sigmund,
Frostbite,
Fun,
drinking linked with, –89
"permission slip" for, –23
G
GABA supplements,
Gastritis,
Gelb, Michael, –57,
Generalizing, –71, ,
Genius Code (Scheele),
The Gifts of Imperfection: Let Go of Who You Think You're Supposed to Be and Embrace Who You Are (Brown),
Gilbert, Daniel,
Gilbert, Elizabeth,
Gillette, King,
Giving back, –83,
Glasser, William, –80,
Gluten intolerance,
Goal setting, –32
excessive,
for exercise (avoiding), –9
gratitude and, –17
James's story, –27
positive pressure and, –22
the positive thinking trap and,
the power of,
reasons for failure in, –29
reviewing objectives in, –32
the short-term trap, –21,
SMART (see SMART goals)
thriving in sobriety and, –25
the Vision Compass and, ,
Goals! How to Get Everything You Want—Faster than You Ever Thought Possible (Tracy),
Gober, O. F.,
The Golden Buddha, –25
Gomez, Javier,
Gordis, Enoch,
Gordon, James,
Gratefulness.org,
Gratitude, –21,
attitude of (see Attitude of gratitude)
the Attraction Solution and, ,
goals and, –17
meditation and, ,
opposite of, –14
as the secret of sobriety, –12
The Gratitude Solution, –21. See also Gratitude
Gray, John,
Green, John, ,
Guilt, –87
Guts: The Endless Follies and Tiny Triumphs of a Giant Disaster (Johnston),
H
Habits
bad, –69
tiny, –66, , ,
Hamilton, Josh, ,
Happiness
drinking linked with, –90
gratitude and,
meditation and,
The Happiness Advantage (Achor),
"Happy, Healthy, Wealthy Game" (teleseminar),
"Happy Hour," –85,
Harris, Dan,
Harry Potter (Rowling),
Harvard Medical School,
Harvard University, ,
Head and neck cancer,
Health, –97. See also Exercise; Nutrition/diet
body's restorative powers and,
drinking-related problems in, –45, –87
ideal vision of, ,
the mind-body connection in, –82
new standards for your new body, –83
top five factors affecting,
Health care professionals. See Doctors/health care professionals
Heart disease, ,
Heart rate monitors,
Hendricks, Gay,
Hero, definition of, –59
Herophilus,
Hershey Company,
Hicks, Esther, , , , –2,
Hicks, Jerry, , , , –2,
High-fructose corn syrup,
High-intensity circuit training (HICT),
High-intensity interval training (HIIT),
Hill, Napoleon, , , , , , ,
Hogan, Ben,
Holland, Isabelle,
Holtz, Lou, ,
Homicide, ,
"Hour of Power,"
Howard, Vernon,
The How of Happiness: A Scientific Approach to Getting the Life You Want (Syubomirsky),
"How" questions, , ,
How to Think Like Leonardo Da Vinci: Seven Steps to Genius Every Day (Gelb), –57
How to Win Friends and Influence People (Carnegie),
Hypnotism,
Hypothermia,
I
"I can't" (refusing to say), –11, ,
"I love myself" (mantra), –101, ,
Immune system, ,
Institute for Integrative Nutrition,
Integrative Medicine (journal),
Introduction to Basic Tapping (video), ,
Irregular heartbeat,
Irving, Washington,
Isolation, , ,
J
Jackson, Samuel L., , , ,
James, Henry, Sr.,
James, William,
Jefferson, Thomas,
Jha, Amishi,
John, Elton, ,
Johnston, Kristen,
Journaling, , ,
awareness increased by,
on fears, –41,
on food/diet,
on gratitude, , –19
importance and benefits of, –48
on isolation and loneliness,
on negative thinking traps, , , –82
"normal drinking" and,
privacy considerations, –47
quit-drinking strategy in, –83,
on success standards, –59
tips for,
on willpower, ,
Jumping to conclusions, , , ,
Jung, Carl,
K
Kabat-Zinn, Jon,
Katie, Byron, , ,
Kefir,
Keller, Helen, ,
Kennedy, John F.,
Kiddard, Jackson,
King, Heather,
King, Martin Luther, Jr., , ,
King, Stephen, , , ,
Kipp, Mastin,
Kirsch, Irving,
Kishline, Audrey,
Kit Kat bars, marketing strategy for,
Knapp, Caroline,
Kripke, Daniel,
L
Labeling, negative, ,
Landers, Ann,
Landmark Forum,
Landy, John,
Lao Tzu,
Laughter, –13
Laughter Yoga,
Law of attraction, , , , , , . See also The Attraction Solution
Law of duality,
Learned helplessness,
Learning Strategies Corporation,
Legacy, –57
The Lie Detector Solution, –201, , , , , . See also Beliefs
Life purpose, –60. See also The Purpose Solution
alcohol as a replacement for,
coming back to, –71
discovering, –54
misconceptions about,
Thomas's story, –60
Life Purpose Exercise, –58,
The Life You've Always Wanted (Ortberg), –44
Lipton, Bruce, , ,
Little Girl Lost (Barrymore),
Lively, Blake,
Liver cancer,
Liver disease,
Llewellyn-Edwards, Mair,
Loehr, Jim,
Loneliness, , ,
Lopez, Jennifer, ,
Lottery winners, bankrupt,
Lovato, Demi,
Lovato Treatment Scholarship Program,
Love
drinking as a substitute for, –28
self-, –101
of your addiction, –100
The Love and Relationship Solution, , –43
cleaning up your messes in, –32
concerns about fairness and, –39
concerns about selfishness and,
considering regrets in,
on the drinking-love substitution, –28
evaluating/changing your associates in, –41
keeping agreements in, –36, –43
on marriage, –40
merging the two yous in, –30
on the myth behind your messes, –33
Love Yourself Like Your Life Depends on It (Ravikant),
Loving What Is: Four Questions That Can Change Your Life (Katie),
Lovins, Amory,
Lowe, Rob, , ,
Lucky Man: A Memoir (Fox),
M
The Magic of Believing: The Science of Setting Your Goal and Then Reaching It (Bristol),
The Magic of Thinking Big (Schwartz),
Magic pill, –400
"Magic Three of Gratitude," –21
Maguire, Tobey,
Maltz, Maxwell, , , ,
Mantras
"I love myself," –101, ,
technique for using, ,
Marines, US,
Marriage, –40
Matthew (gospel),
McGraw, Tim,
McGregor, Ewan, ,
Meditation, , –79, , ,
benefits of, –66
for cleaning up mental clutter, –71
defined and explained, –68
happiness and,
how to practice, –75
Merge, , ,
mindfulness, bad habits, and, –69
myths of, –67
powerful variations in, –77
The Meditation Solution, –79. See also Meditation
Memoirs of recovery,
Memory damage,
Mental contrasting technique,
"Mental Makeover" process, ,
review of, –64
stages of, –56
Merge Meditation, , ,
Miguel, Luis,
Miller, Michael,
Millman, Dan, , , –83
The Mind and Body Solution, , –97. See also Health; Nutrition/diet
Mind-body connection, –82
Mindfulness, –69
Mind reading,
Mindset: The New Psychology of Success (Dweck),
Minimization, –72,
Mission statements,
Mlodinow, Leonard, –6
Moderation Management,
Money, and the Law of Attraction: Learning to Attract Wealth, Health, and Happiness (Hicks and Hicks), –2
Monkey trap,
The Monk Who Sold His Ferrari: A Fable About Fulfilling Your Dreams and Reaching Your Destiny (Sharma),
Morrissey, Mary,
Most Pressing Issue (MPI) (tapping protocol),
Movie Moment, –51, –55
Murphy, Eddie, ,
Murphy, Joseph,
Murray, Andy,
Muscle testing technique,
Music, –82, , , , , , , ,
Myth of "rock bottom," –40,
N
Najemy, Robert Elias, n8
Napping,
National Aeronautics and Space Administration (NASA), –30
National Institute on Alcohol Abuse and Alcoholism,
National Institutes of Health (NIH),
Negative drinking thinking, –69
Negative labeling, ,
Negative thinking traps, –82
Matt's breakthrough, –76
types of, –73
in your life, –80
Negativity
explained, –67
as the opposite of gratitude, –14
News programs, avoiding, –4, ,
Newton, Isaac,
New York Times,
New York Times Magazine,
New York University,
"New you," , ,
guidelines for realizing, –68
new beliefs and, –200
reviewing notes on, –82, , ,
story of, –8,
No-Exceptions Rule, –39
"Normal drinking," –12, –29, –82
abstinence period prior to,
Ann's story, –91
controversy over,
as deprivation, –76
guidelines for, –80
making the decision, –82,
testing the water for, –78
thriving in sobriety through, –81
Nutrition/diet, –83, –97,
free days and, –93
hardwired preferences and, –92
healthy eating strategies in, –94
individual differences and,
the mind-body connection and, –82
90 percent plan in,
O
Obesity/overweight,
Oettingen, Gabriele,
Okung, Russell,
Oldman, Gary,
Omega-3 fats,
One-day-at-a-time approach, –53
"101 New Activities for Your New Life of Thriving in Sobriety," , –21, ,
The 100% Solution, –50, , , , , ,
addressing underlying causes in, –42
central concept of, –33
destiny and decisions in, –32,
do-it-yourself approach in, –43
the E + R = O equation in, –34,
giving up blaming in, –35
giving up complaining in, –36
the myth of "rock bottom" in, –40
the No-Exceptions Rule in, –39
visualization and,
as a vote for living, –45
100 Ways to Motivate Yourself: Change Your Life Forever (Chandler), ,
The One Minute Manager (Blanchard and Johnson),
Optimism. See The Eternal Optimist Solution
Ortberg, John,
Ortner, Nick,
Osho, –28
The Outcome Solution, –32, , , , . See also Goal setting
P
Page, Geraldine,
Pain
as a motivator, ,
reinforcing link to drinking, –82
tapping away,
Pain-pleasure balance, –47
Pantalon, Michael,
Paolini, Christopher,
Parched: A Memoir (King),
Passion, –56
Past, , –53. See also The Pendulum Solution
Peale, Norman Vincent, , ,
The Pendulum Solution, –84, , , , , ,
all-or-nothing mentality in (see All-or-nothing mentality)
the gift of drinking in, –78
the law of duality in,
the pleasure principle in (see Pleasure principle)
quit-drinking strategy in, –83,
visualization and,
Perfectionism, ,
The Perks of Being a Wallflower (Chbosky),
"Permission slip" for fun, –23
Perry, Matthew,
Personalization, , ,
Persuasive Technology Lab,
Phillips, Bill, , , ,
Physical (medical) exam, –45
Pinsky, Drew,
Pinterest,
Placebo effect, –10, ,
The Plan: Eliminate the Surprising "Healthy" Foods That Are Making You Fat—And Lose Weight Fast (Recitas),
Plato, ,
Pleasure principle, –200. See also Pain-pleasure balance
importance of, –79
working with, –82
Pneumonia,
P90X program, , ,
Poitier, Sidney,
Pollack, Harold,
Portman, Natalie, ,
Positive Addiction (Glasser), –80
The Positive Addiction Solution, –424,
benefits of,
exercise in (see Exercise)
laughter in, –13
the "permission slip" for fun in, –23
sleep in, –11
suggested activities for, –21
variety in, –16
Positive choice statement (tapping protocol), –23
Positive pressure, power of, –22
Positive thinking trap, –81
The Power of Full Engagement (Loehr and Schwartz),
The Power of Habit: Why We Do What We Do in Life and Business (Duhigg),
The Power of Intention (Dyer),
The Power of Now: A Guide to Spiritual Enlightenment (Tolle), ,
The Power of Positive Thinking (Peale),
The Power of Your Subconscious Mind (Murphy),
The Power of Your Supermind (Howard),
Prefrontal cortex, –9
Presley, Elvis,
Preston, Kelly,
Presuppositions, , –64
Prince,
"Problem drinker you," –30,
Procrastination, , ,
Proctor, Bob,
Psycho-Cybernetics: A New Way to Get More Living Out of Life (Maltz),
Psychological Science (journal),
The Psychology of Winning: Ten Qualities of a Total Winner (Waitley),
Puddicombe, Andy,
Pujols, Albert,
The Purpose Driven Life: What on Earth Am I Here For? (Warren), ,
The Purpose Solution, –70, , , , , . See also "Before you"; Life purpose; "New you"; Thriving-in-Sobriety Vision Statement
exploring the "why" of behavior, –63
goal of,
leaving the comfort zone, –54
one-day-at-a-time approach, –53
staying on purpose, –69
visualization and,
Q
The Quality Question Solution, –64, . See also Questions
Questions, –64
asking the right, –63
assigning and, –56
the Einstein Solution and, –58
"how," , ,
meditation and, –67,
presuppositions as a hindrance to, , –64
quality of life and, –61
"why," , ,
The Work and, –61
R
Rand, Ayn,
Rating/ranking systems
pain-pleasure,
for relationships, –38,
Ravikant, Kamal,
Reading/books, –87
Ready-fire-aim approach, –64
Reagan, Ronald,
Recitas, Lyn-Genet,
Recreation/free time, , . See also Fun
"Rediscovering Your Joy" (guided meditation), ,
Reed, Kari,
Regrets,
The Relapse Solution, , , , . See also Slips
Relationships, ideal vision of, –64, . See also The Love and Relationship Solution
Reminder phrase (tapping protocol), –22
REM sleep,
Repetition, importance of, , , , –23,
Research Society on Alcoholism,
Resistance, overcoming, –63
Resnick, Robert,
Resveratrol,
Reticular activating system (RAS), –83, , , ,
Review days
Phase I, –38
Phase II, –31
Phase III, –23
Phase IV, –45
Reynolds, David,
Ricard, Matthieu,
Ricci, Christina,
Risks, –36
Robbins, John,
Robbins, Tony, , , , , , , , , ,
Robinson, Diana,
Robinson, Jackie,
"Rock bottom," myth of, –40,
Rockefeller, John D., ,
Rohn, Jim, , , ,
Role models, , , , , , ,
Roller coaster of life, –56
Roosevelt, Eleanor, –42
Rosenthal, Joshua,
Ross, Diana, ,
Rourke, David,
Rowling, J. K.,
Ruth, Babe,
Ryan, Richard,
S
Salt, –92
Scheele, Paul R.,
Schwab, Charles M.,
Schwartz, David J.,
Schwartz, Tony,
Seattle Seahawks,
Secrets of the Millionaire Mind: Mastering the Inner Game of Wealth (Eker),
The Sedona Method,
Self-esteem, , ,
Self-help books, –87
Seligman, Martin,
September terrorist attacks, ,
Serotonin, –37,
drinking impact on, –36
exercise and,
giving back and,
meditation and,
superstress and,
supplements for stimulating, –37
Setup statement (tapping protocol),
The 7 Habits of Highly Effective People (Covey), , , ,
Sex, sobriety and, –86
Sexual assault,
Shaffer, Howard J.,
Shame, –87
Sharma, Robin,
Sheen, Martin,
Sheff, David, –3, ,
Sherman, Cindy,
Shinn, Florence Scovel,
Short-term trap, –21,
"Should" statements, , , , ,
Simon, David, ,
SLAM, NYC,
Sleep, –11
Slips. See also The Relapse Solution
AA view of, –77
awareness and, –74
dealing with, –41, –56
SMART goals, –23, –25, , ,
Smedes, Lewis B.,
Smith, Jada Pinkett,
Smith, Murray, –30
Smoking,
Smoothies, , –94
The Sobernomics Solution, ,
"Sober you," –30,
Sobriety. See also Abstinence; The Emotional Sobriety Solution; The Sobriety for Life Solution; Teetotalism
beliefs about, –86, –90,
defined, ,
deserving and accepting, –87
dietary changes and, –82
happiness and, –90
number one reason for not attaining, –6
perceived difficulty of,
physical changes and,
sex and, –86
during vacations, –7
Sobriety anxiety, –61
The Sobriety for Life Solution, –89
awareness of direction in, –84
defining characteristics in, –87
giving back in, –83,
"Happy Hour" in, –85,
on "normal drinking" (see "Normal drinking")
Sobriety killers, , ,
The Sobriety System, , , , , ,
components of, –73
the subconscious mind and, , ,
visualization and,
The Social Solution, , , ,
Soy intolerance,
Sperry, Roger,
Spielberg, Steven,
Stanford University,
Stein, Ben,
Steindl-Rast, David,
Stomach ulcers,
Stone, Sharon,
Stories I Only Tell My Friends: An Autobiography (Lowe),
Strength training, , –7
Stress,
drinking impact on,
laughter for,
meditation for, –71
super,
tapping to relieve, ,
Stress hormones,
Structural tension, , ,
Stumbling on Happiness (Gilbert),
Stupid juice (alcohol), –28
Subconscious mind, –11
affirmations and, –86, –94
avoiding negatives with, , , –9
behavior influenced by, –5
changing, –10
defined,
first six years of life and, –8
goal setting and, ,
identifying drinking links in,
questions answered by, –58, –61, ,
the recording of your life in,
reprogramming before sleep,
visualization and,
The Subconscious Mind Solution, –11. See also Subconscious mind
Subliminal: How Your Unconscious Mind Rules Your Behavior (Mlodinow), –6
Success
changing your standards of, –59
in relationships,
The Success Principles (Canfield), ,
Sugar, –38, , , –92,
Sugar shock,
Suicide, –98, ,
Superstress,
Supplements, –37
Swayze, Patrick, , , ,
Syubomirsky, Sonja,
T
Talents and strengths,
Tao Te Ching (Lao Tzu),
Tapping into Ultimate Success: How to Overcome Any Obstacle and Skyrocket Your Success (Bruner and Canfield),
The Tapping Solution, , , –29,
affirmations and,
changing recovery with, –15
for core issues, –28
for cravings, , –25
five ways to use, –17
how it works, –16
Jose's story,
for negative drinking-related emotions,
for pain and discomfort,
the protocol for, –23
as the stupidest thing you'll ever do, –14
tapping points,
tapping points diagram,
TED Talks,
Teetotalism, –8, , . See also Abstinence
Television, –4
10% Happier (Harris),
The Test, –19
Thanks! How the New Science of Gratitude Can Make You Happier (Emmons),
Think and Grow Rich (Hill), ,
30-Day Reboot, , , , –30, , , , –40,
"The 30-Day Sobriety Solution" (online coaching program),
The30DaySolution.com. See Companion website
30-Day Vision Statement. See Thriving-in-Sobriety Vision Statement
The 30/60/90 Day Plan, –27, –50
Thoughts
better-feeling, ,
changing,
the Sobriety System and, ,
Thriving
defining characteristics of, –87
by overcoming fear, –37
Thriving in sobriety,
through abstinence, –79
action as a bridge to,
through cutting back, –81
goals and, –25
importance of repeating phrase, , –10
keys to, –37
list of new activities for, , –21
Vision Compass for, –70
visualization for, –42
Thriving-in-Sobriety Vision Statement, –60, , , , , , , ,
core values in, –80
examples of, –60
goals that support, –25, ,
guidelines for,
questions that capture, ,
revisiting,
tiny-habits method and, ,
Tierney, John,
The Time of My Life (Swayze),
Time Travel Technique, , –66, , , , ,
Time Warrior (Chandler),
tiny habits, –66, , ,
Tolle, Eckhart, , , ,
Tolstoy, Leo,
Total Sobriety Affirmation, –89, , –95,
The Total Truth Process, –90, , , , ,
benefits of, –88
stages of, –90
Tracy, Brian, , , , , , ,
Traffic fatalities, alcohol-related,
Transformation (Phillips), ,
Trump, Donald, ,
Tuberculosis,
Twain, Mark, , –68,
Twain, Shania,
U
University of Chicago,
University of Connecticut,
University of Maryland Medical Center,
University of Miami,
University of Rochester,
Urban, Keith,
Ursrey, Lawton,
V
Vacations, sober, –7
Venuto, Tom, ,
Vibrational matching,
Violence, alcohol-related,
Vision, power of, –57
Vision boards, –49, –53,
Vision Compass, –70,
aligning, –67
clarification of objectives with, –64
using to thrive in sobriety, –70
The Vision Solution, –72
corporate vision/mission in,
for the ideal life, –62
life purpose in (see Life purpose)
the Vision Compass in (see Vision Compass)
Vision statements, –67, . See also Thriving-in-Sobriety Vision Statement
Visualization, , , –53,
affirmations and, ,
best times to practice,
breaking the -minute-mile barrier with, –39
Byron's story, –46
enhancing other solutions with, –52
exploding-through, ,
process of, –41
supercharging, –44
for thriving in sobriety, –42
vision board for (see Vision boards)
in your underutilized time,
Volunteering. See Giving back
Vulnerability, fear of, –33
W
Waitley, Denis, ,
Walking,
Ware, Bronnie,
Warren, Rick, ,
Washington Post,
Water intake, –91, ,
Way of the Peaceful Warrior (Millman),
Website for program. See Companion website
Weight, –90, . See also Nutrition/diet
Weight training,
Weil, Andrew, –73,
Wherever You Go, There You Are (Kabat-Zinn),
The "Why Can't You Just Quit?" Solution, –55, –52. See also Willpower
Why Meditate: Working with Thoughts and Emotions (Ricard),
"Why" questions, , ,
Why Your Life Sucks . . . and What You Can Do About It (Cohen),
Wilkes, Rick,
Williams, Venus,
Williamson, Marianne,
Willis, Bruce,
Willpower, –55,
decision fatigue and, –52,
defined, –44
pain-pleasure balance and, –47
role of in life, –49
the truth about,
visualization and, –52
Willpower: Rediscovering the Greatest Human Strength (Baumeister and Tierney),
Willpower illusion,
Wilson, Bill,
Wine
alleged health benefits of,
study on purchasing behavior, ,
Winfrey, Oprah, , ,
Withdrawal
dangers of, , n9
tapping for relief from,
Women
alcohol effect on sleep in,
health consequences of drinking,
strength training for,
The Work, –63,
World Health Organization, ,
Worries, –61, ,
Wright, Frank Lloyd,
Y
Yes! (saying), –41, ,
Yes Man (film),
Yoga, ,
Your Body's Many Cries for Water (Batmanghelidj),
Your Erroneous Zones (Dyer),
Z
Ziglar, Zig, , ,
An Imprint of Simon & Schuster, Inc.
1230 Avenue of the Americas
New York, NY 10020
www.SimonandSchuster.com
Copyright ©2016 by Jack Canfield and David Beebe
Names and identifying details of some of the people portrayed and/or quoted in this book have been changed.
All rights reserved, including the right to reproduce this book or portions thereof in any form whatsoever. For information, address Atria Books Subsidiary Rights Department, 1230 Avenue of the Americas, New York, NY 10020.
First Atria Books hardcover edition January 2016
and colophon are trademarks of Simon & Schuster, Inc.
For information about special discounts for bulk purchases, please contact Simon & Schuster Special Sales at 1-866-506-1949 or business@simonandschuster.com.
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Text design by Paul Dippolito
Jacket Design and Photograph by Tehsin Gul
Author Photographs by Derek Smith and © Studio Victor Sanchez
Library of Congress Cataloging-in-Publication Data
Canfield, Jack.
The 30-day sobriety solution : how to cut back or quit drinking in the privacy of your own home / Jack Canfield and Dave Andrews.
pages cm
Summary: "A groundbreaking program to help you cut back or quit drinking entirely—in the privacy of your own home"—Provided by publisher.
Includes bibliographical references and index.
1. Alcoholics—Rehabilitation. 2. Controlled drinking. 3. Alcoholism—Treatment. I. Andrews, Dave, 1972- II. Title. III. Title: Thirty-day sobriety solution.
HV5276.C36 2015
616.89'106—dc23
2015005948
ISBN 978-1-4767-9295-8
ISBN 978-1-4767-9297-2 (ebook)
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Upholstery is a very specialized trade. We often take on a wide variety of projects. Sometimes those are one-of -kind projects that we are creating from scratch, or we might be making a number of the same type of furniture items, such as cushions, church pews, or restaurant booths. Other times we may be altering the frame, the style, or the cushions on a piece of furniture. Even the most highly skilled of craftspeople need a plan of attack before starting a new type of project. Making the prototype in advance will give you both the knowledge and experience to work out a better plan.
If at all possible, the prototype should be made before we touch the furniture, not to take any of the furniture apart until we have made the prototype. In addition, it is recommended that you have the client look at your prototype before you proceed. You want to make sure that they will be happy with what you are able to do. If the client is not happy with the prototype, you need to decide if you are capable with doing this job. OR, make another prototype. In any event, do not proceed with the job until the client is happy with the prototype AND you re confident that you can duplicate the structure of the prototype on their furniture.
Occassionally we may take on a job that it way above us, that we just aren't capable of doing. Making the prototype in advance of tearing apart the furniture lets us know if we made a mistake in taking on the project. If the prototype fails or we are unable to please the client with the prototye, then it gives a graceful way to get out of it before we make a big costly mistake AND have the client uphappy with us. All we would have to do is give back the client their money and their furniture. Yes, we would be out a little money here, but not nearly as much if we put a lot of time and money into the project and have it all fall apart.
If we cut the fabric before we have a clear understanding of the job, making mistakes can cost us a lot of money. Planning our jobs ahead will serve both us and the client much better.
As an example of preplanning, before beginning building hundreds or thousands of a product, manufactures will create a prototype so they can see how everything fits together and to see if everything works as it is supposed to. The manufactures do have an advantage over an upholsterer though. They can spread the cost of the prototype over the entire production run, so that the cost of the prototype is very small on a "per piece" cost.
Upholsterers, on the other hand, can't usually spread the cost of a prototype over dozens or hundreds of furniture pieces. We can only apply the cost of the prototype to that one job, so we can't afford to spend very much time on making prototypes. However, we also can't afford to make very many mistakes with the client's fabric and/or furniture.
Whenever I'm doing an upholstery job, most of the time I just measure and cut the client's actual fabric. However, sometimes when I'm doing an unusual job, or if I'm uneasy about whether the job will work out as I imagine, I use some substitute fabric to test out my ideas. I keep cheap fabric around to experiment with. Any time I'm trying something new, that I'm unsure about, I'll make a pattern and/or a very simplified (no cording, etc.) prototype out of the cheap fabric to make sure it will fit. If I'm unsure about how to do something, I won't cut the job fabric, but will instead use the cheap fabric. Once I have my prototype the way I want it, I'll use the pattern to make the client's job.
The main idea of making the prototype is (before starting the job) to plan both the job and to plan a way out of a potential disaster (that of wrecking the client's furniture or other project) and then not being able to satisfactorily complete the project. The prototype would help you gain the knowledge and experience needed to make the plan or to proceed without a written plan.
By doing this (and before you have damaged the chair) you should get a pretty good sense of whether or not the job is doable by you using the chosen material. Yes, it is a lot of extra work, but sometimes it may save a disaster OR give you the extra assurance and knowledge that you may need before starting the job.
Then the question would come up, "What type of material (fabric, vinyl, leather, etc.) should I use to make prototypes?". The answer would depend upon what type of projects you will be making. Ideally, you should use a type of material similar to what you will be actually using on the job. However in many cases almost any type of upholstery fabric or vinyl can be used. Depending upon the project I have even used drapery and clothing fabric, whatever I happen to have around. For a while I had a roll of some self-lined drapery fabric, which I used until it was gone.
Ideas: Fabric stores (or even upholstery suppliers) often sell off undesirable fabric very cheaply. Watch for sales. Remember, when making prototypes, you don't care what color it is. The cheap fabric may be very ugly or undesirable - That's probably why they are selling it so inexpensively. But, for a prototype, it doesn't matter if it's an ugly color. You are making the prototype to make sure the project will work and that everything fits.
If none of those fabric ideas are workable, you either purchase some extra of the chosen fabric or you can have the client purchase enough extra for the prototype.
There are numerous ways to make prototypes, depending upon what the project is. Since we are not getting paid to make a prototype and we don't have a large run to divide out the cost, we need to make the prototype as simply as possible. So, much of the time I'll make a stripped-down version of whatever I'm making. I'm mainly checking size and how it fits, so I don't need any cording, special designs, etc. I'll also only sew it up enough to make sure it fits. Keep the fitting, cutting, and sewing as simple as possible.
Occasionally the project may require that you put more details and go to more work to make the prototype. That's just part of cost of doing business. Just accept it an go on with the project.
Should You Charge for Making a Prototype?
Can you charge for the prototype? Sometimes you can, and sometimes you can't. If a making a prototype is necessary or advisable, I will make one whether I get paid for it or not. Being paid for the prototype is not the most important factor. Turning out quality work will repay you for your efforts in the form or happy clients and positive word of mouth advertising.
Whether you can or choose to charge to make a prototype is often a judgement call. Part of the determining factor depends on your skill level and the type of project you are asked to do. If you have beginning skill level AND the project is a common type of upholstery, and you are just trying to figure out how to do it, then I would not recommending charging. It is all part of your learning process, and it is not good to charge the client for your learning process.
One of the uses of making a prototype is in making a pattern for some furniture that has no original covering, or if you are changing the style of the furniture.
When you ask, "How do I make a pattern?", the unasked question I hear is "How do I make a pattern correctly the first time, without making a mistake?". I would direct you back to this article on making Prototypes. Making a prototype is allowing yourself to make a guess using scrap fabric and then try out the results to see how it fits. From that first prototype you see how far off your first guess was, then, if necessary, make a corrected second prototype and see how that fits. Then, if necessary, make any adjustments to your 2nd prototype pattern. Now you have your pattern that you can use to cut the real fabric. I doubt that even "high-tech" pattern makers make a perfect pattern every time.
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{"url":"https:\/\/tobaccocontrol.bmj.com\/content\/11\/1\/20?ijkey=e9cc0367a48694d9888bafe4441aab3f3b9b2aba&keytype2=tf_ipsecsha","text":"Article Text\n\nCigarette acquisition and proof of age among US high school students who smoke\nFree\n1. S Everett Jones1,\n2. D J Sharp2,\n3. C G Husten2,\n4. L S Crossett1\n1. 1Division of Adolescent and School Health, National Center for Chronic Disease Prevention and Health Promotion (NCCDPHP), Centers for Disease Control and Prevention (CDC), Atlanta, Georgia, USA\n2. 2Office on Smoking and Health, NCCDPHP, CDC, Atlanta\n1. Correspondence to:\u2028 Dr Sherry Everett Jones, Centers for Disease Control and Prevention, 4770 Buford Highway, NE, MS K-33, Atlanta, GA 30341, USA;\u2028 sce2{at}cdc.gov\n\n## Abstract\n\nObjective: To determine how US high school students who are under 18 years of age and who smoke obtain their cigarettes and whether they are asked for proof of age.\n\nDesign and setting: Data from the Centers for Disease Control and Prevention's 1995, 1997, and 1999 national Youth Risk Behavior Surveys which employed national probability samples of students in grades 9\u201312 (ages 14\u201318 years).\n\nMain outcome measures: Associations of usual source of cigarettes and request for proof of age with variables such as sex, race\/ethnicity, grade, and frequency of smoking.\n\nResults: In 1999, among current smokers under age 18 years, 23.5% (95% confidence interval (CI), \u22124.5% to +4.5%) usually purchased their cigarettes in a store; among these students, 69.6% (95% CI \u22125.7% to +5.7%) were not asked to show proof of age. As days of past month smoking increased, reliance on buying cigarettes in a store (p < 0.001) and giving someone else money to buy cigarettes (p < 0.001) increased, and usually borrowing cigarettes decreased (p < 0.001). From 1995 to 1999, relying on store purchases significantly decreased (from 38.7% (95% CI \u22124.6% to + 4.6%) to 23.5% (95% CI \u22124.5% to +4.5%)); usually giving someone else money to buy cigarettes significantly increased (from 15.8% (95% CI \u22123.6% to +3.6%) to 29.9% (95% CI \u22124.5% to + 4.5%)).\n\nConclusions: Stricter enforcement of tobacco access laws is needed to support other community and school efforts to reduce tobacco use among youth. Furthermore, effective interventions to reduce non-commercial sources of tobacco, including social, need to be developed and implemented.\n\n\u2022 minors smoking\n\u2022 proof of age\n\u2022 CDC, Centers for Disease Control and Prevention\n\u2022 PSU, primary sampling unit\n\u2022 SAMHSA, Substance Abuse and Mental Health Services Administration\n\u2022 YRBS, Youth Risk Behavior Survey\n\n## Request Permissions\n\nIf you wish to reuse any or all of this article please use the link below which will take you to the Copyright Clearance Center\u2019s RightsLink service. You will be able to get a quick price and instant permission to reuse the content in many different ways.\n\nAmong adults who have ever smoked daily, more than 80% first smoked cigarettes before the age 18 years.1 Thousands of teenagers smoke their first cigarette and become daily smokers each day.2 The age at which smoking begins influences the total number of years of smoking, the number of cigarettes smoked per day in adulthood, and the likelihood of quitting.1,3\u20136 All of these factors affect the risk for developing smoking attributable disease and disability such as lung cancer and other fatal malignancies, atherosclerosis and coronary heart disease, and chronic obstructive pulmonary disease.1,7 The Centers for Disease Control and Prevention (CDC) has estimated that if current patterns of smoking behaviour continue, five million Americans aged 0\u201317 years in 1995 could die prematurely from diseases related to smoking.8 Thus, preventing or delaying initiation is critical to preventing and reducing the morbidity and mortality associated with cigarette smoking.1\n\nNational health objectives set forth in \u201cHealthy People 2010\u201d seek to reduce tobacco use by adolescents and adults,9 and one of the 10 leading health indicators in that report focuses specifically on preventing tobacco use among adolescents. In addition, two national health objectives specifically focus on reducing sales to minors: objective 27-14 is to \u201creduce the illegal buy rate among minors through enforcement of laws prohibiting the sale of tobacco products to minors\u201d, and objective 27-15 is to \u201cincrease the number of states and the District of Columbia that suspend or revoke state retail licenses for violations of laws prohibiting the sale of tobacco to minors\u201d.9\n\nIn 2000, the US Supreme Court held that the Food and Drug Administration did not have the authority to regulate tobacco products, including their marketing and availability.10 The Public Health Service Act 398 (the Synar Amendment), however, which was passed in 1992, makes block grants to states from the Substance Abuse and Mental Health Services Administration (SAMHSA) contingent on states enacting and enforcing laws prohibiting any manufacturer, retailer, or distributor from selling or distributing tobacco products to persons under age 18 years.11,12 All 50 states currently have laws prohibiting the sale of tobacco to minors.12 Numerous studies since the late 1980s have demonstrated, however, that without adequate enforcement, minors are frequently successful in purchasing cigarettes from commercial sources when they try.1,13\u201317 In 1999, most 8th and 10th grade students reported they could get cigarettes \u201cfairly easily\u201d or \u201cvery easily\u201d (72% and 88%, respectively),18 and data from self report surveys confirm that many youth purchase their tobacco from commercial sources.19\u201323 To date, however, no published reports have focused on how the sources of cigarettes for youth have changed over time.\n\nThe purposes of this study were to examine:(1) how high school students under age 18 years (minors) who smoke usually obtain their cigarettes; (2) whether minors' frequency of smoking is associated with their source of cigarettes; (3) secular trends in usual source of cigarettes among minors from 1995 to 1999; and (4) whether minors are asked to show proof of age when they buy cigarettes in a store.\n\n## METHODS\n\n### Study design\n\nThis study used data from the 1995, 1997, and 1999 national school based Youth Risk Behavior Survey (YRBS), which has been conducted biennially by the CDC since 1991 (the first national YRBS was conducted in the spring of 1990). The questionnaires covered six categories of behaviours, including those that contribute to unintentional injuries and violence, tobacco use, alcohol and other drug use, sexual behaviours that contribute to unintended pregnancies and sexually transmitted diseases, dietary behaviours, and physical activity. In 1995, the YRBS queried students about their usual source of cigarettes for the first time.\n\nEach YRBS used a three stage, cluster sample design to obtain a nationally representative sample of students in grades 9 through 12 (ages 14\u201318 years).21\u201323 The target population consisted of all public and private high school students in the 50 states and the District of Columbia. The first stage sampling frame contained primary sampling units (PSUs) made up of large counties or groups of smaller adjacent counties. From this frame, PSUs were selected from 16 strata formed according to the degree of urbanisation and the relative percentages of black and Hispanic students in the PSUs. The PSUs were selected with a probability of selection proportional to their total school enrolment.\n\nIn the second stage, schools were selected from the PSUs with a probability proportional to their school enrolment. To ensure that racial or ethnic subgroups were large enough to analyse subgroup differences, schools with substantial numbers of black and Hispanic students were sampled at relatively higher rates than were other schools. The final stage consisted of randomly selecting, within each chosen school and in each of the four grades, one or two entire classes of a required subject such as English or social studies. All students in the selected classes were eligible to participate.\n\nProcedures were designed to protect the students' privacy by allowing for anonymous and voluntary participation and CDC's institutional review board granted clearance for the survey. Local parental permission procedures were followed before survey administration. A questionnaire containing approximately 90 items was administered in the classroom by trained data collectors. Answers were recorded directly on a computer scannable booklet. For 1995, 1997, and 1999, the school response rates were 70%, 79%, and 77%, respectively; student response rates were 86%, 87%, and 86%; overall response rates were 60%, 69%, and 66%; and sample sizes were 10 904, 16 262, and 15 349.\n\n### Data analysis\n\nIn each survey, smoking status was assessed by the question: \u201cDuring the past 30 days, on how many days did you smoke cigarettes?\u201d Response options ranged from \u201c0 days\u201d to \u201call 30 days\u201d. Students were defined as current smokers if they had smoked on one or more days. In each of the three surveys, usual source of cigarettes (both commercial and non-commercial, including social sources) was assessed by the question: \u201cDuring the past 30 days, how did you usually get your own cigarettes?\u201d Students could choose (only) one response from among the following: \u201cI did not smoke cigarettes in the past 30 days\u201d, \u201cI bought them in a store such as a convenience store, supermarket, or gas station\u201d, \u201cI bought them from a vending machine\u201d, \u201cI gave someone else money to buy them for me\u201d, \u201cI borrowed them from someone else\u201d, \u201cI stole them\u201d, or \u201cI got them in some other way\u201d. Proof of age was assessed in 1999 only, using the question: \u201cWhen you bought cigarettes in a store during the past 30 days, were you ever asked to show proof of age?\u201d Responses included \u201cI did not buy cigarettes in a store during the past 30 days\u201d, \u201cYes\u201d, and \u201cNo\u201d.\n\nA weighting factor was applied to each student record to adjust for non-response and for the varying probabilities of selection, including those resulting from the oversampling of black and Hispanic students. The final, overall weights were scaled so that the weighted count of students equalled the total sample size, and the weighted proportions of students in each grade matched national population projections for each survey year. All estimates were based on weighted data. All analyses were subsetted among current smokers who were under age 18 (sample sizes were 2989 in 1995, 4108 in 1997, and 3631 in 1999). Racial\/ethnic data are presented only for white, black, and Hispanic students because sample sizes in other minority groups were too small for meaningful analysis.\n\nWe used SUDAAN,24 a software package that takes into account the complex sampling design of this survey, to generate all point estimates and 95% confidence intervals (CIs), and to conduct all tests for significance (\u03b1 level was set at p < 0.05). We used \u03c72 tests to assess main effects in students' usual source of cigarettes and being asked for proof of age by sex, race\/ethnicity, and grade. When significant main effects were identified, we used t tests to identify the racial\/ethnic and grade differences in these variables. To examine the relation between the number of days of past month smoking and the usual source of cigarettes, a logistic regression model was used that controlled for sex, grade, and race\/ethnicity, in which days of use was treated as a continuous variable.\n\nTo examine secular trends in students' usual source of cigarettes, we combined YRBS data from 1995, 1997, and 1999 because in those years, the wording about usual source of cigarettes was identical. In combining the data sets, we recoded the strata from each survey year so that strata from one survey year were uniquely identifiable and separate from those of other survey years, essentially creating an additional stratum of \u201ctime\u201d. In subsequent logistic regression models that controlled for sex, grade, and race\/ethnicity, time was treated as a continuous variable in assessing possible linear changes in usual source of cigarettes.\n\n## RESULTS\n\n### Minors' usual source of cigarettes\n\nBought them in a store. Overall, in 1999, 23.5% of current smokers usually got their cigarettes by buying them in a store (table 1). The percentage of students who usually got their cigarettes by buying them in a store varied by sex (\u03c72 = 21.8, df = 1, p < 0.001) and by grade (\u03c72 = 1.8, df = 3, p < 0.001). Males were significantly more likely than females and 12th grade students were significantly more likely than 9th (t = 6.8, p < 0.01), 10th (t = 5.0, p < 0.01), and 11th grade students (t = 2.6, p = 0.01) to buy their cigarettes in a store.\n\nTable 1\n\nMinors' usual source of cigarettes in 1999*\n\nBought them from a vending machine. Only 1.1% of current smokers usually got their cigarettes by buying them from a vending machine. This behaviour did not vary by sex, race\/ethnicity, or grade.\n\nGave someone else money to buy them. Three of 10 (29.9%) current smokers usually got their cigarettes by giving someone else money to buy them. The percentage of students who usually gave someone else money to buy their cigarettes varied by sex (\u03c72 = 9.0, df = 1, p < 0.01) and by race\/ethnicity (\u03c72 = 16.4, df = 2, p < 0.001). Females were significantly more likely than males to give someone else money to buy their cigarettes. White students were significantly more likely to report this behaviour than were black (t = 4.2, p < 0.01) and Hispanic (t = 3.2, p < 0.01) students and Hispanic students were significantly more likely than black students to report this behavior (t = 2.3, p < 0.05).\n\nBorrowed them from someone else. Overall, 30.4% of current smokers usually got their cigarettes by borrowing them. The percentage of students who usually borrowed their cigarettes from someone else varied by sex (\u03c72 = 4.5, df = 1, p < 0.05) and by race\/ethnicity (\u03c72 = 7.8, df = 2, p < 0.05). Significantly more females than males and significantly more black students than white students (t = 2.2, p < 0.05) borrowed cigarettes from someone else.\n\nStole them. Overall, 4.4% of current smokers usually stole their cigarettes. The percentage of students who usually stole their cigarettes varied by sex (\u03c72 = 10.1, df = 1, p < 0.01) and by grade (\u03c72 = 12.6, df = 3, p < 0.01). Males were significantly more likely than females to steal their cigarettes. Eleventh (t = 2.2, p < 0.05) and 9th grade students (t = 3.2, p < 0.01) were significantly more likely than 12th grade students to report stealing their cigarettes. Ninth grade students were significantly more likely than 10th grade students to do so (t = 3.0, p < 0.01).\n\nGot them in some other way. Overall, just over one in 10 (10.7%) current smokers usually got their cigarettes in \u201csome other way\u201d. The percentage of students who usually got their cigarettes in some other way varied by race (\u03c72 = 8.1, df = 2, p < 0.05). Hispanic students were significantly more likely than white students (t = 3.0, p < 0.01) to get their cigarettes in some other way.\n\n### Frequency of smoking and minors usual source of cigarettes\n\nIn 1999, the number of days students reported smoking was associated with the usual source of their cigarettes (table 2). As the number of days of smoking increased, the likelihood of students reporting buying their own cigarettes in a store (p < 0.01) and giving someone money to buy cigarettes (p < 0.01) increased. In contrast, as the number of days of smoking increased, the less likely students were to borrow cigarettes (p < 0.01). Neither buying cigarettes from a vending machine nor stealing them was associated with frequency of smoking. Obtaining cigarettes in \u201csome other way\u201d did not demonstrate a linear pattern with smoking frequency, but students who smoked 1\u20132 days during the past month were significantly more likely than students who smoked 3\u20135 days (t = 3.2, p < 0.01), 6\u20139 days (t = 2.8, p < 0.01), and 20\u201329 days (t = 4.5, p < 0.01) to report getting their cigarettes in this other manner.\n\nTable 2\n\nMinors' usual source of cigarettes in 1999, by frequency of smoking*\n\n### Secular trends in minors' usual source of cigarettes\n\nThe percentage of current smokers who reported they usually got their own cigarettes by buying them in a store significantly decreased from 38.7% in 1995 to 23.5% in 1999 (linear trend, p < 0.001) (table 3). Conversely, giving someone else money to buy cigarettes significantly increased from 1995 (15.8%) to 1999 (29.9%) (linear trend, p < 0.001). Obtaining cigarettes in \u201csome other way\u201d also significantly increased from 6.2% in 1995 to 10.7% in 1999 (linear trend, p = 0.004). Buying cigarettes in a vending machine, borrowing cigarettes from someone else, and stealing cigarettes remained stable from 1995 to 1999.\n\nTable 3\n\nSecular trends in minors' usual source of cigarettes, 1995-1999*\n\n### Not asked proof of age when bought during past 30 days\n\nIn 1999, among current smokers under age 18 years who bought cigarettes in a store during the 30 days preceding the survey, 69.6% were never asked to show proof of age (table 4).\n\nTable 4\n\nPercentage of minors not asked for proof of age when buying cigarettes in a store in 1999*\n\nThe percentage of students who were not asked for proof of age varied by sex (\u03c72 = 5.8, df = 1, p < 0.05). Females were significantly more likely than males to report they had not been asked to show proof of age. Requests for proof of age did not vary across race\/ethnicity or grade.\n\n## DISCUSSION\n\nIn this study, from 1995 to 1999 we found a shift in cigarette acquisition from commercial sources to social sources among high school students. Among current smokers under age 18 years, the percentage of students who usually bought their own cigarettes in a store dropped from 38.7% in 1995 to 23.5% in 1999; students who reported that they usually gave someone else money to buy cigarettes significantly increased from 15.5% to 29.9%.\n\nPreventing minors' access to tobacco by prohibiting retail sales to them has been advocated to help reduce initiation of tobacco use and is recommended as a component of comprehensive tobacco control programmes.1,25\u201327 It is well established that active enforcement of state laws or local ordinances can reduce the percentage of retailers who sell tobacco to minors,1,13,14,25,26,28,29 especially when compliance checks are performed several times per year.30\u201332 Likewise, education of merchants has been shown in some studies to be useful in decreasing the percentage of retailers who sell tobacco to minors, although such education without active enforcement loses effectiveness over time.13,25\n\nAll 50 states currently have laws prohibiting the sale of tobacco to minors. However, without adequate enforcement, minors are frequently successful in purchasing cigarettes when they try. Also, studies suggest social sources are an important means of cigarette acquisition.\n\nData from the 1999 national Youth Risk Behavior Survey showed that among high school students under age 18 who were current smokers, 23.5% usually purchased their own cigarettes in a store, 29.9% usually gave someone else money to buy their cigarettes, and 30.4% usually borrowed cigarettes from someone. From 1995 to 1999, usually buying cigarettes in a store significantly declined; however, usually giving someone else money to buy cigarettes significantly increased.\n\nSome studies have shown that combining community mobilisation with enforcement of access laws, retailer education, school based education, or stronger local laws may reduce the prevalence of youth smoking,13,33\u201335 but such findings are not universal. For example, in a Massachusetts study that combined retailer education and active enforcement, despite a pronounced reduction in the percentage of retailers who sold cigarettes to youth in the intervention communities, there was no difference in self reported access by youth in intervention compared to control communities.14 The authors observed that unless youth in intervention communities report decreased access to commercial sources of cigarettes, and that decrease is greater than any decrease in access that may have occurred in the control communities, it is not logical to expect reduced cigarette use among youth in the intervention communities as a result of the intervention.14\n\nThe 1999 YRBS data suggest that many young smokers who purchased cigarettes in a store were not asked for proof of age. The YRBS does not provide data on the percentage of students who tried unsuccessfully to buy cigarettes. Data from other studies show that when store personnel request proof of age for a cigarette purchase, the likelihood of a sale to an underage buyer is greatly reduced.15,30,31,36 Thus, merchant education programmes to reduce sales of cigarettes to minors should emphasise the need to request proof of age.\n\nConsistent with other studies,20,37\u201341 YRBS data showed that social sources continue to be an important means of cigarette acquisition. For example, in 1999, YRBS data and National Youth Tobacco Survey20 data found that more than half of high school students usually obtained their cigarettes by either giving someone else money to buy them or borrowing them. The Tobacco Policy Options for Prevention study in Minnesota found that more than 90% of 8th\u201310th graders who had ever smoked cigarettes obtained their first cigarette from family members or friends.37 Likewise, Wolfson and colleagues38 found that more than two thirds of students in these grades who reported past month smoking had provided tobacco to another student during that same period. Of those students, 66% provided tobacco to a same age friend, 37% to a younger friend, 17% to a sibling, and 13% to a stranger.\n\nWolfson and colleagues38 as well as others39,40 have found that adolescents who are heavier smokers are the most likely to provide cigarettes to other adolescents; we found that heavier smokers were more likely to obtain their cigarettes by purchase. Thus, it is likely that the original source for a substantial percentage of cigarettes \u201cborrowed\u201d from other minors was from an illegal sale at a retail outlet. High compliance with access laws may consequently reduce the social as well as the commercial availability of cigarettes among youth. However, as an additional means of addressing the social availability of cigarettes, clinical, community, and school based interventions should try to dissuade minors who smoke from providing cigarettes to other minors.\n\nWe found that only a small percentage of current smokers rely mainly on stealing or vending machines to obtain their cigarettes (4% and 1%, respectively). More research is needed to explore what students meant by stealing which may have included shoplifting and taking cigarettes from friends, family, or other smokers. Likewise, more research is needed to identify the extent to which current smokers used vending machines to supplement their usual source of cigarettes, or whether policy changes making vending machines less available, explains why vending machines are rarely a usual source for cigarettes.\n\nCDC has issued best practices guidelines for comprehensive tobacco control programmes that include strategies for enforcing restrictions on minors' access to tobacco.27 The agency recommends that states allocate $0.43 to$0.80 per capita for enforcing youth access regulations. Best practices recommend these per capita amounts need to be added to a base amount for interagency coordination of between $150 000 and$300 000.","date":"2022-07-06 03:13:01","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\": 0.1994652897119522, \"perplexity\": 4616.728696868353}, \"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\/1656104660626.98\/warc\/CC-MAIN-20220706030209-20220706060209-00660.warc.gz\"}"}
| null | null |
\section{Introduction}
For both mathematical and physical reasons one would like to be able to understand anisotropic and inhomogeneous cosmological models in general. As a first step spatially homogeneous spacetimes can be studied. For the case where the matter model is a perfect fluid a lot of results have been already obtained which are summarized in \cite{WE}, see also \cite{HU} for a critical discussion. Usually in observational cosmology it is assumed that there exists an Era which is ``matter-dominated'' where the matter model is a perfect fluid with zero pressure, i.e. the dust model. A kinetic description via collisionless matter enables to study the stability of this model in the following sense. Suppose we have an expanding universe where the particles have certain velocity dispersion. One might think that due to the expansion the velocity dispersion will decay. That this is true has been shown in \cite{RT}, \cite{RU} and \cite{RE} for locally rotationally symmetric (LRS) models in the cases of Bianchi I, II and III. These results have been generalized (in a different direction) to LRS Bianchi IX and in a context which also goes beyond collisionless matter in \cite{PP} and \cite{CH}.\\The LRS models can be diagonalized in a suitable frame where they then stay diagonal if one makes some extra assumptions on the distribution function. A natural question is, what happens if the model is not diagonal? In this paper we will treat the late time dynamics of the \textit{non-diagonal} Bianchi I case assuming small data. That this makes sense was established in \cite{CC} where it was shown that geodesic completeness holds for the general Bianchi I-Vlasov case. In a sense which will be specified later, we assume that the universe is close to isotropic and that the velocity dispersion of the particles is bounded. Then we conclude that the universe will isotropize and have a dust-like behaviour asymptotically. In fact these two properties are intimately linked in the proof, something which is not expected to happen in other Bianchi types, except in the case of a positive cosmological constant where it has been shown \cite{Lee} that isotropization and asymptotic dust-like behaviour occurs in all Bianchi models except Bianchi IX and without the LRS assumption.\\ We hope to be able to extend this result in the near future a) to other Bianchi types, where the spacetime does not (necessarily) isotropize, but some other solution still may act as an 'attractor' b) to remove the small data assumption(s).\\
\section{Bianchi I spacetimes with collisionless matter}
A \textit{Bianchi spacetime} is defined to be a spatially homogeneous spacetime whose isometry group possesses a three-dimensional subgroup $G$ that acts simply transitively on the spacelike orbits. They can be classified by the structure constants of the Lie algebra associated to the Lie group. We will only consider the simplest case where the structure constants vanish, i.e. the case of Bianchi I with the abelian group of translations in $\R^3$ as the Lie group, where the metric has the following form using Gauss coordinates:
\begin{eqnarray}\label{me}
^4 g=-dt^2+g_{ab}(t)dx^adx^b.
\end{eqnarray}
We will use the 3+1 decomposition of the Einstein equations as made in \cite{RA}. We use Gauss coordinates, which implies that the lapse function is the identity and the shift vector vanishes, so comparing our metric with (2.28) of \cite{RA} we have that $\alpha=1$ and $\beta^a=0$. The only non-trivial Christoffel symbols are the following (See (2.44)-(2.49) of \cite{RA}):
\begin{eqnarray}
\Gamma^0_{ab}&=&-k_{ab}\\
\Gamma^a_{0b}&=&-k^a_b
\end{eqnarray}
In terms of coordinate expressions we have then that ($n_0=-1$)
\begin{eqnarray*}
\rho&=&T^{00}\\
j_a&=&T_a^0\\
S_{ab}&=&T_{ab}
\end{eqnarray*}
where $\rho$, $j_a$ and $T_{\mu\nu}$ are the energy density, matter current and energy momentum tensor respectively.
In the 3+1 formulation the second fundamental form $k_{ab}$ is used and rewriting its definition as in (2.29) of \cite{RA} we have:
\begin{eqnarray}\label{a}
\dot{g}_{ab}=-2 k_{ab}.
\end{eqnarray}
Using the Einstein equations as in (2.34) of \cite{RA} and the fact that $g_{ab}$ does not depend on the spatial variables, we have:
\begin{eqnarray}\label{b}
\dot{k}_{ab}=H k_{ab}-2k_{ac}k^c_b-8\pi(S_{ab}-\frac{1}{2}g_{ab}\tr S)-4\pi\rho g_{ab}
\end{eqnarray}
where we have used the notations $\tr S =g^{ab}S_{ab}$, $H=\tr k$. It has been assumed that the cosmological constant vanishes.
From the constraint equations (2.26)-(2.27) of \cite{RA}:
\begin{eqnarray}\label{c}
-k_{ab}k^{ab}+H^2=16\pi\rho
\end{eqnarray}
and we see that no matter current is present since the ``spatial'' Christoffel symbols vanish:
\begin{eqnarray}
T_{0a}=0.
\end{eqnarray}
From (\ref{c}) we see that $H$ never vanishes except for the Minkowski spacetime. We exclude this case and assume now without loss of generality that $H <0$ for all time. If this is not true for a given solution it may be arranged by doing the transformation $t\mapsto-t$.\\
For the matter model we will take the point of view of kinetic theory. This means that we have a collection of particles (in a cosmological context the particles are galaxies or clusters of galaxies) which are described statistically by a non-negative distribution function $f(x^\alpha,p^\alpha)$ which is the density of particles at a given spacetime point with given four-momentum. We will assume that all the particles have equal mass (one can relax this condition if necessary, see \cite{PP}). We want that our matter model is compatible with our symmetry assumption, so we will also assume that $f$ does not depend on $x^a$. In addition to that we will assume that there are no collisions between the particles. In this case the distribution function satisfies the Vlasov equation (See (3.38) of \cite{RA}):
\begin{eqnarray}
\frac{\partial f}{\partial t}+2 k^a_b p^b\frac{\partial f}{\partial p^a}=0.
\end{eqnarray}
where f is defined on the set determined by the equation
\begin{eqnarray*}
-(p^0)^2+g_{ab}p^ap^b=-m^2
\end{eqnarray*}
called the mass shell.
The energy momentum tensor is (compare with (3.37) of \cite{RA}):
\begin{eqnarray}
&& \rho=\int f(t,p)(m^2+g_{ab}p^ap^b)^{\frac{1}{2}}(\det g)^{\frac{1}{2}}dp\\
&&S_{ab}=\int f(t,p)p_ap_b(m^2+g_{ab}p^ap^b)^{-\frac{1}{2}}(\det g)^{\frac{1}{2}}dp\\\label{cu}
&&T_{0a}=\int f(t,p)p_a(\det g)^{\frac{1}{2}}dp
\end{eqnarray}
Here $p:=(p^1,p^2,p^3)$ and $dp:=dp^1 dp^2 dp^3$.
For this kind of matter all the energy conditions hold. In particular $\rho \geq \tr S \geq 0$.
Our system of equations consists of the equations (\ref{a})-(\ref{cu}). For a given Bianchi I geometry the Vlasov equation can be solved explicitly with the result that if $f$ is expressed in terms of the covariant components $p_i$ then it is independent of time. This has the consequence that if $t_0$ is some fixed time and $f_0(p_i)=f(t,p_i)$ then we can express the non-trivial components of the energy momentum tensor as follows:
\begin{eqnarray*}
&& \rho=\int f_{0}(p_{i})(m^2+g^{cd}p_{c}p_d)^{\frac{1}{2}}(\det g)^{-\frac{1}{2}}dp_{1}dp_{2}dp_{3}\\
&& S_{ab}=\int f_{0}(p_{i})p_a p_b(m^2+g^{cd}p_{c}p_d)^{-\frac{1}{2}}(\det g)^{-\frac{1}{2}}dp_{1}dp_{2}dp_{3}.
\end{eqnarray*}
\subsection{Other equations and new variables}
A useful relation concerns the determinant of the metric ((2.30) of \cite{RA}):
\begin{eqnarray}\label{det}
\frac{d}{dt}[\log (\det g)]=-2 H
\end{eqnarray}
Taking the trace of the mixed version of the second fundamental form (2.36 of \cite{RA}):
\begin{eqnarray}\label{im}
\dot{H}=H^2+4\pi \tr S -12\pi \rho
\end{eqnarray}
With (\ref{c}) one can eliminate the energy density and (\ref{im}) reads:
\begin{eqnarray}\label{in}
\dot{H}=\frac{1}{4}(H^2+3k_{ab}k^{ab})+4\pi \tr S
\end{eqnarray}
We can decompose the second fundamental form introducing $\sigma_{ab}$ as the trace-free part:
\begin{eqnarray}\label{TF}
k_{ab}=\sigma_{ab}+\frac{H}{3}g_{ab}
\end{eqnarray}
Then
\begin{eqnarray}\label{tf}
k_{ab}k^{ab}=\sigma_{ab}\sigma^{ab}+\frac{H^2}{3}
\end{eqnarray}
and (\ref{in}) takes the following form:
\begin{eqnarray}\label{yes}
\dot{H}=\frac{1}{2}H^{2}+\frac{3}{4}\sigma_{ab}\sigma^{ab}+4\pi \tr S
\end{eqnarray}
It is obvious that
\begin{eqnarray}\label{ie}
\dot{H}\geq\frac{1}{2}H^{2}
\end{eqnarray}
From the constraint equation (\ref{c}) and (\ref{yes}) it also follows that
\begin{eqnarray}\label{up}
\dot{H}\leq H^2
\end{eqnarray}
From (\ref{ie}) and (\ref{up}) we conclude that
\begin{eqnarray}\label{if}
-(t+C)^{-1}\geq H(t)\geq -2(t+C)^{-1}.
\end{eqnarray}
Let us use the following notation:
\begin{eqnarray}\label{AN}
F=\frac{\sigma_{ab}\sigma^{ab}}{H^2}.
\end{eqnarray}
This quantity is related to the so called \textit{shear parameter}, which is bounded by the cosmic microwave background radiation and is a dimensionless measure of the anisotropy of the Universe (See chapter 5.2.2 of \cite{WE}).
Using this notation and with the help of (\ref{a}), (\ref{b}) and (\ref{yes}) we have
\begin{eqnarray}\label{no}
\dot{F}=H[F(1-\frac{3}{2}F-\frac{8\pi }{H^2} \tr S)-\frac{16\pi}{H^3} S_{ab}\sigma^{ab}]
\end{eqnarray}
From the constraint equation (\ref{c})
\begin{eqnarray}\label{F}
F=\frac{2}{3}-16\pi\frac{\rho}{H^2}
\end{eqnarray}
In general we see that $0\leq F\leq\frac{2}{3}$.\\
\subsection{Special cases}
\subsubsection{Vacuum}
We see that in the vacuum case $F=\frac{2}{3}$ and $\dot{F}=0$. Actually in this case one can write explicitly the solution known as \textit{Kasner solution}:
\begin{eqnarray*}
^{4}g=-dt^2+t^{2p_1}dx^2+t^{2p_2}dy^2+t^{2p_3}dz^2
\end{eqnarray*}
where the constants $p_i$ are called the \textit{Kasner exponents} which satisfy the two \textit{Kasner relations} given by:
\begin{eqnarray*}
p_1+p_2+p_3&=&1 \\
(p_1)^2+(p_2)^2+(p_3)^2&=&1
\end{eqnarray*}
The mean curvature in this case is
\begin{eqnarray*}
H=-t^{-1}
\end{eqnarray*}
Let $\lambda_i$ be the eigenvalues of $k_{ij}$ with respect to $g_{ij}$, i.e., the solutions of
\begin{eqnarray}\label{ev}
\det (k^i_j-\lambda \delta^i_j)=0
\end{eqnarray}
We define
\begin{eqnarray}\label{gke}
p_i=\frac{\lambda_i}{H}
\end{eqnarray}
as the \textit{generalized Kasner exponents}. They satisfy the first but not in general not the second Kasner relation.
\subsubsection{Flat Friedmann with dust}
A special case of Bianchi I is the Friedmann model with flat spatial geometry. The metric in this case is:
\begin{eqnarray*}
^{4}g=-dt^2+a^2(dx^2+dy^2+dz^2)
\end{eqnarray*}
where $a$ is the scale factor. In this case $\sigma_{ab}=0$ which means that $F=0$ and also that $\dot{F}=0$.\\ Moreover in the dust case $S_{ab}=0$ (the Einstein-dust system can be thought of as singular case of the Einstein-Vlasov system, see chapter 3.4 of \cite{RA} for more information) and we can solve (\ref{yes}) obtaining:
\begin{eqnarray*}
H=-2t^{-1}
\end{eqnarray*}
We can also write down the explicit solution of the metric in this case:
\begin{eqnarray*}
^{4}g=-dt^2+t^{\frac{4}{3}}(dx^2+dy^2+dz^2).
\end{eqnarray*}
This is also called the Einstein-de Sitter model.
\subsubsection{Bianchi I: the dust case (with small data)}
Let us look at the dust case not necessarily isotropic. The general solution is known and one can see from the solution (11-1.12) of \cite{HS} that the spacetime will isotropize. Nevertheless we will analyze this case with care, since we will show that the general case behaves asymptotically like it assuming small data. In the dust case:
\begin{eqnarray}\label{dd}
\dot{F}=HF(1-\frac{3}{2}F)\leq 0
\end{eqnarray}
We are interested in the asymptotic behaviour at late times and will assume that $F$ is small, i.e.: $F < \epsilon$. Then it follows from (\ref{yes}):
\begin{eqnarray}\label{hd}
\dot{H}=(\frac{1}{2}+\frac{3}{4}F)H^2\leq(\frac{1}{2}+\epsilon)H^2
\end{eqnarray}
Integration leads to
\begin{eqnarray*}
H \leq -\frac{2-\epsilon}{t+C}
\end{eqnarray*}
Using this inequality in (\ref{dd}) and integrating:
\begin{eqnarray}\label{YOY}
F=O(t^{-2+\epsilon}).
\end{eqnarray}
We can put the equality (\ref{hd}) in the following form:
\begin{eqnarray}\label{II}
-H^{-1}=-H(t_0)^{-1}+\frac{1}{2}(t-t_0)+I_D
\end{eqnarray}
where $I_D$ is
\begin{eqnarray}
I_D=\int^t_{t_{0}} \frac{3}{4} F(s)ds
\end{eqnarray}
Now we will use the fact that we can choose freely the time origin setting $t_{0}=-2H(t_0)^{-1}$. Note that for the general Bianchi I symmetric Einstein-Vlasov-system we know that $H$ takes all values in the range $(-\infty,0)$ (Lemma 2.1 of \cite{IS}) We then obtain
\begin{eqnarray}
H+2t^{-1}\leq4 I_D t^{-2}
\end{eqnarray}
Using (\ref{YOY}) it is clear that $I_D\leq C(t_0)$. Note that with our time origin choice $C=0$ in (\ref{if}), so
\begin{eqnarray}\label{hi}
H\geq-2t^{-1}
\end{eqnarray}
Our result for $H$ is the following:
\begin{eqnarray}\label{1}
H=-2t^{-1}[1+O(t^{-1})]
\end{eqnarray}
This equation in (\ref{dd}) leads after integration to:
\begin{eqnarray}\label{2}
F=O(t^{-2})
\end{eqnarray}
From (\ref{hi}) and (\ref{2}) we can conclude that:
\begin{eqnarray}\label{3}
\sigma_{ab}\sigma^{ab}=O(t^{-4})
\end{eqnarray}
Now from (\ref{TF}) we see that the eigenvalues (\ref{ev}) of the second fundamental form with respect to the induced metric are also the solutions of
\begin{eqnarray*}
\det(\sigma^i_j-[\lambda-\frac{1}{3}H]\delta^i_j)
\end{eqnarray*}
Let us define the eigenvalues of $\sigma_{ij}$ with respect to $g_{ij}$ by $\widehat{\lambda}_i$, we have that:
\begin{eqnarray*}
\widehat{\lambda}_i= \lambda_i-\frac{1}{3}H
\end{eqnarray*}
Note that $\Sigma_i (\widehat{\lambda}_i)^2=\sigma_{ab}\sigma^{ab}$. From (\ref{hi}) and (\ref{3}) we can see that the spacetime isotropizes at late times, in the sense that
\begin{eqnarray*}
p_i= \frac{1}{3} +O(t^{-1})
\end{eqnarray*}
where $p_i$ are the generalized Kasner exponents.\\
Now using (\ref{det}) and (\ref{hi}) we have:
\begin{eqnarray*}
\det g=O(t^4)
\end{eqnarray*}
So the hope would be to show that $\vert g_{ab} \ t^{-\frac{4}{3}} \vert$ can be bounded by a constant.
Let us define
\begin{eqnarray*}
\bar{g}_{ab}&=&t^{-\frac{4}{3}}g_{ab}\\
\bar{g}^{ab}&=&t^{+\frac{4}{3}}g^{ab}.
\end{eqnarray*}
We have then with (\ref{a}) that:
\begin{eqnarray*}
\dot{\bar{g}}_{ab}=-\frac{2}{3}(2t^{-1}+H)\bar{g}_{ab}-2t^{-\frac{4}{3}}\sigma_{ab}
\end{eqnarray*}
Making similar computations as in \cite{Lee} we arrive at:
\begin{eqnarray*}
\Vert \bar{g}_{ab}(t) \Vert \leq \Vert \bar{g}_{ab}(t_0) \Vert + \int^t_{t_0} [\frac{2}{3} \vert 2s^{-1}+H(s)\vert +2(\sigma_{ab}\sigma^{ab}(s))^{\frac{1}{2}}] \Vert \bar{g}_{ab}(s) \Vert ds
\end{eqnarray*}
and with Gronwall's inequality we obtain:
\begin{eqnarray}\label{tt}
\Vert \bar{g}_{ab}(t) \Vert \leq \Vert \bar{g}_{ab}(t_0) \Vert \exp\{ \int^t_{t_0} [\frac{2}{3} \vert 2s^{-1}+H(s)\vert +2(\sigma_{ab}\sigma^{ab}(s))^{\frac{1}{2}}]ds\}\leq C
\end{eqnarray}
Therefore $\bar{g}_{ab}$ is bounded for all $t\geq t_0$. The same holds for $\bar{g}^{ab}$ by similar computations. Thus:
\begin{eqnarray*}
\vert t^{-\frac{4}{3}}g_{ab} \vert \leq C\\
\vert t^{+\frac{4}{3}} g^{ab} \vert \leq C
\end{eqnarray*}
From this we can conclude that:
\begin{eqnarray*}
\Vert \sigma_{ab} \Vert \leq C t^{-\frac{2}{3}}
\end{eqnarray*}
or
\begin{eqnarray*}
\sigma_{ab} = O(t^{-\frac{2}{3}})
\end{eqnarray*}
Looking again at the derivative of $\bar{g}_{ab}$ and putting the facts which have been obtained together, we see that:
\begin{eqnarray*}
\dot{\bar{g}}_{ab}=O(t^{-2})
\end{eqnarray*}
This is enough to conclude that:
\begin{eqnarray*}
g_{ab}=t^{+\frac{4}{3}}[\mathcal{G}_{ab}+O(t^{-2})]\\
g^{ab}=t^{-\frac{4}{3}}[\mathcal{G}^{ab}+O(t^{-2})]
\end{eqnarray*}
where $\mathcal{G}_{ab}$ is the limit of $\bar{g}_{ab}$ as $t$ goes to infinity.
\section{Bianchi I: the general case}
For the general case the basic equations are (\ref{yes}), a modified version of (\ref{b}) where $\gamma$ is a small and positive quantity which is introduced for technical reasons and (\ref{no})
\begin{eqnarray}
&&\partial_{t}(-H^{-1})=\frac{1}{2}+\frac{3}{4}F+4\pi \frac{\tr S}{H^2}\label{aa}
\\
&&\frac{d}{dt}(t^{-\gamma}\bar{g}^{ab})=t^{-\gamma}\bar{g}^{ab}[\frac{2}{3}(2t^{-1}+H)-\gamma t^{-1}]+2t^{-\gamma+\frac{4}{3}}\label{bb}
\sigma^{ab}
\\
&&\dot{F}=H[F(1-\frac{3}{2}F-\frac{8\pi }{H^2} \tr S)-\frac{16\pi}{H^3} S_{ab}\sigma^{ab}]\label{cc}
\end{eqnarray}
We have a number (different from zero) of particles at possibly different momenta and we will define $P$ as the supremum of the absolute value of these momenta at a given time $t$:
\begin{eqnarray}\label{P}
P(t)=\sup \{ \vert p \vert =(g^{ab}p_a p_b)^\frac{1}{2} \vert f(t,p)\neq 0\}
\end{eqnarray}
\begin{theorem}
Consider any $C^{\infty}$ solution of the Einstein-Vlasov system with Bianchi I-symmetry and with $C^{\infty}$ initial data. Assume that $F(t_0)$ and $P(t_0)$ are sufficiently small. Then at late times one can make the following estimates:
\begin{eqnarray}
H(t)&=&-2t^{-1}(1+O(t^{-1}))\\
P(t)&=&O(t^{-\frac{2}{3}+\epsilon})\label{Pp}\\
F(t)&=&O(t^{-2})
\end{eqnarray}
\end{theorem}
\noindent
{\bf Remark} (\ref{Pp}) implies that asymptotically there is a dust-like behaviour (see (\ref{pp})).
\noindent
{\bf Proof}
We will use a bootstrap argument (see chapter 10.3 of \cite{RA} for more information). Let us look at the interval $[t_0,t_1)$. Our bootstrap assumptions are the following:
\begin{eqnarray}
&&F(t)\leq A(1+t)^{-\frac{3}{2}}\label{a1}\\
&&P(t)\leq B(1+t)^{-\frac{7}{12}}\label{a2}.
\end{eqnarray}
where A and B are positive constants which we can choose as small as we want.\\\\
\textit{1. Estimate of $H$}\\\\
Integrating (\ref{aa}) we obtain:
\begin{eqnarray}\label{H}
-H^{-1}=-H(t_0)^{-1}+\frac{1}{2}(t-t_0)+I_G
\end{eqnarray}
with
\begin{eqnarray*}
I_G=\int^t_{t_0}(\frac{3}{4}F+4\pi \frac{\tr S}{H^2})(s)ds\leq \int_{t_0}^t [\frac{3}{4} A (1+s)^{-\frac{3}{2}}+\frac{1}{4} \frac{\tr S}{\rho}(s)]ds
\end{eqnarray*}
where the inequality comes from (\ref{a1}) and (\ref{c}). Consider now an orthonormal frame and denote the components of the spatial part of the energy-momentum tensor in this frame by $\widehat{S}_{ab}$. The components can be bounded by
\begin{eqnarray}\label{pp}
\widehat{S}_{ab} \leq P^2(t) \rho
\end{eqnarray}
so we have that
\begin{eqnarray}\label{ss}
\frac{\tr \widehat{S}}{\rho} \leq 3P^2
\end{eqnarray}
from which follows that:
\begin{eqnarray*}
I_G \leq \frac{18}{4}(A+B^2)
\end{eqnarray*}
Now returning back to (\ref{H}) and setting as in the dust case $t_0=-2H(t_0)^{-1}$ we have
besides
\begin{eqnarray}\label{ho}
H\geq -2t^{-1}
\end{eqnarray}
that
\begin{eqnarray}\label{hh}
H+2t^{-1}\leq 18(A+B^2)t^{-2}
\end{eqnarray}
\\\textit{2. Estimate of $P$}\\\\
Now we will use the second equation (\ref{bb}) to obtain an estimate for the metric. One can show that in the sense of quadratic forms the following is true:
\begin{eqnarray*}
\sigma^{ab} \leq (\sigma_{ab}\sigma^{ab})^{\frac{1}{2}} g^{ab}.
\end{eqnarray*}
Then with the definitions of $\bar{g}^{ab}$ and $F$ and the estimates (\ref{a1}) and (\ref{ho}) we have: :
\begin{eqnarray*}
2t^{-\gamma+\frac{4}{3}}\sigma^{ab} \leq 2t^{-\gamma+\frac{4}{3}}(\sigma_{ab}\sigma^{ab})^{\frac{1}{2}} g^{ab}=2F^{\frac{1}{2}}\vert H \vert t^{-\gamma} \bar{g}^{ab}\leq 4 A^{\frac{1}{2}} (1+t)^{-\frac{3}{4}}t^{-1} t^{-\gamma} \bar{g}^{ab}
\end{eqnarray*}
Now from the last inequality of the first step (\ref{hh}) equation (\ref{bb}) leads to:
\begin{eqnarray*}
\frac{d}{dt}(t^{-\gamma}\bar{g}^{ab})\leq t^{-\gamma}\bar{g}^{ab}[12(A+B^2)t_0 + 4 A^{\frac{1}{2}} (1+t_0)^{-\frac{3}{4}}-\gamma]t^{-1}=-\eta t^{-\gamma}\bar{g}^{ab}t^{-1}
\end{eqnarray*}
$A$ and $B$ have to be chosen in such a way that $\eta$ is positive, then
\begin{eqnarray}\label{neg}
\frac{d}{dt}(t^{-\gamma}\bar{g}^{ab})\leq 0
\end{eqnarray}
from which follows that
\begin{eqnarray*}
\bar{g}^{ab}=O(t^{\gamma})
\end{eqnarray*}
or
\begin{eqnarray*}
g^{ab}=O(t^{-\frac{4}{3}+\gamma})
\end{eqnarray*}
Now from (\ref{neg}) we have:
\begin{eqnarray*}
t^{-\gamma+\frac{4}{3}}g^{ab}(t) \leq t_0^{-\gamma +\frac{4}{3}} g^{ab}(t_0)
\end{eqnarray*}
Using the fact that $p_a$ is constant along the geodesics we can conclude that:
\begin{eqnarray}\label{B}
P(t)\leq {t_0}^{-\frac{\gamma}{2}+\frac{2}{3}}P(t_0)t^{\frac{\gamma}{2}-\frac{2}{3}}\leq Bt^{\frac{\gamma}{2}-\frac{2}{3}}
\end{eqnarray}
since we can choose $P(t_0)$ and $B$ independently as small as we want. In order to improve (\ref{a2}) $\gamma$ has to be smaller then $\frac{1}{6}$. Using the notation $\zeta=\frac{\gamma}{2}$ the last inequality can be expressed as
\begin{eqnarray}\label{b1}
P(t)\leq B t^{-\frac{2}{3}+\zeta}
\end{eqnarray}
where $\zeta < \frac{1}{12}$.\\\\
\textit{3. Estimate of $F$}\\\\
Until now we have an estimate for $H$ and for $P$ in the interval $[t_0,t_1)$. Now we have to improve the estimate for $F$ coming from the bootstrap assumption. The desired estimate is $F(t_1)\le A(1+t_1)^{-2+\epsilon}$. If this
is the case (case I) the bootstrap argument will work and there is nothing more to do.
\begin{center}{\includegraphics[height=6cm]{bootstrap}}
\textit{Case I}
\end{center}
Let us suppose now the opposite, that $F(t_1)> A(1+t_1)^{-2+\epsilon}$. Then define $t_2$ as the smallest number not smaller than $t_0$ with
the property that $F(t_1)\geq A(1+t_1)^{-2+\epsilon}$. In this case, we have to distinguish between the case that $t_2 = t_0$ (Case IIa)
and $t_2 > t_0$ (Case IIb). Let us look now at (\ref{cc}), in particular at the terms in square brackets. By using (\ref{a1})
\begin{eqnarray*}
\frac{3}{2}F \leq \frac{3}{2} A (1+t)^{-\frac{3}{2}} \leq \frac{3}{2} A (1+t_0)^{-\frac{3}{2}} \leq \frac{\delta}{2}
\end{eqnarray*}
where $\delta$ is a positive small constant.
Using (\ref{c}), (\ref{a2}) and (\ref{ss}):
\begin{eqnarray*}
8\pi \frac{ \tr \widehat{S}}{H^2} \leq \frac{3}{2} P^2 \leq \frac{3}{2} B^2 (1+t)^{-\frac{7}{6}}\leq \frac{3}{2} B^2 (1+t_0)^{-\frac{7}{6}}\leq \frac{\delta}{4}
\end{eqnarray*}
With the Cauchy-Schwarz inequality, (\ref{c}), (\ref{pp}) and supposing that $F > A(1+t)^{-2+\epsilon}$ in the interval $[t_2,t_1]$:
\begin{eqnarray*}
\vert 16 \pi \frac{\sigma_{ab}\widehat{S}^{ab}}{H^3} \vert \leq F^{\frac{1}{2}}\frac{(\widehat{S}^{ab}\widehat{S}_{ab})^{\frac{1}{2}}}{\rho}\leq \sqrt{3}F F^{-\frac{1}{2}}P^2
\leq\sqrt{3} A^{-\frac{1}{2}}B^2 (1+t)^{-\frac{1}{6}-\frac{\epsilon}{2}}F \leq \frac{\delta}{4}F
\end{eqnarray*}
Note that although $A^{-\frac{1}{2}}$ may be a big quantity, since $A$ and $B$ are independent we can make $B$ smaller to ``correct'' this.
Using (\ref{hh}) and the last three inequalities in (\ref{cc}) leads to:
\begin{eqnarray*}
\dot{F}\leq (-2+\varepsilon)(1-\delta)Ft^{-1}
\end{eqnarray*}
where $\varepsilon=18(A+B^2)t_0^{-1}$. Now setting $\xi=\varepsilon+2\delta-\varepsilon \delta$ we end up with:
\begin{eqnarray*}
\dot{F} \leq (-2 +\xi )Ft^{-1}
\end{eqnarray*}
which means that
\begin{eqnarray}\label{b2}
F(t_1)\leq F(t_2) {t_2}^{2-\xi} {t_1}^{-2+\xi}
\end{eqnarray}
\textit{Case IIa.} In this case $t_2=t_0$, so (\ref{b2}) means
\begin{eqnarray*}
F(t_1) \leq F(t_0) {t_0}^{2-\xi} {t_1}^{-2+\xi} \leq A {t_1}^{-2+\xi}
\end{eqnarray*}
since we can choose $F(t_0)$ as small as we want. So it follows that in this case:
\begin{eqnarray*}
A {t_1}^{-2+\epsilon} \leq F(t_1) \leq A {t_1}^{-2+\xi}.
\end{eqnarray*}
Situation which is schematically depicted in the following figure.
\begin{center}{\includegraphics[height=6cm]{caseII}}
\textit{Case IIa}
\end{center}
\textit{Case IIb.} In the case IIb we can use the fact that by continuity $F(t_2) \leq A (1+t_2)^{-2+\epsilon}$ holds and then
\begin{eqnarray*}
F(t_1) \leq A (1+t_2)^{-2+\epsilon} {t_2}^{2-\xi} {t_1}^{-2+\xi} \leq A(1+t_2)^{\epsilon-\xi} {t_1}^{-2+\xi}
\end{eqnarray*}
The $\epsilon$ here is also a quantity which we can choose as small as we want and then it follows that in this case
\begin{eqnarray*}
F(t_1) \leq A(1+t_0)^{\epsilon-\xi} {t_1}^{-2+\xi}
\end{eqnarray*}
We can choose $\epsilon$ to be smaller then $\xi$, so
\begin{eqnarray*}
F(t_1) \leq A{t_1}^{-2+\xi}
\end{eqnarray*}
\begin{center}
\includegraphics[height=6cm]{caseIIb}
\textit{Case IIb}
\end{center}
\textit{4. Results of the Bootstrap argument}\\
We have arrived at the statement that at least for a small interval $[t_0,t_1)$ and assuming (\ref{a1})-(\ref{a2}) we obtain the estimates:
\begin{eqnarray}
F(t)\leq A t^{-2+\xi}\label{yy}\\
P(t)\leq B t^{-\frac{2}{3}+\zeta}\label{xx}
\end{eqnarray}
Thus both assumptions (\ref{a1}) and (\ref{a2}) have been improved and using a bootstrap argument we know that the estimates obtained are valid for $t_1=\infty$ assuming small data.
(\ref{hh}) can be expressed as:
\begin{eqnarray}\label{zz}
H= -2t^{-1}(1+O(t^{-1}))
\end{eqnarray}
and is then also valid for the whole interval.\\\\
\textit{5. Improving the estimate of $F$}\\
We want to improve (\ref{yy}), but before that we need an inequality in the other
direction. From (\ref{cc}) we have:
\begin{eqnarray*}
\dot{F} \geq H(F+\sqrt{3}F^{\frac{1}{2}}P^2)
\end{eqnarray*}
Implementing now (\ref{yy})-(\ref{xx}) in this inequality, in particular having in mind the 'B'-dependence of the estimate of $P$ (\ref{B}):
\begin{eqnarray*}
\dot{F} \geq H F +H C(t_0)B^2 t^{-\frac{7}{3}+\epsilon}
\end{eqnarray*}
Using now (\ref{ho}):
\begin{eqnarray*}
\dot{F} \geq -2t^{-1} F -C(t_0)B^2 t^{-\frac{10}{3}+\epsilon}
\end{eqnarray*}
from which follows
\begin{eqnarray*}
t^2 F(t)\geq t_0^2 F(t_0)-\int^t_{t_0} C(t_0)B^2 s^{-\frac{4}{3}+\epsilon} ds
\end{eqnarray*}
and
\begin{eqnarray*}
F(t)\geq t^{-2} (F(t_0)t_0^2-B^2 C(t_0){t_0}^{-\frac{1}{3}+\epsilon}+C(t_0)B^2t^{-\frac{1}{3}+\epsilon}) \geq t^{-2} (F(t_0)t_0^2-B^2 C(t_0){t_0}^{-\frac{1}{3}+\epsilon})
\end{eqnarray*}
$F(t_0)$ is strictly positive. Choosing now $B$ small enough we have the following estimate:
\begin{eqnarray}\label{U}
F(t) \geq C(t_0)t^{-2}
\end{eqnarray}
Putting the last term of (\ref{cc}) with the help of (\ref{xx}) and (\ref{U}) in the following manner:
\begin{eqnarray*}
\vert 16 \pi \frac{\sigma_{ab}\widehat{S}^{ab}}{H^3} \vert \leq C F (F^{-\frac{1}{2}}P^2)=F O(t^{-\frac{1}{3}+\gamma})
\end{eqnarray*}
we can improve (\ref{yy}) implementing (\ref{yy})-(\ref{zz}) in (\ref{cc}) with the result:
\begin{eqnarray}\label{FF}
F= O(t^{-2})
\end{eqnarray}
\\
With these results we obtain the following theorem.
\begin{theorem}\label{t2}
Consider the same assumptions as in the previous theorem. Then
\begin{eqnarray}\label{ke}
p_i= \frac{1}{3} +O(t^{-1})
\end{eqnarray}
and
\begin{eqnarray}\label{lp}
g_{ab}=t^{+\frac{4}{3}}[\mathcal{G}_{ab}+O(t^{-2})]\\\label{ll}
g^{ab}=t^{-\frac{4}{3}}[\mathcal{G}^{ab}+O(t^{-2})]
\end{eqnarray}
where $\mathcal{G}_{ab}$ and $\mathcal{G}^{ab}$ are independent of $t$.
\end{theorem}
\noindent
{\bf Proof}
The conclusions made in the dust case after (\ref{2}) only depend on the estimate of $F$ and $H$ and apply directly to the general case. \\
\section{Conclusions and Outlook}
The result concerning the asymptotics of the metric implies ``asymptotic freezing'' in the expanding direction in the following sense. Consider the metric (4.12) of \cite{HN}, then by comparison with (\ref{lp}) one sees that the off-diagonal degrees of freedom $n_1$,$n_2$ and $n_3$ tend to constants and thus are not important for the dynamics. See \cite{HN} for the importance of asymptotic freezing in the ``other'' direction which has been studied, namely the initial singularity, and \cite{MK} for consequences of that in a quantum version.\\
As already mentioned in the introduction there exist several results concerning the Bianchi I-symmetric Einstein-Vlasov system (without cosmological constant). Almost all of them assume additional symmetries namely the LRS and the reflection symmetry condition (see \cite{IS} for a precise definition of these symmetries). However there exist some results where only the reflection symmetry is assumed. Concerning the expanding direction there is theorem 5.4 of \cite{IS}. Our theorems can be seen as a generalization of that theorem since we obtain the same the result, but a) we also obtain how fast the expressions converge b) we obtain an asymptotic expression for the spatial metric c) we do not assume any of the additional symmetries mentioned. However we used a different kind of restriction namely the small data assumptions.\\
In any case we think it interesting to study the non-diagonal case because although this time there was not an essential difference in the result with respect to the diagonal case, we do not expect that this will always be the case, especially when analyzing the initial singularity. In \cite{HU1} the possible dynamical behaviour towards the past has been determined assuming only the reflection symmetry and already there surprising new features like the existence of heteroclinic networks arose.\\
The situation of several (tilted) fluids leads naturally to the non-diagonal case. The Bianchi I-symmetry implies the absence of a matter current such that a single \textit{tilted} fluid is not compatible with this assumption. However there can be several tilted fluids such that the total current vanishes. In \cite{SU} and \cite{SA} this has been considered in the case of two fluids. What was found is that isotropization occurs if at least one of the two fluids has a speed of sound which is less or equal $\frac{1}{3}$ the speed of light. It is shown in particular for the case of two pressure free fluids in \cite{SA}, which can be seen as a singular solution of the Einstein-Vlasov system.\\
Of course there are many other ways of generalizing results which have been obtained for (single) perfect fluids. See for instance \cite{LB} and references therein for the inclusion of a Maxwell field in the Bianchi I case. In presence of a cosmological constant the results of \cite{Lee} have been generalized even to the Einstein-Vlasov-Maxwell case \cite{NT}. A natural generalization of the Vlasov equation is the case where the collision term is not zero, i.e. the Boltzmann equation. For this case dust-like asymptotics have already been obtained in \cite{ET} for an isotropic spacetime with a cosmological constant and \cite{ND} provides a basis for a possible extension to the asymptotics in the case of Bianchi I with LRS symmetry.\\
Finally we would like to mention that non-diagonal Bianchi I spacetimes are not only of interest in the context of cosmology, see for instance a recent work on the so called ultra-local limit \cite{CV}.
\textbf{Acknowledgements}\\
The author would like to thank Alan D. Rendall for helping along all the steps of this project, from proposing the problem to actually helping to solve it. I am also thankful for many discussions and a lot of concrete advice. This work has been funded by the Deutsche Forschungsgemeinschaft via the SFB 647-project B7.
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LEADERS MAKING A DIFFERENCE
SAFE USE & DISPOSAL
RALI CARES
Casa Grande Alliance Receives a Second Grant, Major Donation of Safe Drug Disposal Kits from RALI
5,000 safe drug disposal kits will be distributed to Casa Grande families to prevent substance misuse
Casa Grande, AZ – The Rx Abuse Leadership Initiative (RALI) today announced a donation of $2,000 and 5,000 safe disposal kits to Casa Grande Alliance. These resources will allow Casa Grande families to safely dispose of unused medications.
RALI, an organization dedicated to fighting the opioid epidemic throughout Arizona and across the country, partnered with Casa Grande Alliance to bring these important disposal kits to the families in the area. As we continue to fight COVID-19, RALI and local partners are also continuing their fight against the opioid crisis and that starts with the proper disposal of prescription medicines as a critical preventative step.
In 2020, RALI donated 8,000 safe drug disposal kits and a grant of $5,000 to support the Casa Grande Alliance, a non-profit charitable organization which has provided prevention services to Casa Grande youth for over 30 years. Casa Grande Alliance focuses on substance misuse prevention education and awareness services, treatment resource information, and coalition mentoring.
"Today's donation supports Arizonans in Casa Grande struggling with opioid addiction, allowing for the safe disposals of drugs and helping combat the opioid epidemic," said Arizona senior Senator Kyrsten Sinema.
"These safe disposal resources will help Casa Grande families remove unused prescription medications from their homes, and reduce the risk of substance misuse," said Bob Shogren, Executive Director of Casa Grande Alliance.
The safe disposal kits will be shared with prevention coalition partners and will be shared with families through prescription drug take back days, back to school and other community events throughout the year. The kits will also be available for free on request by calling the Alliance office at (520) 836-5022.
Grant funds will be used to support expanding efforts to implement the Thrive Resilience and Positive Mental Health prevention curriculum in area middle schools through engaging corporate and community volunteers as program facilitators. Thrive is an evidence supported and trauma informed interactive course designed to empower teens with knowledge and tools to thrive in today's culture. Thrive addresses the challenges facing school age teens with a focus on the risk and protective factors that promote positive choices and healthy habits. The Thrive model is intentional about creating a positive atmosphere that addresses unhealthy behavior while encouraging the participants to see their value, focus on solutions and internalize healthy lifestyles.
Learn more about safe disposal and more ways to address the opioid epidemic at raliusa.org.
The Rx Abuse Leadership Initiative (RALI) supports programs that help prevent the misuse of prescription medicines so that more lives can be saved from the opioid crisis. We do this by bringing together community leaders and elected officials who are committed to finding effective solutions and sharing ideas that will make a difference across the state.
RALI | © 2020, All Rights Reserved.
Thank you for your interest. Your comment has been received.
|
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«Иван Франко» — биографический фильм об общественной и литературной деятельности украинского писателя Ивана Франко, поставленный в году режиссёром Тимофеем Левчуком на Киевской студии художественных фильмов.
Сюжет
Иван Франко становится жертвой Габсбургского режима за свои стихи, литературную и общественную деятельность. Время между свободой и заключением он тратит на работу в газете, просвещение крестьян.
В ролях
Сергей Бондарчук — Иван Франко
Лилия Гриценко — Ольга, жена Ивана Франко
Ирина Скобцева — Людовика Шанкевич
Ярослав Геляс — Михайло Павлык
Елена Лицканович — Анна Павлык
Владимир Балашов — Генрик
Михаил Романов — Михаил Коцюбинский
Лев Снежницкий — Николай Лысенко
Иван Матвеев — Михаил Старицкий
Георгий Бабенко — Гоголинский
Леонид Пархоменко — Михайло Гринчук
Павел Шпрингфельд — Гжибович
Иван Переверзев — митрополит
Дмитрий Милютенко — наместник Галиции
В эпизодах
Игорь Ветров
Аркадий Гашинский
Пётр Мухин
Сергей Петров
Александр Подорожный
Василий Симчич — Терлецкий
Николай Гладков — ''пан Топиковский
Фёдор Радчук
Съёмочная группа
Автор сценария: Леонид Смилянский
Режиссёр-постановщик: Тимофей Левчук
Оператор-постановщик: Николай Кульчицкий
Художник-постановщик: Виктор Мигулько
Композиторы:
Николай Колесса
Борис Лятошинский
Оркестр министерства культуры УССР
Диригент П. Поляков
Директор фильма: С. Бабанов
Ссылки
«Иван Франко» на Рускино.ру
Фильмы СССР 1956 года
Фильмы-биографии СССР
Фильмы Тимофея Левчука
Фильмы:Персонаж:Михаил Коцюбинский
Фильмы:Персонаж:Иван Франко
Фильмы киностудии имени А. Довженко
Фильмы-биографии Украины
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{"url":"https:\/\/www.rongpeng.info\/stable\/index.php\/model-description\/","text":"# Model Description\n\nFollowing the generalized central limit theorem, $$\\alpha$$-Stable models manifest themselves in the capability to approximate the distribution of normalized sums of a relatively large number of independent identically distributed random variables. Besides, $$\\alpha$$-Stable models produce strong bursty results with properties of heavy-tailed distributions and long range dependence [1]. Therefore, they arose in a natural way to characterize the traffic in fixed broadband networks [2,5] and have been exploited in resource management analyses [8,9].\n\n$$\\alpha$$-Stable models, with few exceptions, lack a closed-form expression of the PDF, and are generally specified by their characteristic functions.\n\nDefinition:\n\nA random variable $$X$$ is said to obey $$\\alpha$$-Stable models if there are parameters $$0<\\alpha \\leq 2$$, $$c \\geq 0$$, $$-1\\leq \\beta \\leq 1$$, and $$\\mu \\in \\mathcal{R}$$ such that its characteristic function is of the following form:\n\n\\Phi(\\omega)= E(\\exp j\\omega X)\\\\ =\\left\\{ \\begin{aligned} &\\exp\\left\\{-\\sigma^{\\alpha} \\vert c \\vert^{\\alpha} \\left(1-j\\beta(\\text{sgn} (c)) \\tan \\frac{\\pi \\alpha}{2} \\right) + j\\mu c \\right\\}, \\alpha\\neq 1;\\\\ &\\exp\\left\\{-\\sigma \\vert c \\vert \\left(1+j\\beta(\\text{sgn} (c)) \\ln\\vert c\\vert \\right) + j\\mu c \\right\\}, \\alpha= 1.\\\\ \\end{aligned} \\right.\n\nHere, the function $$E(\\cdot)$$ represents the expectation operation with respect to a random variable. $$\\alpha$$ is called the characteristic exponent and indicates the index of stability, while $$\\beta$$ is identified as the skewness parameter. $$\\alpha$$ and $$\\beta$$ together determine the shape of the models. Moreover, $$c$$ and $$\\mu$$ are called scale and shift parameters, respectively. Specifically, if $$\\alpha=2$$, $$\\alpha$$-Stable models reduce to Gaussian distributions.\n\nFurthermore, for an $$\\alpha$$-Stable modeled random variable $$X$$, there exists a linear relationship between the parameter $$\\alpha$$ and the function $$\\Psi(\\omega) = \\ln\\left\\{- \\text{Re} \\left[ \\ln \\left(\\Phi(\\omega) \\right)\\right] \\right\\}$$ as\n$$\\Psi(\\omega) = \\ln\\left\\{- \\text{Re} \\left[ \\ln \\left(\\Phi(\\omega) \\right)\\right] \\right\\} =\\alpha \\ln (\\omega) + \\alpha \\ln(\\sigma),$$\nwhere the function $$\\text{Re}(\\cdot)$$ calculates the real part of the input variable.\n\nFigure Illustrations:\n\nSymmetric $$\\alpha$$-Stable distributions with unit scale factor. Courtesy to Wikipedia.\n\nSkewed centered Stable distributions with unit scale factor. Courtesy to Wikipedia.\n\nValidation Methodology:\n\nUsually, it\u2019s challenging to prove whether a dataset follows a specific distribution, especially for $$\\alpha$$-Stable models without a closed-form expression for their PDF. Therefore, when a dataset is said to satisfy $$\\alpha$$-Stable models, it usually means the dataset is consistent with the hypothetical distribution and the corresponding properties. In other words, the validation needs to firstly estimate parameters of $$\\alpha$$-Stable models from the given dataset, and then compare the real distribution of the dataset with the estimated $$\\alpha$$-Stable model. Specifically, the corresponding parameters in $$\\alpha$$-Stable models can be determined by quantile methods, or sample characteristic function methods.\n\nUseful references:\n\n1. G. Samorodnitsky, Stable Non-Gaussian Random Processes: Stochastic Models with Infinite Variance. New York: Chapman and Hall\/CRC, 1994.\n2. J. R. Gallardo, D. Makrakis, and L. Orozco-Barbosa, \u201cUse of alpha-Stable self-similar stochastic processes for modeling traffic in broadband networks,\u201d in Proc. SPIE Conf. P. Soc. Photo-Opt. Ins, Boston. Massachusetts, Nov. 1998, vol. 3530, pp. 281\u2013296.\n3. S. M. Koyon and D. B. Williams, \u201cOn the characterization of impulsive noise with $$\\alpha$$-Stable distributions using Fourier techniques,\u201d in Proc. Asilomar Conf. Signals, Systems, Computers, Oct. 1995.\n4. J. B. Hill, \u201cMinimum Dispersion and Unbiasedness: \u2018Best\u2019 Linear Predictors for Stationary ARMA a-Stable Processes,\u201d University of Colorado at Boulder, Discussion Papers in Economics Working Paper No. 00-06, Sep. 2000.\n5. X. Ge, G. Zhu, and Y. Zhu, \u201cOn the testing for alpha-Stable distributions of network traffic,\u201d Comput. Commun., vol. 27, no. 5, pp. 447\u2013457, Mar. 2004.\n6. A. Karasaridis and D. Hatzinakos, \u201cNetwork heavy traffic modeling using alpha-Stable self-similar processes,\u201d IEEE Trans. Commun., vol. 49, no. 7, pp. 1203\u20131214, Jul. 2001.\n7. P. Zagaglia, \u201cEstimation of alpha-Stable distribution parameters using a quantile method,\u201d 25-Jan-2012. [Online]. Available: http:\/\/www.mathworks.com\/matlabcentral\/fileexchange\/34783-estimation-of-alpha-Stable-distribution-parameters-using-a-quantile-method. [Accessed: 09-Oct-2014].\n8. W. Song and W. Zhuang, \u201cResource Reservation for Self-Similar Data Traffic in Cellular\/WLAN Integrated Mobile Hotspots,\u201d in Proc. IEEE ICC 2010, Cape Town, South Africa, May 2010.\n9. J. C.-I. Chuang and N. R. Sollenberger, \u201cSpectrum resource allocation for wireless packet access with application to advanced cellular Internet service,\u201d IEEE J. Sel. Area. Comm., vol. 16, no. 6, pp. 820\u2013829, Aug. 1998.\n10. Rongpeng Li, Zhifeng Zhao, Chen Qi, Xuan Zhou, Yifan Zhou, and Honggang Zhang, \u201cUnderstanding the Traffic Nature of Mobile Instantaneous Messaging in Cellular Networks: A Revisiting to alpha-Stable Models\u201d ,\u00a0IEEE Access,\u00a0vol. 3, pp. 1416-1422, 2015.\n11. Luca Chiaraviglio, Francesca Cuomo, Maurizio Maisto, Andrea Gigli, Josip Lorincz, Yifan Zhou, Zhifeng Zhao, Chen Qi, Honggang Zhang, \u201cWhat is the Best Spatial Distribution to Model Base Station Density? A Deep Dive in Two European Mobile Networks\u201d, IEEE Access, Apr. 2016.\n12. Yifan Zhou, Rongpeng Li, Zhifeng Zhao, Xuan Zhou, and Honggang Zhang, \u201cOn the $$\\alpha$$-Stable Distribution of Base Stations in Cellular Networks\u201d, IEEE Communications Letters, vol. 19, no. 10, pp. 1750-1753, Aug. 2015.","date":"2022-12-01 02:42:51","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\": 0.7399508953094482, \"perplexity\": 4266.4642992388735}, \"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-2022-49\/segments\/1669446710789.95\/warc\/CC-MAIN-20221201021257-20221201051257-00368.warc.gz\"}"}
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{"url":"http:\/\/mathhelpforum.com\/algebra\/100750-help-maths-please.html","text":"1. ## help with a maths please\n\nit is a maths question for students aged around 14 in my country. I am shamed that I don't know how to solve it\n\nThe question is something like:\n\nPerson A has a sum of money on Monday, and he spent $10 EACH day, and then he will save HALF of the money left on that day. After he spent$10 on Friday, he had no more money left. So how much did he orginially have on Monday?\n\nAt first I don't quite understand the question, but here I hope to clarify something that, Person A spent $10 FIRST on each day, then there will be some money left, then he will save half of the money left, and the rest of the money (not saved or spent) will be counted as the starting point of money for the next day. 2. Originally Posted by kenny1999 it is a maths question for students aged around 14 in my country. I am shamed that I don't know how to solve it The question is something like: Person A has a sum of money on Monday, and he spent$10 EACH day, and then he will save HALF of the money left on that day. After he spent $10 on Friday, he had no more money left. So how much did he orginially have on Monday? At first I don't quite understand the question, but here I hope to clarify something that, Person A spent$10 FIRST on each day, then there will be some money left, then he will save half of the money left, and the rest of the money (not saved or spent) will be counted as the starting point of money for the next day.\nIf you have $\\displaystyle \\$x_n$at the start day$\\displaystyle n$you have$\\displaystyle x_{n+1}=(x_n-10)\/2$dollars at the start of the next day. Reversing this we get:$\\displaystyle x_n=2 x_{n+1}+10$Now Friday is day$\\displaystyle 5$and Monday is day$\\displaystyle 1$, and you are told that$\\displaystyle x_5=10$CB 3. If we work backwards After spending$10 on friday he had $0 money left therefore before halving his money on thursday he had$20 left. This meant he spent $10 to get to his total of$20 which meant at start of day he had $30 therefore before halving his money on wednesday he had$60 left. This meant he spent $10 to get to his total of$60 which meant at start of day he had $70 therefore before halving his money on tuesday he had$140 left. This meant he spent $10 to get to his total of$140 which meant at start of day he had $150. therefore before halving his money on monday he had$300 left. This meant he spent $10 to get to his total of$300 which meant at start of day he had $310. lets check Monday 310 spent 10 leaves 300 save half to leave 150 Tuesday 150 spent 10 leaves 140 save half to leave 70 Wednesday 70 spent 10 leaves 60 save half to leave 30 Thirsday 30 spent 10 leaves 20 save half to leave 10 Friday 10 spent 10 to leave 0 4. Yet a third way to do this (akin to Captain Black's way): Suppose he starts with x dollars. Monday he spends$10, leaving x-10. Then he saves 1\/2 of that, 1\/2(x-10)= x\/2- 5, so he has x-10- (x\/2- 5)= x- 10- x\/2+ 5= x\/2- 5 left.\n\nTuesday he spends $10, leaving x\/2- 15 and saves 1\/2 of that, x\/4- 15\/2, so he has x\/2- 15- (x\/4- 15\/2)= x\/4- 15\/2. Wednesday he spends$10, leaving x\/4- 35\/2 and saves 1\/2 of that, x\/8- 35\/4 so he has x\/4- 35\/2- (x\/8- 35\/4)= x\/8- 35\/4.\n\n(You should be able to see a pattern here.)\n\nThursday he spends $10, leaving x\/8- 75\/4 and saves 1\/2 of that, x\/16- 75\/8 so he has (x\/8- 75\/4)- (x\/16- 75\/8)= x\/16- 75\/8. Finally, on Friday he spends$10, leaving x\/16- 155\/8= 0.\n\nSolve that equation for x.\n\n5. hmnnn . . .\n\nx\/16- 155\/8= 0\n\nx\/16 = 155\/8\n\nx = 16(155)\/8\n\nx = 2(155)\n\nx = 310","date":"2018-04-26 13:46:47","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\": 0.8171842098236084, \"perplexity\": 3607.353580842648}, \"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-2018-17\/segments\/1524125948214.37\/warc\/CC-MAIN-20180426125104-20180426145104-00081.warc.gz\"}"}
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TemplateHack.com - Download NewsOn premium blogger template. News On blogger templates is responsive magazine blogger templates. You can use this premium blogger templates to your news blog, newspaper blog, magazine blog, tech blog, health blog, niche blog, authority blog, review blog, movie blog, and many kind of blog.
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Hardcover Paperback eBook
Format: Hardcover Paperback eBook
Volunteer State Book Award (Tennessee)
IRA/CBC Young Adults' Choice
Evergreen Young Adult Book Award (Washington)
ALA Quick Pick for Reluctant Young Adult Readers
ALA Popular Paperbacks for Young Adults
ALA Best Fiction for Young Adults
The first book in the #1 New York Times bestselling Princess Diaries series by Meg Cabot.
Mia Thermopolis is pretty sure there's nothing worse than being a five-foot-nine, flat-chested freshman, who also happens to be flunking Algebra. Is she ever in for a surprise.
First Mom announces that she's dating Mia's Algebra teacher. Then Dad has to go and reveal that he is the crown prince of Genovia. And guess who still doesn't have a date for the Cultural Diversity Dance?
The Princess Diaries is the first book in the beloved, bestselling series that inspired the feature film starring Anne Hathaway and Julie Andrews.
Imprint: HarperTeen
BISAC1 : YOUNG ADULT FICTION / Romance / Contemporary
BISAC2 : YOUNG ADULT FICTION / Royalty
BISAC3 : YOUNG ADULT FICTION / Family / Multigenerational
Meg Cabot was born in Bloomington, Indiana. In addition to her adult contemporary fiction, she is the author of the bestselling young adult fiction series, The Princess Diaries. Over 25 million copies of her novels for children and adults have sold worldwide. Meg lives in Key West, FL, with her husband.
Other Works by Meg Cabot
No Judgments
Bridal Boot Camp
Boy is Back, The + Every Boy's Got One Bundle
The Princess Diaries by Meg Cabot
Romancing the Throne
Nadine Jolie Courtney
Glass Sword
My Lady Jane
Cynthia Hand
The Marked Girl
Lindsey Klingele
Reign of Shadows
Happily Ever After: Companion to the Selection Series
Colleen Oakes
The Heir
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{"url":"https:\/\/cs.stackexchange.com\/questions\/84400\/if-the-difference-between-two-oracles-is-negligible-is-the-difference-between-a","text":"# If the difference between two oracles is negligible, is the difference between a PPT algorithm with these two oracles also negligible?\n\nWe say a negligible function is a function $\\epsilon(n):\\mathbb{N}\\rightarrow \\mathbb{R}$ such that for every positive integer $c$ there exists an integer $N_c$ such that for all $n > N_c$, $$\\epsilon(n)<\\frac{1}{n^c}$$ (From wikipedia)\n\nAssume that two probabilistic polynomial-time algorithms $O_{1},O_{2}$ satisfy that $$\\Sigma_{y \\in \\{\\, 0,1 \\,\\}}\\left\\vert \\mathrm{Pr}\\left[ O_{1}(x) = y \\right] - \\mathrm{Pr}\\left[ O_{2}(x) = y \\right] \\right\\vert \\leq \\epsilon_{1}(n)$$ for all $x$, where $\\left\\vert x \\right\\vert = n$ and $\\epsilon_{1}$ is negligible.\n\nLet $A$ be a probabilistic polynomial-time algorithm. Can we get that $$\\Sigma_{y \\in \\{\\, 0,1 \\,\\}}\\left\\vert \\mathrm{Pr}\\left[ A^{O_{1}}(x) = y \\right] - \\mathrm{Pr}\\left[ A^{O_{2}}(x) = y \\right] \\right\\vert \\leq \\epsilon_{2}(n)$$ for all $x$? Where $\\left\\vert x \\right\\vert = n$ and $\\epsilon_{2}$ is negligible.\n\n\u2022 What are probabilistic polynomial time oracles? Where is the randomness in your first statement? The statement would make sense if you replace the word oracle with the word machine, but in that case the second statement requires modification. \u2013\u00a0Ariel Nov 24 '17 at 10:45\n\u2022 @Ariel I mean $O_{1},O_{2}$ are also probabilistic polynomial-time algorithms. So should I change 'oracles' to 'algorithms' or 'Turing machines'? \u2013\u00a0TeamBright Nov 24 '17 at 11:04\n\u2022 When we say oracles, we're usually talking about languages, a machine with an access to an oracle is a machine which can raise queries of the form \"is this string in the language?\". Thus, it is not clear what is meant by probabilistic polynomial time oracles, since ppt is a property of a machine and not a language. If now $O_1,O_2$ are machines, then you need to be clear about what you mean by $A^{O_1}$, since $O_1$ may reply differently to the same query depending on its randomness. \u2013\u00a0Ariel Nov 24 '17 at 11:13\n\u2022 Perhaps you mean to say that $A$ is a ppt algorithm which simulates another ppt machine during its computation, and you wish to know how the acceptance probability varies between simulating $O_1$ and $O_2$. In that case your notation is fine, but you have to mention this, since the standard way to interpret $A^B$ is that $B$ is a language and $A$ is machine which queries membership to $B$, if $B$ is a machine then it is not always clear (as is in this case) what language you want to associate with it. \u2013\u00a0Ariel Nov 24 '17 at 11:16\n\u2022 Use a \"hybrid argument\", if you know what that means (it comes from the crypto literature). \u2013\u00a0D.W. Nov 24 '17 at 23:23\n\nGiven $x$, define $p_1(x,y) = \\Pr[O_1(x) = y]$ and $p_2(x,y) = \\Pr[O_2(x) = y]$. Let \\begin{align*} \\delta_x &= \\sum_y [\\max(p_1(x,y),p_2(x,y)) - \\min(p_1(x,y),p_2(x,y))] \\\\ &= \\sum_y |p_1(x,y) - p_2(x,y)| \\\\ &\\leq \\epsilon_1(n). \\end{align*} On the other hand, $$\\sum_y [\\max(p_1(x,y),p_2(x,y)) + \\min(p_1(x,y),p_2(x,y))] = \\sum_y [p_1(x,y) + p_2(x,y)] = 2.$$ Therefore $$\\sum_y \\min(p_1(x,y),p_2(x,y)) = 1 - \\frac{\\delta_x}{2}.$$ Consider now the following random process that generates two random variables $R_1,R_2$:\n\n\u2022 For every $y$, with probability $\\min(p_1(x,y),p_2(x,y))$, generate $R_1=R_2=y$.\n\u2022 Otherwise (this happens with probability $\\delta_x\/2$):\n1. For every $y$, with probability $\\frac{p_1(x,y)-\\min(p_1(x,y),p_2(x,y))}{\\delta_x\/2}$ generate $R_1=y$.\n2. For every $y$, with probability $\\frac{p_2(x,y)-\\min(p_1(x,y),p_2(x,y))}{\\delta_x\/2}$ generate $R_2=y$.\n\nThis process is a coupling that generates two random variables $R_1,R_2$ with the following properties:\n\n1. $R_1 \\sim O_1(x)$.\n2. $R_2 \\sim O_2(x)$.\n3. $\\Pr[R_1 \\neq R_2] = \\delta_x \\leq \\epsilon_1(n)$.\n\nLet us go back to your algorithm $A$, and suppose that it runs in time $T(n)$. Use the coupling above to generate two random variables $B_1,B_2$ with the following properties:\n\n1. $B_1 \\sim A^{O_1}(x)$.\n2. $B_2 \\sim A^{O_2}(x)$.\n3. $\\Pr[B_1 \\neq B_2] \\leq T(n) \\epsilon_1(n) =: \\epsilon_2(n)$.\n\nNote that $\\epsilon_2(n)$ is negligible. We have\n\n\\begin{align*} &\\sum_y |\\Pr[A^{O_1}(x) = y] - \\Pr[A^{O_2}(x) = y]| \\\\ = &\\sum_y |\\Pr[B_1 = y] - \\Pr[B_2 = y]| \\\\ = &\\Pr[B_1 \\neq B_2] \\sum_y |\\Pr[B_1=y|B_1 \\neq B_2] - \\Pr[B_2=y|B_1 \\neq B_2]| \\\\ \\leq &\\Pr[B_1 \\neq B_2] \\sum_y (\\Pr[B_1=y|B_1 \\neq B_2] + \\Pr[B_2=y|B_1 \\neq B_2]) \\\\ \\leq &2\\epsilon_2(n), \\end{align*} since given $\\Pr[B_1=y|B_1=B_2] = \\Pr[B_2=y|B_1=B_2]$.","date":"2020-07-09 14:29:14","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\": 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\": 0.9988186359405518, \"perplexity\": 474.1011275251545}, \"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-2020-29\/segments\/1593655900335.76\/warc\/CC-MAIN-20200709131554-20200709161554-00131.warc.gz\"}"}
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Q: On mobile/iOS views, is there a way to prevent my popup from being taller than my page? On my client's site I'm using Magnific Popup to show the license agreement for their product when a "show agreement" link is clicked. So I'm using the inline type for a big long block of text. It works perfectly on the desktop. But it gets all messed up at the bottom on mobile.
If I understand correctly, at desktop views Magnific Popup sets <html> to overflow: hidden and the popup to position: fixed. At mobile views it doesn't do this.
This would be fine, except for that my popup is so tall that it exceeds the height of my page. This means that it starts looking broken at the bottom.
I'd love to make it work on mobile/iOS as it does on desktop, but I'm starting to doubt that this is even possible. If anyone has any ideas I'd love to hear 'em. Thanks!
A: You could add max-height: 100%, overflow-y: scroll on the popup. This way the biggest it can be is the size of the viewport, but users can scroll within it.
A: for Magnific Popup - v1.1.0 - 2016-02-20 what worked for me was
.mfp-bg,
body.mfp-zoom-out-cur {
overflow: hidden !important;
margin: 0 !important;
padding: 0 !important;
height: 100% !important;
}
mfp-bg is the background that can get larger than viewport and and allow scrolling
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| 1,199
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Instant competitive price on all batteries, Car, SUV, Light Commercial, Motorbike, Quad, Jet Ski and Golf Trolleys.
Safe & Secure Nationwide delivery.
At AutoFastFit, we pride ourselves in only keeping the best brands and brands we trust. Auto Fast fit is a family run business established over 40 year ago. We have been selling and fitting batteries since then and take pride in only offering the premium quality car parts at discounted prices. we keep various brand options for each product, which will allow you to choose by price or preferred brand.
Auto Fast fit have been using Yuasa for many years. With our commitment to quality and customer satisfaction, our relationship Yuasa has stood the test of time.
Yuasa are world leaders in valve regulated lead-acid battery design and manufacture and have automotive battery, industrial battery and motorcycle battery distributors all over the world.
A battery is a device for storing electrical energy in a chemical form, and then releasing it as direct current in a controlled way.
All types of batteries contain a positive and a negative electrode immersed in an electrolyte, the whole assembly being within ?a container.
Most Yuasa batteries are lead-acid batteries, which means that they have positive and negative electrodes made of lead compounds in a dilute sulphuric acid electrolyte.
Lead-acid batteries are secondary batteries, which means that they can be recharged after they have been discharged. ?Primary batteries can be discharged only once and then have ?to be thrown away; examples are some types of torch and ?radio batteries.
The positive electrode is made of lead dioxide and the negative electrode is made of porous lead.
When an electrical load (for example lights or a starter-motor) is connected across the battery, a current flows through the electrolyte in the battery and through the external load. This causes the battery to discharge, which results in the chemical composition of both the electrodes changing to lead sulphate.
A battery can be charged by putting a current through the battery from an outside source of electricity such as an alternator, dynamo or charging unit. This converts the lead sulphate back to the original materials of lead dioxide and porous lead.
As the battery becomes charged, the electricity begins to decompose (hydrolyse) the water in the electrolyte into its constituent elements of hydrogen and oxygen, which are released as gas. This is why a battery gases when it is charged.
As the positive and negative electrodes are made of weak materials, they need a mechanical support which is provided by a grid made from a lead alloy; lead on its own would be too soft.
In addition to providing a support for the electrodes (the active material), the grid also conducts electricity from the electrodes to the outside load.
The electrodes are initially made from a mixture of lead oxide and lead sulphate. This is converted into lead dioxide in the positive plate and porous lead in the negative plate when the battery is initially charged.
The negative electrode also contains small amounts of additives to give the battery a good discharge performance at low temperatures to improve starting.
The combination of grid and electrode is normally called a plate.
Most modern separators are made of microporous polyethylene, which has the right properties to meet the demanding conditions within the battery.
What Makes a Battery Maintenance-Free?
30 years ago, batteries lost water at a high rate, and motorists were advised to check the acid level as one of their weekly checks; modern maintenance-free batteries need no water addition throughout their life under normal operating conditions. Incidentally, during the same period, battery life has doubled from 2 years to 4-5 years.
In the past, battery grids were made of an alloy of lead with 10 per cent of antimony; the purpose of the antimony was to give rigidity as pure lead would be too soft on its own. Unfortunately, some of the antimony dissolved in the acid and resulted in the battery losing water.
With improvements in battery technology, we have been able to reduce the antimony content from 10 per cent to 1.5 per cent, and this reduction has resulted in batteries that are low maintenance, needing only yearly attention.
The latest improvement has been the use of 0.1 per cent of calcium as a hardening agent in grids in place of antimony; this causes less contamination of the acid and much reduced water loss, making the battery maintenance-free so no water needs to be added during its operational life.
Modern car charging systems allow only a small current to flow into the battery when it is fully charged. If there is a fault in the alternator, a much higher current will pass through the battery all the time that the car is running. This current will cause the battery to lose water rapidly, destroying the maintenance free characteristics of the battery, and will also reduce the life of the battery by damaging the positive grids.
A dark brown/black colour on the bottoms of the vent-plugs is a strong sign of overcharge.
If an alternator (non Start-Stop vehicle) has a voltage above 14.8 Volts at normal temperatures, this is a generally sign that the charging system is faulty. The common diode fault in the rectifier will see charging voltages of 16.0V at the battery, the alternator should be repaired immediately to prevent any further damage to the battery.
Note with latest Start-Stop vehicles with Brake Energy Regeneration, higher voltages (15.2V) are used to maximise charging efficiencies and reduce alternator charging periods.
Modern charging systems keep the battery in a high state-of-charge while the car is running under most operating conditions. However, the battery will discharge under abnormal conditions or if the car is allowed to stand with a load on, for example, lights. On modern cars when parked, there is normally a constant drain on the battery caused by such components as the computer, alarm system, clock etc, and this will cause the battery to become discharged. Depending on the vehicle, this can take weeks or months.
Vehicle batteries are designed to accept some cycles of discharge and recharge, but are not designed for applications in which there are constant cycles of charge and discharge (deep cycling). Leisure batteries have been designed for these types of application, and have a special construction to enable them to be deep cycled on a continuing basis.
Continual deep cycling of vehicle batteries will cause failure as the positive active material will gradually fall to the bottom of the battery, reducing the ability of the plates to store electricity.
A large number of small black/brown particles in the electrolyte are a strong indication that the battery has been deep cycled.
Sulphation is a normal part of the operation of a battery and occurs whenever a battery is discharged. When the battery is recharged, the sulphation (lead sulphate) is changed back into active material.
If a battery is left flat for a period of time, this sulphation slowly changes its form into one that cannot be changed back into ?active material on charging, so, after charge, the battery will not return to give its original performance. If the sulphation is bad enough, the car will not start. This is the problem normally referred to as sulphation.
Undercharge occurs if the battery is not receiving enough charge to return it to a full state-of-charge; this will slowly cause sulphation. This fault can occur if the car is being used only occasionally for short journeys, or for Start-Stop urban motoring. Undercharge will also occur if the alternator voltage is in the region of 13.6 – 13.8 Volts .
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In today's blog, we are featuring the current startup homes for sale in Lexington and Richland County, SC. These properties prove that you don't have to go broke to own a home. With prices under $125,000, we think you will find that these listings are very affordable on almost any budget. If you have any questions, or would like to arrange a tour, our experienced agents would be happy to be of assistance. Check out this link for more information about the amenities and real estate of the Columbia area.
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Q: Clarification of a sequence - also, sequence of integers becomes non-integer? EDIT: Apparently the sequence is printed wrong!
"Let $a_0 = a_1 = 1$, and recursively define $a_{n+1} = (a^2_0+a^2_1+...+a^2_n) $ n. This sequence begins $1,1,2,3,5,10,28,...$. Not all of its entries are integers, but the first non-integral entry does not occur until $a_{43}$, by which time the value is approximately $5.4093*10^178485291567$"
This is written EXACTLY as above on the wall of my universities Mathematics department.
First of all, I don't understand how the above 'sequence begins' was obtained, nor do I understand what is meant by the 'n.' directly after the recursive definition. I believe they are taking each previous term that was run, and squaring it and adding them all together.
When I try to calculate the first values of the sequence, I get:
$$a_0 = 1, a_1 = 1, a_2 = 2, a_3 = 6, a_4 = 42, a_5 = 1806...$$
Obviously there is something I am not understanding.
Furthermore I am also confused by the fact that this becomes non integer. From my understanding the square of an integer is always an integer(closure under multiplication), the addition of two integers is integer(closure under addition). How could it possibly become non integer?
Sorry if I have used the incorrect tag!
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Every Orient – not just the tool watches - is built super tough, to resist shock, pressure and other damaging forces. This makes them capable enough to take the hardships of daily life....even things like beach volleyball or salty water thrashings! In fact, every Orient is built like an excellent, rugged sports watch just varying in functions and looks. Even the Orient Star! No activity is possibly too-demanding for the Orient watches. That's why it is popular with military personnel and other hazard professionals where it kind of enjoys being a status symbol.Especially, the Orient Classic Automatic Mens Watch; the men find the look and quality just awesome!
That way, the Orient Mako Automatic Diver fits both sides of fashion; from casual outfits to office-wear. These watches are meant for dive-purposes but aesthetically designed to be worn everywhere. A choice of the pro-scuba divers, you can also use it extensively on the land while playing a round of golf; even baseball, soccer and rugby. And any beach sport, so to say. They are built to withstand salt, sun and sand.
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Performance is not available for the most recent month-end until receipt of the fund performance data from Morningstar. This is typically available after five business days after each month-end. The quarterly performance is available by selecting the fund performance menu option.
In addition, Daily Share Prices are available.
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{
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Home » Early Contact » Woolloomooloo Bay
Woolloomooloo Bay
Walloomoolloo, The Seat of Jno Palmer, 1803, by John Bolger (image courtesy Mitchell Library, State Library of NSW - SV1A / Wllo / 3)
The Residence of Edward Riley in Woolloomooloo, 1825, by Joseph Lycett (image courtesy State Library of Victoria - 30328102131561/5)
Location: Woolloomooloo Bay, Woolloomooloo
Author: Paul Irish
Woolloomooloo is the name given to the Yurong Creek valley located immediately east of Sydney Town and the Domain, which later became Sydney's first suburb. In 1793, when Commissary General John Palmer was granted 100 acres at Woolloomooloo, extending from Woolloomooloo Bay to Oxford Street, he also acknowledged this by naming his house Woollamoola after its Aboriginal name (also recorded as Waalamool, Walla-mool and Wallamoula). This later resulted in the suburb and bay being named Woolloomooloo.
Palmer cultivated fruit trees and tobacco on his land in the 1810s. His house was occupied by later assistant commissaries, David Allan and Frederick Drennan, before he sold the estate to Edward Riley in 1822. Throughout this time, Aboriginal people frequented the estate to camp, fish, hunt and conduct ceremony. They were often referred to as the 'Woolloomooloo tribe' in the 19th century, although they also moved around a much broader area.
The land between Woollomoola House and the bay was 'a favourite camping ground' for Aboriginal people accessing the resources of the bay. After payback contests in Hyde Park in the 1810s and 1820s to punish individuals for transgressions, Aboriginal people returned to camp at Woolloomooloo, where 'fires were lit in all directions, and yarning and cracking jokes took place until nearly daylight.' Others, such as Botany Bay man Mahroot, lived with David Allan at Woollomoola House in the 1810s.
Woolloomooloo was also the scene of Aboriginal ceremonies until at least the 1830s. In 1814 an Aboriginal inquest ceremony was held at Woolloomooloo to determine whether Aboriginal man Baggara's death was caused by supernatural means, and in 1831 a ceremony was held under the supervision of Young Bungaree, whose father had died the previous year nearby at Garden Island. The scene was described by the Sydney Herald:
A "corrobbora" of the aborigines took place at Wooloomoolloo on Monday night.Young Bungaree did the honors of the ceremonies. Before the party broke up, his sable Majesty became done up with bull; and in consequence of some pranks played by him he was floored by a waddie, on which a regular melee ensued, the company espousing different sides of the question ; and after a hard fought battle they parted good friends, some of their cobberas having sustained considerable damage.
A young Obed West, growing up over the hill at Paddington in the early 19th century, recalled 'seeing 200 or 300 of the original owners of the soil camped about the bay', during ceremonies at Woolloomooloo.
Aboriginal people continued to live around Woolloomooloo as Woolloomooloo Hill was divided up to house stately villas in the late 1820s and 1830s, and the valley became a residential suburb in the 1840s. The 'Woolloomooloo tribe' attended a Christmas feast for Aboriginal people hosted by Sydney businessman Charles Smith at his home near the Sydney Markets in 1844, and in the 1850s one of their settlements was around where the current Cathedral Street (then Woolloomooloo Street) crossed Yurong Creek.
By the 1860s, when the area was covered in housing and the shore had been replaced by a seawall and wharves, there do not appear to have been further Aboriginal settlements established. A few individuals are briefly mentioned at this time, sometimes living with sympathetic Europeans, and more are likely to have at least passed through the area on their way to town from other settlements to the east such as Rushcutters Bay and Barcom Glen.
A century later in the 1970s and 1980s, Aboriginal and Torres Strait Islander people began moving into community housing at Woolloomooloo and formed a new community. There are currently around 100 indigenous people living in the area, and their stories are only beginning to be explored.
Attenbrow, V, Sydney's Aboriginal Past: Investigating the archaeological and historical records, Sydney: UNSW Press, 2010
Broadbent, J, "The Push East: Woolloomooloo Hill, the first suburb," in Sydney: City of Suburbs, ed. M Kelly, Sydney: New South Wales University Press, 1987, p 12-29
'Domestic Intelligence', 14 November 1831, The Sydney Herald, p 4
Dowling, J S, Reminiscences of a colonial judge, Leichhardt: Federation Press, 1996
Irish, P, Hidden In Plain View: The Aboriginal people of coastal Sydney, Sydney: NewSouth Publishing, 2017
Keith Vincent Smith, King Bungaree: A Sydney Aborigine meets the great South Pacific explorers, 1799-1830 (Kenthurst, NSW: Kangaroo Press, 1992).
Shirley Fitzgerald, 'Woolloomooloo', Dictionary of Sydney, 2008
Testimony of Mahroot, in NSW Legislative Council, Report from the Select Committee on the Condition of the Aborigines, with appendix, minutes of evidence and replies to a circular letter, Sydney: Government Printer, 1845
Darlinghurst Gaol
Barcom Glen
Elizabeth Town
St Mary's Cathedral
Bungaree
Wuganmagulya (Farm Cove)
The Domain and Royal Botanic Gardens
Bennelong Point / Dubbagullee
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\section{Introduction}
\textit{Autonomous System} (AS) is the name given to the networks making up the Internet \cite{RFC1930:1996}. ASes establish interconnections through a protocol called \textit{Border Gateway Protocol} (BGP) \cite{RFC4271}. BGP is a complex protocol that requires a lot of knowledge from the administrators of an AS. Sometimes the human being also forgets to update information, especially those related to routing policy and that reside on important servers such as \textit{Internet Routing Registry}\footnote{http://www.irr.net/} (IRR), for example. IRR is a distributed database of route and route-related information \cite{Braga2010}. The sometimes neglected participation of the human being during the creation and update IRR objects processes, was the motivation for creating a model of agents which could replace the human interventions (made by email). For this reason, was propose the \textit{Autonomous Architecture Over Restricted Domains} (A2RD) into the restricted domain of an AS, applying as use case over the IRR \cite{Braga:2015}. A2RD replaces the human with your agents, \textit{Intelligent Elements} (IEs), establishing a new IRR model, named \textit{innovation IRR} (iIRR), shown in Figure \ref{fig:innovationIRR}.
\begin{figure}[!ht]
\centering
\includegraphics[scale=0.39]{innovationIRR}
\caption{The innovation IRR model established by A2RD}
\label{fig:innovationIRR}
\end{figure}
A2RD specialized IEs, automatically create objects as defined by the \textit{Route Policy Specification Language} \cite{RFC2622, RFC4012}. Those objects that can not be created automatically will receive support from AS administrators through a human-computer cooperation mechanism. Nothing is changed in relation to the present and future IRR structure, characterized by the expectations recommended by the stakeholders to the \textit{Internet Engineering Task Force}\footnote{https://ietf.org/} (IETF) and \textit{Internet Research Task Force}\footnote{https://irtf.org/} (IRTF) disseminated through of their formal documents \cite{RFC2650, RFC2725, RFC3707, RFC7682, RFC7909}. Neither does it affect the security concerns surrounding the IRR and Internet governance \cite{Kuerbis:2017}. Similarly, tools that use IRR databases can be used without any modification. A very useful, among others, is the IRR Powertools\footnote{https://github.com/6connect/irrpt}.
For this paper, \textit{blockchain} is a data structure whose components are chained, with guarantee of immutability of its contents, and consequent integrity of the chain preserved by a cryptography process, with difficult computational reversibility. This definition is much simpler but more computationally oriented than those in which blockchain is associated with crypto-economics or crypto-currencies, and often have confusing definitions, but when it is clear, blockchain is defined as a database \cite{Nakamoto2008, Pilkington:2015}.
On the other hand, by abstracting from property of immutability, the data structure like blockchain is a well-known concept used in computer research and originated in the academic literature of the 1980s and 1990s \cite{narayanan2017bitcoin}. As a simple data structure, for example, in works involving \textit{provenance}, which is used as complementary data documentation containing the description of 'how', 'when', 'where', 'why' the data were obtained and 'who' obtained it \cite{braga2008data}. The blockchain model proposed in 2008 to meet the Bitcoin virtual currency has effectively aroused the interest of the research community mainly by the immutability property that ensures data integrity \cite{prusty2017building, bashir2017mastering}. Immutability and integrity are obtained by a hash encryption mechanism \cite{bakhtiari1995cryptographic, rogaway2004cryptographic}. The combination of these two factors and characteristics associated to the blockchain recommended the application in the A2RD model, with the aim of enhancing communication and collaboration among the IEs \cite{Braga:2017}. This proposal is more simpler than those application of blockchain in Internet Infrastructure with fundamentals in Bitcoin technology, based in the appropriate fact that to run, Internet use resources such as numbers and names \cite{hari2016internet}.
There is no study directly related to this work and there are few blockchain works related to the Internet Infrastructure \cite{angieri2018experiment}. Blockchain still is not a matured technology, there are challenges that need to be considered when designing a platform, to ensure security, reliability and usability. So, there is not related works associated with Internet Infrastructure, because is fact that due to the emergent nature of the topic, the reviewed literature was not published in high-ranking journals with prolonged review cycles \cite{Xu2016}.
The main goal of this paper is to present the \textit{Internet Infrastructure Blockchain} (IIBlockchain), a blockchain architecture to improve the security, knowledge and intelligence in inter-agent communication and collaboration over restrict domains of the \textit{Internet Infrastructure}, developed specifically and therefore independent of any available blockchain platform. The next sections of this paper will be organized as follows. In section 2 we discuss the A2RD model and the needs for inter-agents communication and cooperation. In section 3 we present the architecture of IIBlockchain and the properties inherent to the blocks, their types and the characteristics of the designed chain. In section 4 we discuss the implementation of IIBlockchain showing the main associated properties. In section 5 we present the conclusions and in section 6 we present the proposals for future works.
\section{The A2RD Model}
A2RD is a project that initially proposed the creation of agents with automatic activities replacing human tasks in the environment restricted to the domain of an AS. The use case was the addition and update of objects in IRR server. The application was considered useful mainly because the tasks of the AS administrator did not guarantee the accuracy in its completion nor the permanent need to update the objects making the IRR an unreliable system from the point of view of its contents. A2RD solved this problem.
A new proposal for the A2RD model emerged from this experience \cite{Braga:2017}. The Figure \ref{fig:a2rdEnvironment} shows this new proposal, in which each implementation of A2RD is represented as an agglomeration of IEs in a four layers model.
\begin{figure}[!ht]
\centering
\includegraphics[scale=0.35]{skau01}
\caption{A2RD environment}
\label{fig:a2rdEnvironment}
\end{figure}
A2RD IEs, reach their autonomy and intelligence aided by four components, the \textit{Knowledge Base}, the \textit{Training Data Sets}, and \textit{Domain Datasets}. These first three components are obtained from non-structured databases, in particular, from the \textit{Request for Comments} database, containing documents authored by network operators, engineers and computer scientists, documentary methods, behaviors, research, or innovations applicable to the Internet, all of them, working in groups of the IETF and IRTF, and maintained by RFC-Editor\footnote{https://www.rfc-editor.org/}.
Each AS, of its own free will, may implement its respective A2RD, which is controlled by the IE named \textit{IE Controller}, which receives the identification \textit{x:0}, where \textit{x} is the \textit{AS Number} (ASN).
IEs need to communicate in order to collaborate, learn and cooperate with each other. This communication needs to be secure, that is, the respective \textit{IE controller} must recognize the origin of each pair in their information exchanges. A mechanism called \textit{Dark Think Security} (DTS) has been proposed to ensure the desired security \cite{Braga:2017b}. Although preliminary implementations have revealed that DTS is indeed secure, it has proved to be complex in implementation. In the search for a simpler alternative included \textit{Pretty Good Privacy} (PGP) \cite{garfinkel1995pgp}. Using PGP, an AS$x$ IE controller that wants to communicate with an AS$y$ IE controller, will use the AS$y$ \textit{public key} to encrypt the message, for $\forall x\quad and\quad \forall y\quad such\quad that\quad x \neq y\quad and\quad x,\quad y = 1, ..., n,\quad n \leq$ total ASes present in the \textit{Internet Routing Table}\footnote{http://thyme.rand.apnic.net/current/data-summary}. The AS$y$ controller uses AS$x$ \textit{secret key} to decrypt the message. Thus, for this and for other reasons that we will see in the following section, the recommended solution was a variation of blockchain implementations proposed in the literature, that we named in this paper as \textit{IIBlockchain}, which represents the fourth component, as a cloud, in Figure \ref{fig:a2rdEnvironment}.
\section{IIBlockchain Model and Implementation}
The IIBlockchain model can be seen in Figure \ref{fig:arquiteturaIIBlockchain}, which shows the implementation of A2RD in any two ASes (AS$x$ and AS$y$).
\begin{figure}[ht]
\centering
\includegraphics[scale=0.45]{arquiteturaIIBlockchain1}
\caption{IIBlockchain Architecture implemented over ASx and ASy domains}
\label{fig:arquiteturaIIBlockchain}
\end{figure}
This figure shows that the respective A2RD communicate through encrypted messages. Also, the A2RDs independently maintain a blockchain with properties characteristic of IIBlockchain. These chains contain, in their blocks, data inherent to each A2RD and about the environment of the AS in which they are implemented allowing the cooperation through the exchange of knowledge and information that can help in learning and maintaining the autonomy of their respective IEs. Each A2RD locally maintains a copy of IIBlockchain from each of the other ASes. There is no need to implement an A2RD for a chain to be constructed for an ASN. Specialized IEs of an ASx any guarantee that minimal information is included in chains of other ASes.
\subsection{Block Properties}
A block of any chain type is equivalent to a dictionary structure of the Python language, whose configuration and summary description of the respective keys are shown in Figure \ref{fig:arquiteturaBlockchain}.
\begin{figure}[!ht]
\centering
\includegraphics[scale=0.35]{arquiteturaBlockchain}
\caption{Block Structure}
\label{fig:arquiteturaBlockchain}
\end{figure}
The detail description of block keys are in Table \ref{tab:blockKeys}.
\begin{table}[ht]
\centering
\caption{Description of block dictionary keys}
\label{tab:blockKeys}
\begin{tabular}{|l|l|}
\hline
\multicolumn{1}{|c|}{\textbf{Key}} & \multicolumn{1}{c|}{\textbf{Description}} \\ \hline
\textbf{asn} & \makecell[l]{ASnumber: Identifies the owner number of the string.\\For same string, the value of this key is always the same} \\ \hline
\textbf{block\_seq} & \makecell[l]{Identifies the position of the block within the chain. If\\block $i$ preceding or immediately preceding block $j$ than\\$i < j$ and not necessarily $j = i + 1$. This is due to the fact\\that a block can be removed, from an \textit{ASN} chain, if it\\becomes obsolete. Upon removal, the block is added to\\the \textit{obsolete} chain. The immutability and integrity of\\this \textit{ASN} chain must be restored.} \\ \hline
\textbf{obsoletes\_block\_id} & \makecell[l]{If the value of this key is not empty, so this references\\the \textbf{block\_id} that will be obsoletes} \\ \hline
\textbf{timestamp} & \makecell[l]{Time moment the block was add in the chain} \\ \hline
\textbf{block\_type} & \makecell[l]{Type of the block: block types are not necessarily\\predefined. IEs can create different types of blocks\\through agreements between them during their normal\\activities. Important blocks are, however, predefined. For\\example, the \textit{Genesis} block, which is necessarily the\\first block of any chain. Blocks that represent IRR\\objects always prefix the usual object name with \textit{irr\_}} \\ \hline
\textbf{block\_id} & \makecell[l]{Hash that will identify the block, obtained on the whole\\block, after it is completely filled} \\ \hline
\textbf{previous\_block\_id} & \makecell[l]{\textbf{block\_id} of the previous block of this block} \\ \hline
\textbf{data} & \makecell[l]{Data of the related with the block type} \\ \hline
\textbf{signature} & \makecell[l]{Signature that ensures the owner of the data} \\ \hline
\end{tabular}
\end{table}
\subsection{Chain Properties}
Any chain only exists if it has a 'Genesis' block type as its first block ('block\_seq' = 1). Suppose that AS$x$ wants to add in its chain, a block that will contain its \textit{PGP public key} with which any ASN can encrypt messages that only AS$x$ will understand. At this point, the AS$x$ chain is empty. Suppose $x = 18782$. So, using the IIBlockchain Python class available at GitHub\footnote{https://github.com/juliaobraga/a2rd/} if we add the block of type \textit{PublicKey} we will have a two block chain as can be seen in Figure \ref{fig:chain-2-blocks}. It is important to note that block numbers (\textit{block\_seq}) are sequential ($1$ and $2$, respectively).
\begin{figure}[!ht]
\centering
\includegraphics[scale=0.35]{chain-2-blocks}
\caption{Initial chain that, necessarily, has the block type 'Genesis'}
\label{fig:chain-2-blocks}
\end{figure}
Continuing and add a third block, now an \textit{mntner} IRR object type (\textit{irr\_mntner}). The data is transformed into a string to be signed by the PGP, ensuring data properties to AS18782. Once this is done, the block is added to the chain as the third block. The block added can be seen in Figure \ref{fig:block-3}.
\begin{figure}[!ht]
\centering
\includegraphics[scale=0.35]{block-3}
\caption{Block 3: Adding an IRR object}
\label{fig:block-3}
\end{figure}
To complete these example that illustrate some properties of the chain, let's assume a change in the object \textit{irr\_mntner}. A new data is signed via PGP, and included in the chain, not without first identifying in the \textit{obsoletes \_block\_id}, the block that it is rendering obsolete. The new block is added as 4th block in the AS18782 IIBlockchain and your configuration is shown in Figure \ref{fig:block-4}.
\begin{figure}[!ht]
\centering
\includegraphics[scale=0.35]{block-4}
\caption{Block 4: Makes block 3 obsolete}
\label{fig:block-4}
\end{figure}
\subsection{Chain Transfer}
The chains are compressed and named as \textit{ASxVaaaammddhhmmss.zip}. A specialized IE will take care of this activity and follow up by compacting the chain, sending it to GitHub\footnote{https://github.com/juliaobraga/a2rd} and update the respective version in \textit{wordIETF}. All chains are public, but the \textit{secret keys} are not.
\section{IIBlockchain Implementation}
In this section we make considerations on important topics that deserved special attention during implementation.
\subsection{Space Analysis}
Table \ref{tab:storage} displays some data about storage values, considering the chain created for the example in this paper.
\begin{table}[!ht]
\centering
\caption{Storage Costs Parameters}
\label{tab:storage}
\begin{tabular}{|l|l|r|}
\hline
\multicolumn{1}{|c|}{\textbf{\#}} &
\multicolumn{1}{|c|}{\textbf{Discrimination}} & \multicolumn{1}{c|}{\textbf{Value}} \\ \hline
1 & Block 1 & 1,300 \\ \hline
2 & Block 2 & 1,365 \\ \hline
3 & Block 3 & 3,451 \\ \hline
4 & Block 4 & 3,571 \\ \hline
5 & Total & 9,687 \\ \hline \hline
6 & ASes in routing table (12 Fev 2018) & 59,789 \\ \hline \hline
7 & IRR objects number (ARIN) & 10 \\ \hline \hline
8 & Number of protocols in TCP/IP & 51 \\ \hline \hline
\end{tabular}
\end{table}
We used the \textit{sys.getsizeof} function to determine the amount of bytes occupied by the Python dictionary structure, chosen to represent IIBlockchain. The result is not very good and so we evaluated two alternatives versions. The preferred version was that of larger result values\footnote{https://goshippo.com/blog/measure-real-size-any-python-object/} (lines 1-4 on the table). Suppose each block of the string to be constructed occupies twice as many bytes as the largest block in our example (line 4). So our block occupies \textbf{7,124 bytes}. \textit{American Registry for Internet Numbers}\footnote{https://www.arin.net/resources/routing/templates.html} (ARIN) identifies ten objects to populate its IRR (line 7). Thus, only with IRR objects, the IIBlockchain of an AS spends $7,124 \times 10 = \textbf{71,124 bytes} \sim \textbf{70 Kbytes}$. So, the total bytes to represent the IRR objects for all ASn are: $59,789 \times 70$ Kbytes $= 4,285,675,520 \sim \textbf{4 Gbytes}$. Let us now assume that for each TCP/IP protocol\footnote{http://www.comptechdoc.org/independent/networking/protocol/protnet.html} (line 8) we will need 20 blocks with the largest known double size (knowledge information, for example): $20 \times 7,124 \quad bytes = \textbf{139 Kbytes}$, value that corresponds to $\textbf{0.003\%}$ of the space spent by IRR objects. Certainly there are other types of blocks that IEs will produce. But the largest number of them are obsolete blocks. Very difficult to measure the space to be occupied by obsolete blocks. Only an inaccurate estimate would be possible. One estimate is that 25\% of the blocks will be obsolete. So the total estimated storage space for the IIBlockchain is \textbf{5 Gbytes}. Any operation on IIBlockchain do not require additional space. Therefore the space complexity is \textbf{O(1)} $\sim$ \textbf{O(n)} \cite{costa2015python}.
\subsection{Time Complexity}
The heaviest algorithm we have in operations on IIBlockchain is to search linearly over an array or eventually over a linked list. Then, in the worst case, the complexity of time is O(n) \cite{costa2015python}.
\subsection{Security}
IIBlockchain is public. The security that matters to IIBlockchain will only be verified when a non obsolete block needs to be used. In two stages this is necessary: (a) the integrity of the block and (b) the reliability of the information contained in the block. Stage (a) consists of checking the validity of the hash that identifies the \textit{block\_id}. Stage (b) is the verification that the signature guarantees ownership of the information by the respective AS. If any of the above stages fails, an alert is sent to all implementations of A2RD. Immediately look for the block in the previous version and use it. The existence of the block in the previous version can be verified by the parameter \textit{timestamp} and the name of the version. Meanwhile, specialized IEs will analyze the chain, in order to identify the cause of the breach of trust in the block.
\section{Conclusions}
The authors consider that the objective of allowing a mechanism of relationship between IEs of the various A2RD implementations was achieved. Also, Blockchain is effective in ensuring co-operation and distribution of knowledge that can be shared among IEs in the various domains of ASes. It is a simple, easy-to-understand, and implementation-oriented design with no additional effort required in any programming language. The IIBlockchain has both public and private characteristics and has no inherent concerns or additional difficulties, for this reason. Also, it is worth remembering that IIBlockchain is oriented to the application of Blockchain by agents and not by humans, which certainly decreases complexity.
\section{Future Works}
At this point, it is not possible to determine how the presence of obsolete blocks will influence the operations on an IIBlockchain of some ASN. Implementations in programming languages like Python and others one, does not seem to be a big problem, because dictionaries are indexed and obsolete blocks can be ignored. However, it is necessary to evaluate the possibility of creating a new type of chain: the chain of obsolete blocks, that is to say, the chain consisting of blocks that become obsolete in each ASN chain.
At some point, one A2RD IE may checking the state of the chain and remove obsolete blocks, passing it to the obsolete chain considering:
\begin{itemize}
\item The chain from which the block was removed will be reconstituted to maintain the immutability and integrity. This is achieved by having the next block point to the previous block removed, and a new hash is calculated to identify the next block and successively to the blocks thereof until the end of the chain.
\item The block removed will be inserted in the \textit{obsolete chain} pointed to the last block of this chain. The block's block number ('block\_seq') should be concatenated by a hyphen and another sequence number to the number of the last block of the \textit{obsolete chain}. After this a new hash will be determined to identify this block and the block can be inserted in the \textit{obsolete chain}
\end{itemize}
Complementary, the IIBlockchain design is simple enough for applications in several other networking areas or not. New versions of the implementation will seek to establish independence from block structure and coding.
\section{Thanks}
From Juliao Braga and Jessica Ribas: Supported by CAPES – Brazilian Federal Agency for Support and Evaluation of Graduate Education within the Brazil's Ministry of Education.
\bibliographystyle{sbc}
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\section{Introduction}
The nature of dark matter, which constitutes about $30\%$ of the mass of the
Universe, remains largely unknown. Results from cosmic microwave background
explorers and large-scale galaxy surveys suggest that dark matter is cold with
little velocity dispersion \citep[{\it e.g.}~][]{spergel03,tegmark04}.
If so, then its evolution is mainly governed by its self-gravity
and expressed by Jeans-Vlassov-Poisson equations.
The collisionless nature of dark matter predicts the formation of multi-stream
regions bounded by very high density manifolds known as {\it caustics}.
In a cold dark matter Universe, caustics can form on large scales of
many megaparsecs, manifesting in the filamentary structure of galaxy
distribution \citep{shandarin89} and also at smaller scales
of a few parsecs or kiloparsecs in dark matter haloes. This is well
illustrated in some pionering numerical works \citep{melott89}.
Due to their abundance, the rich observational and
numerical data and their high density contrasts,
haloes are likely areas for the caustics.
Analytic models for the formation and evolution of dark matter haloes
are still rare and most works are based on the selfsimilar
accretion model \citep[]{gott75,gunn77,fillmore84,bertschinger85}.
In this model, first proposed to explain the rotation curve of galaxies,
haloes form by temporally self-similar collapse of dark matter shells onto
an initially over-dense perturbation.
Dark matter shells initially expand until they reach
their turnaround radii where they separate from the
background expansion and collapse. After collapse they re-bounce and collapse
again and the density profile settles asymptotically into a power-law
which is convolved with singular spikes, namely with caustics.
In the following we shall refer to such caustics as "outer caustics".
They are suggestive of the sharp stellar shells observed around
giant ellipticals which can arise in the
merger of galaxies \citep{malin80,quinn84,fort86}.
The main observational difference between the merger and selfsimilar spherical
infall is that the former predicts that the caustics are interleaved with the
caustic radii alternating on opposite sides of the galaxy and
the latter predicts concentric spherical shells.
The spherically symmetric model has been extended to consider
infalling matter with angular momentum and calculated the properties
of an additional kind of "inner caustics" with torus-like topology
\citep{sikivie98,sikivie99}. Such accretion with angular momentum is
more relevant for galaxy-size haloes than for clusters of galaxies dominated
by radial infall.
Here, we focus on the outer caustics of cluster-size haloes and
argue that they can be reasonably approximated by selfsimilar infall models.
In the original version of this model, dark matter is {\it absolutely} cold,
{\it i.e.} with zero velocity dispersion, and caustics are infinitely
thin concentric spherical shells with diverging densities.
However, realistically, dark matter has a small velocity dispersion
and these shells have finite thicknesses. The thicknesses of the caustics
would however remain very small (due to the coldness of dark matter)
and thus they would contain very little mass in spite of their
significant density. Various characteristics of the caustics such as
their density profile, their thickness and their approximate maximum density
for a low velocity dispersion dark matter medium have been recently evaluated
\citep[][hereafter MS05]{mohayaee05}.
Detection of dark matter caustics remains a challenging problem both
for 3-dimensional numerical simulations and for observations.
Dark matter annihilation in the caustics has already been studied
\citep[See {\it e.g.}~][]{sikivie97,hogan01,mohayaee05,pieri05}. Since
the flux of the annihilation products, {\it e.g.}~ $\gamma$-rays
or antiproton flux, depends on the square of the local
density\footnote{See {\it e.g.}~ \citet{donato04} for the antiproton flux
and \citet{bertone05} for a general recent review.}, caustics with their
sharply-peaked densities would be the likely places for significant
emissivity. Such kind of observations are promising for the eventual detection
of dark matter in the caustics. However, the major problem with dark matter
detection through gamma-ray emission is the severe background
contamination of the signal and the low signal-to-noise ratio of
present day observations.
It has been shown that rotation curves of galaxies might be sensitive
to the presence of inner caustics and claimed a marginal detection based
on an ensemble average over 32 rotation curves \citep{kinney00}. Inner
caustic rings are located in the plane of the disk and are likely to
modify rotation curves more efficiently than outer caustics with
spherical symmetry. Moreover, rotation curves only probe the dark
matter potential of galactic haloes where a large amount of tracers
(gas or stars) is available. Therefore, outer caustics which are
located well beyond the observable tracers cannot leave a detectable
imprint on rotation curves.
Gravitational lensing provides a promising alternative tool.
Since lensing probes the projected density profile with no regards to
the nature or dynamical state of the deflecting mass, it should be
sensitive to the caustics. The lensing properties of dark matter caustics
and particularly their efficiency in magnifying and/or producing multiple
images of background sources has already been investigated \citep{charmousis03}.\\
Inner caustics may be dense enough to produce substantial magnification
and small separation multiple images as in {\it micro-lensing} by compact objects.
High magnification events due to such caustics may explain the anomaly in flux
ratios observed in multiply-imaged quasars which are hardly reproduced by a smooth
halo or even subhalos \citep[see {\it e.g}~][]{dalal02,kochanek04}.\\
Conversely, it has been found that outer caustics are inefficient in
magnifying distant sources and would yield at most a few percent net
magnification or shear \citep{charmousis03}. As we shall detail below,
the selfsimilarity of dark matter accretion implies that outer
caustics occur at the same radius provided physical radii are properly
rescaled by the halo mass. Hence the tiny lensing signal of caustics could show up
statistically by averaging over many rescaled haloes.
Such a statistical approch is much more complicate for the lensing-based
detection of inner caustic rings because of the random orientation of rings
(or angular momenta).
In this work, we consider the lensing properties of the outer caustics
only and we propose the {\it weak-lensing} effect as a potential
way to detect caustics. We demonstrate that the caustics will produce sharp
variations in the projected surface mass density around haloes. Depending
on the height and width of caustics, gravitationally-distorted background
galaxies will experience local variations of shear.
If the aforementioned universal property of haloes is fullfilled,
then the rapid progress in X-ray and
lensing observations of cluster of galaxies may offer one possibility to
observe dark matter caustics. Deep and wide surveys such as CFHTLS
will cover fields of view of a few hundreed square degrees and will
provide us with a useful material for the detection of dark matter caustics
through the capability of mass to coherently stretch the image of the
background galaxies. They will provide us with a large enough number
of galaxy clusters\footnote{$\sim 5$ per square degree,
\citep{hennawi05}} to achieve the required level of signal-to-noise
ratio. Wide field spatial surveys will be
even more powerful for the investigation of the lensing properties of
dark matter haloes and their associated caustics. An important
requirement for the detection of caustics is the measurement of virial
radii of the clusters which can be provided by X-rays
\citep[{\it e.g.}~][]{arnaud05}.
Throughout this paper, we assume an Einstein-de Sitter Universe but our
results should be qualitatively similar in a concordance $\Lambda$CDM model.
The role of dark energy becomes important at low redshifts ($\sim
0.2$) which we expect to occur well after the formation of the typical dark
matter haloes we consider here. Furthermore, once a particle turns around
and collapses, it separates from the background expansion and its subsequent
motion should not be affected by the $\Lambda$ term.
The paper is organized as follows. We review the three-dimensional
and projected properties of self-similar haloes and caustics
in Sect. \ref{sec:caustics}. We derive the lensing signal for a single halo,
compare it to the noise level of fiducial observations and estimate
the number of haloes required to achieve a significant signal-to-noise
ratio in Sect. \ref{sec:lensing}, where we also examine the ability of
weak lensing to constrain the velocity dispersion of dark matter particles.
We summarize, discuss the prospectives for future works
and conclude in Sect. \ref{sec:conclu}.
\section{Dark matter caustics}\label{sec:caustics}
\subsection{Tri-dimensional key equations}
In an Einstein-de Sitter Universe a spherical overdensity
expands and then turns around to collapse. After collapse and at late
times, the fluid motion becomes selfsimilar: its form remains
unchanged when its length is re-scaled in terms of the radius of the
shell that is currently at the ``turn around'' and is falling onto the
galaxy for the first time. Physically, selfsimilarity arises because
gravity is scale-free and because mass shells outside the initial
overdensity are also bound and turn around at successively later
times. Self-similar solutions give power-law density profiles
whose exact scaling properties depend on the central boundary
conditions and on whether the fluid is collisionless or collisional
\citep{gott75,gunn77,fillmore84,bertschinger85}. The density profile
obeys a power-law on the scale of the halo which provides an explanation
of the flattening of the rotation curves of the galaxies.
However, on smaller scales the density profile contains many spikes
({\it i.e.} caustics) of infinite density. The position and the time
of formation of these caustics are among the many properties that have
been studied in the selfsimilar infall model \citep{bertschinger85}.
In the presence of a small velocity dispersion the maximum density and
thickness of the caustic shells and their density profiles have been
evaluated in the framework of a selfsimilar collapse model (MS05).
The global halo density profile,
asymptotically reached in this process, is well-approximated by
\begin{equation}\label{eq:rho3Dhalo}
\frac{\rho_{\rm halo}(\lambda)}{\rho_H}
\sim \frac{2.8\,\lambda^{-9/4}}{(1+\lambda^{3/4})^2}\,,
\end{equation}
where $\lambda=r/r_{ta}$ with $r_{ta}$ the present turnaround radius
of the halo and $\rho_H=3H^2/8\pi G$ the background density. The turnaround
radius can be easily computed using the virial radius. Within the virial radius,
$r_{\rm vir}=r_{200}$, the mean density, $\rho_{\rm vir}$, is, by definition,
$200$ times the background density. Thus, using the density profile
\eqref{eq:rho3Dhalo}, we obtain the following relationship between the
turnaround and the virial radii: $r_{\rm ta}\sim\, 4\,r_{\rm vir}$.
For a perfectly cold dark matter medium, the density profile close
to a caustic at $\lambda_k $ is \citep{bertschinger85}
\begin{equation}\label{eq:rho3Dsing}
\frac{\rho_0(\lambda)}{\rho_H}= \frac{G_k}{\sqrt{\lambda_k-\lambda}}\,;
\qquad\qquad \sigma=0.
\end{equation}
with
\begin{equation}
G_k=\frac{\pi^2}{4\sqrt{-2\lambda_k''\,}}\,\frac{e^{-2 \xi_k/3}}{\lambda_k^2 } \;,
\label{Gk}
\end{equation}
where the values of the various quantities $\xi_k$, $\lambda_k$, $\lambda_k''$
[and $\Lambda_k$ which will appear in the coming expression
(\ref{eq:thickness})] are given in Table \ref{table:caustic-parameters}
[see MS05 for a detailed description of these parameters].
\begin{table*}
\centering
\begin{tabular}{@{}cccccccc@{}}\hline\hline
k\,\,\,\,\,\, & $\xi_k$\,\,\,\,\,\, & $\lambda_k$\,\,\,\,\,\, &
$\left(d^2\lambda/d\xi^2\right)_k$ & $\Lambda_k$ & \qquad $\Delta r_k$ (pc)
& \qquad $\rho_{\rm max}/\rho_H/(\sqrt{r_{\rm vir}})\,\, pc^{-1/2}$ & $\rho_{\rm halo}/\rho_H$\\
\hline
1 & 0.985 & 0.368 & -5.86 & -0.0704 & $5.6\, 10^{-4}$ & 233 & 12 \\
2 & 1.46 & 0.237 & -11.2 & -0.0254 & $2.6\, 10^{-4}$ & 431 & 39 \\
3 & 1.76 & 0.179 & -16.7 & -0.0135 & $1.7\,10^{-4}$ & 640 & 82 \\
4 & 1.98 & 0.146 & -22.3 & -0.00854 & $1.2\,10^{-4}$ & 850 & 139 \\
5 & 2.16 & 0.124 & -28.0 & -0.00591 & $9.1\, 10^{-5}$ & 1067 & 210 \\
6 & 2.31 & 0.108 & -33.9 & -0.00437 & $7.3\, 10^{-5}$ & 1290 & 297 \\
7 & 2.43 & 0.096 & -39.8 & -0.00337 & $6.0\,10^{-5}$ & 1532 & 398 \\
8 & 2.55 & 0.087 & -45.7 & -0.00266 & $5.1\, 10^{-5}$ & 1749 & 513 \\
9 & 2.64 & 0.079 & -51.7 & -0.00221 & $4.4\, 10^{-5}$ & 2010 & 640 \\
10 & 2.73 & 0.073 & -57.8 & -0.00182 & $3.8\, 10^{-5}$ & 2253 & 785 \\
\hline\hline
\label{table:caustic-parameters}
\end{tabular}
\caption{\footnotesize The non-dimensional times ($\xi_k$), positions ($\lambda_k$),
thicknesses ($\Delta r_k$), maximum densities ($\rho_{\rm max}$)
of the first ten caustics, the halo density itself ($\rho_{\rm halo}$)
at the positions of these caustics and other parameters used in expressions
(\ref{Gk}), (\ref{eq:rho3Ddef}), (\ref{eq:thickness}) and (\ref{eq:maxdens}).
The present velocity dispersion is that
for neutralinos which is about $0.03$ cm/s. It is worth emphasizing
that the thicknesses of the caustics
do not depend on the halo parameters but only on the velocity
dispersion of dark matter [see expression (\ref{eq:thickness})].
It is instructive to compare the last two columns, which show that for a
cluster-size halo with $r_{\rm vir}\sim 1$ Mpc, the caustic density can be many orders of
magnitude higher than the halo density itself.}
\end{table*}
When the temperature of particles is not strictly zero and the velocity of
particles is distributed according to the distribution function $f(v)$,
caustic positions are shifted by a small value $\delta\lambda$ and
the caustic density is modified as (MS05):
\begin{equation}
\rho_\sigma(\lambda)= \int {\rm d} v\, \rho_0\,[\lambda - \delta\lambda(v)]\,
f(v)\,\,;
\qquad \sigma\not=0 \qquad
\end{equation}
In this work, we choose a top-hat velocity distribution function (MS05).
Then, the density close to the $k$-th caustic in the halo is given by
\begin{equation}\label{eq:rho3Ddef}
\frac{\rho_\sigma(\lambda)}{\rho_H} = \frac{G_k}{\Delta_k} \left\{
\begin{array}{ll}
\sqrt{\lambda_k^+-\lambda} - \sqrt{\lambda_k^--\lambda} &
\text{~~for~}\lambda< \lambda_k^-\;,\\
\sqrt{\lambda_k^+-\lambda} & \text{~~for~}\lambda_k^-<\lambda<\lambda_k^+\;, \\
0 &\text{~~for~}\lambda> \lambda_k^+\;,
\end{array}\right.
\end{equation}
where $\lambda_k^-=\lambda_k-\Delta_k$ and $\lambda_k^+=\lambda_k+\Delta_k$
and the thickness of the $k$-th caustic, $\Delta_k$,
in nondimensional coordinate is given by
\begin{equation}
r_{\rm ita}\, \Delta_k=\Delta r_k={(3\pi)^{2/3}\over 4}
e^{5\xi_k/9}\,\vert\Lambda_k\vert\,\,
t\,\sigma(t)
\label{eq:thickness}
\end{equation}
and $r_{\rm ita}$ is the initial turnaround radius and $\sigma(t)$
is the value of the velocity dispersion of dark matter particles at time $t$
which is that at decoupling re-scaled by the expansion
factor\footnote{Hereafter, velocity dispersion is given at the present time,
$z=0$. For instance, neutralinos have $\sigma\sim 0.03$ cm/s and
axions have $\sigma\sim 10^{-7}$ cm/s.}.
The standard spherical collapse model yields a relation
$r_{\rm ita}=2 r_{\rm vir}$ for a constant overdensity
[see {\it e.g.}~ chapter 5.10 of \citep{padmanabhan02b3}], However, the
real value of the initial turnaround radius would be lower due to the
continuous accretion by the halo.
Thus the physical thickness of
the caustic, $\Delta r_k$, depends only on its position in the halo
and the nature of dark matter.
The maximum density at each caustic position can also be approximated
by the expression (see Table \ref{table:caustic-parameters} and also MS05)
\begin{equation}\label{eq:maxdens}
\rho_{\rm max}={2\,G_k e^{-5\xi_k/18}\over (3\pi)^{1/3}\sqrt{-\Lambda_k\,}}\,\,
\sqrt{r_{\rm ta}\over t\,\,\sigma(t)}\,\, \rho_H
\end{equation}
Expressions \eqref{eq:rho3Ddef}, \eqref{eq:thickness} and
\eqref{eq:maxdens} provide us with a sufficient basis for the evaluation
of magnification and shear due to dark matter caustics. Although in
the rest of this work we directly integrate expression \eqref{eq:rho3Ddef}
and never use \eqref{eq:maxdens}, values for the latter are given
in Table \ref{table:caustic-parameters} to demonstrate the density contrast
of each caustic with respect to its host halo.
Although the selfsimilar model might seem naive, it provides a good
approximation for outer caustics in galaxy-cluster haloes which are
not significantly disrupted by merger and substructures and to a good
approximation are spherical. Furthermore, fluctuations caused by
large scale structure would already be averaged out in the statistical
evaluation of the shear.
\subsection{Projected densities}\label{subsec:projec-dens}
Since we are concerned with the lensing properties of caustics, we have to
calculate the projected density profile for the caustics and for the halo.
The Abel integral relates the 3-dimensional density ($\rho$)
and the 2-dimensional density profiles ($\Sigma$) by
\begin{equation}
\Sigma(\lambda)= 2 r_{ta} \int_{\lambda}^\infty \frac{\rho(\lambda')
\lambda' {\rm d} \lambda'}{\sqrt{\lambda'^2-\lambda^2}}\;.
\end{equation}
We numerically integrate the above expression, for the density profiles
\eqref{eq:rho3Dsing} and \eqref{eq:rho3Ddef}. The halo surface mass
density can be evaluated analytically
if we neglect the $(1+\lambda^{3/4})^2$ term in
equation \eqref{eq:rho3Dhalo}, {\it i.e.} at small scales $\lambda\ll 1$,
yielding the approximate projected halo profile
\begin{equation}
\Sigma_{\rm halo}(\lambda) \simeq r_{ta} 7.56 \lambda^{-5/4}\rho_H\,.
\end{equation}
Let us define the mean projected density enclosed by the cylinder of
radius $\lambda$:
\begin{equation}
\overline{\Sigma}(\lambda)= \frac{2}{\lambda^2}
\int_{0}^\lambda \Sigma(\lambda') \lambda'{\rm d} \lambda'\;.
\end{equation}
Thus, under the hypothesis of small $\lambda$, the mean projected
density for the halo component is
$\overline{\Sigma}_{\rm halo}(\lambda)= \frac{8}{3} \Sigma(\lambda)$.
\begin{figure*}[htbp]
\centering
\resizebox{8.5cm}{!}{\includegraphics{rho_new.eps}}
\resizebox{8.5cm}{!}{\includegraphics{sig_new.eps}}
\caption{\footnotesize {\it Left panel: }
In units of the background density, $\rho_H$, we show the 3D
density profile for the halo (black), for the caustics in a
perfectly cold medium (red) and for the caustics smoothed out by a
warm/hot dark matter with velocity dispersion $\sigma=60\, {\rm km\, s}^{-1}$
(green). Red spikes are all singular with infinite density and
limited here to finite values because of finite resolution. \ \ \
{\it Right panel: } The same colour-coding for the projected 2D
density profiles in units of $\rho_H r_{ta}$. When projected,
caustic peaks are smoother and look like a flight of stairs.
Therefore, we expect low lensing magnifications close to
the caustics (see Section \ref{sec:lensing}).
}
\label{fig:dens3-2}
\end{figure*}
Figure \ref{fig:dens3-2} shows the 3D (left) and 2D (right) density
profiles for the halo and the caustics. We consider the case of a
perfectly cold dark matter with very peaked caustics and the case in
which they are smoothed out by a finite velocity dispersion
$\sigma \sim 60 \, {\rm km\, s}^{-1}$. This value is very high for most cold dark
matter models but its extremity illustrates well the peak dilution
and shows that caustics survive a large thermal softening. When
considering the projected density, instead of spikes we rather see
stairs that come from the analytic $1/\sqrt{r_k-r}$ singularity of
caustics. Consequently even with singular caustics, the projected
density profile is not peaked. The implications for lensing are
discussed in the next section.
\section{Weak lensing}\label{sec:lensing}
\subsection{General equations}
The fundamental quantity for gravitational lensing is the lens potential
$\psi(\vec{\theta})$ at the angular position $\vec{\theta}$ which is related
to the surface mass density $\Sigma(\vec{\theta})$ projected into the lens
plane through :
\begin{equation}
\psi(\vec{\theta}) = \frac{4 G}{c^2} \frac{D_{\rm l} D_{\rm s}}{D_{\rm ls}}
\int {\rm d}^2 \theta' \Sigma(\vec{\theta}') \ln\vert \vec{\theta}-\vec{\theta}'\vert\;,
\end{equation}
where $D_{\rm l}$, $D_{\rm s}$ and $D_{\rm ls}$ are angular distances to the lens,
to the source and between the lens and the source respectively. The deflection
angle $\vec{\alpha}=\vec{\nabla}\psi$ relates a point in the source plane
$\vec{\beta}$ to its image(s) in the image plane $\vec{\theta}$ through the
lens equation $\vec{\beta}=\vec{\theta}-\vec{\alpha}(\vec{\theta})$.
The local relation between $\vec{\beta}$ and $\vec{\theta}$ is the
Jacobian matrix $A_{ij}=\partial \beta_i/\partial \theta_j$ :
\begin{equation}\label{eq:jacob}
A_{ij} = \delta_{ij} - \psi_{,ij} = \left(\begin{array}{cc}
1-\kappa-\gamma_1 & -\gamma_2 \\
-\gamma_2 & 1-\kappa+\gamma_1
\end{array}\right)\;.
\end{equation}
with the convergence $\kappa(\vec{\theta})=\Sigma(\vec{\theta})/\Sigma_{\rm crit}$
directly related to the surface mass density via the critical density
\begin{equation}\label{eq:scrit}
\Sigma_{\rm crit} = \frac{c^2}{4 \pi G}\frac{D_{\rm ls}}{D_{\rm l}D_{\rm s}}\;,
\end{equation}
and the 2-component shear $\gamma=\gamma_1+i \gamma_2$ in complex notation.
The convergence satisfies the Poisson equation $\Delta \psi = 2 \kappa$.
In the weak lensing regime ($\gamma \ll 1$), an elliptical object in the
source plane with complex ellipticity $e_s$ is mapped into an elliptical
image with a different ellipticity $e = e_s + \gamma$.
We refer the reader to the reviews of \citet{mellier99} and \citet{BS01}
for detailed accounts of weak lensing.
For a circularly symmetric lens, $\gamma$ is oriented tangentially
to the lens center and its amplitude at radius $r$ is
$\gamma(r)=(\overline{\Sigma}(r)-\Sigma(r))/\Sigma_{\rm crit}$.
Since sources are randomly oriented, the tangential component of the observed
galaxies is an unbiased estimator of $\gamma$. When averaging the estimate
of $\gamma$ within an aperture of solid angle $\Omega$, containing
$N=\Omega n$ galaxies ($n$ is the number density of sources), the noise
dispersion of $\gamma$ is $\sigma_\gamma=\frac{\sigma_e}{\sqrt{N}}$ where
$\sigma_e\sim0.3$ is the intrinsic dispersion of source ellipticities
(along one component).
\subsection{Shear measurement}
In order to be consistent with our calculations of Sec.
\ref{subsec:projec-dens}, we define a pseudo-shear:
$\Gamma(\lambda)=(\overline{\Sigma}-\Sigma)/\rho_H r_{ta}$
and the corresponding noise level $\Gamma_N=\Sigma_{\rm crit}\sigma_\gamma / \rho_H r_{ta}$.
For an EdS cosmology, and considering an annulus of inner and outer radii
$\lambda_1$ and $\lambda_2$ respectively, it is straightforward to write
$\Gamma_N$ in this useful form:
\begin{multline}
\Gamma_N(\lambda_1,\lambda_2)= \, 2.16\, \frac{D_{os}}{D_{ls}}
\left(\frac{5\, {\rm Mpc}}{r_{ta}} \right)^2 (1+z_l)^3 \times \\
\sqrt{\frac{30\, \mathrm{arcmin}^{-2}}{n}}
\left(\frac{\sigma_e}{0.3}\right) \frac{1}{\sqrt{\lambda_2^2-\lambda_1^2}}\;.
\end{multline}
This expression seems to indicate that the noise level will be lower for nearby
haloes. However, it hides the fact that low redshift haloes require a very
wide sky coverage for the outermost caustics ($\sim r_{\rm ta}/3$) to fit the
field of view of the observation. Consequently, intermediate redshift haloes
($z\sim0.2-0.5$) are the most interesting targets. In addition, nearby
(and thus large angular scale) clusters suffer from noise due to
large-scale structure (LSS) fluctuation integrated along the line-of-sight
and unrelated to the halo we are considering \citep{hoekstra03}.
For scales $\lesssim 15$ arcmin, the smearing of the shear
profile by LSS is minimised.
Figure \ref{fig:Gamma} shows $\Gamma$ as a function of $\lambda$ for the same
values of the thermal velocity dispersions $\sigma=0\, {\rm km\, s}^{-1}$ and $\sigma=60\, {\rm km\, s}^{-1}$.
Comparing these curves, one can see that the sawtooth patterns due to
caustics survive significantly high temperatures.
Next, we consider the noise level for a fiducial halo at redshift $z_l=0.3$
and a turnaround radius $r_{ta}=5\, {\rm Mpc}$ which is a typical value for clusters
(upper green ``binned'' curve). With a single halo the detection of caustics
is impossible. If we are able to stack the signal from a few tens of
clusters (upper blue-binned curve), the noise level will be low enough to
be sensitive to caustics as a whole. However, we would detect a smooth
contribution which is indistinguishable from the halo itself.
Sawtooth patterns cannot be confused with the effect of substructures
since the contribution of the latter would be averaged out over the
azimuthal angle (most outer caustics have spherical symmetry) and once
rescaled, caustics always appear at the same place within haloes.
This is not the case for substructures which can appear at any radius
inside the host halo.
\begin{figure}[htbp]
\centering
\resizebox{\hsize}{!}{\includegraphics{Gamma_new.eps}}
\caption{\footnotesize $\Gamma(\lambda)$ contribution of caustics for two
values of $\sigma$: cold medium $\sigma=0$ (black curve) and warm medium
$\sigma\sim 60$km/s (red curve). The green (resp. blue) ``binned''
curve is the noise level for one (resp. 100 stacked) halo(es).
}
\label{fig:Gamma}
\end{figure}
Consequently, the right way to probe the existence of caustics is to
measure the $\Gamma$ signal in excess/default relative to the extreme value
of $\sigma$, {\it e.g.}~ $\sigma\gtrsim 300 \, {\rm km\, s}^{-1}$ as taken here.
For this purpose, one needs $\gtrsim 100$ stacked clusters.
With the corresponding noise level, it would be possible to test the
thermal smoothing of caustics and put constraints on $\sigma$.
However, the sensitivity is poor and only upper limits
can be put on $\sigma$ with a realistic number of haloes.
For instance with $N=100$ (resp. 250) clusters, we could achieve
a limit $\sigma < 170\, {\rm km\, s}^{-1}$ (resp. $40\, {\rm km\, s}^{-1}$) at a $95.4\%$ confidence level.
When considering galaxies instead of clusters with turnaround radii
about $10$ times smaller, the number of haloes required to achieve the same
detection level is $10^4$ times higher. So using a few $10^5$ galaxies
between $z\sim 0.1-0.5$ would yield the same results.
This required level of signal can easily be achieved
with a wide and moderately deep survey like
the ongoing CFHTLS. Typically, a square-degree field of view will contain
a few such cluster-size haloes with $r_{\rm ta}\sim 5\, {\rm Mpc}$, a few thousand
elliptical galaxies with $r_{\rm ta}\sim 1\, {\rm Mpc}$ and tens of thousands of
spiral galaxies with $r_{\rm ta}\sim 500\, {\rm kpc}$. The total coverage of the
CFHTLS wide survey is 170 square degree and will contain a large enough
number of clusters/galaxies. Furthermore the wide fields of view are
well-suited to measure shear up to the outermost caustic of clusters
($1\, {\rm Mpc}=5\arcmin$ at $z=0.3$ and $4\arcmin$ at $z=0.5$).
Spatial observations provide an improvement on shear measurements: (i)
the intrinsic dispersion in source ellipticities is lowered
$\sigma_e\sim0.2$ and (ii) the density of sources is increased
$n\sim50$ arcmin$^{-2}$. Hence the total number of haloes required to
achieve the same detection level can be lowered by a factor of
three. Future wide spatial surveys like SNAP or DUNE will provide
the required sky coverage.
\subsection{Halo-stacking issues}
So far, we have considered the observational difficulties encountered by
the dispersion in intrinsinc source ellipticities. However,
practical complications such as the difficult signal stacking process should
also be overcome before a detection of the caustics can be achieved.
To do so, high-precision measurements of the location of the center
and the turnaround radius of
each halo are required. Otherwise, imperfect alignment/rescaling would
tend to blur the caustics spikes and reduce the sensitivity.
The center of a well-relaxed cluster coincides within one arc-second with the
center of the halo. Hence the only scaling factor is the turnaround radius
that can be related to the virial radius [see the sentence
following expression (\ref{eq:rho3Dhalo})].
\begin{figure}[htbp]
\centering
\resizebox{\hsize}{!}{\includegraphics{blur_new.eps}}
\caption{\footnotesize Difference between the $\Gamma(\lambda)$ contribution
of cold caustics and the smooth component. We illustrate the blurring
effect of an imperfect knowledge of the turnaround radius of stacked
haloes. The solid black line, dashed green line and dot-dashed
blue line correspond to zero, 3\% and 10\% uncertainties, respectively.
As in \reffig{fig:Gamma}, the binned curve represents
the noise level achieved with 200 stacked haloes. The convolution effect
of error in the assumed/measured value of $r_{\rm ta}$ is important and a
significant detection of caustics requires well-determined turnaround
radii ($\lesssim$ a few percent relative accuracy). The very small scale
oscillations in the plot are numerical artifacts and ideally the only
sawtooth patterns are those due to caustics.
}
\label{fig:blur}
\end{figure}
Figure \ref{fig:blur} shows the blurring of caustics due to an imperfect
knowledge of the turnaround radius of each stacked halo. We consider a
dispersion around the true value of 3\% and 10\%. To properly detect
caustics, one needs a precise estimate of $r_{\rm ta}$.
Provided dark matter is cold enough, $\sigma\lesssim$ a few $\, {\rm km\, s}^{-1}$,
which is a realistic prescription, a reasonable number of stacked
haloes, $\sim 200$, can overcome the loss of a few percents of relative
precision caused by the errors in the determination of the turnaround radius.
Consequently the number of haloes necessary for detection needs to be
increased in order to achieve the necessary level of signal-to-noise
ratio. Moreover, additional external information for the
determination of $r_{\rm ta}$ such as X-rays or dynamical observations
in addition to weak lensing data are indispensable for a convincing
detection of caustics. The present-day state-of-the-art X-ray estimates
for the scale radius is $\lesssim 10\%$ for nearby clusters ($z<0.2$)
\citep{arnaud05,pointecouteau05} and it seems that a similar precision
can be reached at higher redshifts ($0.4<z<0.7$) \citep{kotov05}.
In addition shear, which is used for caustic detection, also provides
constraints on the halo density profile. The virial radius of
some clusters presenting strong and weak lensing features can be measured
with good accuracy ($\Delta r_{200}/r_{200} \lesssim 3$\%)
\citep{broadhurst05b,gavazzi05}. Consequently, future large
cluster samples with X-rays and lensing data of present-day quality
will provide us with the necessary precision to probe dark matter caustics.
\section{Discussion \& conclusion}\label{sec:conclu}
Although the Liouville theorem claims that singularities will survive,
they are likely to develop a complex topology in the course of evolution of
structures under self-gravity. It is not clear to what degree the merging
processes and substructures will smear out the caustics or complicate their
geometries. Here, we have considered the outer caustics of cluster-size
haloes which are expected to have suffered far less from mergers and due to
their relatively large separations are unlikely to have been washed away
by the dispersive-like effect of the substructures. These
caustics are the ones that contribute most to the lensing signal for
the following reasons. Their amplitude relative to the background smooth
halo component is more important as compared to the inner caustics.
The inner caustics smear most from thermalisation and imperfect stacking
and finally, the noise level increases toward the center of haloes thus
giving more weight to the outer caustics.
Hence, we have focused on caustics of cluster-size haloes and have argued
that they can be reasonably approximated by a selfsimilar spherical
accretion model, though the triaxiality of haloes is well established in
numerical simulations \citep{jing02tri}. However, caustic patterns should
exist in triaxial matter distributions. The singularities will have the
same elliptical symmetry and may be properly stacked from one halo to another
by choosing a subsample of apparently circular projected haloes or by
using the shear azimuthal variations to constrain the halo ellipticity.
We expect this effect to be comparable to the uncertainty in the halo scaling
radius (either turnaround or virial).
We have shown that the existence of dark matter caustics could be probed
by properly stacking the weak lensing signal of a reasonable
number of haloes. The main observational limitation is perhaps the
precise estimation of the turnaround radius, $r_{\rm ta}$, of superimposed
haloes but we have shown that the loss of a few percent relative accuracy
in the determination of $r_{\rm ta}$ (or asphericity) can be compensated for
by stacking about $200$ haloes.
Although the sensitivity is low, a detection of caustics provides an upper
bound for the temperature of dark matter, thus excluding hot dark matter
models. The sensitivity is not sufficient to distinguish between various
cold dark matter candidates (like axions or neutralinos) since for
most of the corresponding velocity dispersions, the shear
signal would be similar.\\
However, a detection of caustics would be a strong argument for the existence
of cold dark matter since alternative models like {\small MOND} could not
explain such density singularities and at most could serve
in place of a smooth halo (namely provide an equivalent effective
gravitational potential).\\
Putting constraints on the velocity dispersion of dark matter is a
challenging topic in modern cosmology since it offers
the possibility to pin-down an actual physical parameter of dark matter.
In this paper, we investigated the possibility of such a
measurement with the weak lensing effect of dark matter caustics.
The implicit observational hypothesis is that we can have
a selfsimilar geometrical description of the caustic shell distribution
which depends on a single characteristic scaling
parameter: {\it i.e.}~ the virial radius.
Wide field surveys such as the ongoing CFHTLS accompanied by X-ray observations
can provide the required statistics for a successful detection of caustics.
The number of haloes required to be superimposed will be lowered by a
further factor of 3 for future space-based experiments like SNAP or DUNE.
Here, we have used the first and most common caustic singularity,
that for which the density profile falls with inverse square-root
of the distance from the caustic. Caustics of higher-order singularities
can also appear in collisionless media and have already been
classified \citep{arnold86}. It remains a challenging task to
generalize our work to haloes with non-vanishing eccentricity
where higher-rank caustics would occur and to examine if they
can modify the magnification properties of the lensed images and account
for anomalous image flux ratios.
\begin{acknowledgements}
Special thanks go to Sergei Shandarin for an ongoing collaboration
on dark matter caustics. We also thank Francis Bernardeau, Ed Bertschinger,
Monique Arnaud, Gary Mamon and Etienne Pointecouteau for many helpful
discussions and comments. R.G. is supported at Toulouse from
a CNRS postdoc contract \#1019 and at Oxford by a grant from
the Leverhulme Trust. R.M. is supported by European Gravitational
Observatory grant at the school of astronomy, university of Cardiff, UK.
\end{acknowledgements}
\begin{scriptsize}
\bibliographystyle{aa}
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 5,190
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{"url":"https:\/\/sofdem.github.io\/gccat\/gccat\/Ck_same_partition.html","text":"## 5.210. k_same_partition\n\nOrigin\nConstraint\n\n$\ud835\ude94_\\mathrm{\ud835\ude9c\ud835\ude8a\ud835\ude96\ud835\ude8e}_\\mathrm{\ud835\ude99\ud835\ude8a\ud835\ude9b\ud835\ude9d\ud835\ude92\ud835\ude9d\ud835\ude92\ud835\ude98\ud835\ude97}\\left(\\mathrm{\ud835\ude82\ud835\ude74\ud835\ude83\ud835\ude82},\\mathrm{\ud835\ude7f\ud835\ude70\ud835\ude81\ud835\ude83\ud835\ude78\ud835\ude83\ud835\ude78\ud835\ude7e\ud835\ude7d\ud835\ude82}\\right)$\n\nTypes\n $\\mathrm{\ud835\ude85\ud835\ude70\ud835\ude81\ud835\ude78\ud835\ude70\ud835\ude71\ud835\ude7b\ud835\ude74\ud835\ude82}$ $\\mathrm{\ud835\ude8c\ud835\ude98\ud835\ude95\ud835\ude95\ud835\ude8e\ud835\ude8c\ud835\ude9d\ud835\ude92\ud835\ude98\ud835\ude97}\\left(\\mathrm{\ud835\ude9f\ud835\ude8a\ud835\ude9b}-\\mathrm{\ud835\ude8d\ud835\ude9f\ud835\ude8a\ud835\ude9b}\\right)$ $\\mathrm{\ud835\ude85\ud835\ude70\ud835\ude7b\ud835\ude84\ud835\ude74\ud835\ude82}$ $\\mathrm{\ud835\ude8c\ud835\ude98\ud835\ude95\ud835\ude95\ud835\ude8e\ud835\ude8c\ud835\ude9d\ud835\ude92\ud835\ude98\ud835\ude97}\\left(\\mathrm{\ud835\ude9f\ud835\ude8a\ud835\ude95}-\\mathrm{\ud835\ude92\ud835\ude97\ud835\ude9d}\\right)$\nArguments\n $\\mathrm{\ud835\ude82\ud835\ude74\ud835\ude83\ud835\ude82}$ $\\mathrm{\ud835\ude8c\ud835\ude98\ud835\ude95\ud835\ude95\ud835\ude8e\ud835\ude8c\ud835\ude9d\ud835\ude92\ud835\ude98\ud835\ude97}\\left(\\mathrm{\ud835\ude9c\ud835\ude8e\ud835\ude9d}-\\mathrm{\ud835\ude85\ud835\ude70\ud835\ude81\ud835\ude78\ud835\ude70\ud835\ude71\ud835\ude7b\ud835\ude74\ud835\ude82}\\right)$ $\\mathrm{\ud835\ude7f\ud835\ude70\ud835\ude81\ud835\ude83\ud835\ude78\ud835\ude83\ud835\ude78\ud835\ude7e\ud835\ude7d\ud835\ude82}$ $\\mathrm{\ud835\ude8c\ud835\ude98\ud835\ude95\ud835\ude95\ud835\ude8e\ud835\ude8c\ud835\ude9d\ud835\ude92\ud835\ude98\ud835\ude97}\\left(\ud835\ude99-\\mathrm{\ud835\ude85\ud835\ude70\ud835\ude7b\ud835\ude84\ud835\ude74\ud835\ude82}\\right)$\nRestrictions\n $\\mathrm{\ud835\ude9b\ud835\ude8e\ud835\ude9a\ud835\ude9e\ud835\ude92\ud835\ude9b\ud835\ude8e\ud835\ude8d}$$\\left(\\mathrm{\ud835\ude85\ud835\ude70\ud835\ude81\ud835\ude78\ud835\ude70\ud835\ude71\ud835\ude7b\ud835\ude74\ud835\ude82},\\mathrm{\ud835\ude9f\ud835\ude8a\ud835\ude9b}\\right)$ $|\\mathrm{\ud835\ude85\ud835\ude70\ud835\ude81\ud835\ude78\ud835\ude70\ud835\ude71\ud835\ude7b\ud835\ude74\ud835\ude82}|\\ge 1$ $|\\mathrm{\ud835\ude85\ud835\ude70\ud835\ude7b\ud835\ude84\ud835\ude74\ud835\ude82}|\\ge 1$ $\\mathrm{\ud835\ude9b\ud835\ude8e\ud835\ude9a\ud835\ude9e\ud835\ude92\ud835\ude9b\ud835\ude8e\ud835\ude8d}$$\\left(\\mathrm{\ud835\ude85\ud835\ude70\ud835\ude7b\ud835\ude84\ud835\ude74\ud835\ude82},\\mathrm{\ud835\ude9f\ud835\ude8a\ud835\ude95}\\right)$ $\\mathrm{\ud835\ude8d\ud835\ude92\ud835\ude9c\ud835\ude9d\ud835\ude92\ud835\ude97\ud835\ude8c\ud835\ude9d}$$\\left(\\mathrm{\ud835\ude85\ud835\ude70\ud835\ude7b\ud835\ude84\ud835\ude74\ud835\ude82},\\mathrm{\ud835\ude9f\ud835\ude8a\ud835\ude95}\\right)$ $\\mathrm{\ud835\ude9b\ud835\ude8e\ud835\ude9a\ud835\ude9e\ud835\ude92\ud835\ude9b\ud835\ude8e\ud835\ude8d}$$\\left(\\mathrm{\ud835\ude82\ud835\ude74\ud835\ude83\ud835\ude82},\\mathrm{\ud835\ude9c\ud835\ude8e\ud835\ude9d}\\right)$ $|\\mathrm{\ud835\ude82\ud835\ude74\ud835\ude83\ud835\ude82}|>1$ $\\mathrm{\ud835\ude9c\ud835\ude8a\ud835\ude96\ud835\ude8e}_\\mathrm{\ud835\ude9c\ud835\ude92\ud835\udea3\ud835\ude8e}$$\\left(\\mathrm{\ud835\ude82\ud835\ude74\ud835\ude83\ud835\ude82},\\mathrm{\ud835\ude9c\ud835\ude8e\ud835\ude9d}\\right)$ $\\mathrm{\ud835\ude9b\ud835\ude8e\ud835\ude9a\ud835\ude9e\ud835\ude92\ud835\ude9b\ud835\ude8e\ud835\ude8d}$$\\left(\\mathrm{\ud835\ude7f\ud835\ude70\ud835\ude81\ud835\ude83\ud835\ude78\ud835\ude83\ud835\ude78\ud835\ude7e\ud835\ude7d\ud835\ude82},\ud835\ude99\\right)$ $|\\mathrm{\ud835\ude7f\ud835\ude70\ud835\ude81\ud835\ude83\ud835\ude78\ud835\ude83\ud835\ude78\ud835\ude7e\ud835\ude7d\ud835\ude82}|\\ge 2$\nPurpose\n\nGiven a collection of $|\\mathrm{\ud835\ude82\ud835\ude74\ud835\ude83\ud835\ude82}|$ sets, each containing the same number of domain variables, the $\ud835\ude94_\\mathrm{\ud835\ude9c\ud835\ude8a\ud835\ude96\ud835\ude8e}_\\mathrm{\ud835\ude99\ud835\ude8a\ud835\ude9b\ud835\ude9d\ud835\ude92\ud835\ude9d\ud835\ude92\ud835\ude98\ud835\ude97}$ constraint forces a $\\mathrm{\ud835\ude9c\ud835\ude8a\ud835\ude96\ud835\ude8e}_\\mathrm{\ud835\ude99\ud835\ude8a\ud835\ude9b\ud835\ude9d\ud835\ude92\ud835\ude9d\ud835\ude92\ud835\ude98\ud835\ude97}$ constraint between each pair of consecutive sets.\n\nExample\n$\\left(\\begin{array}{c}\u2329\\begin{array}{c}\\mathrm{\ud835\ude9c\ud835\ude8e\ud835\ude9d}-\u23291,2,6,3,1,2\u232a,\\hfill \\\\ \\mathrm{\ud835\ude9c\ud835\ude8e\ud835\ude9d}-\u23296,6,2,3,1,3\u232a,\\hfill \\\\ \\mathrm{\ud835\ude9c\ud835\ude8e\ud835\ude9d}-\u23292,2,2,1,1,1\u232a\\hfill \\end{array}\u232a,\\hfill \\\\ \u2329\ud835\ude99-\u23291,3\u232a,\ud835\ude99-\u23294\u232a,\ud835\ude99-\u23292,6\u232a\u232a\\hfill \\end{array}\\right)$\n\nThe first argument $\\mathrm{\ud835\ude82\ud835\ude74\ud835\ude83\ud835\ude82}$ of the $\ud835\ude94_\\mathrm{\ud835\ude9c\ud835\ude8a\ud835\ude96\ud835\ude8e}_\\mathrm{\ud835\ude99\ud835\ude8a\ud835\ude9b\ud835\ude9d\ud835\ude92\ud835\ude9d\ud835\ude92\ud835\ude98\ud835\ude97}$ constraint corresponds to 3 collections of variables, while the second argument $\\mathrm{\ud835\ude7f\ud835\ude70\ud835\ude81\ud835\ude83\ud835\ude78\ud835\ude83\ud835\ude78\ud835\ude7e\ud835\ude7d\ud835\ude82}$ defines the 3 sets of values $\\left\\{1,3\\right\\}$, $\\left\\{4\\right\\}$ and $\\left\\{2,6\\right\\}$. The $\ud835\ude94_\\mathrm{\ud835\ude9c\ud835\ude8a\ud835\ude96\ud835\ude8e}_\\mathrm{\ud835\ude99\ud835\ude8a\ud835\ude9b\ud835\ude9d\ud835\ude92\ud835\ude9d\ud835\ude92\ud835\ude98\ud835\ude97}$ constraint holds since:\n\n\u2022 The first and second collections of variables are assigned 3 values in the $\\left\\{1,3\\right\\}$ as well as 3 values in $\\left\\{2,6\\right\\}$.\n\n\u2022 The second and third collections of variables are also assigned 3 values in the $\\left\\{1,3\\right\\}$ as well as 3 values in $\\left\\{2,6\\right\\}$.\n\nTypical\n$|\\mathrm{\ud835\ude85\ud835\ude70\ud835\ude81\ud835\ude78\ud835\ude70\ud835\ude71\ud835\ude7b\ud835\ude74\ud835\ude82}|>1$\nSymmetries\n\u2022 Items of $\\mathrm{\ud835\ude82\ud835\ude74\ud835\ude83\ud835\ude82}$ are permutable.\n\n\u2022 Items of $\\mathrm{\ud835\ude82\ud835\ude74\ud835\ude83\ud835\ude82}.\\mathrm{\ud835\ude9c\ud835\ude8e\ud835\ude9d}$ are permutable.\n\n\u2022 Items of $\\mathrm{\ud835\ude7f\ud835\ude70\ud835\ude81\ud835\ude83\ud835\ude78\ud835\ude83\ud835\ude78\ud835\ude7e\ud835\ude7d\ud835\ude82}$ are permutable.\n\n\u2022 Items of $\\mathrm{\ud835\ude7f\ud835\ude70\ud835\ude81\ud835\ude83\ud835\ude78\ud835\ude83\ud835\ude78\ud835\ude7e\ud835\ude7d\ud835\ude82}.\ud835\ude99$ are permutable.\n\n\u2022 An occurrence of a value of $\\mathrm{\ud835\ude82\ud835\ude74\ud835\ude83\ud835\ude82}.\\mathrm{\ud835\ude9c\ud835\ude8e\ud835\ude9d}.\\mathrm{\ud835\ude9f\ud835\ude8a\ud835\ude9b}$ can be replaced by any other value that also belongs to the same partition of $\\mathrm{\ud835\ude7f\ud835\ude70\ud835\ude81\ud835\ude83\ud835\ude78\ud835\ude83\ud835\ude78\ud835\ude7e\ud835\ude7d\ud835\ude82}$.\n\nArg. properties\n\nContractible wrt. $\\mathrm{\ud835\ude82\ud835\ude74\ud835\ude83\ud835\ude82}$.\n\nKeywords\nArc input(s)\n\n$\\mathrm{\ud835\ude82\ud835\ude74\ud835\ude83\ud835\ude82}$\n\nArc generator\n$\\mathrm{\ud835\udc43\ud835\udc34\ud835\udc47\ud835\udc3b}$$\u21a6\\mathrm{\ud835\ude8c\ud835\ude98\ud835\ude95\ud835\ude95\ud835\ude8e\ud835\ude8c\ud835\ude9d\ud835\ude92\ud835\ude98\ud835\ude97}\\left(\\mathrm{\ud835\ude9c\ud835\ude8e\ud835\ude9d}\\mathtt{1},\\mathrm{\ud835\ude9c\ud835\ude8e\ud835\ude9d}\\mathtt{2}\\right)$\n\nArc arity\nArc constraint(s)\n$\\mathrm{\ud835\ude9c\ud835\ude8a\ud835\ude96\ud835\ude8e}_\\mathrm{\ud835\ude99\ud835\ude8a\ud835\ude9b\ud835\ude9d\ud835\ude92\ud835\ude9d\ud835\ude92\ud835\ude98\ud835\ude97}$$\\left(\\mathrm{\ud835\ude9c\ud835\ude8e\ud835\ude9d}\\mathtt{1}.\\mathrm{\ud835\ude9c\ud835\ude8e\ud835\ude9d},\\mathrm{\ud835\ude9c\ud835\ude8e\ud835\ude9d}\\mathtt{2}.\\mathrm{\ud835\ude9c\ud835\ude8e\ud835\ude9d},\\mathrm{\ud835\ude7f\ud835\ude70\ud835\ude81\ud835\ude83\ud835\ude78\ud835\ude83\ud835\ude78\ud835\ude7e\ud835\ude7d\ud835\ude82}\\right)$\nGraph property(ies)\n$\\mathrm{\ud835\udc0d\ud835\udc00\ud835\udc11\ud835\udc02}$$=|\\mathrm{\ud835\ude82\ud835\ude74\ud835\ude83\ud835\ude82}|-1$\n\nGraph model\n\nParts\u00a0(A) and\u00a0(B) of Figure\u00a05.210.1 respectively show the initial and final graph associated with the Example slot. To each vertex corresponds a collection of variables, while to each arc corresponds a $\\mathrm{\ud835\ude9c\ud835\ude8a\ud835\ude96\ud835\ude8e}_\\mathrm{\ud835\ude99\ud835\ude8a\ud835\ude9b\ud835\ude9d\ud835\ude92\ud835\ude9d\ud835\ude92\ud835\ude98\ud835\ude97}$ constraint.","date":"2023-01-28 22:59:53","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 63, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"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\": 0.459662526845932, \"perplexity\": 873.5500039013463}, \"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\/1674764499695.59\/warc\/CC-MAIN-20230128220716-20230129010716-00421.warc.gz\"}"}
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{"url":"https:\/\/www.studyadda.com\/question-bank\/chemical-analysis-of-organic-compounds_q53\/1411\/104744","text":"\u2022 # question_answer In Victor Mayer?s method 0.2 gm of an organic substance displaced 56 ml of air at STP the molecular weight of the compound [Kerala (Med.) 2003] A) 56 B) 112 C) 80 D) 28\n\nMolecular mass $n=\\frac{M.wt}{E.F.wt}=\\frac{146}{73}=2$ $=\\frac{0.2}{56}\\times 22400=80$.","date":"2020-09-19 07:15:03","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\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.705145537853241, \"perplexity\": 8789.635609514515}, \"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-2020-40\/segments\/1600400190270.10\/warc\/CC-MAIN-20200919044311-20200919074311-00603.warc.gz\"}"}
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{"url":"https:\/\/wiki.sustainabletechnologies.ca\/index.php?title=Retention_swales&diff=13176&oldid=3644","text":"Difference between revisions of \"Retention swales\"\n\nThese sizing equations are suggested for use in calculating the capacity of swales which have a larger proportion of surface flow. i.e. grass swales, rather than bioswales.\nIn many cases the length of swale required will exceed the available space, so that an underground infiltration trench or a dry pond will be a preferred solution.\n\nTriangular channel\n\nSizing a triangular channel for complete volume retention:\n\n${\\displaystyle L={\\frac {151,400Q_{p}^{\\frac {5}{8}}m^{\\frac {5}{8}}S^{\\frac {3}{16}}}{n^{\\frac {3}{8}}\\left({\\sqrt {1+m^{2}}}\\right)^{\\frac {5}{8}}q}}}$\n\nTrapezoidal channel\n\nSizing a trapezoidal channel for complete volume retention: ${\\displaystyle L={\\frac {360,000Q_{p}}{\\left\\{b+2.388\\left[{\\frac {Q_{p}n}{\\left(2{\\sqrt {1+m^{2}-m}}\\right)S^{\\frac {1}{2}}}}\\right]^{\\frac {3}{8}}{\\sqrt {1+m^{2}}}\\right\\}q}}}$\n\nWhere:\n\n\u2022 L = length of swale in m\n\u2022 Qp = peak flow of the storm to be controlled, in m3\/s\n\u2022 m = swale side slope (m\/m)\n\u2022 S = the longitudinal slope (m\/m)\n\u2022 n = Manning's coefficient (dimensionless)\n\u2022 b = bottom width of trapezoidal swale, in m.","date":"2022-08-17 10:30:20","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 2, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"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\": 0.7592395544052124, \"perplexity\": 8606.974560966493}, \"config\": {\"markdown_headings\": false, \"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-2022-33\/segments\/1659882572898.29\/warc\/CC-MAIN-20220817092402-20220817122402-00106.warc.gz\"}"}
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Home » Donetsk: absolute ruination
Donetsk: absolute ruination
Vitaliy Portnikov: Three years ago when new airport terminals were being built in Ukraine in preparation for the forthcoming European Championship soccer games I, unlike many of my compatriots, was not too excited.
Three years ago when new airport terminals were being built in Ukraine in preparation for the forthcoming European Championship soccer games I, unlike many of my compatriots, was not too excited. Ukraine's calamitous economic situation was no secret even then, and it seemed to me that under circumstances such as those setting aside funds from the state budget for the construction of extravagant airport terminals was reckless and wasteful. Of course in those cities where the construction was to take place the public thought otherwise. Even the fact that those huge airports stood empty after the games were over had no effect on the public's good spirits. After all, isn't it better to have a modern airport terminal even if it is barely used than to have that eyesore, that primitive soviet hangar?
Donetsk was among those lucky places that got a new airport terminal. Dnipropetrovsk and Odesa were left with their old ones. Everyone agreed that Donetsk deserved a new terminal. At the time of construction practically the entire Ukrainian government including the leadership in Parliament were natives of Viktor Yanukovich's region. In addition, a friend of the president, the oligarch Rinat Akhmetov built a magnificent stadium in the mining city of Donetsk and instantly the stadium became a fresh symbol for the city. The airport, named in honor of the Russian composer Sergei Prokofieff (who was born in the Donetsk region), nicely rounded out the desired effect to the image of the city. And many residents of Donetsk agreed that, yes, their countrymen stole a hell of a lot of money. But sooner or later, they thought, the stealing would stop while the airport and the stadium would be there for posterity.
Today in Donetsk not even a hint of the airport remains. Not of the new one and not of the old one. The stadium is still sort of there, but that's irrelevant because the home soccer team "Shakhtar," another symbol of Donetsk, has long ago fled the war-torn city. As have two other symbols of Donetsk: Viktor Yanukovich and Rinat Akhmetov. For the time being, those two fled in two opposite directions.
Following the orders of Alexander Zakharchenko (to be precise, the orders were given by his Russian handlers because as a rule the head of the so-called Donetsk Peoples' Republic never makes any decisions on his own) the airport has been completely razed. The airport had been bombarded by DPR artillery, which means, of course, with weapons brought in from Russia. The Kremlin strategists will explain the final and complete destruction of the airport as a necessary step in straightening out the demarcation line and in transforming Donetsk into a hot spot city and other such nonsense. What they have actually done, though, is they have pushed Donetsk and the entire occupied territory into reverse making sure that it will all be decades behind the civilized world.
There is nothing left in Donetsk that one could be proud of. There is no more great soccer, there is no airport, there is no more working industry. The whole country had profited from the industry in Donetsk. Today there is no-thing left. All that has remained in Donetsk are people, scared people, poor people, people who do not comprehend what is happening to them or what will still happen to them, people who have been fooled by Russia and cut off from Ukraine. Donetsk has become a place where the preferred mode of transportation is a tank. It has become a city out of which you cannot fly. It has become a place that instead of being under the administration of government officials is being run by crazy gopniks [member of a criminal subculture] with bulging eyes, the stand-ins for important Muscovites in nice clothes who huddle together as they review the new plans for tomorrow's bombings, killing and assassinations.
Donetsk is no longer a city. Months of occupation have transformed it into a place where senselessness, horror and futility rule and where civilization went out the window like air escaping a punctured balloon.
And this precipitous plunge into obscurity, this cold-blooded destruction of a once thriving city with a population of a million people was all done for the sake of making a petty little Kremlin man with shallow ambitions happy. This city serves as an excellent model for the "Russian world" the wretched little man is poised to build. A "Russian world" built on the bones of those who died under the rubble of the still recently glistening airport terminal. A "Russian world" in the midst of ruined streets, boarded up windows and crippled people. The pathetic little man is building a "world" that is worse than war.
Europeans, and especially those of us who live in the post-Soviet space are living on top of ruins. Seventy years ago our cities were bombed and shelled and all that was left were skeletons of buildings. And suddenly, unexpectedly, it is starting all over again. It seems like today Donetsk is reliving its 700 days of Nazi occupation: in the first days of the so-called Donetsk Peoples' Republic Jews were required to register, prisoners of war are made to fight for their land, and those same prisoners of war are paraded along the streets as the collaborators of today's regime stand watching and ululating. All of this has happened before, fairly recently. The circus "Cosmos," newly ravaged by the current war still adorns the city just like it adorned the city back when it was built on the ruins of the ghetto after the Jews were forced out of Stalino [one of the former names of Donetsk] on their final journey. And the prisoners of war, the "Cyborgs" are paraded in the streets. And a rumpled tyrannical gauleiter is busy spreading horror and devastation unreservedly blatantly as, feeling wholly uninhibited about his task he freely ranges across Donetsk.
Was it yesterday that Hitler died?
Tags: donetsk russia ukraine war
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Taylor Productions
"We are all connected. Our stories are a chain reaction resulting from kindness between strangers."
- Erica L. Taylor
ERICA L. TAYLOR, EXECUTIVE PRODUCER
Erica L. Taylor is the owner and Executive Producer of Taylor Productions, a full-service production company. She is a graduate of Spelman College in Atlanta, GA. In 2012 she became a Producer for A. Smith & Co. Production, one of the largest production companies in Hollywood. Her credits include the multi-award winning docuseries' Unsung and Unsung Hollywood featured on the TV One network and Celebrity Crime Files. Her episodes have reached the highest nightly ratings in primetime network television.
She has produced and hosted episodes featuring rare interviews with stars such as Jerry Seinfeld, Phylicia Rashad, Eddie Murphy, Stevie Wonder, Smokey Robinson, Michael McDonald, Al Green, John Legend, Terrence Howard, Anthony Anderson, Kerry Washington, Kristin Bell, Kevin Hart, Ruby Dee, Ossie Davis, Chris Rock, Snoop Dogg and many more. In 2015, she produced the documentary, "The Invisible Vegan", starring Cedric the Entertainer, John Salley and a host of scholars, which examines the vegan lifestyle movement in the African-American community. In addition to her work behind the scenes, Erica has also served as red carpet host for major events in L.A. and New York. She has been a featured voice talent for numerous businesses, commercials, churches, ceremonies and animations in the U.S., the U.K. and Australia, and was the face of JcPenney's 2017 Holiday Challenge commercial campaign.
IMDB CREDITS
© 2022 by Taylor Productions. All Rights Reserved.
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Pays interdit (Verbotenes Land), ursprünglich L'upyre betitelt, ist ein surrealistisches Gemälde von Wolfgang Paalen, das in der endgültigen Fassung von 1937 ein tropfenförmig stilisiertes Weiblichkeitsidol mit tentakelartigen Fangarmen zeigt, das in prekärer Nähe zu einem Abgrund steht, der sich jäh zum Betrachter hin in dunkel-kristallinen Formen auftut und vor dem drei sphärenförmige Raumkörper schweben, zwei davon wie hereinstürzende, brennende Meteoriten gestaltet. Das Bild ist das erste Ölbild Paalens, das kunstvoll auf der von Paalen erfundenen Technik der Fumage aufbaut und sich auf vielschichtige Weise mit den Zusammenhängen von Todesangst und Weiblichkeit auseinandersetzt, die seiner Ansicht nach an den Bereich der menschlichen Psyche heranführen, in dem sich die künstlichen Trennungen von Ich und Welt entfalten. Das Bild befindet sich in einer Privatsammlung.
Hintergrund
Das Bild bezeichnet den Beginn von Paalens konziser bildnerischer Kritik an der unumschränkt subjektivistischen Haltung des Surrealismus, aus der er später seine umfassend begründete Philosophie der Kontingenz entwickelte. Das Bild begann Paalen in den ersten beiden Oktoberwochen des Jahres 1936 nach einer schweren psychischen Krise. Im August 1936 hatte er erfahren, dass eine länger anhaltende Affäre Pablo Picassos mit seiner Frau Alice (Alice Rahon) zu einer Schwangerschaft und Abtreibung geführt hatte. Paalen äußerte sich später über die Depressionsschübe, die er schließlich in einen regelrechten Schaffensfuror kanalisieren konnte: "Es ist dann, als ob das Feuer, oder der Keim zu ihm, in sich zusammenstürzte, und an seinen Platz alles Entsetzliche treten kann. Tagsüber kann ich vor Wut, Argwohn und Schuld kaum denken, geschweige denn mit irgendjemandem sprechen. Nachts sterbe ich vor Angst, alles könnte zertrümmert werden. Ruhe ist ein solch entfernter Begriff, kaum kenntlich in diesen dunklen Tagen. Vielleicht wird es die Malerei sein, die mich aus diesen Schüben fürchterlichen Dunkels herauszieht und die paar Steine zusammenfügen kann, die ich in der leeren Welt nicht mehr finde. Und wenn dies nicht gelingt, weiß ich mindestens sicher, dass es nicht darum geht, ein Ich zu besitzen, sondern nur einen Ruf ins Leben zu hören, wenn man vor dem absoluten Nichts steht. Mein Sehen hat sich einmal mehr in sich eingekehrt. Mit Fug und Recht kann ich nun sagen, ich sehe wie der alte heidnische Apollonius: von Innen heraus." Nach einer orientierenden Griechenlandreise begann er Mitte Oktober an dem geheimnisvollen Bild zu arbeiten, das ihn bis ins nächste Jahr beschäftigen würde und das von dieser, fast feierlich und mit dem Vokabular des Mystikers Apollonius von Tyana beschriebenen inneren Fall in die Abgründe der Todesangst Zeugnis ablegen sollte: eine apokalyptische Landschaft, dominiert von einer weiblichen Gottheit und herabfallenden, meteorartigen Planeten. Pays interdit ist auch das erste Ölbild, in dem die Fumage in den außerordentlich fein ausgeführten kristallinen Strukturen des unteren Teils kunstvoll eingearbeitet ist. Paalen entwirft sein persönliches Grundmodell des durchlässigen surrealen Seelenbildes in Form einer abgründigen, zersplitterten Landschaft, durchpulst von einer Mischung aus femininer Mystik und romantischem Schauerbild, die an präkeltische Feenmysterien und ihren kosmischen Anspielungen erinnern, wie sie aus der lyrischen Tradition Britanniens bekannt sind. Der Dichterfreund André Breton sprach angesichts dieses Urbildes für die späteren großen Fumagen des Künstlers von Symbolen für eine Art erweiterter Innensicht: "Vielleicht, ja bestimmt ist es für unsere Zeit eine Versuchung des Auges, sich in jenes ideelle Stadium der Schöpfung zu versetzen, in dem die Schmetterlinge ein einziges Band zum Abschneiden bildeten, in dem die Vögel noch alle zusammen eine einzige Musikspirale anstimmten, da die Fische noch ungeschieden im Innern eines Silberschiffchens umherschwammen. (...) Fenster, blind wie Lampen nächtlicher Diebe, Kinder sehen solche Farben, wie sie sich im Rund einer Seifenblase krümmen – leider öffnen sie sich nur von innen. Aber Paalens Verdienst ist es, soweit vorgedrungen zu sein, dass er aus dem Inneren der Seifenblase zu sehen vermochte und uns die Welt von dorther sehen lässt." Durch die Todesangst gelangt der Künstler/Betrachter an den Kern kindlicher Emotion, der Welt der Einheiten gefühlsmäßiger Ähnlichkeiten, in der die Trennungen zwischen den Realitäten aufgehoben sind.
Beschreibung
Ins Auge sticht in diesem Bild vor allem die außerordentliche Farbe im oberen Teil – subtil abgestufte Grüntöne, die aussehen, als seien sie auf Gold gemalt – und im unteren Teil eine feine Ausführung kristallin aufgefächerter Raumstrukturen, Andeutungen von Schleimhäuten und feuchtem, inneren Gewebe. Die Fumage-Flecken lugen nur an einigen Stellen wie schwarze Löcher hervor. Die arm- und beinlose Steinfigur mit ihren ballonförmigen Empfangsorganen – Bauch, Brüste und Kopf – wurde biografisch als ein mythologisiertes Porträt der Freundin Eva Sulzer gedeutet, zu der sich Paalen nach der Krise mit seiner Frau hinwendete: als eine Art Eva der Zukunft, eine Frau, die nicht geboren wurde, sondern ihr Leben unmittelbar den göttlichen Kräften verdankt. Selbst nabellos verkörpert sie den Nabel der Welt, an dem sich Vergangenheit und Zukunft berühren, eine Einheit von Leibesfrucht, Gebärmutter und Mutter, oder wie James Joyce sie beschrieb: "Heva. Nackte Eva. Sie hatte keinen Nabel. Schau. Bauch ohne Fehl, schwanger schwellend, ein Rundschild aus strammem Velin, nein, weißgehäuftes Korn, aufstrahlend und unsterblich, dauernd von Ewigkeit zu Ewigkeit." Paalen hatte mehrfach zuvor die Orakelstätte in Delphi mit dem Omphalos besucht, der aus weißem Stein gehauenen, oben abgerundeten, symbolischen Steinsäule für den Nabel der Welt, die als von einem Blitz ausgelöster Meteorit vom Himmel gefallen und ursprünglich ein Opferstein der Göttin Gaia gewesen sein soll. Delphi ist der Erdgöttin Gaia gewidmet (von »delphos« – griech. Gebärmutter) und war mit ihrer, einst von der weiblichen Priesterin Pythia bespielten Orakelstätte sicher eines der Sehnsuchtsorte auf der inneren Landkarte des Künstlers, der nach tiefen Symbolen für die Geburt und die hellseherischen Sprachformen einer urtümlichen Weiblichkeit suchte, die gleichsam direkt aus dem Uterus kommunizierte.
Paalens Freund und Intimkenner, der deutsche Schriftsteller Gustav Regler, sprach angesichts des Bildes von dessen "Amazonenreich": "Auf einem Planeten, der abseits der großen Straßen / leise und sinnend um sich kreist, / liegt das Reich, (...) und hier fern von ihnen / spricht er mit Frauen, / als gehörten sie seinem fernen Sternenvolk an. (...) Und eine nennt er Königin, / da sie sich nicht verbergen kann; / ihre hohe Gestalt macht jeden Zweig eines Baumes, / unter dem sie steht, / zur blütentragenden Huldigung, / sie schaut auf die Berge, / als ständen dort ihre Paläste; / Küsten sind ihr die Streifen seliger Vereinigung / mit der Sonne, / Das Meer empfängt sie wie die Heimkehrende, / jedesmal wenn sie das Ufer verrät / und es scheint, als lebe sie nun / im Element, das nach dem Puls der Sterne atmet; (...) / Zeit ist ihm Einbruch des Raums / und ist zu bemessen nach der Zahl der Kometen, / die auf ihr Element trafen, / das sie sichtbar machte und leuchtend, / das sie verbrauchte und nährte. / Die Götter aber sind die Geschöpfe / dieser vorbeirauschenden Ströme, / Splitter der sich auflösenden Sternschnuppen, (...) / Sein Gefühl, dass wir immer am Rand der Unendlichkeit gehen, / dass der Abgrund uns begleitet wie ein getreuer Schatten. (...) / wie Meteore in der Wüste." Die Fruchtbarkeitssymbolik der Figur und die größere, transparente der drei Sphären mit den eingeschlossenen Formanspielungen für Erde, Weiblichkeit, Eros und einhüllendem Vorgeburtsraum stehen in kompositorischer Harmonie miteinander, hieratisch schwebend vor dem undurchdringlichen Dickicht des terrestrischen Abgrundes. Die Idee zu den Meteoriteneinschlägen war Paalen vielleicht durch die Lektüre von Camille Flammarions visionären Roman La Fin du Monde gekommen, in dem es der Eva beschieden war, der nach einem Meteoriteneinschlag erkaltenden, absterbenden Erde bei ihrem Untergang bis zur eigenen Vereisung zuzusehen.
Titel
Das Bild wurde vom Künstler nicht auf der Rückseite der Leinwand, wie sonst meist üblich, betitelt. Unter dem Titel L'upyre erscheint es im Katalog der Ausstellung in der Julien Levy Gallery, New York 1940; auf der erhaltenen Ausstellungsliste ist der Titel Pays interdit als Zusatz eingefügt. Das Bild ist eines der ersten Erwerbungen Gordon Onslow Ford, der das Bild wahrscheinlich 1941 in New York erwarb, um auf Paalens Initiative Gelder für die notwendigen Garantien zur Ausreise der in Marseille einsitzenden Surrealisten, insbesondere André Breton zu generieren (es war bis zu diesem Zeitpunkt bei Julien Levy eingelagert). Onslow Ford behielt es seither in seiner Privatsammlung. Es wurde von dort nie für Ausstellungen ausgeliehen. Für Ida Prampolinis große Publikation El Surrealismo y el Arte Fantastico de Mexico, Mexico (IIE) 1969, diente ein Archivfoto von André Caillet aus den Pariser Beständen Paalens, das den Zustand von 1936 wiedergibt, als Druckgrundlage (Abbildung Nr. 44, ganzseitig). Auf dem Foto sind rückseitig beide Titel vermerkt.
Literatur
Andreas Neufert: Wolfgang Paalen. Im Inneren des Wals. Springer, Wien und New York 1999 (Monografie und Werkverzeichnis).
Amy Winter: Wolfgang Paalen. Artist and Theorist of the Avantgarde Praeger, Westport (Connecticut) 2002.
Andreas Neufert: Auf Liebe und Tod. Das Leben des Surrealisten Wolfgang Paalen. Parthas, Berlin 2015, ISBN 978-3-86964-083-9.
Andreas Neufert: Paalen. Life and Work. I. Forbidden Land, The Early and Crucial Years 1905 - 1959. Berlin/Hamburg, 2022, S. 250 (Farbabbildung), 251 (Zustand von 1936, Abb.) und Umschlagbild ISBN 978-3-756-85887-3.
Einzelnachweise
Weblinks
offizielle Webseite über Wolfgang Paalen
Akademie der Bildenden Künste, Karlsruhe
Ausstellung "The Colour of my Dreams - The Revolution in Surrealist Art" Vancouver Art Gallery 2011
Gemälde (20. Jahrhundert)
Surrealismus
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ТОВ «Укртепло» — українська група компаній, що працює на ринку відновлюваної енергетики, один з лідерів галузі. Компанія створена 2011 року і за цей час реалізувала понад 1 000 проектів в 14 регіонах України. Штат працівників – понад 1 400 осіб.
Історія
Компанія розпочала свою діяльність з будівництва твердопаливних котелень і заміщення газу відновлюваними джерелами енергії. 2013 року запущено виробництво твердопаливних котлів нового покоління СЕТ. Наступного, 2014 року, спільно зі «Salix Energy» висаджено першу плантацію енергетичної верби для її подальшої переробки на біопаливо. У 2015 році група компаній «Укртепло» підписала ліцензійну угоду про співпрацю з компанією KARA Energy, одним зі світових лідерів у виробництві промислових котлів.
У 2017 році компанія запустила одну з найбільших в Україні котелень на біопаливі у м. Славутич потужністю 10,5 МВт. У тому ж році розпочали роботу біогазова станція у м. Рівне, міні-гідроелектростанція у Вінницькій області та Центр вирощування енергетичної верби в Київській області, які увійшли в склад групи компаній.
У 2018 році компанія стала інвестором ТОВ "Рівнетеплоенерго" і розпочала масштабну інвестиційну програму модернізації підприємства та заміщення газу відновлюваними джерелами енергії.
Загалом у 2018 році "Укртепло" реалізувала низку проєктів сумарною встановленою потужністю понад 30 МВт.
Наразі компанія веде будівництво біоТЕЦ в місті Овруч, Житомирська область, потужністю 5,9 МВт; місті Токмак, Запорізька область, потужністю 8,6 МВт.
Восени 2019 року розпочали роботу сонячна електростанція на Вінниччині (загальна потужність 4,2 МВт) і біогазова станція в Маріуполі (2,7 МВт).
Напрямки діяльності
Виробництво теплової енергії з біомаси;
Виробництво електроенергії з відновлюваних джерел (біогаз, сонце, гідро);
Вирощування енергетичної верби;
Виробництво твердопаливних котлів.
Примітки
Посилання
Офіційний сайт
Профіль на Facebook
Засновані в Україні 2011
Енергетичні підприємства України
Відновлювана енергетика України
Біопаливна енергетика
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{
"redpajama_set_name": "RedPajamaWikipedia"
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\section{Introduction}
The dynamics of spatially extended systems has been a focus of intense
research activity in the past two decades. In recent years it has
become evident that modeling large interactive systems by finite
dimensional lattices on one hand and fully random networks on the
other, is inadequate, as various networks, ranging from collaborations
of scientists to metabolic networks, do not fit in either paradigm
\cite{RMP_bar}. Some alternate scenarios have been suggested, and one
of the most popular ones is the small-world network \cite{Watts}.
Here one starts with a structure on a lattice, for instance regular
nearest neighbor connections. Then each link from a site to its
nearest neighbor is rewired randomly with probability $p$, {\it i.e.}
the site is connected to another randomly chosen lattice site. This
model is proposed to mimic real life situations in which non-local
connections exist along with predominantly local connections.
There is much evidence that random non-local connections, even in a
small fraction, significantly affects geometrical properties, like
characteristic path length \cite{Watts}. However its {\em
implications for dynamical characteristics is still unclear and even
conflicting}. While the dynamics of coupled oscillators and coupled
maps on regular lattices (known as `coupled map lattices' or CMLs) has
been extensively investigated \cite{cml}, there have been far fewer
studies on the spatiotemporal dynamics of nonlinear elements on
networks of different topologies \cite{dyn_net}. Most studies so far
have indicated that the regularity of systems increase monotonically
with $p$ \cite{sinha}.
In this paper we will provide evidence of a system where the
dependence of spatiotemporal regularity on the degree of randomness in
coupling connections is highly {\em non-universal}. We will show how
this dependence ranges from {\em monotonically increasing} to {\em
monotonically decreasing}, via {\em non-monotonic variation}, as the
local dynamics changes.
Thus we will demonstrate that the interplay between local dynamics and
connectivity acts in non-trivial and non-intuitive ways, and so even
the qualitative effect of random links on spatiotemporal regularity
can be completely reversed by changing the nodal dynamics.
\section{The Model}
Here we consider nonlinear oscillators coupled to nearest neighbors on
a regular ring, with some fraction $p$ of the regular links rewired
randomly. The individual sites (nodes) are modeled by sine circle
maps, which have widespread relevance for oscillatory phenomena
\cite{sinecircle}, and are given as:
$$f(x)=x+\Omega-\frac{K}{2\pi} \sin (2\pi x)$$
wherein $K$ measures the strength of the nonlinear term, and $\Omega$
represents the natural frequency of the map in the absence of
nonlinearity (i.e. when $K=0$). We restrict our studies to the
parameter region: $0\leq\Omega\leq \frac{1}{2\pi}$ and $K=1$. In this
region, the single sine circle map settles down to the spatiotemporal
fixed point, $x^{\star}=\frac{1}{2\pi} \sin^{-1}(\frac{2\pi\Omega}{K})$.
Under diffusive coupling, such a coupled sine-circle map lattice, is
given as:
\begin{equation}
x_{n+1} (i) = (1-\epsilon) f(x_n(i)) + \frac{\epsilon}{2} [f(x_n(i-1)) + f(x_n(i+1))] \pmod{1}
\end{equation}
where $i=1,\ldots L$ denotes the site index, $n$ denotes the time
index, and $\epsilon$ represents the coupling strength between the
sites ($0\leq\epsilon\leq 1$). Periodic boundary conditions have been
used, namely one has a ring of oscillators.
Earlier studies of this coupled map lattice have been carried out for
various types of initial conditions \cite{sinecml1}. In particular,
the evolution of this coupled map lattice with random initial
conditions shows interesting spatiotemporal dynamics including
spatiotemporal fixed points, spatial and spatiotemporal intermittency,
and spatiotemporal chaos \cite{sinecml2}.
Now we introduce randomness in this regular lattice by rewiring the
nearest neighbor links with a probability $p$ to randomly chosen
sites on the lattice. Here we consider the behavior of the system
under {\em static rewiring}, namely, the randomness in spatial
coupling is quenched or ``frozen'' in time. Ensembles of such randomly
rewired systems are studied.
\section{Results}
\subsection{Basin of attraction for the spatiotemporal fixed point}
\begin{figure}[!t]
\begin{center}
\begin{tabular}{ll}
\includegraphics[height=1.8in,width=2.7in]{bas_0.eps}& \includegraphics[height=1.8in,width=3.0in]{bas_04.eps}\\
\includegraphics[height=1.8in,width=2.7in]{bas_1.eps}& \includegraphics[height=1.8in,width=3.0in]{bas_3.eps}\\
\includegraphics[height=1.8in,width=2.7in]{bas_5.eps}& \includegraphics[height=1.8in,width=3.0in]{bas_8.eps}\\\end{tabular}
\end{center}
\caption{Basin of attraction of the spatiotemporal fixed point,
$x^{\star}$, obtained for different random rewiring probabilities: (a) $p=0.0$, (b)
$p=0.04$ (c) $p=0.1$, (d) $p=0.3$, (e) $p=0.5$, and (f) $ p=0.8$.
These plots have been obtained for $50$ rewiring configurations for
a lattice of size $L=200$ after discarding $5000$ transients.
\label{basin}}
\end{figure}
We study the spatiotemporal dynamics of this system, starting from
random initial conditions under varying rewiring probabilities $p$ ($0
\le p \le 1$), for different realizations of static rewiring.
Specifically we obtain the basin of attraction for the spatiotemporal
fixed point, $B$, by calculating the fraction of rewiring
configurations which lead to a spatiotemporally steady state for
different ($\Omega,\epsilon$) values. Figure \ref{basin} shows a gray
scale plot of $B$ in a large region of parameter space, for different
values of $p$. The white areas indicate the parameter regions, where
all initial coupling configurations lead to a spatiotemporal fixed
point, namely all the sites in the system relax to the fixed point
$x^{\star}$ such that $x(i)=x^{\star}$ for all $i=1\ldots N$ and for
all time $n$. The black regions indicate parameter regions where none
of the coupling configurations yield a spatiotemporal fixed pont. The
gray areas indicate parameter regimes where $0 < B < 1$, i.e. the
spatiotemporal fixed point co-exists with other dynamical behaviour,
and the spatiotemporal fixed point is not an attractor of the dynamics
for all coupling configurations.
\begin{figure}[!t]
\begin{center}
\begin{tabular}{ll}
\includegraphics[height=1.8in,width=2.7in]{bs_o0_e5.eps}& \includegraphics[height=1.8in,width=2.7in]{bs_o02_e5.eps}\\
\includegraphics[height=1.8in,width=2.7in]{bs_o04_e5.eps}& \includegraphics[height=1.8in,width=2.7in]{bs_o06_e5.eps}\\
\end{tabular}
\end{center}
\caption{ Variation of basin of attraction $B$ with the
rewiring fraction, $p$ plotted for the circle map frequencies
$\Omega=0, 0.02, 0.04, 0.06$ and coupling strength $\epsilon=0.5$.
\label{e5ovar}}
\end{figure}
Figure \ref{basin}(a) shows the basin of attraction when the rewiring
fraction is equal to zero, or in other words, the ring has only
regular nearest neighbor connections. As the rewiring fraction $p$ is
varied, the spatiotemporal fixed point regions also show a change.
Figure \ref{basin}(b)-(f) display the basin of attraction of the
spatiotemporal fixed point, for $p=0.04, 0.1, 0.3, 0.5$ and $p=0.8$.
We see that the dependence of this basin of attraction on the degree
of random rewiring is qualitatively very different for different
values of $\Omega$ and $\epsilon$. Interestingly this variation
ranges from monotonic increase to monotonic decrease, as well as
non-monotonic behavior, along different ``cuts'' in
($\Omega,\epsilon$) space.
Further, the dependence of spatiotemporal order on rewiring
probability, averaged over a large parameter range, varies
non-monotonically with $p$. This is clear from the fact that the
extent of the spatiotemporal fixed point basin at intermediate $p$ ($p
\sim 0.1-0.3$) in Figs.\ref{basin}(c-d) is much smaller than that for
low and high $p$. So the gray-scale basin plots in Figs.\ref{basin}
(c-d) appear far less ``white'' in general, across large parameter
regimes, as compared to Figs.\ref{basin} (a) and (f).
Figure \ref{e5ovar} shows the variation of the basin of attraction
$B$ with rewiring fraction $p$ at $\epsilon=0.5$ and for
$\Omega=0.0, 0.02, 0.04,$ and for $0.06$. These plots have been
obtained for $50$ rewiring configurations for a lattice of size
$L=200$ after discarding $10000$ transients. When the natural
frequency of the circle map is equal to zero, ($\Omega=0$), the ring
does not yield a spatiotemporal fixed point when coupling connections
are completely regular. However, the regularity of the system
increases as the rewiring fraction $p$ is increased. This can be seen
in Figure \ref{e5ovar}(a), in which a global spatiotemporal fixed
point attractor is obtained for values of the rewiring fraction $p >
0.6$.
\begin{figure}[!t]
\begin{center}
\begin{tabular}{ll}
\includegraphics[height=1.8in,width=2.7in]{bif_o0.eps}& \includegraphics[height=1.8in,width=2.7in]{bif_o06.eps}\\
\end{tabular}
\end{center}
\caption{ Bifurcation diagram in which the state variables $x_n(i)$
($i=1,\ldots,100$) have been plotted as a function of the fraction
of random links, $p$, for a representative coupling configuration,
for the parameter values (a) $\Omega=0.0$ and (b) $\Omega=0.06$ at
$\epsilon=0.5$. Here, $n=1,\ldots,5$ iterations have been plotted
after discarding $5000$ transients. Note that for regions where $0 <
B < 1$, there are rewiring configurations that lead to the
spatiotemporal fixed point, co-existing with rewiring configurations
that yield spatiotemporal chaos. \label{bifur}}
\end{figure}
The bifurcation diagram in Figure \ref{bifur}(a), showing the
spatiotemporal dynamics of the system with respect to the fraction of
random links $p$, further underscores this feature. Here the system
has a complex spatial pattern for lower values of random rewiring
probability. However, it settles down to the spatiotemporal fixed
point ($x^{\star}=0$, in this case) as the fraction of random links
$p$ approaches $1$.
In contrast, the variation of the basin of attraction, $B$, in
the case where the frequency $\Omega$ is equal to $0.02$ is shown in
Figure \ref{e5ovar}(b). Here, we see that the system yields a
spatiotemporal fixed point with probability $1$ for zero rewiring
fraction $p$, but shows a non-monotonic variation as the rewiring
fraction $p$ is changed. We see that though the basin of attraction
decreases to zero in the interval $p\sim 0.1-0.4$, it gradually
increases for rewiring fractions, $p>0.4$, until it again registers a
decrease in the large $p$ limit \cite{foot}. Hence, the basin of
attraction $B$ shows a {\em non-monotonic} variation with change in
$p$. A similar non-monotonic variation is seen in Figure
\ref{e5ovar}(c), where $\Omega=0.04$.
\begin{figure}[!t]
\begin{center}
\begin{tabular}{ll}
\includegraphics[height=1.8in,width=2.7in]{bs_o01_e10.eps}& \includegraphics[height=1.8in,width=2.7in]{bs_o01_e8.eps}\\
\includegraphics[height=1.8in,width=2.7in]{bs_o01_e6.eps}& \includegraphics[height=1.8in,width=2.7in]{bs_o01_e45.eps}\\
\end{tabular}
\end{center}
\caption{ Variation of basin of attraction, $B$ with the
rewiring fraction, $p$ for the circle map frequency, $\Omega=0.01$
and coupling strengths, $\epsilon=1.0, 0.8, 0.6,$ and $0.45$.
\label{o01evar}}
\end{figure}
In the case of $\Omega=0.06$, as displayed in Figure \ref{e5ovar}(d),
the basin of attraction {\em decreases} to zero as the rewiring
fraction is increased. In this case, the system settles to the
spatiotemporal fixed point $x^{\star}$ for smaller rewiring fractions,
but exhibits a complex spatial pattern when the degree of rewiring in
the system is increased. This is further illustrated in the
bifurcation diagram of the system shown in Figure \ref{bifur}(b). This
is exactly the opposite trend to that observed in the case of
$\Omega=0$. So, as the local frequency of the nonlinear oscillator
changes, the effect of random rewiring on spatiotemporal properties is
completely reversed.
Hence, we see that for the same coupling strength $\epsilon$, and for
the same set of rewired configurations, the basin of attraction of the
spatiotemporal fixed point shows a very strong dependence on the local
dynamics, namely on the frequency $\Omega$ of the nonlinear
oscillators. So it is evident that the spatiotemporal regularity
depends crucially, not just quantitatively, but also qualitatively, on
the nodal dynamics.
Similarly, when the nodal dynamics is fixed and the coupling strength
$\epsilon$ is varied, we see that the basin of attraction shows a
non-monotonic variation with change in rewiring fraction $p$. This is
illustrated in Figure \ref{o01evar} where the basin of attraction has
been plotted for $\Omega=0.01$ and for various representative values
of the coupling strength $\epsilon$.
Hence, spatiotemporal regularity of the dynamics on a network depends
quite crucially on the interplay between the nodal dynamics and the
network topology. That is, coupling configurations with the same
degree of randomness may enhance or inhibit spatiotemporal order
depending on the properties of the local oscillators.
\section{Conclusions}
In summary, we have investigated the spatiotemporal dynamics of a
network of coupled nonlinear oscillators, modeled by sine circle maps,
with varying degrees of randomness in coupling connections. We showed
that the variation of the basin of attraction of the spatiotemporal
fixed point, with increasing fraction of random links $p$, crucially
depends on the nature of the local dynamics. Even the qualitative
relationship between spatiotemporal regularity and $p$ changes
drastically as the angular frequency of the oscillators change,
ranging from monotonic increase or decrease, to non-monotonic
variation. Thus it is evident that the influence of random coupling
connections on spatiotemporal order is highly non-universal here and
depends strongly on the angular frequency of the nodal oscillators.
This implies that the delicate interplay between local dynamics and
connectivity is crucial in determining the emergence of spatiotemporal
order in complex networks of dynamical elements.\\
{\bf Acknowledgement:} We would like to thank Prof. N. Gupte for
useful discussions.
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Urmia (dawniej Rezaije) – bezodpływowe, słone jezioro położone w północno-zachodnim Iranie na Wyżynie Armeńskiej. Położone jest w tektonicznym zagłębieniu śródgórskim na wysokości 1275 m. Największe w tym kraju, o zmiennej powierzchni od 3,9 do 5,8 tysiąca km² i głębokości maksymalnej do 16 m. Wysokie zasolenie od 15% do 23%, na brzegach solniska. Występują liczne skaliste wysepki. W pobliżu zachodniego wybrzeża miasto Urmia.
Od lat 1970 jezioro zmniejsza swoją powierzchnię wskutek długotrwałej suszy i dużego poboru wody z zasilających je rzek. Zwiększające się zasolenie sprzyja zakwitom mikroorganizmów (glonów Dunaliella salina lub halobakterii), co sprawia, że okresowo jezioro zmienia barwę na czerwoną. Wiosną 2019 roku intensywne deszcze, najsilniejsze od 50 lat, podniosły poziom wody o 62 cm i zwiększyły powierzchnię jeziora do ok. 3000 km².
Przypisy
Jeziora w Iranie
Jeziora słone w Azji
Azerbejdżan Wschodni
Azerbejdżan Zachodni
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"redpajama_set_name": "RedPajamaWikipedia"
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Isòvol in Catalonia
Destination Guide Spain
in Girona of Catalonia, Spain
Aeròdrom dels Pirineus-Alt Urgell Airport (21 mi)
Girona Airport (58 mi)
Perpignan-Rivesaltes (Llabanère) Airport (59 mi)
Sabadell Airport (61 mi)
Carcassonne Airport (63 mi)
Barcelona International Airport (76 mi)
Castres-Mazamet Airport (85 mi)
Toulouse-Blagnac Airport (89 mi)
Bordeaux-Mérignac (BA 106) Airport (211 mi)
Noteable things around
Madriu-Perafita-Claror Valley (Unesco heritage, 14 mi)
Catalan Romanesque Churches of the Vall de Boí (Unesco heritage, 52 mi)
Historic Fortified City of Carcassonne (Unesco heritage, 64 mi)
Works of Antoni Gaudí (Unesco heritage, 69 mi)
Palau de la Música Catalana and Hospital de Sant Pau, Barcelona (Unesco heritage, 71 mi)
Poblet Monastery (Unesco heritage, 79 mi)
Canal du Midi (Unesco heritage, 88 mi)
Archaeological Ensemble of Tárraco (Unesco heritage, 92 mi)
Episcopal City of Albi (Unesco heritage, 108 mi)
42.378 and 1.818 (Lat./Lng.)
N 42° 22' 39" and E 1° 49' 5"
Spanish, Catalan, Galician, Basque, Occitan
Timezone: Europe/Madrid
Tupuangi
Discover Isòvol
Isòvol in Girona (Catalonia) is a city in Spain about 316 mi (or 509 km) north-east of Madrid, the country's capital city.
Local time in Isòvol is now 06:26 PM (Thursday). The local timezone is named Europe / Madrid with an UTC offset of 2 hours. We know of 9 airports in the vicinity of Isòvol, of which 3 are larger airports. The closest airport in Spain is Aeròdrom dels Pirineus-Alt Urgell Airport in a distance of 21 mi (or 34 km), West. Besides the airports, there are other travel options available (check left side).
There are several Unesco world heritage sites nearby. The closest heritage site is Madriu-Perafita-Claror Valley in Andorra at a distance of 14 mi (or 22 km). The closest in Spain is Catalan Romanesque Churches of the Vall de Boí in a distance of 52 mi (or 22 km), North-West. Looking for a place to stay? we compiled a list of available hotels close to the map centre further down the page.
When in this area, you might want to pay a visit to some of the following locations: Riu de Cerdanya, Ger, Urus, Das and Alp. To further explore this place, just scroll down and browse the available info. Let's start with some photos from the area.
Air Pressure 1015.8 hPa
Wind Speed Light breeze with 5 km/h (3 mph) from North-East
Cloud Conditions Scattered clouds, covering 43% of sky
General Conditions Light rain
Hotels and Places to Stay
Hotel Torre del Remei
4,8 mi
Camí del Remei, 3
17539 Bolvir
Time Information
Checkout: 12:00 - Checkin: 15:00
Weekday: -
Fontanals Golf
C/Fontanals, 2
17538 Soriguerola
Weekday: 0:00 - 24:00
Weekend: 0:00 - 24:00
Chalet del Golf Relais du Silence
Barrio del Golf.
Muntanya I Spa
Calle de Puig, 4
25727 Prullans de Cerdanya
Volando en la Cerdanya
Author: JM GVS
Volando en la Cerdanya, verano de 1999.
Tuckie's First Soaring Flight: Duo Discus from La Cerdanya (LECD)
Author: TUCKIE10
My first Gliding flight, during an Aeroclub Barcelona-SaBadell sortie to La Cerdanya (LECD) to fly in the gliders of the non-powered division of our Aeroclub. Thanks a lot to Rafa Molina,...
Timelapse del vol en globus del 20 de setembre de 2014
Author: Globus de La Cerdanya
Enlairament: Aeròdrom de La Cerdanya. Aterratge: Palau de Cerdanya.
PCATACK - Servidor De Minecraft - Está En Venta
Author: Kikotu Mine
Hola a todos, PCATACK está en venta, interesados contactar en admin@pcatcak.com y se os darán los datos y condiciones. Tambien podeis hacernos llegar vuestra oferta y por favor no contacteis...
LCTV: EL TRINXAT AMB RICARD BORRÀS DEL RESTAURANT CAL JET (GER DE CERDANYA)
Author: TV CERDANYA
"El Trinxat" és un programa de cuina que neix amb l'objectiu de promoure la cuina i gastronomia de la comarca de la Cerdanya. Amb els diferents capítols, La Cerdanya Televisió ofereix als...
LCTV: EL TRINXAT AMB XAVIER GRIFOLL
BTT Cerdanya - Sender Refugi del Gonec fins Pi
Author: GeorgeA76
El sender son aprox uns 8kms que van desde el Refugi fins el poble de Pi de Cerdanya.
Начало Пиреней и плохой погоды
Author: manch192
по пути из Каталонии в Андорру.
Puigpedros 2916 m
Author: Edgar Martinez
Muntanya situada en el municipi de Meranges (La Cerdanya), pujada en família desnivell de 800 metres i una durada de 4:30.
L'herba de Novembre (part III)
Author: Cal Pesolet
Aquesta nit -5ºC, que bé aquest solet ara!
Cerdanya, often la Cerdanya, is a natural comarca and historical region of the eastern Pyrenees divided between France and Spain. Historically it has been one of the counties of Catalonia. Cerdanya has a land area of 1,086 km, divided almost evenly between Spain (50.3%) and France (49.7%). In 2001 its population was approximately 26,500, of whom 53% lived on Spanish territory. Its population density of 24 residents per km² (63 per sq. mile) is one of the lowest in Western Europe.
Located at 42.4467, 1.95278 (Lat. / Lng.), about 8 miles away.
Geography of Catalonia, Pyrenees, Natural regions
Cerdanya (comarca)
Cerdanya is a comarca in northern Catalonia, north-eastern Spain, in the Pyrenees, on the border of Catalonia with France and Andorra. Within Catalonia. Cerdanya is divided between Catalonian provinces of Lleida and Girona. Cerdanya's neighbouring comarques are Alt Urgell, Berguedà, and Ripollès. Cerdanya is in the "vegueria" of Alt Pirineu (or Alto Pirineo), according to "Vegueries of Catalonia law".
Wikipedia Article, Homepage
French Cerdagne
French Cerdagne is the northern half of Cerdanya, which came under French control as a result of the Treaty of the Pyrenees in 1659, while the southern half remained in Spain (as part of Catalonia). Catalonians often refer to French Cerdagne as Upper Cerdanya. It is the only French territory in the Iberian Peninsula, as it is in the south side of the Pyrenees range between Spain and France.
Located at 42.5, 1.96667 (Lat. / Lng.), about 11 miles away.
Linguistic rights, Northern Catalonia, Geography of Pyrénées-Orientales
Alp 2500
Alp 2500 is a ski resort in La Cerdanya, Catalonia, in the Pyrenees mountains of northeastern Spain. It includes the two towns of La Molina and Masella, whose two respective ski areas united to form this resort. The nearest main town is Alp. The resort of Masella serves the mountain of La Tosa. Alp 2500 has over 130 km (80 mi. ) of slopes, and its Hotel Alp is only 50 meters (165 ft. ) from the slopes.
Ski areas and resorts in Catalonia, Pyrenees
Masella
Masella, belonging to Alp's municipality, is a ski resort in La Cerdanya in Girona, Catalunya in the Spanish Pyrenees. It is situated on La Tossa d'Alp mountain. This ski resort is part of the Alp 2500 resort.
Ski areas and resorts in Catalonia, Ski areas and resorts in Spain, Pyrenees
Sud Radio Transmitter Pic Blanc
Sud Radio Transmitter Pic Blanc is a facility for high power medium wave broadcasting located on Pic Blanc, a 2650 metre high mountain at 1°43'1"E and 42°32'5"N in Andorra. Whilst in operation, it was the highest medium wave transmitting station in Europe. It was built in 1972 by Sud Radio and uses a directional antenna consisting of two free-standing 86 metre tall lattice towers. One of these towers is insulated against ground, while the other one is grounded and carries a cage aerial.
Located at 42.5347, 1.71694 (Lat. / Lng.), about 12 miles away.
Buildings and structures in Andorra, Named antennas, Towers in France, Transmitter sites in France
The THEMIS solar power tower is a research and development centre focused on solar energy. It is located near the village of Targassonne, in the department of Pyrénées-Orientales, south of France, 3 kilometres from the world's largest solar furnace in Odeillo.
Buildings and structures in Pyrénées-Orientales, Energy development, Solar power in France, Solar power stations in France
Grau Roig
Grau Roig is a village in Andorra, located in the parish of Encamp. The nearest major settlement is Pas de la Casa, to the east on the border with France.
Located at 42.533, 1.701 (Lat. / Lng.), about 12 miles away.
Populated places in Andorra
Artigas Gardens
The Artigas Gardens (Catalan: Els Jardins de Can Artigas) are a park in La Pobla de Lillet, Catalonia. Built between 1905 and 1906, and were designed by the modernist architect Antoni Gaudí.
Located at 42.2536, 1.975 (Lat. / Lng.), about 12 miles away.
1906 establishments, Antoni Gaudí buildings, Gardens in Catalonia
Pedraforca is a mountain of the Pyrenees, located in the comarca of Berguedà. The mountain's unique form, along with the fact that it is not visibly connected to any other adjacent mountains or ridges, has made it one of the most famous and emblematic mountains in the autonomous community of Catalonia, Spain.
Mountains of Catalonia, Pre-Pyrenees
La Tossa
La Tossa is a mountain of Catalonia, Spain. It has an altitude of 887 metres above sea level.
Located at 42.3167, 1.9 (Lat. / Lng.), about 6 miles away.
Mountains of Catalonia
Esteve Pharmacy
The Esteve Pharmacy is a medieval pharmacy and museum located in the town of Llívia, in the comarca of Cerdanya, Catalonia, Spain. Llívia is a Spanish exclave within the French region of Pyrénées-Orientales.
Located at 42.465, 1.98198 (Lat. / Lng.), about 10 miles away.
Pharmacies, Pharmacy museums, Cerdanya (comarca), History museums in Catalonia
La Cerdanya Aerodrome
La Cerdanya Aerodrome is an airfield located in the Catalan town of Alp, in the Cerdanya county. It was founded in 1971 with the establishment of the now-disappeared Aero Club de la Cerdanya. The Aerdrome grew because of the gliding activity of the Centre de Vol a Vela La Cerdanya, which later became a section of the Aero Club Barcelona-Sabadell.
Airports in Catalonia, Cerdanya (comarca)
Bolvir is a village in the province of Girona and autonomous community of Catalonia, Spain. The municipality covers an area of 10.34 square kilometres and as of 2011 had a population of 393 people.
Populated places in the Province of Girona
Isòvol is a village in the province of Girona and autonomous community of Catalonia, Spain.
Urús is a village in the province of Girona and autonomous community of Catalonia, Spain.
Montellà i Martinet is a village in the province of Lleida and autonomous community of Catalonia, Spain.
Populated places in the Province of Lleida
Prullans
Prullans is a village in the province of Lleida and autonomous community of Catalonia, Spain.
Riu de Cerdanya
Riu de Cerdanya is a village in the province of Lleida and autonomous community of Catalonia, Spain.
Located at 42.3475, 1.8275 (Lat. / Lng.), about 2 miles away.
Grans Magatzems Pyrénées
The Grans Magatzems Pyrénées ('Pyrénées Hyper Centre), also known as Pyrénées Andorra, Pyrénées Department Store or just Pyrénées, is a major department store situated in Andorra la Vella, in Andorra.
Companies of Andorra, Department stores
Cadí Tunnel
Cadí Tunnel is a toll road tunnel in Catalonia, Spain, connecting the comarques of Cerdanya and Berguedà. The tunnel, with a length of 5 kilometers, is part of the C-16 highway and E-9, running under the Serra del Cadí mountain range in the Pre-Pyrenees.
Berguedà, Buildings and structures in Catalonia, Cerdanya (comarca), Pyrenees, Road tunnels in Spain, Toll tunnels, Transport in Catalonia, Tunnels completed in 1984
These are some bigger and more relevant cities in the wider vivinity of Isòvol.
Guardiola de Bergueda
Llivia
el Pont de Bar
Borreda
Pi: Sta. Magdalena de Serinyà, Pi (source)
Bellver de Cerdanya › South-East: Cataluña − Vista Tossa d'Alp estació esquí Masella, Bellver de Cerdanya (source)
Webcams provided by webcam.travel are under the copyright of their owners.
Isóbol, Isòvol
These are the most popular locations in Spain on Tripmondo.
Castello de la Plana
Olopte
Baltarga
Prats
Beders
Sanavastre
Bellver de Cerdanya
Coborriu
Talltendre
Soriguerola
Escadarchs
Girult
el Vilar d'Urtx
Santa Eugenia de Nerella
La Zona Residencial del Golf
Urtx
Ardovol
Ventajola
Queixans
Riutes
A traveler without observation is a bird without wings.
Moslih Eddin Saadi
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Q: Why will `read "1" :: Maybe Int` type check? I wonder why read "1" :: Maybe Int will type check and throw an exception in runtime.
Is it possible that read can ever return a Maybe a? That is what Text.Read.readMaybe is supposed to do.
Prelude> read "1" :: Maybe Int
*** Exception: Prelude.read: no parse
A: In short: you parse the textual representation of the Maybe a type, not a as a non-total function where Nothing is used to specify a parse failure.
Well read is usually the opposite of show. It will thus parse a representation of an object, that is frequently how you would write the object as a cascade of data constructors into an object.
Now Maybe a is a type of the Show family, given the elements it wraps are an instance of Show as well, something like:
instance Show a => Show (Maybe a) where
show Nothing = "Nothing"
show (Just x) = "Just "++ show x
(In reality it is a bit more complex, since it will also introduce brackets in case you wrap a Just 1 in a Just for example).
So the opposite can be parsed as well. For example:
Prelude> read "Nothing" :: Maybe Int
Nothing
Prelude> read "Just 5" :: Maybe Int
Just 5
So a Maybe a as a type of read is not meant for a "non-total" function, but to parse the textual representation of a Maybe a type.
So it parses strings with a prefix "Nothing" and "Just" (and also can parse some such "expressions" with brackets).
A:
I wonder why read "1" :: Maybe Int would type check
Because "1" has the type String and is thus acceptable as an argument to read and Maybe Int implements Read and is thus acceptable as a return type of Read.
and throw an exception in runtime.
Because "1" is not a valid string representation of a Maybe Int.
Is it possible that read can ever return a Maybe a?
Yes, for example read "Just 42" :: Maybe Int is Just 42 and read "Nothing" :: Maybe Int is Nothing.
Basically any string that you might get out of show x where x :: Maybe Int can also be fed as an argument to read to get a Maybe Int.
Or more generally, any output of show x where x :: T and T is an instance of Show and Read, can probably be fed to read to get back a value of type T - though of course instances can be defined arbitrarily, so not every type that implements Read and Show necessarily adheres to that "contract".
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Q: When the jQuery dialog is on I do not want the user to interact with the background If the user clicks an external link, the jQuery UI dialog appears with "ok" and "cancel" buttons and when they hit "ok" it should take them to the external site.
Everything is working as expected, but the problem is with the modal:true; when the dialog is on the user is able to work on the background and I want the background to be grayed out when the popup is on.
$(window).on('load', function(){
$.expr[":"].external = function(a) {
var linkhn = a.hostname.split('.').reverse();
var linkHref = linkhn[1] + "." + linkhn[0];
var domainhn = window.location.hostname.split('.').reverse();
var domainHref = domainhn[1] + "." + domainhn[0];
return !a.href.match(/^mailto\:/) && !a.href.match(/^tel\:/) && linkHref !== domainHref;
};
$("a:external").addClass("ext_link");
});
$(document).ready(function(){
jQuery(document).on("click", ".ext_link", function () {
$("<div>Thank you for visiting You are now being taken to an external site. </div>").dialog().attr('id','dialog-confirm').css('display','none');
var link_val = this;
$('#dialog-confirm').dialog({
title: "External Link",
height: "auto",
width: 410,
resizable: false,
modal: false,
buttons: {
"Ok": function() {
window.open( link_val.href); $(this).dialog("close"); $(this).dialog('destroy').remove();
},
Cancel: function () {jQuery(this).dialog("close"); $(this).dialog('destroy').remove() ;}
}
}).dialog("widget").find(".ui-dialog-titlebar").hide();
return false;
});
});
A: You can use another div which opens up and covers entire page, the below code is written in such manner.
Not disturbing much of your code, I've added <div> which will be hidden on page load. This <div> will be shown when the popup opens, and same <div> will be hidden when dialog closes.
$(document).ready(function() {
jQuery(document).on("click", ".ext_link", function() {
$('#scrLoader').show();
$("<div>Thank you for visiting You are now being taken to an external site. </div>").dialog().attr('id', 'dialog-confirm').css('display', 'none');
var link_val = this;
$('#dialog-confirm').dialog({
title: "External Link",
height: "auto",
width: 410,
resizable: false,
buttons: {
"Ok": function() {
window.open(link_val.href);
$(this).dialog("close");
$(this).dialog('destroy').remove();
},
Cancel: function() {
$('#scrLoader').hide();
jQuery(this).dialog("close");
$(this).dialog('destroy').remove();
}
}
}).dialog("widget").find(".ui-dialog-titlebar").hide();
return false;
});
});
#scrLoader {
background-color: #333;
opacity: 0.8;
position: fixed;
left: 0px;
top: 0px;
z-index: 100;
height: 100%;
width: 100%;
overflow: hidden;
background-image: url('your path to a loader gif');
background-position: center;
background-repeat: no-repeat;
}
<script src="https://code.jquery.com/jquery-1.11.1.min.js"></script>
<script src="https://code.jquery.com/ui/1.11.1/jquery-ui.min.js"></script>
<link rel="stylesheet" href="https://code.jquery.com/ui/1.11.1/themes/smoothness/jquery-ui.css" />
<input type="button" class="ext_link" value="click me" />
<div id="scrLoader" style="display: none;" hidden="true"></div>
You can also a GIF, like a loader GIF, which will be displayed when that particular div is open, so that user understands that some process is going on.
Hope this helps.
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Q: using grunt, is it possible to compile and output a single changed file to a different directory? Many coffee source files in /assets/src/coffee etc (./child/paths and so on) and I'd like to output them to assets/js/ and assets/js/child/paths.
It looks like I've gotten close, but it's not working. Using grunt-contrib-coffee and grunt-contrib-watch.
grunt.initConfig
watch:
coffee:
files: '<%= coffee.src %>',
tasks: 'coffee:dev'
options:
nospawn: true
coffee:
src: 'assets/src/coffee/**/*.coffee'
dev:
options:
sourceMap: true
files: [
expand: true
cwd: "assets/"
src: "/src/coffee/**/*.coffee"
dest: "../js/"
ext: ".js"
]
grunt.loadNpmTasks "grunt-contrib-coffee"
grunt.loadNpmTasks 'grunt-contrib-watch'
# Default task.
grunt.registerTask "default", "watch"
grunt.event.on('watch', (action, filepath) ->
(grunt.log.writeln('\n'+ filepath + ' has ' + action))
dest = "#{path.dirname(filepath.replace("src/coffee", "js"))}"
grunt.config(['coffee', 'dev', 'files', 'src'], [filepath])
grunt.config(['coffee', 'dev', 'files', 'dest'], [dest])
(grunt.log.writeln("src: #{grunt.config(['coffee', 'dev', 'files', 'src'])}"))
(grunt.log.writeln("dest: #{grunt.config(['coffee', 'dev', 'files', 'dest'])}"))
)
Ok, so the output of that looks like:
assets/src/coffee/projAlpha/dl.coffee has changed
src: assets/src/coffee/projAlpha/dl.coffee
dest: assets/js/projAlpha/dl.coffee
but the file actually ends up in: assets/src/coffee/projAlpha/dl.coffee... and it's coffee script. It should be in assets/js/projAlpha/dl.js.
I've gotten the grunt coffee utility to compile all the files at once and put them in the right place. I'd rather they got compiled one at a time though, since I've got a few files now and am adding more all the time.
A: In your glob-pattern file path config, I notice 2 problems:
*
*The glob-pattern options do not come under the "files" key, but
directly under the options key.
*The CWD is only meant for the src files. The dest directory does not
use cwd, so you must specify the full path from the base directory
(where your Gruntfile is).
dev:
options:
sourceMap: true
expand: true
cwd: "assets/src/coffee/"
src: "**/*.coffee"
dest: "assets/js/"
ext: ".js"
This will move, for example, assets/src/coffee/User/controller.coffee to assets/js/User/controller.js.
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Description About Me For Facebook
In fact, following this simple formula below is a great way to writing compelling product descriptions: [Paragraph(s) of Prose] + [Bulleted List of Specs or Product Features] = [Engaging Product Description] 3. The ad format with the lowest CTR is the Inline Like format, which has an average CTR of 0. It is also one of the largest source of traffic for many websites. And all Portals come with Alexa Built-in. Let's change how the world travels, together. But if you think your online options are limited to sites such as Craigslist and eBay, you might be overlooking an even easier option that you probably use every day: Facebook. Your handmade jewelry descriptions have to persuade someone that your jewelry is worth buying And just making a list of materials just doesn't go very far. The printing guide, no trim pieces that overlap and make it quick to put together. The meta description is a snippet of up to about 155 characters - a tag in HTML - which summarizes a page's content. When you share a link on Facebook, the service will automatically set the title, and the description for you. Here's the latest and greatest advice about Facebook events, complete with updated screenshots. They're third-party extensions that non-Facebook developers released for free. Having a great Facebook landing page can also help to engage new users from the first interaction. you can add a short description, set up a group email. This can be a web app that runs in your browser (such as Facebook itself, or a 3rd party tool like Streamyard or BeLive) or an app that runs on your Mac or PC (usually known as an encoder). The kind of. Does anybody know if there is an authoritative list of fields that can be returned by the Facebook Social Graph API? For example the fields returned by an Author object are different to a Company o. When you sign in to your Google Account, you can see and manage your info, activity, security options, and privacy preferences to make Google work better for you. Discover more every day. I am convinced that life is 10% what happens to me and 90% how I react to it. After you've entered these details, you're prompted to upload your profile photo (180 x 180 pixels) and add the new page to your favorites so you can access it from your left sidebar when logged in. Join the Action NOW!. Which one is your favorite? Organize Your About Me Page Into Sections. If it's happening anywhere, it's happening on Twitter. SIGN & SHARE AT – Petition · Make audio description available on ALL films, TV programmes and streaming services. In fact, following this simple formula below is a great way to writing compelling product descriptions: [Paragraph(s) of Prose] + [Bulleted List of Specs or Product Features] = [Engaging Product Description] 3. The purpose of a product description is to supply customers with important information about the features and benefits of the product so they're compelled to buy. Express your self with short and deep meaningful Quotes & Sayings. See Detail Online And Read Customers Reviews Job Description Facebook prices over the online source See people who buy "Job Description Facebook" Make sure the store keep your personal information private before buying Job Description Facebook Make sure you can proceed credit card online to buyJob Description Facebook plus the store protects your. Feb 05, 2009 · "Other types of content, like photos or news stories, have spread rapidly and widely on Facebook, but this is the first time I've noticed a note gain such distribution," Brandee Barker, a. On your Pagevamp site, it appears on your Home Page and/or About Page (depending on your design theme). I'll miss you, of course, come back for cool fonts for Facebook and Instagram at least!. It rarely appears in search results, unless it's voluntarily searched for. These add-ons are not official Facebook apps. Learn how to use the Facebook brand in your marketing. CREATING AN EVENT FROM YOUR PERSONAL PAGE Includes instructions for both public and private/secret events! 1. You can also try out some other best and popular facebook statuses later on. 7 Tactics for Writing the Best Facebook Posts *Every Time* 1. The Voyeurs and the narcissistic posters are the ones that really annoy me. 49 and LA MC ch. Profile definition is - a representation of something in outline; especially : a human head or face represented or seen in a side view. I am a warm, caring, loving & trustworthy person. Hoover's novels fall into the New Adult and Young Adult contemporary romance categories, as well as psychological thriller. We'll examine what makes them particularly effective, as well as ways you can make your own Facebook ads more compelling. This allows me to manually override what is sent to Facebook. The faster you learn to advertise on Facebook, the sooner you'll unlock the full potential of social media advertising. The title, description and thumbnail image all look perfect. View the profiles of people named Find Friends. Our mission is to give people the power to build community and bring the world closer together. Released on Aug. Be sure to like the Page yourself. Let me unpack that. Facebook isn't in its infancy anymore and your status updates shouldn't be either! It's time to get savvy about writing status updates that intrigue, interest, and inspire your friends and. #1 Free Poker App. Magnum Energy ME-MGT-AC-EXT AC Extension Cable The AC Extension Cable is used to provide connection between micro-inverters in the same branch circuit that are more than 6 feet apart. Late July is the sweet spot of summer. For web professionals, our "About me" page can be critical in establishing a true connection with potential clients, and it can set us apart from a sea of other designers and developers. "A description is an arrangement of properties, qualities, and features that the author must pick (choose, select), but the art lies in the order of their release—visually, audibly, conceptually—and consequently in the order of their interaction, including the social standing of every word. "I can check what they have to say about a film. Create a Facebook page for your brand or business. Microsoft account. Search engines show the meta description in search results mostly when the searched-for phrase is within the description, so optimizing the meta description is crucial for on-page SEO. Welcome to Microsoft Support Welcome to Microsoft Support What do you need help with? Windows. Led by our athletes, musicians, employees, distributors and fans, Monster is a lifestyle in a can!. If you need online forms for generating leads, distributing surveys, collecting payments and more, JotForm is for you. Medical Office Receptionist Job Responsibilities:. And, Facebook offers you a diverse range of templates depending on your taste and needs. Here's the latest and greatest advice about Facebook events, complete with updated screenshots. me profiles don't get your inspiration juices flowing I don't know what will. The ad format with the lowest CTR is the Inline Like format, which has an average CTR of 0. No matter what product or service your business provides, you are going to need a strong presence on social media. The latest Tweets from Facebook (@facebook). Feel free to revise this job description to meet your specific job duties and job requirements. Here is a sample "About Me" page that answers these questions: Hi, I'm Jane Smith and I write TransitionMomBlog (who Jane is) to help women make the transition from full-time mom to successful entrepreneur (the reader's problem or goal). Like public groups, everyone can search for and view the name, description and member list of a closed group. So remember to add your most notable keyword at least once or twice in your copy, and don't forget to fill the title and description of the page:. A Twibbon Campaign is your very own microsite where users can support your cause, brand or organisation in a variety of ways. In May 2007, Facebook opened up its developers' platform to allow third-party developers to build applications and widgets that, once approved, could be distributed through the Facebook community. It piques the interest of a listener who invites you to "Tell me a little about yourself," and it provides a brief and compelling answer to the question "Why should I hire you?". Use our online form creator to build contact forms, surveys, event registrations, and more. Schedule an appointment Schedule an Over 1 million entrepreneurs and consultants use about. But since an About Me page is often the first stop your potential photography clients make on a webpage, it's worth putting in the effort to make a memorable one. Let me give a try to see what kind of image you have about me through my self-description. This can happen when a YouTube video is entered into a post before the video has finished processing or while the video is private. Comment on Local Business Posts - If you want a Facebook strategy that really delivers for insurance agents, use Facebook as your business and go to other local business Facebook pages and make comments. Optimize Facebook fan page status updates. These guidelines outline the general rules for using Facebook's brand assets and showcasing Facebook content. Lupe Arias, a Mexican immigrant who lives in Healdsburg and works in packaging for a local winery, said she's been keeping up with the latest through Cal Fire's Facebook page, where the agency is. A Facebook page is your brand name. The process is simple, but requires a definite plan! Set up an event on your Facebook business page – everything happens inside the event. I cannot find a character limit for the Long Description on the Facebook About Page. What is a Facebook short description? The "Short Description" is the brief introduction to your business that shows up on the "About" section of your Facebook Page. CREATING AN EVENT FROM YOUR PERSONAL PAGE Includes instructions for both public and private/secret events! 1. I like to help people to find solutions to their problems & also do a lot of social service at NGO's as I have completed my masters in Social studies. Facebook sort of worked (maybe had to do with wifi) but acted super weird and Messenger wouldn't. I cannot do much to help you with the first two but I can help with hacks for writing your "about me" description and the inspiration part. I am convinced that life is 10% what happens to me and 90% how I react to it. Optimize growth through omni-channel analytics. Tried this one for my blog once :D Aila! In the abject ability of this asylum called world to abhor abnegation of acrimonious accusations, there lies an agile and aggresive, almost an almighty abomination of the aisle called antagonism against. World Series of Poker Game - WSOP. If you need online forms for generating leads, distributing surveys, collecting payments and more, JotForm is for you. Surface devices. UPDATE: On August 14, 2019, Facebook changed privacy options for groups. Personally I've opted for a mix of making the reader a hero and playing on emotional outcome! Key Words Focus:. Over the next few months, we'll be making updates to ranking so people have more opportunities to interact. Facebook groups are powerful. NDERF is the largest NDE website in the world with over 4600 Experiences in over 23 Languages! With your help, NDERF has over half a million readers a month to spread the word of love, peace and global unity. Facebook earns an average of $5. Hello dosto ummid hai aap ache hoge. As the 'me too' movement affirms empowerment through empathy and community-based action, the work is survivor-led and specific to the needs of different communities. If you do not like it, or you want to set this information yourself, this tutorial will help you. Wufoo's online form builder helps you create custom HTML forms without writing code. Like public groups, everyone can search for and view the name, description and member list of a closed group. The wikiHow Tech Team also. Help? Related Help Center FAQs; What tools does Facebook provide to help me protect my intel Another website is offering to help me with my Facebook acco What tools does Facebook provide to help me enforce my intel What categories of my Facebook data are available to me?. Strawverry Supreme's Blog :)title> var a1 = ;var a2 =;var. Tried this one for my blog once :D Aila! In the abject ability of this asylum called world to abhor abnegation of acrimonious accusations, there lies an agile and aggresive, almost an almighty abomination of the aisle called antagonism against. This item is extremely nice product. We provide also a Video Downloader Chrome Extension. In this post, we've outlined 7 things you need to know about the new Facebook update. Share On facebook Share On vk Can You Identify The "Stranger Things" Character From A Simple Description? "It is Dustin's pet demogorgon. There are over ten different Facebook ad types that you can. To adjust the text that shows up here, follow along. I am a student in the United States. Using Facebook to spread the word about your fundraiser is one of the most effective fundraising strategies out there. "Look at my cute children!", "look at me on vacation!", "look at me at the bar!". Create a Facebook group for your cause or passion. Everyone can find and view the group without needing approval to join. Collectively, we connect millions of buyers and sellers around the world. Facebook gives people the power to. Find your yodel. Your about page is one of the most visited pages on your website. Apply Now; JOHN HEALD'SBLOG Know you want to cruise, but not sure what it's really like?. me is a shortened URL service operated by Facebook that redirects users to a person, page, or bot in Messenger. This Moment is Yours Ashford University is an Accredited Online University offering Associate, Bachelor's, Master's, and Doctoral Degrees. She wants to have a meeting with me about my facebook post with our HR department… i am not willing to participate in this, and i dont understand HOW or WHY the HR department is even taking her seriously?…i know facebook isnt protected by any privacy law, but what about freedom of speech ? this is crazy. Note: This item is sheer. Collectively, we connect millions of buyers and sellers around the world. Sign in - Google Accounts. Youtube to facebook thumbnail generator at yt2fb. Although lacking some features of a true IM, it is a revamped and improved version of the Facebook chat bar. Create a professional website for free with the Website. Facebook Video Downloader Online, Download Facebook Videos and Save them directly from facebook to your computer or mobile for Free without Software. Lupe Arias, a Mexican immigrant who lives in Healdsburg and works in packaging for a local winery, said she's been keeping up with the latest through Cal Fire's Facebook page, where the agency is. All of our SDKs and products interact with the Graph API in some way, and our other APIs are extensions of the Graph API, so understanding how the Graph API works is crucial. Facebook Toolbar integrate your Facebook life into your browser. Your About Me Page should be ALL about the value you give to your readers. Quotes Facebook Covers, trendycovers. When writing a business plan, an important task is to clearly describe your business and exactly what it will involve. me over another platform? Which plan is best for me? How do I transfer my domain to a different website? What's my username? Domain configuration specifics; What are Google Analytics ID, Custom Title, and Meta Description? How do I connect my GoDaddy domain? Browse all articles. There are many ways to update Open Graph tags. If you do not like it, or you want to set this information yourself, this tutorial will help you. Whether you're looking to gain a lot of initial support for your fundraiser or you're trying to gain more momentum after a slump, Facebook fundraising can make a real difference. " discount Innovation Researcher Facebook. If you share a page on Facebook, it will look for what's known as open graph markup on your website. That can be due to people not liking your page anymore, or Facebook cleaning up their database. This brief section helps long lost friends quickly catch up to your status in. Another feature that surprisingly isn't here but is sort of an obvious one (at least to me) is a connection between Facebook events and the artist/band's own events – it seems only logical. Hoover's novels fall into the New Adult and Young Adult contemporary romance categories, as well as psychological thriller. By the end of this chapter, you will know how to use the Facebook Ads Manager and how to set up your first Facebook ad campaign. Posted by Melissa Thompson. Create an account or log into Facebook. I love reading people's about page especially those who are in the same industry as me. I am a warm, caring, loving & trustworthy person. It's okay to write a meta description that cuts off halfway through the sentence. Monster Energy is way more than an energy drink. (We've created an in-depth guide to show you exactly how to create Facebook ads!) Take me to Chapter 3. Here is a simple All About Me activity page that is perfect for kids in preschool, pre-k, and kindergarten. Not anymore, with the likes of Twitter's Periscope and Facebook's Facebook Live! From your smartphone or computer you can broadcast live from your home or office, and potentially reach millions of people round the world – instantly!. **The "about me"-page** is one of the most overlooked pages in development and one of the highest ranked pages on many websites. The only shoes you can occupy are your own. Include clearly tagged facts in the description. you can add a short description, set up a group email. Let's change how the world travels, together. Your About page is the soul of your site. Facebook started in the United States as a way for some college kids to stay in touch when they had left campus - and it's evolved since then to become one of the largest social networks in the. It is important to post these links from your business page, as doing so from a personal page can lead to your account being suspended. Facebook Google. They're a perfect place to start real conversations about things that matter to you. There are over ten different Facebook ad types that you can. Publisher's Description. People want to feel like they are human and not just a case number. Ladies Attain Incredible Sexual Pleasure in Seconds By: Paul Rodgers. Here is a simple All About Me activity page that is perfect for kids in preschool, pre-k, and kindergarten. I'm completely swamped with work this week. Let's change how the world travels, together. Welcome back to Twitter. So we created Workplace, a collaboration tool that lets you and your coworkers: - Create groups for your teams and projects, and use them to share unlimited project updates, files, videos, photos, ideas and more. Fast Company is the world's leading progressive business media brand, with a unique editorial focus on innovation in technology, leadership, and design. It's a moment in time when life is simple, pure & good. Detailed, precise instructions with full color photos to teach and guide you along the way are perfect for beginners. Get the Me & My Big Ideas® Small Talk™ Embellishment, I Heart Dad at Michaels. Used 14 Buick Encore Convenience Read Description for sale in Jacksonville - 14 Buick Encore Convenience Read Description posted by Kendra Hamilton in Jacksonville. Having a great Facebook landing page can also help to engage new users from the first interaction. Here are some tips for making those product descriptions more likely to make the sale. That's why I'm concerned. For years, I pictured him slipping pieces of paper with numbers into actual boxes, similar to ballot boxes. The new "Sell" feature, which is. News, email and search are just the beginning. Hoover's novels fall into the New Adult and Young Adult contemporary romance categories, as well as psychological thriller. Sorry it's taken a while for me to get back to you. A simple description would have gone a long way. I'm not weird, I'm just cooler than you. Dana of TheWonderForest. This post will give you 17 killer Facebook post ideas for small business owners that are working NOW, by generating lots of likes, shares and, comments, as well as increasing click throughs to your website. That's why spending time to hone your description is so important to your ultimate longterm success. Take a look at some of the best Facebook ad examples we could find. 12 hours ago · Still, I wanted to go to a gay club and find out for myself. The latest Tweets from Facebook (@facebook). So, take advantage of the option when Facebook prompts you to "Write something" since that text will be considered the SEO title for that update. /{user-id}/feed The feed of posts (including status updates) and links published by this person, or by others on this person's profile. The Facebook Lite app is small, allowing you to save space on your phone and use Facebook in 2G conditions. "Making sure that what. Yet, it will still serve your website's overall SEO. Like public groups, everyone can search for and view the name, description and member list of a closed group. I'll miss you, of course, come back for cool fonts for Facebook and Instagram at least!. I love reading people's about page especially those who are in the same industry as me. Make yourself some and thank me later 😉 This pdf pattern is a beautiful, computer drafted, LAYERED and color coded pattern. You can use these to help you get started to create an engaging about page. A home for film, music, art, theater, games, comics, design, photography, and more. "A description is an arrangement of properties, qualities, and features that the author must pick (choose, select), but the art lies in the order of their release—visually, audibly, conceptually—and consequently in the order of their interaction, including the social standing of every word. Facebook; Twitter. GENERATE STATUS POST TO FACEBOOK Find celebrity. You can find things like short posts about this site, fb profile quotes, funny and creative fb bio status and unique profile for awesome intro quotes and best bio idea, intro, About Me & Intro Quotes - Short Bio, Funny & Clever. SIGN & SHARE AT – Petition · Make audio description available on ALL films, TV programmes and streaming services. "I can check what they have to say about a film. Description path. So— Make your answer like the first of these tell me about yourself examples:. These 7 tips show you how to improve your "about" page to build strong connections with more of your ideal clients At last, you have a chance to get a new client. Facebook Page Manager Job Description On Sale. Optimize Facebook fan page status updates. The new "Sell" feature, which is. Facebook Manual Content Sharing. Use the wizard to set up your Facebook page. I couldn't care less about my current friends on Facebook, they are always calling me and stopping by my house so I don't need to watch them on Facebook. HubSpot offers a full platform of marketing, sales, customer service, and CRM software — plus the methodology, resources, and support — to help businesses grow better. How to create a Facebook page for your Paparazzi Business If you already have a Facebook profile, it's really quite simple. Help your darling drift off to dreamland in this cozy pajama set complete with coordinating scrunchies. " Rebecca Shipton, Social Media Executive, Gymshark. How to Add and Manage Facebook Photos Post photos and albums to share with family and friends. Here's a walkthrough of the basics for creating, joining and leaving groups. The O Mag Insiders are O's on-the-ground ambassadors, hand-selected from thousands of applications and representing the unmatched diversity of O's readers. It's easy! Log in with Facebook. Guaranteed to make you smile!. I just needed a little bit of information to explain what $350 got me in this little black box. You can edit your Facebook About page by going to the Edit Page on the Admin Panel then selecting Update Page Info. Profile definition is - a representation of something in outline; especially : a human head or face represented or seen in a side view. With facebook you can track who looks at your pictures and block the person if you find out if some creeps been looking at your profile. Facebook tracks scary-specific details about your life. CREATING AN EVENT FROM YOUR PERSONAL PAGE Includes instructions for both public and private/secret events! 1. The wikiHow Tech Team also. Turner has a culture that promotes an injury-free environment and provides the safest workplace possible for our employees, subcontractors, clients and others who enter our construction sites. I don't want anything too specific since it is the internet, though, and I like things that are some what humorous. No matter what product or service your business provides, you are going to need a strong presence on social media. #1 Free Poker App. Other users, like Colin McEvoy, an avid movie buff, log in to check on user-submitted movie reviews. This area contains some of the words you put in the Short Description on the Page Info section when you started your Page. Need some inspiration to pump up your Facebook marketing? As the Facebook news feed continues to change, it's important to figure out how to make the platform work for you. I cannot do much to help you with the first two but I can help with hacks for writing your "about me" description and the inspiration part. A great "about" page can make a powerful connection with your prospective photography clients. Whenever you publish a new blog posts Weebly will automatically post the link on your Facebook profile or page. By the time you finish this post, you'll have several ideas you can apply to your own campaigns. Facebook and Instagram gave away the presence of the 'Japan pig' seahorse in Taiwan. I had heard from one of my best gal pals (and Facebook marketing extraordinaire) Amy Porterfield that quote images had a tendency to get shared a lot and sometimes go viral. Facebook alters video to make people invisible to facial recognition Facebook News launches for a subset of U. Free People, a specialty women's clothing brand, is the destination for bohemian fashion that features the latest trends and vintage collections for women who live free through fashion, art, music, and travel. I truly had no idea that this feature existed, so was unsure what it really meant. it gets buried in the full About description that's not visible unless a person clicks on the About. Here are 28 things you need to know about previewing the new design, timeline cover photo, updates, the admin panel, Insights, and custom content. Most inspiring Facebook profile quotes for your cool Facebook bio. When you join Business Manager, coworkers can't view your personal Facebook profile unless you approve their friend requests. On your Pagevamp site, it appears on your Home Page and/or About Page (depending on your design theme). Optimize Facebook fan page status updates. "I have friends like me who are real movie geeks," McEvoy says. Reminds me of a story from when I was little, my dad told me that he didn't want to be an accountant because he didn't want to have to put numbers in boxes all day long. Be the first to review "ME 2017" Cancel reply. Our diverse team is changing the way people connect to the places they visit, so anyone can create their dream vacation. Need some inspiration to pump up your Facebook marketing? As the Facebook news feed continues to change, it's important to figure out how to make the platform work for you. On iOS you can even add an emoji keyboard and type them easily withought having to use FSymbols to access them. #If you are "Today, if you do not want to disappoint, Check price before the Price Up. But they each have distinctions that make them valuable for certain types of marketing. I use a WordPress plugin called Yoast SEO. So, take advantage of the option when Facebook prompts you to "Write something" since that text will be considered the SEO title for that update. The evangelists are harmless even if they tend to over-post. Also these about me status fit to describe your selfies and profile pictures, even you can use them better as Instagram captions. Set in an alternate history where "superheroes" are treated as outlaws, Watchmen embraces the nostalgia of the original groundbreaking graphic novel of the same name while attempting to break new ground of its own. With facebook you can track who looks at your pictures and block the person if you find out if some creeps been looking at your profile. A Twibbon Campaign is your very own microsite where users can support your cause, brand or organisation in a variety of ways. You can craft your Pages in numerous ways - short and long descriptions, a mission statement, product links, milestones, etc. A fully integrated Facebook store. More than 12M "Me Too" Facebook posts, comments, reactions in 24 hours children when a friend of a friend on Facebook suggested something that struck her as a great way to elevate the Harvey. Read or Stay Baffled Tuesday, February 24, 2009. Our mission is to give people the power to build community and bring the world closer together. In a world that's becoming increasingly connected through the Web, it's important that you engage your audience in a personal and friendly way, otherwise you risk just being another faceless web designer among a sea of websites. will consider for employment qualified applicants with criminal histories in a manner consistent with the requirements of SFPC Art. make me a status. I started TransitionMomBlog in 2004 (Jane's. All of our SDKs and products interact with the Graph API in some way, and our other APIs are extensions of the Graph API, so understanding how the Graph API works is crucial. This tell me about yourself example job offer shows how: Tell Us About Yourself Example Job Description. For the first time this doesn't include. Hey, this is my homepage, so I have to say something about myself. Take a look at some of the best Facebook ad examples we could find. "By the end of the first year I was visibly pregnant, and the principal did what principals did in those days: wished me luck, showed me the door, and hired someone else for the job," she said at. Even though Messenger is easily accessible through the Messenger website, your Facebook account on your computer, and the mobile apps, you can install add-ons in some browsers that are designed to make it even easier to use. When entering a YouTube URL to Facebook or Twitter, the auto-populated video title, description, or thumbnail may occasionally be blank or out of date. Sharing the sad feelings can reduce the burden of heart, share sad status on facebook to let your friends know that you are feeling sad. Facebook earns an average of $5. Cover photos for Facebook timeline images. WhatsApp started as an alternative to SMS. Help your darling drift off to dreamland in this cozy pajama set complete with coordinating scrunchies. There are three types of groups on Facebook: public, closed, and secret. The New Facebook Pages with Timeline are here. So— Make your answer like the first of these tell me about yourself examples:. Free timeline images for your social media, blogs or apps: Facebook, Google+, Twitter, Blogger, Wordpress, Pinterest and more. As of March 2019, Facebook supports the Transgender Pride Flag emoji. Instantly reach the people in your life—for free. Does anybody know if there is an authoritative list of fields that can be returned by the Facebook Social Graph API? For example the fields returned by an Author object are different to a Company o. You (hopefully) go back to Facebook to test it out and there's the old thumbnail, hanging around when it's not wanted. Start a Campaign Find out more Since 2009, over 300,000 brands, charities and individuals have used Twibbon to increase awareness, raise money and create buzz around their campaign on Facebook and Twitter. If your group is smaller than 500 people, you can invite your entire group to the event by clicking Invite all members while creating your event. Simple as that. If you'd like your "About Me" page to include a CV, your best bet is to simplify and shorten it up a lot. My marketplace item doesn't show up for other people to view. For larger events, you must select the members you'd like to invite. Not anymore, with the likes of Twitter's Periscope and Facebook's Facebook Live! From your smartphone or computer you can broadcast live from your home or office, and potentially reach millions of people round the world - instantly!. Express yourself without being judged and make new friends. Strawverry Supreme's Blog :)title> var a1 = ;var a2 =;var. Like public groups, everyone can search for and view the name, description and member list of a closed group. Facebook earns an average of $5. will consider for employment qualified applicants with criminal histories in a manner consistent with the requirements of SFPC Art. The Facebook groups serve two purposes for women travelers: There's the crowdsourced rec aspect, sure ― how else are you going to know that Les Ombres has one of Paris' best, most Instagram-worthy views of the Eiffel Tower but that the food is only so-so?― but there's more to it than. Business Manager is a Facebook tool that helps organize and manage your business. MeWe is the Next-Gen Social Network. Your rating. On iOS you can even add an emoji keyboard and type them easily withought having to use FSymbols to access them. But, unknown to you, there's a. The Open Graph protocol enables any web page to become a rich object in a social graph. In this article I'll share Facebook pages from both large and small brands, and tips to incorporate their tactics into your Facebook marketing plan. Learn how to use the Facebook brand in your marketing. If you've tried this beef chili for a crowd or any other recipe on Cultured Palate please take a minute to rate the recipe and leave a comment letting me know how you liked it. Twitter biographies might be the ultimate creative-writing challenge. I respect those who respect me and forget those who forget me. Just go for job headings, dates, and a quick description of your work. I got up to about 30,000 characters (which is a small e-book) before I gave up. 7, 2019, rock band Tool's titular single from their new album Fear Inoculum currently holds the title, clocking in at a length of 10 minutes and 23 seconds. I've worked with mom bloggers for years. Facebook lets you share photos, videos, links, status updates, and much more with your friends. Enjoy the videos and music you love, upload original content, and share it all with friends, family, and the world on YouTube. There are multiple factors that make up a great Facebook page and it's important to consider all of them in the management of your own Facebook efforts. description}}. Hey, guys! I need ideas for my Facebook "About Me" section. Well not easy that easy to come up with the right SEO Title and Meta Brand Description, especially for a non native English speaker! But your simple example helped me understanding and applying your tips and tricks my company website. The fact-checkers, whose work is more and more important for those who prefer facts over lies, police the line between fact and falsehood on a day-to-day basis, and do a great job. Today, my small contribution is to pass along a very good overview that reflects on one of Trump's favorite overarching falsehoods. Namely: Trump describes an America in which everything was going down the tubes under Obama, which is why we needed Trump to make America great again. And he claims that this project has come to fruition, with America setting records for prosperity under his leadership and guidance. "Obama bad; Trump good" is pretty much his analysis in all areas and measurement of U.S. activity, especially economically. Even if this were true, it would reflect poorly on Trump's character, but it has the added problem of being false, a big lie made up of many small ones. Personally, I don't assume that all economic measurements directly reflect the leadership of whoever occupies the Oval Office, nor am I smart enough to figure out what causes what in the economy. But the idea that presidents get the credit or the blame for the economy during their tenure is a political fact of life. Trump, in his adorable, immodest mendacity, not only claims credit for everything good that happens in the economy, but tells people, literally and specifically, that they have to vote for him even if they hate him, because without his guidance, their 401(k) accounts "will go down the tubes." That would be offensive even if it were true, but it is utterly false. The stock market has been on a 10-year run of steady gains that began in 2009, the year Barack Obama was inaugurated. But why would anyone care about that? It's only an unarguable, stubborn fact. Still, speaking of facts, there are so many measurements and indicators of how the economy is doing, that those not committed to an honest investigation can find evidence for whatever they want to believe. Trump and his most committed followers want to believe that everything was terrible under Barack Obama and great under Trump. That's baloney. Anyone who believes that believes something false. And a series of charts and graphs published Monday in the Washington Post and explained by Economics Correspondent Heather Long provides the data that tells the tale. The details are complicated. Click through to the link above and you'll learn much. But the overview is pretty simply this: The U.S. economy had a major meltdown in the last year of the George W. Bush presidency. Again, I'm not smart enough to know how much of this was Bush's "fault." But he had been in office for six years when the trouble started. So, if it's ever reasonable to hold a president accountable for the performance of the economy, the timeline is bad for Bush. GDP growth went negative. Job growth fell sharply and then went negative. Median household income shrank. The Dow Jones Industrial Average dropped by more than 5,000 points! U.S. manufacturing output plunged, as did average home values, as did average hourly wages, as did measures of consumer confidence and most other indicators of economic health. (Backup for that is contained in the Post piece I linked to above.) Barack Obama inherited that mess of falling numbers, which continued during his first year in office, 2009, as he put in place policies designed to turn it around. By 2010, Obama's second year, pretty much all of the negative numbers had turned positive. By the time Obama was up for reelection in 2012, all of them were headed in the right direction, which is certainly among the reasons voters gave him a second term by a solid (not landslide) margin. Basically, all of those good numbers continued throughout the second Obama term. The U.S. GDP, probably the single best measure of how the economy is doing, grew by 2.9 percent in 2015, which was Obama's seventh year in office and was the best GDP growth number since before the crash of the late Bush years. GDP growth slowed to 1.6 percent in 2016, which may have been among the indicators that supported Trump's campaign-year argument that everything was going to hell and only he could fix it. During the first year of Trump, GDP growth grew to 2.4 percent, which is decent but not great and anyway, a reasonable person would acknowledge that — to the degree that economic performance is to the credit or blame of the president — the performance in the first year of a new president is a mixture of the old and new policies. In Trump's second year, 2018, the GDP grew 2.9 percent, equaling Obama's best year, and so far in 2019, the growth rate has fallen to 2.1 percent, a mediocre number and a decline for which Trump presumably accepts no responsibility and blames either Nancy Pelosi, Ilhan Omar or, if he can swing it, Barack Obama. I suppose it's natural for a president to want to take credit for everything good that happens on his (or someday her) watch, but not the blame for anything bad. Trump is more blatant about this than most. If we judge by his bad but remarkably steady approval ratings (today, according to the average maintained by 538.com, it's 41.9 approval/ 53.7 disapproval) the pretty-good economy is not winning him new supporters, nor is his constant exaggeration of his accomplishments costing him many old ones). I already offered it above, but the full Washington Post workup of these numbers, and commentary/explanation by economics correspondent Heather Long, are here. On a related matter, if you care about what used to be called fiscal conservatism, which is the belief that federal debt and deficit matter, here's a New York Times analysis, based on Congressional Budget Office data, suggesting that the annual budget deficit (that's the amount the government borrows every year reflecting that amount by which federal spending exceeds revenues) which fell steadily during the Obama years, from a peak of $1.4 trillion at the beginning of the Obama administration, to $585 billion in 2016 (Obama's last year in office), will be back up to $960 billion this fiscal year, and back over $1 trillion in 2020. (Here's the New York Times piece detailing those numbers.) Trump is currently floating various tax cuts for the rich and the poor that will presumably worsen those projections, if passed. As the Times piece reported:
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It was a dark and stormy night and Lee Crane had been on the hunt all day, and the day before. He wasn't happy about his lack of success, but Chief Sharkey and Riley, who were trying to help him, were not having anymore luck than he was. They had been kind enough to volunteer for this search and he wondered if they were regretting it now. As he ran for cover, he wondered if this lead would turn out to be as fruitless as all the others. Lee knew this bear was quite rare and that he wasn't the only person searching for it, but he'd never expected things to be anywhere near this difficult. He just hoped his efforts were going to be appreciated. After all, tomorrow was Christmas Eve.
When he reached the mall door and stepped inside, he saw it was a mad house of last-minute Christmas Shopping. Why did he always seem to be looking for a Christmas present for his mother the day before said holiday? And why, oh why, did Fiona Crane, every year, tell him that she really didn't want anything for Christmas, but if he happened to see this particular thing, well, he could pick it up for her. The particular thing, whatever it might be from year to year, always seemed to be the thing he was least likely to find, no matter where or when he looked. This year was no different. They had just gotten back from a month and a half at sea and instead of enjoying leave, he was off on another of these impossible quests. Lee was ready to quit and just buy his mother some jewelry or something else that he didn't have to chase all over southern California for.
As he entered the Hallmark store that he'd been directed to, he saw a mob of people, mostly women, descending on a bin that the store clerk had just put down and then retreated swiftly from. Lee was a brave man, but he wasn't foolhardy enough to plunge into that chaos. Just as he decided to wait for the surge to fade a bit, he spotted Sharkey in the thick of things, pushing his way forward with the rest of the group. Soon there was a general groan of disappointment and the remainder of the crowd began to drift away. An elderly woman who outweighed Sharkey by a good hundred pounds pulled at something blue that they both had a grip on, nearly pulling Sharkey over in the process. "I had it first!" she bellowed at him, swatting him over the head with her purse.
Sharkey's face started to turn red and he looked like he was getting ready to sock the woman when Crane decided he'd better intercede. "Chief!" he called as he started to hurry over. The woman took advantage of the distraction and yanked the white speckled blue form from the Chief and bumped past him toward the line at the cash register. Sharkey snarled and started after her with murder in his eyes when Lee stopped him, quietly saying, "Chief, she's a woman."
"No, sir, she's a Sasquatch in pumps!" Sharkey stated loud enough for everyone in the entire store to hear. As the woman turned and huffed in indignation, looking ready to pummel Sharkey with her purse again, Lee bustled Sharkey out into the mall. "I had it! I had it right in my hand!" Sharkey groaned once they were out of the store.
"It was a valiant effort, Chief, but let's try to keep the bloodshed to a minimum," Lee told Sharkey as he patted him on the shoulder. "Where's Riley?"
"He went into the mall to a kiosk that carried those bean bag guys, but with a premium price tag," Sharkey said, then began to lead the way. That made sense. Lee had told them to buy the bear, no matter what it cost and he would reimburse them. "I don't get it. What's so special about these fluff bags that people go more nuts over them than some other stuffed animal?"
"I don't know, Chief. You can ask my mother if you're really curious," Lee replied. Fiona had begun collecting the strangest things ever since he had gone off to Naval Academy, not that she hadn't always been a bit of a packrat. She had the most amazing scrap books of everything he had ever done that had been considered newsworthy. Now some rooms in her house looked like small museums and her beanbag animals in their little plastic boxes were forming an ever growing pyramid against one of her walls. She had taken great pride in introducing him to each one the last time he had been home to see her. He smiled, wondering how big that pyramid was now.
When they reached the kiosk in question, Riley was chatting up the pretty, young lady manning it, helping her bag a shopper's purchase. He noticed them approaching, said something to the girl, then left her and met them just a little away from the small booth. "Any luck, Riley?" Lee asked as they moved out of the way of the majority of mall traffic.
"No, sir," the young sailor replied. "Tina, uh, the girl there, she said that there hasn't been one of those blue bears with the white spots in her booth for a month and that most other stores are emptying them out as quick as they come in."
"Don't I know that," Sharkey grumbled.
Riley looked a little confused at Sharkey's comment, but he continued, "Anyway, Skipper, I talked to my folks to see if maybe they had any of those bears left or they knew anyone who did. My dad said that they're as dry out there as we are over here, that they've had those bears on order for months and have only gotten in about a fifth of their order because of the demand." Lee knew that Riley's parents owned a card store in Massachusetts just a little north of Boston.
"I appreciate that you called, Riley," Lee told him. That was when he remembered that Riley usually would go home if they got leave around the holidays. He had been so happy to have some help chasing around after this silly bear that he hadn't thought about how this was affecting the people aiding him. "Aren't you going home for Christmas?"
Riley gave him a sheepish look. "My flight is in the morning, sir."
Suddenly Lee began to feel a bit guilty. It was nearly eight o'clock. "Have you packed or even finished your own Christmas shopping, Riley?" he asked.
Riley rubbed the back of his neck. "Well, I did have a couple of things to kind of finish up, skipper, but..."
"You go on and do that, then, Riley. Thanks for all your help, but I'm about ready to give up on this whole thing. You have a nice holiday," Lee told the young sailor. Riley smiled and wished him and the Chief a merry Christmas before he moved off, disappearing into the milling crowd.
"You're not really giving up, are you, sir?" Sharkey asked. "We were so close!"
Lee shrugged, saying, "It's getting late, Chief. I'm going to go find her something else and call it a night. You probably have things to finish up yourself, maybe a flight to catch. It was good of you to help me out like this," Lee told him.
Sharkey frowned, plainly unhappy about the search ending like it had, but he fought off the expression and said, "Well, if you're sure, sir. Happy holidays."
"And to you, too, Chief," Lee told him. He found himself unable to help himself from grinning as Sharkey walked away muttering about how he'd had the lousy bear in his hands. Lee went to the nearest jewelry store and settled on earrings for his mother, hoping that she wouldn't be too disappointed that he'd failed to find her 'one little thing' this year.
The next morning, Christmas Eve, Lee went into the Nelson Institute to drop off a couple of little gifts for Admiral Nelson and for Katy, the Admiral's secretary. He'd picked them up last night when he'd finally admitted defeat on his search, along with a little something for Sharkey and Riley for at least trying to help him. He would give them their gifts when everyone returned to the base after the holidays. Once he left the Institute he would be going to the airport to catch him flight home. Katy was wearing a smile as he approached her desk, a strange smile, like she knew something he didn't, something funny. The Admiral's office door was opened, which meant he wasn't there, so Lee half wondered why Katy was still hanging around. He hadn't actually expected to see either of them.
"Happy holidays, Katy," he told her, then put the brightly wrapped box he had for her in front of her on her desk as he sat on the corner. "This one," he handed her the second box, "Is for the old, old man. The Admiral isn't keeping you here too late today, is he?"
Katy just continued to smile at him. "Oh, he told me not to even bother about coming in, but I was pretty sure you'd come in to drop off your gift to him last minute before you headed for home, just like you do every year."
"I don't buy you that good a Christmas gift, do I?" Lee asked with a grin of his own.
"You always get me something nice, Lee, but I stuck around because you owe petty cash fifty seven dollars and I want to make sure the books balance before I go enjoy my holiday," Katy said, resting her chin on one hand. Her face was still lit up with the same silly smile.
"What? Why would I..." Lee started, not understanding what the devil Katy was talking about or why it was amusing. Then, slowly, she lifted her free hand. In it was the blue polka dotted bear that he'd spent the last two days searching for. "Katy, where did you find it? How did you find it?" Lee asked, taking it gently from her. The tag on it's ear was in one of those little plastic protectors and it looked to be in perfect shape, as did the bear itself.
"When you were briefing Chief Sharkey and Riley on your bear hunt two days ago, I overheard what you were looking for. Every year, you go nuts looking for some silly thing, so I thought I'd give you a hand this year, especially since I know those silly bears are about impossible to find. I hit the Internet and I won an auction. I had them same day mail it and I charged it to the Institute petty cash account so that they'd send it right away," she said with the same smile she had been wearing when Lee had first been approaching her.
Lee hadn't even considered looking on a computer for this year's questing beast. He didn't even have a computer at home, never wanting to bother about it when he could type up any reports he had to do here at the Institute, in his office, and he'd never really thought about using the computer here for anything else. The only reason he didn't feel totally stupid was because Riley and Sharkey hadn't thought of it either. "Katy, I could kiss you. In fact, I think I will," Lee said, then gave Katy a warm kiss on the forehead. He fished out his wallet and wrote her a check for the bear. "You are a life saver. An absolute life saver."
Katy just shook her head, still grinning as she took his check, saying, "Merry Christmas, Captain."
Lee tossed the bear into the air and caught it lightly, grinning himself now. "It is now, Katy. It is now."
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