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The STDs of rock reunite in Tokyo
Pussy Cat Face by Steineria & Dustiphilis
TF-14 Pussy Cat Face - EP (2018)
After a 18 year hiatus, the STDs of rock, Steineria & Dustiphilis, have resurfaced in Tokyo, spreading a new EP stran of Pussy Cat Face among stray cats and featuring a double dose of Steineria (Ben's brother Dave on vocals).
released April 22, 2018
Vocals - Dave
Guitar - Ben
Drums/backing vocals - Dustin
All songs written and performed by Steineria & Dustiphilis
Recorded at SOUND STUDIO NOAH (Shinjuku branch) April 22, 2018
Produced, mixed and mastered by Dustiphilis
Executive producer - Steineria
Inspirational thanks to Cat Cafe Calico (Shinjuku) and Brian's Bar (Golden Gai)
©2018 Tingle Finger Recordings
Despite all common sense, VAM is going on tour with a new album!
Try as the world might, The VAM Commanders ("VAM") can't be stopped. Neither snow nor rain nor old age nor fading artistic relevance or the Pacific Ocean stays these rockers from their sacred duty of bringing the thunder. Something they'll be doing on tour with performances at:
9/16 Portland - Ash Street Saloon
9/17 Corvallis - Bombs Away Cafe
9/18 Bend - Volcanic Theatre Pub
9/19 Ashland - Lounge South
9/20 Medford - DowntownART+SOUND
VAM had their heyday in the late '90s, giving Oregon's punk scene a much-needed blast of mirth with kooky songs about mutant walruses and skater-politics paired with high-energy — occasionally naked — performances that often got the band — and occasionally all rock music — banned from returning to the venue. The band recorded and released six independent recordings blending ska, punk, hip-hop and avant-garde weirdness before breaking up in 1998, 2000, 2001, 2004 and who knows how many other times. The band scattered around the Pacific Rim to Ashland, Portland, Corvallis, Boise, Denver and Tokyo. But whenever they were fed enough drinks, a reunion was inevitable, with a dozen or so of them performed over the years.
But thanks to a rare extended stateside appearance from Tokyo-based drummer, Dustin Wasserman, VAM is back on the road again, with a string of Pacific Northwest performances listed below, and This is Not a Time Machine, a new album recorded cross-continentally through the use of file-sharing programs.
And it's all for one reason: the fans.
"For years after we scattered, people kept writing to us asking us to play this show or that, or so they could tell us what VAM songs had meant to them, or that they were learning to play from our albums," says Josh Gross, the band's guitarist. "We just got tired of telling them no."
This is Not a Time Machine is a collection of older tunes the band never got around to recording like it's anti-arena rock anthem, "(Please Don't) Show Your Boobs," the rapped diary of VAM's disastrous first tour, "Highway 2 Hell," the self-titled ode to band hero, "Al Bundy", as well as a series of new songs written specifically for the album, and a handful ported over from side projects.
"The songs written just for the new album are the most mature we've ever done," says Gross. "They are then balanced out by those oldies so immature we didn't bother to even record them back in the day. I know it's too late for the new songs to be VAM classics, but they should be. Like wine, cheese and bagels, I think we've improved with age."
Other than maturity, one thing that sets the band's newer material apart is a more broadly inclusive songwriting process. Joe Perez, the band's hypeman has been in VAM since the start, but This is Not a Time Machine is the first of the band's albums to include songs he wrote.
"The weirdest thing isn't just that Joe wrote songs on the new album, it's that he wrote some of the best songs on it," says lead vocalist Will Shapiro.
The album's title came from Gross, who was the most skeptical of reunions due to his belief that people didn't want new songs or performances so much as to turn back the clock, something the band not only can't do, but something he feels it shouldn't try to do.
"We started out in a small tourist town that wasn't so hot on a bunch of punk kids causing a ruckus," he says. "VAM was a way to take control of our own destinies rather than having them prescribed from on high. It's always been about looking forward, not back."
That sentiment is flushed out in the album's title track, which Gross penned as an anti-nostalgia anthem.
A reuniting rock band that is dedicated to smashing nostalgia might seem like an odd pairing, but VAM whether it was crafting lounge tunes for its punk audience, singing punk songs about chihuahuas, only playing handmade guitars from the band's bass player, performing in only towels, or releasing an EP made up entirely of the same audio track with six different sets of lyrics as a homage to the late great Wesley Willis, VAM have always done things their own way, generally wrong, way.
This is Not a Time Machine will be physical and digitally released worldwide on September 16, 2014 on Tingle Finger Recordings.
Advanced digital release coming soon to the Tingle Store!
Millennium Legends Return w/ Remastered Debut Album
Smoke-Free Class of 2000
Long after the last millennium, debut self-titled album by the Smoke-Free Class of 2000 gets an official remastered world wide release on Tingler Finger. This is where the Tingle all began. Soon to be available on all fine digital retailers and available now in the Tingle Finger Store with exclusive bonus tracks!
Smoke-Free Class of 2000 by Smoke-Free Class of 2000
10th Anniversary Makeover
Slowly going through a site makeover to celebrate out 10th anniversary! Thanks for bearing with us as we polish up the tingle. :-)
2014 VAM Sneak Preview
Sneak preview of things to come in 2014 from VAM. Welcome to the Age of Anti Wrinkle-Free Injections and Happy New Year!
Flowbee Unleashed!
15th anniversary reissued deluxe version of "Relics of The Flowbee Empire," the 1998 debut album from seminal Southern Oregon band The VAM Commanders. On its way to digital records stores everywhere and available now in the Tingle Finger Store with two additional secret bonus tracks only found here!
In the words of the band themselves, "We recorded this album when we were total idiots. The songs are stupid, the recordings are garbage. But we were the best kinds of idiots: those that had yet to learn what we couldn't or shouldn't do, and so pursued every bizarre idea that came into our heads."
To honor the release, The VAM Commanders will be playing a few shows in Southern Oregon, see below:
Friday, Aug. 30 at Johnny B's in Medford, Oregon
Saturday, Aug. 31 at Club 66 in Ashland, Oregon
Ska-punk is Not Dead
In the final midst of mastering their new album, VAM decided to do some shows while in Boise to remind you all that ska-punk is not dead; It's just sleeping in later cause its back hurts in the mornings.
Come see what that looks like with Southern Oregon turds The VAM Commanders and Boise's own Nude Oil and the PirkQlaters. Good times alleged but not guaranteed.
Aug. 2nd, 2013 - Sammy's 9pm
Aug. 3rd, 2013 - The Red Room 9 pm. Donations.
Got Giri?
Just when you thought the Tingle was dead, out pops the lyrical J-pop Masters, GIRI, with their one night masterpiece, Okujyo Maeni. The GIRI tale began in a little Shibuya dormitory. It was there, as if by destiny, 4 young students climbed to the top of the dorm one night with guitar and beercans in hand and their Japanese idol in their hearts. The fruits of their labor came to be known to all by the Giri. But the one night joys did not stop there, music videos were made for the hit single "Patsukin" as well as live performances throughout the streets of Shibuya. If you're not convinced yet, check out more behind the scenes video of GIRI in their glory days featured on Tingle Tube.
Fuzakenna Face Lift
Originally only available in Japan through physical limited edition release, the first album, Japanese Man's Dead Face, by Tokyo International University exchange student superstars, Fuzakenna, has been given a face lift! The power of the Tingle reincarnates this classic mix of Hardcore 4-Track Jams, now remastered wth exclusive bonus tracks only available through the Tingle. Featuring the circuit bending sounds of Octavia and the entire Mellow Dolphin Jazz Orchestra, Fuzakenna's core creators, Dustin Wasseman and Derek Sajbel (aka Dr. Rek) are proud to now share this release digitally to the world. Shall you believe, or will you too be remastered? Have a listen and find out! | {
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Q: CriteriaBuilder OffsetDateTime Comparison I use Springboot, and I'd like to implement a "search" API for an entity that has an "OffsetDateTime" attribute.
The attribute is of type "OffsetDateTime" in my Hibernate entity :
@Column(name = "creation_date")
private OffsetDateTime creationDate;
The attribute that I get from the API is of type "OffsetDateTime" too.
I use the Springboot Specification, with the OffsetDateTime value as criteria.getValue() :
@Override
public Predicate toPredicate(Root<Job> root, CriteriaQuery<?> criteriaQuery, CriteriaBuilder builder) {
return builder.equal(root.get("creationDate"), criteria.getValue());
}
But the above code doesn't return me the entity with the specified date
However, the following code does :
@Override
public Predicate toPredicate(Root<Job> root, CriteriaQuery<?> criteriaQuery, CriteriaBuilder builder) {
Predicate predicate = builder.between(root.<OffsetDateTime>get("creationDate"),
((OffsetDateTime) criteria.getValue()).minus(1, ChronoUnit.MILLIS),
((OffsetDateTime) criteria.getValue()));
}
In my DB I have "2020-03-12 17:25:11.047", and the value I pass to the API is "2020-03-12T17:25:11.047+01:00". I'm in France, so I have a 1 hour offset, and the time is saved as a local time in the db, but that doesn't seem to be the problem as the second solution does return the entity I want.
Do you know why the first solution doesn't return me the entity, and how I could get the entity without having to set a 1 millisecond interval ?
| {
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Бети Бауерс () назив је измишљеног главног лика на сатиричном сајту -{BettyBowers.com}-. Лик Бети Бауерс тренутно тумачи глумица и комичарка Девен Грин, која јој позајмљује глас а појављује се и на бројним фотографијама. Критичари виде Бети као још један допринос дугогодишњој расправи око слике америчког југа.
Биографија Бети Бауерс
Бети Бауерс тврди да има титулу најбоље америчке хришћанке. Према њеној интернет страници, Бети води неколико хришћанских мисионарских организација, међу којима су Усађивање интегритета хришћанским домаћицама () и Баптисти спасавају хомосексуалце (). Чланица је Баптистичке цркве Лендовер, која је, по њеним изјавама, омиљена божја црква. Бети је на фотографијама приказана обично са изразом презира или неодобравања на лицу. Бети, користећи се пародијом, приказује лицемјерје које имају људи у оквиру неких деноминација, тако што једноставно преузима неке од њихових популарних ставова и учења.
Садржај интернет странице
Преко своје интернет странице Бети често објављује сатиричне изјаве, између осталог, о хришћанским десничарима, хомосексуалности и геј правима, креационизму, верском фундаментализму и Републиканској странци.
Бауерс је такође написала и неколико критика филмова. Неке од њених најпознатијих критика су за филмове Хари Потер и камен мудрости, Ханибал и Страдање Христово. Бети тврди да је гледање Харија Потера једносмјерна карта за пакао, и да је то ужасан филм јер детаљно описује враџбине. Ханибал је по њеном мишљењу "одличан приказ праве божије природе", док је Страдање Христово одличан породични филм.
Лик Бети Бауерс креирао је Пол Бредли, који је један од идејних твораца сајтова LandoverBaptist.org и -{Whitehouse.org}-. Бредли је аутор свих садржаја на сајту Бети Бауерс, а такође је аутор књиге из 2002. -{What Would Betty Do?}-, која се такође темељи на лику Бети Бауерс. Бредли је и коаутор књига -{The White House Employee Handbook}- и -{Welcome to Jesusland! (formerly the United States of America)}-, а лик Бети Бауерс појављује се и у овим књигама.
Презиме Бауерс, као и презиме Хардвик које носи Хари, члан Баптистичке цркве Лендовер, алузија је на познати предмет пред Врховним судом САД из 1986. Бауерс против Хардвика.
Референце
Литература
What Would Betty Do? How to Succeed at the Expense of Others in This World and the Next,, Paul Bradley.
Спољашње везе
Званична страница
Профил Бети Бауерс на сајту Лендовер баптистичке цркве
Измишљени ликови
Пародије на религију | {
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Minister of Environment and Climate Change Catherine McKenna speaks during an announcement in Ottawa, Monday August 26, 2019. THE CANADIAN PRESS/Adrian Wyld
Provinces, territories to have input in future price of carbon tax, McKenna says
Catherine McKenna also said the Liberal government's plan for the tax hadn't changed
Aug. 27, 2019 7:55 a.m.
Any decisions about future increases in the carbon tax would take into account the views of provinces and territories, the federal environment minister says, using language that sparked accusations from Conservatives that she was misleading voters about the future of the levy.
But Catherine McKenna also said the Liberal government's plan for the tax hadn't changed and there was "no secret agenda" by the party to pump up the price on carbon beyond the $50 per tonne it will reach in 2022.
McKenna maintained Monday that her language on possible increases in the price on carbon had been consistent, even though in June she said the price of carbon "will not go up," which at the time was taken as a pledge that the price would remain fixed beyond 2022. At the time, she pointed to other aspects of the Liberal government's climate plan as proof of how it would achieve Canada's emissions reduction targets.
On Monday, she said there was still "no intention" to raise the price after 2022, which is when there will be a review of the carbon tax under the terms of the 2016 framework on climate change. If there were any new decision on pricing, it would be the product of extensive consultation, McKenna said.
She added that the government was fulfilling promises set out following a lengthy negotiation with provinces and territories completed in 2016. As for beyond 2022, McKenna said she was not in a position to negotiate anything after that time.
"Look, there will be an election in 2023, and I think that might be a discussion for that election," she said.
The Amazon is on fire. July is the hottest on record. Climate change is real.
Meanwhile Conservative politicians continue to mislead Canadians, using taxpayer dollars to fight climate action rather than fight climate change.
It's about the future we want. 🌎#ChooseForward https://t.co/vkVgfZaUiv
— Catherine McKenna 🇨🇦 (@cathmckenna) August 27, 2019
McKenna denied she was attempting to avoid talking about the future costs of a price on carbon until after this fall's federal election, where the levy is a point of debate.
Conservative finance critic Pierre Poilievre quickly labelled what he saw as an apparent shift in position for this fall's election as a "carbon tax cover-up" in a press conference held earlier in the day.
The federal Conservatives have said they would eliminate the carbon tax if elected in October, and several conservative provincial governments have challenged the price in court.
"If this was such a popular idea, why are they covering it up? Why did Catherine McKenna stand up and deny that the tax would go above $50 (per tonne)? We know why — because they were trying to keep it secret until the election was over when they no longer need voters, but still need their money," Poilievre said.
McKenna criticized the Conservative as having no real plans of their own, likening Poilievre and Leader Andrew Scheer to Ontario Premier Doug Ford in that "they don't understand that we need to take action on climate change."
Liberal candidate and prominent environmentalist Steven Guilbeault — whom McKenna referenced in her remarks — also weighed in, writing on Twitter that walking back a pledge to cap the price at $50 per tonne was "a very good thing" and that the "price should reflect the cost of climate change to society."
READ MORE: Kenney takes aim at Trudeau directly ahead of fall federal election
READ MORE: Justin Trudeau seeks to highlight climate policy in visit to Canada's Far North
READ MORE: Elections Canada to assess 'partisan' climate change rhetoric case by case
Christian Paas-Lang, The Canadian Press
Young B.C. woman missing en route to 100 Mile House has been found
Pregnant woman camps in tent ahead of out-of-town delivery in Williams Lake | {
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\section{Introduction}
Data sets with a small number of observations $n$ and a large number of variables $p$, a.k.a ``small $n$, large $p$'', are common in many applications and
pose big challenges for statistical methods \cite{fan2006statistical}.
Potential approaches to alleviate these challenges
are either to provide more samples, which could be very expensive or even impossible in some applications, or to regularize models using additional sources of information. An example of such an additional source is human expert who may have substantial subject-specific knowledge that can be used to improve data analysis.
In Bayesian statistics, expert-provided information can be formulated as a prior distribution over the parameters to regularize the model. Extracting and incorporating experts' knowledge into statistical models is known as \textit{knowledge elicitation}. When designing an elicitation method, two important choices will affect the success. First is what is assumed of the knowledge of the expert: only domain expertise or additional statistical expertise. In Bayesian statistics, most of the existing knowledge elicitation approaches require the domain expert to be expert, or at least knowledgeable, in statistics as well. The second choice is the assumptions made on the content of knowledge that is elicited, which also translates into the structure of the model used for the elicitation. Most existing methods for eliciting importance of variables for prediction tasks assume independence among the parameters to make the elicitation easier, at the cost of ignoring expert knowledge on dependencies.
In this paper, we propose a method for elicitation that avoids both problems: only domain expertise is required, and the underlying assumptions are generalized from independence of the parameters to pairwise dependencies. Technically, we formulate the problem as a sequential decision-making task of choosing which queries to ask to maximally improve predictions with minimal expert effort. The queries will be about pairwise relationships of features, to expand beyond the earlier assumption of their independence.
With experiments on synthetic and real data, we demonstrate that the approach is able to improve the predictive performance by constructing a more informative covariance matrix using expert feedback.
\textbf{Contribution.} In summary, the main contributions of the paper are: \textbf{(1)} A method for learning a prior with a full covariance matrix (without an independence assumption among features) using information provided by a domain expert, \textbf{(2)} an algorithm for actively eliciting expert's knowledge on pairwise similarities of the features, to maximally improve predictive performance while minimizing the expert's workload.
\section{Related Work}\label{Sec:2}
There exists a rich literature on knowledge elicitation for improving the performance of statistical models.
A number of studies have proposed to elicit scores or point estimates of an unknown parameter or quantity of interest directly from the expert \cite{garthwaite2008use,haakma2011pmd4,o1998eliciting}.
These approaches typically either assume that the expert has a high level of statistical training, to be able to assess and formulate prior distributions, or is assisted by a human facilitator in an elicitation session. The main goal is accuracy of the knowledge instead of time-efficiency, which makes the elicitation burdensome.
In an attempt to make knowledge elicitation more automatic and resource-efficient, Micallef et al.~\shortcite{Micallef2017Interactive} proposed an interactive approach to elicit the expert's knowledge on the relevance of individual features to improve the predictive accuracy of an underlying model. They used a sequential decision making method, multi-armed bandits, to guide the interaction toward features that would likely benefit from the expert's input. Daee et al.~\shortcite{daee2017knowledge} formulated knowledge elicitation as a probabilistic inference problem where expert knowledge about individual features is sequentially extracted to improve predictions in a sparse linear regression task. The work was extended by Sundin et al.~\shortcite{sundin2018improving} by considering information about the direction of a relevant feature. In all these works, independence among features is assumed in the prior distribution. These approaches could be used to complement our method.
In a similar scenario, Xiao et al.~\shortcite{xiao2018optimal} proposed a knowledge elicitation approach for extracting expert knowledge on influential relationships between pairs of variables in a directed acyclic graph, i.e., whether a variable $a$ is likely to be up- or down-stream of variable $b$. Their goal, however, is not prediction but to learn the structure of the graph. Afrabandpey et al.~\shortcite{afrabandpey2017interactive} proposed an interactive method for eliciting knowledge on pairwise feature similarities based on an interactive display and used it to improve predictive performance of linear regression. This work is similar to ours, but differs in two important aspects: First, their method is passive - the queries do not change according to what has been elicited so far - which makes the feedback giving process exhaustive for the expert. Second, the expert feedbacks are only post-hoc connected to the prediction problem through a metric learning process,
while our approach adopts expert feedback directly by constructing an informative prior distribution for the underlying model.
Our method builds upon two further works. Krupka and Tishby~\shortcite{krupka2007incorporating} studied cases where there are meta-features that capture prior knowledge on features. Using these meta-features, they proposed a method to improve generalization of a classification model by constructing a prior covariance (or a Gaussian process) on the parameters without independence assumptions among the variables. Their approach, however, is not a human-in-the-loop system and does not elicit expert knowledge. Yang et al.~\shortcite{yang2007bayesian} proposed a Bayesian framework for actively learning a similarity metric among samples using pairwise constraints labeled by a human agent. The method aims to improve pairwise distances by querying the unlabeled pairs of samples with the greatest uncertainty in relative distance. In contrast, our approach is designed to optimize the predictive performance of the model using feedback on pairs of features and we query pairs based on their expected improvement on predictive performance.
\section{Proposed Approach}\label{Sec:4}
We consider the task of learning a probabilistic predictive function $y = h_{\bm{\theta}}(\bm{x})$, parametrized by $\bm{\theta}$, given a data set $\mathcal{D} = \{(y_i, \bm{x}_i); i = 1,\ldots, n\}$ of $n$ outcomes $y_i$ and feature vectors $\bm{x}_i = [x_{i1}, \ldots, x_{ip}]^{\mathrm{T}}$ pairs. We assume that $n$ is small and cannot be increased, so that it is worthwhile to spend effort on collecting and encoding prior knowledge or other external information. Here, we particularly focus on using knowledge elicitation from domain expert to learn the dependencies between the elements of $\bm{\theta} = [\theta_1, \ldots, \theta_L]^{\mathrm{T}}$,
where $L$ is the total number of parameters of the predictive function. This approach is complementary to many of the previous prior and expert knowledge elicitation approaches
In addition to the data $\mathcal{D}$, we assume the availability of meta-features $\bm{u}_l \in \mathbb{R}^d$ for each parameter $\theta_l$. Our approach to improve the predictive model $h_{\bm{\theta}}$ is then formulated in three components as shown in Figure \ref{model_comp}: (1) An auxiliary mapping $g$ from the meta-features $\bm{u}_l$ to the parameters $\theta_l$, $\theta_l = g_{\bm{\gamma}}(\bm{u}_l)$, with parameters $\bm{\gamma}$. (2) An observation model for expert feedback that encodes the expert knowledge to information about $g$ and consequently to the dependencies between the elements of $\bm{\theta}$. (3) A query algorithm that chooses questions to the expert to optimize the effort of the expert for improving the predictions. Each component is described in more detail in the following sections.
\begin{figure}[bt!]
\centering
\includegraphics[width = \columnwidth]{model_comp.pdf}
\caption{Components of the proposed approach. To improve the predictive function $h_{\bm{\theta}}$, the auxiliary mapping $g_{\bm{\gamma}}$ models dependencies between the parameters $\bm{\theta}$ using the meta-features $\bm{u}$ and the current value of $\bm{\gamma}$. The query algorithm optimizes the workload of the expert by choosing queries that maximize the expected gain in the predictive performance. The expert feedback $f$ then updates $\bm{\gamma}$.}
\label{model_comp}
\end{figure}
To concretize the approach, consider as an example a sentiment analysis task where the goal is to predict a rating assigned by a reviewer to a product from the text of the review. The training data is the set of all reviews given by different reviewers together with their corresponding ratings. The feature vector $\bm{x}$ describes occurrence of keywords in the review text (bag-of-words). Assume linear regression for prediction, $h_{\bm{\beta}}(\bm{x}) = \bm{\beta}^{\mathrm{T}} \bm{x}$, with $\bm{\theta} = \bm{\beta}$ being the regression coefficients. A simple approach to constructing a meta-feature vector $\bm{u}_l$ for each keyword $l$ is to take the vector of occurrences of the keyword in the training set reviews. This implies that features that do not occur in the same documents are dissimilar and vice versa. Using a Gaussian process as the auxiliary mapping $g$ then corresponds to learning a full covariance matrix for the prior of the regression coefficients $\bm{\beta}$ based on the meta-features. Knowledge about the pairwise similarity of the role of the keywords in the rating prediction is sequentially queried from the expert. The rationale is that the expert has knowledge about the correlation among regression coefficients of at least some keywords, i.e., either that two keywords positively affect the output (both cause an increase in the rating) or they negatively affect it (decrease the rating). The extracted knowledge will then be incorporated into the model to improve the prior covariance matrix and thus predictions. The case of prediction task with linear regression is described in detail in Section \ref{Sec:4.1}.
\subsection{Modelling Parameter Dependencies}
The auxiliary mapping $g$ is used to model the dependencies between the parameters $\bm{\theta}$. We model it with a Gaussian process with a zero mean and covariance function $k_{\bm{\gamma}}$, where $\bm{\gamma}$ is a vector of parameters \cite{krupka2007incorporating,rasmussen2006gaussian}. In particular, this implies that $\bm{\theta} \sim \mathcal{N}(\bm{0}, \bm{K})$, where $\bm{K}$ is a covariance matrix (kernel). The element $K_{ij} = k_{\bm{\gamma}}(\bm{u}_i, \bm{u}_j)$ describes the prior covariance between the parameters $\theta_i$ and $\theta_j$ based on the similarity of their meta-features $\bm{u}_i$ and $\bm{u}_j$ (according to the covariance function).
To illustrate the effect of the auxiliary mapping on learning $\bm{\theta}$, consider a two-dimensional special case, with $\theta_1$ and $\theta_2$.
If the prior correlation implied by $\bm{K}$ is equal to one, then $\theta_1 = \theta_2$; that is, the $g$ maps the two meta-feature vectors $\bm{u}_1$ and $\bm{u}_2$ to the same point and, effectively, there is only one parameter to be learned from the data set $\mathcal{D}$. If the prior correlation is zero, learning information about one parameter has no effect on the other, and we need to estimate both of the parameters from $\mathcal{D}$. Of course, often we would be somewhere between these two extremes, such that some statistical strength can be shared between learning of the two parameters.
The covariance function $k_{\bm{\gamma}}$ defines many of the properties (smoothness, flexibility, magnitude, etc.) of the auxiliary mapping based on the meta-features $\bm{u}_i$ and $\bm{u}_j$. Many different covariance functions are possible (see, e.g., \cite{rasmussen2006gaussian}). We use the Gaussian kernel
\vspace*{-0.1cm}
\begin{equation}\label{eqn:gaussiankernel}
k_{\bm{\gamma}}(\bm{u}_{i}, \bm{u}_{j}) = \exp \left( - \frac{\norm{\bm{u}_{i} - \bm{u}_{j}}_{\bm{A}_{\bm{\gamma}}}^{2}}{2} \right),
\end{equation}
where $\bm{A}_{\bm{\gamma}} \in \mathbb{R}^{d \times d}$ is a diagonal matrix defining the distance metric with elements $\gamma_l$, such that $\norm{\bm{u}_{i} - \bm{u}_{j}}_{\bm{A}_{\bm{\gamma}}}^{2} = \sum_l \gamma_l (u_{il} - u_{jl})^2$. Here, the $\bm{\gamma}$ are inverse length scales: they determine how influential each dimension of the meta-feature is in the distance metric; $\gamma_i = 0$ means that the $i^{th}$ dimension of the meta-features does not influence the distance (all features are equal w.r.t.\ this descriptor). Increasing the value from $0$ means that it is increasingly important in defining the distance.
Inference about $\bm{\gamma}$ is done by defining a half-normal prior distribution $\bm{\gamma} \sim \mathcal{N}^{+}\left( \gamma_0\bm{1}_{d \times 1}, \delta \bm{I}_{d \times d} \right)$. The $\gamma_0$ and $\delta$ are constant values
The auxiliary mapping $g$ defines a prior on the parameters $\bm{\theta}$, based on the meta features. It would be attractive to learn $g$ from the data $\mathcal{D}$, but that would require more data than available in the "small $n$, large $p$" case we are targeting. That is why we turn next to learning it based on knowledge elicitation instead.
\subsection{Feedback Model}
A feedback model is used to incorporate expert's knowledge into the model. In this work, we consider feedback on the pairwise similarities of the roles of the parameters $\bm{\theta}$ in the prediction. For example, if the $\bm{\theta}$ are linear regression weights, the expert tells the model which pairs of features affect the prediction output similarly (positively and/or negatively). Expert's feedback will be either ``Similar'', ``Dissimilar'', or ``I don't know''. The latter will be ignored by the model and has no effect on prior covariance and consequently on the predictions. Similar to \cite{yang2007bayesian}, we define the following likelihood for the feedbacks:
\begin{equation}
f_{ij} \sim \mbox{Bernoulli}(q),
\end{equation}
where $f_{ij}$ is the feedback given on the similarity of the features $i$ and $j$ ($f_{ij} = 1$ for similar and $f_{ij} = -1$ dissimilar feedback), $q = \frac{1}{1 + \mbox{exp}\left( \bm{\gamma}^{T}\bm{w}_{ij} - \xi \right)}$ is the parameter of the Bernoulli distribution,
$\bm{w}_{ij} = \left[ \bm{u}_{i} - \bm{u}_{j} \right]^{2}$, and $\xi$ is the threshold determining the similarity/dissimilarity of the two features. Since feedbacks are binary, the feedback model is basically defined as a logistic regression of the distances among features $\bm{w}_{ij}$. Two features are more likely to be similar, $f_{ij} = 1$, only when their distance is less than the threshold $\xi$ and vice versa. To avoid setting the value of the threshold manually, we define a half-normal prior distribution over it, $\xi \sim \mathcal{N}^{+}\left( m_{\xi}, \sigma^{2}_{\xi} \right)$.
\subsection{Query Algorithm}\label{Sec:4.4}
Given the set of pairs of features, we would like to query first the similarity of the pair that will give us maximal improvement on predictive performance. Our query algorithm chooses the pair of features that maximizes the expected utility, which is a standard criterion in decision theory. The utility is task dependent - in our prediction task it is natural to choose the utility to be information gain of the predictions. The same rationale was earlier used successfully by \cite{daee2017knowledge}, for querying individual variables. The larger the information gain, the greater impact the feedback will have on the posterior predictive distribution. This is defined as the expected Kullback--Leibler divergence (KL) between the posterior predictive distribution before seeing the feedback and after giving the feedback:
\begin{equation}
\centering
\mathbb{E}_{\pi(\Tilde{f}_{ij} \mid \mathcal{D},\mathcal{F})}\!\!\!\left[\!\sum_{k}\! \mbox{KL}\!\!\left[ \pi\!\left(\Tilde{y}\!\mid\! \bm{x}_{k},\mathcal{D},\mathcal{F},\Tilde{f}_{ij}\!\right)\!\!\parallel\!\! \pi\!\left(\Tilde{y}\!\mid\! \bm{x}_{k},\mathcal{D},\mathcal{F}\right)\!\right]\!\! \right]
\label{Eq9}
\end{equation}
where $\mathcal{F}$ is the set of feedbacks given up to the current step, and the summation goes over the training data. The expectation is over the unknown feedbacks, given everything observed so far. The posterior predictive distribution of the feedback, $\pi\!\left(\Tilde{f_{ij}}\mid \mathcal{D},\mathcal{F}\right)$, is obtained using the data and all the feedback given by the expert up to the current iteration.
\subsubsection{Computational Complexity}\label{Sec:4.5}
In each iteration, we need to compute the utilities for all pairs of features, except those to which the expert already gave feedback in the previous iterations. The complexity is $O(p^2)$ which is expensive if $p$ is large. To reduce this complexity, we used the idea presented in \cite{xiong2015active}: we construct a smaller pool of the pairs by randomly sampling from the original set of feature pairs, excluding the pairs to which the expert gave feedback previously. We then select the most informative pair from among the pairs in the smaller pool based on their utilities. Denoting the randomly selected pool by $R_{p}$, the objective function for the query algorithm will change to
\begin{equation}\label{Eq10}
(ij)^{*} = \arg\max_{(ij) \in R_{p}} (\mbox{Expected Information Gain}),
\end{equation}
where the expected information gain is computed using Equation~\ref{Eq9}. Although the optimal pair of $R_{p}$ might not necessarily be optimal for the full set, the amount of degradation in the performance is negligible. This is due to the fact that in real data sets with large number of features, there will be significant redundancies among the pairs. The complexity reduces from $O(p^{2})$ to $O(\mid\! R_{p}\!\mid)$, where $\mid\!R_{p}\!\mid$ denotes the cardinality of $R_{p}$.
The above strategy is effective only if the selected pair from $R_p$ can be guaranteed to be near optimal with high probability. A pair is near-optimal if it is among the $\epsilon$ top-ranked pairs in the original set,
where $\epsilon$ is a small scalar (e.g. 0.001). The near-optimality of the selected pair from the smaller pool can be proven by the following proposition:
\textbf{Proposition 1.} The best pair in $R_{p}$ according to Equation~\ref{Eq10} is among the $\epsilon$ top-ranked pairs of the original set with probability $1-(1-\epsilon)^{\mid\!R_{p}\!\mid}$.
\textit{Proof.} Based on the definition of near-optimal pairs, the probability that a pair does not belong to the near-optimal pairs is $1-\epsilon$. Since the size of the smaller pool is $\mid\!R_{p}\!\mid$, the probability of obtaining a near optimal query is $1-(1-\epsilon)^{\mid\!R_{p}\!\mid}$.
By setting $\mid\!R_{p}\!\mid$ to a reasonable multiple of $p$, e.g. $10p$, we reduce the complexity from $O(p^2)$ to $O(p)$, while with high probability (probability of $\sim 0.99$ for a moderate size $p = 400$), the selected pair from $R_{p}$ will be among the top $0.1$ percent pairs in the original set. To increase computational speed, we implemented computation of the utilities in parallel. This is straightforward since utilities of different pairs are independent.
\subsection{Application to Linear Regression}\label{Sec:4.1}
The described approach is general and could, for example, be applied directly to Gaussian process regression where $\bm{\theta}$ would be the predictive function evaluations at the training data points.
In this paper, we apply the method to the important case of linear regression with ``small $n$, large $p$'' data sets, which occurs in a wide array of practical applications. In particular, we take $\bm{\theta} = \bm{\beta}$ to be the regression weights. We assume availability of an expert who has prior knowledge on the pairwise similarities of the role of the features in the prediction task.
The linear regression model is defined as
\begin{equation}
\bm{y} = \bm{X \beta} + \bm{\epsilon},
\end{equation}
where $\bm{X} \in \mathbb{R}^{n \times p}$ is the matrix of predictors, $\bm{y} \in \mathbb{R}^{n \times 1}$ is the vector of all dependent variables, $\epsilon \sim \mathcal{N}(\bm{0}, \sigma^{2}\bm{I})$ is the vector of residuals,
and $\bm{\beta} \in \mathbb{R}^{p \times 1}$ is the regression coefficient vector to be inferred. With these assumptions, $\bm{y \mid X, \beta},\bm{\sigma}^2 \sim \mathcal{N}\left( \bm{X\beta}, \sigma^{2}\bm{I} \right)$. The goal is to learn the posterior distribution of $\bm{\beta}$ given the training data and the expert feedback. The proposed approach assumes the following prior distribution for $\bm{\beta}$:
\begin{equation}
\bm{\beta} \mid \sigma^2, \tau^2, \bm{\gamma} \sim \mathcal{N}\left( \bm{0}, \sigma^{2} \tau^{2} \bm{K} \right),
\end{equation}
where $\bm{K}$ is the covariance matrix defined by the Gaussian covariance function $k_{\bm{\gamma}}$ and we have also introduced a scalar magnitude parameter $\tau^2$. The expert knowledge affects the predictions through its effect on this covariance matrix.
To complete the model formulation, we define inverse gamma distributions for the hyper-parameters $\sigma^{-2} \sim \mbox{Gamma} \left( a_{\sigma}, b_{\sigma} \right)$ and $\tau^{-2}\!\sim\!\mbox{Gamma} \left( a_{\tau}, b_{\tau} \right)$, where $a_{\sigma}$, $b_{\sigma}$, $a_{\tau}$ and $b_{\tau}$ are constant values.
Setting the values of the hyper-parameters is discussed in Section \ref{Sec:5}. Plate diagram of the model is provided in appendix C.
\subsection{Posterior Inference and Prediction}\label{Sec:4.3}
Parameters of the proposed model are $\{ \bm{\beta}, \sigma^{2}, \tau^{2}, \bm{\gamma}, \xi \}$. Due to the complexity of the model, there is no closed-form posterior distribution. Instead, we obtain maximum a posteriori (MAP) estimates of the parameters by implementing the model in the probabilistic programming language Stan \cite{carpenter2016stan} (version 2.17.3, codes in the supplementary material).
To reduce computational burden of computing the MAP estimate of $\bm{\beta}$, which requires the inversion of the covariance matrix $\bm{K}$,
we marginalized the likelihood over $\bm{\beta}$ and $\sigma^{2}$. This results in a Student's t-distribution with $2a_{\sigma}$ degrees of freedom for the marginal likelihood, $\bm{y} \sim \mbox{MVSt}_{2a_{\sigma}}\left( 0, \frac{b_{\sigma}}{a_{\sigma}}\bm{\Sigma} \right)$, with $\bm{\Sigma} = \bm{I} + \tau^{2}\bm{X} \bm{K}\bm{X}^{T}$.
The matrix $\bm{\Sigma}$ is of dimension $n\times n$ which is much smaller than $p \times p$. More details on the marginal likelihood derivation are provided in appendix B.
MAP estimate of $\bm{\gamma}$ is used to compute $\bm{K}$. The joint posterior distribution of $\bm{\beta}$ and $\sigma^{2}$ is then obtained as a Normal-Inverse-Gamma distribution, $\mbox{NIG}(\bm{\mu}^{*},\bm{\Sigma}^{*},a^{*},b^{*})$, with parameters
\vspace*{-0.2cm}
\begin{align*}
\bm{\mu}^{*} &= \left( \left( \tau^{2}\bm{K} \right)^{-1} + \bm{X}^{\mathrm{T}}\bm{X} \right)^{-1}\bm{X}^{T}\bm{y}, \\
\bm{\Sigma}^{*} &= \left( \left( \tau^{2}\bm{K} \right)^{-1} + \bm{X}^{\mathrm{T}} \bm{X} \right)^{-1}, \\
a^{*} &= a_{\sigma} + \frac{N}{2}, \\
b^{*} &= b_{\sigma} + \frac{1}{2}\left[ \bm{y}^{\mathrm{T}}\bm{y} - (\bm{\mu}^{*})^{\mathrm{T}}(\bm{\Sigma}^{*})^{-1}\bm{\mu}^{*} \right].
\end{align*}
Finally, predictions for the future input $\Tilde{\bm{x}} $ can be done using the posterior predictive distribution:
\begin{align}
\pi(\Tilde{y} \mid \bm{y}) &= \int \pi(\Tilde{y} \mid \bm{\beta}, \sigma^{2})\pi(\bm{\beta}, \sigma^{2} \mid \bm{y}) d\bm{\beta}d\sigma^{2} \nonumber \\
&= \mbox{t}_{2a^{*}} \left( \Tilde{\bm{x}}^{T} \bm{\mu}^{*}, \frac{b^{*}}{a^{*}} (1 + \Tilde{\bm{x}}^{T} \bm{\Sigma}^{*} \Tilde{\bm{x}}) \right),
\end{align}
where $t_{2a^{*}}$ denotes the univariate Student's t-distribution with $2a^{*}$ degrees of freedom. Details on computing the KL divergence of Equation \ref{Eq9} for the linear regression model are provided in appendix A.
\iffalse
\begin{multline}
p(\Tilde{y} \mid y) = \int p(\Tilde{y} \mid \bm{\beta}, \sigma^{2})p(\bm{\beta},\sigma^{2}\mid y)d\bm{\beta}d\sigma^{2} = \\
\mbox{MVSt}_{2a^{*}}\left( \Tilde{\bm{x}}^{T}\bm{\mu}^{*}, \frac{b^{*}}{a^{*}}\left( 1 + \Tilde{\bm{x}}^{T}\bm{\Sigma}^{*}\Tilde{\bm{x}} \right) \right)
\end{multline}
\fi
\section{Experimental Results}\label{Sec:5}
In this section, the performance of the proposed method is evaluated in several ``small $n$, large $p$'' regression problems on both simulated and real data with a simulated user. As far as we know, no other method has been proposed for precisely the same task, i.e., improving generalization by constructing a prior distribution using feedback on pairs of features. Therefore, we compare with two natural alternatives:
\begin{itemize}[noitemsep,topsep=0.5ex]
\item[-] random query,
\item[-] non-sequential version of our algorithm, which computes the utilities once, before observing user feedback, and never updates the utilities.
\end{itemize}
\begin{figure*}[ht!]
\centering
\subfloat[][]{
\includegraphics[scale=.3]{c_opt.pdf}
}\hspace{-0.2em}
\subfloat[][]{
\includegraphics[scale=.3]{c_1.pdf}
}\hspace{-0.2em}
\subfloat[][]{
\includegraphics[scale=.3]{c_25.pdf}
}\hspace{-0.2em}
\subfloat[][]{
\includegraphics[scale=.3]{c_100.pdf}
}\hspace{-0.2em}
\caption{Evolution of $\bm{K}$ w.r.t.\ different number of feedbacks queried by the sequential model.}
\label{Fig:3}
\end{figure*}
\subsection{Synthetic Data}
\emph{Data generation}: We simulate data from a linear regression model, $\bm{y} = \bm{X} \bm{\beta}+\bm{\epsilon}$, with $\bm{\epsilon} \sim \mathcal{N}(\bm{0},\sigma^2\bm{I})$ and $\sigma^2 = 5$. The data are generated similarly to \cite{li2010bayesian}, with the difference that instead of manually constructing the optimal regression coefficient, $\bm{\beta}_{opt}$, we construct the optimal $\bm{\gamma}$, denoted by $\bm{\gamma}_{opt}$, and the meta-features. They are used to construct the optimal covariance structure, $\bm{K}_{opt}$, using which we sample $\bm{\beta}_{opt}$ from $\mathcal{N}\left(\bm{0},\sigma^2\tau^2\bm{K}_{opt}\right)$, assuming $\tau^2 = 1$. The idea is to check whether or not the model can learn $\bm{\gamma}_{opt}$ and consequently $\bm{\beta}_{opt}$ using the feedback given by an oracle. We set the number of features to $25$ which are divided into four groups of sizes $10$, $5$, $5$, $5$. Features within each group are highly correlated while features across groups are independent. Meta-features are vectors of size $9$ and dimensions $1$, $2$, $4$, $6$ are assumed to be important for learning the optimum covariance structure, i.e. $\bm{\gamma}_{opt} = \left[1,1,0,1,0,1,0,0,0\right]^T$. The optimum covariance matrix constructed using $\bm{\gamma}_{opt}$ and meta-features is shown in Figure \ref{Fig:3}.a..
Training and test outputs are generated by randomly sampling $\bm{X}_{tr}\in \mathbb{R}^{20\times 25}$ and $\bm{X}_{te}\in \mathbb{R}^{1000\times 25}$ from a standard normal distribution, multiplying them by $\bm{\beta}_{opt}$ and adding normally distributed noise with variance $\sigma^2$.
\emph{Learning of the model and results}: The hyperparameters of the model are $a_{\sigma} = 2$ and $b_{\sigma} = 7$ for $\sigma^2$ and $a_{\tau} = 2$ and $b_{\tau} = 4$ for $\tau^2$, to reflect relatively vague information on the residual variance and scaling parameter, respectively. The prior for $\bm{\gamma}$ is set to $\mathcal{N}^{+}\left(1,0.5\right)$ meaning that \textit{a priori} we expect almost all dimensions of the meta-features to be equally important, i.e., $\bm{\gamma}_{0} \cong \left[1,1,1,1,1,1,1,1,1\right]^{T}$. In other words, any difference in any dimensions of the meta-feature will affect the (dis)similarity of the features. The hyperparameters of the threshold variable are $\mu_{\xi} = 20$ and $\sigma^{2}_{\xi} = 10$ to cover wide ranges of values.
The model was first trained to obtain an estimate of the regression coefficients without any feedback ($\bm{\beta}_0$). The posterior of the regression coefficients is then used to estimate the utility of each pair (to be used in the next round) and to compute the output of the test data. In each round, the simulated user gives one feedback for a pair queried using three different algorithms, i.e., random, non-sequential (using the utilities computed in round $0$) and sequential (updates utilities of each pair, except those to which the user already gave feedback, using estimated parameters in the previous round). Figures \ref{Fig:3}.b-d show how $\bm{K}$ evolves using feedback on pairs queried by the sequential model. The total number of possible feedbacks is $\frac{25\times 24}{2}=300$; using only one third of the feedbacks, the sequential model learned almost the optimal covariance structure
We ran the model $50$ times with different randomly generated data with the setting explained above. The average predictive performances of the model with the different query algorithms are shown in Figure \ref{Fig:4}. The sequential model obtains the same amount of improvement faster than the random and non-sequential models. Both the random and non-sequential models also perform well, which is due to the simple structure of the data.
\begin{figure}[b!]
\centering
\includegraphics[width = 0.6\columnwidth]{mse_vs_100_feedback.pdf}
\caption{Comparison of predictive performances of different query algorithms in synthetic data.}
\label{Fig:4}
\end{figure}
\subsection{Real Data with Simulated Expert}
We tested the proposed method in the task of review ratings prediction from textual reviews, using subsets of Amazon review data and Yelp data. Both data sets contain textual reviews represented as bag-of-words and their corresponding ratings, integer values in the range $ 1 - 5 $. Features correspond to keywords (unigrams and bigrams). For Amazon, we use the \textit{kitchen appliances} subset which contains $5149$ reviews \cite{blitzer2007biographies}. For \textit{Yelp}, we consider $4086$ reviews from the year 2004. In our analysis of both data sets, we removed stop words \cite{Salton1971SMART} and kept features that appeared in at least $100$ reviews. This resulted in data sets containing $340$ features for Amazon and $241$ features for Yelp. From each data set, $1000$ randomly selected reviews were used for training and tesing of the model and the rest as an ``expert data set'' for constructing the simulated expert. Among the $1000$ reviews for the model, $10\%$ were randomly selected for training and the remaining $90\%$ for testing. This resulted in a training set of size $100\times 340$ for Amazon and of size $100\times 241$ for Yelp, both of which small $n$, large $p$. Training data were normalized to have zero mean and unit variance. As meta-features, we used the transpose of the unnormalized training data. This is the simplest possible meta-feature according to which features (keywords) that are not in the same documents are dissimilar and vice versa. Better meta-features can be defined using word2vec \cite{mikolov2013distributed} or more advanced representation of the keywords; here we show that the model works fairly well even with such naive meta-features.
\subsubsection{Simulated Expert Feedback}
To construct the simulated expert, we trained a sparse regression model using LASSO \cite{friedman2010regularization} on the expert data set. Features with positive regression coefficients are considered pairwise similar. Those with negative coefficients are also similar, while features with zero weight are assumed to be difficult for the simulated expert to evaluate and the feedback will be ``I don't know'' for any pair containing at least one of those features.
Since our goal is to evaluate the predictive performance of the models and feedback on these features has no effect on models' performance, we remove all pairs containing any of these features to make the runs faster. For both data sets, there are almost $20$ features in each of the two groups, resulting in $(40\times 39)/2 = 780$ pairs in total. Using proposition 1 for the sequential model, in each iteration we randomly selected $400$ pairs among which the most informative one will be selected to query to the expert.
The hyperparameters of the model were set to the same values as in the synthetic data, with the only difference that for both data sets we set $\tau^2 = 0.01$, obtained by cross-validation.
\subsubsection{Results}
Figure \ref{Fig:5} shows the predictive performance of query algorithms on each data set. Results are averaged over $50$ runs with randomly selected training, test, and expert data. Query algorithms ask one question at a time and the model was ran for $100$ rounds.
For all algorithms and on both data sets, additional knowledge from the simulated expert reduces the prediction error. Yet the amount of reduction depends on the query algorithm. The proposed method in sequential mode obtains fastest improvement. The random model performs better than the non-sequential model. This is expected since the non-sequential model is prone to querying redundant pairs; for instance when there is a cluster of similar features that are highly informative,
asking a few of them is sufficient to inform of their grouping. However, the non-sequential model will query all the possible pairs since it does not update the utilities. To compare the effect of learned covariances using expert feedback on regularizing the model, we also compare to the baselines that make a sparsity assumption to regularize the model: LASSO, Ridge and Elastic net. It can be seen that a relatively small number of expert feedback could regularize the model well and achieve good prediction performance compared to the commonly used regularization methods.
\begin{figure}[!]
\centering
\subfloat[Amazon]{\includegraphics[scale=0.4]{mse_vs_feedback_amazon.pdf}}
\subfloat[Yelp]{\includegraphics[scale=0.4]{mse_vs_feedback_yelp.pdf}}
\caption{Mean squared error w.r.t.\ the number of feedbacks on pairs of features. MSE values are averages over 50 independent runs.}
\label{Fig:5}
\end{figure}
\subsubsection{Knowledge Elicitation vs. Collecting More Samples}
Table \ref{T1} compares the number of pairwise feedback required to obtain the same MSE value achieved by adding additional samples (reviews from the expert data set) to the training set. For the latter, we use two strategies: random selection of samples (shown by \textbf{\textbf{RND}}), and active learning strategy (shown by \textbf{\textbf{ACT}}), which selects samples based on maximizing expected information gain (similar to \cite{seeger2008bayesian}). For feedback collection, we adopt our sequential knowledge elicitation approach (shown by \textbf{\textsc{SeqElc}}). All strategies have the same ``small $n$, large $p$'' setting as starting points with $\bm{X}_{tr} \in \mathbb{R}^{100\times 241}$ for Yelp and $\bm{X}_{tr} \in \mathbb{R}^{100\times 340}$ for Amazon.
The comparison shows the potential of expert knowledge on feature similarities in the prediction when obtaining more samples is impossible or very expensive. According to the table, a particular performance is obtained by a comparable number of expert feedback and additional data. It should be noted that values obtained for the sequential elicitation model are for its best case scenario since we already removed ``I don't know''s which results in a much smaller search pool.
\begin{table}[ht!]
\centering
\caption{Comparison of the number of required samples and feedbacks to reach a particular MSE level. Values are averages over 50 independent runs. Initial MSE values for Yelp and Amazon are $1.88$ and $2.26$, respectively.}\label{T1}
\begin{tabular}{ccccc}
& & \multicolumn{2}{|c|}{More Samples} & More Feedbacks \\ \cline{2-5}
\multicolumn{1}{c}{} & \multicolumn{1}{c|}{MSE} & \multicolumn{1}{c|}{\textbf{\textbf{RND}}} & \multicolumn{1}{c|}{\textbf{\textbf{ACT}}} & \multicolumn{1}{c}{\textbf{\textsc{SeqElc}}} \\ \hline
\multicolumn{1}{c||}{\multirow{2}{*}{Yelp}} & \multicolumn{1}{c|}{1.85} & \multicolumn{1}{c|}{5} & \multicolumn{1}{c|}{5} & \multicolumn{1}{c}{13} \\ \multicolumn{1}{c||}{} & \multicolumn{1}{c|}{1.80} & \multicolumn{1}{c|}{15} & \multicolumn{1}{c|}{9} & \multicolumn{1}{c}{60} \\ \hline
\multicolumn{1}{c||}{\multirow{2}{*}{Amazon}} & \multicolumn{1}{c|}{2.20} & \multicolumn{1}{c|}{20} & \multicolumn{1}{c|}{14} & \multicolumn{1}{c}{55} \\
\multicolumn{1}{c||}{} & \multicolumn{1}{c|}{2.18} & \multicolumn{1}{c|}{27} & \multicolumn{1}{c|}{17} & \multicolumn{1}{c}{90} \\ \hline
\end{tabular}
\end{table}
\section{Discussion and Conclusion}
We proposed a knowledge elicitation approach that incorporates pairwise constraints provided by a human expert for constructing an informative prior distribution.
The knowledge elicitation problem is formulated as sequential probabilistic inference which combines expert knowledge with training data. To avoid overwhelming the expert, we proposed a query selection approach that facilitates efficient interaction. To further increase the efficiency of the interaction, we formulated a theoretically motivated subsampling approach. Results for ``small $n$, large $p$'' problems in simulated and real data with simulated users showed improved prediction accuracy already with a small number of feedbacks.
From our experience, the proposed algorithm works well for moderately high-dimensional problems (e.g., up to 500 predictors). For very high-dimensional problems, with more than thousand predictors, the computations become infeasible due to the large number of pairs. However, the presented approach is general and can be used to complement other existing knowledge elicitation techniques where the user is asked about relevance of features. In this case we can query only pairs of relevant features which significantly improves the feasibility of the model
\section*{Acknowledgments}
This work was financially supported by the Academy of Finland (grants 294238, 319264, and 313195), by the Vilho, Yrj\"{o} and Kalle V\"{a}is\"{a}l\"{a} Foundation of the Finnish Academy of Science and Letters and by Foundation for Aalto University Science and Technology. The authors acknowledged the computational resources provided by the Aalto Science-IT Project.
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Jean Camusat (mort le à Paris) est un libraire-imprimeur français.
Biographie
Fils d'un maître teinturier en drap de Sézanne, il fait son apprentissage chez le libraire parisien Thomas Blaise (). Le , il est reçu maître et sous Louis XIII, il est désigné comme libraire de l'Académie française à la fondation de celle-ci ().
Parmi ses publications, on lui doit les Négociations et traités de paix de Cateau-Cambrésis (1637).
Sa veuve, Denise de Courbes, lui succède. Leur fille épouse Pierre Le Petit, imprimeur, qui reprend le fonds.
Bibliographie
Nicolas Schapira, Un professionnel des lettres au siècle : Valentin Conrart, 2003, (La Librairie de Jean Camusat dans le mouvement d'institutionnalisation des Belles-Lettres (1630-1638) (lire en ligne)
Notes et références
Liens externes
Libraire du XVIIe siècle
Imprimeur français
Date de naissance non renseignée (XVIe siècle)
Décès en juin 1639
Décès à Paris | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 8,500 |
Understand Science
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We thank Dr. Fiona Craig for the pathology slides. University of Pittsburgh Medical Center, Pittsburgh; and the Department of Internal Medicine (B.K.N., S.S.) and Division of Cardiology (B.K.N.),
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Que Invento James Watt James Watt didn't actually invent the steam engine, he just refined it. Spanish. En realidad, James Watt no inventó el motor a vapor, él sólo lo mejoró. Me enteré el otro día de que el Conde de Sandwich no inventó el sandwich, Last Update: 2015-10-13 Usage Frequency:. Questions For Peer Review Among the questions explored
We report the quantitative pathology that occurs in. thank Amy Porter and Kathy Joseph of the Michigan State University Investigative Histopathology Laboratory for their preparation of the.
Speech Pathology Programs In Nj Speech Pathologists assist individuals to improve their communication abilities, including being able to understand others and to express themselves. Speech. Why Did Nikola Tesla Invent The Tesla Coil How to Make a Tesla Coil. Developed in 1891 by Nikola Tesla, the Tesla coil was created to perform experiments in creating high-voltage electrical discharges. Aug 21,
Both positions reflect a deep suspicion of government and mainstream medicine and a rising backlash against scientific consensus in an era when misinformation quickly spreads online. radiology at.
"The promise of machine learning is to augment what a pathologist can do alone," says Ulysses Balis, director of the division of informatics at the University of Michigan's pathology.
School of Medicine Homepage. The Department of Pathology and Laboratory Medicine continues to maintain its primary teaching program at the University of Louisville Hospital, but relies heavily on support for its residency and fellowship training with Norton Hospital, Jewish.
Types of pathological slides accepted: Virtual microscopy* or pathology glass slide/s that adequately represent. pathology report(s) online or they will not be accepted. virtual microscopy slides: The University of Michigan Medical School.
A total of 27 metaplastic carcinomas were analyzed. All slides were obtained with Institutional Review Board approval from the surgical pathology files at the University of Michigan. Hematoxylin and.
The line between true crime and legend can be a blurry one, and in a time before toxicology tests and forensic pathology, stories of mysterious. the late director of the University of Michigan's.
The following are selected medical links: Anatomy. An Online Examination of Human Anatomy and Physiology, Get Body Smart. Anatomy, Dartmouth College. Anatomy, Function, and Innervation of Muscles, Loyola University — Collection of drawings and information for all major muscles.
This initiative started and is hosted at the University of Michigan. For background information on this topic, please view the publications below. The need for the pathology community to sponsor a whole slide imaging repository with technical guidance from the pathology informatics community Hipp JD, Sica J, McKenna B, Monaco J, Madabhushi A.
In a paper posted online on June 19 (hat-tip to Harris Meyer of Modern. a health law expert at the University of Michigan, told Modern Healthcare. Clement hasn't said whether he wrote his paper on.
"We showed him slides of one of our graft patients and Jeff agreed, these were Lewy bodies," says Brundin, who is at the Van Andel Research Institute in Grand Rapids, Michigan. develop such.
Please stop by the Histology and Imaging Core in Room N310 or call to familiarize yourself with our resources, to discuss your histology and imaging needs, or to schedule deliveries to our facility at SLU. Brian Johnson can be contacted by phone (206) 685-6517 or e-mail.
University of Novi Sad in 2016, in a specially equipped classroom. at the Institute of. lected and scanned with NanoZoomer S210 Digital slide scanner. – Hamam atsu. "bird's-eye-view". Key words: Microscopy; Image Processing, Computer- Assisted;. online off-campus access to study materials, which. they spent an.
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After approval by the University of Michigan Institutional Review Board, we retrospectively searched the electronic pathology archives for all cases. sections and stained with hematoxylin and eosin.
Our analysis focused on variations that were not in the Database of single-nucleotide proteins (dbSNP) and/or those that had been associated previously with cancer based on information in the.
Esa Jobs Florida Entomologist William Kern, an associate professor in the entomology and nematology department at UF's Fort Lauderdale Research and Education Center, said in an interview earlier this month that the abundance of. Tim Chapman Miami Herald Staff The Florida Keys and parts of the Panhandle rank among. scientists found the United States is doing a poor job
Welcome to the Cell and Tissue Biology home page! This course explores microanatomy and the many fascinating links between form and function at the microscopic level. To be successful in the M2 pathology course, you must be able to recognize and understand the function of normal cells and tissues. This is the main objective of this course.
If you cannot find a structure on one slide, don't waste a lot of time, simply go to another slide where it may be preserved with better fixation. Posted/Modified on Thursday December 21st: CTB II Histology College of Medicine Introduction 2018 The second semester of Cell and Tissue Biology is organized similar to the first semester.
eRAM Principal Investigator Authorization Request Form. The University of Michigan uses a web-based system called eResearch Animal Management (eRAM) for managing the submission, review, and approval of all applications/protocols involving the use of.
However, current mouse brain dissection techniques usually toss aside this tissue, even though Heiko Braak, Ulm University, Germany. The results appeared online May 5 in the Journal of Neural.
It is our pleasure to present this site as a resource for gross room staff and surgical pathologists. Most principles of gross pathology outlined in these pages are generalizable to most labs, however, some items are specific to The University of Chicago.
Jul 03, 2019 · Developed by researchers at the Institute for Pathology in Basel, Switzerland. Search form and samples in English, database instructions in German. Pathorama. Provides images and slides, created and maintained by researchers at the Institute for Pathology in Basel, Switzerland. Regents of the University of Michigan.
The multiple choice questions in General Pathology, Organ System Pathology, Clinical Pathology, and Extended Matching banks have three formats. For General Pathbology and Organ System Pathology exams with single best answer multiple choice questions, click.
The Internet Pathology Laboratory for Medical Education (University of Utah, College of Medicine) Images of Tissues prepared for Histology LUMEN: Histology Index This site is part of the Loyola University Medical Education Network (LUMEN). Kansas "JayDoc" HistoWeb From the Department of Anatomy & Cell Biology, University of Kansas.
NS398 (COX-2 inhibitor) was purchased from Cayman Chemical (Michigan, MI). ONO-AE3-208 (selective. is a kind gift of Dr. Xiufen Zheng (Department of Pathology and Laboratory Medicine, University of.
2016-2017 Grand Rounds Online Recordings. June 1 Depression Screening in Pregnancy: Improving the Process Gwen Fitz-Gerald, MD Women's Health Fellow, OBGYN University of Michigan. May 25 Controversies in PAG Alla Vash-Margita, MD. Department of Pathology, Department of OBGYN University of Michigan. September 8
Astian Waite, Ohio University. Ali Jandal, University of Wisconsin. Comprehensive coverage of pathology, physiology, pharmacology, and clinical reasoning.
Brenda Newman and Sanjaya Gupta for their assistance in obtaining the dermatologic photographs and pathology slides. From the Louis Stokes. System and Department of Internal Medicine, University of.
Eileen H. Bigio 2 Eileen Bigio received her BSci from the University of Michigan, Ann Arbor, MI, and her MD from the University of Texas Medical Branch, Galveston, TX, USA. She is the Paul E. Steiner.
In the new study, led by scientists from the University of Michigan Comprehensive Cancer Center. The results will be published this week in the online version of PNAS by a team from U-M, the.
Elizabeth Howerth. field of pathology ensures that she and her students are never bored. Where did you earn degrees and what are your current responsibilities at UGA? I received my B.S. from the.
Stephen Hawking Dead Body Found The singer was found dead in the London Hilton on Park Lane. The world lost one of its greatest minds on 14 March as Professor Stephen Hawking died at the age of 76. Hawking had lived with motor. CAMBRIDGE, England: Parts of the world have made huge progress toward stamping out debilitating tropical diseases such
September 1, 2019 @ 9:47 am · Posted in Science Lovers Site · Author:admin
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The source code of zitat.json is licensed under the [MIT License](https://opensource.org/licenses/MIT). The open book under [CC-BY-SA](https://creativecommons.org/licenses/by-sa/2.0/) <a href="http://fabforge.ch">fabforge, Fabian Dennler</a>. | {
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New Brighton rape investigation closed
Police had appealed for information after incident reported on Bank Holiday Monday
Get our MyWirral newsletter, for the best news, pictures, opinions and video from across the peninsula
Police said they are no longer investigating an allegation that a woman was raped as she went on a morning walk in New Brighton .
Detectives launched an appeal for information after reports of the attack on the 45-year-old in the area near to the Derby Pool on Monday, August 28.
The woman was said to have been hit from behind, causing her to fall to the floor, before being dragged up a hill and raped.
But today Merseyside Police said a "full and detailed investigation" had been conducted and the case was now closed.
The force said detectives were no longer looking for an attacker.
Police said they are no longer investigating an incident in New Brighton
A police spokesman said: "Having conducted a full and detailed investigation into this allegation, Merseyside Police can confirm we are no longer looking for an offender into this allegation of rape and the case is now closed.
"We would like thank the public for their support during the course of the investigation and reassure residents and visitors to the coastal area, that we will always thoroughly investigate all such allegations and will work with partners to ensure the safety of the community."
Police patrols had been increased in the area in the wake of the rape allegation, and a Facebook group was set up to bring together women who were too afraid to run or walk alone.
Merseyside Police
LGBTWoman handed in her notice with no savings to gamble on dream jobLeanne decided to pursue her dream job | {
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require 'memory_profiler'
require_relative '../lib/restpack_serializer'
class SimpleSerializer
include RestPack::Serializer
attributes :id, :title
end
simple_model = {
id: "123",
title: 'This is the title',
}
# warmup
SimpleSerializer.as_json(simple_model)
report = MemoryProfiler.report do
SimpleSerializer.as_json(simple_model)
end
puts "="*64
puts "Simple Serializer:"
puts "="*64
report.pretty_print(detailed_report: false)
class ComplexSerializer
include RestPack::Serializer
attributes :a, :b, :c, :d, :e, :f, :g, :h, :i, :j, :k, :l, :m, :n, :o, :p, :q, :r, :s, :t
end
complex_model = {
a: 1, b: 2, c: 3, d: 4, e: 5, f: 6, g: 7, h: 8, i: 9, j: 10,
k: 11, l: 12, m: 13, n: 14, o: 15, p: 16, q: 17, r: 18, s: 19, t: 20,
}
# warmup
ComplexSerializer.as_json(complex_model)
report = MemoryProfiler.report do
ComplexSerializer.as_json(complex_model)
end
puts "="*64
puts "Complex Serializer:"
puts "="*64
report.pretty_print(detailed_report: false)
| {
"redpajama_set_name": "RedPajamaGithub"
} | 1,501 |
Sir Edward Lewknor or Lewkenor (1542 – 19 September 1605) was a prominent member of the puritan gentry in East Anglia in the later Elizabethan period, and an important voice on religious matters in the English Parliament.
Origins and young life
Edward was the eldest son of the courtier Edward Lewknor of Kingston Buci, Sussex, and his wife Dorothy, daughter of Robert Wroth and Jane Hawte, and sister of Sir Thomas Wroth. His father grew up in the wardship of Robert Wroth (an associate of Thomas Cromwell and Richard Rich), who left directions in his will (1536) for the marriage of his ward to his daughter Dorothy. The elder Lewknor's career as a courtier benefited from the high favour in which King Edward VI held his brother-in-law Thomas Wroth, one of the Gentleman of the Privy Chamber, whose wife Mary was a daughter of Richard Rich. However, with King Edward's death and the accession of Queen Mary in 1553, Wroth (a strong favourer of the Protestant reform) went with Sir John Cheke and Sir Anthony Cooke into exile abroad.
The elder Lewknor, who was reputedly Groom Porter to both monarchs, kept his position at court, but became implicated in the "Dudley conspiracy" (of Henry Dudley and Henry Peckham) to depose Queen Mary and install her sister Elizabeth when he used his situation to procure a copy of King Henry VIII's will on their behalf. In 1556 he was found guilty of treason, attainted, and imprisoned in the Tower of London under deferral of execution awaiting a possible pardon. At this time the Queen sought urgently to force Sir Thomas Wroth to return to England, but without success, and after three months in the Tower attended by his wife and one of his daughters Lewknor expired there in September 1556. His son Edward at the age of 14 therefore faced a complete reversal of his childhood status and expectations when his father was buried at the Tower.
Many lands, including the manor and advowson of Hamsey, East Sussex, were restored to his mother in February 1556/57 by Mary's Letters Patent. In the first year of Elizabeth an act was passed, on the petition of Lewknor's four sons (Edward, Thomas, Stephen and William) and six daughters (Jane, Maria, Elizabeth, Anne, Dorothie and Lucrece) to restore them to their blood, lineage and degree. This restored all their ancestral hereditaments excepting those held in use, possession or reversion by their father at the time of his treason and attainder, or any which either Mary or Elizabeth should have found cause to withhold. They were therefore entitled to make their pedigrees as Lewknor's heirs as if he had never been attainted, and to make conveyances thereof, except of lordships, honours and other benefits to which their Majesties were entitled on account of the attainder.
His fortunes so far restored, Edward was educated at St John's College, Cambridge, matriculating a pensioner at Easter 1559 and graduating B.A. in 1561, and was a fellow of the college from 1561 to 1563. He entered the Middle Temple in 1562 to study law. His son recorded in his father's printed epitaph that he next found some service in the royal household of Queen Elizabeth. His next brother Thomas Lewknor (presumably the same who matriculated from Trinity College, Cambridge in Lent term 1557–58 and graduated B.A. in 1562–63) was presented Rector of Hamsey by the Diocesan 'by lapsed authority' in 1563, remaining until 1568.
Marriage and relocation to Suffolk
Around 1570 Edward married Susan, daughter of Sir Thomas Heigham of Higham Hall, Suffolk and his wife Martha, daughter of Sir Thomas Jermyn of Rushbrooke Hall. While his mother Dorothy Lewknor remained of Kingston Buci, in consequence of his marriage Edward moved to Suffolk, settling at Denham near Bury St Edmunds, Suffolk, near to Rushbrooke and Higham, and established his family there, where the male line continued in three generations. This placed him firmly within the kinship of the central East Anglian gentry, and, so far as his immediate Jermyn and Heigham relations were concerned, with a group embodying the radical puritan interest in Suffolk. Lewknor assumed this role naturally and energetically: the twin social pillars of the magistracy and ministry working together under the authority of this particular family group (which had a strong parliamentary presence) form the subject of an oft-quoted case-study by Professor Collinson.
Susan Heigham's father Sir Thomas Heigham was the grandson and senior heir of John Heigham (died c. 1522), whose younger brother Clement Heigham of Lavenham (died 1500) was father of Sir Clement Heigham of Barrow, Suffolk (died 1571) Speaker of the House of Commons in 1554, an open Catholic, and a notable persecutor of Protestants. Speaker Higham's son Sir John Heigham (died 1626), however, with whom Lewknor had more to do, was a central patron of the puritan movement in East Anglia. The Jermyns were similarly bi-partisan. Martha Jermyn's father Sir Thomas died in 1552, and her brother Sir Ambrose Jermyn (died 1577) was reportedly a fervent Roman Catholic and strong persecutor of Protestants in East Anglia during the reign of Queen Mary, but by another account took immediate steps to curb the excesses of commissioners as soon as Elizabeth came to the throne. His son, Sir Robert Jermyn (died 1614), however, was an uncompromising puritan and patron, and the associate of John Heigham.
Martha Heigham held the manor of Denham as her jointure and may have been responsible for building Denham Hall (beside the church), the old fabric of which remains behind its later facade. Strongly puritan in sympathy, she lived down to 1593. Her minister there was Robert Pricke, alias Oldmayne, whose family name was apparently changed to evade persecution during Mary's reign. In 1577 Oldmayne baptized his son Timothy at Denham, and remained minister there for 30 years throughout the time of Edward and Susan Lewknor. In 1581 Robert Jermyn's sister Frances died leaving endowments for Fellowships at St John's and Trinity College, Cambridge, granting Robert the choice of appointments, and she gave copies of the Tremellius bible to several East Anglian ministers including Richard Pricke and John Knewstub. Upon the foundation of Emmanuel College, Cambridge in 1584, Sir Robert's heir Thomas Jermyn was at once enrolled, Sir Robert himself endowed a Fellowship there, and a lasting connection was begun in which the Lewknors followed.
Parliament
Lewkenor was sponsored in a successful Parliamentary career by Puritan sympathisers such as the Earl of Leicester, with whose help in 1571 he was elected MP for Tamworth. In 1572 he was elected MP for New Shoreham, near his ancestral domains. He was then elected for Maldon in 1584 and 1586. Lewknor, Sir John Heigham (knighted 1579, MP for Ipswich in 1584 and for Suffolk in 1586) and Sir Robert Jermyn (MP for Suffolk in the same parliaments) led a strongly Puritan faction in Parliament, often working together in committee, advocating the importance of a learned clergy and the reform of episcopal powers and activities, with which Jermyn in particular came into direct confrontation.
In 1584 Lewkenor was involved with a bill for the more reverent observation of the Sabbath – which, as an intervention in Church affairs, met with royal resistance. Later in that year he served on a committee to consider petitions for the liberties of godly preachers. In 1585 he offered a petition concerning abuses in the ministry on behalf of the people of Sussex, simultaneously overseeing the formulation of an official prayer of thanksgiving to God for the great benefits bestowed upon the realm by Queen Elizabeth, to be used in Parliamentary proceedings. In late 1586, in test or proof of this loyalty, he, Heigham and Jermyn were appointed with others to consider a means by which Mary, Queen of Scots might be brought to the execution of justice.
This, however, did not protect him when, in 1587, a revised Book of Common Prayer and accompanying bill were put before the House by Anthony Cope, M.P. for Banbury, Oxfordshire. It was hoped thereby to reform certain problems in ecclesiastical affairs, and the proposer asked for it to be read and to be approved to replace the existing books in all churches. Lewkenor was among those who spoke, solemnly but unsuccessfully, in favour of its reading. These proceedings caused immediate royal disapproval, and when an issue of freedom of speech was raised the Member doing so (Peter Wentworth) was sent to the Tower of London. On the following day Cope and three others including Edward Lewkenor were also imprisoned there. Sir John Heigham and Sir Robert Jermyn were among those appointed 11 days later to consider their release: their durance lasted about a month.
Later life
Lewkenor was not in the Parliament of 1588–89. In 1589, when he sat for Maldon again, his mother Dorothy Lewknor died at Kingston Buci, making Edward sole executor responsible for her legacies. In these she and he were bound by a recognizance of two thousand marks made with her kinsman Sir Francis Walsingham in 1570, limiting to £1000 any bequests or payments thereof made to unmarried daughters, with which she exactly complied. In 1594 Lewknor sold the manor and advowson of Hamsey, which in 1563 had been granted to him in reversion to take effect after his mother's death. In the previous year, he once more sitting for Maldon, his mother-in-law Martha Heigham died at Denham, also making Edward her sole executor and leaving him very extensive estates, Denham itself coming to him in Susan's share of the matrilineal inheritance divided between the two Heigham daughters.
Martha by her will established a scholarship at Emmanuel College (which it fell to Edward Lewknor to implement) on condition that it be enjoyed by Timothy Oldmayne when he should be ready to take it up, which Timothy accordingly did in 1595, proceeding to BA in 1598–99 and MA in 1602. Robert Jermyn, the younger son of Sir Robert, matriculated from Emmanuel in 1597 and graduated BA in 1599–1600. The Suffolk preacher Richard Blackerby, meanwhile, of Trinity College (admitted 1587, BA c. 1590), who was greatly influenced by the teaching of William Perkins, on leaving Cambridge lived in the household of Sir Robert Jermyn as his chaplain, and then for two years lived at Denham in the same capacity to the Lewknors, before marrying Timothy Oldmayne's sister. Lewknor's elder son, Edward, was admitted to Emmanuel in 1599.
Edward Lewknor was MP for Newport, Cornwall in 1598. He continued active in parliamentary business of various kinds, including the extended consideration of proposed bills for relief of the poor and prevention of idle beggars in November 1597. Having been knighted by King James I in 1603, he was returned as MP for Maldon in 1604, and resumed his intense involvement in questions of church and religion. In particular he strongly advocated that the requirement of subscription should extend only to the Thirty-nine Articles and not to the Prayer-book, so that the "godly ministers" should not be excluded from the established ministry.
The younger Edward Lewknor (the second of Denham) was admitted pensioner at Emmanuel College in July 1604, and his elder brother graduated BA in 1605. Called home from Cambridge to Denham with a neighbour's son in 1605, to avoid a smallpox outbreak, the friend brought the infection with him which, at the beginning of October 1605, claimed the lives of their mother and father on consecutive days.
Death and exequies
The dates of death for Dame Susan (who died first) and Sir Edward vary slightly between the tomb inscription (2 and 3 October), the printed epitaph and the funeral certificate (3 and 4 October). They were buried in St Mary's church, Denham on 5 October 1605, and Sir Edward was succeeded as heir by his elder son Edward Lewknor.
The funeral, which was held on 9 January following, was a formal heraldic occasion, his sons, daughters and sons-in-law attending as mourners, the standard being borne by his sister Mary's son John Machell, and the pennon by Edward as Chief Mourner. Robert Prick alias Oldmayne delivered a funeral sermon which was published. Edward the son erected an elaborate canopied table monument featuring painted stone carvings of Sir Edward, his wife and their eight children at prayer, within a chapel in the church recently built for that or another purpose. He also published a Threnody for his father, in which Latin, English, Greek and Hebrew verse tributes from many university theologians were collected, including some lines from William Bedell, then of Emmanuel College and afterwards of Horringer, and from Joseph Hall, also of Emmanuel, then minister at Hawstead.
The funeral was directed by the Richmond and Somerset Heralds (John Raven and Robert Treswell). The heraldry of the tomb includes as a canopy centrepiece a shield with many quarterings alluding to the ancestry of Lewkenor's great-grandfather, another Sir Edward (d. 1522), both in his paternal descent from the Bardolph, Tregoz, Noel and D'Oyly, the Dallingridge and Echingham families, and in his maternal Camoys and De Braose inheritance through Elizabeth (Isabella) Radmylde. It is an emblazoning to represent the House of Lewkenor of Kingston Buci in that branch, no additional heraldry being shown for the intervening generations. The meaning and contemporary understanding of this descent is shown in an extensive pedigree drawn up in 1612 and 1615 in the time of the younger Sir Edward Lewkenor, who in 1610 became son-in-law of Sir Henry Neville.
In an equivalent position at either end of the canopy are impalements showing the same quarterings for Lewkenor (dexter) with eight-quarters for Heigham (sinister). Individual Lewkenor impalements for the marriages of Sir Edward's children are displayed on the transoms of the canopy, those at the eastern side being prepared for the two sons with the sinister pales left invitingly blank. The Latin tomb inscription (no doubt written by his son Edward) refers to his loyal and valuable services for court, parliament and commonwealth, which earned him the approbation of all good men, and his work to introduce the preaching of the Gospel in Denham. The Christian virtues of Dame Susan, her devout modesty, chastity, generosity and kindness to the poor are also commended.
Sir Edward died possessed of considerable estates (including the half of Sir Thomas Heigham's estate which his wife had inherited), to which his eldest son was heir. The Inquisition post mortem was held on 9 January 1605/06.
Children
The children of Sir Edward Lewkenor and his wife Susan Heigham are shown as follows:
Dorothie (1575–1603), married Robert Castell, armiger, of East Hatley, Cambridgeshire. She is said to have died without issue, though a son Robert was christened at Denham in 1598. She died before her parents, and is not among the mourners depicted on Sir Edward's tomb. Sir Robert remarried and had five children, the elder son being named Robert.
(Sir) Edward (1586–1618), of Denham Hall, was admitted pensioner at Emmanuel College, Cambridge in 1599 and proceeded to B.A. in 1604–05. He married (?1607 or 1610) Mary, daughter of Sir Henry Neville and Ann Killegrew of Billingbear House, Berkshire, by whom he had six children. He was knighted in 1606, was M.P. for West Looe in the Parliament of 1614 and served as High Sheriff of Suffolk in 1617, while holding which office he died. He was buried at Denham.
(Sir) Robert (1588–1636), was admitted pensioner at Emmanuel College in 1604. He was knighted in 1607, married Mary (daughter and coheir of Alexander Hamon of Acrise, Kent), by whom he had five children. Sir Robert was to inherit the manor of Kingston Buci, but also inherited the manor of Acrise from his father-in-law, and was High Sheriff of Kent in 1630.
Hester (d. 1612), married (1601) Robert Quarles of Romford, Essex, eldest son of James Quarles of Ufford near Peterborough, Clerk of the Green Cloth. Robert, knighted in 1608, was brother of the poet Francis Quarles. Robert made two further marriages.
Anne (d. 1608), married (c. 1598) Godfrey Rodes, armiger, of Great Houghton, Yorkshire, eldest son of the second marriage of the judge Sir Francis Rodes of Barlborough Hall. They had five children.
(Martha, died in childhood).
Martha (d. before 1639), married Thomas Gurney, armiger, eldest son of Henry Gurney of Ellingham, Norfolk. They had eight children. She survived her husband and was buried at Barsham, Norfolk.
Sarah, married Thomas Stuard, armiger, son of Thomas Stuard of Barton Mills, Suffolk (and probably grandson of Simeon Stuard of Lakenheath). Six of their children were christened at Denham between 1608 and 1619.
Elizabeth (b. 1591), married (before 1618) Thomas Catelyn (possibly second son of Richard Catelyn or Catlin, Serjeant-at-arms, of Wingfield Castle). Three of their children were christened at Denham between 1619 and 1622.
Susan (d. 1609), without issue.
References
External links
Entry in Oxford DNB
1542 births
1605 deaths
Alumni of St John's College, Cambridge
Members of the Middle Temple
English Puritans
Members of the pre-1707 English Parliament for constituencies in Cornwall
English MPs 1571
English MPs 1572–1583
English MPs 1584–1585
English MPs 1586–1587
English MPs 1589
English MPs 1593
English MPs 1597–1598
English MPs 1604–1611
Members of Parliament for Maldon
People from Hamsey | {
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You will find it, which gives the code: ...\n4 replies | 47 view(s)\n\u2022 Today,\u00a010:48\nMarkFL replied to a thread The Fonz and Geometry in Chat Room\nYes, and I was just pointing out that there can be other reasons a student fails besides lack of innate ability to understand the material, or an...\n5 replies | 63 view(s)\n\u2022 Today,\u00a010:18\nMarkFL replied to a thread The Fonz and Geometry in Chat Room\nIf a child's parents consistently put a child down, then I think this can have negative consequences on the child. I think there are a great many...\n5 replies | 63 view(s)\n\u2022 Yesterday,\u00a023:08\nI disagree with this...I think it is the societal attitude that it's okay to fail at math that is part of the problem. Someone says to their friends,...\n9 replies | 94 view(s)\n\u2022 Yesterday,\u00a022:23\nIf we have 2000 people, 300 of which are women, then the probability that all 300 women will be on the same team is given by: P(A)=\\frac{{1700...\n5 replies | 50 view(s)\n\u2022 Yesterday,\u00a022:01\nI think your second method is correct. Suppose we call the teams $X$ and $Y$...and now we need only look at one team, so let's look at team $X$. If...\n5 replies | 50 view(s)\n\u2022 Yesterday,\u00a019:04\nMarkFL replied to a thread Solar Eclipse 2017 in Chat Room\nYesterday during the big event, we had pervasive heavy cloud cover and intermittent rain. Today, sunny and clear all day. Story of my life...(Giggle)\n8 replies | 233 view(s)\n\u2022 August 20th, 2017,\u00a001:29\nMarkFL posted a visitor message on Peter's profile\nHey Peter! (Wave) I edited your post to remove the duplicate content. Sorry for the late reply, I was busy \"powering through\" a tedious 3 hour...\n\u2022 August 17th, 2017,\u00a002:10\nSmall quibble...axis of symmetry is: t=-\\frac{1}{105} So, since the parabola opens up, the vertex is a minimum, so the minimum distance will be...\n8 replies | 174 view(s)\n\u2022 August 17th, 2017,\u00a000:59\nFor a parabola of the form: f(x)=ax^2+bx+c We know the axis of symmetry is at: x=-\\frac{b}{2a} So, for:\n8 replies | 174 view(s)\n\u2022 August 16th, 2017,\u00a022:42\nOverview: This product is designed to auto-post a welcome thread for all new users once they have completed all verifications, and\/or returning...\n0 replies | 28 view(s)\n\u2022 August 16th, 2017,\u00a021:58\nIsn't this question a duplicate of the following? 231.12.3.65 Determine the smallest distance between a point and a line\n1 replies | 45 view(s)\n\u2022 August 16th, 2017,\u00a017:25\nHey freedomdorm! I saw you posted this update on to another question so I gave you your own thread. 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\section{Introduction}
\label{Sec:Introduction}
Central venous catheter (CVC) lines are essential in the care of patients with severe diseases treated in surgical, intensive care and oncological units with fluid and transfusion therapy, including total parenteral nutrition, antibiotic therapy and also for chemotherapy purposes \cite{johansson2013advantages}.Traditionally, clinicians used non-tunneled or tunneled CVCs by centrally inserting catheters into the superior vena cava (SVC) via the subclavian or the internal jugular veins depending on the indication and on how long the patient will require the CVCs. Since direct puncture of one of the great veins at the upper thoracic aperture by CVCs are difficult to perform and carries serious complications such as pneumothorax and hemothorax \cite{maki2006risk}, peripherally inserted central catheter (PICC) was introduced to clinical practice for easy access, longer usage and fewer complications alternative to traditional CVCs \cite{hammarskjold2008peripherally}. The PICC is a thin and long flexible catheter made of biocompatible material, either silicone or polyurethane, inserted percutaneously into the basilic or cephalic vein in the forearm, often with the help of ultrasound or fluoroscopy guidance. The catheter is then advanced into the central circulation with tip of the catheter most often placed in the SVC or at the junction of the superior vena cava and the right atrium \cite{maki2006risk}.
Mispositioned or migration of PICCs can have potentially serious complications such as thrombus formation or cardiac arrhythmia \cite{funaki2002central}. As a result, PICC positioning is always confirmed with a chest radiograph (CXR) immediately after the insertion. This requires timely and accurate interpretation by a radiologist. Delays in treatment initiation can be substantial particularly when this radiograph is one of many in a long list waiting to be interpreted \cite{tomaszewski2017time}. Deep learning techniques, however, may help prioritize and triage the review of radiographs to the top of a radiologist's queue, improving workflow and turnaround time.
If the misplaced tip of PICC can be automatically detected, the diagnosis time can be shortened and the complication rate can be reduced by repositioning or removing it. To achieve this, the existing studies tried to automatically track the whole line of PICC and its tip together with the aid of image processing, pattern recognition, and recently deep learning (DL)-based technology \cite{keller2007semi, yu2020detection, yi2020automatic, ambrosini2017fully, lee2018deep, subramanian2019automated}. The expert clinicians generally detect the position of the PICC tip by following the line from the relatively visible position of the PICC line on the outside to the inside of the lung. Following this doctor's diagnosis process, these aforementioned studies further strengthened the interpretability by allowing the model to predict the entire PICC line rather than simply predicting the tip position. In other words, these studies detected the tip based on the segmented shape after segmenting the whole PICC line. In particular, even with the latest DL-based technology, the PICC tip is very small so difficult to learn and provide exact location of the tip. Therefore, it is necessary to segment the entire PICC line in order to compensate for this inaccuracy issue of prediction result for the tip position.
However, there still exist some technical limitations in accurately predicting the tip location even with the help of PICC full line segmentation results. The typical limitation is the multiple fragments phenomenon (MFP): In the process of predicting the PICC line by the model, it is not predicted as one complete line as the ground truth, but multiple divided lines are provided. These MFPs occur frequently even with the gold standard DL-based models such as FCN \cite{long2015fully} and U-Net (UNET) \cite{ronneberger2015u} as shown in Figure \ref{fig1:MFP}. This MFP makes the prediction model cause both false detection and non-detection of the actual PICC line, thereby making it difficult for the clinician to determine the actual tip position (i.e., distinguish where the correct end of the PICC catheter is) even with the aid of these automatic diagnosis models by tracking their PICC line estimates.
\begin{figure}[t!]
\centering
\includegraphics[width=0.8\textwidth]{Figure1.jpg}
\caption{Illustration of MFPs and the corresponding tip detection problem of the existing AI models: (a) ROI of CXR image (b) Ground truth PICC line (c) Original CXR image (d) Ground truth tip (e) line prediction by FCN (f) line prediction by UNET (g) line prediction by proposed MFCN (blue arrow, used as tracking path of PICC tip). In the CXR image, if there exists an object whose shape is similar to that of PICC such as a spine and clavicle (green border image), or if the actual PICC line is shown as blurred due to being overlapped by some anatomical structures (brown border image), a false-negative (i.e., break) or false-positive error occurs in the PICC segmentation result. As the AI model tracks this PICC segmentation result (blue arrow) and selects the unbroken lowest point of it as the tip location (orange circle), so these errors provide a significant error in the precise location prediction of the actual tip.}
\label{fig1:MFP}
\end{figure}
Existing DL-based studies introduced the process of extracting the entire PICC line to effectively detect the tip, but in this process, the MFP was not directly solved. This makes it difficult to accurately identify the location of the tip in the extracted PICC line estimate, limiting its clinical use. Specifically, there have been studies to detect the tip position by dividing the entire structure of the PICC line \cite{ambrosini2017fully, subramanian2019automated}, but they still have the problem of MFP as they assume that the complete PICC line is extracted. Yu \textit{et al}. detected the tip position more precisely by performing object detection on the tip position separately in addition to PICC line segmentation \cite{yu2020detection}. And Yi \textit{et al}. tried to solve the difficulties of data annotation by creating a virtual PICC using the generated model \cite{yi2020automatic}. However, neither of these studies focused on directly solving the MFP to improve the performance of tip detection. The most relevant study to supplement MFP is that published by Lee \textit{et al}. \cite{lee2018deep}. They proposed a post-processing technique using the hough transform \cite{duda1972use, kiryati1991probabilistic} applied to the PICC line segmentation result and tried to resolve the MFP to improve the tip detection performance. However, these results are sensitive to the hough transform parameter, so it is difficult to have a common parameter in which MFP does not occur in all images.
Our study focused on the MFP problem of existing DL-based PICC tip detection models and proposed a method generally applied to these existing models to solve the MFP problem so consistently improve their performance of PICC tip detection. We call this method the multi-fragment complementary network (MFCN). The proposed MFCN consisted of the following three stages: Stage 1. Backbone network for PICC line segmentation, Stage 2. Patch-based PICC line segmentation network, Stage 3. PICC line reconnection network.
Stage 1 is an arbitrary network for PICC line segmentation, and any existing proposed model can be applied. That is, the proposed MFCN is the result solving the MFP problem of PICC line segmentation of Stage 1 by applying two models of Stage 2 and 3 at the next steps. Therefore, the main contribution of our study is in these Stage 2 and Stage 3 models.
Stage 2 model of MFCN, the patch-based segmentation model, extracts a small patch in a whole CXR image by using a random patch method and use this patch as an input to the model rather than the whole CXR image. Because the patch-based approach focuses more on the PICC lines compared to a model that takes the entire image as input, it can better preserve features of sparse signals such as PICC lines that may be lost due to the down sampling process within the model. In addition, it is useful noting that the patch-based approach can generate multiple patches from one image so provide sufficiently good performance even on a smaller training dataset \cite{zhao2018deep, coupe2011patch}. Similarly with these results, the proposed MFCN has also superior PICC line extraction and tip detection even with a small number of training samples, due to the patch-based characteristic of Stage 2 model.
Though Stage 2 effectively address the MFP problem caused by the sparseness of the PICC line and small training data, it is still difficult to completely solve the MFP issue through the patch-based approach of Stage 2 alone, if the PICC line is partially covered by anatomical structures or its edges are weakly expressed, Therefore, we proposed another network named PICC line reconnection network as Stage 3 that randomly creates a virtual disconnection on PICC line, allowing the network to perceive the disconnection extrinsically and complement it as a single PICC line. Through this method, it was possible to effectively improve the disconnection phenomenon caused by bone occlusion, thereby further improving the tip detection result.
In summary, the proposed MFCN has the following main contributions to overcome the limitations of existing PICC tip detection techniques:
\begin{enumerate}
\item (Multi-stage configuration to improve the performance of tip detection) By composing the proposed model in a multi-stage method, it can be combined with the existing conventional model to improve the performance of the existing model.
\item (Second stage for optimizing PICC sparse line extraction) Through the patch-based segmentation technique, the network can focus more on the sparse area of PICC line in the entire CXR image, and the non-detection and false detection of this line are further improved.
\item (Third stage for enhancing the line breakage robustness) By generating virtual multiple broken lines from the truth/whole PICC line and training the network to generate a complete PICC line from them, the network output can be robust to the MFP. Through this, it is possible to effectively improve the breakage caused by the overlapping of the PICC and other anatomical structures.
\end{enumerate}
We applied the proposed MFCN to the existing gold standard five DL-based models and experimentally evaluated further improvement in tip detection and PICC line extraction performance. Code is available at \href{https://github.com/kskim-phd/MFCN}{MFCN-link}.
\begin{figure}[t!]
\centering
\includegraphics[width=0.8\textwidth]{Figure2.jpg}
\caption{Schematic illustration of (a) baseline model and (b) proposed MFCN: MFCN consists of three stages where the supplementary process of second and third stages is added to the existing model (the first stage) to improve its PICC line restoration performance, thereby enabling precise tip detection.}
\label{fig2:overview}
\end{figure}
\section{Methods}
\label{Sec:Methods}
\subsection{Overview of the proposed MFCN} \label{Sec:Overview}
We described the training and prediction process of the baseline method and the proposed MFCN in Figure \ref{fig2:overview}. The proposed MFCN (Figure \ref{fig2:overview}(b)) is a scheme designed to be additionally combined with any conventional PICC line segmentation network (Figure \ref{fig2:overview}(a)). Specifically, the proposed model consists of a total of three stages (Figure \ref{fig2:overview}(b)): the first stage is the conventional segmentation network (Figure \ref{fig2:overview}(a)), the second stage is the proposed patch-based segmentation network, and the third stage is the proposed line reconnection network. Both of the second and third stages are added to the first stage network to improve the PICC line segmentation performance and finally to detect the tip more accurately.
In MFCN, the model for each stage is trained separately (illustrated as green line) with input and output data pre-processed (illustrated as black line) by some proposed external modules (e.g., random patch generation module in the second stage and virtual multi-fragment line generation (VMFL) module in the third stage). Specifically, the random patch generation module in the second stage generates a partial image by randomly cropping a patch containing PICC from the original CXR image in training data. Then the second stage trains the network to extract the partial PICC line corresponding to this generated patch by taking it as input. In the third stage, we generate a virtual multi-fragmented PICC line through the VMFL module and let the network to estimate its truth PICC line by taking it as input.
\begin{figure}[t!]
\centering
\includegraphics[width=0.8\textwidth]{Figure3.jpg}
\caption{Schematic illustration of the first stage model: (a) the training and (b) inference phases}
\label{fig3:first}
\end{figure}
In the inference phase, the trained model at each stage is combined together as the model output at the current stage is used as the input of that in the next stage as shown in the blue line in Figure \ref{fig2:overview}(b). Specifically, in the case of the second stage, segmentation result for the partial PICC line given by each patch output is aggregated as the complete prediction result of the whole PICC line through majority voting. And this prediction result for the whole PICC line is used as the input of the third stage model. As a result, as the CXR image goes through the stages of the inference phase, it can be observed from the result image of each stage at the bottom of Figure \ref{fig2:overview} that the complete PICC line is gradually extracted without any break or interruption.
It is useful to note that the architectures of the proposed second and third stage models do not have any specific structure and can be applied to any architecture of the existing networks for segmentation (e.g., FCN \cite{long2015fully}, U-Net (UNET) \cite{ronneberger2015u}, FC-DenseNet (FCDN) \cite{jegou2017one}, Attention U-Net (AUNET) \cite{oktay2018attention}). For the architectures of the proposed second and third stage models, we selected FCDN among existing segmentation networks, as it performs better or similar compared to the other models. We detailed it in section \ref{Sec:backbone}.
\subsection{The first stage network}
The first stage network is a model that receives a whole CXR image as an input and provides a binarized map of the same size as an output, consisting of 1 for pixels belonging to PICC and 0 for pixels not belonging to PICC. The first stage model can be set as any conventional PICC line segmentation network like the baseline model as shown in Figure \ref{fig2:overview}(a). The goal of the proposed MCFN is to improve the first stage model's segmentation performance by adding the second and third stage models. In the experimental section, we set up various existing models as this first stage network and proved that the proposed MFCN consistently improved performance for each model.
\subsubsection{Training phase for the first stage network}
Figure \ref{fig3:first}(a) depicts the learning process of the first stage model. The original CXR image was resized to have 1024$\times$1024 resolution, then the contrast-limited adaptive histogram equalization (CLAHE) \cite{pizer1990contrast, reza2004realization} was performed as pre-processing so that the PICC could be seen more clearly. After that, the pre-processed image was used as an input of the first stage backbone network, and the network was trained to let the segmentation result of PICC line have a pixel value of 1 and the other areas have a pixel value of 0. Since individual pixel output values of the model were expressed as probability values between 0 and 1, we followed the conventional approach by extracting the PICC line through minimizing (the weighted) cross-entropy loss.
\begin{figure}[t!]
\centering
\includegraphics[width=0.8\textwidth]{Figure4.jpg}
\caption{Description of various examples with varying thresholds for the final PICC line prediction results of the first stage network}
\label{fig4:thresh}
\end{figure}
\subsubsection{Inference phase for the first stage network}
In the inference phase of the first stage network, different from the training phase, more relaxed thresholding is given to allow false-positive (FP) appropriately, but set to reduce false-negative (FN). The rest of the process proceeds in the same process as the training process to obtain the model output. Note that each pixel in the first stage probability map (i.e., after the softmax layer) is distributed between 0 and 1. In this study, we binarized it based on a threshold of 0.01 to make the final PICC mask. While most existing works select 0.5 as this threshold value, we set it to 0.01 to further reduce FN even if some FP of the PICC line is allowed.
As shown in Figure \ref{fig4:thresh}, the PICC prediction result obtained through a low thresholding value is thicker and has less breakage. However, lowering the threshold also cause FP like sporadic noise and in particular it still does not fundamentally solve the MFP, which is further resolved through next stages.
\subsection{The second stage network: Patch-wise PICC segmentation network}
The proposed second network corrects the prediction result of the PICC line of the first stage network through patch-based PICC segmentation. The training and testing methods were covered in Sections \ref{Sec:patch_train} and \ref{Sec:patch_inference} respectively, and prior to these, in Section \ref{Sec:patch_generation}, the method of generating patch data is introduced. As the second stage network learns by extracting multiple local patch images focused on the PICC from a single whole CXR image, it increases the relative PICC area within the input image of the network with preserving the resolution of the original CXR image. These make the network more aware of the PICC area without degradation such as by downsampling, thereby enhancing the MFP problem.
\subsubsection{Data pre-processing: Random patch generation}
\label{Sec:patch_generation}
The main difference of the proposed second stage model to the first stage one is that it does not take as input the entire CXR image but rather a patch composed of its partial region. The patch generation process was performed differently in the training and testing process of the model as follows. Each patch was made to have a size of 512$\times$512, while the original CXR image, which the patch is extracted from, has the size of 2017$\times$2017-3408$\times$3040 (Table \ref{Table1:dataset}).
For training phase, we were given the truth binary masks of PICC line for CXR training data. Within each CXR individual image of the training data, we randomly selected a two-dimensional coordinate in the truth PICC area and randomly generated a patch so that it could contain this coordinate at a random location within the patch. In this way, 100 patches were generated from each sample in training data, therefore the data was augmented 100 times. We cropped the original CXR and PICC mask images at the same location to generate 100 patch pairs and used them as input and output for model training. We presented the overall process of generating these pairs in Figure \ref{fig5:patch}.
For inference phase, we were given the binary mask prediction results of PICC line for CXR testing data as the first stage model's outputs. We then randomly selected a two-dimensional coordinate in the predicted PICC line area (i.e., the positive region of pixel value equal to 1 in this binary mask prediction) and randomly generated a patch for it to include this coordinate at a random location. We randomly produced 200 patches from each CXR test image through this way and let them to be taken individually as input of the second stage model.
\begin{figure}[t!]
\centering
\includegraphics[width=0.8\textwidth]{Figure5.jpg}
\caption{Illustration of the patch generation module in the training phase: (a) Randomly selecting a two-dimensional coordinate in the PICC area, (b) Generating a patch by cropping the CXR image to include the coordinate, (c) Creating a pair of CXR and PICC mask sub-images in the same section as the patch and use it as an input and output for model training, (d) Repeat the process of (a)-(c) 100 times}
\label{fig5:patch}
\end{figure}
\begin{figure}[t!]
\centering
\includegraphics[width=0.8\textwidth]{Figure6.jpg}
\caption{Schematic illustration of the second stage model: (a) the training and (b) inference phases}
\label{fig6:secon}
\end{figure}
\subsubsection{Training phase for the second stage network}
\label{Sec:patch_train}
Figure \ref{fig6:secon}(a) depicts the learning process of the second stage model. For each sample (i.e., patient) in training data, 100 patch pairs were generated as detailed in Section \ref{Sec:patch_generation}. Each patch pair consists of the CXR partial image and partial mask of truth PICC corresponding to the same area and they were taken as the input and output label of the second stage network, thereby learning the network to correctly estimate the PICC partial mask as its output. For each patch, CLAHE was applied as a preprocessing to improve the image recognition rate of the network. Though any segmentation network can be applied as a backbone of the second stage model, for simplicity, we adopted FCDN proposed by Jegou \textit{et al}. \cite{jegou2017one}. Each pixel value of the model output is expressed as a probability value between 0 and 1, and the binary cross entropy loss is applied in learning the network to output 1 for the target PICC region.
\subsubsection{Inference phase for the second stage network}
\label{Sec:patch_inference}
The inference phase of the second stage model is illustrated in Figure \ref{fig6:secon}(b), which consists of a process similar to the training phase but mainly differs in the following two aspects: 1) The input patch was generated based on the prediction result of the PICC mask (i.e., the output of the first stage model), not the PICC truth mask, 2) An additional process is required to create a complete PICC segmentation mask by converting all prediction results of patch unit into one prediction result of the whole image unit. We performed it by developing a pixel-wise majority voting approach as shown in the green box in Figure \ref{fig6:secon}(b).
Specifically, the second stage model is designed to extract the PICC line corresponding to the input patch region, which implies that the individual patch output of the model focus only on a specific region of interest in the entire CXR image. The proposed pixel-wise majority voting approach is the post-processing of the model's output patches to produce a whole PICC segmentation/prediction mask by combining all prediction results of patches for some partial regions of the PICC mask. We illustrated its detailed process in Figure \ref{fig7:majority}. Given 200 patches of the model's outputs for partial PICC line estimates, the pixel-wise majority voting approach mainly consists of the following three steps: (a) Select a specific coordinate on whole CXR image, (b) Calculate the average value of the selected coordinate for all patches including the corresponding coordinate. (c) Assign a binary value at the selected coordinate as a result of applying the binary thresholding to this average value, (d) Repeat the process of (a), (b), and (c) for every coordinate on whole CXR image. We set the threshold to 0.7 to produce a final prediction result of the PICC mask (as a binary map with the same size as the whole CXR image), with a value of 1 (positive), if the corresponding average value is greater than or equal to the threshold, and 0 (negative) otherwise.
In Figure \ref{fig7:majority}, we exemplified a case where only 4 patches contain a certain coordinate. Given three patches predict the corresponding coordinate value as positive (i.e., 1) but one patch predicts false (i.e., 0), the average result is given as 0.75. As it is higher than our threshold 0.7, so we finally determined the corresponding pixel value as positive (i.e., 1). Though we took a simple example of 4 patches in Figure \ref{fig7:majority}, 200 patches are created in fact so that multiple patches sufficiently overlap for each coordinate, helping to filter the errors of minor patches more stably. Therefore, this result indicates that 25\% of patch errors are filtered from the proposed pixel-wise voting approach, making PICC segmentation result and its MFP improved more than those of the first stage network.
\begin{figure}[t!]
\centering
\includegraphics[width=0.8\textwidth]{Figure7.jpg}
\caption{Illustration of the pixel-wise majority voting scheme: Suppose that there exist 4 output patches of the second stage model including a specific coordinate on the whole CXR image, the pixel values of the corresponding coordinate are averaged, binarized via a hard thresholding, and assigned to the corresponding coordinate. Through this process, the entire PICC line is predicted by reconstructing individual patches into one whole image.}
\label{fig7:majority}
\end{figure}
\subsection{The third stage network: Line reconnection network}
The second network result effectively improves the MFP problem, but does not completely solve the problem of micro-breaking of the PICC line due to the occlusion of the bone and the PICC line. To solve this, we created a virtual break of the PICC line and let the third stage network recognize it. We first introduce the process of generating a virtual break in Section \ref{Sec:VMFLG} and then the learning/testing phase of the network in Sections \ref{Sec:third_train} and \ref{Sec:third_inference}.
\subsubsection{Data pre-processing: Virtual multi-fragment line generation (VMFLG)}
\label{Sec:VMFLG}
Figure \ref{fig8:VMFLG} introduces the overall process to create a virtual multi-fragment line of PICC. We segment the PICC mask in Step 1, select a two-dimensional ($x$,$y$)-coordinate in Step 3 in this PICC area, remove a circle area of radius randomly ranged from 10 to 50 pixels around this coordinate to make a breakpoint in PICC in Steps 3-4, repeat this removal process (Step 5), and finally generated the virtual multi-fragment line of PICC. We generate these virtual lines by 10 for every PICC image for training the network. We segment the PICC mask in Step 1 and specify where the breakpoint will be made in Step 2. We designed this virtual PICC line to maintain its original tip (Step 2). As it makes the network explicitly aware of the tip location, the network does not predict further extension of the PICC line beyond the tip.
\begin{figure}[htb!]
\centering
\includegraphics[width=0.8\textwidth]{Figure8.jpg}
\caption{Virtual multi-fragment line generation (VMFLG) algorithm}
\label{fig8:VMFLG}
\end{figure}
\subsubsection{Training phase for the third stage network}
\label{Sec:third_train}
We learned the third stage model by taking as its input data of the virtual multi-fragment PICC lines generated by the VMFLG and let it predict the actual PICC line as its output by minimizing the pixel-wise cross entropy loss between the PICC ground truth mask and the model output. It is useful to note that as stage 1 and stage 2 models use CXR data as input but the corresponding stage 3 model uses binary image as input, we did not proceed with any separate preprocessing such as CLAHE in the stage 3 model.
\begin{figure}[htb!]
\centering
\includegraphics[width=0.8\textwidth]{Figure9.jpg}
\caption{Schematic illustration of the third stage model: (a) the training and (b) inference phase}
\label{fig9:third}
\end{figure}
\subsubsection{Inference phase for the third stage network}
\label{Sec:third_inference}
As input of the stage 3 network pretrained as in Section \ref{Sec:third_train}, we took the PICC line segmentation result of the stage 2 model. Then, we got the final segmentation result of the PICC line from its output. This process is illustrated in Figure \ref{fig9:third}(b).
Through this three-stage refining operation, a more complete PICC line can be estimated than the existing AI methods (i.e., the output result of the first stage network). We tracked down from the top of the PICC prediction line to the bottom until there existed a breakpoint and the final tip location is obtained by selecting the coordinate with this breakpoint.
\section{Results}
\label{Sec:Results}
\subsection{Dataset}
\subsubsection{Data collection and setup for internal validation data}
CXR images of patients from 2017-01-01 to 2020-12-31 were collected as a format of digital imaging and communications in medicine (DICOM) from X-ray devices (Manufacturer: GE Healthcare, Samsung Electronics) and they all were anonymized. All collected CXR images were posterior-anterior (PA) type, and their size is ranged from 2017$\times$2017 to 3408$\times$3040 pixels, but most of the images were composed of 2021×2021. Among them, we did not include cases in which a CVC other than PICC was inserted or only a part of the chest was visible. The study design was approved by the institutional review board of our institution (approval number: 2021-05-164). The requirement for informed consent was waived owing to the retrospective nature of this study.
A total of 280 images collected were divided into 130 as data for learning and 150 as data for testing (Table \ref{Table1:dataset}). In the process of dividing, the number of cases where the PICC was inserted from the right side or was misplaced were randomly divided without fixing them at a certain ratio. As a result, in the training (testing) set, 15 and 7 (22 and 13) samples were the right-side PICC insertion and misposition cases. Among the training dataset, 100 samples were used for training the network and 30 were used as validation data. Ground truth of PICC line mask for collected data was annotated by board certified radiologists as a form of binary image (foreground pixel=1, background pixel=0). For this annotation, they used the functions of drawing essential region of international (brush and change) supported by OsiriX (open-source software; www.osirixviewer.com) \cite{rosset2004osirix, rosset2005general}. Then, the PICC ground truth masks and their PICC tip endpoint coordinates have passed follow-up review by board certified radiologists.
\begin{table}[hbt!]
\footnotesize
\centering
\resizebox{0.7\linewidth}{!}{%
\begin{tabular}{ccc}
\hline
& \begin{tabular}[c]{@{}l@{}}Learning set (\#130)\end{tabular} & Test set (\#150) \\ \hline
Minimum image size (pixel) & \begin{tabular}[c]{@{}c@{}}2021 × 2021\end{tabular} & \begin{tabular}[c]{@{}c@{}}2017 × 2017\end{tabular} \\
Maximum image size (pixel) & \begin{tabular}[c]{@{}c@{}}3408 × 3040\end{tabular} & \begin{tabular}[c]{@{}c@{}}3040 × 2902\end{tabular} \\
View point & Posterior-Anterior & Posterior-Anterior \\
Pixel spacing (mm) & 0.125, 0.14, 0.143, 0.194 & 0.14, 0.143, 0.194 \\
\begin{tabular}[c]{@{}l@{}}Right insertion case (\#)\end{tabular} & 15 & 22 \\
Misposition case (\#) & 7 & 13 \\ \hline
\end{tabular}%
}
\caption{Characteristics of training and test set of CXR data for internal validation}
\label{Table1:dataset}
\end{table}
An ideal location of the PICC is defined as being located at the junction of the superior vena cava and the right atrium which is the level of the lower aspect of the bronchus intermedius (Figure \ref{fig10:CXR}) \cite{li2018randomized}. In our study, we defined the misposition of PICC as the case where the PICC tip endpoint was located above the azygos vein confluence or in the right atrium or ventricle level (Figure \ref{fig10:CXR}).
\begin{figure}[htb!]
\centering
\includegraphics[width=0.8\textwidth]{Figure10.jpg}
\caption{CXR images of collected dataset for PICC insertion: (a) an ideally located PICC catheter case, (b) mispositioned PICC catheter case - tip located too high, (c) mispositioned PICC catheter case - tip located too low, (red area) ground truth PICC mask, trachea (orange area), azygos vein confluence (blue area)}
\label{fig10:CXR}
\end{figure}
\subsubsection{Data collection and setup for external validation data} \label{Sec:external_data}
For external validation, we used the publicly available dataset of the Royal Australian and New Zealand college of radiologists (RANZCR). This dataset consists of more than 40,000 CXRs among ChestXRAY14 dataset provided by the national institutes of health \cite{wang2017chestx}. The RANZCR is a not-for-profit professional organization for clinical radiologists and radiation oncologists in Australia, New Zealand, and Singapore. The RANZCR dataset consists of endotracheal tube, nasogastric tube, central venous catheter (CVC), and Swan-Ganz catheter, and is divided into abnormal, borderline, and normal depending on the location. For the verification of baseline and proposed models, 280 data were randomly selected from normal CVC images including PICC (1200 images).
Among them, 100, 30, and 150 data were used as training, validation (for hyperparameter tuning), test datasets respectively. The image size of the collected data was ranged from 1610×1734 to 3056×3056 and the case where PICC was inserted from the right (left) side was distributed to 44\% (56\%) in the training and validation dataset and 50\% (50\%) in the test dataset.
\subsubsection{Data preprocessing}
As the collected CXR images have characteristics of low-pixel contrast and high-noise \cite{sandborg2006comparison, baath2005nodule}, we performed the following two pre-processing approaches to normalize their contrast and dimension.
The first pre-processing is to increase image contrast of the input image by applying the contrast limited adaptive histogram equalization (CLAHE) \cite{pizer1990contrast, reza2004realization}. CLAHE has been widely applied to many medical images as it can improve contrast and reduce noise implication. In this study, we used CLAHE as the pre-processing step of each model using the entire CXR image (e.g., the first stage model) or the model using the patch image of CXR image (e.g., the second stage model). Specifically, we applied CLAHE to the entire CXR image and in the first stage model each patch after generating multiple patches from one entire CXR image in the second stage model.
The second pre-processing is to resize the original CXR image. Note that the collected CXR image consists of various image sizes from 2017$\times$2017 to 3408$\times$3040 pixels (Table \ref{Table1:dataset}) with an average size of 2021$\times$2021 pixels. The first and third stage models received up to images of size 1024$\times$1024 as input due to GPU memory problems, so we resized the input image size at 1024×1024 in the first and third stage models. In the second stage model, the patch of size 512×512 was extracted from the original CXR image without using any resize on the original image in order to preserve it as it is.
\begin{figure}[htb!]
\centering
\includegraphics[width=0.8\textwidth]{Figure11.jpg}
\caption{Illustration of application with CLAHE: the original CXR image (a) without or (b) with CLAHE and the patch of CXR image (c) without or (d) with CLAHE.}
\label{fig11:CLAHE}
\end{figure}
\subsection{Implementation detail}
\subsubsection{Setup for conventional method and proposed MFCN}
MFCN was applied to five conventional models to verify the effect of improving their performances by MFCN. These conventional models consist of three representative DL-based models developed to solve the general semantic segmentation problem (i.e., FC-DenseNet (FCDN) \cite{jegou2017one}, UNET \cite{ronneberger2015u}, and Attention U-Net (AUNET) \cite{oktay2018attention}) and two latest DL-based models developed to detect PICC tip more precisely (FC-DenseNet with hough transform (FCDN-HT) \cite{lee2018deep} and UNET with Region Proposal Network (UNET-RPN) \cite{yu2020detection}). FCDN-HT is a model in which the probabilistic hough transform \cite{duda1972use, kiryati1991probabilistic} provided by OpenCV is added to the FCDN model result as a post-processing process. Though authors of FCDN-HT used a naive fully convolutional network (FCN) rather than its dense adaptation (FCDN), as they suggested that updating FCN with a dense architecture (e.g., FCDN) can further improve tip detection accuracy \cite{lee2018deep, wang2019dense}, we adopted FCDN instead of FCN in reproducing their work. We also used the HT parameter values as suggested by the authors \cite{lee2018deep}. UNET-RPN is a model that detects the location of the PICC tip by additionally combining the RPN module of Faster R-CNN \cite{ren2015faster} with UNET.
We set the above five existing individual models as the first stage model of MFCN, and for simplicity, we applied FCDN for both second and third stage models of MFCN. Accordingly, the validity of the proposed technique was verified by determining whether there was a performance improvement when the second/third stage model was added (i.e., proposed scheme) compared to when only the first stage model was used (i.e., basic scheme). It is useful to note that the base network of the second and third models in MFCN can be set as any existing segmentation model. The detailed performance comparison was presented in Section \ref{Sec:backbone}.
\subsubsection{Hyperparameter setup for proposed MFCN}
The proposed MFCN was trained for 100 epochs for each experiment with initial learning weight set to 0, the batch size was set to 2, and Adam optimizer \cite{kingma2014adam} with a learning rate of $1e^{-4}$ was used. In order to prevent overfitting, the dropout rate \cite{srivastava2014dropout} was set to 0.2 and early stopping was performed based on the validation loss. Weighted binary cross entropy was used as a loss function for model training and validation, and the balance weight was set to 0.5 in background. All experiments were run on two V100 graphics processing units (GPUs) and Pytorch (1.4.0) under Python 3.6.
\subsection{Evaluation metrics}
PICC segmentation accuracy and tip detection accuracy were measured for quantitative evaluation of the proposed MFCN. The PICC segmentation result is evaluated by calculating the Dice similarity coefficient (DSC) between the ground truth PICC mask and the model segmentation result as formulated as follows:
\begin{equation}\label{eqn:DSC}
\textup{DSC} = {\frac{2|\textup{GT} \cap \textup{PD}|}{|\textup{GT}| + |\textup{PD}|}}
\end{equation}
where $\textup{GT}$ is the pixel region of PICC ground truth mask and $\textup{PD}$ is that of its model prediction. Tip detection accuracy is evaluated using root mean square error (RMSE) to evaluate the distance between ground truth tip position coordinates and predicted tip position coordinates. The RMSE was calculated as follows:
\begin{equation}\label{eqn:RMSE}
\textup{RMSE} = \sqrt{\sum\limits_{i=1}^n \frac{(x_{pred} - x_{gt})^2+(y_{pred} - y_{gt})^2}{n}}
\end{equation}
where $x_{gt}$ and $y_{gt}$ are $x$ and $y$ coordinates of the ground truth tip, $x_{pred}$ and $y_{pred}$ are $x$ and $y$ coordinates of the predicted tip, and $n$ denotes the total number of test images.
\subsection{Internal validation result} \label{Sec:internal valid}
\subsubsection{PICC tip location detection}
We presented the performance comparison results between the proposed MFCN and the existing technologies for PICC tip location detection in Table \ref{Table2:inter_r}. We presented in the first column the mean and variance of RMSE, in the second column the ratio (\%) of test samples for the predicted PICC segmentation line result to be derived as one complete line (correctly estimated), and in the third column the ratio (\%) of test samples when their RMSE is sufficiently low (i.e., below 1cm). As a result, the existing results showed an average RMSE of 20 mm or more, whereas the MFCN showed an average RMSE of 10 mm or less, thereby consistently improving the results of each of the existing models by reducing their RMSE by less than half (the first column in Table \ref{Table2:inter_r}). The ratio of the number of reconstructed single complete PICC lines without MFP was less than 50\% on average in the existing model, but when the proposed method was applied, it was more than 90\%. Therefore, the proposed MFCN has the MFP problem improvement rate by more than 40\% (the second column in Table \ref{Table2:inter_r}). In addition, the proposed MFCN increased the precision/correct detection of PICC tip location (i.e., RMSE is less than 1 cm) by at least 10\% (the third column in Table \ref{Table2:inter_r}).
\begin{table}[hbt!]
\footnotesize
\centering
\resizebox{0.7\textwidth}{!}{%
\begin{tabular}{ccccccc}
\hline
& \multicolumn{2}{c}{RMSE (mean±sd, mm)} & \multicolumn{2}{c}{No MFP (\%)} & \multicolumn{2}{c}{$|RMSE|$ \textless 1cm (\%)} \\ \cline{2-7}
\multirow{-2}{*}{\begin{tabular}[c]{@{}c@{}}Conventional\\ Model name\end{tabular}} & Baseline & \textbf{MFCN} & Baseline & \textbf{MFCN} & Baseline & \textbf{MFCN} \\ \hline
FCDN \cite{jegou2017one} & 23.37 ± 32.12 & \textbf{9.37 ± 18.13} & 49 & \textbf{93} & 60 & \textbf{80} \\
UNET \cite{ronneberger2015u} & 34.98 ± 39.93 & \textbf{9.11 ± 16.23} & 47 & \textbf{89} & 48 & \textbf{81} \\
AUNET \cite{oktay2018attention} & 35.80 ± 41.52 & \textbf{10.98 ± 21.05} & 35 & \textbf{84} & 47 & \textbf{78} \\
FCDN-HT \cite{lee2018deep} & 17.16 ± 28.25 & \textbf{9.36 ± 18.22} & 62 & \textbf{90} & 71 & \textbf{81} \\
UNET-RPN \cite{yu2020detection} & 22.93 ± 16.46 & \textbf{9.77 ± 18.87} & 25 & \textbf{87} & 26 & \textbf{81} \\ \hline
Average & 26.85 & \textbf{9.72} & 43.6 & \textbf{88.6} & 50.4 & \textbf{80.2} \\ \hline
\end{tabular}%
}
\caption{Internal validation result for PICC tip location detection: Comparison of RMSE results between the existing methods and those applied with the proposed MFCN}
\label{Table2:inter_r}
\end{table}
\subsubsection{PICC line segmentation}
We also presented the PICC line segmentation results in Table \ref{Table3:inter_s}. When the proposed MFCN was applied to the existing method, Dice score performance was improved in all cases, and it was confirmed that the sample probability of extracting the PICC line with high accuracy of Dice score 0.95 or higher was at least 10\% higher on average compared to the existing method.
\begin{table}[hbt!]
\footnotesize
\centering
\resizebox{0.7\textwidth}{!}{%
\begin{tabular}{ccccc}
\hline
& \multicolumn{2}{c}{Dice score (mean±sd, mm)} & \multicolumn{2}{c}{Dice score \textgreater 0.95 (\%)} \\ \cline{2-5}
\multirow{-2}{*}{\begin{tabular}[c]{@{}c@{}}Conventional\\ Model name\end{tabular}} & Baseline & \textbf{MFCN} & Baseline & \textbf{MFCN} \\ \hline
FCDN \cite{jegou2017one} & 0.91 ± 0.16 & \textbf{0.92 ± 0.17} & 60 & \textbf{76} \\
UNET \cite{ronneberger2015u} & 0.90 ± 0.16 & \textbf{0.92 ± 0.17} & 59 & \textbf{75} \\
AUNET \cite{oktay2018attention} & 0.90 ± 0.16 & \textbf{0.92 ± 0.17} & 55 & \textbf{75} \\
FCDN-HT \cite{lee2018deep} & 0.90 ± 0.14 & \textbf{0.92 ± 0.17} & 47 & \textbf{79} \\
UNET-RPN \cite{yu2020detection} & 0.91 ± 0.12 & \textbf{0.92 ± 0.17} & 52 & \textbf{76} \\ \hline
Average & 0.904 & \textbf{0.92} & 54.6 & \textbf{76.2} \\ \hline
\end{tabular}%
}
\caption{Internal validation result for PICC line segmentation: Comparison of Dice score results between the existing methods and those applied with the proposed MFCN}
\label{Table3:inter_s}
\end{table}
\subsubsection{Visualization result}
Figure \ref{fig12:inter_visual} shows some prediction samples of the PICC line and tip through the existing model and the proposed model. It shows that accurate tip position detection was difficult in the existing model due to MFP but MFCN effectively solved it. In other words, although false-negative and false-positive of the model, which are the causes of MFP, occurred in the conventional model in Figures \ref{fig12:inter_visual}(c)-(e) (i.e., orange and green arrows respectively), the proposed method effectively solves this problem and accurately detects the tip position. Compared to the existing FCDN, the existing FCDN-HT decreased false-negatives in a small area (e.g., the first case in Figures \ref{fig12:inter_visual}(c) and (d)), but the disconnection was not resolved when false-negative appeared in a large area (e.g., the first and fourth cases in Figures \ref{fig12:inter_visual}(c) and (d)). In addition, it is observed in some cases (e.g., the seventh case in Figures \ref{fig12:inter_visual}(c) and (d)) that FCDN-HT increases false-positive so RMSE compared to FCDN. On the other hand, when our MFCN was applied, false-negative (e.g., the first and fourth cases in Figure \ref{fig12:inter_visual}(f)) and false-positive (e.g., the seventh case in Figure \ref{fig12:inter_visual}(f)) of a wide area were effectively improved, and finally RMSE for PICC tip location detection was significantly reduced as shown in Table \ref{Table2:inter_r}.
\begin{figure}[htb!]
\centering
\includegraphics[width=0.8\textwidth]{Figure12.jpg}
\caption{Internal validation examples for PICC tip detection and line segmentation through each model: (a) input CXR image, (b) ground truth PICC mask, (c)-(e) results from conventional models, (f) result from our model; The ground truth and predicted tip were marked with blue and red circle respectively. The orange arrow denotes false-negatives (i.e., when a break occurs in the line of the catheter) and the green arrow indicates false-positives (i.e., in the case of noise). The RMSE of predicted tip and Dice score of predicted PICC line were described below each image.}
\label{fig12:inter_visual}
\end{figure}
\subsection{External validation result}
\subsubsection{PICC tip location detection} \label{Sec:external_tip_detection}
In Sections \ref{Sec:internal valid}, we validated our technique with internal data from our institution. For more objective performance verification, this section compared and evaluated the performance of the proposed MFCN and the existing technologies by using the public data (i.e., RANZCR) as introduced in Section \ref{Sec:external_data} for external verification.
As the image in RANZCR dataset is originally given in the form of a JPG image rather than a DICOM, it is difficult to determine the pixel spacing value, so we measured RSME in pixels of JPG image not mm. Accordingly, it was impossible to calculate the frequency of samples with RMSE within 1cm so that we omitted to show this result in this experiment.
The quantitative performance comparison results were presented in Table \ref{Table4:external_r}. Similarly with internal validation results, we also observed that MFCN consistently improved each baseline model even in this external validation, by reducing the mean RMSE by more than half (i.e., the first column in Table \ref{Table4:external_r}) and by increasing no MFP rate by more than 10\% and achieving more than 90\% (i.e., the second column in Table \ref{Table4:external_r}). These results assisted in demonstrating the objective superiority of the proposed MFCN.
\begin{table}[hbt!]
\footnotesize
\centering
\resizebox{0.7\textwidth}{!}{%
\begin{tabular}{ccccc}
\hline
& \multicolumn{2}{c}{RMSE (mean±sd, pixels)} & \multicolumn{2}{c}{No MFP (\%)} \\ \cline{2-5}
\multirow{-2}{*}{\begin{tabular}[c]{@{}c@{}}Conventional\\ Model name\end{tabular}} & Baseline & \textbf{MFCN} & Baseline & \textbf{MFCN} \\ \hline
FCDN \cite{jegou2017one} & 95.90 ± 173.21 & \textbf{43.06 ± 88.70} & 71 & \textbf{96} \\
UNET \cite{ronneberger2015u} & 263.70 ± 299.97 & \textbf{71.90 ± 142.03} & 43 & \textbf{91} \\
AUNET \cite{oktay2018attention} & 187.98 ± 243.62 & \textbf{56.64 ± 126.43} & 46 & \textbf{94} \\
FCDN-HT \cite{lee2018deep} & 89.80 ± 161.768 & \textbf{49.32 ± 99.86} & 85 & \textbf{96} \\
UNET-RPN \cite{yu2020detection} & 177.98 ± 217.105 & \textbf{63.96 ± 153.33} & 67 & \textbf{95} \\ \hline
Average & 163.07 & \textbf{56.98} & 62.4 & \textbf{94.4} \\ \hline
\end{tabular}%
}
\caption{External validation result for PICC tip location detection: Comparison of RMSE results between the existing methods and those applied with the proposed MFCN}
\label{Table4:external_r}
\end{table}
\subsubsection{Visualization result} \label{Sec:external_visual}
We also showed in Figure \ref{fig13:exter_visual} model prediction examples of the PICC line and tip through the existing model and the proposed model in this external validation. Similarly with the results of internal validation, it is generally observed in Figure \ref{fig13:exter_visual} that false-negative and false-positive, the cause of MFP occurrence, appeared the same in external validation of the existing model. In the external verification, it was observed in some cases (e.g., the fifth and sixth cases in Figure \ref{fig13:exter_visual}) that the RMSE of existing FCDN-HT increased compared to its previous version (FCDN) in the case of false-positive. On the other hand, when our MFCN is applied in FCDN, the false-positive is removed so the tip position is not extended incorrectly (e.g., the fifth and sixth cases in Figure \ref{fig13:exter_visual}(f)), and the false-negative of a wide area is also effectively improved (e.g., the second and fourth cases in Figure \ref{fig13:exter_visual}(f)). As such, it can be confirmed through those examples that the proposed MFCN effectively resolves the MFP and thereby reduces the RMSE of PICC tip detection in large margins as shown in Table \ref{Table4:external_r}.
\begin{figure}[htb!]
\centering
\includegraphics[width=0.8\textwidth]{Figure13.jpg}
\caption{External validation examples for PICC tip detection and line segmentation through each mode}
\label{fig13:exter_visual}
\end{figure}
\section{Discussion}
\label{Sec:Discussion}
\subsection{Causes of MFP and how to solve them through our work}
Typically, the causes of MFP can be classified into the following four categories:
For the first reason, as the CXR image is taken by projecting the 3D structure in 2D, a part of the catheter may be obscured by the anatomical structure \cite{yi2020automatic}. If the catheter overlaps with the anatomical structure, the catheter edge can be indistinguishable as the bone and the catheter's pixel values are similar, as shown in Figure \ref{fig1:MFP} \cite{yu2020detection}. Then, a lot of prediction errors can occur from such overlapping parts. Specifically, it is confused with a bone having a linear structure partially similar to PICC, such as a spine or rib, and is incorrectly predicted as a catheter \cite{keller2007semi}.
As PICC is a very thin tube structure with an average pixel-level thickness ranged from 3 to 6, it is very sparse occupying on average only about 0.14\% of the total CXR image. Due to such sparsity or pixel-level class imbalance for segmentation, it is easy to treat the entire portion corresponding to the sparse area (e.g., PICC) as noise or to classify it as background pixels \cite{greenland2016sparse}. There exists an attempt to address this issue by adopting the class-balanced cross-entropy (BCE) loss function \cite{xie2015holistically}. However, even if the class-balanced loss is considered, the PICC estimate can be easily divided into multi-fragments due to false negatives for some pixels, making it difficult to determine the exact location of the tip.
For the third reason, using the full CXR image as input makes it difficult to extract the PICC line, decreasing the accuracy for extracting the PICC. It is worth noting that segmentation task requires extensive down sampling or pooling within the internal path of CNN. This characteristic makes the latent features of PICC easily removed, especially when the network input takes the whole CXR image with original resolution. It is because the PICC line is relatively sparse compared to the entire CXR image.
For the last reason, X-ray images are expensive to acquire and manual labeling is time-consuming, making it difficult to acquire large and diverse databases \cite{bullock2019xnet, sharma2010automated}. In order to extract a more accurate PICC line, the label data obtained by accurately extracting PICC lines from training data should be required to train the model. However, the tip detection and masking process is difficult and time consuming because the PICC tip is in many cases obscured by the shadow of the spine on the CXR images. Though reducing the training data can be regarded as an alternative, in this case the trained model is highly overfitted, decreasing the accuracy of PICC line extraction in the actual diagnostic test.
\subsection{Related works for PICC line and tip detection}
PICC tip prediction studies for early detection of movement have been conducted using various techniques such as CXRs \cite{wechsler1984misplaced, harako2004optimizing, bailey2000immediate}. electrocardiogram (ECG) \cite{gao2018safety, oliver2016ecg}, and ultrasound \cite{moureau2003using, nicholson2010development}, among which CXRs were used as a gold-standard \cite{li2018randomized, black2000central}.
In particular, interest in computer-aided detection (CAD) for the PICC tip location in CXR images is increasing significantly. It is because computer-aided detection (CAD) can be used to help radiologists interpret medical images and reduce mistakes, and its performance has dramatically improved due to recent advances in artificial intelligence.
Several traditional CADs for segmenting the catheter have been proposed. As a representative technique, Keller \textit{et al} proposed a semi-automated system for detecting catheters on CXRs \cite{keller2007semi}. By quantitatively analyzing the object intensity between the catheter line and the tip through this method through image processing and pattern recognition techniques, it was possible to secure the position of the tip more accurately than the existing methods. However, this method has a limitation in that it is difficult to perform pattern analysis on the intensity of the data because the profile of the object is different depending on the X-ray intensity and the imaging environment. It was also reported that this algorithm has problems such as stopping when the PICC overlaps with anatomical structures, mentioned as the first cause of MFP.
Recent advances in DL technology applied to medical imaging have shown great potential for increasing diagnostic accuracy and image interpretation speed, and these DL-based approaches also have been introduced in tip and line detection for PICC misposition diagnosis.
Henderson \textit{et al} proposed a method to accurately detect the presence and type of catheters, and as a result, they succeeded in classifying the presence or absence of four catheters of interest (NGT, ETT, UAC, UVC) on radiographs of the chest and abdomen of newborns with 95\% precision \cite{henderson2021automatic}. However, though their technique efficiently detects the presence of catheter and the type of catheter, it does not provide the position of the PICC tip, so there is a limitation in that the expert clinicians can directly diagnose the misposition from this CAD result.
In order to overcome this limitation, there have been attempts to directly extract PICC lines based on DL. Subramanian \textit{et al} used a large-scale CVC data, classified four common CVC types by using random forest, and roughly identified their potential fragments through a UNET-based model \cite{subramanian2019automated}. However, their results were an initial study to obtain the approximate shape of the PICC line, and they did not try to directly improve the MFP problem as in our study to make tip detection precise.
\subsection{Related works for MFP improvement}
Recent studies have attempted to improve MFP to accurately detect PICC tip detection based on predicted segmentation results.
Lee \textit{et al} proposed a cascading segmentation AI system containing two fully convolutional neural networks to improve MFP and detect tips more accurately \cite{lee2018deep}. Their cascading system tried to improve the catheter tip detection accuracy by supplementing the false-negative through the Hough line transform algorithm. However, as they reported, their system still did not perform perfectly in cases that could be confused with similar appearing artifacts or structures (e.g., edges of bone structures) with PICC, suggesting the need for additional research resolving the corresponding false-positives \cite{lee2018deep}. Specifically, as shown in experiments in Appendix, we found that it was difficult for their algorithm to effectively solve the MFP problem of various CXR images because the parameters of the Hough line transformation for correcting the PICC line were different for each CXR input image. Our method mainly differs from their algorithm in that we additionally improve the false-positives by proposing a DL-based MFP improvement technique (i.e., the third stage network for line reconnection). Compared to Hough line transform-based one \cite{lee2018deep}, our DL-based approach experimentally further improves FPs and thus the tip detection performance without being sensitive to parameters like the Hough transform, verifying the effectiveness of our technique.
Ambrosini \textit{et al} proposed a technique for correcting the MFP by connecting the negative areas between two positive points in the segmentation prediction result when the negative area is sufficiently small \cite{ambrosini2017fully}. However, this technique does not compensate for a wide undetected area and cannot correct for false detection, suggesting the need for additional research \cite{ambrosini2017fully}. Based on the higher radiation dose fluoroscopy image as used in \cite{ambrosini2017fully}, there was almost no false-positive. However, as in the case of the more normal or low-dose CXR as assumed in our study, the more false-positive of the network may occur (e.g., Figure \ref{fig1:MFP}), so improvement should be considered when solving the MFP. The proposed study is mainly different from the previous research \cite{ambrosini2017fully} in that our method is able to further resolve even a large undetected area thanks to the technical characteristics, and it also improves the false-positive at the same time, by letting the network recognize the position of tip, which is the end point of PICC, together when learning for MFP calibration.
Yu \textit{et al} also detected the tip position more precisely by performing object detection on the tip position separately in addition to PICC line segmentation \cite{yu2020detection}. However, their tip position detection method through object detection was designed to be affected by the PICC line segmentation result, so the inaccuracy of the PICC line segmentation result affects the performance of their object detection-based tip position detection. In this aspect, resolving the MFP problem of PICC line segmentation can improve tip detection performance, but their results did not take this into account. Focusing on these issues, we reconstructed their results, applied the proposed technology, and confirmed the performance improvement, verifying the effectiveness of our work in comparison with their method.
\subsection{Limitation of our study}
This study has the following three limitations. First, the CXR images collected for internal validation were limited to only low-dose images so may generate various kinds of noise, though we supplemented it through external validation. Second, unlike the existing studies using portable X-rays \cite{yu2020detection, lee2018deep}, our study was conducted using Chest PA. Compared to portable X-rays, chest PA may have relatively more fixed positions of the shoulder and heart and clear image. For this reason, the learning model through chest PA may show different results from the existing studies conducted with portable X-rays. However, we expected that our method will be effective even in portable X-ray as well as it was not limited to PA but general types in external validation. Lastly, for simplicity, our study was conducted with images containing only PICC. In other words, the proposed study was focused on the possibility that there could be a performance improvement compared to the existing technology, so the data were limited to data with only PICC. However, the tip detection accuracy of all models may be degraded when various types of catheters are taken simultaneously in the CXR image. Therefore, a study to evaluate the performance of the proposed and other techniques may be of interest as a follow-up study in the case of CXR images including a catheter other than PICC.
\section{Conclusions}
\label{Sec:Conclusions}
In this study, we propose a multi-stage network to improve the PICC tip detection performance of the existing DL-based models by solving the MFP occurring in their segmentation results. To achieve it, the proposed scheme is designed to add two networks to the conventional model for PICC line segmentation. The first added model affects as accurately extracting PICC line with little data by allowing the network to effectively focus on the sparsely expressed PICC area in the CXR image. The second added model was designed to recognize and restore noise (false-positive) confusing with the actual PICC line and the unexpected PICC line breakage (false-negative) due to partially obscured by anatomical structures or weakly expressed edges. With extensive experiments through internal validation and external validation, we verified our work by showing that it consistently improves tip position detection performance of existing models by more than 63\%. We also strengthened the clinical significance by showing the validity of this study in the migrated data. These all aspects suggest that our fully-automatic PICC tip localization approach can play a high auxiliary role in detecting abnormal migration of the PICC tip by doctors, further contributing to the prevention of complications.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 1,453 |
Q: Problema, estructura de datos, multilistas Hola tengo un código que se supone son multilistas, en mi caso particular se listan oficinas y empleados
#include<iostream>
#include<conio.h>
#include<stdio.h>
#include <stdlib.h>
#include <string.h>
using namespace std;
struct empleado
{
int codigo;
float sueldo;
string cargo;
string nombre;
empleado *ap_emp;
}*emp;
struct oficina
{
int codigo;
string nombre;
oficina *ap_o;
empleado *ap_e;
}*cola,*cab,*nuevo,*busca1,*busca2;
void capturar(void);
void menu_of(void);
void menu_emp(void);
void capturar_of(void);
void listar_of (void);
void borrar_of (void);
El profesor nos indica que se debe adicionar a la estructura empleado, la variable sueldo, siguiente a esto y es donde tengo el problema supongo en lógica es "Generar un reporte (listado) donde muestre el sueldo pagado por oficina.
Mi pregunta es y puede que la respuesta sea sencilla, solo seria adicionar la variable sueldo al listar_of?
La otra idea que tengo seria crear el listado de empleados, añadirle la variable sueldo a ese listar pero no sabria como representar el total de los sueldos por oficina
A: Segun entiendo a tu problema y lo que te dijo el profesor es que quiere que el sueldo se comporte como una lista encadenada, pq digo esto es pq observo que la variable sueldo ya esta en la estructura empleado.
Por lo que a la hora de ponerla como lista encadenada tendras que replicar todas los procedimiento tal y como haces con empleado y oficina.
La lista encadenada que tienes es similar a esta imagen:
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 5,493 |
Xironogiton cassiensis är en ringmaskart som beskrevs av Holt 1974. Xironogiton cassiensis ingår i släktet Xironogiton och familjen kräftmaskar. Inga underarter finns listade i Catalogue of Life.
Källor
Kräftmaskar
cassiensis | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 5,741 |
Have you ever stood in front of a blank wall in your home and broken into a cold sweat thinking about what it might cost to fill it? Perspire no more! Here are some ideas you can do yourself, on a pretty tight budget, to make your walls sing.
Look no further than the children in your family (immediate or extended) for a hot lead on personalized wall decor. If you have photos like these, consider having them blown up and made into canvas prints on a wrapped frame.
Honestly, if you find pictures of kids as cute as these, who cares if they're actually family or not!
Adopt the same wrapped-canvas approach but use different sizes and different poses to achieve this great look. A sign adds a singularly personal touch, and making one can be a fun project.
Or simply gather your favorite photos; buy identical, inexpensive white frames at your local craft store or discount retailer; and mount your pictures with white mats (different image sizes are fine). Voilà! Now that empty wall croons.
If some of your photos are black and white and some are color, consider having the color ones converted. You can even do this yourself with a scanner and printer.
… creating a triptych like this one. Cool, isn't it? Don't think you have to limit yourself to a realistic pattern; an abstract fabric can be equally effective.
And then there are bird prints. Antique, new or pulled from the pages of a book (just imagine finding a volume full of Audubon illustrations in a thrift store) and framed in simple black, they are absolutely stunning. Using a sizzling green wall paint as the backdrop doesn't hurt a bit, either.
Calendars are one of my favorite sources for wall art. Birds, hats, Italian tourism posters, French advertising posters — all are available in totally adequate prints in calendars, screaming to be framed. Whimsical, sinister, serious … no matter your mood, there is a decorative calendar to match it.
This Mincing Mockingbird calendar is available for 2014 as well.
These leaves make an organic (not to mention clever) statement on the wall. This would be a particularly fun project to enjoy with your kids or grandkids or neighborhood children. Have your diminutive helpers collect the leaves, then press them between the pages of a nice, heavy book before mounting them on paper and hanging them on the wall.
Or hang them from clipboards.
While we're on the subject of children, kids' art is some of the most joyous, unconstrained, charming and heartwarming work on the planet. (And it's really cheap!) It does not have to be framed; just hang it on the wall and enjoy. Your little ones will be absolutely delighted, and will probably deluge you with enough material to keep your walls ever changing and ever vital.
If a child can create these terrific works of abstract art, so can we! Buy a canvas as large as your wall will handle, get out your finger paints and let that creative child inside of you loose.
The thing about abstracts is that the more abstract they are, the better.
Authentic French advertising posters are practically guaranteed to break any but the flushest bank. Fortunately, many are readily available as reprints, at a fraction of the cost of the real thing. Few things match them for graphic impact and occasionally rowdy humor.
Given their color and personality, posters as a genre are splendid for walls. I particularly like finding ones that are specific to my region, like the chicken festival our neighboring city of Petaluma is renowned for. But really, any poster you love will do. There are even websites where you can create a custom poster.
Then there are maps, like this wall-size beauty. You could personalize it with decorative tags that let your kiddos know where they live, and where their extended family lives. Last time we were in Seattle, we showed our twin granddaughters a map indicating where our home in California was, and where their home in the Seattle area was. They were so delighted, they instantly wanted to nominate us for Grandparents of the Year.
Vintage windows are another winning way to fill a wall. You can hang them as is or use the individual panes as frames for art you have collected, such as greeting cards, family photos or calendar art.
Don't limit yourself to "art." Painting stripes on that empty wall can provide sensational impact and be a top-notch design element. Vertical stripes in bold colors like these are all that wall could ever need or want.
OK, now you can stop staring at that blank wall and turn in into the centerpiece of your home. Post your pics when you are done, so we can all enjoy. | {
"redpajama_set_name": "RedPajamaC4"
} | 7,523 |
Rzadki Las – część wsi Jadowniki Mokre w Polsce, położona w województwie małopolskim, w powiecie tarnowskim, w gminie Wietrzychowice.
W latach 1975–1998 Rzadki Las administracyjnie należał do województwa tarnowskiego.
Przypisy
Jadowniki Mokre | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 9,969 |
import { union, mapValues } from 'lodash';
import renderBlockHtml from './renderers/render_html_block';
import renderKramdownList from './renderers/render_kramdown_list';
import renderKramdownText from './renderers/render_kramdown_text';
import renderIdentifierInstanceText from './renderers/render_identifier_instance_text';
import renderIdentifierParagraph from './renderers/render_identifier_paragraph';
import renderFontAwesomeHtmlInline from './renderers/render_font_awesome_html_inline';
import renderSoftbreak from './renderers/render_softbreak';
const htmlInlineRenderers = [renderFontAwesomeHtmlInline];
const htmlBlockRenderers = [renderBlockHtml];
const listRenderers = [renderKramdownList];
const paragraphRenderers = [renderIdentifierParagraph];
const textRenderers = [renderKramdownText, renderIdentifierInstanceText];
const softbreakRenderers = [renderSoftbreak];
const executeRenderer = (renderers, node, context) => {
const availableRenderer = renderers.find(renderer => renderer.canRender(node, context));
return availableRenderer ? availableRenderer.render(node, context) : context.origin();
};
const buildCustomHTMLRenderer = customRenderers => {
const renderersByType = {
...customRenderers,
htmlBlock: union(htmlBlockRenderers, customRenderers?.htmlBlock),
htmlInline: union(htmlInlineRenderers, customRenderers?.htmlInline),
list: union(listRenderers, customRenderers?.list),
paragraph: union(paragraphRenderers, customRenderers?.paragraph),
text: union(textRenderers, customRenderers?.text),
softbreak: union(softbreakRenderers, customRenderers?.softbreak),
};
return mapValues(renderersByType, renderers => {
return (node, context) => executeRenderer(renderers, node, context);
});
};
export default buildCustomHTMLRenderer;
| {
"redpajama_set_name": "RedPajamaGithub"
} | 8,199 |
using Magellan.Diagnostics;
namespace Magellan.Framework
{
/// <summary>
/// Represents a request to go to the previous page, optionally removing the current page from the WPF
/// navigation journal.
/// </summary>
public class BackResult : ActionResult
{
private readonly bool removeFromJournal;
/// <summary>
/// Initializes a new instance of the <see cref="BackResult"/> class.
/// </summary>
/// <param name="removeFromJournal">if set to <c>true</c> [remove from journal].</param>
public BackResult(bool removeFromJournal)
{
this.removeFromJournal = removeFromJournal;
}
/// <summary>
/// When implemented in a derived class, performs the bulk of the action rendering.
/// </summary>
/// <param name="controllerContext">The controller context.</param>
protected override void ExecuteInternal(ControllerContext controllerContext)
{
TraceSources.MagellanSource.TraceInformation("BackResult is rendering for request '{0}'. RemoveFromJournal is {1}", controllerContext.Request, removeFromJournal);
var dispatcher = controllerContext.Request.Navigator.Dispatcher;
dispatcher.Dispatch(
delegate
{
var navigationService = controllerContext.Request.Navigator;
navigationService.GoBack(removeFromJournal);
});
}
}
} | {
"redpajama_set_name": "RedPajamaGithub"
} | 9,604 |
Yousif Thomas Mirkis OP (Mosul, Iraque, 21 de junho de 1949) é o arcebispo católico caldeu de Kirkuk-Sulaimaniya.
Yousif Thomas Mirkis estudou pela primeira vez no seminário de Saint Jean em Mosul. Ele então foi para a França para continuar seus estudos. Lá Mirkis juntou-se à ordem dominicana. Ele recebeu seu doutorado em teologia católica pela Universidade de Estrasburgo e um diploma em etnologia pela Universidade de Paris-Nanterre. Mirkis recebeu o Sacramento da Ordem em 26 de março de 1980.
Em 1989, Yousif Thomas Mirkis co-fundou a Faculdade de Teologia e Filosofia no Babel College em Bagdá. De 1989 a 2001 foi professor no Babel College. Mirkis também foi Superior do Convento Dominicano em Bagdá de 1994 a 2000. Em 1995 tornou-se diretor das revistas Al-Fiker Al-Masihi e Al-Nasira. Em 2006, Yousif Thomas Mirkis fundou a Academia de Ciências Humanas em Bagdá. É membro da Associação Católica Internacional de Imprensa.
O Sínodo dos Bispos Católicos Caldeus o elegeu Arcebispo de Kirkuk. O Papa Francisco aprovou sua eleição como Arcebispo de Kirkuk em 11 de janeiro de 2014. O patriarca católico caldeu da Babilônia, Luís Rafael I Sako, doou-o, assim como Habib Al-Naufali e Saad Sirop, em 24 de janeiro do mesmo ano como bispo; Os co-consagradores foram o Bispo da Cúria no Patriarcado da Babilônia, Shlemon Warduni, e o Arcebispo Latino de Bagdá, Jean Benjamin Sleiman OCD.
Ver também
Arcebispos católicos do Iraque | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 6,111 |
Deliciously addictive chocolate chip peanut butter cookies!
Preheat oven to 350 degrees. In a food processor, mix together all ingredients (except pretzels and chocolate chips) until incorporated.
Scoop out batter and place into large mixing bowl, fold in pretzels and chocolate chips. Pam spray a baking sheet and drop by spoonfuls.
Bake cookies at 350 degrees for 15 minutes. Makes about 16 cookies. | {
"redpajama_set_name": "RedPajamaC4"
} | 33 |
\section{INTRODUCTION}
Open quantum systems have been a subject of interest for many years\cite{LeggettRMP87,Grabert88}.
A great deal of effort has been dedicated to numerically calculating the time evolution of such model systems, and
several numerically rigorous approaches have been developed for studying spin-boson systems and Brownian oscillator systems.
These approaches include the quasiadiabatic propagator path integral (QUAPI)\cite{Makri2014}, the density matrix renormalization group (DMRG)\cite{AlexPlenio}, and the
reduced hierarchical equations of motion (HEOM) methods\cite{heomHigh,TanimuraPRA90,heom,TanimuraJPSJ06,TJCP2012,Tanimura2014,Tanimura2015,Shi09,YanPade10A, TJCP2012,Cao13sto,Wu15eHeom,Kleine16chev,DueanCao17,Yan2012,Shi14, Chen15}.
Although the relaxation processes exhibited by a model system under external perturbations are now well understood, these processes of complex systems consisting of many energy states and/or potential-energy surfaces defined in multidimensional configuration spaces have not been thoroughly explored due to a lack of computational power. This is due to the fact that the quantum dynamics of an open $N$-state system must be described using an $N \times N$ reduced density matrix in order to have time-irreversible processes described by a non-Hermitian propagator, while the quantum dynamics of an isolated $N$-state system are described using an $N \times 1$ column or a $1 \times N$ row vector. Moreover, if we consider systems that are strongly influenced by heat baths and
need to adopt a nonperturbative approach, such as HEOM\cite{ SakuraiJPC11,KatoJPCB13,SakuraiJPSJ13,IkedaJCP17,kramerGPU,kramer,Tsuchimoto,CaoGHEOM1,CaoGHEOM2},
more computational resources are necessary.
For this reason, the memory required to compute the density matrix elements becomes a serious issue when studying large systems.
\textcolor{black}{Methodologies based on wave functions for the full Hamiltonian have been developed in order to avoid the reduced description of the system.
The multiconfiguration time-dependent Hartree (MCTDH) approach\cite{ML-MCTDH1,ML-MCTDH2,WangTHoss1,WangTHoss2} employs time-dependent basis sets to represent the total wave function. Then, a variational principle is applied to derive the optimal equation of motion in order to reduce the bath degrees of freedom.
This kind of approach has wider applicability than the reduced equation of motion. With the MCTDH approach, we can treat nonlinear system-bath couplings and anharmonic bath modes\cite{WangTHoss2}, which cannot be treated with the conventional HEOM approach. However, the number of bath modes must be increased until convergence is reached. This implies that the study of long-time behavior requires more basis sets, which makes the calculation more difficult.
Moreover, the time evolution obtained with the wave-function-based approach describes time-reversible processes and, thus, the thermal equilibrium state cannot be obtained with this approach.}
The stochastic unraveling method\cite{Strunz14sto, Strunz15sto,Strunz17sto,Zhao16sto,Zhao17sto} is another approach to reduce the computational costs of simulations for open quantum systems. While the stochastic trajectories obtained from this approach are useful to analyze a role of noise, the efficiency of calculations is not always high because the sampling of stochastic variables is not simple, and many of these approaches have to employ auxiliary variables, including auxiliary density operators (ADOs), in addition to stochastic variables.
In the present paper, we derive hierarchical Schr\"{o}dinger equations of motion (HSEOM) for wave functions.
The time evolution of the reduced density matrix elements can be obtained by numerically integrating the HSEOM with respect to $t$ along the contour in the complex time plane with the aid of a bath correlation function expressed in terms of a set of special functions. This expression maintains the stability of the HSEOM while integrating along the contour in the direction of decreasing time.
\section{Hierarchical Schr\"{o}dinger Equations of Motion}
We consider a system $S$ coupled to a bath $R$ of harmonic oscillators. The Hamiltonian of the total system is given by\cite{LeggettRMP87,Grabert88}
\begin{align}
\hat H_{tot} &= \hat H_S - \hat V\sum\limits_j {k_j \hat x_j} + \sum\limits_{j} {\left( \frac{\hat p_j^2 }{2m_j } + \frac{1}{2} m_j \omega _j^2 \hat x_j^2 \right) },
\end{align}
where $\hat H_S$ is the Hamiltonian of the system and $\hat V$ is the system part of the system-bath interaction.
The bath degrees of freedom are treated as an ensemble of harmonic oscillators,
with the momentum, position, mass, and frequency of the $j$th bath oscillator given by $\hat{p}_{j}$, $\hat{x}_{j}$, $m_{j}$, and $\omega_{j}$, respectively. The quantity $k_j$ is the coupling constant for the interaction between the system and the $j$th oscillator.
The heat bath is characterized by the spectral density function, defined as
\begin{align}
J(\omega) \equiv \sum_{j }\left( \frac{k_{j}^2}{2m_{j}\omega_{j}}\right) \delta(\omega-\omega_{j}),
\end{align}
and the inverse temperature $\beta \equiv 1/k_{\mathrm{B}}T$, where $k_\mathrm{B}$ is the Boltzmann constant.
\begin{figure}[t]
\centering
\includegraphics[scale=0.7]{contourmod3.pdf}
\caption{The contour $C$ in the complex time plane. \label{fig:contour2}}
\end{figure}
We consider a multitime correlation function,
\begin{align}
\Psi_{AB}(t; t')= \mathrm{tr}\{ \hat{A}(t) \hat{\rho}_{tot}(0) \hat{B}(t') \},
\end{align}
where $\hat A$ and $\hat B$ are operators acting on the system $S$, and $\hat{\rho}_{tot}(0)$ is the initial state of the density operator for the total system.
For the contour illustrated in Fig. \ref{fig:contour2}, we can express the correlation function in path-integral form. In order to simplify the derivation, we adopt factorized initial conditions at $t=0$ as $\hat {\rho}_{tot}(0)=\hat{\rho}_{S}(0) \otimes \hat{\rho}^{eq}_{R}$ and do not consider the time evolution from $t=0$ to $0-i \beta \hbar$ along the contour $C_0$\cite{Tanimura2014,Tanimura2015}. If necessary, the thermal equilibrium state for the total system can be obtained from these conditions by integrating the HSEOM for a sufficiently large time $t$.
Because the operators depend only on the system variable as ${A(\hat{q})}$, ${B(\hat{q})}$, and $V(\hat{q})$, where $\hat{q}$ is the position or spin operator, we can trace over the bath degrees of freedom.
For a harmonic heat bath, we can evaluate $\Psi_{AB}(t;t')$ analytically as\cite{ TanimuraJPSJ06,Tanimura2014,Tanimura2015}
\begin{align}
\Psi_{AB}(t; t')=& \int dq_{i}' \int dq_{i} \int _{C} \mathcal{D}[\tilde{q}(\cdot)] A(q, t)B(q', t') \nonumber \\
&\times \exp \left[ \frac{i}{\hbar} \int_{C} d\tau L_{S}(\dot{\tilde{q}}, \tilde{q}, \tau) \right. \nonumber \\
&- \frac{1}{{\hbar}^2} \left. \int _{C} d\tau \int_{C'} \hspace{-1pt} d\tau' V(\tilde{q}, \tau) \alpha(\tau-\tau')
V(\tilde{q}, \tau') \right] \nonumber \\
&\times
\braket{ q_{i} | \hat{\rho}_{S}(0) | q_{i}'}.
\end{align}
where $L_{S}(\dot{\tilde{q}}, \tilde{q}, \tau)$ is the Lagrangian for the system Hamiltonian $\hat H_S$ and the path integral is indicated by $\int \mathcal{D}[\tilde{q}(\cdot)]$. The contour $C'$, along which the integration over $\tau'$ is carried out, is $C$ up to $\tau$. The integrals here are carried out in the direction of the arrow in Fig. \ref{fig:contour2}. The position of the system along the contour $\tilde{q}$ is $q$ or $q'$, depending on whether the contour integral is along $C_{1}$ or $C_{2}$.
The variables $A(q, t)$, $B(q', t') $, and $V(\tilde{q}, \tau)$ are the path-integral representation of ${A(\hat{q})}$, ${B(\hat{q})}$, and $V(\hat{q})$ respectively. For the case of a half-spin system, see the Appendix.
The bath correlation function $\alpha(t)$ is defined as
\begin{align}
\label{eq:bathcorr}
\alpha(t) \equiv \hbar \int_{0}^{\infty} d \omega J(\omega) \left\{
\coth\left(\frac{\beta \hbar \omega}{2}\right) \cos \omega t - i \sin \omega t \right\}
\end{align}
We then rewrite the correlation function as $\Psi_{AB}(t; t') = \int dq_{i}' \braket{ q_{i}'| \phi_{C} (q'_{i}) }$, where $ \ket{\phi_{C} (q'_{i})} $ is the reduced wave function (RWF) integrated along the contour with the initial wave function $\hat{\rho}_{S}(0)\ket{q'_{i}}$. We can also evaluate the correlation function in terms of an energy-state representation as $\Psi_{AB}(t;t') = \sum_{n'_{i}} \braket{n'_{i}|\phi_{C}(n'_{i})}$. In the following, we derive the equations of motion for $\ket{ \phi_{C} (n'_{i})}$ in hierarchical form.
The HEOM have been derived for Drude-type\cite{heomHigh, TanimuraPRA90,heom,TanimuraJPSJ06,Tanimura2014,Tanimura2015,
Shi09,YanPade10A,Yan2012}, Brownian-type\cite{TJCP2012}, and Lorentzian-type\cite{kramer} spectral densities by expressing $\alpha(t)$ as a sum of exponential functions as $\alpha(t)=\sum_k c_k e^{-a_k|t|}$, where $c_k$ and $a_k$ are real or complex constants. Here, we express the bath correlation function using special functions $\{\varphi_{k}(t) \}$\cite{Wu15eHeom, DueanCao17,Kleine16chev} because the exponential form of $\alpha(t)$ becomes unstable in the time integration along the returning contour $C_2$.
The bath correlation function is now expressed as
$\alpha(t) = \sum_{k = 0} ^{K-1} c_{k} \varphi_{k} (t)$, where $c_{k}$ are complex constants and
the number of basis elements is restricted to some value $K$ to facilitate the numerical computations.
In order to obtain a closed set of equations, we choose the set of special functions $\{ \varphi_{k}(t) \}$ so as to ``approximately'' satisfy the relation
\begin{align}
\frac{d}{dt} \varphi_{k}(t) = \sum_{k'=0}^{K-1} \eta_{k, k'} \varphi_{k'} (t),
\end{align}
where $\eta_{k,k'}$ are the expansion coefficients. Although this type of decomposition requires more hierarchical terms than the conventional HEOM formalism employing the exponential-function decomposition scheme, in particular to study long-time behavior, this allows us to study wider classes of spectral densities at any temperature, including a sub-Ohmic spectral density at zero temperature\cite{DueanCao17}.
Using the above relation, we obtain the HSEOM by differentiating the RWF and auxiliary wave functions (AWFs) along the contours $C_{1}$ and $C_{2}$ in the same way as in the conventional HEOM approach\cite{TanimuraJPSJ06, Tanimura2014,Tanimura2015}.
They take the following form:
\begin{align}
\frac{\partial}{\partial s} \ket{\phi_{\vec{n}} (s; n'_{i})} = &
\mp \frac{i}{\hbar} \hat{H}_{S} \ket{\phi_{\vec{n}} (s; n'_{i}) } \nonumber \\
&
\pm \sum_{k=0}^{K-1} \sum_{k'=0}^{K-1} \eta_{k, k'} n_{k}
\ket{ \phi_{\vec{n} - \vec{e}_{k} + \vec{e}_{k'}} (s; n'_{i})} \nonumber \\
& \mp \frac{i}{\hbar} \hat{V} \sum_{k=0}^{K-1} c_{k} \ket{ \phi_{\vec{n} + \vec{e}_{k}} (s; n'_{i})} \nonumber \\
&
\mp \frac{i}{\hbar} \hat{V} \sum_{k=0}^{K-1} n_{k} \varphi_{k} (0)
\ket{ \phi_{\vec{n} - \vec{e}_{k}} (s; n'_{i})},
\label{HSEOMC1}
\end{align}
and the AWFs are expressed in terms of a line integral as follows:
\begin{gather}
\ket{ \phi_{\vec{n}} (s; n'_{i}) } =
\sum_{n, n_{i}} \ket{n} \int dq \braket{n|q} \int dq_{i} \int _{0}^{s} \mathcal{D} [\tilde{q}(\tau(\cdot))] \nonumber \\
\begin{aligned}[b]
&\times
\prod_{k=0}^{K-1}
\left(\hspace{-1pt}-\frac{i}{\hbar} \int _{0}^{s} \hspace{-7.5pt}ds'' \frac{d\tau(s'')}{d s''}
\varphi_{k}(\tau(s)-\tau(s'')) V(\tilde{q}, \tau(s'')) \hspace{-1pt} \right) ^{n_{k}} \\
&\times \exp\left[ \frac{i}{\hbar} \int _{0}^{s} ds' \frac{d\tau(s')}{ds'}
L_{S}(\dot{\tilde{q}}, \tilde{q}, \tau(s')) \right] \mathcal{F}(s, V) \\
&\times
\braket{q_{i}|n_{i} } \braket{ n_{i} |\hat{\rho}_{S}(0)| n'_{i} },
\end{aligned}
\end{gather}
\textcolor{black}{where the influence functional is expressed as
\begin{gather}
\mathcal{F} (s, V) = \exp \left[-\frac{1}{{\hbar}^2} \int_{0}^{s} ds' \frac{d\tau(s')}{ds'}
\int_{0}^{s'} ds'' \frac{d\tau(s'')}{ds''} \right. \nonumber \\
\left. \times V(\tilde{q}, \tau(s')) \sum_{k=0}^{K-1} c_{k} \varphi_{k}(\tau(s')-\tau(s'')) V(\tilde{q}, \tau(s'')) \right],
\end{gather}}
and we have introduced the time variable $\tau(s)$ for $0 \leq s \leq 2t$ defined as
\begin{align}
\tau(s) \equiv \left\{
\begin{array}{lll}
s, & 0 \leq s \leq t, & \mbox{for $C_{1}$}\\
2t-s, & t \leq s \leq 2t, & \mbox{for $C_{2}$}.
\end{array}
\right .
\end{align}
Accordingly, we define $\tilde{q}$ such that $\tilde{q} = q$ for $0 \leq s \leq t$ and
$\tilde{q} = q'$ for $t \leq s \leq 2t$.
In Eq. \eqref{HSEOMC1}, the upper signs of $\mp$ and $\pm$ correspond to $0 \leq s \leq t$, while the lower signs correspond to $t \leq s \leq 2t$.
The vector $\vec{n} = (n_{0}, n_{1}, \ldots , n_{k}, \ldots, n_{K-1})$, used as a subscript here, distinguishes the AWFs and $\ket{\phi_{\vec{n} = \vec{0}}(s;n'_{i})}$ corresponds to the RWF. Each $n_{k}$ is a non-negative integer, and $\vec{e}_{k}$ is the unit vector of the $k$th element. The level of the hierarchy, $N$, is given by $N = \sum_{k=0}^{K-1} n_{k}$. We choose a maximum value of this level, $N_{\max}$. Any AWF whose level is higher than $N_{\max}$ is set to zero, in order to obtain a closed set of equations.
In order to compute the correlation function, we integrate Eq. \eqref{HSEOMC1} with the upper signs from the initial wave function, $\ket{ \phi _{\vec{n}} (s=0; n'_{i})} $, up to the time $s=t$. At $t$, we apply the operator $\hat{A}$ to $\ket{ \phi_{\vec{n}} (s=t; n'_{i})} $ as $\hat{A} \ket{ \phi_{\vec{n}} (s=t; n'_{i}) } \rightarrow \ket{\phi_{\vec{n}} (s=t; n'_{i}) } $.
Then, after the time integration of Eq. \eqref{HSEOMC1} with the lower signs along the contour $C_2$ up to the time $s = 2t - t'$, we apply the operator $\hat{B}$ as $\hat{B} \ket{ \phi_{\vec{n}} (s=2t-t'; n'_{i})} \rightarrow \ket{ \phi_{\vec{n}} (s=2t-t'; n'_{i})}$. We obtain a wave function with a fixed initial wave function $\ket{\phi_{\vec{0}}(s=2t; n'_{i})}$ after continuing the integration up to $s=2t$. For the calculations of the two-body correlation function, we must iterate the above-mentioned calculation with all the different initial states $\ket{n'_{i}}$. A possible number of initial states is equivalent to the number of system states, and hence we must iterate the calculation $N$ times for an $N$-state system. We then obtain the two-body correlation function with the equation
\begin{align}
\Psi_{AB}(t;t') = \sum_{n'_{i}} \braket{ n'_{i}| \phi_{\vec{0}}(s=2t; n'_{i})}.
\end{align}
For the calculations of the equilibrium correlation function, we can start from any initial state, with the time $t'$, at which $\hat{B}$ is applied to the system, chosen to be sufficiently large, because the steady-state solution of the HSEOM is a correlated equilibrium state\cite{Tanimura2014,Tanimura2015}.
The number of operators to be applied is not restricted to two, and we can evaluate the higher-order nonlinear response functions by increasing this number\cite{TanimuraJPSJ06}.
We can also evaluate the reduced density matrix elements, $\braket{i| \mathrm{tr}_{R}\{\hat{\rho}_{tot}(t)\} |j} $, with $\hat B$ chosen to be the unit operator and $\hat{A}$ chosen such that $\hat{A} = \ket{j}\bra{i}$.
Here, in order to reduce the number of iterations, we introduce a ``localized initial state'' of the form $\hat{\rho}_{S}^{loc}(0) = \ket{k}\bra{k}$. This initial state enables us to evaluate the two-body correlation functions with the equation
\begin{align}
\Psi_{AB}(t;t') = \braket{k|\phi_{\vec{0}}(s=2t; n'_{i} = k)},
\end{align}
reducing the number of iterations $N$ to $1$ for $N$-state systems.
By appropriately choosing the transformation matrix $\hat{C}$, we can calculate the two-body correlation function from the desired initial conditions by using the result from the localized initial state $\hat{\rho}_{S}^{loc}(0)$ with the equation
$\Psi_{AB}(t;t') = \mathrm{tr}\{\hat{A}(t) \hat{C}(0) \hat{\rho}_{S}^{loc} \hat{C}^{\dagger}(0)\hat{B}(t')\}$.
\section{numerical results}
We now report the results of numerical simulations that demonstrate the applicability and the validity of the HSEOM, given in Eq. \eqref{HSEOMC1}. We first consider the spin-boson case, with the system Hamiltonian given by
\begin{align}
\label{spinBoson}
\hat{H}_{S} = -\frac{1}{2}\hbar \omega_{0}\hat{\sigma}^{z},
\end{align}
and the system part of the system-bath interaction given by
\begin{align}
\hat{V} = -\frac{1}{2}\hbar \hat{\sigma}^{x},
\end{align}
where $\hat{\sigma}^{x}$ and $\hat{\sigma}^{z}$ are Pauli matrices.
We tested Bessel functions\cite{Kleine16chev} and harmonic-oscillator wave functions\cite{Wu15eHeom} to express the bath correlation function $\alpha(t)$. We found that Bessel functions allow for a more efficient treatment than the harmonic-oscillator wave functions for an Ohmic spectral density. In terms of Bessel functions of the first kind, $J_{k}(t)$, the bath correlation function is expressed as
\begin{align}
\alpha(t) = \sum_{k=0}^{K-1} c_{k} J_{k}(\Omega t),
\label{specialfunc}
\end{align}
and $c_k$ are approximated as
\begin{align}
\label{coefficient}
c_{k}\equiv \hbar \Omega
\int_{-1}^{1} dx (2 - \delta_{0, k})(-i)^{k} T_{k}(x)\frac{J(\Omega x)}{1- e^{-\beta \hbar \Omega x}}.
\end{align}
\textcolor{black}{
This equation is derived with the aid of the Jacobi-Anger identity\cite{Guanhua12chev, Kleine16chev},
\begin{gather*}
e^{-i \Omega x t} = J_{0}(\Omega t) + \sum_{k=1}^{\infty} 2(-i)^{k} T_{k}(x) J_{k}(\Omega t), \nonumber \\
\forall t \in \mathbb{R}, \forall x \in [-1, 1].
\end{gather*}
Here, $T_{k}$ is a Chebyshev polynomial and in order to use this identity we have modified Eq. \eqref{eq:bathcorr} in the following form:
\begin{align}
\alpha(t)
& = \hbar \int_{-1}^{1} dx \frac{J(\Omega x) e^{-i \Omega x t}}{1 - e^{- \beta \hbar \Omega x}} .
\label{eq:bathcorrmod}
\end{align}
We can reduce the range of the integration in Eq. (\ref{eq:bathcorrmod}) from $(-\infty, \infty)$ to $[-\Omega, \Omega]$ with the appropriate cutoff frequency $\Omega$ because the spectral density decays to $0$ as $|\omega| \to \infty$.
In the zero-temperature limit ($\beta \hbar \to \infty$), Eq. \eqref{eq:bathcorrmod} is not exact,
and for this case we evaluate $c_{k}$ using the following equations instead of Eq. \eqref{coefficient}:
for the real part (even $k$),
\begin{align}
c_{k} = \frac{\hbar \Omega}{2} \int_{-1}^{1} dx (2 - \delta_{0, k})(-i)^{k} T_{k}(x) \mathrm{sgn}(x) J(\Omega x),
\end{align}
and for the imaginary part (odd $k$),
\begin{align}
c_{k} = \frac{\hbar \Omega}{2} \int_{-1}^{1} dx (2 - \delta_{0, k})(-i)^{k} T_{k}(x) J(\Omega x).
\end{align}}
We can differentiate $J_{k}(t)$ with respect to $t$ by setting
\begin{align}
\eta_{k, k'} = & \left \{
\begin{array}{ll}
\Omega/2 & (k' = k -1)\\
-\Omega/2 & (k' = k + 1),
\end{array}
\right .
\end{align}
$\eta_{0, 1} = -\Omega $, and, otherwise, $\eta_{k, k'} = 0$. Here, we have approximated the time derivative of the $(K-1)$th function as
$d J_{K-1}(\Omega t) /dt \simeq \Omega J_{K-2}(\Omega t) / 2$
for the sake of numerical computations.
\textcolor{black}{This approximation is accurate when we choose the number of Bessel functions $K$ to satisfy the condition $J_{K}(\Omega t) \simeq 0$ for all $t \in [0, T]$, where $T$ is the length of the simulation time.
This indicates that even when the bath correlation function is expressed with a small number of Bessel functions, we need to set a larger value for $K$ for longer time simulations.
By contrast, in the case of the conventional HEOM, the number of exponential functions does not depend on $T$.}
We considered the Ohmic spectral density with the exponential cutoff
\begin{align}
J(\omega) =\eta \omega e^{-|\omega| / \gamma},
\end{align}
and the circular cutoff \cite{Ando98, Guanhua12chev}
\begin{align}
J(\omega) = \zeta \omega\sqrt{1 - (\omega/\nu)^{2}},
\end{align}
where $\gamma$ and $\nu$ are the cutoff frequencies. We find that if we choose $\nu = \gamma$ and $\zeta = 2 \eta / e$, where $e$ is the base of the natural logarithm, the numerical results obtained with these two types of cutoffs exhibit similar behavior under the condition $\omega_{0} \ll \gamma$, where $\omega_{0}$ is the characteristic frequency of the system with the Hamiltonian given in Eq. \eqref{spinBoson}. For the exponential cutoff, we set $\Omega$ manually with the condition $\gamma < \Omega$, and for the circular cutoff, we evaluated $\Omega$ analytically as $\Omega = \nu$.
It should be noted that in the case of the Ohmic spectral density with the circular cutoff, the imaginary part of the bath correlation function defined by $\alpha(t)=\alpha'(t)-i\alpha''(t)$ is analytically evaluated as\cite{Ando98}
\begin{align}
\alpha''(t) = c_1 J_{1}(\nu t) + c_3 J_{3}(\nu t),
\end{align}
where $c_1=c_3=\pi \hbar \zeta \nu^{2}/{8}$. In the high-temperature limit $\beta \hbar \to 0$, the real part of the bath correlation function reduces to $\alpha'(t) = {\pi} {\zeta \nu}(J_{0}(\nu t) + J_{2}(\nu t))/2\beta$.
This indicates that for the construction of the HSEOM, the circular cutoff allows for a more efficient approach than the exponential cutoff.
\begin{figure}[t]
\centering
\includegraphics[scale=0.5]{resall.pdf}
\caption{The imaginary part of the Fourier transform of the first-order response function $R^{(1)}(\omega)$ for a spin-boson system with an Ohmic spectral density with a circular cutoff (red) and an exponential (exp.) cutoff (blue).
Results for two cases, in which $\beta \hbar = 3$ (solid curve) and $\beta \hbar \to \infty$ (zero-temperature case, dashed curve) are displayed.
The unit of the frequency $\omega$ is set to the characteristic frequency of the system $\omega_{0}$ in Eq. \eqref{spinBoson}.
\label{fig:response}}
\end{figure}
In Fig. \ref{fig:response}, we depict the imaginary part of the Fourier transform of the first-order response function for the spin-boson system,
$R^{(1)}(\omega) = \int_{0}^{\infty} dt e^{-i \omega t}R^{(1)}(t)$, where $R^{(1)}(t)$ is defined by
\begin{align}
\label{eq:response}
R^{(1)}(t) &\equiv -\frac{i}{2}\braket{[\hat{\sigma}^{x}(t), \hat{\sigma}^{x}]}_{eq} \nonumber \\
&= \mathrm{Im} [\Psi_{\sigma^{x} \sigma^{x}}(t;t_{0})].
\end{align}
We can employ the localized initial state as $\hat{\rho}_{S}^{loc}(0) = \ket{1}\bra{1}$ and reduce the number of iterations
because the total equilibrium state is obtained at time $t_{0}$ from this initial state.
In the numerical calculations, we chose the system parameters as $\omega_{0}=\pi$, and the bath parameters as $\hbar \zeta= 0.35, \nu=6$, and $\Omega = 20$ in the case of the exponential cutoff and $\Omega = 6$ in the case of the circular cutoff. Two temperature cases ($\beta \hbar =3$ and $\beta \hbar \to \infty$) are depicted in Fig. \ref{fig:response}. In both cases,
the number of basis elements, $K$, was set to $80$ for the exponential cutoff and $20$ for the circular cutoff, and the maximum level of the hierarchy, $N_{\max}$, was set to $3$. The number of AWFs used to solve the HSEOM in the case of the exponential and circular cutoffs was $91881$ and $1771$, respectively. This indicates that the circular cutoff allows for a more efficient construction of the hierarchy, while the results are similar, as illustrated in Fig. \ref{fig:response}.
To confirm the numerical accuracy of our computations, we calculated the same variable using the extended hierarchical equations of motion (eHEOM)\cite{Wu15eHeom} approach with the same set of Bessel functions. The results obtained from the HSEOM and eHEOM are almost identical (not shown).
\textcolor{black}{
It should be noted that in the case that we use the same function set for approximating the bath correlation function, the eHEOM require more ADOs than the HSEOM because, with the eHEOM, we need two sets of special functions, one representing the real part and one representing the imaginary part of the bath correlation function, while we need only one set to represent Eq. \eqref{specialfunc} in the HSEOM case.
}
By contrast, the HSEOM require more time integrations than the eHEOM because we have to integrate along $C_1$ and $C_2$ consecutively in the HSEOM case, while these integrations can be carried out simultaneously in the eHEOM case.
\textcolor{black}{
Moreover, when we calculate over longer time periods $T$, both the HSEOM and the eHEOM require more AWFs or ADOs in order to obtain convergent results because the long-time behavior can be described only by a larger set of Bessel functions.
}
\begin{figure}[t]
\centering
\includegraphics[scale=0.5]{fig3.pdf}
\caption{The time evolution of the ground-state (red) and first-excited-state (blue) populations in the (i) weak $\hbar \zeta = 0.01$ (solid line), (ii) intermediate $\hbar \zeta = 0.1$ (dashed line), and (iii) strong $\hbar \zeta = 0.5$ (dot-dashed line) coupling cases calculated from the quantum annealing simulation at the zero temperature.
The unit of the time $t$ is set to $t_{f}$ in Eq. \eqref{eq:qa}.
\label{fig:qa}}
\end{figure}
Next we demonstrate quantum annealing\cite{Nishimori98} of a 10 qubit system for the ferromagnetic $p$-spin model. The system Hamiltonian is expressed as\cite{Chakra13QA}
\begin{align}
\hat{H}_{S}(t) = \left(1 - \frac{t}{t_f}\right) \hat{H}_{0} + \frac{t}{t_f}\hat{H}_{1},
\label{eq:qa}
\end{align}
where
\begin{align}
\hat{H}_{0} = -\hbar \Gamma \sum_{i=0}^{\mathcal{N}-1} \hat{\sigma}_{i}^{x},
\end{align}
and $\Gamma$ is the magnitude of the transverse magnetic field in the $x$ direction and $\hat{\sigma}_{i}^{\alpha}$ ($\alpha=x, y,$ and $z$) is the Pauli operator of the $i$th site. The targeting Hamiltonian where we want to find the ground state is given by\cite{Jorg10pspin}
\begin{align}
\hat{H}_{1} = - \hbar \mathcal{N} \left(\sum_{i=0}^{\mathcal{N}-1} \frac{\hat{\sigma}_{i}^{z}}{\mathcal{N}}\right)^{p}.
\label{eq:pspin}
\end{align}
The system part of the interaction is expressed as
\begin{align}
\hat{V} = \hbar \sum_{i=0}^{\mathcal{N}-1} \hat{\sigma}_{i}^{z}.
\end{align}
We chose the system parameters as $\mathcal{N} = 10, \Gamma = 1, p = 5$, and $t_{f} = 1$ and the bath parameters for the Ohmic spectral density with a circular cutoff as $\beta \hbar \to \infty$ (zero-temperature case), $\nu = 3$. We consider the (i) weak-, (ii) intermediate-, and (iii) strong-coupling cases, $\hbar \zeta=0.01$, 0.1, and 0.5, respectively.
\textcolor{black}{We carried out numerical calculation using a PC with 3.00 GHz Dual Intel Xeon CPU (total $24$ cores). The number of basis elements and the maximum level of the hierarchy were set to $K = 5, N_{\max} = 3$ for the (i) weak- and (ii) intermediate-coupling cases and $K = 5, N_{\max} = 5$ for the (iii) strong-coupling case. As mentioned before, we have to employ the larger number of Bessel functions $K$ for larger $T$. Here, we found that $K$ is proportional to $T$. In this simulation, the length of the simulation time $T$ was set to $1$ for all three cases, and thus we set the same value $K = 5$, while we had to set larger $N_{\max}$ for the (iii) strong-coupling case. As a result, the total numbers of AWFs used in the calculations were $N_{tot} = 56$ for (i) and (ii), and $252$ for (iii), which required $14.0$ and $26.3$ MB of computational memory, respectively. The computation time on the Xeon PC for (i) and (ii) was $3$ minutes, whereas that for (iii) was $14$ minutes. We note that $N_{\max}$ also depends on the characteristic frequency of the system, $\omega_c$.
Here, for the ferromagnetic $p$-spin model defined as Eq. \eqref{eq:pspin}, we have $\omega_c \propto \mathcal{N}$ because the energies of the ground state and the most unstable state are $-\hbar \mathcal{N}$ and $\hbar \mathcal{N}$, respectively, while the other energy states are almost $0$. Thus, in the case of the $4$ qubit system, we had less AWFs as $N_{\max}=2$ for (i) and (ii), and $N_{\max}=4$ for (iii), while $K$ did not change. }
As the initial conditions, we set all elements of the reduced density matrix to be the same, and hence the transformation matrix of the localized initial state is defined as $\braket{i|\hat{C}|j} = \delta_{j, 0}/32$.
In Fig. \ref{fig:qa}, we depicted the time evolution of the populations of the ground state, $\ket{E_g} = \bigotimes _{i=0}^{\mathcal{N}-1} \ket{1}_{i}$, and the first-excited-state, $\ket{E_e} = \ket{0}_{j} \bigotimes_{i=0, i\neq j}^{\mathcal{N}-1} \ket{1}_{i}$ (for the definitions of $\ket{0}$ and $\ket{1}$, see the Appendix). As was reported in the previous study with a perturbative Markovian approach\cite{Luci18QA}, the ground-state population is larger for the intermediate system-bath coupling case than the weak-coupling case. We found, however, that the ground-state population already reaches the maximum values in the intermediate-coupling case, while the increase of the population is faster for the stronger-coupling case.
Although the demonstrated calculations are too small to be practical results, this is the largest annealing simulation in terms of a quantum dissipative approach. In addition, this simulation was carried out at zero temperature in a quantum mechanically rigorous manner merely using a personal computer. This is because, with the HSEOM, we can reduce the size of the density matrices from $N^2$ to $N$ for $N$-state systems.
\section{Concluding remarks}
We developed the HSEOM for wave functions utilizing contour integration.
\textcolor{black}{With this formalism, we can reduce the size of the density matrices from $N^2$ to $N$ for $N$-state systems, and for this reason the HSEOM is computationally much more efficient than the conventional HEOM, in particular for larger systems such as a system described in a single \cite{SakuraiJPC11,KatoJPCB13,SakuraiJPSJ13,IkedaJCP17} and multidimensional coordinate space\cite{IkedaCP18}.
In addition, the HSEOM approach enables us to simulate the zero-temperature case or sub-Ohmic spectral density case.}
At this stage, however, it is necessary to employ a large set of Bessel functions, in particular, to study long-time behavior, due to the time profiles of Bessel functions, with which longer time behavior can be described only by a longer series of functions. To fully take advantage of the scalability of HSEOM in comparison to the HEOM, an efficient truncation scheme and the introduction of more appropriate special functions to describe the longer time behavior are necessary. We leave these tasks to future studies.
\acknowledgments
The authors would like to thank A. Kato (Institute for Molecular Science) for a valuable comment regerding using the spectral density with the circular cutoff. The financial support from a Grant-in-Aid for Scientific Research (A26248005) from the Japan Society for the Promotion of Science is acknowledged.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 2,664 |
Q: Using GDB for debugging netlink communication I have a multi-threaded application that communicates with a kernel module using netlink sockets. One of the threads in user mode application works as a server and kernel module works as a client. Roughly the kernel code is as follows:
timeout = 3500;
netlink_unicast();
wait:
__set_current_state(TASK_INTERRUPTIBLE);
timeout = schedule_timeout(timeout);
__set_current_state(TASK_RUNNING);
if (!timeout)
{
printk(KERN_ERR "No response received\n");
return -1;
}
if (message_status != UPDATED)
{
printk(KERN_ERR "Somebody woke us up before we got a reply. Time left %d\n", timeout);
__set_current_state(TASK_INTERRUPTIBLE);
goto wait;
}
The message_status variable is updated in the netlink callback when the user mode application replies to this message. So basically the idea is to send a message and then wait at max timeout jiffies for the reply.
Now, using gdb, if I add a break point in any function that is called by netlink server thread in user mode, the break point is never hit and the kernel log is flooded with messages like
Somebody woke us up before we got a reply. Time left 3499
Somebody woke us up before we got a reply. Time left 3499
Somebody woke us up before we got a reply. Time left 3499
Somebody woke us up before we got a reply. Time left 3499
..
..
Somebody woke us up before we got a reply. Time left 3498
Until I finally get
No response received
What is causing the kernel thread to wake up from the timeout and how should I debug the user mode code?
PS: I am using 2.6.32-71.el6.x86_64 on RHEL 6.0
A: Use gdb. In gdb, you can use "info threads" to see the list of threads. you can jump to a specific thread with the command "thread " where n is the desired thread. You can set specific threads to break using "break : thread ". See this section of the manual to control behavior of the program relative to thread stopping. ie. you can specify that all threads stop while you work on just one thread. https://sourceware.org/gdb/onlinedocs/gdb/Thread-Stops.html#Thread-Stops
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 8,619 |
Huntington is the name of two places in the State of South Carolina:
Huntington, Laurens County, South Carolina
Huntington, Sumter County, South Carolina | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 7,847 |
/**
* THIS FILE IS AUTO-GENERATED
* DON'T MAKE CHANGES HERE
*/
import { createTyped } from '../../factoriesNumber.js';
export var typedDependencies = {
createTyped: createTyped
}; | {
"redpajama_set_name": "RedPajamaGithub"
} | 9,554 |
<?xml version="1.0" encoding="UTF-8"?>
<selector
xmlns:android="http://schemas.android.com/apk/res/android">
<item android:state_focused="true" android:state_checked="true" android:drawable="@drawable/btn_record0" />
<item android:state_focused="true" android:state_checked="false" android:drawable="@drawable/btn_record1" />
<item android:state_checked="false" android:drawable="@drawable/btn_record1" />
<item android:state_checked="true" android:drawable="@drawable/btn_record0" />
</selector> | {
"redpajama_set_name": "RedPajamaGithub"
} | 9,813 |
Harry Holt (1911 – 14 kwietnia 2004 w Casselberry, Floryda), amerykański twórca filmów animowanych.
Współpracował z Waltem Disenyem przy produkcji znanych filmów, m.in. Królewna Śnieżka i siedmiu krasnoludków i Lady and the Tramp. Był jednym z głównych projektantów Walt Disney World w Orlando.
Amerykańscy twórcy filmów animowanych
Urodzeni w 1911
Zmarli w 2004 | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 4,193 |
import _ from 'lodash';
export default /*@ngInject*/ function($rootScope, $scope) {
_.extend(this, {
select(champion) {
if($scope.currentChampion != champion) {
$rootScope.$broadcast('champion.updated', champion);
}
$scope.currentChampion = champion;
}
});
$scope.$on('champion.clicked', ($event, champion) => {
this.select(champion);
});
$scope.currentChampion = null;
}; | {
"redpajama_set_name": "RedPajamaGithub"
} | 3,094 |
Local: 210-888-9653 | Toll Free: 866-604-7814
Cantrell, Anthony B.
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Reliable, Dedicated Representation
» 8 accused of drug charges for cocaine trafficking, some in Texas
8 accused of drug charges for cocaine trafficking, some in Texas
On behalf of Law Offices of Anthony B. Cantrell | Jul 1, 2014 | Uncategorized
Apparently, a 1,400-mile stretch between Texas and another coastal state acted as a pipeline for the transport of an illegal drug. Authorities in Texas and one other state recently arrested a total of eight people on federal drug charges for allegedly participating in the transport and distribution of the cocaine. It is believed that they may be part of a larger organization for drug trafficking.
Authorities received a tip from one of their confidential sources that an organization was transporting roughly 200 kilograms of the illegal drug cocaine through Texas every month. After multiple issues along this trek — such as money, vehicles and drugs being stolen from the organization — the group gathered for a meeting at the house of an individual that is believed to be one of the bosses. Surveillance was gathered on the subject matter of the meeting.
Additionally, three separate sources along with five defendants who agreed to cooperate with authorities all said that the cocaine came from somewhere in Mexico. The drugs were allegedly placed into a section of an 18-wheeler that is commonly known as a pumpkin head. Traditionally housing gears that are necessary for the axle, the trucks were rigged to leave this area empty while still allowing the vehicle to function properly. After the drugs were loaded, produce may have been later loaded into the truck for a cover as a legitimate operation.
Some of the eight arrests were made in Texas, and those accused of acting within this drug-trafficking group are facing drug charges at the federal level. Some of the men in particular have been further accused of acting as principal administrators in a continuing criminal enterprise. Lesser charges include possession of cocaine with the intent to distribute. Those alleged to have taken part in this cocaine trafficking will likely review all charges and evidence alongside their counsel. Doing so can provide insight in to how to best move forward in order to procure the most favorable outcome possible.
Source: Sun Sentinel, "Texas-Palm Beach County cocaine route busted; 8 facing federal charges", Brett Clarkson, June 26, 2014
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Пармен Павлович Маркелия (1900 год, село Рене-Шешелети, Сухумский округ, Кутаисская губерния, Российская империя — неизвестно, село Рене-Шешелети, Гальский район, Абхазская АССР, Грузинская ССР) — председатель колхоза имени Дзигуа Гальского района, Абхазская АССР, Грузинская ССР. Герой Социалистического Труда (1948).
Биография
Родился в 1900 году в крестьянской семье в селе Рене-Шешелети (сегодня — Шешелета Гальского района). С раннего возраста трудился в сельском хозяйстве. Во время коллективизации был одним из основателей колхоза имени Дзигуа, названный именем односельчанина-революционера Павла Евтимовича Дзигуа. В послевоенные годы — председатель этого же колхоза.
В 1947 году колхоз сдал государству в среднем с каждого гектара по 72 центнера кукурузы на участке площадью 16 гектаров. Указом Президиума Верховного Совета СССР от 21 февраля 1948 года удостоен звания Героя Социалистического Труда за «получение высоких урожаев кукурузы и пшеницы в 1947 году» с вручением ордена Ленина и золотой медали «Серп и Молот» (№ 713).
Этим же Указом званием Героя Социалистического Труда были награждены труженики колхоза имени Дзигуа бригадир Владимир Битгаевич Кавшбая, звеньевые Акакий Мусуркаевич Кавшбая и Никандро Елизбарович Тунгия.
После выхода на пенсию проживал в селе Рене-Шешелети. Дата смерти не установлена.
Примечания
Литература
Ссылки
Председатели колхозов | {
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Home»News»Elon Musk's net worth: Elon Musk could buy every NFL team and still have more than $100 billion left
Elon Musk's net worth: Elon Musk could buy every NFL team and still have more than $100 billion left
By The West News October 29, 2021 Updated: October 29, 2021 2 Mins Read
Imagine being so wealthy that you could purchase all of the NFL franchises. There's someone out there who can, and you've most likely heard his name. Elon Musk's Tesla just had a 3.78 percent increase in its valuation, implying that the owner's fortune has risen to previously unimaginable heights.
Elon Musk's net worth: What is the value of Tesla's founder?
According to the Bloomberg Billionaires Index, Musk's net worth has risen to $302 billion as of October 28, a gain of $132 billion in just one year. That's more than Bill Gates and Warren Buffett, both of whom have long been on lists of the world's wealthiest people.
With Musk's wealth, he could acquire every club in the four major American sports leagues: the National Football League, Major League Baseball, National Basketball Association, and National Hockey League (all four leagues are valued at $260 billion by Front Office Sports).
Even if Musk decides to buy every NFL team, he'll still have more than $100 billion to spend on whatever he wants.
Most valuable NFL team in 2021
According to Forbes, the Dallas Cowboys will be the most valuable club in the NFL in 2021, which isn't surprising given that they've topped this list practically every year since Jerry Jones took over as owner.
According to Forbes, the Dallas Cowboys are worth $6.5 billion in 2021, $1.5 billion more than the second-placed New England Patriots.
The average NFL franchise is worth $3.5 billion, so if Musk wanted to acquire all of them, he'd have to shell out at least $112 billion.
For the 15th straight year, the Dallas Cowboys are the most valuable franchise in the NFL 🏈
(via Forbes) pic.twitter.com/gqpZ6QURnD
— ESPN (@espn) August 5, 2021
It's incredible to think that Cowboys owner Jerry Jones spent 'just' $150 million for the franchise in 1989. Jones, on the other hand, steadily expanded the squad through streaming, revenue, and broadcast arrangements. The AT&T Stadium, which is one of the best in the NFL, also contributes to the franchise's overall value.
Despite the fact that the Cowboys' worth was declining due to the epidemic, Forbes named them the most valuable sports team in the world in 2020.
Elon Musk Money News NFl Sports
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TheWestNews is a publication where we share the latest news regarding entertainment, gaming, sports, and local American news. Want to be featured or have some tip for us then reach at "[email protected]"
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\section{Introduction:}
The future FAIR facility at GSI, Darmstadt, will explore the equation of state (EoS) of strongly interacting matter for intermediate temperatures $T$ and high baryon
densities $n_b$
around isospin symmetry, that is for proton fractions $Y_p \sim 0.5$.
Supernovae (SNe) and binary mergers hold environments with similar conditions for $T$ and $n_b$ but with $Y_p \leq 0.3$.
As will be discussed in the scope of this article, core-collapse SNe with matter at a low value of $Y_p$ and dynamical timescales in the range of ms, provide conditions
suitable for a phase transition to strange quark matter.
Such a scenario was recently studied in \cite{Sagert09} applying the MIT bag approach for the EoS of quark matter and using low critical densities for
its onset.
Simulations with different progenitor models and two different
bag constants led to SN explosions accompanied by a significant neutrino
burst which can be observed by present and future neutrino detectors \cite{Dasgupta09}.
In the following, we will introduce in more detail the hybrid EoS used in the above work and analyze its influence on the dynamics of the PNS evolution.
We will discuss the compatibility with heavy ion (HI) data and pulsar observations. Furthermore we will include first order corrections from the strong
interaction constant $\alpha_s$
and study its influence on the maximum mass of the cold hybrid star configurations.
\section{Initial setup for the equation of state}
For the hadronic part of the quark-hadron EoS we use the relativistic mean field approach by \cite{Shen:1998gq}, while quark matter is
described by the MIT bag model. Due to their small current mass, the up and down quarks are treated as massless, while for the strange quark we
chose $m_s=100$MeV which is well within the limits set by the Particle Data Group \cite{Amsler09}.
If quark masses are fixed and no corrections from the strong coupling constant $\alpha_s$ are included, the critical densities for the phase transition are
directly given by the bag parameter $B$ for which we applied two values, $B^{1/4}=165$MeV and $B^{1/4}=162$MeV.
For the construction of the phase transition we choose the Gibbs approach, where a mixed phase of quarks and
hadrons is present \cite{Hempel09prd,Glendenning92}.
\begin{SCfigure}
\includegraphics[width=6.5cm]{figure1}
\caption{The phase diagram for the quark matter phase transition for SN matter (solid lines) and HI collisions (dashed lines).
Thin lines denote the beginning of the mixed phase, thick lines mark the onset of the pure quark phase.}
\label{sn_hi}
\end{SCfigure}
Figure \ref{sn_hi} shows two phase diagrams with the pure hadronic and quark phases and the mixed phase
for $B^{1/4}=165$MeV. As can be seen, the onset of strange quark matter (denoted as \textit{uds}) for a proton fraction of $Y_p = 0.3$
happens already around saturation density $n_0$. For $B^{1/4}=162$MeV the critical densities are even smaller.
However, these values do not contradict with results from HI collisions due to two main reasons. First, supernova dynamics happen
on timescales of ms, whereas weak processes operate within $10^{-6} - 10^{-8}$s and have therefore enough time to produce strangeness.
Consequently, phase transitions can be considered from hadronic to three flavor quark matter in weak equilibrium \cite{Mintz09}.
For HI collisions, dynamical timescales are much shorter, of the order of $10^{-23}$s and
therefore not long enough for strangeness to be produced and equilibrated by weak interactions.
Consequently, for such systems, it seems to be more appropriate to consider a phase transition from hadronic to quark matter composed only of up and down quarks.
The higher the number of quark flavours and therefore the number of degrees of freedom, the softer is the EoS in the mixed phase and the lower is the critical density for its onset.
The second main difference for SN and HI environments is the proton fraction in the two systems, being $Y_p \leq 0.3$ for the first and $Y_p \sim 0.5$ in the second
case.
Due to the symmetry energy of hadronic matter, its isospin symmetric state is energetically favored. For a proton
fraction $Y_p < 0.5$, the energy of hadronic matter is higher and the
additional asymmetry pressure stiffens the EoS. This stiffness results in an earlier onset of the mixed phase with its softer EoS.
Consequently, a low value of $Y_p$ leads to smaller critical densities than for isospin symmetric matter.
Figure \ref{sn_hi} shows two phase diagrams, for SN environments and HI collisions, for $B^{1/4}=165$MeV, illustrating that a low onset of quark matter in SN environments is compatible
with a high critical density in HI collisions, which, for the chosen $B$ and small $T$, is up to $5n_0$.
However, the exact location of the critical density for different $T$ varies in dependence of the models for the quark and hadron EoSs, or the
inclusion of finite size effects.\\
The softening in the mixed phase, as seen in figure \ref{eos_yp03}, is caused by the growing quark fraction $\chi$.
Figure \ref{frac_yp03} shows the fractions of positive charge $Y_C$ in quark and hadronic matter in the pure and mixed phases. In the quark phase $Y_C$
is given by $\left(2/3 \,\, n_u - 1/3 \,\, n_d - 1/3 \,\, n_s \right)/n_b$, whereas $n_u$, $n_d$ and $n_s$ are the up, down and strange quark number densities.
For the hadronic phase,
the charge fraction corresponds to the proton fraction $Y_p$.
As shown in figure \ref{frac_yp03}, $Y_C$ in the quark phase can be very low and even negative.
Therefore, with increasing $\chi$, the charge fraction in the quark phase can compensate $Y_C = Y_p$ of hadronic matter, and the latter
can consequently
approach isospin symmetry towards the end of the mixed phase. At this point, due to the soft EoS in the isospin symmetric hadronic phase and the large number of
degrees of
freedom, the mixed phase EoS is very soft. However, the vanishing of hadronic degrees of freedom causes a significant stiffening when the pure quark phase sets in.
\begin{figure}
\subfigure{
\includegraphics[width=6.5cm]{figure2a}
\label{eos_yp03}}
\subfigure{
\includegraphics[width=6.5cm]{figure2b}
\label{frac_yp03}}
\caption{(a) Hybrid EoS for $B^{1/4}=165$MeV and $\alpha_s=0$, together with the EoSs for the pure hadronic and quark phases at $Y_p = 0.3$
and $T=15$MeV;
(b) Charge fractions in quark and hadronic matter in the mixed phase for a total $Y_C = 0.3$ and temperature $T=15$MeV using $B^{1/4}=165$MeV
and $\alpha_s=0$.}
\label{eos_total}
\end{figure}
Nevertheless, in the simple MIT bag model, the EoS of the pure quark phase is still much softer than the one for hadronic matter giving low maximum masses for
hybrid stars.\\
Up to now, the highest precisely measured mass is the one
for the Hulse-Taylor pulsar with $1.4414 \pm 0.0002$ solar masses M$_\odot$. A new candidate might be the recently studied J1903+0327,
a millisecond pulsar with a main sequence star companion. Due to the large eccentricity of the binary system, the
advance of periastron can be measured giving a value of 1.67$\pm 0.01$M$_\odot$ for the mass of J1903+0327 \cite{Freire09}.
The mass-radius relations in figure \ref{mr_as03} show that while hybrid stars for $B^{1/4}=165$MeV and $B^{1/4}=162$MeV are
above the Hulse-Taylor constraint of 1.44M$_\odot$, their maximum masses are smaller than 1.67$\pm0.01$M$_\odot$.
A possibility to increase the maximum masses of hybrid stars within the MIT bag model is the inclusion of first order corrections from the strong interaction
constant $\alpha_s$ \cite{Farhi84}.
Figure \ref{comparison} shows on the example of $B^{1/4}=165$MeV how the inclusion of $\alpha_s$ corrections shifts the critical density to higher values,
increasing the
pressure
in the mixed and the pure quark phases. A low density for the onset of quark matter can be obtained again by decreasing the value for $B$.
However, the new parameter set for $B$ and $\alpha_s$ leads to a stiffer EoS in the mixed and quark phases which results in higher maximum masses of hybrid stars.
This is
shown in figure \ref{mr_as03} where the parameter set of $B^{1/4}=155$MeV with $\alpha_s=0.3$ leads to a hybrid star maximum mass of $\sim 1.67$M$_\odot$ and, at the same
time, has a similar
critical density
for the onset of quark matter as $B^{1/4}=165$MeV with $\alpha_s=0$.
\begin{figure}
\subfigure{
\includegraphics[width=6.5cm]{figure3a}
\label{comparison}}
\subfigure{
\includegraphics[width=6.5cm]{figure3b}
\label{mr_as03}}
\caption{(a) The inclusion of first order corrections from the strong interaction constant $\alpha_s$ for quarks in the MIT bag model leads to an increase in
the critical density. This can be compensated by reducing the value of $B$. The reduction in $B$ and inclusion of $\alpha_s$ results in a higher pressure in the mixed
and quark phases
and therefore a higher hybrid star maximum mass (b).}
\end{figure}
\section{Quark matter in supernovae}
We performed core-collapse simulations of low and intermediate mass
Fe-core progenitors in spherical symmetry with two different bag constants $B^{1/4}=165$MeV and
$B^{1/4}=162$MeV for the quark matter EoS. Our numerical model is based on general relativistic radiation
hydrodynamics and three flavor Boltzmann neutrino transport (for details see \cite{Liebendoerfer04} and references therein).
The conditions for the appearance of quark matter, i.e. the beginning of the mixed phase, are already obtained at the Fe-core bounce
at central densities close to and slightly above $n_0$. However, the produced small quark fraction
initially does not influence the SN dynamics and the evolution proceeds like in a normal core collapse supernova. A hydrodynamic shock wave forms,
travels outwards and looses energy due to the disintegration
of infalling heavy nuclei and production of neutrinos. The latter become observable in the neutrino spectra as a neutrino
burst dominated by electron neutrinos as the shock wave propagates
across the neutrinospheres (i.e. the neutrino energy and flavor
dependent spheres of last scattering). These energy losses turn the expanding shock quickly into a
standing accretion shock already $\sim 5$ms after bounce.
As discussed previously, the reason for the unchanged dynamics are the
relative stiffness and similarity of the mixed phase EoS to the hadronic one at small quark fractions and $Y_p$ close to isospin symmetry.
However, as matter continues to be accreted on the surface of the PNS, the density and temperature in its interior increases and a growing volume enters
the mixed phase.
The quark matter fraction in the mixed phase rises
and the PNS interior moves up to softer regions of the EoS, where it becomes gravitational unstable.
A contraction proceeds into a collapse till pure quark matter is reached and the EoS stiffens again due to the disappearance of the additional
hadronic degrees of freedom. The collapse halts and a second shock front forms at the phase boundary between the mixed and hadronic phases.
This second shock front moves outwards and turns into a shock wave when it reaches the PNS surface where the density drops over several orders of magnitude.
Hereby, the decrease in density accelerates the shock wave to velocities of the order of the vacuum speed of light.
Shock heating of infalling hadronic matter leads to a lift of degeneracy and an increase in its proton fraction accompanied by the production of
anti-neutrinos.
As soon as the shock wave propagates over the neutrinospheres, a second neutrino burst, dominated by anti-neutrinos is released.
The delay of this second burst after the first deleptonization burst contains correlated information about the progenitor model, the hadronic and quark EoSs,
and the quark-hadron phase transition. For more details, see \cite{Sagert09}.
\section{Conclusions}
Because of the different proton fractions of matter in terrestrial and astrophysical laboratories, such as the future FAIR facility at GSI and
supernovae or compact star mergers, on the one hand and their similarities in $T$ and $n_b$ on the other,
the study of heavy ion collisions and explosive astrophysical scenarios can
complement each other in probing the phase diagram of strongly interacting matter, also in regard to the phase transition from hadronic to quark matter.
However, the study of possible observable signals and impacts of quark matter in astrophysical systems requires
hydrodynamical simulations with an input of an appropriate quark-hadron equation of state.
In this article we present such an approach where a quark matter phase
transition has been implemented in a hadronic equation of state for a large range of temperatures, proton fractions and densities.
Applying the latter to simulations of core-collapse supernovae, we find that a quark matter phase transition can cause the formation of a second shock wave
which leads to the
explosion of the star, accompanied by a second neutrino burst. The latter is
dominated by anti-neutrinos, which can be observed by future and present neutrino detectors. If found, the second neutrino peak can give correlated
information about the progenitor mass and the critical density for the onset of quark matter.
\paragraph{Acknowledgement}
The project was funded by the Swiss National Science Foundation grant. no. PP00P2-
124879/1 and 200020-122287 and the Helmholtz Research School for Quark Matter Studies,
the Italian National Institute for Nuclear Physics, the Graduate Program for Hadron and Ion
Research (PG-HIR), the Alliance Program of the Helmholtz Association (HA216/EMMI) and
the DFG through the Heidelberg Graduate School of Fundamental Physics.
The work of G.~P. is supported by the Deutsche Forschungsgemeinschaft
(DFG) under Grant No. PA 1780/2-1. The authors are
additionally supported by CompStar, a research networking program of the European Science
Foundation, and the Scopes project funded by the Swiss National Science Foundation grant.
no. IB7320-110996/1.
~
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\section{Introduction}
Frustrated magnetism is fertile ground for several interesting phenomena. This is typically best understood in the $S \rightarrow \infty$ limit where frustration gives rise to a large classical ground state degeneracy. The effects of this degeneracy persist even as we move away from the classical limit. Its most significant consequence is to determine the nature of ordering, if at all long range magnetic order emerges in the system.
This selection of order by fluctuations is captured by the `order by disorder' (ObD) paradigm\cite{Chalker2011, Villain1980, Shender1982, Henley1989}.
In the case of quantum fluctuations, this is typically captured by small $\mathcal{O}(1/S)$ corrections. They break the classical degeneracy by their zero point energies to give rise to ordering. Likewise, weak thermal fluctuations at low temperatures, can break degeneracy by allowing for varying entropies. Both lead to long range order in a fluctuation-selected ground state.
A new selection paradigm, order by singularity (ObS), has recently been proposed by two of the current authors. We briefly recapitulate its gist here; details can be found in Ref.~\onlinecite{Khatua2019}. We start with a general principle that holds in the semi-classical large-$S$ limit : the low energy physics of a cluster of quantum spins maps to that of a single particle moving on the classical ground state space (CGSS). In particular, the low-lying energy states of a spin cluster have a one-to-one relation with those of the corresponding single particle problem. This mapping can be seen from the spin path integral formulation combined with a large-$S$ semiclassical approach. However, this path integral-based argument can be carried out only in systems where the CGSS is a smooth manifold. Nevertheless, the mapping is conjectured to hold for systems with non-manifold CGSS' as well. As proof of principle, it was shown to hold true for the XY quadrumer. Remarkably, this example brings out a distinctive localization phenomenon arising from self-intersection in the CGSS.
In the single particle picture, these self-intersection points or singularities mimic impurities to create bound states.The particle is then tied down in bound states at low energies, preventing ergodic sampling of the CGSS. For the magnetic cluster, this manifests as a preference for certain classical ground states over others.
As a mechanism for state selection, ObS can be distinguished from ObD as follows.
As we approach the classical $S\rightarrow \infty$ limit, state selection due to ObS becomes stronger. This is because the mapping between the spin system and the single particle problem becomes exact in this limit.
In contrast, selection due to ObD weakens with increasing $S$, eventually vanishing in the classical limit. As quantum fluctuations are $\mathcal{O}(1/S)$ corrections, their effects diminish with increasing $S$.
In this article, we provide two new examples of ObS in clusters with Kitaev-like couplings. The small size of the clusters allows us to explicitly map out their CGSS'. In both cases, we find interesting CGSS topology with self-intersections. By mapping the spin problem to a particle moving on the CGSS, we find localization within bound states, heralding ObS. As this selection behaviour determines the physics at large $S$, it sheds light on the semiclassical behaviour of Kitaev models.
The Kitaev model was proposed in 2006 as an artificial system that allows for an exact solution in terms of free fermions and $\mathbb{Z}_2$ gauge fields\cite{Kitaev2006}. It describes spin-$1/2$ moments on a honeycomb lattice with nearest-neighbour Ising-like $x-x$, $y-y$ and $z-z$ bonds. The model has received tremendous interest from the point of view of fundamental physics\cite{Kitaev2009,Nussinov2013,Perreault2016,Zhou2017,Rao2017,Hermanns2018} as well as from a materials angle\cite{Rau2016,Takagi2019}.
Several extensions of the model have been proposed to different lattices, couplings, etc. A particularly interesting extension is realized by promoting the spins to the semiclassical limit with $S\gg 1/2$. This leads to several interesting phenomena: an exponentially large classical ground state space\cite{Baskaran2008}, local plaquette-centred conserved quantities\cite{Baskaran2008}, equivalence to a height model\cite{Chandra2010}, power law correlations in certain variables\cite{Chandra2010},
spin liquid behaviour even in the semiclassical limit\cite{Rousochatzakis2018}, etc. The seeds of some of these features appear in a simple and tractable form in the two clusters that we study in this article.
The remainder of this article is structured as follows. In Sec.~\ref{sec.classical}, we review what is known about the Kitaev model in the classical and semi-classical limits. In the process, we recapitulate the definition of a cartesian state -- a key notion in following sections.
We next discuss a toy problem of a particle moving on two intersecting circles in Sec.~\ref{sec.twocircles}. This sets the stage for studying Kitaev clusters, highlighting the key role of bound states. In Sec.~\ref{sec.clusters}, we introduce the two clusters and their symmetries. We move on to the Kitaev square in Sec.~\ref{sec.square} where we construct the CGSS, interpret its features and discuss the quantum spectrum. We also discuss two independent tests for the nature of the low energy states. We discuss the tetrahedron on similar lines in Sec.~\ref{sec.tetrahedron}. We conclude with a summary and discussion.
\begin{figure*}
\includegraphics[width=2\columnwidth]{Kitaev_Cartesian_b_mod.pdf}
\caption{(a) The Kitaev model on the honeycomb lattice. Bonds have $x-x$ (red), $y-y$ (green) or $z-z$ (blue) couplings depending on their orientation.
(b) A dimer cover on the honeycomb lattice. (c) A cartesian state constructed from the dimer cover. On a dimer of type $u$ $~(u=x,y,z)$, the two spins are chosen to lie along $+u$ and $-u$ directions. There are two choices for each dimer corresponding to choosing one of the spins to point along $+u$.}
\label{fig.cartesian}
\end{figure*}
\section{The Kitaev model in the classical limit}
\label{sec.classical}
The Kitaev model is described by the Hamiltonian
\begin{eqnarray}
H = K\Big[
\sum_{\langle ij \rangle_x} \hat{S}_{i}^x ~\hat{S}_{j}^x
+ \sum_{\langle ij \rangle_y} \hat{S}_{i}^y ~\hat{S}_{j}^y
+ \sum_{\langle ij \rangle_z} \hat{S}_{i}^z ~\hat{S}_{j}^z \Big],
\label{eq.Ham}
\end{eqnarray}
with $\langle ij \rangle_{x/y/z}$ representing nearest neighbour bonds on the honeycomb lattice. There are three types of bonds with Ising-like couplings in the $x$, $y$ and $z$ components respectively, as shown in Fig.~\ref{fig.cartesian}(left). We will assume $K>0$ for concreteness; the results and statements that follow can be easily modified to suit the $K<0$ case.
While the original Kitaev model is formulated for $S=1/2$ moments, there is a growing body of work on this model with spins elevated to arbitrary $S$. In this section, we summarize the salient results that are known about the model in the classical $S\rightarrow \infty$ limit.
The seminal work of Baskaran, Sen and Shankar\cite{Baskaran2008} (BSS hereafter) brought out, among other things, rich structure in the CGSS of the Kitaev model.
A convenient starting point to understand this structure is the notion of `cartesian' states. To define a cartesian state, we begin with a nearest-neighbour dimer cover of the honeycomb lattice, as shown in Fig.~\ref{fig.cartesian}(centre). On each dimer, we take the two spins at its end points and align them as follows. One spin is aligned along the `bond direction' while the other is placed in the opposite direction. For example, on a dimer on an x-bond, one spin is taken to point along the $\hat{x}$ direction with the other pointing along $-\hat{x}$. This gives the lowest energy contribution from this bond. There are two such spin configurations on each dimer, leading to an exponentially large number of possibilities for a given dimer cover. An example spin configuration is shown in Fig.~\ref{fig.cartesian}(right) corresponding to the dimer cover shown in Fig.~\ref{fig.cartesian}(centre).
In addition to the degeneracy of spin alignments, we have an exponentially large number of choices for a dimer cover on the underlying honeycomb lattice. Clearly, the set of all cartesian states is very large, scaling exponentially with the system size. Remarkably, every cartesian state is a ground state of the classical Kitaev Hamiltonian. Even more remarkably, a given cartesian state can be smoothly transformed into other cartesian states via a continuous one-parameter transformation. All intermediate states are also classical ground states of the problem. With this picture, BSS envisages the CGSS as `an exponentially large number of isolated points connected by flat valleys'.
A more rigorous discussion of the CGSS was given by Chandra et. al. through a mapping to electrostatics\cite{Chandra2010}. This potentially reveals new classical ground states beyond those enumerated by BSS. However, it is difficult to explicitly construct these states and to determine their connectivity. Chandra et. al. draws several conclusions: (a) the CGSS is an $(N+1)$-dimensional manifold, where $2N$ is the number of sites, (b) the cartesian states are `extrema' in the CGSS, (c) in the zero-temperature partition function, the cartesian states contribute a larger weight compared to other states, and (d) there is no selection of states by fluctuations in the $T\rightarrow 0$ limit. In this article, we present a detailed study of two clusters wherein these types of issues can be more readily examined.
More recently, Rousochatzakis et. al. provide an illuminating discussion of the Kitaev problem in the large $S$ limit\cite{Rousochatzakis2018}. They introduce a new parametrization for the classical ground state space. In the limit of large-$S$, weak quantum fluctuations play a dramatic role by `selecting' a subset of this space, constructed from star-like dimer covers on the honeycomb lattice. The low-energy physics is restricted to fluctuations within this sector. It takes a remarkable form, mapping to the toric code problem on the Kagome lattice. The $\mathbb{Z}_2$ gauge theory structure is inherited from local conserved quantities that were first pointed out by BSS. The current article, albeit restricted to small clusters, points out selection effects beyond the quantum fluctuation paradigm, arising from the topology of the ground state space itself.
Our study of Kitaev clusters can be seen as a progression of earlier work extending the Kitaev structure to systems beyond the honeycomb lattice.
Kitaev physics has been studied in one-dimensional and even three-dimensional systems\cite{Saket2010,Mandal2009,Trebst2017}. The essential requirement is three-fold coordination of nearest neighbour bonds. Lattices with six-fold coordination, such as the triangular lattice, can also host Kitaev-type couplings\cite{Jackeli2015,Avella2018}.
Significant insights have been gleaned from analysing these problems in the classical and semi-classical limits. This has also revealed new physics beyond the original Kitaev formulation. A particularly elegant example is the crystallization of $\mathbb{Z}_2$ vortices on the triangular lattice\cite{Rousochatzakis2016,Seabrook2019}.
\section{Particle on two intersecting circles: a toy problem }
\label{sec.twocircles}
Before discussing the Kitaev problem at hand, we first discuss a simple example of dynamics on a non-manifold space. This sets the stage for discussions of Kitaev clusters in the following sections. We consider a space of two circles with unit radius that are centred at the origin, as shown in Fig.~\ref{fig.twocircles}(left). While the first circle lies in the XY plane, the second lies in the YZ plane. The circles intersect at two points, $\pm \hat{y}$. We refer to these as self-intersections as the space intersects itself at these points. This space is a `non-manifold': while it is one-dimensional at generic points, it does not have well-defined dimensionality in the vicinity of the self-intersection points. We now consider a single particle moving on this space. At generic points, the particle moves along one of the circles. At a self-intersection point, it is allowed to move from one circle to another. For reasons that are explained below, we are interested in the low energy behaviour of this particle, i.e., in stationary states with the lowest energy.
\begin{figure*}
\includegraphics[width=7in]{two_circles_b_mod.pdf}
\caption{(a) Space of two circles in orthogonal planes. The intersection points are shown in yellow. The space is discretized, with the particle allowed to hop between nearest neighbours. Note that a generic point has two neighbours, while the intersection points have four. (b) Numerically obtained ground state wavefunction with the discretization mesh chosen to have 16 sites on each circle.
The base represents the XY and the YZ circles, as the wavefunction is the same on both circles. As the wavefunction is purely real, we represent it by the heights of red dots from the base.
Note that wavefunction is peaked at the intersection points along the Y axis. (c) The numerically obtained first excited state. As with the ground state, this wavefunction is purely real and takes the same form on both circles.
The wavefunction has opposite sign at the two intersection points ($\pm \hat{y}$).}
\label{fig.twocircles}
\end{figure*}
The eigenstates for this problem cannot be calculated using standard quantum mechanical tools, unlike, say, a particle on a single circle. For example, we cannot define a gradient operator on this space. We take an alternative approach by discretizing this space to build a tight binding Hamiltonian. As shown in Fig.~\ref{fig.twocircles}(a), a generic point is connected to two neighbours that lie on the same circle. In contrast, a self-intersection point is connected to four neighbouring sites, two on each circle. For a given mesh size (discretization), the spectrum can be easily obtained numerically. The resulting wavefunctions in the ground state and the first excited state are shown in Figs.~\ref{fig.twocircles}(b) and (c).
The two lowest energy states in the tight binding problem are qualitatively different from the other, higher energy, states. They are `bound states' that are localized around the self-intersection points. To see this, we consider the limit of dense discretization, where the self-intersection points are separated by a large number of intermediate points. Focussing on the vicinity of one self-intersection, we label sites as $(n,A/B)$, where $A$ and $B$ denote the two circles and the integer $n$ represents sites on each circle. We take $n=0$ to be the intersection point with $(0,A)\equiv (0,B)$. We propose an ansatz for the bound state given by
\begin{eqnarray}
\psi_{n,A/B} = \frac{1}{\mathcal{N}} \exp[-\alpha n],
\label{eq.bound}
\end{eqnarray}
where $\mathcal{N}$ is the normalization constant and $\alpha$ is a decay constant that is to be determined. This wavefunction is purely real. It is symmetrically distributed on the two circles, decaying exponentially as we move away from the self-intersection point.
Assuming that it is an eigenstate of the Hamiltonian with eigenvalue $E$, the Schr\"odinger equation at a generic site takes the form $E = -t (e^{\alpha} + e^{-\alpha})$. At the intersection point ,the Schr\"odinger equation takes the form $E = -4t e^{-\alpha}$. From these two relations, we find $\alpha =\frac{\ln3}{2}$.
To examine its bound nature, we compare it with unbound states in the problem. Away from the intersection point, the space resembles a circle. Eigenstates in this region resemble solutions on a circle with the dispersion relation, $E_{unbound} = -2 t \cos k$, where $k$ is the one-dimensional momentum quantum number. These states have energies in the range, $[-2t,2t]$. Crucially, the state in Eq.~\ref{eq.bound} lies below this window, with energy $ E_{bound} = -4t/\sqrt{3} \approx -2.3094 t$. This signifies that the bound state does not hybridize with delocalized modes. More importantly, it indicates that the bound state is the lowest energy state in the problem.
In the full space with two circles, we have two bound states with one at each self-intersection point. When the discretization is not too dense, the bound state wavefunctions overlap in the intermediate region. This results in mixing which splits them into a symmetric and an anti-symmetric combination. The symmetric state, with lower energy, becomes the ground state, while the anti-symmetric state becomes the first excited state. Their wavefunctions are shown in Figs.~\ref{fig.twocircles} (b) and (c). The splitting between the symmetric and anti-symmetric state decreases as we make the discretization more dense. The individual bound state wavefunction in Eq.~\ref{eq.bound} has a localization length of $\frac{1}{\alpha} $ lattice spacings. If the number of intervening lattice points is increased, the overlap between the two bound states decreases. In the limit of very dense discretization, we have independent bound states that are sharply localized around the self-intersection points.
The tight binding results on the two-circle-space provide a framework to understand the results on spin clusters below. The spin clusters have CGSS' that are non-manifold spaces, analogous to the two-circle-space described here. In each cluster, the low energy physics maps to a particle moving on the corresponding CGSS. The spin quantum number, ${S}$, loosely corresponds to the denseness of the tight binding mesh.
As $S$ increases, the mesh becomes denser with a larger number of sites. Such an interpretation for $S$ was given in Ref.~\onlinecite{Khatua2019} in the context of the XY quadrumer (see Tables I and II therein). As we will show in the sections below, the results in Kitaev clusters are also consistent with this interpretation.
The two-circle problem brings out the following three aspects that carry over to the spin
clusters:
(i) The spectrum contains a set of low energy states that is well separated from other, higher energy, states. The number of such states is the same as the number of self-intersection points in the CGSS. (ii) These low energy states are admixtures of bound states that form around self-intersection points, e.g., the ground state is a symmetric combination of all bound states. Their wavefunctions are peaked at the intersection points. (iii) In the dense discretization limit, each low energy eigenstate is associated with one self-intersection point, being sharply localized in its vicinity.
\section{Kitaev clusters}
\label{sec.clusters}
\begin{figure}
\includegraphics[width=\columnwidth]{clusters_mod.pdf}
\caption{The Kitaev square (a) and tetrahedron (b) clusters.}
\label{fig.clusters}
\end{figure}
We consider the Hamiltonian of Eq.~\ref{eq.Ham} on the square and tetrahedral clusters shown in Fig.~\ref{fig.clusters}. The tetrahedron can be obtained from the square by introducing diagonal bonds with $z-z$ couplings. We take the Kitaev coupling to be antiferromagnetic with $K>0$, without loss of generality. This can be seen by a combination of spin rotations: Keeping the spin at site 1 fixed, we rotate (i) the spin at site 2 by $\pi$ about the Z axis (i.e., $\{\hat{S}_2^x,~\hat{S}_2^y,~\hat{S}_2^z\} \rightarrow \{-\hat{S}_2^x,~-\hat{S}_2^y,~\hat{S}_2^z\} $), (ii) the spin at site 3 by $\pi$ about the Y axis (i.e., $\{\hat{S}_3^x,~\hat{S}_3^y,~\hat{S}_3^z\} \rightarrow \{-\hat{S}_3^x,~\hat{S}_3^y,~-\hat{S}_3^z\} $), and (iii) the spin at site 4 by $\pi$ about the X axis (i.e., $\{\hat{S}_4^x,~\hat{S}_4^y,~\hat{S}_4^z\} \rightarrow \{\hat{S}_4^x,~-\hat{S}_4^y,~-\hat{S}_4^z\} $).
Rewriting the spin operators in the new rotated bases, we obtain the same Hamiltonian but with $K \rightarrow -K$. A similar transformation applies in the Kitaev model on the honeycomb lattice\cite{Rousochatzakis2015}.
The cartesian states shown in Fig.~\ref{fig.cartesian} are for the honeycomb lattice with $K>0$. They take a modified form for the $K<0$ case : starting from a dimer cover, the two spins in each dimer are aligned in parallel fashion along or opposite to the bond direction. There are two possible spin orientations for a given dimer.
The clusters shown in Fig.~\ref{fig.clusters} have a Hilbert space of dimension $(2S+1)^4$ with states labelled as $\vert m_1,m_2,m_3,m_4\rangle$, where $m_i$'s represent $S_z$ quantum numbers. This Hilbert space grows rapidly with $S$, placing constraints on numerical exact diagonalization. We use the following two symmetries to find the spectra: (i) The square and tetrahedron Hamiltonians are symmetric under $\pi$-rotation about the Z axis. This allows us to identify even and odd sectors, characterized by even/odd values of $m_{tot}=\sum_i m_i$. (ii) The Hamiltonians are invariant under a combination of operations: a cyclic permutation of sites followed by a global spin rotation about $\hat{z}$ by $\pi/2$. This is depicted in Fig.~\ref{fig.permutation_rotation}. Applying this symmetry four times is equivalent to an identity operation. This allows us to identify a pseudomomentum quantum number, $q=2\pi j/4$, with $j=0,1,2,3$. These two symmetries can be applied independently. We construct reduced Hamiltonian blocks by grouping together states for each $q$ value, with $m_{tot}$ restricted to either even or odd values.
\begin{figure}
\includegraphics[width=\columnwidth]{permutation_rotation_mod.pdf}
\caption{The figure (a) shows the Kitaev tetrahedron. The Kitaev square can be obtained by simply removing the diagonal (z) bonds. The figure (b) shows the cluster after a circular permutation of the four sites. The figure (c) is obtained after a subsequent global $\pi/2$-rotation in spin space about the spin-$z$ axis. }
\label{fig.permutation_rotation}
\end{figure}
\section{Kitaev square}
\label{sec.square}
The Kitaev square is shown in Fig.~\ref{fig.clusters}(left). It can be viewed as a simple realization of a compass model on a four-site chain\cite{Nussinov2013}.
It can also be thought of as a one-dimensional Kitaev chain as studied by BSS in Ref.~\onlinecite{Baskaran2008}, with four sites and periodic conditions. This provides a simple starting point to understand the connectivity of classical ground states.
BSS introduced the notion of cartesian states and showed that they are connected by smooth, energy-preserving transformations. This is illustrated in Fig.~\ref{fig.deform} on the Kitaev square, depicting a one-parameter transformation
that interpolates between two cartesian states. At the cartesian end points, the ground state energy receives contributions solely from bonds that hold dimers (in the parent dimer cover). At intermediate states, this energy is distributed among intervening bonds as well. Similar connecting pathways can exist between other pairs of Cartesian states.
The complete ground state space can be derived by applying the method of Lagrange multipliers, as shown by BSS in Ref.~\onlinecite{Baskaran2008}. Below, we describe the geometry and connectivity of the ground state space, with the explicit derivation presented in Appendix.~\ref{App.squareCGSS}.
\begin{figure}
\includegraphics[width=\columnwidth]{Kitaev_square_deform.pdf}
\caption{A smooth one-parameter transformation that connects two Cartesian states. At $\phi=0$, we have a Cartesian state, corresponding to dimers on horizontal ($x$) bonds. At $\phi=90^\circ$, we have a Cartesian state corresponding to dimers on vertical ($y$) bonds. Intermediate values of $\phi$ interpolate between these states, with each spin rotating as indicated. In each state, we show the bond energies (in units of $K/S^2$) in parentheses. }
\label{fig.deform}
\end{figure}
\subsection{Space of classical ground states}
The CGSS consists of four sectors, $C_i$ with $i=1,2,3,4$ as shown in Tab.~\ref{tab.squareCGSS}. The states in each sector are described by a free angle variable, $\phi$. In geometric terms, each sector can be viewed as a circle. We will see below that the circles intersect at points, as in the two-circle problem discussed in Sec.~\ref{sec.twocircles} above.
To better understand the connectivity of this space, we take these circles to be embedded in an abstract four-dimensional space with coordinates $(xyuv)$. Note that $x$, $y$, $u$ and $v$ are directions in the embedding space, distinct from directions in spin space. The distinction will be clear from context in the arguments below.
To examine if the circles $C_i$ intersect, we first consider $C_1$ and $C_2$.
As can be seen from the spin configurations in Tab.~\ref{tab.squareCGSS}, a generic point in $C_1$ does not appear in $C_2$ as all the four spins $\mathbf{S}_i$ cannot be the same. However, there are two points in common, corresponding to $\phi=0$ and $\pi$ in both. We visualize the connectivity of $C_1$ and $C_2$ as shown in Fig.~\ref{fig.fourcircles}. We take $C_1$ to be a circle in the $(xy)$ plane, centred at the origin with unit radius. Each point on this circle corresponds to a certain value for the angle $\phi$, with $\phi=0$ and $\phi=\pi$ representing points that lie on the positive-$x$ and negative-$x$ axes. We represent these points as $X$ and $\bar{X}$ respectively. Similarly, we take $C_2$ to be a circle in the $(xv)$ plane with unit radius and centre at the origin. We once again take $\phi=0,\pi$ to represent points where the circle intersects the positive- and negative-$x$ axis, coinciding with $X$ and $\bar{X}$. As the two circles lie in orthogonal planes, they share a common diameter on the $x$ axis whose ends at $X$ and $\bar{X}$ constitute two points of intersection. We see that $C_1$ and $C_2$ resemble the space of two intersecting circles described in Sec.~\ref{sec.twocircles}.
Proceeding in the same manner, we take $C_3$ and $C_4$ to lie in the $(uv)$ and $(uy)$ planes respectively. The connectivity of pairs of circles can be seen in Fig.~\ref{fig.fourcircles}. For example, $C_1$ and $C_4$ intersect at two points ($Y$ and $\bar{Y}$), while $C_1$ and $C_3$ do not intersect.
An interesting geometry emerges with four circles embedded in four dimensions. Each circle intersects two other circles, sharing one common diameter with each of the them. At the same time, it remains completely distinct from the fourth circle.
\begin{table}
\begin{tabular}{|c|c|c|c|c|c|}
\hline
$~$ & $~$ & $\mathbf{S}_1$ & $\mathbf{S}_2$ & $\mathbf{S}_3$ & $\mathbf{S}_4$ \\
\hline
$C_1$ & $xy$& $( C_\phi, S_\phi) $ & $(-C_\phi,-S_\phi)$ & $(C_\phi,S_\phi)$ & $(-C_\phi,-S_\phi)$ \\ \hline
$C_2$ & $xv$ & $( C_\phi, S_\phi) $ & $(-C_\phi,S_\phi)$ & $(C_\phi,-S_\phi)$ & $(-C_\phi,-S_\phi)$ \\ \hline
$C_3$ & $uv$ & $( C_\phi, S_\phi) $ & $(-C_\phi, S_\phi )$ & $(-C_\phi,-S_\phi)$ & $(C_\phi,-S_\phi)$ \\ \hline
$C_4$ & $uy$ & $( C_\phi, S_\phi) $ & $(-C_\phi, -S_\phi )$ & $(-C_\phi,S_\phi)$ & $(C_\phi,-S_\phi)$\\
\hline
\end{tabular}
\caption{Classical ground states of the Kitaev square. We have four families denoted by $C_i$, with $i=1,2,3,4$. States in each family are parametrized by an angle $\phi$, with $C_\phi = \cos\phi$ and $S_\phi = \sin \phi$. As all classical ground states lie in the XY plane, we only show the $(x,y)$ components for each spin. }
\label{tab.squareCGSS}
\end{table}
\begin{figure}
\includegraphics[width=0.75\columnwidth]{four_circles.pdf}
\caption{CGSS of the Kitaev square with four circles embedded in four dimensions. Each circle lies in the plane indicated, e.g., the $C_1$ circle lies in the $(xy)$ plane. }
\label{fig.fourcircles}
\end{figure}
\subsection{Physical interpretations of CGSS features}
Remarkably, the points of intersection between circles are all Cartesian states. For example, $C_1$ and $C_2$ intersect when $\phi=0,\pi$ ($X$ and $\bar{X}$ respectively), corresponding to states $\{\mathbf{S}_1, \mathbf{S}_2, \mathbf{S}_3, \mathbf{S}_4\} = \pm S \{\hat{x},-\hat{x},\hat{x},-\hat{x}\}$. Here, $\phi=0$ and $\pi$ correspond to the $+$ and $-$ signs respectively. To recapitulate the definition of cartesian states, they are obtained from a dimer cover by orienting spins to maximally satisfy the bonds on each dimer. Here, these two states can be understood to emerge from a dimer cover with dimers on bonds $(1,2)$ and $(3,4)$ (see Fig.~\ref{fig.clusters}). As these bonds have $x-x$ couplings, the spins are oriented along $\pm \hat{x}$ to maximally satisfy these bonds. The intersection points $U$ and $\bar{U}$ also maximally satisfy the $x-x$ bonds, i.e., they correspond to cartesian states constructed from the same dimer cover. In contrast, the points $Y$, $\bar{Y}$, $V$ and $\bar{V}$ maximally satisfy the $y-y$ bonds. These states are shown in Fig.~\ref{fig.sq_cartesian}.
As seen in Fig.~\ref{fig.fourcircles}, pairs of cartesian states are connected by quarter arcs, e.g., $X$ and $Y$ are connected by a quarter arc in $C_1$. Such an arc represents a smooth transformation that takes us from one cartesian to another, while preserving the classical energy. This is precisely the transformation depicted in Fig.~\ref{fig.deform} above.
\begin{figure}
\includegraphics[width=\columnwidth]{sq_cartesian.pdf}
\caption{Cartesian states on the Kitaev square.}
\label{fig.sq_cartesian}
\end{figure}
\subsection{Spectrum in the quantum spin-$S$ problem}
We have demonstrated that the CGSS for the Kitaev square consists of four circles, with the circles intersecting at points. This can be seen as a higher dimensional generalization of the two-circle space discussed in Sec.~\ref{sec.twocircles} above. We assert that the low energy spectrum of the Kitaev square cluster maps to a particle moving on this space. We present results from numerical exact diagonalization of the spin problem for various $S$ values below. We find striking features in the low energy spectrum that can be understood in analogy with the two-circle problem. In particular, we find the aspects outlined at the end of Sec.~\ref{sec.twocircles} to hold true here.
In Fig.~\ref{fig.sq_spectra}, we show the low energy spectrum for three different values of $S$. We find a set of eight states at the bottom of the spectrum. As $S$ increases, these eight states progressively separate from the other, higher energy, states. We note that eight is precisely the number of self-intersection points in the CGSS of this problem. Equivalently, it is the number of cartesian states in the Kitaev square, as shown in Fig.~\ref{fig.sq_cartesian}. This is consistent with the insight gained in Sec.~\ref{sec.twocircles} in the two-circle problem.
In Fig.~\ref{fig.binding_spread}, we plot two quantities that characterize the low energy spectrum. We have eight low-lying `bound' states that are separated from higher `unbound' states. To quantify the separation, we define the binding energy as $E_b = E_9 - \bar{E}$. Here, $E_9$ is the energy of the ninth state, i.e., the energy of the lowest unbound state. The average of the eight lowest states is denoted as $\bar{E}$. In Fig.~\ref{fig.binding_spread}, we see that the binding energy increases linearly with $S$. This shows that state selection becomes stronger with increasing $S$. In the $S\rightarrow\infty$ limit, all classical ground states have the same energy to $\mathcal{O}(S^2)$. However, the bound states are selected due to an $\mathcal{O}(S)$ binding energy. We define a second quantity, $\Delta E$, as the standard deviation of the lowest eight energy eigenvalues. This represents the spread in the energies of the bound states, serving as a measure of hybridization. This is comparable to the energy difference between symmetric and antisymmetric combinations of bound states in Sec.~\ref{sec.twocircles}. We find that $\Delta E$ decreases with increasing $S$, in analogy with making the discretization finer in the two-circle problem. It is well described by a fit function of the form $\Delta E(S) =0.92016\,S^{3/2}\,\exp(-2.0708\sqrt{S}) $.
$\Delta E$ vanishes exponentially in the $S \rightarrow \infty$ limit. In this limit, we expect to have eight degenerate ground states, each corresponding to an independent bound state at a cartesian intersection point.
\begin{figure*}
\includegraphics[width=2\columnwidth]{sq_energy_specs_mod_b.pdf}
\caption{Low energy spectra in the Kitaev square for three different spin values, $S = 4,6,8$ (a, b, c respectively). The spectra have been shifted by the classical ground state energy ($E_{cgs} = -2KS^2$) and scaled by the coupling strength, $K$. The lowest eight states are shown with blue diamonds in order to distinguish them from higher energy states (magenta squares).
}
\label{fig.sq_spectra}
\end{figure*}
\begin{figure}
\includegraphics[width=2.5in]{E_b_spread_square_corr}
\caption{Binding energy and spread of the low-lying set of eight eigenvalues. The binding energy is shown using blue squares. The plotted curve is the fitting function, given by $E_b (S) = 0.317375 + 0.108314 S$. The spread is shown using magenta circles. The corresponding fitting curve is given by $\Delta E(S) =0.92016\, S^{3/2}\,\exp(-2.0708\sqrt{S})$.
}
\label{fig.binding_spread}
\end{figure}
\subsection{Character of low lying states}
\label{ssec.weight}
We next examine the character of the eight low-lying states, labelled as $\vert \phi_{low.}^i \rangle$, with $i=1,\ldots,8$. We surmise that these arise from bound states that are localized at self-intersection points in the CGSS. In turn, the self-intersection points correspond to cartesian states. To test this notion, we plot the `cartesian weight' in the low-lying states in Fig.~\ref{fig.sq_proj}. We calculate this as follows.
We first adapt the classical notion of the cartesian state to the quantum spin-$S$ context. This is achieved using coherent states\cite{Auerbach_book}. For example, the cartesian state $X$ in Fig.~\ref{fig.fourcircles}, corresponding to $\{\mathbf{S}_1, \mathbf{S}_2, \mathbf{S}_3, \mathbf{S}_4\} =S \{\hat{x},-\hat{x},\hat{x},-\hat{x}\}$, is written as
\begin{eqnarray}
\vert C_X \rangle =
\exp \big[ {-i\frac{\pi}{2} \{ \hat{S}_1^y - \hat{S}_2^y +\hat{S}_3^y -\hat{S}_4^y \}} \big] \vert S,S,S,S\rangle.
\label{eq.cartX}
\end{eqnarray}
Here, $\vert S,S,S,S \rangle$ is the state with all spins polarized along $\hat{z}$. We write the seven other cartesian states in the same fashion. We seek to quantify the contribution of these eight cartesian states to the eight low-lying states in the spectrum.
However, a subtlety arises here as the cartesian states are not mutually orthogonal. For example,
$\langle C_X \vert C_Y \rangle \neq0$, where $\vert C_Y\rangle$ corresponds to $\{\mathbf{S}_1, \mathbf{S}_2, \mathbf{S}_3, \mathbf{S}_4\} =S\{\hat{y},-\hat{y},\hat{y},-\hat{y}\}$.
In order to disentangle these states, we use a Gram-Schmidt procedure to find $\vert \Phi_j \rangle$, $j=1,\ldots,8$, a set of eight mutually orthogonal states that are linear combinations of cartesian states. These span an eight-dimensional subspace of the full Hilbert space. We define the `cartesian weight' of a low-lying state as its weight in this subspace, given by $P_i = \sum_{j=1}^8 \vert\langle \Phi_j \vert \phi_{low.}^i \rangle \vert^2$. If $\vert \phi_{low.}^i \rangle$ has no contributions from cartesian states, $P_i$ would be zero. In contrast, if it is composed entirely of cartesian states, $P_i$ would be unity. Based on the results of the two-circle problem in Sec.~\ref{sec.twocircles}, we expect the cartesian weight of the eight low energy states to be finite and less than unity.
As seen in Fig.~\ref{fig.twocircles}, the two lowest states in the two-circle problem are indeed localized at the intersection points. However, they are not singularly localized with delta-function-like nature. Rather, they decay exponentially with the strongest amplitude at the cartesian points. We expect the eight lowest states in the Kitaev square to be of the same nature. We expect them to have a significant fraction of their weight contributed from cartesian states, but not their entire weight.
Our results for the cartesian weight are shown in Fig.~\ref{fig.sq_proj} for various $S$ values. The figure plots two quantities. The first is the cartesian weight of the ground state, i.e., the lowest of the eight low-lying states. The second is the average cartesian weight over all eight low-lying states. In both cases, the cartesian weight is a significant fraction, e.g., the $S=5$ ground state has a $\sim$56$\%$ contribution from the cartesian states. We emphasize that this represents a very large contribution. The cartesian states are only eight elements in the Hilbert space of size $11^4 = 14641$. Yet, these eight states carry more than half the weight of the ground state. From Fig.~\ref{fig.sq_proj}, we note that the cartesian contribution in the ground state is always less than the average cartesian weight over all eight states. This can be understood by analogy with the two-circle problem. The ground state there is a symmetric combination of bound states at the two intersection points. It has significant weight in the intermediate regions due to constructive interference. As a consequence, the weight at the intersection points is somewhat diminished. In contrast, the first excited state, being an anti-symmetric combination, has a larger weight at the intersection points. In the same manner, we believe that the ground state of the Kitaev square is a symmetric combination of bound states. As a result, it has a smaller cartesian weight than the other seven states.
The $S$-dependence of the cartesian weight can be seen in Fig.~\ref{fig.sq_proj}. We find a smooth evolution with $S$ if we separate integer and half-integer values of $S$ as shown. In Appendix.~\ref{App.Berry}, we demonstrate that a non-trivial Berry phase emerges that distinguishes these two cases. This is in line with arguments presented in Ref.~\onlinecite{Khatua2019}. The spin problem maps to that of a single particle moving on the CGSS. When the spin system evolves along a closed path in the CGSS space, it can accrue a Berry phase. This is a well known ingredient in the spin path integral formulation. In the mapping to the single particle picture, this translates to an Aharonov-Bohm phase that can alter the spectrum. Here, there is a path within the CGSS which accrues a Berry phase when $S$ is a half-integer, but not when $S$ is an integer.
The $S$-dependence is captured by polynomial fits to the data as shown in Fig.~\ref{fig.sq_proj}. From the fit functions, we surmise that the cartesian weight extrapolates to a non-zero value as $S\rightarrow\infty$. As we approach this limit, the number of cartesian states remains fixed at eight while the Hilbert space size grows exponentially. Despite this, the cartesian states retain a finite weight at $S\rightarrow \infty$.
In summary, the low energy physics of the Kitaev square is dominated by cartesian states. We see this in the spectrum as a set of eight low-lying states, energetically separated from all other states. These states are, in fact, quantum analogues of the classical cartesian states. The energy gap to other states increases with increasing $S$, indicating that cartesian states determine the low energy behaviour in the classical $S\rightarrow\infty$ limit. We provide an independent test of these results in the following subsection.
\begin{figure}
\includegraphics[width=2.5in]{proj_sqr_mod.pdf}
\caption{Cartesian weight in the low-lying states of the Kitaev square for (a) integer and (b) half-integer values of $S$. The blue squares show the cartesian weight in the ground state vs. $S$. The red circles show the average cartesian weight of the eight low-lying states. For integer $S$ (top), the fitting curves are given by $f(S) = 0.474367 + 0.677225 /S$ and $g(S) = 0.426014 + 0.692372/S$. For half-integer $S$ (bottom), the fitting curves are $f(S) = 0.476134 + 0.663209/S $ and $g(S) = 0.440098 + 0.667208/S $.}
\label{fig.sq_proj}
\end{figure}
\subsection{Cartesian fidelity of the low-lying states}
\label{ssec.fidelity}
We have argued that the lowest energy states of the Kitaev square are essentially admixtures of the eight cartesian states. It follows that we can recover the cartesian states by suitably mixing the low energy states. In order to achieve this, we define a resolving operator,
\begin{eqnarray}
\nonumber \hat{O}_{sq,res.} &=& \lambda_{12} (\hat{S}_1^x - \hat{S}_2^x ) + \lambda_{34} (\hat{S}_3^x - \hat{S}_4^x ) \\
&+& \lambda_{14} (\hat{S}_1^y - \hat{S}_4^y ) + \lambda_{23} (\hat{S}_2^y - \hat{S}_3^y ),
\label{eq.Osq}
\end{eqnarray}
where the $\lambda$ coefficients are chosen to be substantially different from one another. We have one coefficient for each bond, linearly coupling to the Ising antiferromagnetic moment along the bond direction. For example, the bond $(1,2)$ has an $x-x$ coupling in the Kitaev square Hamiltonian. We have one term associated with this bond in $\hat{O}_{sq,res.}$, given by $ \lambda_{12} (\hat{S}_1^x - \hat{S}_2^x )$. This term serves as a diagnostic for cartesian states in the following manner.
We evaluate its expectation value in a cartesian state, i.e., in the quantum spin-$S$ version of a cartesian state.
If the cartesian state has a dimer on this bond, this term contributes $ \pm 2\lambda_{12} S$, with the $+$ or $-$ sign depending on the orientations of spins on this dimer. In a cartesian state which does not have a dimer on this bond, this term has expectation value zero. Thus, this term resolves two specific cartesian states. In the same way, each term in $\hat{O}_{sq,res.}$ serves as an indicator for two cartesian states.
Our premise is that the eight low-lying states in the spin-$S$ Kitaev square problem are essentially composed of cartesian states. We test this notion by examining the expectation values of the resolving operator in the low-lying states. We find its matrix elements, $O_{mn} = \langle \phi_{low.}^m \vert \hat{O}_{sq,res.} \vert \phi_{low.}^n \rangle$. We now diagonalize the $8 \times 8$ matrix that has $O_{mn}$ as its entries. We find that its eight eigenvalues are approximately given by $(\pm \lambda_{12} \pm \lambda_{34}),~ (\pm \lambda_{14} \pm \lambda_{23})$. These expressions correspond precisely to the expectation values of $\hat{O}_{sq,res.}$ in the eight cartesian states. This shows that the eight low-lying states can be mixed with one another to realize the cartesian states. Note that the low-lying states span an eight-dimensional subspace, as do the cartesian states. We proceed to define a single parameter that quantifies the equivalence between them.
As noted above, the eigenvalues of $O_{mn}$ are close to expectation values of $\hat{O}_{sq,res.}$ in the cartesian states. As the $\lambda$'s in Eq.~\ref{eq.Osq} are chosen to significantly differ from one another, we can clearly distinguish the eigenvalues and identify them with corresponding cartesian states.
This establishes a one-to-one relationship between the \textit{eigenstates} of $\hat{O}_{sq,res.}$ (mixtures of the eight low-lying states) and cartesian states.
We label the eigenstates as $\vert \ell_{\alpha} \rangle$, with $\alpha=1,\ldots,8$. We express the associated cartesian states as $\{ \mathbf{S}_{\alpha,j} , j=1,\ldots,4\}$, denoting the (classical) orientation of the $j^{th}$ spin in the $\alpha^{th}$ cartesian state.
To quantify the fidelity of this relationship, we define vectors $\mathbf{v}_{\alpha,j}$ as follows.
Here, $\alpha=1,\ldots,8$ identifies one of the eigenvectors of $O_{mn}$ while $j=1,\ldots,4$ represents one of the four sites in the Kitaev square. We define $ \mathbf{v}_{\alpha,j} \equiv \langle \ell_\alpha \vert \hat{\mathbf{S}}_j \vert \ell_\alpha \rangle$. As each $\vert \ell_\alpha \rangle$ maps to one particular cartesian state, we find that each vector $\mathbf{v}_{\alpha,j}$ closely resembles the spin configuration of a cartesian state. The fidelity of this mapping is seen by defining a quantity,
\begin{eqnarray}
F_\alpha =\frac{1}{4 S^2} \sum_{j=1}^4 \mathbf{v}_{\alpha,j} \cdot \mathbf{S}_{\alpha,j}.
\label{eq.Falpha}
\end{eqnarray}
If the eight low-lying states were composed purely of cartesian states, the states $\vert \ell_\alpha \rangle$ would be precisely the cartesian states. This would be reflected in the spin expectation values, with $\mathbf{v}_{\alpha,j}= \mathbf{S}_{\alpha,j} $. The quantity $F_\alpha$ would then take its maximum value of unity. In practice, we expect the low-lying states to not just be composed of cartesian states, but to have some additional contributions from nearby states. For example, in the particle picture, the bound state wavefunctions also have non-zero contributions from points that are close to the self-intersection points. As a consequence, we expect $F_\alpha$ to be generically less than unity. In Fig.~\ref{fig.sq_fidelity}, we plot $\bar{F}$, i.e., $F_\alpha$ averaged over all $\alpha$, as a function of $S$. We see that $\bar{F}$ increases with $S$ and, more importantly, approaches unity as $S\rightarrow \infty$. This indicates that the eight low-lying states are indeed essentially composed of cartesian states. Their cartesian character increases with increasing $S$.
\begin{figure}
\includegraphics[width=2.5in]{fidelity_xy_b.pdf}
\caption{Cartesian fidelity in the Kitaev square as a function of $S$. The data is fit using $\bar{F}(S) = 0.97699 - 0.25367/S $. }
\label{fig.sq_fidelity}
\end{figure}
\subsection{Scaling relations in the spectrum}
\label{ssec.scaling}
We have demonstrated that the eight low-lying states correspond to cartesian states. In turn, these correspond to self-intersection points in the CGSS. In Fig.~\ref{fig.binding_spread}, we have described two quantities, the binding energy and the spread. The former increases linearly with $S$, while the latter decreases with $S$. We now rationalize these empirical observations with suitable scaling arguments.
The low energy physics of the Kitaev square maps to a single particle moving on the CGSS. We model the dynamics of the particle using a tight binding description. This involves two parameters: the hopping amplitude $t$ as well as the arc length $L$. The latter represents the density of the tight binding mesh. The CGSS consists of line segments that connect cartesian points, e.g., we have an arc that connects the points $X$ and $Y$ within $C_1$, as seen in Fig.~\ref{fig.fourcircles}. In the tight binding scheme, we take this arc to consist of $L$ sites. The evolution of the spectrum with $S$ is encoded in the tight binding parameters. We now argue that these parameters scale with $S$ in a characteristic manner with $t\sim S$ and $L\sim \sqrt{S}$.
The CGSS is a generalization of the two-circle problem presented above. While the CGSS for the Kitaev square is bigger, the nature of the self-intersections is precisely the same. Within the tight binding scheme, both cases lead to bound states with a decay constant, $\alpha$. This quantity is independent of $t$ and $L$. It depends solely on the connectivity of the CGSS at the self-intersection point. As a consequence, we expect $\alpha$ to be independent of $S$. As argued in Sec.~\ref{sec.twocircles}, when the self-intersection points are well separated, we have bound states with binding energy $(4/\sqrt{3}-2)t$. This is the difference in energy between the bound state and the lowest delocalized state. This quantity is directly proportional to $t$ and is independent of $L$. As we empirically find that the binding energy scales as $S$ (to leading order, see Fig.~\ref{fig.binding_spread}), we conclude that $t$ scales linearly with $S$.
To determine the scaling of $L$ with $S$, we appeal to the example of the XY dimer discussed in Ref.~\onlinecite{Khatua2019}. The corresponding CGSS is a circle, resembling the CGSS of the Kitaev square at generic points. The low energy physics of the dimer maps to a particle on a circle, which can be encoded as a tight binding model. The resulting parameters, $t$ and $L$, must scale in the same way with $S$ as in the case of the Kitaev square. The spectrum of the XY dimer was explicitly worked out in Ref.~\onlinecite{Khatua2019} (see Fig.~3 therein). It was shown that it maps to a particle on a ring. In particular, the low energy states have energies given by $\epsilon\sim a_0 m^2$, where $m$ is an integer. The scale factor $a_0$ represents the inverse of the moment of inertia of the particle. Crucially, we find that $a_0$ is an $\mathcal{O}(S^0)$ quantity (to leading order in $S$). In the tight binding description, $a_0$ corresponds to the ratio $t/L^2$. As we have argued that $t \sim S$ and $a_0 \sim S^0$, we arrive at $L \sim \sqrt{S}$.
In the Kitaev square, we have bound states that form at the eight self-intersection points. These states hybridize among themselves. The spread in their energies is proportional to the overlap between bound states centred at the ends of an arc,
\begin{eqnarray}
E_{overlap} \sim \langle \psi_0\vert \hat{H}_t \vert \psi_{L} \rangle \sim E_{bound} \sum_{n=0}^L e^{-\alpha n} e^{-\alpha (L-n)}.
\end{eqnarray}
Here, the `$\sim$' sign indicates proportionality upto constants that are independent of $S$. We have bound states, $ \vert \psi_0 \rangle$ and $ \vert \psi_L \rangle$, localized at the ends of the arc. The operator $\hat{H}_t$ represents the hopping Hamiltonian on the arc. To a good approximation, $\vert \psi_L \rangle$ is an eigenstate of $\hat{H}_t$ with eigenvalue $E_{bound}$. Here, $E_{bound}$ is the energy of a bound state at a well separated self-intersection point, as derived in Sec.~\ref{sec.twocircles}. It is proportional to the hopping amplitude, $t$. In evaluating the overlap, we have used the explicit form of the bound state wavefunction given in Eq.~\ref{eq.bound}. For simplicity, we have assumed that the overlap only receives contributions from sites on the intervening arc, denoted by the index $n$. The contributions from sites on other arcs will be negligible.
We find $E_{overlap} \sim E_{bound} L e^{-L \alpha}$. Using the scaling relations for $t$ and $L$, we have $E_{overlap} \approx a S^{3/2} \exp(-b\sqrt{S})$. In Fig.~\ref{fig.binding_spread}, we have fit $\Delta E$ to this functional form, obtaining $a$ and $b$ as fitting parameters.
We have argued that parameters in the effective tight binding model scale as $t\sim S$ and $L\sim \sqrt{S}$. These scaling relations are consistent with the numerically obtained spectrum in the Kitaev square problem. In particular, they provide a rationalization for the binding energy increasing linearly with $S$.
These scaling relations may be more general applicable. We find that they are broadly consistent with the spectrum of the XY quadrumer, where $t$ and $L$ for a suitable tight binding model were found as fitting parameters\cite{Khatua2019}.
\section{Kitaev tetrahedron}
\label{sec.tetrahedron}
We now move to the Kitaev tetrahedron that has $z-z$ couplings in addition to those present in the Kitaev square. We first describe the classical ground state space of this problem, before discussing its spectrum.
\begin{figure*}
\includegraphics[width=1.5\columnwidth]{eight_spheres_d.pdf}
\caption{CGSS of the Kitaev tetrahedron with eight spheres embedded in six dimensions. Each sphere lies in a three-dimensional subspace as indicated. For example, the $\Sigma_1$ sphere lies in the space spanned by $x$, $y$ and $z$ coordinates. }
\label{fig.eightspheres}
\end{figure*}
\subsection{Classical ground state space}
As with the Kitaev square, the method of Lagrange multipliers can be used to find the conditions necessary for achieving a classical ground state. We present details about energy minimization in App.~\ref{App.tetCGSS} and the resulting classical ground state framework in App.~\ref{App.tetCGSS_b}. We now proceed to describe the CGSS and its connectivity here.
\begin{table*}
\begin{tabular}{|c|c|c|c|c|c|}
\hline
$~$ & $~$ & $\mathbf{S}_1$ & $\mathbf{S}_2$ & $\mathbf{S}_3$ & $\mathbf{S}_4$ \\
\hline
$\Sigma_1$ & ${xyz}$ & $( S_\theta C_\phi,S_\theta S_\phi,C_\theta) $ & $( -S_\theta C_\phi,-S_\theta S_\phi,C_\theta)$ & $( S_\theta C_\phi,S_\theta S_\phi,-C_\theta)$ & $( -S_\theta C_\phi,-S_\theta S_\phi,-C_\theta)$ \\ \hline
$\Sigma_2$ & ${xvz}$ & $( S_\theta C_\phi,S_\theta S_\phi,C_\theta) $ & $( -S_\theta C_\phi,S_\theta S_\phi,C_\theta)$ & $( S_\theta C_\phi,-S_\theta S_\phi,-C_\theta)$ & $( -S_\theta C_\phi,-S_\theta S_\phi,-C_\theta)$ \\ \hline
$\Sigma_3$ & ${uvz}$ & $( S_\theta C_\phi,S_\theta S_\phi,C_\theta) $ & $( -S_\theta C_\phi,S_\theta S_\phi,C_\theta)$ & $( -S_\theta C_\phi,-S_\theta S_\phi,-C_\theta)$ & $( S_\theta C_\phi,-S_\theta S_\phi,-C_\theta)$ \\ \hline
$\Sigma_4$ & ${uyz}$ & $( S_\theta C_\phi,S_\theta S_\phi,C_\theta) $ & $( -S_\theta C_\phi,-S_\theta S_\phi,C_\theta)$ & $( -S_\theta C_\phi,S_\theta S_\phi,-C_\theta)$ & $( S_\theta C_\phi,-S_\theta S_\phi,-C_\theta)$ \\ \hline
$\Sigma_5$ & ${xyw}$ & $( S_\theta C_\phi,S_\theta S_\phi,C_\theta) $ & $( -S_\theta C_\phi,-S_\theta S_\phi,-C_\theta)$ & $( S_\theta C_\phi,S_\theta S_\phi,-C_\theta)$ & $(-S_\theta C_\phi,-S_\theta S_\phi,C_\theta)$ \\ \hline
$\Sigma_6$ & ${xvw}$ & $( S_\theta C_\phi,S_\theta S_\phi,C_\theta)$ & $( -S_\theta C_\phi,S_\theta S_\phi,-C_\theta)$ & $( S_\theta C_\phi,-S_\theta S_\phi,-C_\theta)$ & $( -S_\theta C_\phi,-S_\theta S_\phi,C_\theta)$ \\ \hline
$\Sigma_7$ & ${uvw}$ & $( S_\theta C_\phi,S_\theta S_\phi,C_\theta)$ & $( -S_\theta C_\phi,S_\theta S_\phi,-C_\theta)$ & $( -S_\theta C_\phi,-S_\theta S_\phi,-C_\theta)$ & $( S_\theta C_\phi,-S_\theta S_\phi,C_\theta)$ \\ \hline
$\Sigma_8$ & ${uyw}$ & $( S_\theta C_\phi,S_\theta S_\phi,C_\theta)$ & $( -S_\theta C_\phi,-S_\theta S_\phi,-C_\theta)$ & $( -S_\theta C_\phi,S_\theta S_\phi,-C_\theta)$ & $( S_\theta C_\phi,-S_\theta S_\phi,C_\theta)$ \\ \hline
\end{tabular}
\caption{Classical ground states of the Kitaev tetrahedron. We have eight families denoted by $\Sigma_i$, with $i=1,\ldots, 8$. States in each family are parametrized by two angles, $\theta$ and $\phi$, with $C_{\theta/\phi} = \cos(\theta/\phi)$ and $S_{\theta/\phi} = \sin (\theta/\phi)$. }
\label{tab.tetCGSS}
\end{table*}
Unlike the Kitaev square, the tetrahedron also possesses non-coplanar classical ground states. By systematically analyzing the ground state conditions, we account for all ground states using two continuous variables and eight discrete choices. We thus have a CGSS composed of eight sectors, $\Sigma_i$ with $i=1,\ldots,8$, as shown in Tab.~\ref{tab.tetCGSS}. Each sector is parametrized by two angles, $\theta$ and $\phi$. These angles describe the orientation of the first spin, $\mathbf{S}_1$, in standard spherical coordinates. As this suggests, these angles satisfy the periodicity of a sphere, e.g., $\phi \equiv \phi+2\pi$. The orientations of the remaining three spins vary from sector to sector as shown in Tab.~\ref{tab.tetCGSS}. From these arguments, we deduce that each sector represents a two-sphere (${S}^2$), parametrized by the two angles $\theta$ and $\phi$. We thus have eight spheres as the CGSS. As we will see below, these spheres are not distinct as they intersect with one another. We will describe the space by suitably adapting the arguments from the Kitaev square case discussed above.
To describe the connectivity of the space, we take the spheres to be embedded in an abstract six-dimensional space with coordinates $(xyzuvw)$. The labels $x$, $y$, etc. represent directions in the embedding space and not in spin space. We first consider the sector $\Sigma_1$ as described in Tab.~\ref{tab.tetCGSS}. Each element in this sector corresponds to a choice of $(\theta,\phi)$. We visualize this as a unit sphere in the subspace spanned by the $x$, $y$ and $z$ coordinates, i.e., as the set of points satisfying $(x^2 + y^2 + z^2 = 1;~u=v=w=0)$. The angles, $\theta$ and $\phi$, parametrize this spherical surface. We take $\theta$ to be the polar angle, measured from the $z$ axis. The azimuthal angle, $\phi$, is taken to be measured from the $x$ axis. For example, $(\theta=\pi/2,\phi=\pi/2)$ corresponds to the point $(x,y,z,u,v,w)=(0,1,0,0,0,0)$. The $\Sigma_1$ sphere is shown at top left in Fig.~\ref{fig.eightspheres}. The figure shows three great circles where the sphere intersects the $xy$, $yz$ and $zx$ planes. We will see below that these great circles have an interesting physical interpretation.
In the same manner, we represent the $\Sigma_{2,\ldots,8}$ sectors with spheres. Each sphere lies in the subspace formed by three coordinates, as indicated in Tab.~\ref{tab.tetCGSS} and shown in Fig.~\ref{fig.eightspheres}. In $\Sigma_{1,\ldots,4}$, we take the polar angle to be measured from the $z$ axis. As $\Sigma_{5,\ldots,8}$ do not extend into the $z$ direction, we measure the polar angle from the $w$ direction. In the same manner, in $\Sigma_{1}$, $\Sigma_2$, $\Sigma_5$ and $\Sigma_6$, we measure the azimuthal angle from the $x$ direction. In the remaining four, we measure it from the $u$ direction.
Crucially, the spheres intersect one another. The geometry is much more complex than in the Kitaev square CGSS with two types of intersections: one-dimensional and zero-dimensional. To give an example of a one-dimensional intersection, we consider $\Sigma_1$, which lies in $(xyz)$ subspace, and $\Sigma_5$ which resides in $(xyw)$ subspace. These two spheres overlap along a great circle that lies in the $xy$ plane.
There are many other such one-dimensional intersections, e.g., $\Sigma_1$ (xyz) and $\Sigma_2$ (xvz) overlap along a great circle in the $zx$ plane. We call these `one-dimensional' as the locus of intersection is a circle.
In contrast, we have a separate class of intersections that are zero-dimensional. For example, we take $\Sigma_1$ (xyz) and $\Sigma_3$ (uvz). These two spheres share a common diameter along the $z$ direction. They intersect at precisely two points given by $(x,y,z,u,v,w) = (0,0,\pm 1, 0,0,0)$. The locus of intersection here is composed of distinct `zero-dimensional' points. There are several such zero-dimensional intersections as can be seen in Fig.~\ref{fig.eightspheres}. We also have pairs of spheres that do not intersect, e.g., $\Sigma_1$ (xyz) and $\Sigma_7$ (uvw) do not have any points in common.
\subsection{Physical interpretation of CGSS features}
The zero-dimensional singularities in this space occur along the six cardinal directions of the embedding space. They are marked as $X$, $\bar{X}$, $Y$, $\bar{Y}$, $Z$, $\bar{Z}$, $U$, $\bar{U}$, $V$, $\bar{V}$, $W$ and $\bar{W}$ in Fig.~\ref{fig.eightspheres}. Note that there are twelve such points. These points have a remarkable interpretation in the physical spin problem: they correspond to cartesian states on the tetrahedron. For example, the point $X$ corresponds to $\{ \mathbf{S}_1, \mathbf{S}_2, \mathbf{S}_3, \mathbf{S}_4 \} = S \{ \hat{x}, -\hat{x}, \hat{x}, -\hat{x}\}$. This corresponds to a dimer cover with dimers placed on $(12)$ and $(34)$ bonds. The spins on the dimers have been aligned along $\hat{x}$ and $-\hat{x}$ so as to maximally satisfy these bonds. A simple analysis shows that there are only three possible dimer covers on the tetrahedron. With each dimer cover having two dimers and each dimer having two possible spin configurations, we have twelve cartesian states in total. The eight cartesian states of the Kitaev square, shown in Fig.~\ref{fig.sq_cartesian}, are also cartesian states of the tetrahedron. The four additional cartesian states of the tetrahedron are shown in Fig.~\ref{fig.ttet_cartesian}. Note that the Kitaev square CGSS can be viewed as a slice of the tetrahedron CGSS. The tetrahedron CGSS of Fig.~\ref{fig.eightspheres} is embedded in six dimensions spanned by (xyzuvw). Its subset that is contained in the four-dimensional space spanned by (xyuv) gives the Kitaev square CGSS of Fig.~\ref{fig.fourcircles}.
\begin{figure}
\includegraphics[width=\columnwidth]{tet_cartesian.pdf}
\caption{Additional cartesian states that emerge in the Kitaev tetrahedron.}
\label{fig.ttet_cartesian}
\end{figure}
In the context of the Kitaev problem on the honeycomb lattice, BSS pointed out that cartesian states could be connected by smooth energy-preserving transformations. This property holds for the tetrahedron as well. In the geometric picture of the CGSS, these transformations are the great circles along the axis planes.
In Fig.~\ref{fig.eightspheres}, we see several such smooth transformations that connect cartesian states. For example, $Z$ is connected to $X$, $\bar{X}$, $Y$, $\bar{Y}$, $U$, $\bar{U}$ and $V$, $\bar{V}$ by quarter-arcs. At the same time, we note that there are pairs of cartesian states that are not connected by simple arcs. For example, starting from $Z$, we cannot reach $W$ or $\bar{W}$ via simple arcs. However, we may reach these points by multiple segments, e.g., by going through $X$. This lack of direct connectivity can be understood from the analysis in BSS. The cartesian states $Z$ and $W$ correspond to the same dimer cover, but with different spin orientations on a given dimer. The BSS transformation does not connect such states.
In the honeycomb lattice Kitaev problem, Chandra et. al. show that the space of ground states is much larger than the set of cartesian states and the valleys that connect them\cite{Chandra2010}. However, it is somewhat difficult to construct these additional states following their formalism. Here, in the example of the Kitaev tetrahedron, we clearly see this physics at play. The cartesian states form a set of zero-dimensional points, with twelve distinct points along the axes. The valleys that connect them are one-dimensional, forming great circles as shown in Fig.~\ref{fig.eightspheres}. However, the CGSS is clearly much larger with the two-dimensional surfaces of the spheres. These additional states lead to new connection pathways on the CGSS.
In summary, the CGSS is composed of eight spheres, embedded in six dimensions. Intersections between spheres make this space a non-manifold. Certain pairs of spheres intersect along great circles while certain pairs only share a common diameter. We also have pairs of spheres that do not intersect at all.
The nature of the CGSS is much more involved than the intersecting circles of the Kitaev square. In the Kitaev square, the CGSS was generically one-dimensional (circles) with zero-dimensional intersections (points). Here, the CGSS is generically two-dimensional (spheres) with intersections that are one-dimensional (circles) and zero-dimensional (points).
\subsection{Particle on two intersecting sheets}
\label{ssec.twosheets}
Before describing the quantum eigenvalue spectrum of the Kitaev tetrahedron, we discuss a toy problem that gives us a suitable framework. We expect the low energy physics of the Kitaev tetrahedron to map to a single particle problem, where the particle moves on the CGSS space of eight intersecting spheres. This space is a non-manifold that appears to be two-dimensional at a generic point, but has one-dimensional and zero-dimensional self-intersections. What is the low energy behaviour of a particle residing in this space? The insight gleaned from the two circle problem in Sec.~\ref{sec.twocircles} does not suffice to address this question. Working in the same spirit, we construct the simplest toy problem that has the same type of self-intersections.
We consider a space composed of two sheets, as shown in Fig~\ref{fig.twosheets}(top). The sheets, $ABCD$ and $A'B'C'D'$ are taken to be squares. Each sheet is taken to have periodic boundaries with opposite sides identified, i.e., $AB \equiv DC$, $AD\equiv BC$, $A'B' \equiv D'C'$ and $A'D'\equiv B'C'$. The two sheets are assumed to intersect along two perpendicular lines, $L\tilde{L}$ and $M\tilde{M}$, with these lines intersecting at a point $O$. Note that $L$ and $\tilde{L}$ represent the same point due to periodic boundaries, as do $M$ and $\tilde{M}$.
This geometry represents the simplest non-manifold space that has the same qualitative features as the Kitaev tetrahedron CGSS. At generic points, it appears two-dimensional. However, it has intersections that are one-dimensional and zero-dimensional. The former are the lines $L\tilde{L}$ and $M\tilde{M}$, while the latter is the point $O$ that lies at the intersection of $L\tilde{L}$ and $M\tilde{M}$.
\begin{figure}
\includegraphics[width=3in]{two_sheets_mod.pdf}
\caption{Toy problem with two sheets. (a) Geometry of the two sheets intersecting along perpendicular lines. (b) Ground state wavefunction on one of the two sheets. The size of the marker at each site is proportional to the squared amplitude at the site. All sites have the same phase. We show only one sheet as the wavefunction is the same on the other sheet as well. }
\label{fig.twosheets}
\end{figure}
In order to study the dynamics of a particle on this space, we discretize this space and adopt a tight binding approach. The squares $ABCD$ and $A'B'C'D'$ are both replaced with $N\times N$ meshes with periodic boundaries. Points along the common lines $L\tilde{L}$ and $M\tilde{M}$ are identified. A generic point in this tight binding problem has four nearest neighbours that lie on the same sheet. A point that lies on one of the intersection lines, but not on the other, has six nearest neighbours: two on the common line and two on each sheet. Finally, the common point $O$ has four nearest neighbours: two on each intersection line with all four points shared by both sheets. We construct the corresponding tight binding Hamiltonian and diagonalize it numerically. The resulting spectrum contains, in order of increasing energy, (i) a sharply localized ground state that is centred at $O$ and decays in all directions, (ii) a large number of semi-localized states that are peaked along one of the common lines, (iii) extended states. We focus on the ground state that provides a truly localized state. Its wavefunction is plotted in Fig.~\ref{fig.twosheets}(bottom).
We now summarize the lessons learned from the toy problem. We have studied a particle moving on a space with two one-dimensional intersection lines. The lines themselves intersect, giving rise to a zero-dimensional singular point. In this scenario, we find only one truly localized state that is centred on the zero-dimensional singularity. Crucially, as the lowest energy state, this state dominates the low energy dynamics of the particle. We now make a connection to the Kitaev tetrahedron CGSS shown in Fig.~\ref{fig.eightspheres}. We have spheres that intersect along lines, with the lines themselves intersecting at points.
\begin{figure*}
\includegraphics[width=2\columnwidth]{tet_energy_specs_mod_b.pdf}
\caption{Low energy spectra in the Kitaev tetrahedron for $S=6,7,8$ (a, b, c respectively). The spectra are shifted by the classical ground state energy and scaled by the coupling strength $K$. The lowest twelve states are shown using blue diamonds, in order to distinguish them from higher states (magenta squares).}
\label{fig.spectrum_tet}
\end{figure*}
\begin{figure}
\includegraphics[width=2.5in]{E_b_spread_tet}
\caption{Binding energy and spread of the low-lying set of twelve eigenvalues. The binding energy is shown using blue squares. The plotted curve is the fitting function, given by $E_b (S) = 0.386788 + 0.079194 S$. The spread is shown as magenta circles. The dashed line is a guide to the eye.
}
\label{fig.tet_binding_spread}
\end{figure}
\subsection{Spectrum in the spin-$S$ quantum problem}
The low energy spectrum for the Kitaev tetrahedron is shown in Fig.~\ref{fig.spectrum_tet} for various $S$ values. We interpret its features in terms of the single particle problem on the eight-sphere-CGSS of Fig.~\ref{fig.eightspheres}. Crucially, the lowest energy states are a set of twelve levels. As $S$ increases, the twelve progressively separate from the other, higher energy, states. Fig.~\ref{fig.spectrum_tet} shows the spectrum for $S=6,7,8$. For smaller $S$ values, we find that the twelve states do not separate out completely from the higher states. This is possibly due to the presence of many one-dimensional singularities in the CGSS. In the problem of two intersecting sheets in Sec.~\ref{ssec.twosheets}, there are many `semi-localized' states that are centred on one-dimensional lines. We expect a large number of such states in the eight-sphere CGSS. As they hybridize with one another, they can acquire a large spread in energy. We believe the lowest state from this set is comparable in energy with the highest of the low-lying twelve-fold set. For small $S$ values, this makes it difficult to identify the twelve low-lying states from the numerics. As $S$ increases, this hybridization decreases, with the twelve-fold set becoming clearly visible for $S\geq 5.5$.
We plot two quantities that describe the low energy spectrum in Fig.~\ref{fig.tet_binding_spread}. As in the Kitaev square, we define the binding energy as $E_b = E_{13} - \bar{E}$. Here, $E_{13}$ is the energy of the thirteenth state and $\bar{E}$ is the mean of the twelve lowest energy states. We see that $E_b$ increases linearly in $S$, in line with the scaling arguments in Sec.~\ref{ssec.scaling}. We also plot the spread, $\Delta E$, defined as the standard deviation of the twelve lowest energy states. In analogy with Kitaev square, we expect the spread to decrease with increasing $S$ and to vanish in the $S\rightarrow\infty$ limit. Indeed, we see that the spread decreases with $S$. Due to the limited number of data points, we are not able to find a meaningful fitting function that describes $\Delta E (S)$. As a consequence, we cannot quantitatively address the $S\rightarrow \infty$ limit.
Nevertheless, in analogy with the Kitaev square, we surmise that a twelve-fold degenerate ground state emerges as $S\rightarrow\infty$. We argue that these states are related to the twelve cartesian states of the tetrahedron. This can be understood from the problem of two intersecting sheets in Sec.~\ref{ssec.twosheets} which had a non-degenerate ground state, localized at the point-like singularity. Here, the CGSS of the tetrahedron has twelve point-like singularities, corresponding to cartesian states. The twelve low-lying states arise from bound states around these twelve points. We discuss quantitative tests of this notion below.
\subsection{Character of low lying states }
We next present a test of the hypothesis that the twelve low-lying states are essentially composed of cartesian states. We follow the same steps as in Sec.~\ref{ssec.weight} above to quantify the cartesian weight in the low-lying states. The only difference is that we have 12 Cartesian states on the tetrahedron as opposed to 8 on the square.
In Fig.~\ref{fig.tet_proj}, we plot the cartesian weight of the low-lying states of the Kitaev tetrahedron. The two curves correspond to cartesian weight (a) of the ground state (the state with the lowest energy among the twelve), and (b) averaged over the twelve low-lying states. We find sizeable cartesian weight in both. For example, the ground state at $S=7$ has a cartesian weight of $\sim 30\%$. Here, the twelve cartesian states are a minuscule subset of the full Hilbert space that contains $15^4 = 50,625$ states. Nevertheless, they constitute more than a quarter of the weight in the ground state.
Fig.~\ref{fig.tet_proj} shows the $S$-dependence of the cartesian weights. As with the Kitaev square, we find a smooth variation with $S$ only if we separate integer and half-integer cases. This indicates a role for Berry phases, that is beyond the scope of our discussion.
Crucially, in both integer and half-integer cases, the cartesian weight extrapolates to non-zero values as $S\rightarrow\infty$. In this limit, the full Hilbert space grows exponentially while the number of cartesian weights remains fixed at twelve. And yet, the cartesian states support a finite fraction of the ground state weight. We interpret this result as follows: the low-lying states are admixtures of bound states formed around zero-dimensional intersections in the CGSS. Their cartesian weight is less than $100\%$ because the bound states are not delta-function-localized. They contain contributions from non-cartesian states that are in the vicinity of the intersection points.
These results, put together, show that the twelve low-lying states are essentially composed of cartesian states. In this sense, the cartesian states solely determine the low-energy physics of the Kitaev tetrahedron.
\begin{figure}
\includegraphics[width=2.5in]{proj_tet_mod.pdf}
\caption{Cartesian weight in the low-lying states of the Kitaev tetrahedron for (a) integer and (b) half-integer values of $S$. The blue squares show the cartesian weight in the ground state vs. $S$. The red circles show the average cartesian weight of the twelve low-lying states. For integer $S$ (top), the data are fit using $f(S) = 0.16907 + 1.12538/S $ and $g(S) = 0.11449 + 1.30306/S $. For half-integer $S$ (bottom), the fitting curves are $f(S) = 0.18512 + 0.97489/S $ and $g(S) = 0.12233 + 1.2582/S $.}
\label{fig.tet_proj}
\end{figure}
\subsection{Cartesian fidelity of the low-lying states}
\label{ssec.tet_projection}
As with the Kitaev square, we next discuss an independent quantitative test for the cartesian character of the low-lying states. We show that the low-lying states can be mixed into a form that reproduces the twelve classical cartesian states. We define a resolving operator,
\begin{eqnarray}
\hat{O}_{tet,res.} &=& \hat{O}_{sq,res.}+ \lambda_{13} (\hat{S}_1^z - \hat{S}_3^z ) + \lambda_{24} (\hat{S}_2^z - \hat{S}_4^z ),~~~~
\end{eqnarray}
where $\hat{O}_{sq,res.}$ has been defined in Eq.~\ref{eq.Osq}. We have two additional terms due to the two additional bonds in the tetrahedron Hamiltonian. As discussed in Sec.~\ref{ssec.fidelity}, these terms resolve cartesian states with dimers on the $z-z$ bonds.
Starting the matrix elements of $\hat{O}_{tet,res.}$ in the low-lying states, we define the cartesian fidelity as in Sec.~\ref{ssec.fidelity} above. All details of the definition carry over from the Kitaev square to the tetrahedron, but for the number of cartesian states changing from eight to twelve.
In Fig.~\ref{fig.tet_fidelity}, we plot $\bar{F}$, i.e., $F_\alpha$, averaged over all $\alpha$, for various values of $S$. We see that $\bar{F}$ is very large, increases with $S$ and extrapolates to unity as $S\rightarrow \infty$. This demonstrates that the twelve low-lying states can be mixed to recover cartesian states with high fidelity.
\begin{figure}
\includegraphics[width=2.5in]{fidelity_xyz_b.pdf}
\caption{ Cartesian fidelity in the Kitaev tetrahedron vs. $S$. The data is fit using $\bar{F}(S) = 1.07978 - 2.54565/S $. }
\label{fig.tet_fidelity}
\end{figure}
\section{Summary and discussion}
We have presented low energy descriptions for two Kitaev clusters, the square and the tetrahedron. We have explicitly enumerated the classical ground states in each case, demonstrating that they form self-intersecting spaces. The Kitaev square leads to a space with four circles embedded in four dimensions, while the tetrahedron leads to eight spheres that are embedded in six dimensions.
We understand the low energy spectra of the spin clusters in terms of a particle moving on these spaces. In both clusters, the low-energy dynamics of this particle is determined by bound states that form at self-intersection points. The intersection points have a very interesting interpretation as `Cartesian' states that were first proposed in Ref.~\onlinecite{Baskaran2008}. Our results show conclusively that Cartesian states, although few in number, completely determine the low energy physics. The validity of this picture improves with $S$, becoming exact in the classical $S\rightarrow\infty$ limit. Our results shed light on the semiclassical physics of Kitaev-type problems. More generally, they provide an enlightening example of order by singularity.
The Kitaev model on the honeycomb lattice also exhibits strong frustration for higher spins. Theoretical studies have discussed possible interesting features for $S\geq 1$\cite{Koga2018,Oitmaa2018,Suzuki2018,Minakawa2019}. An interesting proposal has been put forth for realizing higher-spin Kitaev models in materials\cite{Stavropoulos2019}. In the large-$S$ limit, previous studies have sketched the contours of the ground state space, using the notion of Cartesian states as a convenient starting point. Our results on two clusters suggest a fresh perspectives that prompts a reexamination of earlier results. In particular, on the honeycomb lattice, Chandra et. al.\cite{Chandra2010} have suggested that the space of ground states is a manifold with Cartesian states as extremal points. From an analysis of thermal fluctuations, they further argue that there is no selection of Cartesian states. Here, we have explicitly demonstrated that the two clusters have self-intersecting ground state spaces with clear non-manifold nature. Our analysis also shows that Cartesian states are strongly selected, not by fluctuation contributions to energy but by bound state formation. An exciting future direction is to investigate whether these features carry over to the honeycomb lattice.
There is a large body of work on Kitaev-Heisenberg models, where Kitaev interactions coexist with Heisenberg couplings\cite{Chaloupka2010}. The effects of an additional Heisenberg interaction have also been studied in the classical limit\cite{Price2013}. In this context, our results on the Kitaev-tetrahedron assume significance. We have characterized the space of classical ground states in the pure Kitaev limit. This space of eight spheres persists as the ground state space even in the presence of antiferromagnetic Heisenberg couplings. This can be seen as follows. On the tetrahedron, the Heisenberg interaction can be re-expressed as the square of the total spin. It is minimized in configurations where the sum of four spins vanishes. The set of all such states has been shown to form a non-manifold space that is generically five-dimensional\cite{Khatua2018}. Here, as seen from Tab.~\ref{tab.tetCGSS}, all configurations in the Kitaev-tetrahedron-CGSS have zero total spin. Thus, they continue to be minimum energy states when a Heisenberg interaction is introduced. This indicates that order by singularity operates in the Kitaev-Heisenberg tetrahedron as well.
The Kitaev-tetrahedron-CGSS of Fig.~\ref{fig.eightspheres} can be viewed as a slice of the larger non-manifold CGSS of a Heisenberg tetrahedron.
Our analysis has strong overlaps with the study of quantum graphs. The low energy physics of the Kitaev clusters is dominated by bound states formed at intersection points. These points are connected by pathways, allowing for hybridization among the bound states. At low energies, the clusters can be faithfully modelled as a set of discrete points that are connected by channels. This has strong connections to quantum graph models\cite{Pauling1936,Kottos1997,Keating2008,Harrison2011,Alexandradinata2018}. It is conceivable that more general Kitaev models can be modelled as quantum graphs with a larger number of nodes and connecting pathways. This could allow for new ways of understanding Kitaev spin liquids.
The results presented here are a convincing demonstration of order by singularity. This is only the second known example, after the quantum XY quadrumer studied in Ref.~\onlinecite{Khatua2019}. In Kitaev clusters, Cartesian states are essentially a classical concept. Nevertheless, they acquire a dominant role in the quantum problem. In the $S\rightarrow\infty$ limit, the quantum ground states become the same as cartesian states. They are separated from other classical ground states by an $\mathcal{O}(S)$ binding energy.
This opens the door to several interesting questions. Is there state selection in the purely classical model with thermal fluctuations? Can order by singularity be distinguished from order by disorder in an experimental context? We hope future studies will be able to answer these questions.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 9,677 |
HomeFeaturesRaising a glass to Charles Henry Roe
Raising a glass to Charles Henry Roe
17/09/2020 Aaron Hilson Features, Heritage, History, Industry Heritage
Legendary Leeds-based coachbuilder Charles Henry Roe has been the subject of two rather different tributes, reports Nick Larkin
In the first of two reminders of the well-known coach builder Charles Roe, an event is planned for 2021 to mark 100 years since Roe began operations at the legendary Cross Gates factory in Leeds. Secondly a Wetherpoons pub called the Charles Henry Roe has finally opened nearby, after delays caused by the coronavirus lockdown.
Mr Roe remained Managing Director of Chas H Roe Limited until 1952, by which time the company's products were considered by many to be the best quality on the market, forming the backbone of many municipal and some BET fleets, as well as double-deckers being snapped up by independents.
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"redpajama_set_name": "RedPajamaCommonCrawl"
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Written by:chanaka inojPosted on: 9th March 2017 9th March 2017
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\section{Introduction}
Kac's~\cite{Kak66} question \textquotedblleft Can one
hear the shape of a drum?\textquotedblright\ is part of the scientific pop
culture~\cite{Wiki}. The technical side of the question concerns our ability
to completely specify\ the geometry of a domain from the eigenvalues of its
Laplacian. The question has been reinterpreted in the study of Schr\"{o}dinger
operators on metric graphs by Gutkin and Smilansky~\cite{Gutkin01} and
restated in Algebraic Graphs Theory as \textquotedblleft Which graphs are
determined by their spectrum?\textquotedblright\ by van Dam and Haemers~\cite{vanDam03}. (Through this work, the \emph{spectrum} of a matrix $M$,
denoted by $S_{M}$, is the set of its eigenvalues.) While we commonly
employ different types of matrices to encode the structure of graphs, none has
yet been shown to efficiently provide a \emph{complete graph invariant}%
, \emph{i.e.}, a parameter that does not change under a permutation of the vertex labels. The spectrum of the adjacency matrix, for
example, is a common invariant and easily seen to satisfy the
\textquotedblleft if\textquotedblright\ part of this statement; however, it is
not a complete invariant, given the fact that co-spectral non-isomorphic
graphs are abundant~\cite{Godsil82a,Godsil82b} (see for instance Supplementary Information Section A). In the same spirit, physical scenarios
have suggested various notions of refined spectra as a tool for distinguishing
graphs, with partial degrees of success~\cite{Audenaert07a,Audenaert07b,Audenaert07b}. A
common intersection for these approaches is Quantum Mechanics, arguably due to
the popularization of quantum dynamics on graphs at the beginning of the last
decade~\cite{Konno08}.
It is interesting, not only from the historical point of view, to
observe that the strong link between Physics and graphs is via
the Ising model, perhaps the most studied model in Statistical Mechanics.
Originally proposed in 1925~\cite{Ising25} as a simplified description of the
magnetic properties of materials, the Ising model has found a vast number of
applications from Biology to Solid State Physics. Its great importance is
emphasized by exact solutions and numerical techniques for the identification
of phase transitions and critical phenomena~\cite{Huang90}. The Ising model
framework seems particularly suitable to observe differences between Classical
and Quantum Mechanics in terms of spectral information, since the quantum case
is directly obtained by adding an appropriate (transverse)\ magnetic field to
the classical Hamiltonian.
In what follows, we map a graph into an Ising model and interpret its
energy spectrum as a graph invariant, before and after the
\textquotedblleft switch\textquotedblright\ from Classical to Quantum
Mechanics. We demonstrate with exhaustive numerical examples that the
quantum spectrum is a stronger invariant and propose a general
framework to define physically meaningful graph
polynomials. Determining whether the quantum energy spectrum is a
complete invariant remains an open problem. We perform experiments on
a programmable annealer with superconducting flux technology~\cite{Johnson10}. Our purpose is to \textquotedblleft hear the shape
of an Ising model\textquotedblright, by generating statistics of low
energy states as the outcome of a noisy evolution. The experiment is
run disregarding whether or not the state of the device follows an
adiabatic path along its instantaneous ground state, therefore against
the prescription for successful annealing~\cite{Santoro92}. In other
words, we are not only interested in the ground state but,
unconventionally, in the full output of a noisy computation. We obtain
data on non-isomorphic graphs that are distinguished by their quantum
energy spectra but not by the classical ones.
\section{Results}
{\bf Classical Cospectrality and Ising models.} The Hamiltonian of the \emph{Ising
model}~\cite{Cipra87} (or, equivalent, $2$\emph{-state Potts model}) on a
graph $G$, with $n$ vertices $V(G)$ and edges $E(G)$, is defined by the
diagonal matrix
\begin{equation}
H(G,J):=J\sum_{\{i,j\}\in E(G)}H(i,j) \equiv J\sum_{\{i,j\}} [A(G)]_{i,j} H(i,j)
\label{eq:IsingHamiltonian}
\end{equation}
where, for each edge
$\{i,j\}$, $H(i,j):=\bigotimes_{k=1}^{n}H(k)$ is a $2^{n}\times2^{n}$ matrix,
with $H(k)=\sigma_{z}$ if $k=i,j$ and $H(k)=I$, otherwise. $A(G)$ is the \emph{adjacency matrix}
with $[A(G)]_{i,j}=1$ if $\{i,j\}\in E(G)$ and $[A(G)]_{i,j}=0$, otherwise. $\sigma_{z}$
is the Pauli matrix in the $z$-th coordinate axis, $I$ is the identity matrix,
and $J$ is the strength of interaction. From now on, whenever the interaction strength is not expressly indicated as, \emph{e.g.}, in $H(G)$, we implicitly
set $J=1$ for all edges. The \emph{partition function} of the Ising model on
$G$ is
\begin{equation}
Z(G,v)=\mathrm{Tr}(e^{-\beta H(G)}), \label{par}%
\end{equation}
where $\beta:=(k_{B}T)^{-1}$ and $v=e^{\beta J}-1$; $k_{B}$ is Boltzmann's
constant, $T\in\mathbb{R}^{\geq0}$ is the temperature. By the
Fortuin-Kasteleyn~\cite{Fortuin72} combinatorial identity, $Z(G,v)$ is an
evaluation of the \emph{Tutte polynomial}~\cite{Tutte54a,Tutte54b}, %
which is a fundamental invariant that determines many parameters
including girth, chromatic number, \emph{etc}. Remarkably, the Jones
polynomial of a knot is contained in the Tutte polynomial~\cite{Welsch93}.
Recall that, formally, $G$ and $G^{\prime}$ are \emph{isomorphic} if they are
the same graph up to a relabeling of the vertices. This is denoted by $G\cong
G^{\prime}$. It is not hard to find graphs with the same Tutte polynomial (T-equivalent) that are not isomorphic~\cite{Mier04a,Mier04b}:\ for example, all trees on the same number of vertices.
Observe that two graphs $G$ and $G^{\prime}$ have the same partition function if and only if they share the same spectrum of the Hamiltonian in Eq.~(\ref{eq:IsingHamiltonian}) (\emph{i.e.} $Z(G,v)=Z(G^{\prime},v) \Leftrightarrow S_{H(G)}=S_{H(G^{\prime
})}$). We say that $G$ and $G^{\prime}$
are \emph{co-Ising} if $S_{H(G)}=S_{H(G^{\prime})}$. Since the Tutte polynomial is a generalization of the partition function, if two graphs
are T-equivalent then they share the same energy spectrum and thus are co-Ising. Thus, we know the following:%
\begin{eqnarray}
G\cong G^{\prime}\Rightarrow S_{H(G)}=S_{H(G^{\prime})} \nonumber \\
S_{H(G)}=S_{H(G^{\prime})}\nRightarrow G\cong G^{\prime}.
\end{eqnarray}
Intuitively, we may attempt a refinement by adding a longitudinal field. The
Hamiltonian of the \emph{Ising model on }$G$ \emph{with longitudinal field} is
defined by the diagonal matrix
\begin{equation}
H_{L}(G,J,h):=H(G,J)+hM,
\end{equation}
where $M:=\sum_{i=1}^{n}K(i)$ is a $2^{n}\times2^{n}$ matrix, with $K(i)=\bigotimes
_{k=1}^{n}H_{L}(k)$, $H_{L}(k)=\sigma_{z}$ if $k=i$ and $H_{L}(k)=I$
otherwise. Physically $h M$ can be interpreted as a constant external magnetic field applied to all
vertices. Again, we set $J=1$ and $h=1$ unless they are explicitly indicated.
We say that two graphs $G$ and $G^{\prime}$ are \emph{longitudinal field
co-Ising} if $S_{H_{L}(G,J,h)}=S_{H_{L}(G^{\prime},J,h)}$ for all values of
$J$ and $h$. The following equation summarizes what we know about graphs with
this property (see Supplementary Information Section A and B for examples):%
\begin{align}
\stackrel{\forall J,h} {S_{H_{L}(G,J,h)} \; =\; S_{H_{L}(G^{\prime},J,h)}} &\Rightarrow \stackrel{\forall J} {S_{H(G,J)}%
=S_{H(G^{\prime},J)}\nonumber }\\
S_{H_{L}(G)} =S_{H_{L}(G^{\prime})}&\nLeftrightarrow S_{H(G)}%
=S_{H(G^{\prime})}\label{exam} \nonumber \\
{\forall J,h} \;{S_{H_{L}(G,J,h)} = S_{H_{L}(G^{\prime},J,h)}} &\nRightarrow G\cong G^{\prime}.
\end{align}
From the diagonal matrices $H(G)$ and $M$, we can define the \emph{energy} and
\emph{magnetization} vectors as $\mathbf{e}_{\sigma}(G)=H(G)_{\sigma,\sigma}$
and $\mathbf{m}_{\sigma}=M_{\sigma,\sigma}$, where $\sigma=0,2,...,2^{n}-1$
runs over the classical states of the Ising model on $G$, where $0$ denotes
the ground state. With the use of these vectors, the \emph{bivariate Ising
polynomial} is defined as~\cite{Andren09}:
\begin{equation}
Z(G;x,y)=\sum_{\sigma}x^{\mathbf{e}_{\sigma}(G)}y^{\mathbf{m}_{\sigma}}.
\label{bi}%
\end{equation}
Notice that the spectrum $S_{H_{L}(G,J,h)}$ can be obtained from
$Z(G;x,y)$ for all values of the constants $J$ and $h$, since a change
in these parameters is just a rescaling of the coefficients $x$ and
$y$. The Ising polynomial generalizes the partition function in
Eq.~\eqref{par} because $Z(G,e^{-J\beta},1)=Z(G,e^{J\beta}-1)\,$,
encodes the matching polynomial, is related to the van der Waerden
polynomial, and is contained in a more general polynomial introduced
by Goldberg, Jerrum and Paterson~\cite{Jerrum03a,Jerrum03b,Jerrum03c}. The bivariate Ising
polynomial in Eq.~\eqref{bi} can be intuitively generalized by working
with \emph{any} physical observable in addition to energy and
magnetization. If we denote by $\mathbf{o}_{\sigma}^{k}$ the
eigenvalues of a diagonal matrix (or observable) $\Lambda^{k}$, we can
then define a multivariate polynomial
\begin{equation}
Z(G;x,y,z_{k})=\sum_{\sigma}x^{\mathbf{e}_{\sigma}(G)}y^{\mathbf{m}_{\sigma}}%
{\displaystyle\prod\limits_{k}}
z_{k}^{\mathbf{o}_{\sigma}^{k}}. \label{mu}%
\end{equation}
An example is given by the (permutationally invariant) spin-glass order
parameter used by Hen and Young~\cite{Hen12}.
\\
{\bf Quantum Cospectrality.} The invariants that we have so far considered belong to Classical
Physics. We can now move into a quantum mechanical regime by adding a
further field. The Hamiltonian of the \emph{quantum Ising model} on
$G$, as proposed by Lieb, Schultz, and Mattis~\cite{Lieb61} (see also~\cite{Sachdev99}) is defined by the matrix%
\begin{equation}
H_{T}(G,J,h,\Delta):=H_{L}(G,J,h)+\Delta M_{T},
\end{equation}
where $\Delta\in\mathbb{R}$ is a transverse external magnetic field; here
$M_{T}:=\sum_{i=1}^{n}T(i)$ is a $2^{n}\times2^{n}$ matrix, with
$T(i)=\bigotimes_{k=1}^{n}H_{T}(k)$, $H_{T}(k)=\sigma_{x}$ if $k=i$ and
$H_{T}(k)=I$ otherwise. As in the longitudinal case, $M_{T}$ does not depend
on $G$. Two graphs $G$ and $G^{\prime}$ are said to be \emph{quantum
co-Ising} if $S_{H_{T}(G,J,h,\Delta)}=S_{H_{T}(G^{\prime},J,h,\Delta)}$ for
all values of $J$, $h$ and $\Delta$. It follows from the definition that two graphs are quantum co-Ising if they are isomorphic. The quantum partition function is defined
analogously to the classical one:
\begin{equation}
Z_{T}(G,\beta,J,h,\Delta)=\mathrm{Tr}(e^{-\beta H_{T}(G,J,h,\Delta)}).
\end{equation}
Two graphs are quantum co-Ising if and only if they have the same quantum
partition function. The \textquotedblleft if\textquotedblright\ part of
this statement comes directly from the definition. For the \textquotedblleft
only if\textquotedblright\ part, observe that in the limit $\beta
\rightarrow\infty$, $Z_{T}(G)\simeq\nu_{0}e^{-\beta E_{0}}$
determines the lowest eigenvalue $E_{0}$ with its multiplicity $\nu_{0}$.
Similarly, in the same limit $Z_{T}(G)e^{\beta E_{0}}/\nu_0$ determines the value and multiplicity of
the second smallest eigenvalue. The whole spectrum is obtained iteratively. The statement above and its proof are valid only for systems of finite size. It is a well-known fact that different Hamiltonians can have the same partition function in the thermodynamic limit.
We tested numerically the converse of this fact by computing the smallest
eigenvalue for $h=J=\Delta=1$. We tested all graphs with $n\leq9$, all bipartite graphs with $n\leq11$, all vertex
transitive graphs with $n\leq15$, all regular graphs with $n\leq11$, and all
trees with $n\leq14$ (also considered in~\cite{Andren09}). We failed to find a
counterexample. Hence,%
\begin{eqnarray}
G \cong G^{\prime}\Rightarrow S_{H_{T}(G)}=S_{H_{T}(G^{\prime})} \nonumber \\
S_{H_{T}(G)} =S_{H_{T}(G^{\prime})}\overset{?}{\Rightarrow}G\cong
G^{\prime}.
\end{eqnarray}
The transverse field Ising Hamiltonian is a sum of non-commuting terms and
determining its full spectrum requires the diagonalization of a $2^{n}%
\times2^{n}$ matrix. We cannot generalize directly the quantum partition
function to a generating Ising polynomial as done in the classical case --
when eigenvalues are integers (for $J=h=1$) -- although we can
use the well-known Suzuki-Trotter formalism to obtain a classical
approximation~\cite{Dutta}; the direct calculation of the eigenvalues is
notoriously expensive, due to the size of the problem, and prone to errors,
making it difficult to numerically show the existence of non-isomorphic
quantum co-Ising graphs. A reasonable first approximation for this task is to
compute the absolute largest eigenvalue. That is what we have done in our
tests. Taking into account such difficulties, finding non-isomorphic quantum
co-Ising graphs is an open problem. Natural candidates are graphs for which
isomorphism testing is known to be harder to solve (\emph{e.g.}, graphs for
which the Weisfeiler-Lehman algorithm fails)~\cite{Arvind05}. Nevertheless, we
emphasize that spectral information provided by Quantum Mechanics is more
accurate than Classical Mechanics. It must be said that there are only a few
precise (and in fact negative)\ statements about the physically inspired graph
invariants which have been introduced recently (see~\cite{Audenaert07a,Audenaert07b,Audenaert07c, Hen12}
and the references therein) and that purely numerical analysis does not
guarantee sufficient generality.
\\
\begin{figure}
\centering
\includegraphics[width=0.95\columnwidth]{Figure1Rev}
\caption{The statistical distribution of measurement outcomes $N_{occ}$ on the pairs $\{G_{13}%
, G_{13}^{\prime}\}$ obtained by averaging over $100$ cycles for each of the $100$ different embeddings considered ($10000$ programming cycles in total). The horizontal red line
corresponds to the median of the data while the edges of the blue boxes correspond to the
$1$st and $3$rd quartile. Each red cross is an outlier measurement. The outcomes have been filtered after choosing the pair of classical observables \{$\mathbf{e}_{0}$, $\mathbf{m}_{0}$\}. Data showed in the left panels correspond to the choice $J=h=1/7$. In the right panels $J=h=1$, that is the maximum strength of the couplings allowed by the hardware. With the given choice of classical observables, the distribution of measurement outcomes is not able to distinguish the two graphs, nor at the classical, neither at the quantum level.}%
\label{data13a}%
\end{figure}
\begin{figure*}
\centering
\includegraphics[width=0.95\columnwidth]{Figure2Rev}
\caption{The statistical distribution of measurement outcomes $N_{occ}$ on the pairs $\{G_{13}%
, G_{13}^{\prime}\}$. The outcomes have been now filtered after choosing a triplet of classical observables
\{$\mathbf{e}_{0}$, $\mathbf{m}_{0}$, $\Omega^{2}$\}. Data showed in the left panels correspond to the choice $J=h=1/7$. In the right panels $J=h=1$. Using a third observable distinguishes the two graphs at the classical level.}%
\label{data13b}%
\end{figure*}
\begin{figure*}
\centering
\includegraphics[width=0.95\columnwidth]{Figure3Rev}
\caption{The statistical distribution of measurement outcomes $N_{occ}$ for the pairs
$\{G_{27},G_{27}^{\prime}\}$. $J=h=1/7$ in the left panels. $J=h=1$ in the right panels. Filtering the outcomes after choosing the triplet
\{$\mathbf{e}_{0}$, $\mathbf{m}_{0}$, $\Omega^{2}$\} does not distinguishes the graphs at the classical level, and the introduction of additional observables is needed. The shape of the two distributions is also the same, meaning that the two graphs are not distinguished at the quantum level either.}%
\label{data27}%
\end{figure*}
{\bf Experiments.} Disregarding computational complexity aspects,
we have highlighted that from the theoretical point of view one can
hear the shape of certain quantum Ising models, while it is not
possible for the classical analogue. We subsequently encode on the
same physical system pairs of non-isomorphic graphs that are
co-spectral, longitudinal field co-Ising (and consequently co-Ising),
but not quantum co-Ising. Rather remarkably, our set up finds an experimental
implementation in the optimization technique called \emph{quantum
annealing}~\cite{Finnila,Kadowaki,Brooke99,Santoro92}. In this
technique, the system evolves adiabatically according to the following time-dependent Hamiltonian%
\begin{equation}
H_{QA}(G,J,h,\Delta,s)=sH_{L}(G,J,h)+(1-s)\Delta M_{T}, \label{qa}%
\end{equation}
where $s=t/T_{tot}$; $t$ is a time parameter and $T_{tot}$ is the total
duration of the dynamics. At the beginning of the computation, the system is prepared in the ground state of the initial
simple Hamiltonian $H_{QA}(G,J,h,\Delta,0)=\Delta M_{T}$. On the basis of the adiabatic theorem~\cite{Farhi00}, adiabatic quantum
annealing with general Hamiltonians has been shown to be a universal model of
computation by Aharonov \emph{et al.}~\cite{Aharonov07}. In synthesis, the
core idea is to evolve the system slowly enough towards a final ground state,
which is the solution of a computational task. While the success of this
paradigm depends on the ability of avoiding level crossings with \emph{ad hoc}
annealing schedules, Brooke \emph{et al.}~\cite{Brooke99} experimentally
observed that tunneling can hasten convergence to the solution.
In the setting specified by Eq.~\eqref{qa}, we are interested in measuring the
observables $\mathbf{e}_{0}$, $\mathbf{m}_{0}$, and $\mathbf{o}_{0}^{k}$. In a
realistic situation, temperature and environment will usually excite the
system. While these effects are disruptive in the standard applications of
quantum annealing, we regard such a non-ideal implementation as a way to
generate the statistics of low energy states on which we measure the
corresponding observables. For this purpose, we run experiments on a D-Wave
Vesuvius\ programmable annealer. The hardware consists of $503$ usable logical
bits\ on an integrated circuit with superconducting flux qubits (see~\cite{Johnson10}
for details on the technology). Quantum effects on the chip are currently
under investigation and there is evidence of quantum annealing on random spin
glass problems~\cite{Boixo12a,Boixo12b,SSSVa,SSSVb,Vinci}. The Hamiltonians that can be realized with the
device are exactly of the type in Eq.~\eqref{qa}, where $s$ is a non-linear
function of time. The most general form of the final Hamiltonian $H_{L}$ is given by
an Ising model whose possible spin interactions are constrained by the chip
architecture. A particular limitation of the hardware is that measurements can
be performed only at the end of the evolution. Thus, the maximal information
that we can extract is encoded in the multivariate polynomials of Eq.~\eqref{mu}. On the other hand, the final state of the chip is a result of a
dynamics also governed by the transversal field $M_{T}$. In fact, our experiments attempt to identify the effects of $M_{T}$ in the final statistics after the measurement outcomes are filtered out using various type of multivariate polynomials.
We have tested the annealer on two pairs of non-isomorphic graphs $G$ and
$G^{\prime}$ ($G_{13}$ and $G_{13}^{\prime}$, $G_{27}$ and $G_{27'}^{\prime}$, in Supplementary Information Section B and C) such that $S_{A(G)}%
=S_{A(G^{\prime})}$, $S_{H_{L}(G,J,h)}=S_{H_{L}(G^{\prime},J,h)}$, and
$S_{H_{T}(G)}\neq S_{H_{T}(G^{\prime})}$, \emph{i.e.}, with equal spectra of the adjacency matrix, equal classical
spectra, even with a longitudinal field, and different quantum spectra. To illustrate a possible (arbitrary)\ refinement as introduced
by Eq.~\eqref{mu}, we include an extra observable, $\Omega^{2}$, corresponding to
the next-nearest neighbor interaction energy:\ $\Omega^{k}=\sum
_{i,j}H(i,j)[A^{k}(G)]_{i,j}$. Notice that $H(G)=\Omega^{1}/2$. Figure~\ref{data13a} shows the statistics of measurement outcomes when the states are distinguished through the doublet of observables
\{energy, magnetization\} on the pairs $\{G_{13}, G_{13}^{\prime}\}$, for $J=h=1/7$ and $J=h=1$. These are respectively the smallest and the largest values that can be reliably set on the hardware. The final states are organized according to the values of the two observables. As a consequence of the fact that the two graphs are co-Ising, the measured values of the pairs \{energy, magnetization\} are the same, and cannot be used to distinguish the two graphs. Moreover, the shape of the two distributions is also the same up to statistical errors. The shape of this distribution is assumed to be a
consequence of (noisy) open system quantum
dynamics~\cite{Boixo12a,Boixo12b} (see Supplementary Information Section D for a comparison between experimental and thermal statistics). This means that we are not able to identify differences in the final distributions that may arise due to the different quantum spectra, \emph{i.e.} due to non-equivalent quantum evolution along the annealing schedule.
The graphs are indistinguishable by
measuring energy and magnetization only. However, they become
distinguishable in Figure~\ref{data13b} by measuring the triplet \{energy, magnetization,
$\Omega^{2}$\}, as clearly visible in the statistics obtained
with the chip. The pair $\{G_{27}, G_{27}^{\prime}\}$ is not
distinguished by the triplet on the experimental data, as showed in Figure~\ref{data27}. It should be possible, in principle, to classically distinguish these graphs with the introduction of additional observables. Similarly to what happens for the $G_{13}$ pair, there are no noticeable differences in the shape of the final distributions that can detect differences in the quantum spectra.
\section{Conclusions}
The interplay between combinatorics and the
classical Ising model is well-established. We have introduced a
general family of physically meaningful graph polynomials suggesting a
hierarchy of graph invariants. We have demonstrated that the quantum
Ising model is a finer sieve to distinguish graphs than its classical
analogue by considering the quantum partition function as a graph
invariant. We have tested experimentally its distinguishability power
on a D-Wave programmable annealer, by taking graphs with different
quantum spectra and the same classical Ising partition function. We
used the hardware unconventionally to generate the statistics of low
energy eigenvalues rather than focusing on the ground state. The data
obtained can distinguish one pair of graphs when measuring with
respect to a classical refinement of the partition function. We did not find any measurable difference in the
statistics of measurement outcomes of the two pairs that can be related to non-equivalent quantum dynamics. Notice that
the transverse field spectra are very similar (Fig.~9 in the
Supplementary Material). Of course, differences expected in an ideal quantum
system are possibly lost due to decoherence when approaching the
classical regime at the end of the adiabatic evolution.
Going beyond the scope of this work, it would be
interesting to compare the experimental data with numerical
simulations of the corresponding open quantum spin system at finite
temperature~\cite{Albash12}. We propose two approaches to amplify the
differences in the quantum spectra: (a) reduce substantially the
annealing time; (b) perform measurements when the transverse field is
on. Both approaches require a modification of the current control of
the hardware. Another interesting goal is to define other efficient
observables, such as $\Omega^2$, that would amplify the possible
differences in the measurement statistics. From the theoretical point
of view a natural open question is whether the transverse field alone
is sufficient to define a complete spectral graph invariant.
\section{Methods}
{\bf Experimental data collection.} In order to
collect enough statistics for averaging over biases and systematic errors, we
have considered $100$ embeddings in the chip for each graph. To average over
precision errors when setting the intended couplings on the machine, we have
run $100$ programming cycles for each embedding. For each cycle, we have performed $1000$
measurements. All the experiments have been performed choosing the shortest annealing time allowed by the hardware ($T_{tot} = 20\mu s$) in order to minimize the effects of thermal excitations.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 1,683 |
Absent Biden Looms Over Iowa Kickoff Event as Opponents Take Aim
Tyler Pager &
Misyrlena Egkolfopoulou
1:30 PM IST, 10 Jun 2019 10:27 PM IST, 10 Jun 2019 1:30 PM IST, 10 Jun 2019 10:27 PM IST, 10 Jun 2019
(Bloomberg) -- The Democrats' 2020 dilemma was on display at the first major event of the Iowa calendar, as the man who wasn't there, Joe Biden, was once again the subject of veiled attacks by a pack of challengers who have so far been unable to dislodge him as the front-runner.
Senator Bernie Sanders, Biden's closest competitor, took the most pointed swipe at the former vice president, but each of the 19 candidates gathered Sunday night for the Iowa Democratic Hall of Fame dinner tried to show they were the one to lead the party against President Donald Trump.
"There are some well-intentioned Democrats and candidates who believe that the best way forward is a 'middle ground' strategy that antagonizes no one, that stands up to nobody and that changes nothing," Sanders said without naming Biden. "It is a failed political strategy that I fear could end up with the re-election of Donald Trump."
Biden missed the dinner to attend his granddaughter's graduation, but he'll be in Iowa for campaign stops on Tuesday and Wednesday. He also skipped last weekend's California Democratic Convention, where 14 candidates spoke. He'll join up with the crowd for the first time at a weekend of events in South Carolina in two weeks. At the end of the month, the first debate among the Democratic candidates will be held in Miami.
Poll Lead
Biden's strategy of staying away from the pack has worked so far to keep him in the lead in national and most state polls. A Des Moines Register/CNN/Mediacom poll released Saturday showed him still leading in the state, but other candidates, primarily Senator Elizabeth Warren and South Bend, Indiana, Mayor Pete Buttigieg are rising.
Buttigieg, 37, made implicit criticism of Biden, 76, part of his message of generational change.
"We're not going to win by playing it safe or promising a return to normal," he said. "We are where we are because normal broke. We Democrats can no more promise to return to the '90s than Republicans can deliver on their promise to return to the '50s."
Ro Foege, a former state legislator who attended the dinner, said he agreed with the sentiment that Biden should cede way to younger leaders.
"I think we needed younger ideas and newer people to be in office," Foege, 80, said. "Of course, if he ended up as our candidate, I would fully support him. I like Joe Biden a lot as a person. I don't have anything against him. But, I can say this as an old guy, it's time for us to move on to younger people in leadership."
Internet Entrepreneur
The only candidate to mention Biden by name was Andrew Yang, an entrepreneur who has found pockets of support in online forums. Yang began his speech, by saying, "Joe Biden must really not like to travel."
The gathering of the other candidates in Iowa followed a rough week for the former vice president that began with accusations of plagiarism aimed at his climate change proposal and ended with him flip-flopping on the Hyde Amendment restricting federal funding of abortion. For decades, Biden supported the measure, which is regularly added to federal funding bills, but he reversed his position on Thursday after intense pressure from the Democratic base and allies.
Troy Price, the chair of Iowa's Democratic Party, said Biden still has the benefits of his long history in the party and high name recognition from his two terms as Barack Obama's vice president.
"You know, stuff happens, people aren't able to come," Price said after the Hall of Fame event. "We totally get it. He called today to express how he wished he could be here."
The rest of the candidates mostly stuck to their stump speeches. Senator Kamala Harris of California leaned in her background as a prosecutor, outlining the "case" she would prosecute against President Donald Trump.
Washington Governor Jay Inslee called for a full-scale effort to defeat climate change.
Warren, who has separated herself from the field with a litany of detailed policy proposals, called for instituting a wealth tax on the country's wealthiest individuals to pay for programs like canceling student debt and universal child care.
Beyond the brief speeches at the Hall of Fame dinner — or as Representative Tim Ryan of Ohio joked, "It's been a pleasure speed-dating with you" — campaigns looked to demonstrate their organizational skills, making it abundantly clear that a changed primary map hasn't diminished Iowa's role as a critical clearinghouse for presidential nominees.
The candidates have fanned out across the country to campaign, seeking viral moments as part of their effort to build name recognition and support among the party's diverse base. California's earlier primary date has also forced candidates to devote more attention there. But, this weekend showed candidates still believe Iowa, where the first nominating contest is held next February, can't be overlooked.
"Iowa is a state where organizing matters," Price said. "You can't just put it all on TV or all in mail or all in digital ads. You have to come on the ground and you have to do the work to reach out to voters, connecting with voters and talk about your policy."
Senator Amy Klobuchar of Minnesota had supporters on top of pickup trucks, shaking tambourines, ringing cow bells and holding signs while cheering for "Amy!" Immediately across the street, amid a plethora of "Amy for America" signs that had been planted earlier, Harris organizers were chanting "Ka-ma-la" through megaphones and blasting soundtracks like "Respect" by Aretha Franklin.
'Warren Warriors'
Warren's supporters had taken on two sides of the street, and with signs that read "Warren Warriors," were chanting 'I'm a Warren Democrat!" Next to them, Beto O'Rourke's campaign parked a taco truck as organizers stood holding "Beto for America" signs.
Just a few feet away, organizers for Senator Kirsten Gillibrand, former Representative John Delaney and Senator Cory Booker had set up shop back-to-back, holding up signs and in some instances, cut-out letters of their candidates' names. A few Delaney organizers paraded around with bag pipes.
A few blocks away from the hotel, Buttigieg spoke to his supporters at a picnic organized by his campaign, which featured a live band, food trucks and outdoor games. A large crowd of supporters cheered on Buttigieg as he tested his skills at a game and as he joined the band on stage to play a Miles Davis song on the keyboard.
Meanwhile, Sanders joined workers at a McDonald's before leading them on a march to the hotel where the dinner was held. Sanders arrived at the hotel with protesters demanding a $15 minimum wage. Just before entering the hotel, Sanders came face-to-face with Harris supporters who chanted, "It's time for a woman in the White House!"
Follow All The Political News In India On BloombergQuint | {
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1 & 2 TIMOTHY
MACARTHUR BIBLE STUDIES
© 2007 John F. MacArthur, Jr.
All rights reserved. No portion of this book may be reproduced, stored in a retrieval system, or transmitted in any form or by any means—electronic, mechanical, photocopy, recording, or any other—except for brief quotations in printed reviews, without the prior permission of the publisher.
Published in Nashville, Tennessee, by Nelson Books, an imprint of Thomas Nelson. Nelson Books and Thomas Nelson are registered trademarks of HarperCollins Christian Publishing, Inc.
Nelson Books titles may be purchased in bulk for education, business, fundraising, or sales promotional use. For information, please email SpecialMarkets@ThomasNelson.com.
Published in association with the literary agency of Wolgemuth & Associates, Inc.
Produced with the assistance of the Livingstone Corporation. Project staff include Jake Barton, Betsy Todt Schmitt, and Andy Culbertson. Project editors: Mary Horner Collins, Amber Rae, and Len Woods.
Scripture quotations marked NKJV are taken from the The New King James Version®. Copyright © 1982 by Thomas Nelson, Inc. Used by permission. All rights reserved.
"Unleashing God's Truth, One Verse at a Time" is a trademark of Grace to You. All rights reserved.
"Keys to the Text" material taken from the following sources:
_1 Corinthians._ MacArthur New Testament Commentary Series. Copyright © 1984, 1996 by John MacArthur. Published by Moody Press, Chicago, Illinois. Used by permission.
_The MacArthur Study Bible_ (electronic ed.). John MacArthur, General Editor. Copyright © 1997 by Word Publishing. All rights reserved. Used by permission.
_Nelson's New Illustrated Bible Dictionary, Rev. ed._ R. F. Youngblood, F. F. Bruce, R. K. Harrison, editors. Copyright © 1995 by Thomas Nelson Publishers. Used by permission.
_Our Sufficiency in Christ_ (electronic ed.) Copyright © 1997 by John F. MacArthur. Published by Word Publishing: Dallas, Texas. Use by permission.
Cover Art by Holly Sharp Design
Interior Design and Composition by Joel Bartlett, Livingstone Corporation
ISBN-13: 978-0-7180-3514-3
ISBN-13: 978-0-7180-3533-4 (eBook)
EBOOK INSTRUCTIONS
In this ebook edition, please use your device's note-taking function to record your thoughts wherever you see the bracketed instructions [Your Notes] or [Your Response Here]. Use your device's highlighting function to record your response whenever you are asked to checkmark, circle, underline, or otherwise indicate your answer(s).
CONTENTS
_Ebook Instructions_
_Introduction to 1 Timothy_
1 Beware of False Doctrine!
_1 Timothy 1:1–20_
2 The Importance of Prayer
_1 Timothy 2:1–8_
3 The Role of Women
_1 Timothy 2:9–15_
4 Qualifications for Leadership
_1 Timothy 3:1–16_
5 False Teaching versus Truth
_1 Timothy 4:1–16_
6 Pastoral Responsibilities
_1 Timothy 5:1–6:2_
7 The Man of God
_1 Timothy 6:3–21_
_Introduction to 2 Timothy_
8 Not Ashamed
_2 Timothy 1:1–18_
9 Be Diligent
_2 Timothy 2:1–26_
10 Equipped for Good Works
_2 Timothy 3:1–17_
11 Preaching with Integrity
_2 Timothy 4:1–5_
12 Last Words
_2 Timothy 4:6–22_
INTRODUCTION TO 1 TIMOTHY
This is the first of two inspired letters Paul wrote to his beloved son in the faith. Timothy received his name, which means "one who honors God," from his mother (Eunice) and grandmother (Lois), devout Jews who became believers in the Lord Jesus Christ (2 Tim. 1:5). They taught Timothy the Old Testament Scriptures from his childhood (2 Tim. 3:15). His father was a Greek (Acts 16:1) who may have died before Timothy met Paul.
Timothy was from Lystra (Acts 16:1–3), a city in the Roman province of Galatia (part of modern Turkey). Paul led Timothy to Christ (1:2, 18; 1 Cor. 4:17; 2 Tim. 1:2), undoubtedly during his ministry in Lystra on his first missionary journey (Acts 14:6–23). When he revisited Lystra on his second missionary journey, Paul chose Timothy to accompany him (Acts 16:1–3). Although Timothy was very young (probably in his late teens or early twenties, since about fifteen years later Paul referred to him as a young man, 4:12), he had a reputation for godliness (Acts 16:2). Timothy was to be Paul's disciple, friend, and co-laborer for the rest of the apostle's life, ministering with him in Berea (Acts 17:14), Athens (Acts 17:15), and Corinth (Acts 18:5; 2 Cor. 1:19), and accompanying him on his trip to Jerusalem (Acts 20:4). He was with Paul in his first Roman imprisonment and went to Philippi (2:19–23) after Paul's release. In addition, Paul frequently mentions Timothy in his epistles (Rom. 16:21; 2 Cor. 1:1; Phil. 1:1; Col. 1:1; 1 Thess. 1:1; 2 Thess. 1:1; Philem. 1). Paul often sent Timothy to churches as his representative (1 Cor. 4:17; 16:10; Phil. 2:19; 1 Thess. 3:2), and 1 Timothy finds him on another assignment, serving as pastor of the church at Ephesus (1:3). According to Hebrews 13:23, Timothy was imprisoned somewhere and released.
AUTHOR AND DATE
Many modernist critics delight in attacking the plain statements of Scripture and, for no good reason, deny that Paul wrote the Pastoral Epistles (1, 2 Tim., Titus). Ignoring the testimony of the letters themselves (1:1; 2 Tim. 1:1; Titus 1:1) and that of the early church (which is as strong for the Pastoral Epistles as for any of Paul's epistles, except Romans and 1 Corinthians), these critics maintain that a devout follower of Paul wrote the Pastoral Epistles in the second century. As proof, they offer five lines of supposed evidence: (1) the historical references in the Pastoral Epistles cannot be harmonized with the chronology of Paul's life given in Acts; (2) the false teaching described in the Pastoral Epistles is the fully developed Gnosticism of the second century; (3) the church organizational structure in the Pastoral Epistles is that of the second century and is too well developed for Paul's day; (4) the Pastoral Epistles do not contain the great themes of Paul's theology; and (5) the Greek vocabulary of the Pastoral Epistles contains many words not found in Paul's other letters, nor in the rest of the New Testament.
While it is unnecessary to dignify such unwarranted attacks by unbelievers with an answer, occasionally such an answer does enlighten. Thus, in reply to the critics' arguments, the following points are given: (1) This contention of historical incompatibility is valid only if Paul was never released from his Roman imprisonment mentioned in Acts. But he was released, since Acts does not record Paul's execution, and Paul himself expected to be released (Phil. 1:19, 25–26; 2:24; Philem. 22). The historical events in the Pastoral Epistles do not fit into the chronology of Acts because they happened after the close of the Acts narrative, which ends with Paul's first imprisonment in Rome. (2) While there are similarities between the heresy of the Pastoral Epistles and second-century Gnosticism, there are also important differences. Unlike second-century Gnosticism, the false teachers of the Pastoral Epistles were still within the church (see 1:3–7), and their teaching was based on Judaistic legalism (1:7; Titus 1:10, 14; 3:9). (3) The church organizational structure mentioned in the Pastoral Epistles is, in fact, consistent with that established by Paul (Acts 14:23; Phil. 1:1). (4) The Pastoral Epistles do mention the central themes of Paul's theology, including the inspiration of Scripture (2 Tim. 3:15–17); election (2 Tim. 1:9; Titus 1:1–2); salvation (Titus 3:5–7); the deity of Christ (Titus 2:13); His mediatory work (1 Tim. 2:5); and substitutionary atonement (2:6). (5) The different subject matter in the Pastoral Epistles required a different vocabulary from that in Paul's other epistles. Certainly a pastor today would use a different vocabulary in a personal letter to a fellow pastor than he would in a work of systematic theology.
The idea that a "pious forger" wrote the Pastoral Epistles faces several further difficulties: (1) The early church did not approve of such practices and surely would have exposed this as a ruse, if there had actually been one (see 2 Thess. 2:1–2; 3:17). (2) Why forge three letters that include similar material and no deviant doctrine? (3) If a counterfeit, why not invent an itinerary for Paul that would have harmonized with Acts? (4) Would a later, devoted follower of Paul have put the words of 1 Timothy 1:13, 15 into his master's mouth? (5) Why would he include warnings against deceivers (2 Tim. 3:13; Titus 1:10), if he himself were one?
The evidence seems clear that Paul wrote 1 Timothy and Titus shortly after his release from his first Roman imprisonment (about AD 62–64), and then wrote 2 Timothy from prison during his second Roman imprisonment (about AD 66–67), shortly before his death.
BACKGROUND AND SETTING
After being released from his first Roman imprisonment (see Acts 28:30), Paul revisited several of the cities in which he had ministered, including Ephesus. Leaving Timothy behind there to deal with problems that had arisen in the Ephesian church, such as false doctrine (1:3–7; 4:1–3; 6:3–5), disorder in worship (2:1–15), the need for qualified leaders (3:1–14), and materialism (6:6–19), Paul went on to Macedonia, from where he wrote Timothy this letter to help him carry out his task in the church (see 3:14–15).
HISTORICAL AND THEOLOGICAL THEMES
First Timothy is a practical letter containing pastoral instruction from Paul to Timothy (see 3:14–15). Since Timothy was well versed in Paul's theology, the apostle had no need to give him extensive doctrinal instruction. This epistle does, however, express many important theological truths, such as the proper function of the law (1:5–11), salvation (1:14–16; 2:4–6); the attributes of God (1:17); the Fall (2:13–14); the person of Christ (3:16; 6:15–16); election (6:12); and the second coming of Christ (6:14–15).
INTERPRETIVE CHALLENGES
Scholars disagree over the identity of the false teachers (1:3) and the genealogies (1:4) involved in their teaching. What it means to be "delivered to Satan" (1:20) has also been a source of debate. The letter contains key passages in the debate over the extent of the atonement (2:4–6; 4:10). Paul's teaching on the role of women (2:9–15) has generated much discussion, particularly his declaration that they are not to assume leadership roles in the church (2:11–12). How women can be saved by bearing children (2:15) has also confused many. Whether the fact that an elder must be "the husband of one wife" excludes divorced or unmarried men has been disputed, as well as whether Paul refers to deacons' wives or deaconesses (3:11). Those who believe Christians can lose their salvation cite 4:1 as support for their view. There is a question about the identity of the widows in 5:3–16—are they needy women ministered to by the church, or an order of older women ministering to the church? Does "double honor" accorded to elders who rule well (5:17–18) refer to respect or money? These will all be dealt with in the notes provided by the passages.
NOTES
[Your Response Here]
**1**
BEWARE OF FALSE DOCTRINE!
_1 Timothy 1:1–20_
DRAWING NEAR
Paul had a miraculous encounter with Christ that turned his life around. He calls himself an "insolent man" who had received God's mercy and grace. What person do you know (or have heard about) who has an amazing "before-and-after" testimony of how God transformed his or her life? What about that person's story encourages you?
[Your Response Here]
Why is it important to know what you believe, and why you believe it?
[Your Response Here]
As you begin this study, ask God to show you more about His mercy and grace.
[Your Response Here]
THE CONTEXT
In two brief verses that introduce the letter, the apostle Paul demonstrates his great concern for the church at Ephesus. His passion was the result of three years of ministry there. In order to help his young protégé battle the false teaching that was infiltrating the church, Paul threw all of his apostolic authority behind the young pastor. Not only that, Paul also prayed that God would give his beloved child in the faith the grace, mercy, and peace needed to navigate a difficult situation.
Despite its rich spiritual history, the Ephesian church was targeted by false teachers just as Paul had warned (Acts 20:29–30). Paul wrote this epistle to prepare Timothy for the onslaught of these enemies of the gospel. The opening charge in 1:3–11 sets the stage for all that will follow. Paul discusses four things that are true of false teachers: their doctrinal deviations, their mission, their motives, and their legacy.
Some scholars argue that Paul's words in verses 12 through 17 are a parenthetical thought unrelated to the flow of thought in 1 Timothy. This is a weak argument, however, in light of Paul's overall purpose. Paul's intent was to warn his young associate of the dangers of the false teachers. Since they were teaching an erroneous view of the law, Paul purposed to show how a proper understanding of the law results in conviction of sin and an appreciation of grace. Here then is a contrast between the glory of the true gospel and the bankruptcy of false doctrine.
KEYS TO THE TEXT
_Ephesus:_ Timothy was in the city of Ephesus, the capital of the Roman province of Asia (Asia Minor, modern Turkey). Located at the mouth of the Cayster River, on the east side of the Aegean Sea, Ephesus was perhaps best known for its magnificent temple of Artemis, or Diana, one of the seven wonders of the ancient world. It was also an important political, educational, and commercial center, ranking with Alexandria in Egypt and Antioch of Pisidia, in southern Asia Minor. The church here may have been started by Priscilla and Aquila, a gifted couple, who had been left in Ephesus by Paul on his second missionary journey (Acts 18:18–19). Later, Paul firmly established this fledgling church on his third missionary journey (Acts 19), and he pastored it for some three years. After Paul left, Timothy pastored the congregation for perhaps a year and a half.
_The Law:_ The Mosaic law is in view here, not just law in general. Paul said that the would-be teachers wanted to impose circumcision and the keeping of Mosaic ceremonies on the church as necessary for salvation. These "Judaizers" plagued the early church, attempting to add to the gospel the legalistic requirements of the Old Testament. The law is good or useful because it reflects God's holy will and righteous standard (Ps. 19:7; Rom. 7:12) and accomplishes its purpose in showing sinners their sin and their need for a Savior (Rom. 3:19; Gal. 3:24).
UNLEASHING THE TEXT
Read 1:1–20, noting the key words and definitions next to the passage.
**1 Timothy 1:1–20 (NKJV)**
**1** _Paul, an apostle of Jesus Christ, by the commandment of God our Savior and the Lord Jesus Christ, our hope,_
**_apostle of Jesus Christ_** (v. 1)—"One who is sent with a commission." An apostle was chosen and trained by Jesus Christ to proclaim His truth during the formative years of the church. Because Paul was not among the original Twelve, he needed to defend his apostleship (see 2 Cor. 12:11–12; Acts 1:2; 2:42; Eph. 2:20).
**_God our Savior_** (v. 1)—This is a title unique to the Pastoral Epistles (1 & 2 Tim., Titus) that has its roots in the Old Testament (Ps. 25:5; 27:9; Mic. 7:7; Hab. 3:18). God is by nature a saving God and the source of our salvation.
**_Jesus Christ, our hope_** (v. 1)—Christians have hope for the future because Christ purchased salvation for them on the cross in the past (Rom. 5:1–2), sanctifies them through His Spirit in the present (Gal. 5:16–25), and will lead them to glory in the future.
**2** _To Timothy, a true son in the faith: Grace, mercy, and peace from God our Father and Jesus Christ our Lord._
**_true son in the faith_** (v. 2)—Only Timothy and Titus received this special expression of Paul's favor. The Greek word for "son" is better translated "child," which emphasizes Paul's role as spiritual father to Timothy. "True" speaks of the genuineness of Timothy's faith (see 2 Tim. 1:5). Timothy was Paul's most cherished pupil and protégé (1 Cor. 4:17).
**_Grace, mercy, and peace_** (v. 2)—This familiar greeting of Paul's appears in all his epistles (see Rom. 1:7), but with the addition here of "mercy" (see 2 Tim. 1:2). Mercy frees believers from the misery that accompanies the consequences of sin.
**3** _As I urged you when I went into Macedonia—remain in Ephesus that you may charge some that they teach no other doctrine,_
**_when I went into Macedonia—remain in Ephesus_** (v. 3)—Before Paul left Ephesus, he likely began the confrontation with the expulsion of Hymenaeus and Alexander (v. 20), then assigned Timothy to stay on and complete what he had begun.
**_charge_** (v. 3)—This refers to a military command; it demands that a subordinate obey an order from a superior (see 2 Tim. 4:1).
**_some_** (v. 3)—The false teachers were few in number yet had a wide influence. Several reasons point toward these men being elders in the church at Ephesus and in the churches in the surrounding region: (1) they presumed to be teachers (v. 7), a role reserved for elders (3:2; 5:17); (2) Paul himself had to excommunicate Hymenaeus and Alexander, which implies they occupied the highest pastoral positions; (3) Paul detailed the qualifications of an elder (3:1–7), implying that unqualified men, who needed to be replaced by qualified ones, were occupying those roles; (4) Paul stressed that sinning elders were to be publicly disciplined (5:19–22).
**_teach no other doctrine_** (v. 3)—This is a compound word made up of two Greek words that mean "of a different kind" and "to teach." The false teachers were teaching doctrine different from apostolic doctrine (see 6:3–4; Gal. 1:6–7); this had to do with the gospel of salvation. Apparently they were teaching another gospel and not the "glorious gospel of the blessed God" (v. 11).
**4** _nor give heed to fables and endless genealogies, which cause disputes rather than godly edification which is in faith._
**_fables and endless genealogies_** (v. 4)—Legends and fanciful stories manufactured from elements of Judaism (v. 7; see Titus 1:14), which probably dealt with allegorical or fictitious interpretations of Old Testament genealogical lists. In reality, they were "doctrines of demons" (4:1), posing as God's truth (see 4:7).
**5** _Now the purpose of the commandment is love from a pure heart, from a good conscience, and from sincere faith,_
**_the commandment_** (v. 5)—See verse 3, where the verb form "charge" is used (also in v. 8). The purpose of the charge in verses 3–4 is the spiritual virtue defined in verse 5. Timothy was to deliver this charge to the church. The goal of preaching the truth and warning of error is to call people to true salvation in Christ, which produces a love for God from a purified heart (2 Tim. 2:22; 1 Pet. 1:22), a cleansed conscience (Heb. 9:22; 10:14), and genuine faith (Heb. 10:22).
**_love_** (v. 5)—This is the love of choice and the will, characterized by self-denial and self-sacrifice for the benefit of others, and it is the mark of a true Christian (John 13:35; 1 John 4:7–8). In contrast, false doctrine produces only conflict and resulting "disputes" (vv. 4; 6:3–5).
**_good conscience_** (v. 5)—The Greek word for "good" refers to that which is perfect and produces pleasure and satisfaction. God created man with a "conscience" as his self-judging faculty. Because God has written His law on man's heart, man knows the basic standard of right and wrong. When he violates that standard, his conscience produces guilt, which acts as the mind's security system and produces fear, guilt, shame, and doubt as warnings of threats to the soul's well-being (see John 8:9; 1 Cor. 8:7, 10–12; Titus 1:15). On the other hand, when a believer does God's will, he enjoys the affirmation, assurance, peace, and joy of a good conscience (see Acts 23:1; 24:16; 2 Tim. 1:3; Heb. 13:18).
**6** _from which some, having strayed, have turned aside to idle talk,_
**_idle talk_** (v. 6)—This refers to speech that is aimless and has no logical end. It is essentially irrelevant and will not accomplish anything spiritual or edifying to believers. It can also be translated "fruitless discussion." False doctrine leads nowhere but to the deadening end of human speculation and demonic deception (see 6:3–5).
**7** _desiring to be teachers of the law, understanding neither what they say nor the things which they affirm._
**_desiring to be teachers_** (v. 7)—The false teachers wanted the kind of prestige enjoyed by Jewish rabbis; but they were not concerned at all about truly learning the law and teaching it to others (see 6:4; Matt. 23:5–7). Instead, they imposed on believers in Ephesus a legalistic heresy that offered salvation by works.
**8** _But we know that the law is good if one uses it lawfully,_
**9** _knowing this: that the law is not made for a righteous person, but for the lawless and insubordinate, for the ungodly and for sinners, for the unholy and profane, for murderers of fathers and murderers of mothers, for manslayers,_
**_not made for a righteous person_** (v. 9)—Those who think they are righteous will never be saved (Luke 5:32) because they do not understand the true purpose of the law. The false teachers, with their works system of personally achieved self-righteousness (in their own minds), had shown clearly that they misunderstood the law completely. It was not a means to self-righteousness, but a means to self-condemnation, sin, conviction, repentance, and pleading to God for mercy (v. 15).
**_lawless . . . profane_** (v. 9)—These first six characteristics, expressed in three couplets, delineate sins from the first half of the Ten Commandments, which deal with a person's relationship to God. "Lawless" describes those who have no commitment to any law or standard, which makes such people "insubordinate" or rebellious. Those who are "ungodly" have no regard for anything sacred, which means they are "sinners" because they disregard God's law. "Unholy" people are indifferent to what is right, which leads them to be the "profane," those who step on or trample what is sacred (see Heb. 10:29).
**_murderers of fathers . . . perjurers_** (vv. 9–10)—These sins are violations of the second half of the Ten Commandments—those dealing with relationships among people. These specific sins undoubtedly characterized the false teachers, since they are characteristic behaviors related to false doctrine (v. 10). "Murderers of fathers" and "mothers" is a violation of the Fifth Commandment (Exod. 20:12; see 21:15–17), which forbids everything from dishonor to murder. "Manslayers" (or "murderers") is in violation of the Sixth Commandment (Exod. 20:13). "Fornicators" and "sodomites" (or "homosexuals") violate the Seventh Commandment (Exod. 20:14), which prohibits sexual activity outside the marriage bed. Because the theft of children was commonplace in Paul's day, he mentions "kidnappers" in connection with the Eighth Commandment (Exod. 20:15), which prohibits stealing. Finally, "liars" and "perjurers" are violators of the Ninth Commandment (Exod. 20:16).
**10** _for fornicators, for sodomites, for kidnappers, for liars, for perjurers, and if there is any other thing that is contrary to sound doctrine,_
**_sound doctrine_** (v. 10)—This is a familiar emphasis in the Pastoral Epistles (see 2 Tim. 4:3; Titus 2:1). "Sound" refers to that which is healthy and wholesome. It is the kind of teaching that produces spiritual life and growth, which implies that false doctrine produces spiritual disease and debilitation.
**11** _according to the glorious gospel of the blessed God which was committed to my trust._
**_the glorious gospel_** (v. 11)—The gospel reveals God's glory; that is, the perfections of His person or His attributes, including His holiness (hatred of sin) and justice (demand of punishment for violations of His law) and grace (forgiveness of sin). Those particular attributes are key to any effective gospel presentation.
**_committed_** (v. 11)—This Greek word refers to committing something of value to another and can be translated "entrusted." God entrusted Paul with the communication and guardianship of His revealed truth. (see 2:7; 6:20–21; Rom. 15:15–16; 1 Cor. 4:1–2; 9:17; 2 Cor. 5:18–20; Gal. 2:7; Col. 1:25; 1 Thess. 2:4).
**12** _And I thank Christ Jesus our Lord who has enabled me, because He counted me faithful, putting me into the ministry,_
**_counted me faithful_** (v. 12)—God's sovereign purpose for Paul and for all believers works through personal faith. Until Paul was turned by the Holy Spirit from self-righteous works (see Phil. 3:4–7) to faith alone in Christ, he could not be used by God. He was in the same condition as the useless false teachers (vv. 6–7).
**13** _although I was formerly a blasphemer, a persecutor, and an insolent man; but I obtained mercy because I did it ignorantly in unbelief._
**_a blasphemer, a persecutor, and an insolent man_** (v. 13)—This verse indicates that experience of Paul when he saw himself, in the light of God's law, for who he really was (see notes on Rom. 7:7–12). A "blasphemer" speaks evil of and slanders God. Paul violated the first half of the Ten Commandments through his overt attacks against Christ (see Acts 9:4–5; 22:7–8; 26:9, 14–15). As a "persecutor" and an "insolent man," Paul violated the second half through his attacks on believers. The Greek word for "insolent man" can be translated "violent aggressor," indicating the violence Paul heaped on Christians (see v. 20).
**_because I did it ignorantly in unbelief_** (v. 13)—Paul was neither a Jewish apostate nor a Pharisee who clearly understood Jesus' teaching and still rejected Him. He was a zealous, fastidious Jew trying to earn his salvation, thus lost and damned. His plea of ignorance was not a claim to innocence nor an excuse denying his guilt. It was simply a statement indicating that he did not understand the truth of Christ's gospel and was honestly trying to protect his religion. His willing repentance when confronted by Christ (see Rom. 7:9; Phil. 3:8–9) is evidence that he had not understood the ramifications of his actions—he truly thought he was doing God a service (Acts 26:9).
**14** _And the grace of our Lord was exceedingly abundant, with faith and love which are in Christ Jesus._
**_grace_** (v. 14)—God's loving forgiveness, by which He grants salvation apart from any merit on the part of those He saves (see notes on Rom. 3:24; Gal. 1:6)
**_faith and love_** (v. 14)—attitudes frequently linked with salvation in the New Testament (see Eph. 1:15; 3:17; Col. 1:4, 23). They are gifts of God's grace in Christ.
**15** _This is a faithful saying and worthy of all acceptance, that Christ Jesus came into the world to save sinners, of whom I am chief._
**_This is a faithful saying_** (v. 15)—A phrase unique to the Pastoral Epistles (see 3:1; 4:9; 2 Tim. 2:11; Titus 3:8), which announces a statement summarizing key doctrines. The phrase "worthy of all acceptance" gives the statement added emphasis. Apparently, these sayings were well known in the churches as concise expressions of cardinal gospel truth.
**_to save sinners_** (v. 15)—This faithful saying was based on the statements of Jesus recorded in Matthew 9:13.
**_I am chief_** (v. 15)—This is literally "first," in rank. Few could be considered a worse sinner than someone who blasphemed God and persecuted His church (see 1 Cor. 15:9; Eph. 3:8). Paul's attitude toward himself dramatically changed (see Phil. 3:7–9; Rom. 7:7–12).
**16** _However, for this reason I obtained mercy, that in me first Jesus Christ might show all longsuffering, as a pattern to those who are going to believe on Him for everlasting life._
**_for this reason_** (v. 16)—Paul was saved so that God could display His gracious and merciful patience with the most wretched sinners.
**_longsuffering_** (v. 16)—refers to patience with people
**_a pattern_** (v. 16)—This refers to a model or example. Paul was living proof that God could save any sinner, no matter how bad he might be. The account of Paul's conversion has been instrumental in the salvation of many. Paul's testimony is repeated six other times in the New Testament (Acts 9, 22, 26; Gal. 1–2; Phil. 3:1–14).
**17** _Now to the King eternal, immortal, invisible, to God who alone is wise, be honor and glory forever and ever. Amen._
**18** _This charge I commit to you, son Timothy, according to the prophecies previously made concerning you, that by them you may wage the good warfare,_
**_prophecies previously made concerning you_** (v. 18)—The Greek word for "previously made" literally means "leading the way to," implying that a series of prophecies had been given about Timothy in connection with his receiving his spiritual gift. These prophecies specifically and supernaturally called Timothy into God's service.
**_wage the good warfare_** (v. 18)—Paul urged Timothy to fight the battle against the enemies of Christ and the gospel.
**19** _having faith and a good conscience, which some having rejected, concerning the faith have suffered shipwreck,_
**_faith . . . faith_** (v. 19)—The first is subjective and means continuing to believe the truth. The second is objective, referring to the content of the Christian gospel.
**_shipwreck_** (v. 19)—A good conscience serves as the rudder that steers the believer through the rocks and reefs of sin and error. The false teachers ignored their consciences and the truth, and as a result, suffered shipwreck of the Christian faith (the true doctrine of the gospel), which implies severe spiritual catastrophe. This does not imply loss of salvation of a true believer (see notes on Rom. 8:31–39) but likely indicates the tragic loss that comes to the apostate. They had been in the church, heard the gospel, and rejected it in favor of the false doctrine defined in verses 3–7. Apostasy is a turning away from the gospel, having once claimed to accept it (see notes on Heb. 2:3–4; 3:12–15; 10:26–31).
**20** _of whom are Hymenaeus and Alexander, whom I delivered to Satan that they may learn not to blaspheme._
**_Hymenaeus and Alexander_** (v. 20)—Hymenaeus is mentioned in 2 Timothy 2:17 in connection with Philetus, another false teacher. Alexander may be the opponent of the faith referred to in 2 Timothy 4:14–15. Nothing else is known about these two men.
**_I delivered to Satan_** (v. 20)—Paul put both men out of the church, thus ending their influence and removing them from the protection and insulation of God's people. They were no longer in the environment of God's blessing, but under Satan's control. In some instances God has turned believers over to Satan for positive purposes, such as revealing the genuineness of saving faith, keeping them humble and dependent on Him, enabling them to strengthen others, or offering God praise (see Job 1:1–22; Rev. 7:9–15). God hands some people over to Satan for judgment, such as King Saul (1 Sam. 16:12–16; 28:4–20), Judas (John 13:27), and the sinning member in the Corinthian church (see 1 Cor. 5:1–5).
**_may learn not to blaspheme_** (v. 20)—Paul learned not to blaspheme when confronted by the true understanding of the law and the gospel. That was what those men needed. God, the inspired text seems to indicate, would teach them and show them grace as he had Paul. But that evangelistic work could not go on at the expense of the purity of the church.
1) What specific instructions does Paul give Timothy regarding false teachers?
[Your Response Here]
_(Verses to consider: 2 Cor. 2:17; Titus 1:10–11)_
2) In what way does Paul describe what the false teachers had done (vv. 4–7, 19)?
[Your Response Here]
3) What is the "glorious gospel" (v. 11)?
[Your Response Here]
4) How does Paul's personal testimony relate to his warning against false teachers?
[Your Response Here]
_(Verses to consider: Acts 9:1–9; John 1:17; Rom. 1:5; 1 Cor. 15:9; Eph. 3:8)_
5) What does Paul mean when he urges Timothy to "wage the good warfare" (v. 18)?
[Your Response Here]
GOING DEEPER
Paul wrote fervently to Timothy because he deeply loved the church at Ephesus and had been concerned about them for some time. For what Paul said to the leaders when he left Ephesus, read Acts 20:25–31.
**25** _"And indeed, now I know that you all, among whom I have gone preaching the kingdom of God, will see my face no more._
**26** _Therefore I testify to you this day that I am innocent of the blood of all men._
**27** _For I have not shunned to declare to you the whole counsel of God._
**28** _Therefore take heed to yourselves and to all the flock, among which the Holy Spirit has made you overseers, to shepherd the church of God which He purchased with His own blood._
**29** _For I know this, that after my departure savage wolves will come in among you, not sparing the flock._
**30** _Also from among yourselves men will rise up, speaking perverse things, to draw away the disciples after themselves._
**31** _Therefore watch, and remember that for three years I did not cease to warn everyone night and day with tears._
EXPLORING THE MEANING
6) Summarize Paul's main concern when he left the leaders at Ephesus. What was his final advice?
[Your Response Here]
7) Read John 8:44. Who or what is the ultimate source of false doctrine?
[Your Response Here]
_(Verses to consider: 2 Cor. 11:13–14; 1 John 4:1)_
8) Read Titus 1:15–16. What further insights does this related passage offer regarding false teachers?
[Your Response Here]
TRUTH FOR TODAY
All believers have a responsibility to be on the alert for false teachers. What do we watch for? First, look at their understanding of Scripture, and ask if their teaching is biblically sound. Do they place extra-biblical teachings on a par with the Bible? Do they handle accurately the Word of truth (2 Tim. 2:15)?
Second, examine their goals. Do they seek to love, honor, and glorify God? Or do they pursue self-love, material wealth, or personal happiness? Does their message speak of purity of heart, a good conscience, and non-hypocritical faith?
Third, examine their motives. Are they humble and selfless? Or do they seek the preeminence?
Finally, examine the effect of their teaching. Did their followers understand clearly the gospel of Jesus Christ? Do they define the gospel properly? Do they use the law properly, as part of the gospel message, or do they promote works righteousness?
Those who pass the above checks should be welcomed as brothers in Christ, even if we differ with them at some points of interpretation or doctrine. Those who do not are to be rejected, no matter what experiences they may have had, or what else they may teach. Constant vigilance is our defense against those who would enslave all of us to a false gospel.
REFLECTING ON THE TEXT
9) Paul considered Timothy a "son" and discipled and mentored him in the faith. Who in your life could serve as a "Paul" to you? Who can you take under your wing as a "Timothy"?
[Your Response Here]
10) What specific changes do you need to make in your daily life to live with "a good conscience"?
[Your Response Here]
11) Think about your own salvation story. How can you use your experience to encourage others this week?
[Your Response Here]
PERSONAL RESPONSE
Write out additional reflections, questions you may have, or a prayer.
[Your Response Here]
ADDITIONAL NOTES
[Your Response Here]
**2**
THE IMPORTANCE OF PRAYER
_1 Timothy 2:1–8_
DRAWING NEAR
When has your prayer life been most vibrant? To what do you attribute this?
[Your Response Here]
Do you think prayer really changes things? Why?
[Your Response Here]
THE CONTEXT
The Ephesian church may have become lax in praying for the lost since Paul urged Timothy to make it a priority again. The Judaistic false teachers in Ephesus, by a perverted gospel and the teaching that salvation was only for Jews and Gentile proselytes to Judaism, would have certainly restricted evangelistic praying—interceding for the salvation of others. Their religious exclusivism (salvation only for the elite) would preclude the need for prayer for the lost.
The fact that Paul begins his discourse on church affairs with this particular topic indicates the important role that prayer is to play in the life of the church. If God's primary objective for His church involved fellowship, knowledge of the Scriptures, or conformity to the image of Christ, His plan would be best accomplished by bringing us to heaven immediately. But these are not the central functions of the church on earth. God has left us here to reach the lost. And before the church carries out this mission in the world, it must first grasp the breadth of the gospel call. This requires coming to terms with evangelistic praying. This particular passage calls for Christians to intercede for the lost in general. Furthermore, it raises the question of whether God hears such prayers, as well as what part they play in God's eternal plan.
KEYS TO THE TEXT
_Supplications and Intercessions:_ Paul mentions two types of prayers. The Greek word for "supplication" comes from a root word that means "to lack," "to be deprived," or "to be without." Thus this kind of prayer occurs because of a need. The lost have a great need for salvation, and believers should ask God to meet that need. This word "intercession" comes from a root word meaning "to fall in with someone" or "to draw near so as to speak intimately." The verb from which this word derives is used of Christ's and the Spirit's intercession for believers (Rom. 8:26; Heb. 7:25). Paul desires the Ephesian Christians to have compassion for the lost, to understand the depths of their pain and misery, and to come intimately to God pleading for their salvation.
_Ransom:_ This describes the result of Christ's substitutionary death for believers—which He did voluntarily (John 10:17–18)—and reminds us of Christ's own statement in Matthew 20:28 that He would be "a ransom for many." Not all will be ransomed (though His death would be sufficient), but only the many who believe by the work of the Holy Spirit and for whom the actual atonement was made. Christ did not pay a ransom only; He became the object of God's just wrath in the believer's place—He died his death and bore his sin (see 2 Cor. 5:21; 1 Pet. 2:24).
UNLEASHING THE TEXT
Read 2:1–8, noting the key words and definitions next to the passage.
**1 Timothy 2:1–8 (NKJV)**
**1** _Therefore I exhort first of all that supplications, prayers, intercessions, and giving of thanks be made for all men,_
**_all men_** (v. 1)—The lost in general, not the elect only. God's decree of election is secret—believers have no way of knowing who is elect until they respond. The scope of God's evangelistic efforts is broader than election (Matt. 22:14; John 17:21, 23).
**2** _for kings and all who are in authority, that we may lead a quiet and peaceable life in all godliness and reverence._
**_kings and all who are in authority_** (v. 2)—Because so many powerful and influential political rulers are hostile to God, they are often the targets of bitterness and animosity. But Paul urges believers to pray that these leaders might repent of their sins and embrace the gospel, which meant that the Ephesians were even to pray for the salvation of the Roman emperor, Nero, a cruel and vicious blasphemer and persecutor of the faith.
**_a quiet and peaceable life_** (v. 2)—"Quiet" refers to the absence of external disturbances; "peaceable" refers to the absence of internal ones. While it remains uncompromising in its commitment to the truth, the church is not to agitate or disrupt the national life. When it manifests love and goodness to all and prays passionately for the lost, including rulers, the church may experience a certain amount of religious freedom. Persecution should only be the result of righteous living, not civil disobedience (see Titus 3:1–4; 1 Pet. 2:13–23).
**_godliness and reverence_** (v. 2)—"Godliness" is a key word in this letter (3:16; 4:7–8; 6:3, 5–6, 11; see 2 Tim. 3:5; Titus 1:1), indicating that there needed to be a call back to holy living, which had been negatively affected by the false doctrine. Godliness refers to having the proper attitude and conduct before God in everything; "reverence" can be translated "moral earnestness," and refers to moral dignity and holy behavior before men.
**3** _For this is good and acceptable in the sight of God our Savior,_
**4** _who desires all men to be saved and to come to the knowledge of the truth._
**_desires all men to be saved_** (v. 4)—The Greek word for "desires" is not that which normally expresses God's will of decree (His eternal purpose), but God's will of desire. There is a distinction between God's desire and His eternal saving purpose, which must transcend His desires. God does not want people to sin. He hates sin with all His being (Ps. 5:4; 45:7); thus, He hates its consequences—eternal wickedness in hell. God does not want people to remain wicked forever in eternal remorse and hatred of Himself. Yet, God, for His own glory, and to manifest that glory in wrath, chose to endure "vessels . . . prepared for destruction" for the supreme fulfillment of His will (Rom. 9:22). In His eternal purpose, He chose only the elect out of the world (John 17:6) and passed over the rest, leaving them to the consequences of their sin, unbelief, and rejection of Christ. Ultimately, God's choices are determined by His sovereign, eternal purpose, not His desires.
**_the knowledge of the truth_** (v. 4)—meaning "to be saved"; see 2 Timothy 3:7
**5** _For there is one God and one Mediator between God and men, the Man Christ Jesus,_
**_there is one God_** (v. 5)—There is no other way of salvation (Acts 4:12); hence there is the need to pray for the lost to come to know the one true God (see Deut. 4:35, 39; 6:4; Isa. 43:10; 44:6; 45:5–6, 21–22; 46:9; 1 Cor. 8:4, 6).
**_Mediator_** (v. 5)—This refers to someone who intervenes between two parties to resolve a conflict or ratify a covenant. Jesus Christ is the only "Mediator" who can restore peace between God and sinners (Heb. 8:6; 9:15; 12:24).
**_the Man Christ Jesus_** (v. 5)—The absence of the article before "Man" in the Greek suggests the translation "Christ Jesus, Himself a man." Only the perfect God-Man could bring God and man together (see Job 9:32–33).
**6** _who gave Himself a ransom for all, to be testified in due time,_
**_for all_** (v. 6)—This should be taken in two senses: (1) there are temporal benefits of the atonement that accrue to all men universally (see 4:10), and (2) Christ's death was sufficient to cover the sins of all people. Yet the substitutionary aspect of His death is applied to the elect alone (see above and 2 Cor. 5:14–21). Christ's death is therefore unlimited in its sufficiency, but limited in its application. Because Christ's expiation of sin is indivisible, inexhaustible, and sufficient to cover the guilt of all the sins that will ever be committed, God can clearly offer it to all. Yet only the elect will respond and be saved, according to His eternal purpose (see John 17:12).
**_in due time_** (v. 6)—at the proper time in God's redemptive plan (see Gal. 4:4)
**7** _for which I was appointed a preacher and an apostle—I am speaking the truth in Christ and_ _not lying—a teacher of the Gentiles in faith and truth._
**_for which_** (v. 7)—Paul's divine commission was based on the truths delineated in verses 3–6.
**_preacher_** (v. 7)—The Greek word derives from the verb that means "to herald," "to proclaim," or "to speak publicly." Paul was a public herald proclaiming the gospel of Christ.
**_I am speaking the truth . . . not lying_** (v. 7)—Paul's emphatic outburst of his apostolic authority and integrity is to emphasize that he was a teacher of the Gentiles.
**_teacher of the Gentiles_** (v. 7)—This is the distinctive feature of Paul's apostolic appointment, which demonstrates the universal scope of the gospel. Paul's need to make this distinction suggests he was dealing with some form of Jewish exclusivism that had crippled the Ephesians' interest in praying for Gentiles to be saved.
**8** _I desire therefore that the men pray everywhere, lifting up holy hands, without wrath and doubting._
**_men_** (v. 8)—This is the Greek word for "men" as opposed to women. God intends for men to be the leaders when the church meets for corporate worship. When prayer for the lost is offered during those times, the men are to lead it.
**_everywhere_** (v. 8)—Paul's reference to the official assembly of the church (see 1 Cor. 1:2; 2 Cor. 2:14; 1 Thess. 1:8)
**_lifting up holy hands_** (v. 8)—Paul is not emphasizing a specific posture necessary for prayer, but a pre-requisite for effective prayer. Though this posture is described in the Old Testament, so are many others. The Greek word for "holy" means "unpolluted" or "unstained by evil." "Hands" symbolize the activities of life; thus "holy hands" represent a holy life. The basis of effective prayer is a righteous life (James 5:16).
**_without wrath and doubting_** (v. 8)—"Wrath" and righteousness are mutually exclusive (James 1:20; see Luke 9:52–56). A better translation for "doubting" is "dissension," and it refers to a hesitant reluctance to be committed to prayer. "Effectual, fervent" prayer is effective (James 5:16). The two refer to one's inner attitude.
1) For whom did Paul command prayers to be made?
[Your Response Here]
2) What reasons are given for these commands to "pray for all men"?
[Your Response Here]
3) What is significant about the command to pray "lifting up holy hands" (v. 8)?
[Your Response Here]
_(Verses to consider: 1 Kings 8:22; Neh. 8:6; Ps. 28:2; 63:4; 134:2)_
GOING DEEPER
Paul encouraged Timothy to pray for all people. For insight into what Jesus said about prayer, read Matthew 6:5–15.
**5** _"And when you pray, you shall not be like the hypocrites. For they love to pray standing in the synagogues and on the corners of the streets, that they may be seen by men. Assuredly, I say to you, they have their reward._
**6** _But you, when you pray, go into your room, and when you have shut your door, pray to your Father who is in the secret place; and your Father who sees in secret will reward you openly._
**7** _And when you pray, do not use vain repetitions as the heathen do. For they think that they will be heard for their many words._
**8** _"Therefore do not be like them. For your Father knows the things you have need of before you ask Him._
**9** _In this manner, therefore, pray: Our Father in heaven, hallowed be Your name._
**10** _Your kingdom come. Your will be done on earth as it is in heaven._
**11** _Give us this day our daily bread._
**12** _And forgive us our debts, as we forgive our debtors._
**13** _And do not lead us into temptation, but deliver us from the evil one. For Yours is the kingdom and the power and the glory forever. Amen._
**14** _"For if you forgive men their trespasses, your heavenly Father will also forgive you._
**15** _But if you do not forgive men their trespasses, neither will your Father forgive your trespasses._
EXPLORING THE MEANING
4) What is Jesus' main point in verses 5–8?
[Your Response Here]
5) What part does forgiveness play in our prayer life?
[Your Response Here]
6) How does this teaching on prayer compare with what you discovered in 1 Timothy 2:1–8?
[Your Response Here]
7) What does Paul's command to pray for all people imply? Will everyone be saved? (See Eph. 1:3–5).
[Your Response Here]
_(Verses to consider: Rom. 1:18–32; 9:22–23)_
TRUTH FOR TODAY
The greatest example of evangelistic praying is our Lord Himself. Isaiah 53:12 tells us He "interceded for the transgressors." On the cross He prayed, "Father, forgive them; for they do not know what they are doing" (Luke 23:34). God answered those prayers with three thousand converts on the Day of Pentecost, and countless thousands more through the centuries.
Do we pray for the lost like that? Do we have the passion that inspired John Knox to cry out, "Give me Scotland or I die"? Is our attitude that of George Whitefield, who prayed, "O Lord, give me souls or take my soul"? Can we, like Henry Martyn, say, "I cannot endure existence if Jesus is to be so dishonored"?
God honors evangelistic prayer. Standing among those who killed Stephen was a young man named Saul of Tarsus. Could it be that the great apostle's salvation was in answer to Stephen's prayer, "Lord, do not hold this sin against them"? Evangelism begins with the evangelistic prayer.
REFLECTING ON THE TEXT
8) List five prominent figures who have great influence in our culture. How might God use your faithful prayers to change them (and the world through them)? How can you pray for them?
[Your Response Here]
9) If every Christian in your church imitated your personal prayer habits, how much prayer would be taking place? What, if anything, needs to change in your prayer life?
[Your Response Here]
PERSONAL RESPONSE
Write out additional reflections, questions you may have, or a prayer.
[Your Response Here]
ADDITIONAL NOTES
[Your Response Here]
**3**
THE ROLE OF WOMEN
_1 Timothy 2:9–15_
DRAWING NEAR
How would you answer a skeptic's charge that Christianity is demeaning to women?
[Your Response Here]
What women, in your church or other spheres, do you greatly admire? Why?
[Your Response Here]
THE CONTEXT
Few topics are as hotly debated as the subject of the role of women in the church. Sadly, this debate no longer looks to the pages of God's Word in order to find a solution. Long-held beliefs are being abandoned in favor of new and culturally acceptable feminist doctrines. Churches, schools, and seminaries are increasingly jettisoning the bedrock truths upon which they were founded. Countless books continue to be written which articulate and defend these new views concerning the role of women in the church. Ironically, many of these same authors once held the traditional, biblical view. But due to the pressure of feminism, these church leaders have sacrificed biblical integrity for cultural acceptance. The Bible passages that clearly delineate women's roles are constantly reinterpreted, or else they are ignored because of the supposed "anti-woman bias" of the biblical writers.
Since the church at Ephesus was overrun with false teachers, it is not surprising to discover that they also wrestled with the issue of gender roles. Apparently, some of the women in the church were leading lives of impurity (see 5:6, 11–15; 2 Tim. 3:6), and their inappropriate behavior carried over into the worship services of the church. Under the guise of coming together to worship, these women were calling attention to themselves and proving to be a serious distraction to the rest of the body. Since worship is central to the life of the church, Paul confronted the issue immediately in his letter to Timothy.
Contrary to much popular belief, this passage is as culturally relevant as any other New Testament passage.
KEYS TO THE TEXT
_Silence and Submission:_ "Silence" ("quiet") and "submission" ("to line up under") were to characterize the role of a woman as a learner in the context of the church assembly. Paul explains his meaning in verse 12: Women are to be silent by not teaching, and they are to demonstrate submission by not usurping the authority of the pastors or elders. Elsewhere Paul says that _every_ spirit-filled Christian is to be a humble, submissive Christian (Eph. 5:21). No believer is inherently superior to any other believer. In their standing before God, they are equal in every way (Gal. 3:28). All believers are to submit to each other. Wives are to submit to their husbands, and children are to submit to their parents (Eph. 6:1–3). Believers must submit to government laws and ordinances (Rom. 13:1; 1 Pet. 2:13). Younger men should submit to older men (1 Pet. 5:5a). God desires _every_ believer to be submissive in the ways He has ordained.
_Woman's Role from Creation:_ A woman's subordinate role did not result after the Fall as a cultural, chauvinistic corruption of God's perfect design; rather, God established her role as part of His original creation (1 Tim. 2:13). God made woman after man to be his suitable helper (see 1 Cor. 11:8–9). The Fall actually corroborates God's divine plan of creation (see Gen. 3:1–7). By nature Eve was not suited to assume the position of ultimate responsibility. By leaving Adam's protection and usurping his headship, she was vulnerable and fell, thus confirming how important it was for her to stay under the protection and leadership of her husband (see 5:11–12; 2 Tim. 3:6–7). Adam then violated his leadership role, followed Eve in her sin, and plunged the human race into sinfulness—all connected with violating God's planned roles for the sexes. Ultimately, the responsibility for the Fall rests with Adam, since he chose to disobey God by being deceived.
UNLEASHING THE TEXT
Read 2:9–15, noting the key words and definitions next to the passage.
**1 Timothy 2:9–15 (NKJV)**
**9** _In like manner also, that the women adorn themselves in modest apparel, with propriety and moderation, not with braided hair or gold or pearls or costly clothing,_
**_adorn . . . modest apparel_** (v. 9)—The Greek word for "adorn" means "to arrange," "to put in order," or "to make ready." A woman is to arrange herself appropriately for the worship service, which includes wearing decent clothing that reflects a properly adorned, chaste heart.
**_propriety and moderation_** (v. 9)—The Greek word for "propriety" refers to modesty mixed with humility, which carries the underlying idea of shame. It can also refer to a rejection of anything dishonorable to God, or refer to grief over sin. "Moderation" basically refers to self-control over sexual passions. Godly women hate sin and control their passions so as not to lead another into sin.
**_braided hair or gold or pearls or costly clothing_** (v. 9)—These specific practices were causing distraction and discord in the church. Women in the first century often wove gold, pearls or other jewelry into their hair styles ("braided hair") to call attention to themselves and their wealth or beauty. The same was true of those women who wore "costly clothing." By doing so they would draw attention to themselves and away from the Lord, likely causing the poorer women to be envious. Paul's point was to forbid the preoccupation of certain women with flaunting their wealth and distracting people from worshiping the Lord.
**10** _but, which is proper for women professing godliness, with good works._
**11** _Let a woman learn in silence with all submission._
**_Let a woman learn_** (v. 11)—Women are not to be the public teachers when the church assembles, but neither are they to be shut out of the learning process. The form of the Greek verb translated "let . . . learn" is an imperative: Paul is commanding that women be taught in the church. That was a novel concept, since neither first-century Judaism nor Greek culture held women in high esteem. Some of the women in Ephesus probably overreacted to the cultural denigration they had typically suffered and took advantage of their opportunity in the church by seeking a dominant role in leadership.
**12** _And I do not permit a woman to teach or to have authority over a man, but to be in silence._
**_I do not permit_** (v. 12)—The Greek word for "permit" is used in the New Testament to refer to allowing someone to do what he desires. Paul may have been addressing a real situation in which several women in Ephesus desired to be public preachers.
**_to teach_** (v. 12)—Paul used a verbal form of this Greek word that indicates a condition or process and is better translated "to be a teacher." This was an important, official function in the church. Thus Paul is forbidding women from filling the office and role of the pastor or teacher. He is not prohibiting them from teaching in other appropriate conditions and circumstances.
**_to have authority over_** (v. 12)—Paul forbids women from exercising any type of authority over men in the church assembly, since the elders are those who rule (5:17). The elders are all to be men (as is clear from the requirements in 3:2, 5).
**13** _For Adam was formed first, then Eve._
**14** _And Adam was not deceived, but the woman being deceived, fell into transgression._
**15** _Nevertheless she will be saved in childbearing if they continue in faith, love, and holiness, with self-control._
**_she_** (v. 15)—That Paul does not have Eve in mind here is clear because the verb translated "will be saved" is future, and he also uses the plural pronoun "they." He is talking about women after Eve.
**_will be saved_** (v. 15)—In this context this is better translated "will be preserved." The Greek word can also mean "to rescue," "to preserve safe and unharmed," "to heal," or "to deliver from." It appears several times in the New Testament without reference to spiritual salvation (see Matt. 8:25; 9:21–22; 24:22; 27:40, 42, 49; 2 Tim. 4:18). Paul is not advocating that women are eternally saved from sin through childbearing or that they maintain their salvation by having babies, both of which would be clear contradictions of the New Testament teaching of salvation by grace alone through faith alone (Rom. 3:19–20) which is sustained forever (Rom. 8:31–39). Paul is teaching that even though a woman bears the stigma of being the initial instrument who led the race into sin, women may be preserved or freed from that stigma by raising a generation of godly children (see 5:10).
**_in childbearing_** (v. 15)—Because mothers have a unique bond and intimacy with their children and spend far more time with them than do fathers, they have far greater influence in their lives and thus a unique responsibility and opportunity for rearing godly children. While a woman may have led the human race into sin, women have the privilege of leading many out of sin to godliness. Paul is speaking in general terms; God does not want all women to be married, let alone bear children.
**_if they continue in faith, love, and holiness, with self-control_** (v. 15)—The godly appearance, demeanor, and behavior commanded of believing women in the church (vv. 9–12) is motivated by the promise of deliverance from any inferior status and the joy of raising godly children.
1) What instructions concerning dress did Paul give to Timothy for the women in his congregation?
[Your Response Here]
_(Verses to consider: Gen. 24:53; Isa. 3:16–24; Prov. 31:22; 1 Pet. 3:3–4)_
2) What behavior is expected from women professing godliness, and what is their God-ordained role in the church? What vitally important role do they play in the home?
[Your Response Here]
_(Verses to consider: 1 Cor. 14:34–35; Titus 2:3–5)_
3) Summarize what this passage says about God's design for women from creation (vv. 13–14)?
[Your Response Here]
_(Verses to consider: Gen. 2:18; 3:1–7)_
GOING DEEPER
In his book to the church at Corinth, Paul related the theological foundation for his teaching on women's roles. Read 1 Corinthians 11:1–16.
**1** _Imitate me, just as I also imitate Christ._
**2** _Now I praise you, brethren, that you remember me in all things and keep the traditions just as I delivered them to you._
**3** _But I want you to know that the head of every man is Christ, the head of woman is man, and the head of Christ is God._
**4** _Every man praying or prophesying, having his head covered, dishonors his head._
**5** _But every woman who prays or prophesies with her head uncovered dishonors her head, for that is one and the same as if her head were shaved._
**6** _For if a woman is not covered, let her also be shorn. But if it is shameful for a woman to be shorn or shaved, let her be covered._
**7** _For a man indeed ought not to cover his head, since he is the image and glory of God; but woman is the glory of man._
**8** _For man is not from woman, but woman from man._
**9** _Nor was man created for the woman, but woman for the man._
**10** _For this reason the woman ought to have a symbol of authority on her head, because of the angels._
**11** _Nevertheless, neither is man independent of woman, nor woman independent of man, in the Lord._
**12** _For as woman came from man, even so man also comes through woman; but all things are from God._
**13** _Judge among yourselves. Is it proper for a woman to pray to God with her head uncovered?_
**14** _Does not even nature itself teach you that if a man has long hair, it is a dishonor to him?_
**15** _But if a woman has long hair, it is a glory to her; for her hair is given to her for a covering._
**16** _But if anyone seems to be contentious, we have no such custom, nor do the churches of God._
EXPLORING THE MEANING
4) What does this passage mean when it discusses "headship"?
[Your Response Here]
5) Read Galatians 3:28. How does this verse put to rest any notion that Christianity views men as superior to women?
[Your Response Here]
6) Read Luke 8:2–3. How did Jesus give honor to women during His earthly ministry?
[Your Response Here]
_(Verses to consider: Mark 5:25–34; Luke 10:38–42; 13:11–13; John 4:1–30)_
TRUTH FOR TODAY
God has perfectly balanced the roles of the sexes. Men are to be the leaders in the church and the family. Women are kept from any accusation of inferiority through the godly influence they have in the lives of their precious children. For the church to depart from this divine order is to perpetuate the disaster of the Fall.
REFLECTING ON THE TEXT
7) How do you feel about Paul's teaching about women in this passage? Why?
[Your Response Here]
8) What does it mean for men and women to dress appropriately?
[Your Response Here]
9) If you are a woman, how can you modify your habits of dress to better conform to the commands in this passage? How can you modify your heart and attitude to do the same?
[Your Response Here]
10) What criticism can a church expect if it preaches and enacts the principles taught in this passage? How do you know?
[Your Response Here]
11) What godly woman (or women) has God used in your life to help you grow in the faith? How can you show appreciation this week for that spiritual investment?
[Your Response Here]
PERSONAL RESPONSE
Write out additional reflections, questions you may have, or a prayer.
[Your Response Here]
**4**
QUALIFICATIONS FOR LEADERSHIP
_1 Timothy 3:1–16_
DRAWING NEAR
Paul moves to the business of running a church. Of primary importance to any church is that its leaders set an example for the flock. On a scale of 1–10 (1 = "terrible"; 10 = "terrific"), how would you rate your church leaders in this area?
[Your Response Here]
What attributes does our society generally view as indispensable for leadership?
[Your Response Here]
In your opinion, what are the marks of a good leader?
[Your Response Here]
THE CONTEXT
Paul's purpose in writing this letter was to instruct Timothy regarding the church. Clearly, there is an inseparable link between the spiritual quality of a congregation and the godliness of its leaders. Not surprisingly, church leadership is a major focus of teaching in the New Testament. This passage delineates those qualifications for pastors and deacons.
The qualifications given by the Spirit stand in sharp contrast to the unqualified leaders that had assumed positions in the church at Ephesus. The epistle indicates the presence of some leaders who were propagating false doctrine (1:3; 4:1–3, 7; 6:3–5). They overemphasized the law and twisted the gospel (1:7–11). Also, certain women had wrongly assumed power. All needed to be publicly rebuked.
Rather than emphasize the duties of elders and deacons, Paul emphasized the character qualities that should mark a leader of God's church. The duties of church leaders were evident, but the individual qualifications needed clarification.
KEYS TO THE TEXT
_Bishop:_ The word means "over" and identifies the men who are responsible to lead the church. The New Testament uses the words "bishop," "elder," "overseer," and "pastor" interchangeably to describe the same men. Bishops (pastors, overseers, elders) are responsible to lead, preach, teach, help the spiritually weak, care for the church, and ordain other leaders.
_Deacons_ : This word comes from a word group meaning "to serve," and originally referred to menial tasks such as waiting on tables (see Acts 6:1–4). "Deacon" came to denote any service in the church. Deacons serve under the leadership of elders, helping them exercise oversight in the practical matters of church life. Scripture defines no official or specific responsibilities for deacons; they are to do whatever the elders assign them or whatever spiritual ministry is necessary.
UNLEASHING THE TEXT
Read 3:1–16, noting the key words and definitions next to the passage.
**1 Timothy 3:1–16 (NKJV)**
**1** _This is a faithful saying: If a man desires the position of a bishop, he desires a good work._
**_desires . . . desires_** (v. 1)—Two different Greek words are used. The first means "to reach out after." It describes external action, not internal motive. The second means "a strong passion," and refers to an inward desire. Taken together, these two words aptly describe the type of man who belongs in the ministry—one who outwardly pursues it because he is driven by a strong internal desire.
**2** _A bishop then must be blameless, the husband of one wife, temperate, sober-minded, of good behavior, hospitable, able to teach;_
**_must_** (v. 2)—The use of this Greek particle stresses emphatically that living a blameless life is absolutely necessary for church leaders.
**_blameless_** (v. 2)—This means literally "not able to be held" in a criminal sense; there is no valid accusation of wrongdoing that can be made against him. No overt, flagrant sin can mar the life of one who must be an example for his people to follow (see v. 10; 4:16; 5:7; Ps. 101:6; 2 Thess. 3:9; Heb. 13:7; 1 Pet. 5:3). This is the over-arching requirement for elders; the rest of the qualifications elaborate on what it means to be blameless.
**_the husband of one wife_** (v. 2)—In Greek, this is literally a "one-woman man." This says nothing about marriage or divorce (for comments on that, see note on v. 4). The issue is not the elder's marital status, but his moral and sexual purity. This qualification heads the list, because it is in this area that leaders are most prone to fail. Various interpretations of this qualification have been offered. Some see it as a prohibition against polygamy—an unnecessary injunction since polygamy was not common in Roman society and clearly forbidden by Scripture (Gen. 2:24), the teaching of Jesus (Matt. 19:5–6; Mark 10:6–9), and Paul (Eph. 5:31). A polygamist could not even have been a church member, let alone a church leader. Others see this requirement as barring those who remarried after the death of their wives. But, as already noted, the issue is sexual purity, not marital status. Further, the Bible encourages remarriage after widowhood (5:14; 1 Cor. 7:39). Some believe that Paul here excludes divorced men from church leadership. That again ignores the fact that this qualification does not deal with marital status. Nor does the Bible prohibit all remarriage after divorce (see Matt. 5:31–32; 19:9; 1 Cor. 7:15). Finally, some think that this requirement excludes single men from church leadership. But if that were Paul's intent, he would have disqualified himself (1 Cor. 7:8). A "one-woman man" is one totally devoted to his wife, maintaining singular devotion, affection, and sexual purity in both thought and deed. To violate this is to forfeit blamelessness and no longer be "above reproach" (Titus 1:6–7).
**_temperate_** (v. 2)—The Greek word literally means "wineless" but is here used metaphorically to mean "alert," "watchful," "vigilant," or "clear-headed." Elders must be able to think clearly.
**_sober-minded_** (v. 2)—A "sober-minded" man is disciplined, knows how to properly order his priorities, and is serious about spiritual matters.
**_good behavior_** (v. 2)—The Greek word means "orderly." Elders must not lead chaotic lives. If they cannot order their own lives, how can they bring order to the church?
**_hospitable_** (v. 2)—This comes from a compound Greek word meaning "love of strangers" (see Heb. 13:2). As with all spiritual virtues, elders must set the example; their lives and homes are to be open so all can see their spiritual character.
**_able to teach_** (v. 2)—This is used only here and in 2 Timothy 2:24. This is the only qualification relating to an elder's giftedness and spiritual ability, and the only one that distinguishes elders from deacons. The preaching and teaching of God's Word is the over/pastor/elder's primary duty (4:6, 11, 13; 5:17).
**3** _not given to wine, not violent, not greedy for money, but gentle, not quarrelsome, not covetous;_
**_not given to wine_** (v. 3)—This is more than a mere prohibition against drunkenness (see Eph. 5:18). An elder must not have a reputation as a drinker; his judgment must never be clouded by alcohol (see Prov. 31:4–5), and his lifestyle must be radically different from the world and lead others to holiness, not sin.
**_not violent_** (v. 3)—Literally "not a giver of blows," this means that elders must react to difficult situations calmly and gently, and under no circumstances with physical violence.
**_not greedy for money_** (v. 3)—The better Greek manuscripts omit this phrase. See the note below on "not covetous." The principle is included, however, in Titus 1:7 and 1 Peter 5:2.
**_gentle_** (v. 3)—considerate, genial, gracious, quick to pardon failure, and one who does not hold a grudge
**_not quarrelsome_** (v. 3)—"peaceful," "reluctant to fight"; one who does not promote disunity or disharmony
**_not covetous_** (v. 3)—Elders must be motivated by love for God and His people, not money (see 1 Pet. 5:2). A leader who is in the ministry for money reveals a heart set on the world, not the things of God. Covetousness characterizes false teachers (Titus 1:11; 2 Pet. 2:1–3, 14; Jude 11), but not Paul's ministry (Acts 20:33; 1 Cor. 9:1–16; 2 Cor. 11:9; 1 Thess. 2:5).
**4** _one who rules his own house well, having his children in submission with all reverence_
**_who rules his own house well_** (v. 4)—The elder's home life, like his personal life, must be exemplary. He must be one who "rules" (presides over, has authority over) "his own house" (everything connected with his home, not merely his wife and children) "well" (intrinsically good; excellently). Issues of divorce should be related to this matter. A divorced man gives no evidence of a well-managed home, but rather that divorce shows weakness in his spiritual leadership. If there has been a biblically permitted divorce, it must have been so far in the past as to have been overcome by a long pattern of solid family leadership and the rearing of godly children.
**_submission_** (v. 4)—This is a military term referring to soldiers ranked under one in authority. An elder's children must be believers (see note on "faithful" in Titus 1:6), well-behaved, and respectful.
**5** _(for if a man does not know how to rule his own house, how will he take care of the church of God?);_
**_take care of the church of God_** (v. 5)—An elder must first prove in the intimacy and exposure of his own home his ability to lead others to salvation and sanctification. There he proves God has gifted him to set the example of virtue, serve others, resolve conflicts, build unity, and maintain love. If he cannot do those essential things there, why would anyone assume he would be able to do them in the church?
**6** _not a novice, lest being puffed up with pride he fall into the same condemnation as the devil._
**_not a novice, lest . . . puffed up with pride_** (v. 6)—Putting a new convert into a leadership role would tempt him to pride. Elders, therefore, are to be drawn from the spiritually mature men of the congregation (see notes on 5:22).
**_fall into the same condemnation as the devil_** (v. 6)—Satan's condemnation was due to pride over his position. It resulted in his fall from honor and authority (Isa. 14:12–14; Ezek. 28:11–19). The same kind of fall and judgment could easily happen to a new and weak believer put in a position of spiritual leadership.
**7** _Moreover he must have a good testimony among those who are outside, lest he fall into reproach and the snare of the devil._
**_good testimony . . . outside_** (v. 7)—A leader in the church must have an unimpeachable reputation in the unbelieving community, even though people there may disagree with his moral and theological stands. How can he make a spiritual impact on those who do not respect him (see Matt. 5:48)?
**8** _Likewise deacons must be reverent, not double-tongued, not given to much wine, not greedy for money,_
**_reverent_** (v. 8)—serious in mind and character; not silly or flippant about important matters
**_not double-tongued_** (v. 8)—Deacons must not say one thing to some people and something else to others; their speech must not be hypocritical, but honest and consistent.
**_not given to much wine_** (v. 8)—not preoccupied with drink (see note on v. 3)
**_not greedy_** (v. 8)—Like elders (see note on v. 3), deacons must not abuse their office to make money. Such a qualification was especially important in the early church, where deacons routinely handled money, distributing it to those in need.
**9** _holding the mystery of the faith with a pure conscience._
**_the mystery_** (v. 9)—See 1 Corinthians 2:7; Ephesians 3:4–5. Appearing frequently in Paul's writings (see Rom. 11:25; 16:25; Eph. 1:9; 3:9; 6:19; Col. 2:2), the word "mystery" describes truth previously hidden, but now revealed, including Christ's incarnation (v. 16), Christ's indwelling of believers (Col. 1:26–27), the unity of Jews and Gentiles in the church (Eph. 3:4–6), the gospel (Col. 4:3), lawlessness (2 Thess. 2:7), and the rapture of the church (1 Cor. 15:51–52).
**10** _But let these also first be tested; then let them serve as deacons, being found blameless._
**_first be tested_** (v. 10)—The present tense of this verb indicates an ongoing evaluation of deacons' character and service by the church.
**11** _Likewise, their wives must be reverent, not slanderers, temperate, faithful in all things._
**_their wives_** (v. 11)—The Greek word rendered "wives" can also be translated "women." Paul likely here refers not to deacons' wives but to the women who serve as deacons. The use of the word "likewise" as an introduction (see v. 8) suggests a third group in addition to elders and deacons. Also, since Paul gave no requirements for elders' wives, there is no reason to assume these would be qualifications for deacons' wives.
**_not slanderers_** (v. 11)—"Slanderers" is the plural form of _diabolos_ —a title frequently given to Satan (Matt. 13:39; Luke 4:3, 5–6, 13; 8:12; 1 Pet. 5:8; 1 John 3:8; Rev. 2:10; 12:9, 12; 20:2, 10). The women who serve must not be gossips.
**_temperate_** (v. 11)—See the note on verse 2.
**_faithful in all things_** (v. 11)—Women servants in the church, like their male counterparts (see note on v. 2), must be absolutely trustworthy in all aspects of their lives and ministries.
**12** _Let deacons be the husbands of one wife, ruling their children and their own houses well._
**_the husbands of one wife_** (v. 12)—See the note on verse 2.
**_ruling . . . their own houses well_** (v. 12)—See the note on verse 4.
**13** _For those who have served well as deacons obtain for themselves a good standing and great boldness in the faith which is in Christ Jesus._
**14** _These things I write to you, though I hope to come to you shortly;_
**_I hope to come to you shortly_** (vv. 14–15)—The Greek grammar suggests Paul's meaning is "These things I write, although I had hoped to come to you sooner." Delayed in Macedonia, Paul sent Timothy this letter.
**15** _but if I am delayed, I write so that you may know how you ought to conduct yourself in the house of God, which is the church of the living God, the pillar and ground of the truth._
**_how you ought to conduct yourself_** (v. 15)—The second half of this verse expresses the theme of this epistle—setting things right in the church.
**_house of God_** (v. 15)—This is better translated "household." Believers are members of God's household (Gal. 6:10; Eph. 2:19; Heb. 3:6; 1 Pet. 4:17) and must act accordingly. This is not a reference to any building, but to the people who make up the true church.
**_church of the living God_** (v. 15)—The church is God's possession (Eph. 1:14; Titus 2:14; 1 Pet. 2:9). The title "the living God" has a rich Old Testament heritage (Josh. 3:10; 1 Sam. 17:26, 36; 2 Kings 19:4, 16; Ps. 42:2; 84:2; Isa. 37:4, 17; Jer. 10:10; 23:26; Dan. 6:20, 26; Hos. 1:10).
**_pillar and ground_** (v. 15)—Paul's imagery may have referred to the magnificent temple of Diana (Artemis) in Ephesus, which was supported by 127 gold-plated marble pillars. The word translated "ground" appears only here in the New Testament and denotes the foundation on which a building rests. The church upholds the truth of God's revealed Word.
**_the truth_** (v. 15)—the content of the Christian faith recorded in Scripture and summed up in verse 16
**16** _And without controversy great is the mystery of godliness: God was manifested in the flesh, justified in the Spirit, seen by angels, preached among the Gentiles, believed on in the world, received up in glory._
**_God . . . glory_** (v. 16)—This verse contains part of an early church hymn, as its uniformity, rhythm, and parallelism indicate. Its six lines form a concise summary of the truth of the gospel.
**_mystery of godliness_** (v. 16)—"Mystery" is that term used by Paul to indicate truth hidden in the Old Testament age and revealed in the New Testament (see note on v. 9). "Godliness" refers to the truths of salvation and righteousness in Christ, which produce holiness in believers; namely, the manifestation of true and perfect righteousness in Jesus Christ.
**_God was manifested_** (v. 16)—The better manuscripts read "He who" instead of "God." In either case, the reference is clearly to Christ, who manifested the invisible God to mankind (John 1:1–4; 14:9; Col. 1:15; Heb. 1:3; 2 Pet. 1:16–18).
**_in the flesh_** (v. 16)—This does not refer to sinful, fallen human nature here (see Rom. 7:18, 25; 8:8; Gal. 5:16–17), but merely humanness (see John 1:14; Rom. 1:3; 8:3; 9:5; 1 Pet. 3:18; 1 John 4:2–3).
**_justified in the Spirit_** (v. 16)—"Justified" means "righteous," so that "spirit" may be written with lower case "s," indicating a declaration of Christ's sinless spiritual righteousness (John 8:46; 2 Cor. 5:21; Heb. 4:15; 5:9; 7:26; 1 Pet. 2:21–22; 1 John 2:1), or it could refer to His vindication by the Holy Spirit (Rom. 1:4).
**_seen by angels_** (v. 16)—both by fallen (see Col. 2:15; 1 Pet. 3:18–20) and elect (Matt. 28:2; Luke 24:4–7; Acts 1:10–11; Heb. 1:6–9) angels
**_preached among the Gentiles_** (v. 16)—or, nations (see Matt. 24:14; 26:13; 28:19–20; Mark 13:10; Acts 1:8)
**_received up in glory_** (v. 16)—Christ's ascension and exaltation showed that the Father was pleased with Him and accepted His work fully (see Acts 1:9–10; Phil. 2:8–11; Heb. 1:3).
1) What qualities should be present in the lives of the bishops (elders) who lead the church?
[Your Response Here]
_(Verses to consider: Phil. 3:17; 2 Tim. 2:15, 24; Titus 1:6–9)_
2) Identify the actions or character flaws that can disqualify one from being a leader in the church.
[Your Response Here]
_(Verses to consider: Matt. 6:24; 2 Tim. 2:24–25; Titus 1:7)_
3) What is a deacon, and what is expected of one?
[Your Response Here]
4) What requirements did Paul set for women serving in the church?
[Your Response Here]
5) Why was Paul's instruction necessary?
[Your Response Here]
GOING DEEPER
Writing to another church leader, Titus, Paul talked about how leaders were to be chosen. Read Titus 1:4–9.
**4** _To Titus, a true son in our common faith: Grace, mercy, and peace from God the Father and the Lord Jesus Christ our Savior._
**5** _For this reason I left you in Crete, that you should set in order the things that are lacking, and appoint elders in every city as I commanded you—_
**6** _if a man is blameless, the husband of one wife, having faithful children not accused of dissipation or insubordination._
**7** _For a bishop must be blameless, as a steward of God, not self-willed, not quick-tempered, not given to wine, not violent, not greedy for money,_
**8** _but hospitable, a lover of what is good, sober-minded, just, holy, self-controlled,_
**9** _holding fast the faithful word as he has been taught, that he may be able, by sound doctrine, both to exhort and convict those who contradict._
EXPLORING THE MEANING
6) Compare this list of qualifications with the one given Timothy. What is similar? What is different?
[Your Response Here]
7) Read 1 Peter 5:1–3. What added insights does this passage reveal about the right motives for those who lead God's church?
[Your Response Here]
_(Verses to consider: 2 Cor. 4:1–7; 1 Thess. 1:5)_
8) Read Mark 10:42–45. How did Jesus radically redefine leadership in His kingdom?
[Your Response Here]
TRUTH FOR TODAY
The most important qualities leaders can demonstrate are not intelligence, a forceful personality, glibness, diligence, vision, administrative skills, decisiveness, courage, humor, tact, or any other similar natural attribute. Those all play a part, but the most desirable quality for any leader is integrity. While integrity is most desirable in secular leadership, its absence is fatal to spiritual leadership. Integrity is living what you teach and preach. That is why all the qualifications for leaders given in this passage describe their moral character. It is not the typical list a corporate analyst might come up with, because the issue is not leadership skills, but spiritual example. One who would lead people to Christlikeness must be a pattern of godly behavior for his people to follow. He must be above reproach in his moral life, home life, spiritual maturity, and public reputation.
REFLECTING ON THE TEXT
9) As you read through the list of leadership qualities found in chapter 3, which positive one(s) would you like to see more in your life? What negative traits do you need to put behind you?
[Your Response Here]
10) Many church traditions recite the Apostles' Creed or the Nicene Creed. In 3:14–16, we find another statement of common belief (probably an early church hymn). If you were to summarize in a handful of statements what you believe, what would those statements be?
[Your Response Here]
11) What truths in Paul's "hymn" really stand out to you? Use these words as a model to write out your own hymn of praise to the Lord.
[Your Response Here]
PERSONAL RESPONSE
Write out additional reflections, questions you may have, or a prayer.
[Your Response Here]
**5**
FALSE TEACHING VERSUS TRUTH
_1 Timothy 4:1–16_
DRAWING NEAR
What kind of acceptance and tolerance do you think the Bible advocates?
[Your Response Here]
How does this compare or contrast with the brand of "tolerance" championed by our culture?
[Your Response Here]
When, if ever, do you think it is appropriate to confront another person about a false teaching they are following?
[Your Response Here]
THE CONTEXT
Since the beginning of time, the earth has been at the center of the cosmic war between God and Satan. God reveals Himself through His Word and calls on people to respond. Satan attempts to blind human beings to the truth of God. The result is that many people believe satanic perversions to be the truth.
Ephesus was clearly inundated with false teachers. In chapters 2–3, the apostle Paul addressed some of the problems caused by these purveyors of spiritual error. He restated God's standards for leadership in the church and ended chapter 3 with a hymn affirming the essential truth of Christianity: the person and work of Jesus Christ. Now Paul deals directly with the false teachers themselves, focusing on their origin and content. He asserts that any tolerance of error is dishonoring to the God of truth. No deviations are to be allowed, and anyone who champions ungodly ideas is to be publicly rebuked.
KEYS TO THE TEXT
_Godliness:_ This is a key word throughout the entire letter (3:16; 4:7–8; 6:3, 5–6, 11), indicating the need for the church to be called back to their pattern of holy living, which had been negatively affected by false doctrine. Godliness refers to having the proper attitude and response to God. It refers to the truths of salvation and righteousness in Christ, which produce holiness in believers—a manifestation of true and perfect righteousness in Jesus Christ.
_Doctrine:_ A body of beliefs about God, humankind, Christ, the church, and other related concepts that are considered authoritative and thus worthy of acceptance by all members of the community of faith. Christ condemned the doctrine of the Pharisees because it was of human origin (Matt. 15:9; Mark 7:7). After Pentecost, Christian doctrine began to be systematized (Acts 2:42). The earliest doctrine of the Christian church declared: (1) that Jesus was the Messiah, the Christ; (2) that God had raised Him from the dead; and (3) that salvation was by faith in His name. These three truths were presented as a clear fulfillment of the promises of the Old Testament. Paul taught that true doctrine is essential for Christian growth (Eph. 4:11–16; 1 Tim. 4:6; 6:3; Titus 1:9) and that false doctrine destroys the church (Eph. 4:14; 2 Tim. 4:3). ( _Nelson's New Illustrated Bible Dictionary_ )
UNLEASHING THE TEXT
Read 4:1–16, noting the key words and definitions next to the passage.
**1 Timothy 4:1–16 (NKJV)**
**1** _Now the Spirit expressly says that in latter times some will depart from the faith, giving heed to deceiving spirits and doctrines of demons,_
**_the Spirit expressly says_** (v. 1)—Paul repeats to Timothy the warning he had given many years earlier to the Ephesian elders (Acts 20:29–30). The Holy Spirit through the Scriptures has repeatedly warned of the danger of apostasy (see Matt. 24:4–12; Acts 20:29–30; 2 Thess. 2:3–12; Heb. 3:12; 5:11–6:8; 10:26–31; 2 Pet. 3:3; 1 John 2:18; Jude 18).
**_in latter times._** (v. 1)—The period from the first coming of Christ until His return (Acts 2:16–17; Heb. 1:1–2; 9:26; 1 Pet. 1:20; 1 John 2:18). Apostasy will exist throughout that period, reaching a climax shortly before Christ returns (see Matt. 24:12).
**_depart from the faith_** (v. 1)—Those who fall prey to the false teachers will abandon the Christian faith. The Greek word for "depart" is the source of the English word "apostatize" and refers to someone moving away from an original position. These are professing or nominal Christians who associate with those who truly believe the gospel, but defect after believing lies and deception, thus revealing their true nature as unconverted (see 1 John 2:19).
**_deceiving spirits_** (v. 1)—This refers to those demonic spirits, either directly or through false teachers, who have wandered away from the truth and lead others to do the same. The most defining word to describe the entire operation of Satan and his demons is "deception" (see John 8:44).
**_doctrines of demons_** (v. 1)—This is not teaching about demons, but false teaching that originates from them. To sit under such teaching is to hear lies from the demonic realm (Eph. 6:12; James 3:15). The influence of demons will reach its peak during the Tribulation (2 Thess. 2:9; Rev. 9:2–11; 16:14; 20:2–3, 8, 10). Satan and demons constantly work the deceptions that corrupt and pervert God's Word.
**2** _speaking lies in hypocrisy, having their own conscience seared with a hot iron,_
**_speaking lies in hypocrisy_** (v. 2)—Literally "hypocritical lie-speakers," this refers to the human false teachers who propagate demon doctrine (see 1 John 4:1).
**_seared_** (v. 2)—This is a medical term referring to cauterization. False teachers can teach their hypocritical lies because their consciences have been desensitized (see Eph. 4:19), as if all the nerves that make them feel had been destroyed and turned into scar tissue by the burning of demonic deception.
**3** _forbidding to marry, and commanding to abstain from foods which God created to be received with thanksgiving by those who believe and know the truth._
**_forbidding to marry, and commanding to abstain from foods_** (v. 3)—This is a sample of the false teaching at Ephesus. Typically, it contained elements of truth, since Scripture commends both singleness (1 Cor. 7:25–35) and fasting (Matt. 6:16–17; 9:14–15). The deception came in making such human works a prerequisite for salvation—a distinguishing mark of all false religion. This ascetic teaching was probably influenced both by the Jewish sect known as the Essenes and contemporary Greek thought (which viewed matter as evil and spirit as good). Paul addressed this asceticism in Colossians 2:21–23. Neither celibacy nor any form of diet saves or sanctifies.
**4** _For every creature of God is good, and nothing is to be refused if it is received with thanksgiving;_
**_every creature of God is good_** (v. 4)—The false teachers' asceticism contradicted Scripture, which teaches that since God created both marriage and food (Gen. 1:28–31; 2:18–24; 9:3), they are intrinsically good (Gen. 1:31) and to be enjoyed with gratitude by believers. Obviously food and marriage are essential for life and procreation.
**5** _for it is sanctified by the word of God and prayer._
**_sanctified_** (v. 5)—This means to be set apart or dedicated to God for holy use. The means for accomplishing this are through thankful prayer and an understanding that the Word of God has set aside the temporary Mosaic dietary restrictions (Mark 7:19; Acts 10:9–15; Rom. 14:1–12; Col. 2:16–17). Contrast the unbeliever whose inner corruption and evil motives corrupt every good thing (Titus 1:15).
**6** _If you instruct the brethren in these things, you will be a good minister of Jesus Christ, nourished in the words of faith and of the good doctrine which you have carefully followed._
**_nourished . . . words of faith . . . good doctrine_** (v. 6)—Continual feeding on the truths of Scripture is essential to the spiritual health of all Christians (2 Tim. 3:16–17), but especially of spiritual leaders like Timothy. Only by reading the Word, studying it, meditating on it, and mastering its contents can a pastor fulfill his mandate (2 Tim. 2:15). Timothy had been doing so since childhood (2 Tim. 3:15), and Paul urged him to continue (see v. 16; 2 Tim. 3:14). "Words of faith" is a general reference to Scripture, God's revealed truth. "Good doctrine" indicates the theology Scripture teaches.
**7** _But reject profane and old wives' fables, and exercise yourself toward godliness._
**_reject profane and old wives' fables_** (v. 7)—In addition to being committed to God's Word (see note on v. 6), believers must avoid all false teaching. Paul denounced such error as "profane" (worldly; the opposite of what is holy) "fables" _(mytho_ s, from which the English word _myths_ derives), fit only for "old wives" (a common epithet denoting something fit only for the uneducated and philosophically unsophisticated).
**_exercise yourself_** (v. 7)—"Exercise" is an athletic term denoting the rigorous, self-sacrificing training an athlete undergoes.
**8** _For bodily exercise profits a little, but godliness is profitable for all things, having promise of the life that now is and of that which is to come._
**_profits a little_** (v. 8)—Bodily exercise is limited both in extent and duration; it affects only the physical body during this earthly life.
**_profitable for all things_** (v. 8)—in time and eternity
**9** _This is a faithful saying and worthy of all acceptance._
**10** _For to this end we both labor and suffer reproach, because we trust in the living God, who is the Savior of all men, especially of those who believe._
**_trust_** (v. 10)—This could also be "hope." Believers are saved in hope (see Rom. 8:24), and live and serve in light of that hope of eternal life (Titus 1:2; 3:7; see also Rom. 5:2). Working to the point of exhaustion and suffering rejection and persecution are acceptable because believers understand they are doing God's work—which is the work of salvation. That makes it worth all of the sacrifices (Phil. 1:12–18, 27–30; 2:17; Col. 1:24–25; 2 Tim. 1:6–12; 2:3–4, 9–10; 4:5–8).
**_the Savior of all men, especially of those who believe_** (v. 10)—Paul is obviously not teaching universalism, that all people will be saved in the spiritual and eternal sense, since the rest of Scripture clearly teaches that God will not save everyone. In fact, most adults will reject Him and spend eternity in hell (Matt. 25:41, 46; Rev. 20:11–15). Yet, the Greek word translated "especially" must mean that all men enjoy God's salvation in some way like those who believe enjoy His salvation. The simple explanation is that God is the Savior of all men, in a temporal sense, while He is the Savior of believers in an eternal sense. Paul's point is that while God graciously delivers believers from sin's condemnation and penalty because He was their substitute (2 Cor. 5:21), all men experience some earthly benefits from the goodness of God. Those benefits are (1) common grace—a term that describes God's goodness shown to all mankind universally (Ps. 145:9) in restraining sin (Rom. 2:15) and judgment (Rom. 2:3–6), maintaining order in society through government (Rom. 13:1–5), enabling man to appreciate beauty and goodness (Ps. 50:2), and showering him with temporal blessings (Matt. 5:45; Acts 14:15–17; 17:25); (2) compassion—the broken-hearted love of pity God shows to undeserving, unregenerate sinners (Exod. 34:6–7; Ps. 86:5; Dan. 9:9; Matt. 23:37; Luke 19:41–44; see Isa. 16:11–13; Jer. 48:35–37); (3) admonition to repent—God constantly warns sinners of their fate, demonstrating the heart of a compassionate Creator who has no pleasure in the death of the wicked (Ezek. 18:30–32; 33:11); and (4) the gospel invitation—salvation in Christ is indiscriminately offered to all (Matt. 11:28–29; 22:2–14; John 6:35–40; Rev. 22:17; see also John 5:39–40). God is, by nature, a saving God. That is, He finds no pleasure in the death of sinners. His saving character is revealed even in how He deals with those who will never believe, but only in those four temporal ways. See the notes on 2:6.
**11** _These things command and teach._
**12** _Let no one despise your youth, but be an example to the believers in word, in conduct, in love, in spirit, in faith, in purity._
**_Let no one despise your youth_** (v. 12)—Greek culture placed great value on age and experience. Since Timothy was in his thirties, still young by the standards of that culture, he would have to earn respect by being a godly example. Because he had been with Paul since a young teenager, Timothy had much experience to mature him, so that looking down on him because he was under forty was inexcusable.
**_be an example . . . in purity_** (v. 12)—Paul lists five areas (the better Greek manuscripts omit "in spirit") in which Timothy was to be an example to the church: "word" (speech; see Matt. 12:34–37; Eph. 4:25, 29, 31); "conduct" (righteous living; see Titus 2:10; 1 Pet. 1:15; 2:12; 3:16); "love" (self-sacrificial service for others; see John 15:13); "faith" (not belief, but faithfulness or commitment; see 1 Cor. 4:2); "purity" (especially sexual purity; see 3:2). Timothy's exemplary life in those areas would offset the disadvantage of his youth.
**13** _Till I come, give attention to reading, to exhortation, to doctrine._
**_Till I come_** (v. 13)—See the note on 3:14.
**_give attention . . . to doctrine_** (v. 13)—These things were to be Timothy's constant practice; his way of life. "Reading" refers to the custom of public reading of Scripture in the church's worship service, followed by the exposition of the passage that had been read (see Neh. 8:1–8; Luke 4:16–27). "Exhortation" challenges those who hear the Word to apply it in their daily lives. It may involve rebuke, warning, encouragement, or comfort. "Doctrine" (teaching) refers to systematic instruction from the Word of God (see 3:2; Titus 1:9).
**14** _Do not neglect the gift that is in you, which was given to you by prophecy with the laying on of the hands of the eldership._
**_the gift_** (v. 14)—This refers to that grace given to Timothy and to all believers at salvation, which consisted of a God-designed, Spirit-empowered spiritual ability for the use of ministry (see Rom. 12:4–8; 1 Cor. 12:4–12; 1 Pet. 4:10–11). Timothy's gift (see 2 Tim. 1:6) was leadership with special emphasis on preaching (2 Tim. 4:2) and teaching (vv. 6, 11, 13; 6:2).
**_by prophecy_** (v. 14)—Timothy's gift was identified by a revelation from God (see note on 1:18) and apostolic confirmation (2 Tim. 1:6), probably when he joined Paul on the apostle's second missionary journey (Acts 16:1–3).
**_laying on of the hands of the eldership_** (v. 14)—See the note on 5:22. This public affirmation of Timothy's call to the ministry likely took place at the same time as the prophecy (see 2 Tim. 1:6). His call to the ministry was thus confirmed subjectively (by means of his spiritual gift), objectively (through the prophecy made about him), and collectively (by the affirmation of apostles and the church, represented by the elders).
**15** _Meditate on these things; give yourself entirely to them, that your progress may be evident to all._
**_progress_** (v. 15)—The word was used in military terms of an advancing force and in general terms of advancement in learning, understanding, or knowledge. Paul exhorted Timothy to let his progress toward Christlikeness be evident to all.
**16** _Take heed to yourself and to the doctrine. Continue in them, for in doing this you will save both yourself and those who hear you._
**_to yourself and to the doctrine_** (v. 16)—The priorities of a godly leader are summed up in his personal holiness and public teaching. All of Paul's exhortations in verses 6–16 fit into one or the other of those two categories.
**_you will save . . . yourself_** (v. 16)—Perseverance in believing the truth always accompanies genuine conversion (see Matt. 24:13; John 8:31; Rom. 2:7; Phil. 2:12–13; Col. 1:23).
**_those who hear you_** (v. 16)—By careful attention to his own godly life and faithful preaching of the Word, Timothy would continue to be the human instrument God used to bring the gospel and to save some who heard him. Though salvation is God's work, it is His pleasure to do it through human instruments.
1) What do Paul's harsh words about the purveyors of false teaching tell you about the importance of truth (vv. 1–5)?
[Your Response Here]
_(Verses to consider: Matt. 24:4–12; Acts 20:2–30; Col. 2:16–23)_
2) Describe the personal character qualities of an excellent minister spotlighted by Paul in 4:6–11.
[Your Response Here]
3) What ministry standards of excellence are expected of church leaders (4:12–16)?
[Your Response Here]
_(Verses to consider: 1 Pet. 4:10–11)_
4) Note the advice Paul gives to Timothy in verses 12–14. What does it mean to be an "example" of these things?
[Your Response Here]
GOING DEEPER
Paul never taught what he himself did not do. Read about his faithful leadership in 1 Thessalonians 2:7–12.
**7** _But we were gentle among you, just as a nursing mother cherishes her own children._
**8** _So, affectionately longing for you, we were well pleased to impart to you not only the gospel of God, but also our own lives, because you had become dear to us._
**9** _For you remember, brethren, our labor and toil; for laboring night and day, that we might not be a burden to any of you, we preached to you the gospel of God._
**10** _You are witnesses, and God also, how devoutly and justly and blamelessly we behaved ourselves among you who believe;_
**11** _as you know how we exhorted, and comforted, and charged every one of you, as a father does his own children,_
**12** _that you would walk worthy of God who calls you into His own kingdom and glory._
EXPLORING THE MEANING
5) How did Paul model the spiritual virtues of love and servanthood when ministering to the Thessalonians?
[Your Response Here]
6) For what purpose did Paul exhort and encourage these churches? What was his ultimate goal for them?
[Your Response Here]
7) Read 2 Peter 2:1 and Revelation 12:9. What role does the enemy play in propagating false doctrine? What end awaits both Satan and false teachers?
[Your Response Here]
8) Read 1 Corinthians 9:24–27. In what ways is spiritual self-discipline the path to godly living?
[Your Response Here]
_(Verses to consider Matt. 25:21; 2 Cor. 7:1; 2 Tim. 2:3–5)_
TRUTH FOR TODAY
The single greatest tool of leadership is the power of an exemplary life. The Puritan writer Thomas Brooks said, "Example is the most powerful rhetoric." Setting an example of godly living that others can follow is the _sine qua non_ of excellence in ministry. When a manifest pattern of godliness is missing, the power is drained out of preaching, leaving it a hollow, empty shell. A minister's life is his most powerful message, and must reinforce what he says or he may as well not say it. Authoritative preaching is undermined if there is not a virtuous life backing it up.
REFLECTING ON THE TEXT
9) Paul spoke to Timothy of the need to be "nourished in the words of faith" (v. 6). Describe your biblical diet. Are you being nourished regularly through the reading of the Scriptures, or are you malnourished? What needs to change?
[Your Response Here]
10) What spiritual disciplines do you need to practice this week in order to pursue godliness with more consistency?
[Your Response Here]
11) This passage speaks of being an example to other believers and living in such a way that your spiritual progress is obvious to all. Evaluate yourself in these regards. What kind of an example are you? How evident is your spiritual progress? What one change can you make that would make a real difference in your spiritual growth?
[Your Response Here]
PERSONAL RESPONSE
Write out additional reflections, questions you may have, or a prayer.
[Your Response Here]
ADDITIONAL NOTES
[Your Response Here]
**6**
PASTORAL RESPONSIBILITIES
_1 Timothy 5:1–6:2_
DRAWING NEAR
When it comes to caring for the elderly and needy, who on the following list should bear the responsibility:
the government?
the extended family?
the church?
the individuals themselves?
Why do you think so?
[Your Response Here]
Think about different pastors or elders you have known. Who stands out in your mind as having served with exceptional commitment and excellence? What sets them apart? How have you personally benefited from their ministry?
[Your Response Here]
THE CONTEXT
No amount of formal training can prepare a pastor for every contingency he will face in the Lord's work. This is true now and it was true in the first century. Thus, it is not surprising to find a passage like this one that contains a broad array of Spirit-inspired counsel for Timothy, the young leader of the Ephesian church.
In this passage Paul discusses several areas of church business. He gives the Scriptural mandate to respect the older men and women in the church, and to care for women who have lost their husbands. God's great concern for widows only reinforces this command (see Deut. 26:10–12; Ps. 68:5; James 1:27). Paul then explains how to restore proper pastoral oversight, and sets forth the church's obligations to honor, protect, rebuke, and select elders. He offers instructions for servants and masters, so perhaps the Ephesian believers were struggling to maintain a biblical work ethic in the world of slavery. One can only imagine the great delight Timothy must have felt when he first read this relevant and immensely practical bit of wise, heaven-sent counsel.
KEYS TO THE TEXT
_Exhort:_ Literally "to call to one's side," this emphasizes a strong urging, directing, and insisting on following the principles for correct behavior in the workplace. This Greek word refers to coming alongside someone to help, and is related to a title for the Holy Spirit (see John 14:16, 26; 15:26; 16:7). It may best be translated "strengthen." We are to strengthen our fellow believers (see Gal. 6:1–2) in the same way the Scripture and the Holy Spirit do.
_Bondservants:_ This can be translated "slaves." First-century slaves resembled the indentured servants of the American colonial period. In many cases, slaves were better off than day laborers, since much of their food, clothing, and shelter was provided. The system of slavery served as the economic structure in the Roman world, and the master-slave relationship closely parallels the modern employer-employee relationship. This term also refers to people who are in submission to another, and is often used in connection with Jesus serving the Father (Phil. 2:7), and believers serving God (1 Pet. 2:16; Rom. 1:1; Gal. 1:10; 2 Tim. 2:24; James 1:1) and other believers (Gal. 5:13).
UNLEASHING THE TEXT
Read 5:1–6:2, noting the key words and definitions next to the passage.
**1 Timothy 5:1–6:2 (NKJV)**
**1** _Do not rebuke an older man, but exhort him as a father, younger men as brothers,_
**_rebuke_** (v. 1)—Some translations add "sharply" to the word "rebuke," which fills out the intensity of the Greek term. An older sinning believer is to be shown respect by not being addressed with harsh words (see 2 Tim. 2:24–25).
**_an older man_** (v. 1)—in this context, the Greek is indicating older men generally, not the office of elder. the younger Timothy was to confront sinning older men with deference and honor, which is clearly inferred from Old Testament principles (see Lev. 19:32; Job 32:4, 6; Prov. 4:1–4; 16:31; 20:29).
**2** _older women as mothers, younger women as sisters, with all purity._
**3** _Honor widows who are really widows._
**_Honor_** (v. 3)—This means "to show respect or care," "to support," or "to treat graciously." Although it includes meeting all kinds of needs, Paul had in mind here not only this broad definition but primarily financial support (see Exod. 20:12; Matt. 15:1–6; 27:9).
**_really widows_** (v. 3)—Not all widows are truly alone and without resources. Financial support from the church is mandatory only for widows who have no means to provide for their daily needs.
**4** _But if any widow has children or grandchildren, let them first learn to show piety at home and to repay their parents; for this is good and acceptable before God._
**_widow has children or grandchildren_** (v. 4)—Families, not the church, have the first responsibility for their own widows.
**_repay their parents_** (v. 4)—Children and grandchildren are indebted to those who brought them into the world, reared them, and loved them. Fulfilling this responsibility is a mark of godly obedience (see Exod. 20:12).
**5** _Now she who is really a widow, and left alone, trusts in God and continues in supplications and prayers night and day._
**_left alone_** (v. 5)—See the note on verse 3. The form of this Greek word denotes a permanent condition of being forsaken and left without resources. She is "really" a widow, since there is no family to support her.
**_trusts in God_** (v. 5)—a continual state or settled attitude of hope in God (see 1 Kings 17:8–16; Jer. 49:11). Since she has no one else, she pleads with God as her only hope.
**6** _But she who lives in pleasure is dead while she lives._
**_dead while she lives_** (v. 6)— a widow who lives a worldly, immoral, ungodly life may be alive physically, but her lifestyle proves she is unregenerate and spiritually dead (see Eph. 2:1).
**7** _And these things command, that they may be blameless._
**_blameless_** (v. 7)—Means "above reproach," so that no one can fault their conduct.
**8** _But if anyone does not provide for his own, and especially for those of his household, he has denied the faith and is worse than an unbeliever._
**_if_** (v. 8)—This would be better translated "since." Paul negatively restated the positive principle of verse 4, using the Greek construction that implies the condition is true, suggesting that there were numerous violations of that principle at Ephesus. Any believer who fails to obey this command is guilty of (1) denying the principle of compassionate Christian love (see John 13:35; Rom. 5:5; 1 Thess. 4:9); and (2) being "worse than an unbeliever." Most pagans naturally fulfill this duty, so believers who have God's command and power to carry it out and do not, behave worse than pagans (see 1 Cor. 5:1–2.).
**9** _Do not let a widow under sixty years old be taken into the number, and not unless she has been the wife of one man,_
**_under sixty_** (v. 9)—In New Testament culture, sixty was considered retirement age. By that age, older women would have completed their child-rearing and would have the time, maturity, and character to devote their lives in service to God and the church. They also would not be likely to remarry and become preoccupied with that commitment.
**_be taken into the number_** (v. 9)—More clearly rendered, "be put on the list." This was not a list of those widows eligible for specially recognized church support (all widows in the church who had no other means of support were; v. 3), but rather those eligible for specially recognized church ministry (see Titus 2:3–5).
**_the wife of one man_** (v. 9)—Literally "one-man woman" (see 3:2, 12). It does not exclude women who have been married more than once (see v. 14; 1 Cor. 7:39), but it refers to a woman totally devoted and faithful to her husband, a wife who had displayed purity of thought and action in her marriage.
**10** _well reported for good works: if she has brought up children, if she has lodged strangers, if she has washed the saints' feet, if she has relieved the afflicted, if she has diligently followed every good work._
**_has brought up children_** (v. 10)—This views the godly widow as a Christian mother who has nourished or reared children that have followed the Lord (see note on 2:15).
**_washed the saints' feet_** (v. 10)—This refers to the menial duty of slaves. It is used literally and metaphorically of widows who have humble servants' hearts (see John 13:5–17).
**_every good work_** (v. 10)—See Dorcas in Acts 9:36–39.
**11** _But refuse the younger widows; for when they have begun to grow wanton against Christ, they desire to marry,_
**_to grow wanton_** (v. 11)—This would be better translated "to feel the impulses of sensual desires"—an expression that includes all that is involved in the marriage relationship, including sexual passion. Paul saw the danger that younger widows might want to escape from their vows to remain single (see note on v. 12) and be devoted only to God's service (see Num. 30:9); he knew the negative impact such feelings could have on young widows' personal lives and ministry within the church. Such women were also marked out by false teachers as easy prey (2 Tim. 3:6–7), causing them to leave the truth (v. 15).
**12** _having condemnation because they have cast off their first faith._
**_cast off their first faith_** (v. 12)—in classical Greek, "faith" could also mean "pledge." Taken that way here, it refers to a specific covenant young widows made when asking to be included on the widows' list. Likely, they promised to devote the rest of their lives in service to the church and the Lord. Though well-meaning at the time of their need and bereavement, they were surely to desire marriage again (see v. 11), and thus renege on their original pledge.
**13** _And besides they learn to be idle, wandering about from house to house, and not only idle but also gossips and busybodies, saying things which they ought not._
**_gossips_** (v. 13)—Such people speak nonsense, talk idly, make empty charges, or even accuse others with malicious words. This idleness and talk also made them suitable targets for the false teachers (1:6).
**_busybodies_** (v. 13)—Literally "one who moves around," this implies that such people pry into things that do not concern them; they do not mind their own business.
**14** _Therefore I desire that the younger widows marry, bear children, manage the house, give no opportunity to the adversary to speak reproachfully._
**_bear children_** (v. 14)—The younger widows were still of childbearing age. Although they had lost their first husbands, there was still the potential privilege and blessing of remarrying and having children (see notes on 2:15; see Ps. 127:3, 5).
**_manage the house_** (v. 14)—The Greek term denotes all the aspects of household administration, not merely the rearing of children. The home is the domain where a married woman fulfills herself in God's design (see Titus 2:4–5).
**15** _For some have already turned aside after Satan._
**_Satan_** (v. 15)—the devil, the believer's adversary (see Job 1:6–12; 2:1–7; Isa. 14:12–15; Ezek. 28:12–15; Rev. 12:9)
**16** _If any believing man or woman has widows, let them relieve them, and do not let the church be burdened, that it may relieve those who are really widows._
**_woman_** (v. 16)—Paul restates the message of verses 4–8 with the addition that as the situation warrants, Christian women are included in this responsibility for support of widows.
**17** _Let the elders who rule well be counted worthy of double honor, especially those who labor in the word and doctrine._
**_elders_** (v. 17)—This identifies the "bishop" (3:1) or overseer, who is also called pastor (Eph. 4:11) (see notes on 3:1–7; Titus 1:6–9).
**_rule well_** (v. 17)—Elders are spiritual rulers in the church (see 1 Thess. 5:12–13; Heb. 13:7, 17).
**_double honor_** (v. 17)—Elders who serve with greater commitment, excellence, and effort should have greater acknowledgment from their congregations. This expression does not mean such men should receive exactly twice as much remuneration as others, but because they have earned such respect, it should be paid to them more generously.
**_especially_** (v. 17)—This means "chiefly" or "particularly." Implicit is the idea that some elders will work harder than others and be more prominent in ministry.
**_labor_** (v. 17)—Literally "work to the point of fatigue or exhaustion," this Greek word stresses the effort behind the work more than the amount of work.
**_word and doctrine_** (v. 17)—This would be better translated "preaching and teaching" (see note on 4:13). The first emphasizes proclamation, along with exhortation and admonition, and calls for a heart response to the Lord. The second is an essential fortification against heresy and puts more stress on instruction.
**18** _For the Scripture says, "You shall not muzzle an ox while it treads out the grain," and, "The laborer is worthy of his wages."_
**_for the Scripture says_** (v. 18)—a typical formula for introducing biblical references, in this instance both an Old Testament (Deut. 25:4) and New Testament (Luke 10:7) one. It is also very significant that this is a case of one New Testament writer (Paul) affirming the inspiration of another by referring to Luke's writing as "Scripture" (see 2 Pet. 3:15–16), which shows the high view that the early church took of New Testament Scripture.
**19** _Do not receive an accusation against an elder except from two or three witnesses._
**_two or three witnesses_** (v. 19)—Serious accusations against elders must be investigated and confirmed by the same process as established in Matthew 18:15–20. This process for the whole church also applies to elders. This demand does not place elders beyond successful accusation, but protects them from frivolous, evil accusers, by demanding the same process of confirmation of sin as for all in the church.
**20** _Those who are sinning rebuke in the presence of all, that the rest also may fear._
**_Those who are sinning_** (v. 20)—elders who continue in any kind of sin after the confrontation of two or three witnesses, especially any that violates the qualifications to serve (3:2–7)
**_in the presence of all_** (v. 20)—This refers to the other elders and the congregation. The third step of confrontation, established in Matthew 18:17, is to tell the church, so that they can all confront the person and call him to repentance.
**21** _I charge you before God and the Lord Jesus Christ and the elect angels that you observe these things without prejudice, doing nothing with partiality._
**_charge . . . God . . . Lord_** (v. 21)—See 6:13; 2 Timothy 4:1.
**_the elect angels_** (v. 21)—This refers to "chosen angels," the unfallen angels, as opposed to Satan and his demons. This indicates that God's sovereign purpose to choose those beings who would be part of His eternal kingdom included angels whom He chose to eternal glory. Christians are also called "elect" (Rom. 8:33; 11:7; Col. 3:12; 2 Tim. 2:10; Titus 1:1; 1 Pet. 1:2; 2 John 1, 13).
**_without prejudice . . . partiality_** (v. 21)—All discipline of elders is to be done fairly, without prejudgment or personal preference, according to the standards of Scripture.
**22** _Do not lay hands on anyone hastily, nor share in other people's sins; keep yourself pure._
**_Do not lay hands on . . . hastily_** (v. 22)—This refers to the ceremony that affirmed a man's suitability for and acceptance into public ministry as an elder/pastor/overseer. This came from the Old Testament practice of laying hands on a sacrificial animal to identify with it (Exod. 29:10, 15, 19; Lev. 4:15; see also Num. 8:10; 27:18–23; Deut. 34:9; Matt. 19:15; Acts 8:17–18; 9:17; Heb. 6:2). "Hastily" refers to proceeding with this ceremony without a thorough investigation and preparation period to be certain of the man's qualifications (as in 3:1–7).
**_nor share in other people's sins_** (v. 22)—This refers to the sin of hasty ordination, which makes those responsible culpable for the man's sin of serving as an unqualified elder and, thus, misleading people.
**_keep yourself pure_** (v. 22)—Some versions translate "pure" as "free from sin." Paul wanted Timothy, by not participating in the recognition of unqualified elders, to remain untainted by others' sins. The church desperately needed qualified spiritual leaders, but the selection had to be carefully executed.
**23** _No longer drink only water, but use a little wine for your stomach's sake and your frequent infirmities._
**_No longer drink only water_** (v. 23)—Water in the ancient world was often polluted and carried many diseases. Therefore Paul urged Timothy not to risk illness, not even for the sake of a commitment to abstinence from wine. Apparently Timothy avoided wine so as not to place himself in harm's way (see note on 3:3).
**_use a little wine . . . infirmities_** (v. 23)—Paul wanted Timothy to use wine which, because of fermentation, acted as a disinfectant to protect his health from the harmful effects of impure water. With this advice, however, Paul was not advocating that Timothy lower the high standard of behavior for leaders (see Num. 6:1–4; Prov. 31:4–5).
**24** _Some men's sins are clearly evident, preceding them to judgment, but those of some men follow later._
**_sins are clearly evident_** (v. 24)—The sins of some men are manifest for all to see, thus disqualifying them out of hand for service as elders.
**_preceding them to judgment_** (v. 24)—The known sins of the unqualified announce those men's guilt and unfitness before all. "Judgment" refers to the church's process for determining men's suitability to serve as elders.
**_follow later_** (v. 24)—The sins of other candidates for elder will come to light in time, perhaps even during the scrutiny of the evaluation process.
**_under the yoke_** (v. 1)—a colloquial expression describing submissive service under another's authority, not necessarily describing an abusive relationship (see Matt. 11:28–30)
**_masters_** (v. 1)—The Greek word for "master," while giving us the English word "despot," does not carry a negative connotation. Instead, it refers to one with absolute and unrestricted authority.
**_all honor_** (v. 1)—This translates into diligent and faithful labor for one's employer (see Eph. 6:5–9; Col. 3:22–25).
**_His doctrine_** (v. 1)—This is the revelation of God summed up in the gospel. How believers act while under the authority of another affects how people view the message of salvation Christians proclaim (see Titus 2:5–14). Displaying a proper attitude of submission and respect, and performing quality work, help make the gospel message believable (Matt. 5:48).
**_believing masters_** (v. 2)—The tendency might be to assume one's equality in Christ with a Christian master and disdain the authority related to work roles. On the contrary, working for a Christian should produce more loyal and diligent service out of love for the brethren.
**25** _Likewise, the good works of some are clearly evident, and those that are otherwise cannot be hidden._
**6:1** _Let as many bondservants as are under the yoke count their own masters worthy of all honor, so that the name of God and His doctrine may not be blasphemed._
**2** _And those who have believing masters, let them not despise them because they are brethren, but rather serve them because those who are benefited are believers and beloved. Teach and exhort these things._
1) What counsel does Paul give for dealing with sin in the spiritual family (5:1–2, 19–20)?
[Your Response Here]
2) How were widows to be cared for (5:3–16)? What distinctions were made, and why?
[Your Response Here]
_(Verses to consider: Exod. 22:22–24; Deut. 26:10–12; James 1:27)_
3) Put in your own words the gist of Paul's instruction about biblical eldership (5:17–25).
[Your Response Here]
_(Verses to consider: Acts 20:28; 1 Thess. 5:12, 13; Heb. 13:7, 17)_
4) What principles did Paul give regarding acceptable behavior for Christian employees (6:1–2)?
[Your Response Here]
_(Verses to consider: 1 Cor. 10:31; Eph. 6:5–8; Col. 3:22–25; Titus 2:9–10)_
GOING DEEPER
For more of Paul's teaching about employee/employer relationships, read Ephesians 6:5–9.
**5** _Bondservants, be obedient to those who are your masters according to the flesh, with fear and trembling, in sincerity of heart, as to Christ;_
**6** _not with eyeservice, as men-pleasers, but as bondservants of Christ, doing the will of God from the heart,_
**7** _with goodwill doing service, as to the Lord, and not to men,_
**8** _knowing that whatever good anyone does, he will receive the same from the Lord, whether he is a slave or free._
**9** _And you, masters, do the same things to them, giving up threatening, knowing that your own Master also is in heaven, and there is no partiality with Him._
EXPLORING THE MEANING
5) What attitudes should Christian employers and employees have? Why do you think Paul gave these specific instructions?
[Your Response Here]
6) Read Luke 7:11–17 for an encounter that Jesus had with a needy widow. What makes the raising of this young man especially poignant? What do we learn about the heart of God from this miracle?
[Your Response Here]
7) Read 1 Corinthians 9:1–14. What does Paul say here about elders being entitled to financial support?
[Your Response Here]
_(Verses to consider: Luke 10:7; Phil. 4:10–20)_
TRUTH FOR TODAY
For the believer, work is a sacred duty. A Christian sees everything he does in reference to his relationship with God. The Reformers stressed that point. There is no aspect of life or conduct, however apparently insignificant, which should not be directed to the glory of God. Every legitimate job has intrinsic value because it is the arena in which believers live out their Christian lives. Christianity is not a hothouse religion, but one that survives and triumphs in the real world. Believers most commonly interact with that world in the work place, as they live out their faith on their jobs. They are to be a "city that is set on a hill" (Matt. 5:14). Christians must be concerned that their conduct on the job shows others the power of Jesus Christ to transform a life. Believers' work performance will bring either praise or blasphemy to the name of God.
REFLECTING ON THE TEXT
8) Think about a practical and specific way in which you can be a more excellent employee this week. Write down your ideas.
[Your Response Here]
9) Do you have any close Christian friends who are engaged in sinful or questionable behaviors? What is God leading you to do—exhort them gently, pray for them, other?
[Your Response Here]
10) What widows in your church can you encourage and help this week? List some specific ways you could offer assistance.
[Your Response Here]
PERSONAL RESPONSE
Write out additional reflections, questions you may have, or a prayer.
[Your Response Here]
**7**
THE MAN OF GOD
_1 Timothy 6:3–21_
DRAWING NEAR
In this study, Paul warns Timothy about the dangers of greed. What material possessions do you worry most about losing? Why?
[Your Response Here]
If you can, describe a time in your life when you truly experienced contentment. Explain the circumstances.
[Your Response Here]
THE CONTEXT
As this letter comes to a close, Paul wraps up his instructions to Timothy by giving some further identifying markers for false and corrupt teachers in the church. He counsels the young pastor what to teach those who are rich in material possessions, those who have more than the mere essentials of food, clothing, and shelter. Paul does not condemn such people, nor command them to get rid of their wealth. He does call them to be good stewards of their God-given resources.
He fervently urges his protégé to resist all these temptations and to cling to his divine calling. Timothy was the "man of God" for the church at Ephesus. His effectiveness would depend upon what he fought for and what he fled from.
KEYS TO THE TEXT
_Contentment:_ This Greek word means "self-sufficiency"; stoic philosophers used it to describe a person who was unflappable and unmoved by external circumstances. Christians ought to be satisfied and sufficient, for God Himself is the source of true contentment. They should have no need to seek for more than what God has already supplied in and through Himself.
_Man of God:_ A term used in the New Testament only for Timothy (see 2 Tim. 3:17). As a technical term it is used about seventy times in the Old Testament, always to refer to a man who officially spoke for God (see Deut. 33:1). This indicates that the letter is primarily directed to Timothy, exhorting him to be faithful and strong in light of persecution and difficulty—particularly with Paul's death drawing near. The man of God is known by what he flees from (v. 11), follows after (v. 11), fights for (v. 12), and is faithful to (vv. 13–14). The key to his success in all these endeavors can be found in the perfection produced in him by the Scriptures (2 Tim. 3:16–17).
UNLEASHING THE TEXT
Read 6:3–21, noting the key words and definitions next to the passage.
**1 Timothy 6:3–21 (NKJV)**
**3** _If anyone teaches otherwise and does not consent to wholesome words, even the words of our Lord Jesus Christ, and to the doctrine which accords with godliness,_
**_If anyone teaches . . ._** (vv. 3–5)—Paul identifies three characteristics of false teachers: (1) they "teach otherwise"—a different doctrine, or any teaching that contradicts God's revelation in Scripture; (2) they do "not consent to wholesome words"—they do not agree with sound, healthy teaching, specifically the teaching contained in Scripture; and (3) they reject "doctrine which accords with godliness"—teaching not based on Scripture will always result in an unholy life. Instead of godliness, false teachers will be marked by sin.
**4** _he is proud, knowing nothing, but is obsessed with disputes and arguments over words, from which come envy, strife, reviling, evil suspicions,_
**_disputes and arguments over words_** (v. 4)—"Disputes" refers to idle speculation; "arguments over words" literally means "word battles." Because proud, ignorant false teachers do not understand divine truth (2 Cor. 2:14), they obsess over terminology and attack the reliability and authority of Scripture. Every kind of strife is mentioned to indicate that false teachers produce nothing of benefit out of their fleshly, corrupt, and empty minds (v. 5).
**5** _useless wranglings of men of corrupt minds and destitute of the truth, who suppose that godliness is a means of gain. From such withdraw yourself._
**_destitute of the truth_** (v. 5)—These false teachers are in a state of apostasy; that is, although they once knew and seemed to embrace the truth, they turned to openly reject it. The Greek word for "destitute" means "to steal," "to rob," or "to deprive", and its form here indicates that someone or something was pulled away from contact with the truth (it does not mean they were ever saved).
**_a means of gain_** (v. 5)—Almost always behind all the efforts of the hypocritical, lying (4:2), false teachers is the driving motivation of monetary gain.
**_From such withdraw yourself._** (v. 5)—This phrase does not appear in the better manuscripts, although the idea expressed is self-evident.
**6** _Now godliness with contentment is great gain._
**7** _For we brought nothing into this world, and it is certain we can carry nothing out._
**8** _And having food and clothing, with these we shall be content._
**_having food and clothing . . . be content_** (v. 8)—the basic necessities of life are what ought to make Christians content. Paul does not condemn having possessions, as long as God graciously provides them (v. 17). He does, however, condemn a self-indulgent desire for money, which results from discontentment (see Matt. 6:33).
**9** _But those who desire to be rich fall into temptation and a snare, and into many foolish and harmful lusts which drown men in destruction and perdition._
**_desire to be rich fall into temptation_** (v. 9)—"Desire" refers to a settled wish born of reason and clearly describes those guilty of greed. The form of the Greek verb for "fall" indicates that those who have such a desire are continually falling into temptation. Greedy people are compulsive—they are continually trapped in sins by their consuming desire to acquire more.
**_destruction and perdition_** (v. 9)—Such greed may lead these people to suffer the tragic end of destruction and hell. These terms refer to the eternal punishment of the wicked.
**10** _For the love of money is a root of all kinds of evil, for which some have strayed from the faith in their greediness, and pierced themselves through with many sorrows._
**_love of money_** (v. 10)—This is literally "affection for silver." in the context, this sin applies to false teachers specifically, but the principle is true universally. Money itself is not evil since it is a gift from God (Deut. 8:18); Paul condemns only the love of it (see Matt. 6:24), which is so characteristic of false teachers (see 1 Pet. 5:2; 2 Pet. 2:1–3, 15).
**_strayed from the faith_** (v. 10)—This means they have strayed from the body of Christian truth. Gold has replaced God for these apostates, who have turned away from pursuing the things of God in favor of money.
**11** _But you, O man of God, flee these things and pursue righteousness, godliness, faith, love, patience, gentleness._
**_these things_** (v. 11)—love of money and all that goes with it (vv. 6–10), along with the other proud obsessions of false teachers (vv. 3–5)
**_righteousness, godliness_** (v. 11)—"Righteousness" means to do what is right, in relation to both God and man, and it emphasizes outward behavior. "Godliness" (see note on 2:2) refers to one's reverence for God and could be translated "God-likeness."
**12** _Fight the good fight of faith, lay hold on eternal life, to which you were also called and have confessed the good confession in the presence of many witnesses._
**_Fight the good fight of faith_** (v. 12)—The Greek word for "fight" gives us the English word _agoniz_ e, and was used in both military and athletic endeavors to describe the concentration, discipline, and extreme effort needed to win. The "good fight of faith" is the spiritual conflict with Satan's kingdom of darkness in which all men of God are necessarily involved.
**_lay hold on eternal life_** (v. 12)—Paul is here admonishing Timothy to "get a grip" on the reality of the matters associated with eternal life, so that he would live and minister with a heavenly and eternal perspective.
**_to which you were also called_** (v. 12)—refers to God's effectual, sovereign call of Timothy to salvation (see note on Rom. 1:7)
**_good confession_** (v. 12)—Timothy's public confession of faith in the Lord Jesus Christ, which likely occurred at his baptism and again when he was ordained to the ministry (4:14; 2 Tim. 1:6)
**13** _I urge you in the sight of God who gives life to all things, and before Christ Jesus who witnessed the good confession before Pontius Pilate,_
**_urge . . . God . . . Christ_** (v. 13)—See 5:21; see note on 2 Timothy 4:1.
**_the good confession before Pontius Pilate_** (v. 13)—Knowing that such a confession would cost Him His life, Jesus nevertheless confessed that He was truly the King and Messiah (John 18:33–37). He never evaded danger; He boldly and trustfully committed Himself to God who raises the dead.
**14** _that you keep this commandment without spot, blameless until our Lord Jesus Christ's appearing,_
**_this commandment_** (v. 14)—This refers to the entire revealed Word of God, which Paul charged Timothy to preach (2 Tim. 4:2). Paul also repeatedly encouraged Timothy to guard it (v. 20; 1 Tim. 1:18–19; 4:6, 16; 2 Tim. 1:13–4; 2:15–18).
**_appearing_** (v. 14)—This refers to the Lord's return to earth in glory (see 2 Tim. 4:1–8; Titus 2:13) to judge and to establish His kingdom (Matt. 24:27, 29–30; 25:31). Christ's imminent return ought to motivate the man of God to remain faithful to his calling until he dies or the Lord returns (see Acts 1:8–11; 1 Cor. 4:5; Rev. 22:12).
**15** _which He will manifest in His own time, He who is the blessed and only Potentate, the King of kings and Lord of lords,_
**_in His own time_** (v. 15)—the time, known only to Him, that God established in eternity past for Christ to return
**_Potentate_** (v. 15)—This word comes from a Greek word group that basically means "power," but here it is best translated "sovereign." God is absolutely sovereign and omnipotently rules over everything everywhere.
**_King of kings and Lord of lords_** (v. 15)—a title used of Christ (Rev. 17:14; 19:16) is here used of God the Father. Paul probably used this title for God to confront the cult of emperor worship, intending to communicate that only God is sovereign and worthy of worship.
**16** _who alone has immortality, dwelling in unapproachable light, whom no man has seen or can see, to whom be honor and everlasting power. Amen._
**_whom no man has seen or can see_** (v. 16)—God in spirit is invisible (see 1:17; Job 23:8–9; John 1:18; 5:37; Col. 1:15) and, therefore, unapproachable in the sense that sinful man has never seen nor can he ever see His full glory (see Exod. 33:20; Isa. 6:1–5).
**17** _Command those who are rich in this present age not to be haughty, nor to trust in uncertain riches but in the living God, who gives us richly all things to enjoy._
**_haughty_** (v. 17)—This means "to have an exalted opinion of oneself." Those who have an abundance of worldly possessions are constantly tempted to look down on others and act superior. Riches and pride often go together, and the wealthier a person is, the more he is tempted to be proud (Prov. 18:23; 28:11; James 2:1–4).
**_uncertain riches . . . gives us richly_** (v. 17)—Those who have much tend to trust in their wealth (see Prov. 23:4–5). But God provides far more security than any earthly investment can ever give (Eccl. 5:18–20; Matt. 6:19–21).
**18** _Let them do good, that they be rich in good works, ready to give, willing to share,_
**_ready to give_** (v. 18)—The Greek word means "liberal" or "bountiful." Those believers who have money must use it in meeting the needs of others, unselfishly and generously (see Acts 4:32–37; 2 Cor. 8:1–4).
**19** _storing up for themselves a good foundation for the time to come, that they may lay hold on eternal life._
**_storing up . . . a good foundation_** (v. 19)—"Storing up" can be translated "amassing a treasure," while "foundation" can refer to a fund. The idea is that the rich in this world should not be concerned with receiving a return on their earthly investment. Those who make eternal investments will be content to receive their dividends in heaven (see Luke 16:1–13).
**_lay hold on eternal life_** (v. 19)—See the note on verse 12.
**20** _O Timothy! Guard what was committed to your trust, avoiding the profane and idle babblings and contradictions of what is falsely called knowledge—_
**_what was committed to your trust_** (v. 20)—This translates one Greek word, which means "deposit." The deposit Timothy was to guard was the truth—the divine revelation that God committed to his care. Every Christian, especially if he is in ministry, has that sacred trust to guard the revelation of God (see 1 Cor. 4:1; 1 Thess. 2:3–4).
**_what is falsely called knowledge_** (v. 20)—This refers to false doctrine—anything claiming to be the truth that is in fact a lie. False teachers typically claim to have the superior knowledge (as in Gnosticism). They claim to know the transcendent secrets, but actually are ignorant and infantile in their understanding (see Col. 2:8).
**21** _by professing it some have strayed concerning the faith. Grace be with you. Amen._
**_Grace be with you._** (v. 21)—Paul's closing salutation is plural, i.e., "you all"—it goes beyond Timothy to the entire congregation at Ephesus. All believers require the grace of God to preserve the truth and pass it on to the next generation.
1) What clues does Paul give Timothy for identifying false teachers (vv. 3–5)?
[Your Response Here]
_(Verses to consider: Gal. 1:6–9; 2 Pet. 2:10–22; 3:14–16; Jude 4, 8–16)_
2) In what ways is the love of money a snare (vv. 6–10)?
[Your Response Here]
_(Verses to consider: Deut. 8:11–18; Prov. 11:24–25; Matt. 6:19–21, 24)_
3) Circle all the commands that Paul gives Timothy in verses 11–14. Summarize the heart of Paul's exhortation to Timothy. Why does he instruct Timothy in this way?
[Your Response Here]
4) What new insights about the glory of God do you gain from Paul's glorious description (vv. 14–16)?
[Your Response Here]
GOING DEEPER
Paul reminds us that our God is majestic and awesome. God is the Source of all that we could ever need in life, therefore when we pursue God and His glory, we will experience true contentment. The Old Testament prophet, Isaiah, also experienced the glory of God. Read Isaiah 6:1–8.
**1** _In the year that King Uzziah died, I saw the Lord sitting on a throne, high and lifted up, and the train of His robe filled the temple._
**2** _Above it stood seraphim; each one had six wings: with two he covered his face, with two he covered his feet, and with two he flew._
**3** _And one cried to another and said: "Holy, holy, holy is the L ORD of hosts; the whole earth is full of His glory!"_
**4** _And the posts of the door were shaken by the voice of him who cried out, and the house was filled with smoke._
**5** _So I said: "Woe is me, for I am undone! Because I am a man of unclean lips, and I dwell in the midst of a people of unclean lips; for my eyes have seen the King, the L ORD of hosts."_
**6** _Then one of the seraphim flew to me, having in his hand a live coal which he had taken with the tongs from the altar._
**7** _And he touched my mouth with it, and said: "Behold, this has touched your lips; your iniquity is taken away, and your sin purged."_
**8** _Also I heard the voice of the Lord, saying: "Whom shall I send, and who will go for Us?" Then I said, "Here am I! Send me."_
EXPLORING THE MEANING
5) What happened to Isaiah when he saw the Lord high and lifted up?
[Your Response Here]
6) How is this scene reminiscent of the charge given to Timothy in verses 13–16?
[Your Response Here]
7) Read Isaiah 43:13. What does this verse proclaim about the God whom Timothy is being charged to serve? How do you think this attribute of God would encourage Timothy or other men in his position?
[Your Response Here]
_(Verses to consider: Deut. 4:35; 1 Kings 8:23; Ps. 18:31; Isa. 45:5–6, 21–22)_
8) For more insight about money matters, read 2 Corinthians 9:6–7. What does this passage say should be our attitude toward money and giving?
[Your Response Here]
_(Verses to consider: Prov. 27:24; Eccl. 5:15; Mark 8:36; Phil. 4:11)_
TRUTH FOR TODAY
What are the danger signs of loving money? First, those who love money are more concerned with making it than with honesty, or giving a quality effort. Believers must pursue truth and excellence, for which money may be the reward. Second, those who love money never have enough. Like the leech's daughters of Proverbs 30:15, all they can say is "Give, give." Such people stand in sharp contrast to Paul, who wrote to the Philippians, "I have learned to be content in whatever circumstances I am" (Phil. 4:11). Third, those who love money tend to flaunt it. They derive an inordinate pleasure from wearing, driving, or living in what money buys. Fourth, those who love money resent giving it. They want to use it all for their own selfish gratification. Lastly, those who love money will often sin to get it. They will cheat on their income tax or their expense account, or pilfer from work. Those who compromise their principles for money betray a heart that loves money more than God, righteousness, and truth.
REFLECTING ON THE TEXT
9) In what ways are you guilty of loving money? How can you overcome this sinful tendency?
[Your Response Here]
10) How does your view of money affect your level of contentment in life?
[Your Response Here]
11) How fiercely and intensely are you fighting "the good fight of faith"? What would a renewed commitment to the battle look like in your life today?
[Your Response Here]
12) Compose your own "doxology" to God (see Paul's example in 6:15–16). What attributes of God are most amazing to you?
[Your Response Here]
PERSONAL RESPONSE
Write out additional reflections, questions you may have, or a prayer.
[Your Response Here]
ADDITIONAL NOTES
[Your Response Here]
INTRODUCTION TO 2 TIMOTHY
This epistle is the second of two inspired letters Paul wrote to his son in the faith, Timothy. For biographical information on Timothy, see the "Introduction to 1 Timothy." It is titled with the name of the addressee (1:2), as are Paul's other personal letters to individuals (Timothy, Titus, and Philemon).
AUTHOR AND DATE
For discussion of Paul's authorship of the Pastoral Epistles see the "Introduction to 1 Timothy: Author and Date." Paul wrote this final epistle shortly before his martyrdom, about AD 67.
BACKGROUND AND SETTING
Paul was released from his first Roman imprisonment for a short period of ministry, during which he wrote 1 Timothy and Titus. However, in the book of 2 Timothy we find Paul once again in a Roman prison (1:16; 2:9), apparently rearrested as part of Nero's persecution of Christians. Unlike Paul's confident hope of release during his first imprisonment (Phil. 1:19, 25–26; 2:24; Philem. 22), this time he had no such hopes (4:6–8). In his first imprisonment in Rome (about AD 60–62), before Nero had begun the persecution of Christians (AD 64), he was only under house arrest and had opportunity for much interaction with people and ministry (Acts 28:16–31). At this time, five or six years later (about AD 66–67), however, he was in a cold cell (4:13), in chains (2:9), and with no hope of deliverance (4:6). Abandoned by virtually all of those close to him for fear of persecution (see 1:15; 4:9–12, 16) and facing imminent execution, Paul wrote to Timothy, urging him to hasten to Rome for one last visit with the apostle (4:9, 21). Whether Timothy made it to Rome before Paul's execution is not known. According to tradition, Paul was not released from this second Roman imprisonment but suffered the martyrdom he had foreseen (4:6).
In this letter, Paul, aware the end was near, passed the non-apostolic mantle of ministry to Timothy (see 2:2) and exhorted him to continue faithful in his duties (1:6), hold on to sound doctrine (1:13–14), avoid error (2:15–18), accept persecution for the gospel (2:3–4; 3:10–12), put his confidence in the Scripture, and preach it relentlessly (3:15–4:5).
HISTORICAL AND THEOLOGICAL THEMES
It seems that Paul may have had reason to fear that Timothy was in danger of weakening spiritually. This would have been a grave concern for Paul since Timothy needed to carry on Paul's work (see 2:2). While there are no historical indications elsewhere in the New Testament as to why Paul was so concerned, there is evidence in the epistle itself from what he wrote. This concern is evident, for example, in Paul's exhortation to "stir up" his gift (1:6), to replace fear with power, love, and a sound mind (1:7), to not be ashamed of Paul and the Lord, but willingly suffer for the gospel (1:8), and to hold on to the truth (1:13–14). Summing up the potential problem of Timothy, who might be weakening under the pressure of the church and the persecution of the world, Paul calls him to (1) generally "be strong" (2:11), the key exhortation of the first part of the letter, and to (2) continue to "preach the word" (4:2), the main admonition of the last part. These final words to Timothy include few commendations but many admonitions, including about twenty-five imperatives.
Since Timothy was well versed in Paul's theology, the apostle did not instruct him further doctrinally. He did, however, allude to several important doctrines, including salvation by God's sovereign grace (1:9–10; 2:10), the Person of Christ (2:8; 4:1, 8), and perseverance (2:11–13); plus Paul wrote the crucial text of the New Testament on the inspiration of Scripture (3:16–17).
INTERPRETIVE CHALLENGES
This letter contains no major challenges involving theological issues. There is limited data regarding several individuals named in the epistle; for example, Phygellus and Hermogenes (1:15), Onesiphorus (1:17; see 4:19), Hymenaeus and Philetus (2:17–18), Jannes and Jambres (3:8), and Alexander (4:14).
**8**
NOT ASHAMED
_2 Timothy 1:1–18_
DRAWING NEAR
In this second epistle Paul knew his time left on earth was short, so he tries to motivate Timothy to persevere in the faith. What motivates you to keep growing spiritually? Why?
[Your Response Here]
Have you ever felt ashamed of being a Christian? If so, what attitudes or fears keep you from holding fast to the faith?
[Your Response Here]
THE CONTEXT
The first five verses of this letter comprise a beautiful greeting from the apostle Paul to his young protégé, serving as a pastor in Ephesus. Scholars agree this is the last letter ever penned by Paul. This motivating salutation is relevant not only to a first-century Christian leader but also to modern-day Christians—parents, Sunday-school teachers, church staff members, missionaries, students, neighbors, and friends. In short, it contains wise principles for any and every believer who wants to grow in his or her faith and who desires to be used by God to make a difference in the lives of others. It portrays a beautiful example of servanthood and love.
Paul focuses on the issue of "not being ashamed of Christ." Paul bases his appeal on the motivations for serving Christ given in the first five verses. By helping Timothy remember the apostle's authority, his unselfish concern for others, his heart of gratitude, his habits of faithful intercession, his expressed affection, and his frequent words of affirmation, Paul hopes to generate within his young colleague a courageous, unapologetic witness and obedience to the will of the Lord. Only a holy boldness (like that modeled by Paul) will enable Timothy to persevere in the face of increasing hostility.
KEYS TO THE TEXT
_Spiritual Gifts:_ The Greek word for _spiritual_ literally means "pertaining to the Spirit." Spiritual gifts are divine enablements for ministry that the Holy Spirit gives in some measure to all believers. They should be exercised under the Spirit's control and used for the building of the church to Christ's glory. The word _gifts_ comes from the Greek word _charisma,_ and means essentially "gift of grace" or "free gift."
_Holy Calling:_ As always in the New Testament epistles, this calling is not a general invitation to sinners to believe the gospel and be saved; rather, it refers to God's effectual call of the elect to salvation. This calling results in holiness—first our imputed holiness (known as _justification_ ), then our imparted holiness (known as _sanctification_ ), and finally our completed holiness (that is, our _glorification_ ).
UNLEASHING THE TEXT
Read 1:1–18, noting the key words and definitions next to the passage.
**2 Timothy 1:1–18 (NKJV)**
**1** _Paul, an apostle of Jesus Christ by the will of God, according to the promise of life which is in Christ Jesus,_
**_apostle of Jesus Christ by the will of God_** (v. 1)—An apostle was "one who is sent with a commission." An apostle was chosen and trained by Jesus Christ to proclaim His truth during the formative years of the church. Paul's call was according to God's sovereign plan and purpose (see 1 Cor. 1:1; 2 Cor. 1:1; Eph. 1:1; Col. 1:1).
**_promise of life . . . in Christ Jesus_** (v. 1)—the gospel, which promises that those who are spiritually dead, but by faith embrace the gospel's message, will be united to Christ and find eternal life in Him (John 3:16; 10:10; 14:6; Col. 3:4)
**2** _To Timothy, a beloved son: Grace, mercy, and peace from God the Father and Christ Jesus our Lord._
**_Timothy, a beloved son_** (v. 2)—Only Timothy and Titus received this special expression of Paul's favor. The Greek word for "son" is better translated "child," which emphasizes Paul's role as spiritual father to Timothy.
**_Grace . . . our Lord_** (v. 2)—More than a standard greeting by Paul, this expressed his genuine desire for God's best in Timothy's life.
**3** _I thank God, whom I serve with a pure conscience, as my forefathers did, as without ceasing I remember you in my prayers night and day,_
**4** _greatly desiring to see you, being mindful of your tears, that I may be filled with joy,_
**_greatly desiring to see you_** (v. 4)—Because of Paul's affection for Timothy and the urgency of the hour in Paul's life, as he faced death, Paul had an intense yearning to see Timothy again (see 4:9, 13, 21).
**_mindful of your tears_** (v. 4)—Paul perhaps remembered this occurring at their latest parting, which occurred after a short visit to Ephesus, following the writing of 1 Timothy, and prior to Paul's arrest at Troas (see note on 4:13) and his second imprisonment in Rome. Years before, Paul had a similar parting with the elders at Ephesus.
**5** _when I call to remembrance the genuine faith that is in you, which dwelt first in your grandmother Lois and your mother Eunice, and I am persuaded is in you also._
**_Lois . . . Eunice_** (v. 5)—Mention of their names suggests that Paul knew them personally, perhaps because he (with Barnabas) led them to faith in Christ during his first missionary journey (see Acts 13:13–14:21). The women were true Old Testament Jewish believers, who understood the Scripture well enough to prepare themselves and Timothy (3:15) to immediately accept Jesus as Messiah when they first heard the gospel from Paul.
**6** _Therefore I remind you to stir up the gift of God which is in you through the laying on of my hands._
**_stir up the gift of God_** (v. 6)—This seems to indicate Paul was unsatisfied with Timothy's level of current faithfulness. "Stir up" means literally "to keep the fire alive," and "gift" refers to the believer's spiritual gift (regarding Timothy's spiritual gift, see notes on 4:2–6; 1 Tim. 4:14). Paul reminds Timothy that as a steward of his God-given gift for preaching, teaching, and evangelizing, he could not let it fall into disuse.
**_laying on of my hands_** (v. 6)—See 1 Timothy 4:14; 5:22; 6:12. Paul might have done this at the time of Timothy's conversion, in which case it would have corresponded to when Timothy received his spiritual gift. The expression may also refer to an extraordinary spiritual endowment, which was received or enhanced at some point after his conversion.
**7** _For God has not given us a spirit of fear, but of power and of love and of a sound mind._
**_a spirit of fear_** (v. 7)—The Greek word, which can also be translated "timidity," denotes a cowardly, shameful fear caused by a weak, selfish character. The threat of Roman persecution, which was escalating under Nero, the hostility of those in the Ephesian church who resented Timothy's leadership, and the assaults of false teachers with their sophisticated systems of deceptions may have been overwhelming Timothy. But if he was fearful, it didn't come from God.
**_power_** (v. 7)—Positively, God has already given believers all the spiritual resources they need for every trial and threat (see Matt. 10:19–20). Divine power—effective, productive spiritual energy—belongs to believers (Eph. 1:18–20; 3:20; see also Zech. 4:6).
**_love_** (v. 7)—See the note on 1 Timothy 1:5. This kind of love centers on pleasing God and seeking others' welfare before one's own (see Rom. 14:8; Gal. 5:22, 25; Eph. 3:19; 1 Pet. 1:22; 1 John 4:18).
**_sound mind_** (v. 7)—This refers to a disciplined, self-controlled, and properly prioritized mind. This is the opposite of fear and cowardice that causes disorder and confusion. Focusing on the sovereign nature and perfect purposes of our eternal God allows believers to control their lives with godly wisdom and confidence in every situation (see Rom. 12:3; 1 Tim. 3:2; Titus 1:8; 2:2).
**8** _Therefore do not be ashamed of the testimony of our Lord, nor of me His prisoner, but share with me in the sufferings for the gospel according to the power of God,_
**_the testimony of our Lord_** (v. 8)—This refers to the gospel message concerning Jesus Christ. Paul did not want Timothy to be "ashamed" to name the name of Christ because he was afraid of the potential persecution (see vv. 12, 16).
**_me His prisoner_** (v. 8)—Being linked to Paul, who was a prisoner because of his preaching of the gospel, could have put Timothy's life and freedom in jeopardy (see Heb. 13:23).
**9** _who has saved us and called us with a holy calling, not according to our works, but according to His own purpose and grace which was given to us in Christ Jesus before time began,_
**_not . . . works, but . . . grace_** (v. 9)—This truth is the foundation of the gospel. Salvation is by grace through faith, apart from works (see Rom. 3:20–25; Gal. 3:10, 11; Eph. 2:8–9; Phil. 3:8–9). Grace is also the basis for God's sustaining work in believers (see Phil. 1:6; Jude 24–25).
**_according to His own purpose_** (v. 9)—God's sovereign plan of election
**_in Christ Jesus_** (v. 9)—His sacrifice made God's salvation plan possible, because He became the substitute sacrifice for the sins of God's people (see 2 Cor. 5:21).
**_before time began_** (v. 9)—The same Greek phrase appears in Titus 1:2. The destiny of God's chosen was determined and sealed from eternity past (John 17:24; see Eph. 1:4–5; Phil. 1:29; 1 Pet. 1:2).
**10** _but has now been revealed by the appearing of our Savior Jesus Christ, who has abolished death and brought life and immortality to light through the gospel,_
**_appearing_** (v. 10)—"Epiphany" is the English equivalent of this Greek word, which is most often used of Christ's second coming (4:18; 1 Tim. 6:14; Titus 2:13), but here of His first coming.
**_abolished death . . . immortality to light_** (v. 10)—"Abolished" means "rendered inoperative." Physical death still exists, but it is no longer a threat or an enemy for Christians (1 Cor. 15:54–55; Heb. 2:14). It was not until the Incarnation and the gospel that God chose to fully make known the truth of immortality and eternal life, a reality only partially understood by Old Testament believers (see Job 19:26).
**11** _to which I was appointed a preacher, an apostle, and a teacher of the Gentiles._
**_preacher . . . teacher_** (v. 11)—See 1 Timothy 2:7.
**12** _For this reason I also suffer these things; nevertheless I am not ashamed, for I know whom I have believed and am persuaded that He is able to keep what I have committed to Him until that Day._
**_I also suffer_** (v. 12)—See verse 8; see also 2 Corinthians 4:8–18; 6:4–10; 11:23–28; Galatians 6:17; Philippians 3:10.
**_I am not ashamed_** (v. 12)—Paul had no fear of persecution and death from preaching the gospel in a hostile setting, because he was so confident God had sealed his future glory and blessing (see Rom. 1:16).
**_know whom I have believed_** (v. 12)—"Know" describes the certainty of Paul's intimate, saving knowledge—the object of which was God Himself. The form of the Greek verb translated "I have believed" refers to something that began in the past and has continuing results. This knowing is equal to "the knowledge of the truth" (3:7; 1 Tim. 2:4).
**_He is able to keep_** (v. 12)—See Jude 24–25.
**_what I have committed_** (v. 12)—Paul's life in time and eternity had been given to his Lord. He lived with unwavering confidence and boldness because of the revealed truth about God's power and faithfulness, and his own experience of an unbreakable relationship to the Lord (Rom. 8:31–39).
**_that Day_** (v. 12)—This is also called "Day of Christ" (see Phil. 1:10), when believers will stand before the judgment seat and be rewarded (see 1 Cor. 3:13; 2 Cor. 5:10; 1 Pet. 1:5).
**13** _Hold fast the pattern of sound words which you have heard from me, in faith and love which are in Christ Jesus._
**_sound words_** (v. 13)—See 1 Timothy 4:6; 6:3. This refers to the Scripture and the doctrine it teaches.
**_from me_** (v. 13)—Paul had been the source of this divine revelation (see 2:2; 3:10, 14; Phil. 4:9).
**_faith and love . . . in Christ Jesus_** (v. 13)—"Faith" is confidence that God's Word is true, and "love" is kindness and compassion in teaching that truth (see Eph. 4:15).
**14** _That good thing which was committed to you, keep by the Holy Spirit who dwells in us._
**_That good thing . . . committed to you_** (v. 14)—the treasure of the good news of salvation revealed in the Scripture
**15** _This you know, that all those in Asia have turned away from me, among whom are Phygellus and Hermogenes._
**_Asia_** (v. 15)—a Roman province that is part of modern Turkey; this is not a reference to the entire region of Asia Minor
**_Phygellus and Hermogenes_** (v. 15)—Nothing else is known about these two men, who apparently had shown promise as leaders, had been close to Paul, and were well known among the Asian churches, but deserted Paul under the pressure of persecution.
**16** _The Lord grant mercy to the household of Onesiphorus, for he often refreshed me, and was not ashamed of my chain;_
**_Onesiphorus_** (v. 16)—This was one of Paul's loyal coworkers who had not deserted Paul but had befriended him in prison and was not ashamed or afraid to visit the apostle there regularly and minister to his needs. Since Paul asks Timothy to greet those in his house (4:19), the family obviously lived in or near Ephesus.
**17** _but when he arrived in Rome, he sought me out very zealously and found me._
**_when he arrived in Rome_** (v. 17)—Onesiphorus was perhaps on a business trip and the text implies that his search involved time, effort, and possibly even danger.
**18** _The Lord grant to him that he may find mercy from the Lord in that Day—and you know very well how many ways he ministered to me at Ephesus._
**_Ephesus_** (v. 18)—Onesiphorus's faithfulness began here many years earlier, when Paul ministered on his third or fourth missionary journey.
1) How does Paul attempt to motivate his "beloved son" in the faith?
[Your Response Here]
2) Paul offered a number of ways that Timothy could resist being ashamed of the gospel (vv. 6–14). Summarize these.
[Your Response Here]
3) Why did Paul share with Timothy the contrasting actions of his associates in ministry (1:15–18)? How was he hoping to both challenge and encourage Timothy through this?
[Your Response Here]
GOING DEEPER
In Paul and Timothy's day, suffering for their faith was common. Read about another apostle's experience of persecution in Acts 4:1–21.
**1** _Now as they spoke to the people, the priests, the captain of the temple, and the Sadducees came upon them,_
**2** _being greatly disturbed that they taught the people and preached in Jesus the resurrection from the dead._
**3** _And they laid hands on them, and put them in custody until the next day, for it was already evening._
**4** _However, many of those who heard the word believed; and the number of the men came to be about five thousand._
**5** _And it came to pass, on the next day, that their rulers, elders, and scribes,_
**6** _as well as Annas the high priest, Caiaphas, John, and Alexander, and as many as were of the family of the high priest, were gathered together at Jerusalem._
**7** _And when they had set them in the midst, they asked, "By what power or by what name have you done this?"_
**8** _Then Peter, filled with the Holy Spirit, said to them, "Rulers of the people and elders of Israel:_
**9** _If we this day are judged for a good deed done to a helpless man, by what means he has been made well,_
**10** _let it be known to you all, and to all the people of Israel, that by the name of Jesus Christ of Nazareth, whom you crucified, whom God raised from the dead, by Him this man stands here before you whole._
**11** _This is the 'stone which was rejected by you builders, which has become the chief cornerstone.'_
**12** _Nor is there salvation in any other, for there is no other name under heaven given among men by which we must be saved."_
**13** _Now when they saw the boldness of Peter and John, and perceived that they were uneducated and untrained men, they marveled. And they realized that they had been with Jesus._
**14** _And seeing the man who had been healed standing with them, they could say nothing against it._
**15** _But when they had commanded them to go aside out of the council, they conferred among themselves,_
**16** _saying, "What shall we do to these men? For, indeed, that a notable miracle has been done through them is evident to all who dwell in Jerusalem, and we cannot deny it._
**17** _But so that it spreads no further among the people, let us severely threaten them, that from now on they speak to no man in this name."_
**18** _So they called them and commanded them not to speak at all nor teach in the name of Jesus._
**19** _But Peter and John answered and said to them, "Whether it is right in the sight of God to listen to you more than to God, you judge._
**20** _For we cannot but speak the things which we have seen and heard."_
**21** _So when they had further threatened them, they let them go, finding no way of punishing them, because of the people, since they all glorified God for what had been done._
EXPLORING THE MEANING
4) What impresses you about the apostles' demeanor in this passage?
[Your Response Here]
5) Why do you think they could be so bold?
[Your Response Here]
6) Read Psalm 119:46. What attitude does the psalmist demonstrate in this verse? Why is this an important attitude for believers to have?
[Your Response Here]
7) Read 1 Peter 4:10–11. How does God want us to use our gifts? To what end?
[Your Response Here]
_(Verses to consider: Rom. 12:3–7; Eph. 4:11–16; 1 Tim. 4:14)_
TRUTH FOR TODAY
Faithful ministry in the Lord's service is always bittersweet. It brings suffering and joy, disappointment and gratitude. Duty can bring the deepest pain or the highest joy. Spiritual duty unfulfilled brings untold dissatisfaction, regret, and anguish, no matter how easy unfaithfulness may be. On the other hand, spiritual duty fulfilled brings untold satisfaction and happiness, whatever the cost of faithfulness. The Christian who is obedient to his duty under the Lord can say with Peter, "If anyone suffers as a Christian, let him not feel ashamed, but in that name let him glorify God" (1 Pet. 4:16).
REFLECTING ON THE TEXT
8) Have you ever suffered or been made fun of because of your faith in Jesus? Explain what happened.
[Your Response Here]
9) What are your spiritual gifts (or gift)? (If you don't know, what steps can you take to discover them?)
[Your Response Here]
10) What would it look like in your life to "stir up" your gift? How would this benefit the church of which you are a member?
[Your Response Here]
11) If God has indeed given you a spirit of power (1:7) and not of fear, in what ways can you hold fast to the truth of the gospel? What ministry or outreach can you attempt for God's glory this week?
[Your Response Here]
12) Perhaps you know a younger believer like Timothy. Name two things you could do to encourage this young saint to have a bolder Christian walk.
[Your Response Here]
PERSONAL RESPONSE
Write out additional reflections, questions you may have, or a prayer.
[Your Response Here]
**9**
BE DILIGENT
_2 Timothy 2:1–26_
DRAWING NEAR
Think about any experiences you have had (or have heard about) in the following spheres:
serving in the military
playing an organized sport
farming (or having a garden)
[Your Response Here]
Describe one difficult aspect of this activity.
[Your Response Here]
Describe one life lesson you learned through doing it.
[Your Response Here]
THE CONTEXT
The apostle Paul wrote to Timothy, pastor at Ephesus, because he sensed the young man was vacillating. Perhaps he was questioning his gifts, his calling, or his likely success. Facing obvious difficulties, whatever their nature, Timothy was clearly discouraged. The gist of Paul's counsel was that Timothy did not need more from God; rather, he needed to appropriate all that God had already given him. He needed encouragement to be diligent, to use his gifts, and to resist the false teachers that had infiltrated the flock.
Paul discussed several important elements of a strong and vibrant Christian life and used the vivid pictures of a teacher, a soldier, an athlete, and a farmer. Perhaps anticipating questions from Timothy, Paul then offered some powerful motives for faithfulness. From there Paul moved to inspire and encourage Timothy to be, first and foremost, a man of the Word. He urged the young pastor to maintain a firm hold on the truth and to pass that truth on to others. Only a thorough knowledge of the Scriptures would enable Timothy to recognize, resist, and rebuke falsehood. If Timothy wanted to be acceptable to God and prepared for every good work, he would have to avoid sin and walk in purity. No matter where you are in your Christian walk, you will find practical, convicting, and encouraging counsel.
KEYS TO THE TEXT
_Diligence:_ This word denotes zealous persistence in accomplishing a goal. Timothy, like all who preach or teach the Word, was to give his maximum effort to impart God's Word completely, accurately, and clearly to his hearers.
_Word of Truth:_ This refers to all of Scripture in general and the gospel message in particular (John 17:17; Eph. 1:13; Col. 1:5). God's Word is sufficient, comprehensive, completely without error, and able to meet every need and fulfill the desires of every heart. If we obey it, we will be blessed in whatever we do. Spiritual leaders must once again embrace the sufficiency of Scripture and call their people back to it. Individual Christians must covenant with God to be men and women of the Word, finding their resources there and applying them to every aspect of their lives. You'll never know what the Word can do if you don't study and apply it. It isn't enough to simply say you believe it. It must occupy an exalted place in your life. Since God Himself exalts it and magnifies it (Ps. 138:2), we should do likewise.
UNLEASHING THE TEXT
Read 2:1–26, noting the key words and definitions next to the passage.
**2 Timothy 2:1–26 (NKJV)**
**1** _You therefore, my son, be strong in the grace that is in Christ Jesus._
**_my son_** (v. 1)—Paul had led Timothy to Christ during his first missionary journey (see 1 Cor. 4:17; 1 Tim. 1:2, 18).
**_be strong_** (v. 1)—Here is the main admonition in the first part of the letter. Paul is calling for Timothy to overcome his apparent drift toward weakness and renew his commitment to his ministry.
**2** _And the things that you have heard from me among many witnesses, commit these to faithful men who will be able to teach others also._
**_heard from me_** (v. 2)—See the notes on 1:13; see 3:14. During Timothy's many years of close association with Paul, he had heard divine truth, which God had revealed through the apostle.
**_among many witnesses_** (v. 2)—This refers to individuals such as Silas, Barnabas, and Luke, and many others in the churches who could attest to the divine authenticity of Paul's teaching—a needed reminder to Timothy in light of the many defections at Ephesus (see 1:15).
**_faithful men who will be able to teach others_** (v. 2)—Timothy was to take the divine revelation he had learned from Paul and teach it to other faithful believers—those with proven spiritual character and giftedness, who would in turn pass on those truths to another generation. From Paul to Timothy to faithful teachers to others encompasses four generations of godly leaders. That process of spiritual reproduction, which began in the early church, is to continue until the Lord returns.
**3** _You therefore must endure hardship as a good soldier of Jesus Christ._
**_a good soldier_** (v. 3)—The metaphor of the Christian life as warfare (against the evil world system, the believer's sinful human nature, and Satan) is a familiar one in the New Testament (see 2 Cor. 10:3–5; Eph. 6:10–20; 1 Thess. 4:8; 1 Tim. 1:18; 4:7; 6:12). Here Paul is dealing with conflict against the hostile world and persecution (see v. 9; 1:8; 3:11–12; 4:7).
**4** _No one engaged in warfare entangles himself with the affairs of this life, that he may please him who enlisted him as a soldier._
**_entangles himself_** (v. 4)—Just as a soldier called to duty is completely severed from the normal affairs of civilian life, so also must the good soldier of Jesus Christ refuse to allow the things of the world to distract him (see James 4:4; 1 John 2:15–17).
**5** _And also if anyone competes in athletics, he is not crowned unless he competes according to the rules._
**_competes in athletics_** (v. 5)—The Greek verb expresses the effort and determination needed to compete successfully in an athletic event (see 1 Cor. 9:24). To those familiar with the Olympic Games and the Isthmian Games (held in Corinth), this would be a useful picture of spiritual effort and untiring pursuit of the victory.
**_crowned . . . rules_** (v. 5)—All an athlete's hard work and discipline will be wasted if he or she fails to compete according to the rules. This is a call to obey the Word of God in the pursuit of spiritual victory.
**6** _The hardworking farmer must be first to partake of the crops._
**_The hardworking farmer_** (v. 6)—"Hardworking" is from a Greek verb meaning "to labor to the point of exhaustion." Ancient farmers worked long hours of backbreaking labor under all kinds of conditions, with the hope that their physical effort would be rewarded by a good harvest. Paul is urging Timothy not to be lazy or indolent, but to labor intensely (see Col. 1:28–29) with a view to the harvest (see 1 Cor. 3:6–7).
**7** _Consider what I say, and may the Lord give you understanding in all things._
**_Consider_** (v. 7)—The Greek word denotes clear perception, full understanding, and careful consideration. The form of the verb suggests a strong admonition by Paul, not mere advice, to give deep thought to what he was writing.
**8** _Remember that Jesus Christ, of the seed of David, was raised from the dead according to my gospel,_
**_Remember . . . Jesus Christ_** (v. 8)—The supreme model of a faithful teacher (v. 2), soldier (vv. 3–4), athlete (v. 5), and farmer (v. 6). Timothy was to follow His example in teaching, suffering, pursuing the prize, and planting the seeds of truth for a spiritual harvest.
**_of the seed of David_** (v. 8)—As David's descendant, Jesus is the rightful heir to his throne (Luke 1:32–33). The Lord's humanity is stressed.
**_raised from the dead_** (v. 8)—The resurrection of Christ is the central truth of the Christian faith (1 Cor. 15:3–4, 17, 19). By it, God affirmed the perfect redemptive work of Jesus Christ (see Rom. 1:4).
**9** _for which I suffer trouble as an evildoer, even to the point of chains; but the word of God is not chained._
**_I suffer . . . but the word . . . is not chained_** (v. 9)—Paul contrasts his imprisonment for the sake of the gospel to the unfettered power of the Word of God.
**10** _Therefore I endure all things for the sake of the elect, that they also may obtain the salvation which is in Christ Jesus with eternal glory._
**_for the sake of the elect_** (v. 10)—those of the elect, having been chosen for salvation from before the world began, who had not yet come to faith in Jesus Christ (see Acts 18:10; Titus 1:1)
**_the salvation which is in Christ Jesus_** (v. 10)—There is salvation in no one else (Acts 4:12; Rom. 8:29; Eph. 1:4–5). The gospel must be proclaimed (Matt. 28:19; Acts 1:8) because the elect are not saved apart from faith in Christ (Rom. 10:14).
**_eternal glory_** (v. 10)—the ultimate outcome of salvation (see Rom. 5:2; 8:17)
**11** _This is a faithful saying: For if we died with Him, we shall also live with Him._
**_faithful saying_** (v. 11)—The saying is in verses 11–13.
**_died with Him . . . live with Him_** (v. 11)—This refers to believers' spiritual participation in Christ's death and resurrection (Rom. 6:4–8), including also the possibility of suffering martyrdom for the sake of Christ, as the context would indicate.
**12** _If we endure, we shall also reign with Him. If we deny Him, He also will deny us._
**_endure_** (v. 12)—Believers who persevere give evidence of the genuineness of their faith (see Matt. 10:22; John 8:31; Rom. 2:7; Col. 1:23).
**_reign with Him_** (v. 12)—in His future eternal kingdom (Rev. 1:6; 5:10; 20:4, 6)
**_If we deny Him, He also will deny us_** (v. 12)—Speaks of a final, permanent denial, such as that of an apostate (see note on 1 Tim. 1:19), not the temporary failure of a true believer like Peter (Matt. 26:69–75). Those who so deny Christ give evidence that they never truly belonged to Him (1 John 2:19) and face the fearful reality of one day being denied by Him (Matt. 10:33).
**13** _If we are faithless, He remains faithful; He cannot deny Himself._
**_faithless_** (v. 13)—This refers to a lack of saving faith, not to weak or struggling faith. Unbelievers will ultimately deny Christ because their faith was not genuine (see James 2:14–26).
**_He remains faithful; He cannot deny Himself._** (v. 13)—As faithful as Jesus is to save those who believe in Him (John 3:16), He is equally faithful to judge those who do not (John 3:18). To act any other way would be inconsistent with His holy, unchangeable nature (see Heb. 10:23).
**14** _Remind them of these things, charging them before the Lord not to strive about words to no profit, to the ruin of the hearers._
**_strive about words_** (v. 14)—Arguing with false teachers, i.e., deceivers who use human reason to subvert God's Word, is not only foolish (Prov. 14:7) and futile (Matt. 7:6), but dangerous (vv. 16–17). This is the first of three warnings to avoid useless arguments (see 1 Tim. 4:6–7; 6:3–5; 2 Pet. 1–3).
**_ruin_** (v. 14)—The Greek word means "overturned," or "overthrown." It appears only one other time in the New Testament (2 Pet. 2:6), where it describes the destruction of Sodom and Gomorrah. Because it replaces the truth with lies, false teaching brings spiritual catastrophe to those who heed it. The ruin can be eternal.
**15** _Be diligent to present yourself approved to God, a worker who does not need to be ashamed, rightly dividing the word of truth._
**_rightly dividing_** (v. 15)—Literally "cutting it straight," this refers to the exactness demanded by such trades as carpentry, masonry, and Paul's trade of leatherworking and tentmaking. Precision and accuracy are required in biblical interpretation beyond all other enterprises because the interpreter is handling God's Word. Anything less is shameful.
**16** _But shun profane and idle babblings, for they will increase to more ungodliness._
**_shun profane and idle babblings_** (v. 16)—Such destructive heresy leads only to "more ungodliness." Heresy can't save or sanctify. This is Paul's second such warning (see vv. 14, 23).
**17** _And their message will spread like cancer. Hymenaeus and Philetus are of this sort,_
**_cancer_** (v. 17)—The word refers to a disease which spreads rapidly in a deadly manner. The metaphor emphasizes the insidious danger of false teaching. It attacks and consumes one's life.
**_Hymenaeus_** (v. 17)—See the note on 1 Timothy 1:20.
**_Philetus_** (v. 17)—Alexander's replacement as Hymenaeus's accomplice
**18** _who have strayed concerning the truth, saying that the resurrection is already past; and they overthrow the faith of some._
**_the resurrection is already past_** (v. 18)—Like the false teachers who troubled the Corinthians (1 Cor. 15:12), Hymenaeus and Philetus denied the reality of believers' bodily resurrection. They probably taught that believers' spiritual identification with Christ's death and resurrection (Rom. 6:4–5, 8) was the only resurrection they would experience, and that had already happened. Such heretical teaching reflects the contemporary Greek philosophical view that matter was evil and spirit was good.
**_overthrow the faith_** (v. 18)—This speaks of those whose faith was not genuine (see Matt. 24:24). Genuine saving faith cannot be finally and completely overthrown. False, non-saving faith is common (see Matt. 7:21–27; 13:18–22; John 2:23–25; 6:64–66; 8:31; 1 John 2:19).
**19** _Nevertheless the solid foundation of God stands, having this seal: "The Lord knows those who are His," and, "Let everyone who names the name of Christ depart from iniquity."_
**_the solid foundation of God_** (v. 19)—This is likely a reference to the church (see 1 Tim. 3:15), which cannot be overcome by the forces of hell (Matt. 16:18) and is made up of those who belong to Him.
**_seal_** (v. 19)—This is a symbol of ownership and authenticity. Paul gives two characteristics of those with the divine seal of authenticity.
**_"The Lord knows those who are His"_** (v. 19)—This is likely a reference to Numbers 16:5. He "knows," not in the sense of awareness, but as a husband knows his wife, in the sense of intimate relationship (see John 10:27–28; Gal. 4:9). God has known His own ever since He chose them before time began.
**_"Let everyone . . . depart from iniquity."_** (v. 19)—This statement is likely adapted from Numbers 16:26 and reflects a second mark of God's ownership of believers, their pursuit of holiness (see 1 Cor. 6:19–20; 1 Pet. 1:15–16).
**20** _But in a great house there are not only vessels of gold and silver, but also of wood and clay, some for honor and some for dishonor._
**_vessels_** (v. 20)—The Greek word is very general and was used to describe various tools, utensils, and furniture found in the home. In this "great house" analogy, Paul contrasts two kinds of utensils or serving dishes.
**_some for honor_** (v. 20)—In a wealthy home, the ones made of precious "gold and silver" were used for honorable purposes such as serving food to the family and guests.
**_some for dishonor_** (v. 20)—Those made of "wood and clay" were not for any honorable use, but rather those uses which were repulsive—disposing of garbage and the filthy waste of the household (see 2 Cor. 4:7).
**21** _Therefore if anyone cleanses himself from the latter, he will be a vessel for honor, sanctified and useful for the Master, prepared for every good work._
**_anyone_** (v. 21)—This refers to whoever wants to be useful to the Lord for noble purposes. Even a common wood bucket or clay pot becomes useful when purged and made holy.
**_cleanses himself_** (v. 21)—The Greek word means "to thoroughly clean out," or "to completely purge." For any wastebucket in the house to be used for a noble purpose, it would have had to be vigorously scoured, cleansed, and purged of all vestiges of its former filth.
**_the latter_** (v. 21)—This refers to the vessels of dishonor (v. 20). Associating with anyone who teaches error and lives in sin is corrupting (Prov. 1:10–19; 13:20; 1 Cor. 5:6, 11; 15:33; Titus 1:16)—all the more so when they are leaders in the church. This is clearly a call to separate from all who claim to serve God, but do so as filthy implements useful only for the most dishonorable duties.
**22** _Flee also youthful lusts; but pursue righteousness, faith, love, peace with those who call on the Lord out of a pure heart._
**_youthful lusts_** (v. 22)—not merely illicit sexual desires, but also such lusts as pride, desire for wealth and power, jealousy, self-assertiveness, and an argumentative spirit
**23** _But avoid foolish and ignorant disputes, knowing that they generate strife._
**_disputes . . . strife_** (v. 23)—Paul's third warning to avoid useless arguments with false teachers (see notes on vv. 14, 16)
**24** _And a servant of the Lord must not quarrel but be gentle to all, able to teach, patient,_
**_able to teach_** (v. 24)—This is one word in Greek meaning "skilled in teaching" (see note on 1 Tim. 3:2).
**25** _in humility correcting those who are in opposition, if God perhaps will grant them repentance, so that they may know the truth,_
**_those who are in opposition_** (v. 25)—This refers primarily to unbelievers (captive to Satan, v. 26), but also could include believers deceived by the "foolish and ignorant" (v. 23) speculations of the false teachers; and, possibly, the false teachers themselves.
**_God . . . will grant them repentance_** (v. 25)—All true repentance is produced by God's sovereign grace (Eph. 2:7), and without such grace human effort to change is futile.
**_know the truth_** (v. 25)—See the note on 3:7. When God, by grace, grants saving faith, it includes the granting of repentance from sin. Neither is a human work.
**26** _and that they may come to their senses and escape the snare of the devil, having been taken captive by him to do his will._
**_the snare of the devil_** (v. 26)—Deception is Satan's trap. He is an inveterate, scheming, clever, and subtle purveyor of lies (see Gen. 3:4–6; John 8:44; 2 Cor. 11:13–15; Rev. 12:9).
1) Paul uses three analogies to highlight several indispensable qualities of a strong spiritual life (2:1–7). What is the main point of each analogy?
[Your Response Here]
2) Summarize the beliefs and convictions that enabled Paul to persevere in a life of sacrificial ministry (vv. 8–13).
[Your Response Here]
3) What kind of false teaching did Timothy combat in the Ephesian church (vv. 14–19)? What antidote does Paul offer Timothy for this teaching?
[Your Response Here]
_(Verses to consider: Matt. 24:24; 1 Thess. 2:4; 1 Tim. 1:3–4, 18–19; 2 Pet. 2:1–2)_
4) Note the illustration of a house containing vessels for honor and for dishonor (2:20–26). How do the two differ? How does an individual go from being a vessel for dishonor to a vessel for honor?
[Your Response Here]
GOING DEEPER
For more encouragement to stay faithful, read Romans 8:31–39.
**31** _What then shall we say to these things? If God is for us, who can be against us?_
**32** _He who did not spare His own Son, but delivered Him up for us all, how shall He not with Him also freely give us all things?_
**33** _Who shall bring a charge against God's elect? It is God who justifies._
**34** _Who is he who condemns? It is Christ who died, and furthermore is also risen, who is even at the right hand of God, who also makes intercession for us._
**35** _Who shall separate us from the love of Christ? Shall tribulation, or distress, or persecution, or famine, or nakedness, or peril, or sword?_
**36** _As it is written: "For Your sake we are killed all day long; We are accounted as sheep for the slaughter."_
**37** _Yet in all these things we are more than conquerors through Him who loved us._
**38** _For I am persuaded that neither death nor life, nor angels nor principalities nor powers, nor things present nor things to come,_
**39** _nor height nor depth, nor any other created thing, shall be able to separate us from the love of God which is in Christ Jesus our Lord._
EXPLORING THE MEANING
5) How does the truth conveyed in this beloved passage help you to endure through tough times?
[Your Response Here]
6) Are you persuaded of God's love for you? Why or why not? How can the truths of this passage encourage you in this area?
[Your Response Here]
7) Read 1 Thessalonians 2:7. How and why are gentleness and humility important traits for all Christians, but especially for Christian leaders?
[Your Response Here]
_(Verses to consider: Prov. 15:1; 22:4; Matt. 11:29; 21:5; Gal. 5:22–23; Eph. 4:2; Phil. 2:3)_
TRUTH FOR TODAY
Several years ago, engineers in New Jersey were building a bridge over the mouth of a river on the Atlantic coast. As they were putting down pilings, they came across the hull of an old ship that was buried in the sand. To keep the bridge on the planned route, the hull would have to be removed. After they tried every mechanical means they could think of, the ship remained in place. A young engineer suggested placing several large barges above the hull on either side, running cables underneath the hull, and attaching them tightly to the barges at low tide. When the tide rose, the hull was loosened some. At the next low tide the cables were tightened again, and at high tide the ship was loosened some more. After following that procedure for several cycles of tides, the ship eventually was freed. What humanly devised mechanical force could not accomplish, the immeasurably greater forces of nature accomplished easily.
Many Christians and churches are like that hull, embedded in spiritual immobility. They recognize the problem and try every human means to extricate themselves, but to no avail. But what His children cannot accomplish in their own strength, their heavenly Father can do by the power of His Spirit.
REFLECTING ON THE TEXT
8) In what areas of your spiritual life do you feel "embedded in immobility"?
[Your Response Here]
9) How can you exercise more diligence and discipline in your relationship with God?
[Your Response Here]
10) Paul and Timothy suffered for their faith. How do you think you might fare if you lived in a country where Christians were openly and routinely persecuted?
[Your Response Here]
11) How does knowing God's Word help you discern truth from falsehood?
[Your Response Here]
PERSONAL RESPONSE
Write out additional reflections, questions you may have, or a prayer.
[Your Response Here]
**10**
EQUIPPED FOR GOOD WORKS
_2 Timothy 3:1–17_
DRAWING NEAR
What person or persons have had the role of a spiritual mentor in your life? What significant lessons have you learned from them?
[Your Response Here]
What is your favorite book of the Bible? Why?
[Your Response Here]
THE CONTEXT
Paul had three great goals in life. First, he desired to know Christ intimately. Second, he was devoted to defending the truth of God (that is, the Scripture). Third, he longed to serve Christ and His church with an even greater passion than his earlier opposition to the gospel. These consuming priorities are clearly seen in this letter.
In chapter 3, Paul gives his sternest command to avoid, expose, and battle spiritual impostors and spiritual heresy in the church. By pointing out his own example of faithfulness and by reiterating their biblically based convictions, Paul urged Timothy to be a strong and faithful defender of the faith. He reminded his young colleague in ministry of the rich resource he had in the Word of God.
No other passage in the New Testament gives such a concise yet thorough description of the nature of God's Word. In a handful of verses, the power of Scripture to save sinners and sanctify believers is clearly shown. No minister and no ministry can succeed unless it is rooted in and built upon the eternal foundation of God's truth. The perils faced by Christians and the church are daunting; but they are no match for the awesome, living Word of God.
KEYS TO THE TEXT
_Inspiration:_ The revelation of God was captured in the writings of Scripture (both Old and New Testaments) by means of "inspiration," which means "breathed out by God" or "God-breathed." Sometimes God told the Bible writers the exact words to say (e.g., Jer. 1:9), but more often He used their minds, vocabularies, and experiences to produce His own perfect infallible, inerrant Word. It is important to note that inspiration applies only to the original autographs of Scripture, not the Bible writers; there are no inspired Scripture writers, only inspired Scripture. So identified is God with His Word that when Scripture speaks, God speaks (cf. Rom. 9:17; Gal. 3:8). Scripture is called "the oracles of God" (Rom. 3:2; 1 Pet. 4:11), and cannot be altered. The Word of God was protected from human error in its original record by the ministry of the Holy Spirit. This ministry of the Spirit extended to both the part (the words) and to the whole in the original writings.
_Equipped:_ This refers to being made fit or complete, enabled to meet all the demands of godly ministry and righteous living. Scripture is the key to this process. The Word accomplishes this in the life of the man of God and in all who follow him.
UNLEASHING THE TEXT
Read 3:1–17, noting the key words and definitions next to the passage.
**2 Timothy 3:1–17 (NKJV)**
**1** _But know this, that in the last days perilous times will come:_
**_the last days_** (v. 1)—This phrase refers to this age, the time since the first coming of the Lord Jesus.
**_perilous times_** (v. 1)—"Perilous" is used to describe the savage nature of two demon-possessed men (Matt. 8:28). The word for "times" had to do with epochs, rather than clock or calendar time. Such savage, dangerous eras or epochs will increase in frequency and severity as the return of Christ approaches (v. 13). The church age is fraught with these dangerous movements accumulating strength as the end nears.
**2** _For men will be lovers of themselves, lovers of money, boasters, proud, blasphemers, disobedient to parents, unthankful, unholy,_
**3** _unloving, unforgiving, slanderers, without self-control, brutal, despisers of good,_
**4** _traitors, headstrong, haughty, lovers of pleasure rather than lovers of God,_
**5** _having a form of godliness but denying its power. And from such people turn away!_
**_having a form of godliness but denying its power_** (v. 5)—"Form" refers to outward shape or appearance. Like the unbelieving scribes and Pharisees, false teachers and their followers are concerned with mere external appearances (see Titus 1:16). Their outward form of Christianity and virtue makes them all the more dangerous.
**6** _For of this sort are those who creep into households and make captives of gullible women loaded down with sins, led away by various lusts,_
**_gullible women_** (v. 6)—Weak in virtue and the knowledge of the truth, and weighed down with emotional and spiritual guilt over their sins, these women were easy prey for the deceitful false teachers.
**7** _always learning and never able to come to the knowledge of the truth._
**_the knowledge of the truth_** (v. 7)—First Timothy 2:4 uses this same phrase, equating it with being saved. Here Paul identified those women (v. 6) and men who were often jumping from one false teacher or cult to another without ever coming to an understanding of God's saving truth in Jesus Christ. The present age, since the coming of Jesus Christ, has been loaded with perilous false teaching that can't save (see vv. 14, 16–17; 1 Tim. 4:1).
**8** _Now as Jannes and Jambres resisted Moses, so do these also resist the truth: men of corrupt minds, disapproved concerning the faith;_
**_Jannes and Jambres_** (v. 8)—Although their names are not mentioned in the Old Testament, they were likely two of the Egyptian magicians who opposed Moses (Exod. 7:11, 22; 8:7, 18–19; 9:11). According to Jewish tradition, they pretended to become Jewish proselytes, instigated the worship of the golden calf, and were killed with the rest of the idolaters. Paul's choice of them as examples may indicate that the false teachers at Ephesus were practicing deceiving signs and wonders.
**_disapproved_** (v. 8)—The same word is translated "debased" in Romans 1:28 and comes from a Greek word meaning "useless" in the sense of being tested (like metal) and shown to be worthless.
**9** _but they will progress no further, for their folly will be manifest to all, as theirs also was._
**_folly . . . manifest_** (v. 9)—Sooner or later, it will be clear that these false teachers are lost fools, as became clear in the case of Jannes and Jambres.
**10** _But you have carefully followed my doctrine, manner of life, purpose, faith, longsuffering, love, perseverance,_
**11** _persecutions, afflictions, which happened to me at Antioch, at Iconium, at Lystra—what persecutions I endured. And out of them all the Lord delivered me._
**_persecutions_** (v. 11)—from a Greek verb that literally means "to put to flight." Paul had been forced to flee from Damascus (Acts 9:23–25), Pisidian Antioch (Acts 13:50), Iconium (Acts 14:6), Thessalonica (Acts 17:10), and Berea (Acts 17:14).
**_Antioch . . . Iconium . . . Lystra_** (v. 11)—As a native of Lystra (Acts 16:1), Timothy vividly recalled the persecution Paul faced in those three cities.
**_the Lord delivered me_** (v. 11)—See 4:17–18; Psalms 34:4, 6, 19; 37:40; 91:2–6, 14; Isaiah 41:10; 43:2; Daniel 3:17; Acts 26:16–17; 2 Corinthians 1:10. The Lord's repeated deliverance of Paul should have encouraged Timothy in the face of persecution by those at Ephesus who opposed the gospel.
**12** _Yes, and all who desire to live godly in Christ Jesus will suffer persecution._
**_who desire to live godly in Christ Jesus will suffer persecution_** (v. 12)—Faithful believers must expect persecution and suffering at the hands of the Christ-rejecting world (see John 15:18–21; Acts 14:22).
**13** _But evil men and impostors will grow worse and worse, deceiving and being deceived._
**14** _But you must continue in the things which you have learned and been assured of, knowing from whom you have learned them,_
**_from whom you have learned_** (v. 14)—See the note on 1:13. To further encourage Timothy to stand firm, Paul reminds him of his godly heritage. The plural form of the pronoun "whom" suggests Timothy was indebted not just to Paul but to others as well (1:5).
**15** _and that from childhood you have known the Holy Scriptures, which are able to make you wise for salvation through faith which is in Christ Jesus._
**_from childhood_** (v. 15)—This is literally "from infancy." Two people whom Timothy was especially indebted to were his mother and grandmother (see note on 1:5), who faithfully taught him the truths of Old Testament Scripture from his earliest childhood, so that he was ready to receive the gospel when Paul preached it.
**_you have known the Holy Scriptures_** (v. 15)—literally "the sacred writings," a common designation of the Old Testament by Greek-speaking Jews
**_wise for salvation_** (v. 15)—The Old Testament Scriptures pointed to Christ (John 5:37–39) and revealed the need for faith in God's promises (Gen. 15:6; see Rom. 4:1–3). Thus, they were able to lead people to acknowledge their sin and need for justification in Christ (Gal. 3:24). Salvation is brought by the Holy Spirit using the Word.
**_faith which is in Christ Jesus_** (v. 15)—Though not understanding all the details involved (see 1 Pet. 1:10–12), Old Testament believers including Abraham (John 8:56) and Moses (Heb. 11:26) looked forward to the coming of the Messiah (Isa. 7:14; 9:6) and His atonement for sin (Isa. 53:5–6). So did Timothy, who responded when he heard the gospel.
**16** _All Scripture is given by inspiration of God, and is profitable for doctrine, for reproof, for correction, for instruction in righteousness,_
**_All Scripture_** (v. 16)—Grammatically similar Greek constructions (Rom. 7:12; 2 Cor. 10:10; 1 Tim. 1:15; 2:3; 4:4) argue persuasively that the translation "all Scripture is given by inspiration . . ." is accurate. Both Old Testament and New Testament Scripture are included.
**_doctrine_** (v. 16)—This refers to the divine instruction or doctrinal content of both the Old Testament and the New Testament (see 2:15; Acts 20:18, 20–21, 27; 1 Cor. 2:14–16; Col. 3:16; 1 John 2:20, 24, 27). The Scripture provides the comprehensive and complete body of divine truth necessary for life and godliness (see Ps. 119:97–105).
**_reproof_** (v. 16)—This refers to rebuke for wrong behavior or wrong belief. The Scripture exposes sin (Heb. 4:12–13) that can then be dealt with through confession and repentance.
**_correction_** (v. 16)—The restoration of something to its proper condition. The word appears only here in the New Testament but was used in extrabiblical Greek of righting a fallen object or helping back to their feet those who had stumbled. Scripture not only rebukes wrong behavior but also points the way back to godly living (see Ps. 119:9–11; John 15:1–2).
**_instruction in righteousness_** (v. 16)—Scripture provides positive training ("instruction" originally referred to training a child) in godly behavior, not merely the rebuke and correction of wrong behavior (Acts 20:32; 1 Tim. 4:6; 1 Pet. 2:1–2).
**17** _that the man of God may be complete, thoroughly equipped for every good work._
**_man of God_** (v. 17)—This is a technical term for an official preacher of divine truth (see the note on 1 Tim. 6:11).
**_complete_** (v. 17)—capable of doing everything one is called to do (see Col. 2:10)
**_thoroughly equipped_** (v. 17)—Through the Scriptures, believers are enabled to meet all the demands of godly ministry and righteous living. The Word not only accomplishes this in the life of the man of God, but also in all who follow him (Eph. 4:11–13).
1) What kinds of sins did Paul say would become more prevalent in the last days (3:1–9)? Why?
[Your Response Here]
2) What do you learn about Paul's "mentoring" methods (3:10–14)? How did Timothy carefully follow Paul's example?
[Your Response Here]
3) What character qualities did Paul model for his protégé?
[Your Response Here]
_(Verses to consider: Acts 20:18–21; Rom. 8:18; 1 Cor. 4:16–17; Eph. 5:2; Phil. 1:17–18)_
4) Look at the amazing statements about the Word of God in verses 15–17. What is its nature? Why did God give us the Scriptures?
[Your Response Here]
GOING DEEPER
The Old Testament psalmist wrote often about the power and truth of God's Word. Read Psalm 119:9–32.
**9** _How can a young man cleanse his way? By taking heed according to Your word._
**10** _With my whole heart I have sought You; oh, let me not wander from Your commandments!_
**11** _Your word I have hidden in my heart, that I might not sin against You._
**12** _Blessed are You, O L ORD! Teach me Your statutes._
**13** _With my lips I have declared all the judgments of Your mouth._
**14** _I have rejoiced in the way of Your testimonies, as much as in all riches._
**15** _I will meditate on Your precepts, and contemplate Your ways._
**16** _I will delight myself in Your statutes; I will not forget Your word._
**17** _Deal bountifully with Your servant, that I may live and keep Your word._
**18** _Open my eyes, that I may see wondrous things from Your law._
**19** _I am a stranger in the earth; do not hide Your commandments from me._
**20** _My soul breaks with longing for Your judgments at all times._
**21** _You rebuke the proud—the cursed, who stray from Your commandments._
**22** _Remove from me reproach and contempt, for I have kept Your testimonies._
**23** _Princes also sit and speak against me, but Your servant meditates on Your statutes._
**24** _Your testimonies also are my delight and my counselors._
**25** _My soul clings to the dust; revive me according to Your word._
**26** _I have declared my ways, and You answered me; teach me Your statutes._
**27** _Make me understand the way of Your precepts; so shall I meditate on Your wonderful works._
**28** _My soul melts from heaviness; strengthen me according to Your word._
**29** _Remove from me the way of lying, and grant me Your law graciously._
**30** _I have chosen the way of truth; Your judgments I have laid before me._
**31** _I cling to Your testimonies; O L ORD, do not put me to shame!_
**32** _I will run the course of Your commandments, for You shall enlarge my heart._
EXPLORING THE MEANING
5) How would you characterize the psalmist's attitude toward God's Word?
[Your Response Here]
_(Verses to consider: Ps. 19; 119:69–77, 97, 103, 127–133)_
6) List several benefits stated in Psalm 119 of knowing and obeying the Word.
[Your Response Here]
7) Read Hebrews 4:12–13. What does this passage say about the manner in which God's Word exposes sin in a believer's life?
[Your Response Here]
TRUTH FOR TODAY
The church today faces times of unparalleled difficulty and danger. As extraordinary opportunities for spreading the gospel increase with rapidity, attacks on the church are also increasing with great speed. Heresy, apostasy, self-will, and their accompanying moral decadence are engulfing the evangelical church. Like cancer cells that rebel against the body, these evils are in rebellion against God by corrupting and weakening the church, the body of Christ. Also like cancer cells, the evils multiply rapidly and choke out and destroy normal cells. Much like white cells in the blood, which will not attack cancerous cells because they are identified with the body, many naive and careless church leaders take no action against corruption in the church simply because the corruption hides behind the guise of orthodoxy. Simply put, much of the church is in rebellion against the Lord.
REFLECTING ON THE TEXT
8) Look over the list of sinful behaviors in the last days (vv. 1–7). Do you see any that you have tolerated in your own heart? If so, which ones?
[Your Response Here]
9) How much does pop culture promote these very attitudes and actions? How can you respond to the cultural pull?
[Your Response Here]
10) Chapter 3 makes clear that Timothy followed Paul and that Paul served as a spiritual mentor to the younger Timothy. What older and wiser Christian do you know who might be willing to serve as a mentor to you in the Christian life? Is there a younger Christian in whom you might be able to invest your life?
[Your Response Here]
11) This chapter concludes with a declaration of the inspiration and power of God's Word. How equipped by Scripture are you? Check each of the following statements that are true of your life:
_____ I have read the Bible cover to cover.
_____ I regularly take notes and listen attentively to the preached Word of God.
_____ I make it a habit to memorize Scripture.
_____ I know how to study the Bible for myself (figuring out what it says, what it means and how it applies to my life).
_____ I spend time meditating on scriptural truths that I've learned.
What needs to change in your view and approach to studying and knowing the Bible? Why is this important?
[Your Response Here]
Ask God to show you how to become better equipped to serve Him, and to renew your love for His Word.
PERSONAL RESPONSE
Write out additional reflections, questions you may have, or a prayer.
[Your Response Here]
ADDITIONAL NOTES
[Your Response Here]
**11**
PREACHING WITH INTEGRITY
_2 Timothy 4:1–5_
DRAWING NEAR
What is the most powerful sermon you can recall hearing? What made it so meaningful?
[Your Response Here]
What qualities do you identify as part of great preaching?
[Your Response Here]
THE CONTEXT
Paul hand-picked Timothy to pastor this growing congregation and to defend the faith, restoring the church to orthodoxy. Paul did not focus on Timothy's external success, but on his internal condition. Paul did not discuss church programs or size; on the contrary, he concentrated on church health. And since a church's health almost always mirrors the spiritual well-being of its leaders, Paul addressed Timothy's own motives and character.
In many regards, 2 Timothy is a spiritual inventory. It focuses on issues such as commitment, faithfulness, integrity, and discipline. No preacher of truth can ever be powerful in public unless and until he is first powerful in his private life. Although 4:1–5 is directed first and foremost to Timothy, it contains a valuable commission to all believers in every era. Why? Churches are obligated to hold their pastors accountable to these divine precepts.
KEYS TO THE TEXT
_Preaching:_ Preaching that does not strive to communicate God's truth to man is not legitimate preaching. The preacher who avoids doctrine because he thinks it is too technical or impractical has abdicated his biblical responsibility. Called to speak with the authority of God, the preacher must be an expositor of God's Word. Moving stories, moralistic advice, psychology, comedy, and opinion all are void of certainty. Only the authoritative proclamation of the Word fits the intent of God in the call to preach. Paul commanded Timothy to stick with the confrontational preaching of the powerful Word. There is no closed season on the Word. We must proclaim it constantly and incessantly.
_Evangelist:_ Used only two other times in the New Testament (see Acts 21:8; Eph. 4:11), this word always refers to a specific office of ministry for the purpose of preaching the gospel to non-Christians. Based on Ephesians 4:11, it is very basic to assume that all churches would have both pastor-teachers and evangelists. But the related verb "to preach the gospel" and the related noun "gospel" are used throughout the New Testament not only in relation to evangelists but also to the call for every Christian, especially preachers and teachers, to proclaim the gospel. Paul did not call Timothy to the office of an evangelist, but to "do the work" of one.
UNLEASHING THE TEXT
Read 4:1–5, noting the key words and definitions next to the passage.
**2 Timothy 4:1–5 (NKJV)**
**1** _I charge you therefore before God and the Lord Jesus Christ, who will judge the living and the dead at His appearing and His kingdom:_
**_I charge you_** (v. 1)—Or better "command"; the original Greek has the idea of issuing a forceful order or directive (see 2:14; 1 Tim. 1:18; 5:21).
**_before God and the Lord Jesus Christ_** (v. 1)—The Greek construction also allows the translation "in the presence of God, even Christ Jesus," which is probably the best rendering since He is about to be introduced as the judge (see John 5:22). Everyone who ministers the Word of God is under the omniscient scrutiny of Christ (see 2 Cor. 2:17; Heb. 13:17).
**_Christ, who will judge_** (v. 1)—The grammatical construction suggests imminency—that Christ is about to judge. Paul is emphasizing the unique accountability that all believers, and especially ministers of the Word of God, have to Christ as Judge. Service to Christ is rendered both under His watchful eye and with the knowledge that as Judge He will one day appraise the works of every believer (see 1 Cor. 3:12–15; 4:1–5; 2 Cor. 5:10). That is not a judgment of condemnation, but one of evaluation. With regard to salvation, believers have been judged already and declared righteous—they are no longer subject to the condemnation of sin (Rom. 8:1–4).
**_the living and the dead_** (v. 1)—Christ will ultimately judge all men in three distinct settings: (1) the judgment of believers after the Rapture; (2) the sheep and goats judgment of the nations, in which believers will be separated from unbelievers (Matt. 25:31–33), for entrance into the millennial kingdom; and (3) the Great White Throne judgment of unbelievers only (Rev. 20:11–15). Here, the apostle is referring to judgment in a general sense, encompassing all those elements.
**_His appearing_** (v. 1)—The Greek word translated "appearing" literally means "a shining forth" and was used by the ancient Greeks of the supposed appearance to men of a pagan god. Here, Paul is referring generally to Christ's second coming, when He will judge "the living and the dead" (see previous note) and establish His millennial and eternal kingdom (see note on 1 Tim. 6:14).
**2** _Preach the word! Be ready in season and out of season. Convince, rebuke, exhort, with all longsuffering and teaching._
**_the word_** (v. 2)—the entire written Word of God, His complete revealed truth as contained in the Bible (see 3:15–16; Acts 20:27)
**_Be ready_** (v. 2)—The Greek word has a broad range of meanings, including suddenness (Luke 2:9; Acts 12:7) or forcefulness (Luke 20:1; Acts 4:1; 6:12; 23:27). Here the form of the verb suggests the complementary ideas of urgency, preparedness, and readiness. It was used of a soldier prepared to go into battle or a guard who was continually alert for any surprise attack—attitudes which are imperative for a faithful preacher.
**_in season and out of season_** (v. 2)—The faithful preacher must proclaim the Word when it is popular and/or convenient, and when it is not; when it seems suitable to do so, and when it seems not. The dictates of popular culture, tradition, reputation, acceptance, or esteem in the community (or in the church) must never alter the true preacher's commitment to proclaim God's Word.
**_Convince, rebuke_** (v. 2)—This reflects the negative side of preaching the Word (the "reproof " and "correction"; see 3:16). The Greek word for "convince" refers to correcting behavior or false doctrine by using careful biblical argument to help a person understand the error of his actions. The Greek word for "rebuke" deals more with correcting the person's motives by convicting him of his sin and leading him to repentance.
**_exhort . . . teaching_** (v. 2)—the positive side of preaching (the "doctrine" and "instruction"; see 3:16)
**3** _For the time will come when they will not endure sound doctrine, but according to their own desires, because they have itching ears, they will heap up for themselves teachers;_
**_not endure_** (v. 3)—This refers to holding up under adversity and can be translated "tolerate." Paul here warns Timothy that, in the dangerous seasons of this age, many people would become intolerant of the confrontational, demanding preaching of God's Word (1:13, 14; 1 Tim. 1:9–10; 6:3–5).
**_sound doctrine_** (v. 3)—See the notes on 1:13; 1 Timothy 4:6; cf. Titus 2:1.
**_their own desires . . . itching ears_** (v. 3)—Professing Christians or nominal believers in the church follow their own desires and flock to preachers who offer them God's blessings apart from His forgiveness, and His salvation apart from their repentance. They have an itch to be entertained by teachings that will produce pleasant sensations and leave them with good feelings about themselves. Their goal is that men preach "according to their own desires." Under those conditions, people will dictate what men preach, rather than God dictating it by His Word.
**4** _and they will turn their ears away from the truth, and be turned aside to fables._
**_fables_** (v. 4)—This refers to false ideologies, viewpoints, and philosophies in various forms that oppose sound doctrine (see 2 Cor. 10:3–5; 1 Tim. 1:4; 4:7; Titus 1:14; 2 Pet. 1:16).
**5** _But you be watchful in all things, endure afflictions, do the work of an evangelist, fulfill your ministry._
1) Why is preaching such a serious calling?
[Your Response Here]
_(Verses to consider: 1 Cor. 3:12–15; Gal. 1:10; James 3:1–2)_
2) According to this passage, what should the job description of the preacher encompass?
[Your Response Here]
_(Verses to consider: Matt. 3:1–2; 1 Cor. 2:1–5; 2 Tim. 1:13–14; 2:15; 1 Pet. 3:15)_
3) What obstacles will preachers of the truth encounter in the last days?
[Your Response Here]
_(Verses to consider: Isa. 6:8–10; 1 Tim. 4:1–3)_
GOING DEEPER
In a related passage, Paul talks further about his work. Read Colossians 1:24–29.
**24** _I now rejoice in my sufferings for you, and fill up in my flesh what is lacking in the afflictions of Christ, for the sake of His body, which is the church,_
**25** _of which I became a minister according to the stewardship from God which was given to me for you, to fulfill the word of God,_
**26** _the mystery which has been hidden from ages and from generations, but now has been revealed to His saints._
**27** _To them God willed to make known what are the riches of the glory of this mystery among the Gentiles: which is Christ in you, the hope of glory._
**28** _Him we preach, warning every man and teaching every man in all wisdom, that we may present every man perfect in Christ Jesus._
**29** _To this end I also labor, striving according to His working which works in me mightily._
EXPLORING THE MEANING
4) How does Paul describe his own preaching ministry in this passage?
[Your Response Here]
_(Verses to consider: 2 Cor. 4:5; Gal. 1:10–11)_
5) What is the mystery Paul preached about?
[Your Response Here]
6) Read Jeremiah 5:30–31. What observation did the prophet make? How have you seen this truth verified throughout the history of the church? How do you see it verified currently?
[Your Response Here]
_(Verses to consider: Ezek. 33:31–32; Acts 17:21; Rom. 1:18; 2 Cor. 4:4)_
7) Read 2 Corinthians 4:4–5. How did Paul's preaching contrast with the self-centered preaching of the false teachers? What is the answer for combating false and self-centered preaching?
[Your Response Here]
TRUTH FOR TODAY
There are gifted orators who can sway an audience with the power of their persuasive rhetoric. There are men who are erudite, knowledgeable, well-trained, and worldly-wise, who can cause other men to change their minds about certain matters. There are men who can relate moving stories that tug at a hearer's heart and move him emotionally. Throughout the history of the church, including our own time, God has chosen to endow some ministers with such abilities. But God also has chosen not to bless every faithful preacher in those particular ways. Nevertheless, He charges them with the same task of preaching His Word, because the spiritual power and effectiveness of preaching does not rest in the skill of the speaker, but in the truth.
REFLECTING ON THE TEXT
8) How can you encourage your own preacher/pastor this week?
[Your Response Here]
9) Even if God hasn't called you to preach, He has called you to share His truth with others. What people in your life seem to be most receptive to the Word of God right now? What will you do to take advantage of this window of opportunity?
[Your Response Here]
10) Paul used the anticipated return of Christ (and subsequent judgment) to motivate Timothy to preach faithfully. What does the second advent motivate you to change about your life?
[Your Response Here]
PERSONAL RESPONSE
Write out additional reflections, questions you may have, or a prayer.
[Your Response Here]
ADDITIONAL NOTES
[Your Response Here]
**12**
LAST WORDS
_2 Timothy 4:6–22_
DRAWING NEAR
Suppose you were allowed to write a short final letter to your dearest loved ones. What topics would you discuss? What counsel would you give, and why?
[Your Response Here]
Does the prospect of standing before Christ fill you with joy and anticipation, or with fear and trepidation? Why?
[Your Response Here]
THE CONTEXT
Last words are always revealing. Napoleon supposedly said, "I die before my time; and my body will be given back to the earth, to become the food of worms." Gandhi reportedly declared, "For the first time in fifty years I find myself in a slough of despond. All about me is darkness. I am praying for light." Clearly, as men and women stand on the brink of eternity, they are seldom able to mask their true feelings, thoughts, and fears.
As the apostle Paul neared the end of his life, however, he was able to look back without regret or remorse. In fact, his mood is one of triumph, and his tone is hopeful. Most scholars believe this was the last letter Paul ever wrote. In this final chapter he examines his life from three perspectives: the present reality of the end of his life, for which he was ready; the past, when he had been faithful; and the future, as he anticipated his heavenly reward.
In the closing verses of this letter, Paul brought his young ministry associate up to date on the spiritual condition, activities, and whereabouts of certain men and women who had either helped or harmed his ministry. Here we see deeply into the heart of this wonderful man of God. Read this section carefully, and you will be challenged by the examples—both good and bad—of the people who either aided or opposed Paul in his quest to live to the glory of God by helping to build up the church of Jesus Christ.
KEYS TO THE TEXT
_Crown of Righteousness:_ The Greek word for "crown" literally means "surrounding," and it was used of the plaited wreaths or garlands placed on the heads of dignitaries and victorious military officers or athletes. Linguistically, crown "of righteousness" can mean either that righteousness is the source of the crown, or that righteousness is the nature of the crown. Like the "crown of life" (James 1:12), the "crown of rejoicing" (1 Thess. 2:19), the "imperishable crown" (1 Cor. 9:25), and the "crown of glory" (1 Pet. 5:4)—in which life, rejoicing, imperishability, and glory describe the nature of the crown—the context here seems to indicate that the crown represents eternal righteousness.
UNLEASHING THE TEXT
Read 4:6–22, noting the key words and definitions next to the passage.
**2 Timothy 4:6–22 (NKJV)**
**6** _For I am already being poured out as a drink offering, and the time of my departure is at hand._
**_already_** (v. 6)—meaning his death was imminent
**_a drink offering_** (v. 6)—in the Old Testament sacrificial system, this was the final offering that followed the burnt and grain offerings prescribed for the people of Israel (Num. 15:1–16). Paul saw his coming death as his final offering to God in a life that had already been full of sacrifices to Him.
**_my departure_** (v. 6)—This refers to Paul's death. The Greek word essentially refers to the loosening of something, such as the mooring ropes of a ship or the ropes of a tent; thus it eventually acquired the secondary meaning of "departure."
**7** _I have fought the good fight, I have finished the race, I have kept the faith._
**_have fought . . . have finished . . . have kept_** (v. 7)—The form of the three Greek verbs "have fought, have finished, have kept" indicates completed action with continuing results. Paul saw his life as complete—he had been able to accomplish through the Lord's power all that God called him to do. He was a soldier (2:3–4; 2 Cor. 10:3; 1 Tim. 6:12; Philem. 2), an athlete (1 Cor. 9:24–27; Eph. 6:12), and a guardian (1:13–14; 1 Tim. 6:20–21).
**_the faith_** (v. 7)—the truths and standards of the revealed Word of God
**8** _Finally, there is laid up for me the crown of righteousness, which the Lord, the righteous Judge, will give to me on that Day, and not to me only but also to all who have loved His appearing._
**_that Day_** (v. 8)—See the note on 1:12.
**9** _Be diligent to come to me quickly;_
**_Be diligent to come to me quickly_** (v. 9)—Paul longed to see his beloved co-worker, but it was imperative that Timothy make haste because Paul knew his days were numbered (v. 6).
**10** _for Demas has forsaken me, having loved this present world, and has departed for Thessalonica—Crescens for Galatia, Titus for Dalmatia._
**_Demas_** (v. 10)—He had been one of Paul's closest associates, along with Luke and Epaphras (see Col. 4:14; Philem. 24).
**_forsaken_** (v. 10)—This Greek word means "to utterly abandon," with the idea of leaving someone in a dire situation. Demas was a fair-weather disciple who had never counted the cost of genuine commitment to Christ. His kind are described by our Lord in Matthew 13:20–21 (see John 8:31; 1 John 2:1).
**_loved this present world_** (v. 10)—See James 4:4.
**_Thessalonica_** (v. 10)—Demas may have considered this city a safe haven.
**_Crescens_** (v. 10)—In contrast to Demas, Crescens must have been faithful and dependable, since Paul sent him to Galatia, a Roman province in central Asia Minor, where Paul ministered on each of his three missionary journeys.
**_Titus_** (v. 10)—Paul's closest friend and coworker next to Timothy (Titus 1:5)
**_Dalmatia_** (v. 10)—also known as Illyricum (Rom. 15:19), a Roman province on the east coast of the Adriatic Sea, just north of Macedonia
**11** _Only Luke is with me. Get Mark and bring him with you, for he is useful to me for ministry._
**_Luke_** (v. 11)—the author of the Gospel of Luke and Acts, and Paul's devoted friend and personal physician, who could not carry the burden of ministry in Rome by himself
**_Get Mark and bring him with you_** (v. 11)—Evidently Mark lived somewhere along the route Timothy would take from Ephesus to Rome. The one who was the author of the Gospel of Mark (sometimes called John), cousin of Barnabas (Col. 4:10), and devoted fellow worker (Philem. 24), had once left Paul and Barnabas in shame, but had become by this time a valued servant.
**12** _And Tychicus I have sent to Ephesus._
**_Tychicus_** (v. 12)—Paul had either sent him to Ephesus earlier, or he was sending him there to deliver this second letter to Timothy, just as Tychicus had previously delivered Paul's letters to the churches at Ephesus (Eph. 6:12), Colosse (Col. 4:7), and possibly to Titus.
**13** _Bring the cloak that I left with Carpus at Troas when you come—and the books, especially the parchments._
**_cloak_** (v. 13)—a large, heavy wool garment that doubled as a coat and blanket in cold weather, which Paul would soon face (v. 21)
**_Carpus_** (v. 13)—an otherwise unknown acquaintance of Paul whose name means "fruit"
**_Troas_** (v. 13)—a seaport of Phyrgia, in Asia Minor
**_the books, especially the parchments_** (v. 13)—"Books" refers to papyrus scrolls, possibly Old Testament books. "Parchments" were vellum sheets made of treated animal hides and thus extremely expensive. They may have been copies of letters he had written or blank sheets for writing other letters. That Paul did not have these already in his possession leads to the possible conclusion that he was arrested in Troas and had no opportunity to retrieve them.
**14** _Alexander the coppersmith did me much harm. May the Lord repay him according to his works._
**_Alexander the coppersmith_** (v. 14)—This is probably not the same man whom Paul delivered to Satan along with Hymenaeus (1 Tim. 1:20), since Paul singles him out as the one who was a "coppersmith." This Alexander, however, may have been an idol maker (see Acts 19:24).
**_did me much harm_** (v. 14)—Alexander opposed Paul's teaching and likely spread his own false doctrine. He may have been instrumental in Paul's arrest and may even have borne false witness against him (see Acts 19:23–41).
**_May the Lord repay him_** (v. 14)—Paul left vengeance in God's hands (Deut. 32:35; Rom. 12:19).
**15** _You also must beware of him, for he has greatly resisted our words._
**16** _At my first defense no one stood with me, but all forsook me. May it not be charged against them._
**_first defense_** (v. 16)—the Greek word for "defense" gives us the English words "apology" and "apologetics." It referred to a verbal defense used in a court of law. In the Roman legal system, an accused person received two hearings: the _prima acti_ o, much like a contemporary arraignment, established the charge and determined if there was a need for a trial. The _secunda actio_ then established the accused's guilt or innocence. The defense Paul referred to was the _prima acti_ o.
**_May it not be charged against them._** (v. 16)—like Stephen (Acts 7:60) and the Lord Himself (Luke 23:24)
**17** _But the Lord stood with me and strengthened me, so that the message might be preached fully through me, and that all the Gentiles might hear. Also I was delivered out of the mouth of the lion._
**_But the Lord stood with me_** (v. 17)—The Lord fulfills His promise never to "leave or forsake" His children (Deut. 31:6, 8).
**_the message might be preached fully through me_** (v. 17)—As he had done in the past (Acts 26:2–29), Paul was able to proclaim the gospel before a Roman tribunal.
**_all the Gentiles might hear_** (v. 17)—By proclaiming the gospel to such a cosmopolitan, pagan audience, Paul could say that he had reached all the Gentiles with the gospel. This was a fulfillment of his commission (Acts 9:15–16; 26:15–18).
**_the mouth of the lion_** (v. 17)—See Daniel 6:26–27. This was a common figure for mortal danger (Ps. 22:21; 35:17), which was a common occurrence for Paul (see Acts 14:19; 2 Cor. 4:8–12; 6:4–10; 11:23–27). Peter pictured Satan as a lion in 1 Peter 5:8.
**18** _And the Lord will deliver me from every evil work and preserve me for His heavenly kingdom. To Him be glory forever and ever. Amen!_
**_will deliver me from every evil work_** (v. 18)—On the basis of the Lord's present work, strengthening Paul and standing with him, Paul had hope for the Lord's future work. He knew God would deliver him from all temptations and plots against him (2 Cor. 1:8–10).
**_preserve me for His heavenly kingdom_** (v. 18)—Paul knew the completion of his own salvation was nearer than when he first believed (see Rom. 13:11; 2 Cor. 5:8; Phil. 1:21).
**19** _Greet Prisca and Aquila, and the household of Onesiphorus._
**_Prisca and Aquila_** (v. 19)—Paul first met these two faithful friends in Corinth after they fled Italy (see note on Acts 18:2). They ministered for some time in Ephesus (Acts 18:18–19), later returned to Rome for a period of time (Rom. 16:3), and had returned to Ephesus.
**_the household of Onesiphorus_** (v. 19)—See the note on 1:16.
**20** _Erastus stayed in Corinth, but Trophimus I have left in Miletus sick._
**_Erastus_** (v. 20)—probably the city treasurer of Corinth, who sent greetings through Paul to the church at Rome (see Rom. 16:23)
**_Corinth_** (v. 20)—leading city in Greece
**_Trophimus_** (v. 20)—a native of Asia, specifically Ephesus, who had accompanied Paul from Greece to Troas (see Acts 20:4)
**_Miletus_** (v. 20)—a city and seaport in the province of Lycia, located forty miles south of Ephesus (see Acts 20:15)
**21** _Do your utmost to come before winter. Eubulus greets you, as well as Pudens, Linus, Claudia, and all the brethren._
**_before winter_** (v. 21)—In view of the coming season and the cold Roman jail cell, Paul needed the cloak for warmth. He would also have less opportunity to use the books and parchments as the duration of light grew shorter in winter.
**_Eubulus . . . Pudens, Linus, Claudia_** (v. 21)—The first three names are Latin, which could indicate they were from Italy and had been members in the church at Rome. "Claudia" was a believer and close friend of whom nothing else is known.
**22** _The Lord Jesus Christ be with your spirit. Grace be with you. Amen._
**_Grace be with you._** (v. 22)—This is the same benediction as in Paul's previous letter to Timothy (see note on 1 Tim. 6:21). The "you" is plural, which means it extended to the entire Ephesian congregation.
1) Sensing that his time on earth was drawing to a close, how did the apostle Paul summarize his life (4:6–8)?
[Your Response Here]
_(Verses to consider: 2 Cor. 11:23–29; 2 Pet. 1:12–15)_
2) As Paul looked to the future, what was his hope?
[Your Response Here]
_(Verses to consider: Prov. 24:12; Matt. 5:11–12; Phil. 3:14; Heb. 11:6)_
3) Paul lists a number of individuals at the end of this epistle. What facts are revealed about each of these associates and enemies of Paul?
[Your Response Here]
GOING DEEPER
After Jesus' resurrection, He appeared to His disciples. Read what Jesus commanded in Matthew 28:16–20.
**16** _Then the eleven disciples went away into Galilee, to the mountain which Jesus had appointed for them._
**17** _When they saw Him, they worshiped Him; but some doubted._
**18** _And Jesus came and spoke to them, saying, "All authority has been given to Me in heaven and on earth._
**19** _Go therefore and make disciples of all the nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit,_
**20** _teaching them to observe all things that I have commanded you; and lo, I am with you always, even to the end of the age." Amen._
EXPLORING THE MEANING
4) What significant truths and commands did Christ communicate in His final words? How did Paul fulfill these?
[Your Response Here]
5) What echoes of Christ's final words do you hear in Paul's last words?
[Your Response Here]
_(Verses to consider: Luke 24:44–51; Acts 1:6–9)_
6) Read Philippians 1:21. How did Paul view death? Why?
[Your Response Here]
_(Verses to consider: Isa. 25:8; Hos. 13:14; 1 Cor. 9:25; 15:53–55)_
TRUTH FOR TODAY
In 1904, William Borden, a member of the Borden dairy family, finished high school in Chicago and was given a world cruise as a graduation present. Particularly while traveling through the near East and Far East, he became heavily burdened for the lost. After returning home, he spent seven years at Princeton University, the first four in undergraduate work and the last three in seminary. While in school, he penned these words in the back of his Bible: "No reserves."
Although his family pleaded with him to take control of the business, which was foundering, he insisted that God's call to the mission field had priority. After disposing of his wealth, he added, "No retreat" after "No reserves." On his way to China to witness to the Muslims there, he contracted cerebral meningitis in Egypt and died within a month. After his death, someone looking through his Bible discovered these final words: "No regrets." He knew that the Lord does not require success, only faithfulness.
REFLECTING ON THE TEXT
7) How does the life of Demas serve as a warning to you today? How does the life of John Mark serve as a hopeful reminder?
[Your Response Here]
8) Fast forward in your mind to the end of your life. Now look back. What kind of life do you want to have lived? How do you wish to be remembered? Using the answers to those questions, make a short list of things that you want God to begin changing in your life.
[Your Response Here]
9) What is the most meaningful lesson you've learned from your study of 1 & 2 Timothy?
[Your Response Here]
10) How do you want your life to be different as a result?
[Your Response Here]
PERSONAL RESPONSE
Write out additional reflections, questions you may have, or a prayer.
[Your Response Here]
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Available at your local Christian Bookstore
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# Table of Contents
1. Cover Page
2. Title Page
3. Copyright Page
4. Ebook Instructions
5. Contents
6. Introduction to 1 Timothy
7. 1. Beware of False Doctrine!: 1 Timothy 1:1-20
8. 2. The Importance of Prayer: 1 Timothy 2:1-8
9. 3. The Role of Women: 1 Timothy 2:9-15
10. 4. Qualifications for Leadership: 1 Timothy 3:1-16
11. 5. False Teaching versus Truth: 1 Timothy 4:1-16
12. 6. Pastoral Responsibilities: 1 Timothy 5:1-6:2
13. 7. The Man of God: 1 Timothy 6:3-21
14. Introduction to 2 Timothy
15. 8. Not Ashamed: 2 Timothy 1:1-18
16. 9. Be Diligent: 2 Timothy 2:1-26
17. 10. Equipped for Good Works: 2 Timothy 3:1-17
18. 11. Preaching With Integrity: 2 Timothy 4:1-5
19. 12. Last Words: 2 Timothy 4:6-22
## List of Pages
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| {
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Halfdan (Alfdeni, født ca. 758, død efter 807) var formentlig en person i den danske kongeslægt.
Der vides kun lidt om ham, da han kun optræder i et par samtidige kilder.
I 782 oplyser de Frankiske rigsannaler, at Halfdan sammen med Osmund og Godfred dukker op som udsendinge fra kong Sigfred ved Karl den Stores rigsdag i Sachsen ved Paderborn, men yderligere oplysninger foreligger ikke.
I 807 oplyser franske annaler, at "Alfdeni" (Halfdan) med et stort følge underkaster sig Karl den Store. Han betegnes som "Northmannorum dux", det vil sige en mindre nordisk fyrste. Med sig havde han sine fire sønner: Anulo, Hemming, Harald Klak og Reginfred. Dette sker på et tidspunkt, da den danske konge hed Godfred. Denne var i 804 indbudt til møde med Karl den Store efter, at denne havde afsluttet underkuelsen af sakserne, og han mødte med en stor flåde, men mødet kom ikke i stand. I 808 foretager Godfred sit angreb på abodritterne, hvorunder handelspladsen Reric afbrændes og købmændene tvangsforflyttes til Hedeby. Det er nærliggende at formode, at Halfdan har været imod den konfrontationspolitik i forhold til Karl den Store, som Godfred stod for, og at dette har ført ham til beslutningen i 807. Der kan også ligge en intern magtkamp bag. Historikerne formoder, at hans valg var påvirket af besøget i 782, selvom dette ikke kan bevises.
Hans senere skæbne kendes ikke, men formodentlig er han blevet vel modtaget og har fået en ærefuld plads ved hoffet, og flere af hans sønner optræder senere som lensmænd for Karl.
Noter
Litteratur
Peter Sawyer: "Da Danmark blev Danmark. Fra ca. år 700 til ca. 1050" (i: Olaf Olsen (red.): Gyldendal og Politikens Danmarkshistorie; bind 3; København 1988; )
Poul Skaaning: Vikingestormen. Togter mod Vesteuropa 793-937; Viborg 2006;
Eksterne henvisninger
Annales Regni Francorum Frankiske Annaler
Sagnkonger | {
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Santa Maria Futebol Clube, mais conhecido como Santa Maria FC ou simplesmente Santa Maria , é um clube português sedeado na freguesia de Galegos Santa Maria em Barcelos. É mais conhecido pela sua equipa de futebol, que joga atualmente na AF Braga Pro-Nacional, a competição mais importante do Distrito de Braga.
Fundado a 25 de dezembro de 1943, é um dos clube mais representativos do concelho de Barcelos, juntamente com o Gil Vicente FC, AFC Martim e o GFC Pousa. As alcunhas da equipa são "Galegos", "Santa". Os seus jogos de futebol em casa são realizados no Estádio da Devesa, inaugurado em 1944 e que tem uma capacidade de 4000 lugares.
O Santa Maria FC tem um total de 6 títulos conquistados, todos de carácter regional. Ganhou 1 título da AF Braga Divisão de Honra, 1 título AF Braga 1º Divisão, 1 título AF Braga 2º Divisão e 3 títulos da AF Braga Taça.
História
A Fundação
Desde as primeiras décadas do séc. XX que a cidade de Barcelos foi conhecendo diversas modalidades desportivas, uma das quais o futebol que acompanhou a popularidade que o país inteiro também seguia de perto.
No decorrer destas primeiras décadas vários clubes na cidade foram sendo fundados e muitos acabaram por cair, pois as dificuldades em sustentar um clube amador de futebol eram muitas. No entanto ao redor das freguesias que circundam a cidade a formação de equipas com o intuito para a prática desportiva ainda não era uma realidade. Assim sendo, apenas na década de quarenta do século passado era fundado em pleno Natal de 1943, um dos clubes mais representativos do concelho de Barcelos, o Santa Maria Futebol Clube, na freguesia de Galegos Santa Maria, e que mais tarde se tornaria uma das referencias do futebol e do desporto barcelense a nível nacional.
Os anos de Ouro
Em 1987–88, sobe pela primeira vez à antiga II Divisão, depois de ter conquistado títulos regionais em 1966–67 e em 1984–85. Contudo, o último lugar ditou a descida à III Divisão. Em 1994–95 consegue subir novamente, desta vez à II Divisão B, mas é novamente despromovido na competição. Isto provocou tal impacto que o Santa Maria chegou a estar na 1ª Divisão da AF Braga (o terceiro nível da associação), depois de três despromoções consecutivas. Contudo, acabou em primeiro lugar nessa época e voltou a estar na Divisão de Honra da AF Braga durante algumas épocas.
O novo milénio
Em 2012–13 subiu novamente aos escalões profissionais(ao Campeonato Nacional de Seniores, depois de estar na III Divisão), mas devido a uma reformulação do sistema de ligas de futebol, a equipa manteve-se no mesmo nível. Entre as épocas de 2013 e 2015, o Galegos ficou conhecido em Portugal como o Tomba Gigantes, resultado das históricas partidas para a Taça de Portugal, com o CD Nacional em 2013-14, vencendo na Devesa por 1-0 e com a Académica de Coimbra, na época a seguir vencendo de novo na Devesa por 1-0 chegando nesse ano aos oitavos de final da prova rainha. Embora a campanha na Taça tenha sido muito positiva para o clube, no campeonato a situação é diferente e volta a descer aos distritais, chegando a descer para a Divisão de Honra da AF Braga, 2º maior campeonato da associação.
O ano a seguir a descida, em 2017-18 o clube de Galegos sagra-se campeão subindo ao Pro-Nacional, competição que até 2019-20 ainda disputa, conseguindo terminar em 14º lugar, conseguindo a permanência.
Plantel para 2022-23
Renovações:
João Salgueiros (Treinador) - + 1 ano de contrato(jun. 2023)
Fábio Costa - + 1 ano de contrato(jun. 2023)
Branca - + 1 ano de contrato(jun. 2023)
Dani Coelho - + 1 ano de contrato(jun. 2023)
David Rodrigues - + 1 ano de contrato(jun. 2023)
Eduardo Campos - + 1 ano de contrato(jun. 2023)
João Rodrigues - + 1 ano de contrato(jun. 2023)
Luís Salgueiros - + 1 ano de contrato(jun. 2023)
Pedrinho - + 1 ano de contrato(jun. 2023)
Naifas - + 1 ano de contrato(jun. 2023)
Pedro Esteves - + 1 ano de contrato(jun. 2023)
Tinoco - + 1 ano de contrato(jun. 2023)
Vitinha - + 1 ano de contrato(jun. 2023)
Xavi - + 1 ano de contrato(jun. 2023)
Rúben Borges - + 1 ano de contrato(jun. 2023)
Miguel Coelho - + 1 ano de contrato(jun. 2023)
Afonso Abreu - + 1 ano de contrato(jun. 2023)
Contratações:
Tiago Gonçalves - FC Famalicão (Sub-23) (jun. 2023)
João Rocha - FC Marinhas (jun. 2023)
Tiago São Bento - GD Lagoa (jun. 2023)
Subidas das Camadas Jovens:
Simão Fernandes - Sub23
Saídas:
Salgueiro - Fim de carreira desportiva
Plantel Sub-23 para 2022-23
Infraestruturas
Estádio da Devesa
O Estádio da Devesa, é um estádio de futebol situado na freguesia de Galegos Santa Maria, em Barcelos e tem capacidade para 4.000 pessoas. Foi inaugurado em 1944, e é usado pela equipa sénior e pela equipa de juniores do clube. O campo contem atualmente 3 bancadas sendo 1 coberta.
Campo José Crisóstomo Gonçalves
Requalificado em 2021, o antigo campo de pelado, foi renovado de forma acolher melhores condições para a prática desportiva. É utilizado pelos escalões de formação do clube. Atualmente conta com um relvado sintético e com uma zona de balneários junto ao recinto. O Campo José Crisóstomo Gonçalves está localizado a sul do Estádio da Devesa.
Pavilhão EB 2,3 de Manhente
Utilizado pelo futsal feminino do Santa Maria FC, o pavilhão é pertença à Escola Básica de Manhente, freguesia vizinha de Galegos Sta. Maria.
Histórico Futebol Masculino
Títulos
Presenças
Classificações por época (2015–atual)
Partir de 2020-21 o campeonato passou a disputar em séries e play-off de campeão
Legenda das cores na pirâmide do futebol português
1º nível (1ª Divisão / 1ª Liga)
2º nível (até 1989/90 como 2ª Divisão Nacional, dividido por zonas, em 1990/91 foi criada a 2ª Liga)
3º nível (até 1989–90 como 3ª Divisão Nacional, depois de 1989–90 como 2ª Divisão B/Nacional de Seniores/Campeonato de Portugal, e após 2020-21 como Liga 3)
4º nível (entre 1989–90 e 2012–13 como 3ª Divisão, entre 1947–48 e 1989–90, após 2013–14 como 1ª Divisão Distrital, após 2020-21 como Campeonato de Portugal)
5º nível (desde 2020-21 como 1º Divisão Distrital: Pró Nacional)
6º nível (desde 2020-21 como 2º Divisão Distrital: Divisão de Honra)
7º nível (desde 2020-21 como 3º Divisão Distrital: 1º Divisão)
Jogadores
Treinadores
Histórico do Futebol de Formação
Títulos nas Camadas Jovens
Equipamentos
Emblema
Santa Maria Futebol Clube
Santa Maria Futebol Clube
Desporto em Barcelos | {
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Election 101
Search CNN
Wildfire Tracker
Biden begins transition plans as Trump refuses to concede
By Melissa Macaya and Meg Wagner, CNN
Updated 8:09 a.m. ET, November 20, 2020
President-elect Joe Biden is moving forward with transition plans, but said he needs access to President Trump's vaccine distribution plans as Covid-19 cases surge.
Trump meanwhile refuses to accept he lost the election and is challenging the results.
Here is who could serve in top roles of the Biden administration.
Our live coverage has ended. Read more about Biden's transition here.
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8:09 a.m. ET, November 20, 2020
Witness corroborates claim that Lindsey Graham asked about tossing ballots in Georgia
From Wes Bruer and Marshall Cohen
Sen. Lindsey Graham arrives for a Senate Judiciary Committee hearing on November 10 on Capitol Hill in Washington, DC. Susan Walsh/Pool/Getty Images
A staffer for Georgia Secretary of State Brad Raffensperger said Tuesday that he participated in a controversial phone call with Sen. Lindsey Graham and said he heard Graham ask if state officials could throw out ballots.
The comments from the staffer, election implementation manager Gabriel Sterling, corroborate Raffensperger recent claims about the phone call with Graham, who is one of President Donald Trump's most outspoken allies.
Earlier this week, Raffensperger accused Graham of asking him to "look hard and see how many ballots you could throw out," referring to absentee ballots that skewed heavily in favor of President-elect Joe Biden. Graham denied the claim, saying that it was "ridiculous" that he tried to pressure Raffensperger to throw out legally cast ballots.
In response to a question from CNN about the incident, Sterling said on Tuesday, "What I heard was basically discussions about absentee ballots and if a potentially … if there was a percentage of signatures that weren't really, truly matching, is there some point we could get to, we could say somebody went to a courtroom could say well, let's throw (out) all these ballots because we have no way of knowing because the ballots are separated."
"There is no physical ability for this office to do anything along those lines," Sterling continued, referring to throwing out absentee ballots that have already been deemed legal by local election officials. "If somebody wanted to go that route, they could go the court route."
Graham's comments "might have gone a little to the edge of" what people deem acceptable, Sterling said, but added that he understands why Raffensperger and Graham might have interpreted the conversation differently.
"The President is going to continue to fight, his supporters continue to fight," Sterling said. "Our job is to continue to follow the law, and we were answering process questions… that's what we were doing on the call."
12:23 p.m. ET, November 17, 2020
Rep. Cedric Richmond reflects on what it means to join the Biden-Harris administration
From CNN's Sarah Mucha
Rep. Cedric Richmond speaks during a press conference in New Orleans on November 17. WVUE-DT
Rep. Cedric Richmond, who the Biden-Harris transition just formally announced will take a role in the White House as a senior adviser and director of public engagement, spoke about his new position in a news conference in New Orleans Tuesday.
Calling it "one of the hardest decisions" of his life, Richmond said, "I am not leaving the people of Louisiana. I am not leaving the people of the second Congressional District. I am New Orleans through and through. I bleed black and gold."
The former Black Caucus Chair called it a "sad day" to announce that he is leaving something that he "fought so hard to get," and to say that he's leaving something that "means so much" to him but said he believes he will better serve Louisiana in his new role, citing as one example his ability to advise cabinet secretaries, particularly on the subject of education.
"And so this new role will allow me to offer advice to the President when he wants it, maybe sometimes when he doesn't want it. I will also be in an office in the West Wing. And when you talk about the needs of Louisiana, you want someone in the West Wing," he assured.
Richmond said that he will play an "active role" in finding his Congressional replacement and intends to talk to candidates to learn their impression of Congress. He said that candidates' views of constituent services and "playing well with others," are important factors.
On Trump's refusal to concede, Richmond argued, "I fully expect it to be an orderly transition."
"I think that he is having a hard time coming to grasp with the real facts and not alternative facts that the election is over. Joe Biden won in a landslide. The people have spoken," Richmond said.
Biden will participate in a coronavirus call with a group of bipartisan governors Thursday
From CNN's Betsy Klein and Dan Merica
President-elect Joe Biden delivers remarks during a press briefing at the Queen Theater on November 16 in Wilmington, Delaware. Joe Raedle/Getty Images
President-elect Joe Biden is expected to participate in a call on the coronavirus pandemic with a bipartisan group of the nation's governors on Thursday.
The call between Biden and members of the National Governors' Association (NGA) executive committee will be facilitated by the NGA in conjunction with the Biden transition team, an NGA spokesperson and Biden transition official said.
"Joe Biden is going to be talking to the governors on Thursday. We're arranging a call. The governors are the ones who have been handling this war, frankly. Joe Biden wants to engage with them right away and I think that's smart," NGA chairman and New York Gov. Andrew Cuomo announced Monday during an appearance on MSNBC.
The call is expected to be closed to press and details on an agenda were not immediately available.
The executive committee group is made up of: Gov. Andrew Cuomo of New York, Gov. Asa Hutchinson of Arkansas, Gov. Kay Ivey of Alabama, Gov. Jared Polis of Colorado, Gov. Larry Hogan of Maryland, Gov. Charlie Baker of Massachusetts, Gov. Gretchen Whitmer of Michigan, Gov. Michelle Lujan Grisham of New Mexico and Gov. Gary Herbert of Utah.
The call comes as the Trump administration continues to block the Biden transition, with the Biden team, public health, and national security experts sounding the alarm on the potential consequences.
White House coronavirus task force member Dr. Anthony Fauci stressed the need for a smooth transition during an appearance on CNN Tuesday morning, specifically noting the importance of "communication with health groups in different states" and "getting interaction at a formal level with the governors."
Vice President Mike Pence, who has hosted 41 conference calls with governors since the onset of the pandemic, led a briefing call on Monday, the first such call he participated in since Sept. 29.
While Monday's call addressed granular detail of vaccine deployment, officials also discussed the worsening pandemic. There was, however, no mention of the transition.
1:22 p.m. ET, November 17, 2020
House Republicans will hold leadership votes today
From CNN's Phil Mattingly, Daniella Diaz and Kristin Wilson
House Republicans will meet in-person at a hotel near Capitol Hill — with a waiver from the DC government amid an uptick in Covid-19 cases — to hold their leadership votes.
The top tier of the leadership is expected to be re-elected, with House Minority Leader Kevin McCarthy, his top deputy Rep. Steve Scalise of Louisiana and Wyoming Rep. Liz Cheney, the GOP conference chair, on a glide path to hold onto their roles.
The leadership team, on the heels of an election performance that surprised even some if the conference's own members, is newly ascendant in its power, both inside the conference and in the chamber writ large.
McCarthy, who has to this point successfully bridged the gap between restive hardline conservatives inside the conference and more traditional GOP members, heads a unified operation that has already started turning its attention toward winning back the majority in 2022.
House Democrats, even with races are still outstanding, are on track to hold the slimmest majority for either party in nearly two decades. Republicans leaders can already point to an incoming freshman class that is more diverse than any in recent memory for the party, after a recruiting emphasis on women, minority candidates and veterans led to at least nine pickups for the party.
That number is expected to grow in the days and weeks ahead, with GOP challengers in position to pick up a handful of outstanding seats.
Rep. Tom Emmer is also set to be reelected to lead another two-year term as the chairman of the National Republican Congressional Committee.
GOP leaders will hold a news conference at 5 p.m. ET after the election to discuss the outcome.
President-elect Biden announces 9 key members of White House senior staff
President-elect Joe Biden delivers remarks about the U.S. economy during a press briefing at the Queen Theater on November 16 in Wilmington, Delaware. Joe Raedle/Getty Images
President-elect Joe Biden has announced new members of the White House staff Tuesday, filling nine new senior-level positions in his administration mainly with loyal advisors and staffers who served on his presidential campaign.
Campaign chief strategist Mike Donilon will be a senior advisor, along with former Black Caucus Chair Cedric Richmond, who will also serve as Director of the White House Office of Public Engagement.
CNN previously reported that Richmond, who acted as a national co-chair of Biden's campaign, would leave Congress to join the White House in a senior advisor role.
Longtime Biden aide Steve Ricchetti, who served as Chairman of Biden's campaign and once acted as Biden's Chief of Staff while he was vice president, will serve as Counselor to the President.
Dana Remus, who served as General Counsel of the Biden-Harris campaign, will be Counsel to the President, and Annie Tomasini, who was seen on the road with Biden as his traveling Chief of Staff, will become Director of Oval Office Operations.
Julie Rodriguez will be the Director of the White House Office of Intergovernmental Affairs. Rodriguez served as National Political Director and traveling Chief of Staff for Kamala Harris' presidential campaign before joining Biden's campaign as a deputy campaign manager.
Some key members of Jill Biden's staff were also announced Tuesday: Anthony Bernal, who acted as deputy campaign manager and Jill Biden's chief of staff during the campaign, will serve as senior advisor to the future first lady, and Julissa Reynoso Pantaleon will be her chief of staff.
The transition team also tweeted the announcement:
10:47 a.m. ET, November 17, 2020
The first woman to lead a winning Democratic presidential race will now be joining Biden's administration
From CNN's Dan Merica and Jeff Zeleny
Jen O'Malley Dillon was President-elect Joe Biden's campaign manager. Andre Chung/The Washington Post/Getty Images
Jen O'Malley Dillon will join President-elect Joe Biden's incoming administration as a deputy chief of staff, a source familiar with the matter tells CNN.
The expected move, first reported by NBC News, is the latest in a long line of expected senior White House hires as Biden moves to fill out his administration.
O'Malley Dillon will be joining Ron Klain, who was announced as Biden's incoming chief of staff last week, and Rep. Cedric Richmond, who sources tell CNN is expected to leave Congress and join the Biden White House in a senior role.
Here are some things to know about O'Malley Dillon:
She was Biden's campaign manager, joining his team in March after he consolidated support among most of his primary rivals.
She helped transform a shoestring primary organization, which struggled to raise money, into a general election juggernaut that ultimately made Donald Trump a one-term president.
She was the first woman to lead a winning Democratic presidential race.
She has held a number of top jobs within the universe of Democratic organizations, including executive director of the Democratic National Committee and the founding partner at Precision Strategies, a Democratic consulting firm.
O'Malley Dillon has long told friends that she had no interest in working in the West Wing after the campaign, but after working in top jobs on numerous political campaigns — including former Rep. Beto O'Rourke's failed 2020 primary campaign and both of Barack Obama's presidential campaigns — the Democratic operative has never served in the White House.
That historical pull, said a person familiar with her decision, proved too much to turn down. O'Malley Dillon is expected to have the operations portfolio in the White House — a role Jim Messina played in Obama's first term.
Read up here on who else could serve in top roles of the Biden administration.
Rudy Giuliani has filed to appear in Pennsylvania election case scheduled for today
From CNN's Katelyn Polantz
Rudy Giuliani, President Trump's personal lawyer, speaks at a news conference in the parking lot of a landscaping company on November 7 in Philadelphia. Bryan R. Smith/AFP/Getty Images
Rudy Giuliani, President Trump's personal lawyer, formally told the court that he will represent the Trump campaign in its long shot case to block Pennsylvania from certifying votes.
The case and whether it should be dismissed will be argued in federal court on Tuesday.
The hearing will take place before Judge Matthew Brann in Williamsport in the Middle District of Pennsylvania. Brann is an Obama appointee, but is a longtime Republican.
Some context: Trump has refused to concede the election and continues to make false claims of widespread voter fraud with no evidence.
On top of the fraud claims, his campaign and GOP allies have filed numerous and flimsy legal challenges in the days following the Nov. 3 election, with some attempting to deprive Biden of the Electoral College votes he's set to receive to become president.
On Friday, nine cases meant to attack Biden's win in key states were denied or dropped.
Trump agency official tasked with transition process had pre-election talk with predecessor who handled 2000
From CNN's Kristen Holmes
General Services Administration Administrator Emily Murphy speaks at the Department of Homeland Security's St. Elizabeths Campus Center Building in Washington, DC on June 21, 2019. Susan Walsh/AP
General Services Administrator Emily Murphy had a call with David Barram, the GSA administrator during the 2000 election, before this year's election, according to a source with direct knowledge of the call.
As administrator, Murphy is the person tasked with officially affirming President-elect Joe Biden has won the election on behalf of the Trump administration — something Trump hasn't done himself.
She needs to sign a letter to release funds to the Biden transition team through a process called ascertainment. This would mark the first formal acknowledgment from the Trump administration that Biden has in fact won the election, but it would also unlock access to national security tools to streamline background checks and additional funds to pay for training and incoming staff.
Barram, a Bill Clinton political appointee, ascertained Bush as then winner of the 2000 election following the historic Bush v Gore recounted that ended up in the Supreme Court.
The call between Barram and Murphy was set up by mutual associates as a way for him to discuss his experience with her, the source said.
Recently, post-election, Barram said that this year's election is "dramatically different," than what happened in 2000. "It was all about Florida. One state, and something like 537 votes. Everyone knew that once Florida was settled, the winner would become clear," Barram has said.
Murphy has still not issued an ascertainment letter that would officially trigger the transition period for the federal government.
AP first reported on the call between Barram and Murphy.
Fauci: "It's important at every level to have a smooth transition"
Dr. Anthony Fauci testifies during a US Senate Senate Health, Education, Labor, and Pensions Committee hearing in Washington, DC, on September 23. Graeme Jennings/Pool/AFP/Getty Images
Dr. Anthony Fauci told CNN's Jim Sciutto that he has not yet had contact with President-elect Joe Biden and called the smooth transition of power "important" to fighting the coronavirus pandemic.
"Transitions are important and if you don't have a smooth transition, you would not optimize whatever efforts you're doing right now," Fauci said.
The director of the National Institute of Allergy and Infectious Diseases noted that he has served six administrations which amounted to five transitions of power.
"I have been involved as a health person in the transition. It is really quite important as I used the metaphor the other day, it's like a relay race in which you're passing the baton and you don't want to slow down what you're doing but you want the person to whom you're giving the baton to be running with it as opposed to stopping and starting all over again," Fauci said, adding that's the "reason why it's important at every level to have a smooth transition."
Fauci said the level of communication needed to pass the baton would include communicating to the incoming administration what the level of supply is, getting interaction at "a formal level" with the governors and understanding "every detail" of the vaccine program.
"Not only the two vaccines that have fortunately been shown to be very effective but where we are in Operation Warp Speed with regard to the other candidates which are coming into their own in the sense of clinical trial, accumulating data. All of those things can be done in partnership," the nation's top infectious disease expert said.
Biden warned yesterday that President Trump's unwillingness to accept the outcome of the 2020 election could hamper the incoming Biden administration's ability to rapidly distribute a coronavirus vaccine.
"More people may die if we don't coordinate," Biden told reporters Monday in Delaware.
Biden's comment comes as Trump refuses to acknowledge the reality that he lost the presidential election. | {
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Silas Alexander Ramsay (August 27, 1850 – December 5, 1942) was a Canadian politician and merchant in Alberta, Canada. He served as the 14th mayor of Calgary.
A native of Quebec, Ramsay first travelled to the west with the Wolseley Expedition in a suppression effort to the Red River Rebellion in 1870. Before returning home, he visited the Calgary area and hunted buffalo. This was prior to the initial Fort Calgary settlement, which happened in 1875.
In 1883, Ramsay returned to Calgary and established several businesses. In the 1885 North-West Rebellion, he was a Government dispatch rider. He served eight total years on the city council as an alderman and was also mayor from January 5, 1904, to January 2, 1905, during which time he was a stringent supporter of municipal ownership, working to establish a lighting and water system for the city.
After his retirement in Calgary from his business, he moved to Vancouver, British Columbia, where he died in 1942.
Early life, career
The son of William and Sarah (née Mohr) Ramsay, Silas Alexander Ramsay was born at Aylmer, Quebec in 1850. He attended public schools in his birthplace, completing high school. At the age of nine in 1860, Ramsay would witness the cornerstone lying ceremony of the Canadian Parliament buildings at Parliament Hill. He moved to Almonte, Ontario around 1867 and lived there for three years, when he participated the suppression of the Red River Rebellion in a faction commanded by Garnet Wolseley, 1st Viscount Wolseley. During that time he participated in the Wolseley Expedition, travelling through Port Arthur and then embarking westward, in a journey of around three months, to Fort Garry (presently Winnipeg). Being the first trip he undertook Canadian West, he also visited the Calgary area and hunted buffalo, prior to Fort Calgary's establishment in 1875. He would later home via railway through Ottawa after heading through Montana and St. Paul, Minnesota. There he would open up a general store and operate it for around eight years, when he closed up and became a wool merchant for four years.
Intrigued by the opportunity and potential it held, in 1883, Ramsay decided to move west, settling in the village of Calgary, in the North-West Territories, which was then the terminus of the Canadian Pacific Railway. At Calgary he would ranch and enter the agricultural product manufacturing business as an agent for an Ontario company, producing buggies, wagons, ploughs, and mowers. This was one of the first such businesses in the province of Alberta. He was also an agent for a sewing machine company, with an office located on Stephen Avenue. When the North-West Rebellion of 1885 broke out, Ramsay would be involved in it, serving as a government dispatch messenger and later a scout. During his rebellion duties, he was attacked in encounter with local First Nations peoples, forcing him to fire shots from his rifle in self-defence. In Calgary he also built the Ramsay Block, on a piece of land, opposite of the city's old post office.
Civic politics
Keenly interested in Calgary's civic politics, Ramsay first served as an alderman on the Calgary City Council from January 7, 1895, to January 3, 1899, and January 6, 1902, to January 5, 1904. A strong supporter of public ownership of utilities, he also served a stint as chairman of the council's Water and Light Committee, in which he oversaw the installation of the city's first electric lighting system, as well as the purchase of the water system by the municipality from a private company. He was later lauded for this action by the Calgary Albertan, who stated that it had helped set the foundations the municipal utility system that was later established and improved upon of Calgary. He was an Independent.
On December 7, 1903, municipal nominations day for the upcoming election, Ramsay was acclaimed as mayor of Calgary, with no opposing nominees for the office. Ramsay served as mayor until January 5, 1905, when he was succeeded by John Emerson. During his term, the city moved to establish a numbering system for its streets, and the Canadian Pacific Railway initiated an irrigation project east of the city, which would later become Chestermere Lake, Alberta. He did not seek re-election as mayor in the 1904 election, instead accepting a nomination to once again serve as alderman. He was later elected and would serve a final aldermanic term, from January 2, 1905, to January 14, 1907. He later retired from his business around 1921 and moved to Vancouver.
Personal life
Ramsay married Jessie Ann Wilson in Alamonte on April 18, 1876. Together they had four children: Bertha Maud, Robert Wilson, Charles Henry, and Percival Clod. One of his brothers served as mayor of Prince Albert, Saskatchewan. He was active member of the Calgary Rifle Club, and the Methodist church. In 1939, at the age of 90, Ramsay travelled to Winnipeg to visit the site of the Fort Garry gate, where he had travelled almost 70 years prior. At the time it was noted that he was one of the last remaining survivors of the Wolseley Expedition. He died at his daughter's home in Vancouver, British Columbia on December 5, 1942, at the age of 92. He was survived by his daughter and two sons. His wife predeceased him on May 16, 1925, in Vancouver.
It was said about him that he was "one of those wholesome toilers in behalf of the people who never grow old in years and energy." A 1912 biography in the publication History of the province of Alberta noted that Ramsay was a man of "broad mental grasp, cosmopolitan ideas and notable business sagacity", with a "thorough understanding of life, its principles and possibilities" that was "honoured and respected by all". His former residence was in the present-day Calgary neighbourhood of Ramsay, situated east of the Elbow River and south of the CPR tracks, which is named in his honour.
References
Bibliography
Mayors of Calgary
Politicians from Gatineau
1850 births
1942 deaths
19th-century Canadian politicians
20th-century Canadian politicians | {
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\section{Introduction}
Semialgebraic proof systems, also called certificates of nonnegativity, are systematic methods to prove nonnegativity of polynomials over semialgebraic sets. One of the most successful approaches for constructing theoretically efficient algorithms for polynomial optimization problems is the Sum of Squares (SoS) certificate~\cite{GrigorievV01,Nesterov00,parrilo00,schor87},
For a wide variety of combinatorial optimization problems, SoS provides the best available algorithms~\cite{AroraRV09,GoemansW95,BarakRS11,GuruswamiS11,Lovasz79}.
The strength of this method has also come to light for Max CSP~\cite{LeeRagSteu15} and problems in robust estimation~\cite{KothariSS18}, dictionary learning~\cite{BarakKS15,SchrammS17}, tensor completion and decomposition~\cite{BarakM16,HopkinsSSS16,PotechinS17}, and problems arising from statistical physics~\cite{GhoshJJPR20}.
However, the SoS algorithm also admits certain weaknesses. It is known to struggle with solving certain combinatorial optimization problems, e.g.,~\cite{BhaskaraCVGZ12,Cheung07,Grigoriev01b,KurpiszLM17,Tulsiani09}.
In a seminal example, Grigoriev showed that a $\Omega(n)$ degree SoS certificate is needed to detect a simple integrality argument for the {Knapsack} problem \cite{Grigoriev01}, see also~\cite{GrigorievHP02,KurpiszLM16,Laurent03a}.
A degree $n^{\Omega(\varepsilon)}$ SoS algorithm was proved to be unable to asymptotically certify an upper bound smaller than 2 times the optimal value for Sherrington-Kirkpatric Hamiltonian~\cite{BandeiraK19,GhoshJJPR20}.
Moreover, the degree $\Omega(\sqrt{n})$ SoS hierarchy was proved to have problems scheduling unit size jobs on a single machine to minimize the number of late jobs, see~\cite{KurpiszLM17b}, even though the problem is known to be solvable in polynomial time using the Moore-Hodgson algorithm~\cite{Moore68}. Finally, various examples where the SoS hierarchy fares very badly have been shown for the planted clique~\cite{BarakHKKMP16,MekaPW15} and Max CSP problems~\cite{KothariMOW17,ThapperZ17}.
The discrepancy between the excellent performance of the SoS hierarchy and its limitations has been studied extensively throughout the last decade. Thus, a natural question arises: what factors determine the difficulty of solving a problem for the SoS method?
A prominent example that was studied through the lens of this question is the Max Cut problem, which not only lies at the center of SoS research but was also one of the first problems for which lower bounds of the SoS rank were studied. Grigoriev proved that SoS needs at least degree $\lfloor\frac{n}{2} \rfloor$ to certify the size of the maximum cut in an odd clique of $n$ vertices~\cite{Grigoriev01}, for alternative proofs see also~\cite{GrigorievHP02,KurpiszLM16,Laurent03a}. In a breakthrough paper nearly two decades later, Parrilo showed that the Grigoriev's lower bound is tight by proving that every $n$-variate polynomial of degree $2$, nonnegative over the Boolean hypercube has an SoS certificate of degree at most $\lceil\frac{n}{2}\rceil$, see~\cite{FawziSP15}.
Subsequently, the analog of the results by Grigoriev and Parrilo for higher degree symmetric functions recently appeared in~\cite{KurpiszLM16c, SakueTKI17}, respectively.
Many of the problem instances with large lower bounds of the SoS rank target known limitations of the SoS method such as an issue with dealing with integrality constraints. Indeed, certifying the size of the maximum cut in a clique can be transformed into the problem of proving nonnegativity of the \emph{Symmetric Quadratic Function} (SQF) of the form $q_{\left\lceil\frac{n}{2}\right\rceil}(\mathbf{x})$ over the Boolean hypercube, where, throughout this paper, $q_k:\{0,1\}^n\to\mathbb{R}$ is a multivariate polynomial of the form
\begin{equation}\label{eq:SQF}
q_k(\mathbf{x}):=(|\mathbf{x}|-k)(|\mathbf{x}|-k+1).
\end{equation}
The optimization of degree $2$ polynomials over the Boolean hypercube plays a central role in Theoretical Computer Science.
This claim is supported by the fact that high degree optimization problems attracted limited attention, especially since solving an NP-complete problem can be reduced in polynomial time to proving nonnegativity of a degree-$4$ even form~\cite{MurtyK87}. Moreover, if an SQF has a complex root with a corresponding conjugate root, the polynomial is globally nonnegative and admits an SoS certificate of degree $2$. Similarly, there exists an SoS certificate of nonnegativity of degree $2$ for SQFs over the Boolean hypercube if the roots are real and placed outside the interval $[0,n]$. Hence, the only interesting case is when the roots are real and located within some interval $[k-1,k]$ for $k \in \{1,\ldots,n\}$.
Finding an SoS representation of the symmetric function $q_k$ has gained significant attention in the SoS community. However, up to this day, the exact SoS rank for $q_k$ is not known. The most recent result towards a characterization of the SoS rank of $q_k$ provides a lower and upper bound of the SoS degree that approximates the function $q_k$ with SoS polynomials in $l_1$ and $l_\infty$ norm~\cite{LeePWY16}.
However, since finding an exact SoS certificate is at least as difficult as providing an approximate SoS representation, the result implies that for $k\geq 2$, $q_k$ does not admit an SoS certificate of degree smaller than $\Omega\left( \sqrt{k(n-k)} \right)$. Moreover, in~\cite{LeePWY16}, Lee, Prakash, de Wolf, and Yuen conjectured that the lower bound of the SoS approximate representation with error at most $\varepsilon$ in the $l_\infty$ norm is expected to be $ \Omega\left( \sqrt{k(n-k)}+ \sqrt{n \log(1/\varepsilon)} \right)$. They support the conjecture by arguing about similarity with approximating $n$-bit OR functions~\cite{Paturi92,Wolf10}. This conjecture, if true, would imply a lower bound on the exact SoS certificate for SQFs of $\Omega(n)$, even for small, constant values of $k$. Proving this conjecture is left as an open question in~\cite{LeePWY16}.
In this paper, we refute the Lee---Prakash---de Wolf---Yuen (LPdWY) conjecture. We show that certifying SQFs is easier than representing $n$-bit OR functions. More specifically, we prove the following theorem.
\begin{theorem}
\label{thm:SQF_SoS_degree}
For any $k \in \{2,\ldots, \lceil \frac{n}{2} \rceil \} $, there exists a degree $O(\sqrt{nk}\log (n) )$ SoS certificate of nonnegativity for the Boolean function $q_k$ as in~\eqref{eq:SQF}.
\end{theorem}
We motivate the research on the SoS degree of the SQFs $q_k$ by connecting it to two combinatorial optimization problems.
We first consider the instance of the \textsc{Min Knapsack} (MK) problem. For $P\geq 2$, the problem is defined as:
\begin{eqnarray}
\mbox{MK:}
\qquad \min \sum_{i \in [n]} x_i & \quad \mbox{s.t.} & \sum_{i \in [n] } x_i \geq \frac{1}{P}, \qquad \mathbf{x}\in\{0,1\}^n .
\label{eq:MK_def}
\end{eqnarray}
For $P=2$, the problem was previously considered by Cook and Dash \cite{cook2001matrix}. They proved that the Lovasz-Schrijver hierarchy rank is $n$. For the Sherali-Adams hierarchy, Laurent proved that the rank is also equal to $n$ and raised the open question to find the rank for the SoS hierarchy~\cite{Laurent03}.
For $n = 2$, they also proved that the SoS rank is $2$, but the discussion for general $n$ was left as an open question.
Currently, it is known that the SoS rank of the MK problem for $P=2$ falls within $\Omega(\sqrt{n})$ and $\lceil \frac{ n+ 4\lceil \sqrt{n} \rceil }{2} \rceil$, see~\cite{Kurpisz19}. In this paper, we prove an upper bound on the SoS rank for the MK problem.
\begin{theorem}\label{thm:MK_SoS_rank}
The SoS rank for the MK problem is $\Omega(\sqrt{n}\log(P))$
\end{theorem}
The existing lower bound for general $P$ (see Lemma 14 of \cite{Kurpisz19}) is $\Omega(\sqrt{n\log(P)})$, so this is tight when $P$ is constant, though for larger $P$ there is a gap of $O(\sqrt{\log(P)})$.
We also consider the following instance of the \textsc{Set Cover} (SC) problem:
\begin{eqnarray}
\mbox{SC:}
\qquad \min \sum_{i \in [n]} x_i & \quad \mbox{s.t.} & \sum_{i \in [n] \setminus\{j\}} x_i \geq 1 \qquad \forall j \in [n], \qquad \mathbf{x}\in\{0,1\}^n.
\end{eqnarray}
This instance was considered in~\cite{BienstockZ04} and it is known that the SoS hierarchy cannot solve this problem with a degree smaller than $\Omega(\sqrt{n})$~\cite{Kurpisz19}.
In~\cite{BienstockZ04}, Bienstock and Zuckerberg raised the question of what the actual SoS rank of this polytope is, conjecturing that, based on numerical experiments, the SoS rank is at least $\frac{n}{4}$.
In this paper, using the SoS certificate for SQFs in Theorem~\ref{thm:SQF_SoS_degree}, we refute the Bienstock---Zuckerberg conjecture and provide a nearly tight SoS rank for the SC problem:%
\begin{theorem}\label{thm:SC_SoS_rank}
The SoS rank for the SC problem is at most $O(\sqrt{n} \log (n))$.
\end{theorem}
\section{Preliminaries}\label{sec:Preliminaries}
For $n\in \mathbb{N}$, let $[n]=\{1,\ldots,n\}$. For $\mathbf{x}\in \mathbb{R}^n$, let $\mathbb{R}[\mathbf{x}]=\mathbb{R}[x_1,\ldots,x_n]$ be the ring of \emph{$n$-variate real polynomials}.
For a set of polynomials $\cG \subseteq \mathbb{R}[x]$, the corresponding \emph{semialgebraic set} is
\begin{align*}
\cG_+ \ := \ \{ \mathbf{x} \in \mathbb{R}^n~ |~ g(\mathbf{x})\geq 0 \text{ for all } {g \in \cG} \} \subseteq \mathbb{R}^n.
\end{align*}
Throughout this paper, we consider optimization problems on the Boolean hypercube $\{0,1\}^n$ and therefore, for $\cH:=\{ \pm (x_1^2-x_1),\ldots,\pm(x_n^2-x_n) \}$, we assume that $\cG$ is of the form
\begin{align*}
\cG \ := \ \cH \cup \{g_1,\ldots,g_m:~g_i \in \mathbb{R}[\mathbf{x}] \text{ for all } ~ i \in [m] \} ,
\end{align*}
where $m\in \mathbb{N}_{> 0}$. This implies that $\mathcal{G}_+\subseteq \{0,1\}^n$.
Moreover, define the \emph{cone of nonnegative polynomials with respect to a given semialgebraic set, $\mathcal{G}_+$,} as
\begin{align*}
\cK(\cG_+) \ := \ \{f \in \mathbb{R}[\mathbf{x}] \ | \ f(\mathbf{x}) \geq 0 \text{ for all } \mathbf{x} \in \cG_+\}.
\end{align*}
For given $f \in \mathbb{R}[\mathbf{x}]$ and $\cG\subseteq \mathbb{R}[\mathbf{x}]$, define the corresponding \emph{Constrained Polynomial Optimization Problem} (CPOP) as
\begin{align*}
\label{eq:intro_POP}
\begin{aligned}
f^* \ := \ \min\{f(\mathbf{x})~ |~ \mathbf{x} \in \cG_+\} \ = \ \max\{\lambda \in \mathbb{R}~ |~ f-\lambda \in \cK(\cG_+)\}.
\end{aligned}
\end{align*}
Generally, since CPOP is NP-hard, it is desirable to find a proper subset that is a good inner approximation of $\cK(\cG_+) $ such that the corresponding program is computationally \emph{tractable}.
The \emph{SoS method} approximates the cone $\cK(\cG_+)$ by using the set of \emph{sum of square polynomials}. We define the set of finite sum of squares polynomials as
$\Sigma := \{s\mid s = \sum_{i=1}^{k}s_i^2, s_i\in \mathbb{R}[\mathbf{x}] \ \forall i\in [k], k \in \mathbb{N}_{>0}\}$
and let
$\Sigma_{n,d}:= \{s\mid s = \sum_{i=1}^{k}s_i^2, s_i\in \mathbb{R}[\mathbf{x}] \text{ and } \deg(s_i) \leq d \ \forall i\in [k], k \in \mathbb{N}_{>0}\}$
denote the
polynomials which are sums of squares of polynomials of degree at most $d$.
We define the \emph{hierarchy of certificates of nonnegativity depending on $d,n \in\mathbb{N}$} as
\begin{equation*}
\Sigma_{n,d}^{\cG}:= \left\{ s_0+\sum_{i=1}^m s_i g_i~|~s_i \in\Sigma_{n,d},~g_i \in \cG \ \forall i \in [m] \ \text{and} \ s_0\in \Sigma_{n, 2 \left\lceil \frac{2d +\deg(\cG)}{2} \right\rceil} \right\},
\end{equation*}
where $\deg(\cG)=\max\{\deg(g)~|~g \in \cG\}$.
The \emph{degree $d$ SoS certificate} for $f$ being nonnegative over $\cG_+$ is $f \in \Sigma_{n,d}^{\cG}$. Moreover, throughout the paper we say that a multivariate polynomial $f$ is \emph{a degree $d$ SoS modulo Boolean axioms} if $f \in \Sigma_{n,d}^\cH$.
The \emph{degree $d$ SoS program} for CPOP~is
\begin{equation}
\label{eq:intro_SoS_d_CPOP}
f^{d}_\Sigma \ := \ \quad \max\{\lambda \in \mathbb{R}~ |~ f-\lambda \in \Sigma_{n,d}^{\cG}\}
\end{equation}
and is called \emph{exact} if $f^d_\Sigma=f^*$. The smallest degree $d$ such that the degree $d$ SoS program is exact is called the \emph{SoS rank}.
Over the Boolean hypercube, the degree $d$ SoS program can be solved via a \emph{semidefinite program} (SDP)
of size $O(m \sum_{k=0}^d \binom{n}{k})$. Moreover, the degree $n$ SoS program is exact, see, e.g.,~\cite{BarakS16,Lasserre01z,Laurent03}.
Throughout this paper, we often encounter the following type of multivariate polynomials.
\begin{definition}\label{def: symmetric polynomial}
A polynomial $f:~\{0,1\}^n\to\mathbb{R}$ is \emph{symmetric} if there exists a univariate polynomial $\tilde{f}~:\mathbb{R}\to\mathbb{R}$ such that
$$
f(\mathbf{x})=\tilde{f}\left(\sum_{i=1}^n x_i\right)
$$
for all $\mathbf{x}\in \{0,1\}^n$.
\end{definition}
With this in mind, let $|\mathbf{x}|:= \sum_{i=1}^nx_i$ for any $\mathbf{x}\in \{0,1\}^n$.
To prove SoS rank upper bounds, we consider symmetric multivariate polynomials over $\{0,1\}^n$ as univariate polynomials over $[0,n]$ and apply one of the many results on SoS certificates for univariate polynomials.
\begin{remark}
\label{rem:univariate_to_multivaraite_SoS}
Throughout this paper, we make frequent use of the fact that SoS certificates for polynomials over $[0,n]$ translate to SoS certificates for symmetric polynomials over $\{0,1\}^n$. More formally, if a univariate polynomial $\tilde{f}:\mathbb{R}\to \mathbb{R}$ has an univariate SoS certificate of degree $d$ on $[0,n]$, then the multivariate polynomial $f:\{0,1\}^n\to\mathbb{R}$ such that $f(\mathbf{x}):=\tilde{f}(|\mathbf{x}|)$ has a degree $d$ SoS certificate of nonnegativity over the Boolean hypercube.
\end{remark}
In this paper, we use the following theorem to prove the SoS rank for univariate polynomials.
\begin{theorem}[{\cite[Theorem 3.72]{blekherman2012semidefinite}}]\label{thm:Blekherman_TheSecond}
Let $a<b$. Then the univariate polynomial $p(x)$ is nonnegative on $[a,b]$ if and only if it can be written as
$$
\begin{cases}
p(x)=s(x)+(x-a)(b-x)\cdot t(x) & \text{if} \ \deg(p) \ \text{is even,}\\
p(x)=(x-a) \cdot s(x)+(b-x)\cdot t(x) & \text{if} \ \deg(p) \ \text{is odd,}\\
\end{cases}
$$
where $s,t$ are sum of squares. In the first case, we have $\deg(p)=2d$, $\deg(s)\leq 2d$, and $\deg(t)\leq 2d-2$. In the second, $\deg(p)=2d+1$, $\deg(s)\leq 2d$, and $\deg(t)\leq 2d-2$.
\end{theorem}
Finally, throughout the paper we use degree-$d$ Chebyshev polynomials of the first type, which were used in several applications for bounds of sum of squares ranks, i.e., \cite{Kurpisz19, SlotL19, potechin2020sum}.
We frequently use the following lemma.
\begin{lemma}
\label{lem:Chebyshev_1-c/n_properties}
Let $n , d \in \mathbb{N}$ such that $d \leq n$. Then,
\begin{enumerate}
\item For all $c\in [0, n]$,
$$
T^2_{ d}\left(-1-\frac{c}{n}\right) \geq \frac{1}{4}\left(-1-\sqrt{\frac{2c}{n}}\right)^{2d }$$
and
$$
T^2_{ d}\left(-1-\frac{c}{n}\right) \leq \left(-1-2\sqrt{\frac{2c}{n}}\right)^{2d }.
$$
Moreover, for constant $c$ and $n$ big enough,
$$
T^2_{ d}\left(-1-\frac{c}{n}\right) \leq \left(-1-\sqrt{\frac{2c+1}{n}}\right)^{2d }.
$$
\item For all $c\in (n, \infty)$, $T^2_{ d}\left(-1-\frac{c}{n}\right) \leq \left(-1-3\frac{c}{n}\right)^{2d }$.
\end{enumerate}
\end{lemma}
\begin{proof}
It holds that:
\begin{enumerate}
\item Consider the characterization of Chebyshev polynomials for $x \geq |1|$ given in \cite[Equation 1.12]{Rivlin74}:
$$
T_d(x)=\frac{1}{2}\left( \left( x-\sqrt{x^2-1}\right)^d + \left( x+\sqrt{x^2-1}\right)^d\right).
$$
For $x =-1-\frac{c}{n}$ and $c \in [0, n]$, we have
$$
T^2_{ d}\left(-1-\frac{c}{n}\right) \geq \frac{1}{4} \left( \left(-1-\frac{c}{n}\right)-\sqrt{\left(-1-\frac{c}{n}\right)^2-1}\right)^{ 2d}
\geq \frac{1}{4}\left(-1-\sqrt{\frac{2c}{n}}\right)^{2d }
$$
and
\begin{align}
T^2_{ d}\left(-1-\frac{c}{n}\right) \leq & \left( \left(-1-\frac{c}{n}\right)-\sqrt{\left(-1-\frac{c}{n}\right)^2-1}\right)^{ 2d} \nonumber \\
& \leq \left( \left(-1-\frac{c}{n}\right)-\sqrt{\frac{2c}{n} +\frac{c^2}{n^2} }\right)^{ 2d} \nonumber \\
& \leq \left( -1-\sqrt{\frac{c}{n}}-\sqrt{\frac{2c}{n} +\frac{c}{n} }\right)^{ 2d} \leq \left(-1-2\sqrt{\frac{2c}{n}}\right)^{2d }.
\end{align}
Moreover, we have
$$
T^2_{ d}\left(-1-\frac{c}{n}\right) \leq \left( \left(-1-\frac{c}{n}\right)-\sqrt{\left(-1-\frac{c}{n}\right)^2-1}\right)^{ 2d}
\leq \left(-1-\sqrt{\frac{2c+1}{n}}\right)^{2d },
$$
where the last inequality holds for $n$ large compared to $c$.
\item For $x =-1-\frac{c}{n}$ and $c \in (n, \infty)$, we have
\begin{align}
T^2_{ d}\left(-1-\frac{c}{n}\right) \leq & \left( \left(-1-\frac{c}{n}\right)-\sqrt{\left(-1-\frac{c}{n}\right)^2-1}\right)^{ 2d} \nonumber \\
& \leq \left( \left(-1-\frac{c}{n}\right)-\sqrt{\frac{2c}{n} +\frac{c^2}{n^2} }\right)^{ 2d} \nonumber \\
& \leq \left( -1-\frac{c}{n}-\sqrt{\frac{2c^2}{n^2} +\frac{c^2}{n^2} }\right)^{ 2d} \leq \left(-1-3\frac{c}{n}\right)^{2d }.
\end{align}
\end{enumerate}
\end{proof}
\section{SoS rank for SQFs}\label{section:SoSRankForSQFs}
In this section, we refute the LPdWY conjecture stated in~\cite{LeePWY16} by proving Theorem~\ref{thm:SQF_SoS_degree}.
To prove Theorem~\ref{thm:SQF_SoS_degree}, it is sufficient to prove the following theorem.
\begin{theorem}
\label{thm:exists_s(x)_st_q(x)-s(x)geq0}
For all $n \in \mathbb{N}$ and all $k \in [n]$, there exists a univariate polynomial $s(x)$ of degree $O(\sqrt{kn}\log(n))$ such that
\begin{enumerate}
\item $s\left(\sum_{i=1}^{n}{x_i}\right)$ is a sum of squares (modulo the Boolean axioms).
\item For all $x \in [0,n]$, $(x-k+1)(x-k) - s(x) \geq 0$.
\end{enumerate}
\end{theorem}
Indeed, by Theorem~\ref{thm:exists_s(x)_st_q(x)-s(x)geq0} and Theorem 6, there exist sum of squares polynomials $s,~s_1$ and $s_2$ of degree $O(\sqrt{kn} \log(n))$ s.t.
$$
(x-k+1)(x-k) = s(x) + s_1(x) +s_2(x)x(n-x).
$$
We now make the following observations:
\begin{enumerate}
\item By Theorem 8, $s(\sum_{i=1}^n x_i)$ is a sum of squares polynomial modulo the Boolean axioms.
\item $s_1(\sum_{i=1}^n x_i),~s_2(\sum_{i=1}^n x_i)$ are sum of squares polynomials.
\item $\sum_{i=1}^n x_i = \sum_{i=1}^n x_i^2 - \sum_{i=1}^n\left(x_i^2- x_i\right)$ is a sum of squares polynomial modulo the Boolean axioms.
\item $n-\sum_{i=1}^n x_i = \sum_{i=1}^n \left(1-x_i \right) = \sum_{i=1}^n \left( \left( x_i -1 \right)^2 - \left(x_i^2 -x_i \right) \right)$ is a sum of squares polynomial modulo the Boolean axioms.
\end{enumerate}
Putting everything together, the multivariate polynomial $q_k(\mathbf{x})$ has an $O(\sqrt{kn} \log(n))$ SoS certificate modulo the Boolean axioms of the form
$$
q_k\left(\mathbf{x}\right) = s\left(\sum_{i=1}^n x_i\right) + s_1\left(\sum_{i=1}^n x_i\right) +s_2\left(\sum_{i=1}^n x_i\right)\left( \sum_{i=1}^n x_i \right) \left(n-\sum_{i=1}^n x_i\right).
$$
Before we prove Theorem~\ref{thm:exists_s(x)_st_q(x)-s(x)geq0}, we make the following observation which shows that our upper bound for $q_k(x)$ applies for any symmetric quadratic function with roots in $[k-1,k]$
\begin{corollary}
\label{cor:SQF_SoS_degree_closer_roots_crude_bound}
For any $k \in \{1, \ldots , \lceil n/2 \rceil\}$ and any $a\leq b \in [k-1,k]$, a polynomial
$$
f_k:=(x-a)(x-b)
$$
admits an SoS certificate over the Boolean hypercube of degree at most the degree of an SoS certificate over the Boolean hypercube for polynomial $q_k$.
\end{corollary}
\begin{proof}
We have $f_k(x) \geq \left((k-a)(b-k+1) + (k-b)(a-k+1)\right)q_k(x)$ as
{\small
\begin{align*}
&(|x| - a)(|x| - b) \\
&= \left((k-a)(|x|- k + 1) + (a-k+1)(|x| - k)\right)\left((k-b)(|x|- k + 1) + (b-k+1)(|x| - k)\right) \\
&= (k-a)(k-b)(|x|- k + 1)^2 + (a-k+1)(b-k+1)(|x|- k)^2 \\
&+\left((k-a)(b-k+1) + (k-b)(a-k+1)\right)(|x| - k + 1)(x - |k|)
\end{align*} }
and invoke Theorem~\ref{thm:SQF_SoS_degree} to conclude the proof.
\end{proof}
\subsection{Proof of Theorem~\ref{thm:exists_s(x)_st_q(x)-s(x)geq0}}
We construct $s(x)$ in two steps. We first construct a polynomial $s_1(x)$ which is a sum of squares (modulo the Boolean axioms), is less than or equal to $(x-k+1)(x-k)$ on the interval $[0,2k-1]$, and is not too large on the interval $[2k-1,n]$. We then construct a polynomial $s_2(x)$ which is a sum of squares, is less than or equal to $1$ on the intervals $[0,k-1]$ and $[k,2k-1]$, is greater than or equal to $1$ on the interval $[k-1,k]$, and is very small on the interval $[2k-1,n]$. We then take $s(x) = s_1(x)s_2(x)$.
More precisely, we have the following conditions on $s_1$ and $s_2$:
\begin{enumerate}
\item $s_1\left(\sum_{i=1}^{n}{x_i}\right)$ is a sum of squares (modulo the Boolean axioms) and $s_2(x)$ is a sum of squares.
\item For all $x \in [k-1,k]$, $\frac{s_1(x)}{(x-k+1)(x-k)} \geq 1$ and $s_2(x) \geq 1$.
\item For all $x \in [0,k-1] \cup [k,2k-1]$, $\frac{s_1(x)}{(x-k+1)(x-k)} \leq 1$ and $s_2(x) \leq 1$.
\item For all $x \in [2k-1,n]$, $\left|\frac{s_1(x)}{(x-k+1)(x-k)}\right| \leq n^{40k}$ and $s_2(x) \leq n^{-40k}$.
\item $s_1(x)$ has degree $O(k)$ and $s_2(x)$ has degree $O(\sqrt{nk}\log(n))$.
\end{enumerate}
\begin{proposition}
If $s_1(x)$ and $s_2(x)$ satisfy the above conditions and we take $s(x) = s_1(x)s_2(x)$ then $s\left(\sum_{i=1}^{n}{x_i}\right)$ is a sum of squares (modulo the Boolean axioms) and for all $x \in [0,n]$, $(x-k+1)(x-k) - s(x) \geq 0$.
\end{proposition}
\begin{proof}
We make the following observations:
\begin{enumerate}
\item Since $s_1\left(\sum_{i=1}^{n}{x_i}\right)$ is a sum of squares (modulo the Boolean axioms) and $s_2(x)$ is a sum of squares, the product $s\left(\sum_{i=1}^{n}{x_i}\right) = s_1\left(\sum_{i=1}^{n}{x_i}\right)s_2\left(\sum_{i=1}^{n}{x_i}\right)$ is a sum of squares (modulo the Boolean axioms).
\item For all $x \in [0,k-1] \cup [k,2k-1]$, since $(x-k+1)(x-k) \geq 0$, $\frac{s_1(x)}{(x-k+1)(x-k)} \leq 1$, and $0 \leq s_2(x) \leq 1$,
\[
(x-k+1)(x-k) - s(x) = (x-k+1)(x-k)\left(1 - s_2(x)\frac{s_1(x)}{(x-k+1)(x-k)}\right) \geq 0.
\]
\item For all $x \in [k-1,k]$, since $(x-k+1)(x-k) \leq 0$, $\frac{s_1(x)}{(x-k+1)(x-k)} \geq 1$, and $s_2(x) \geq 1$,
\[
(x-k+1)(x-k) - s(x) = (x-k+1)(x-k)\left(1 - s_2(x)\frac{s_1(x)}{(x-k+1)(x-k)}\right) \geq 0.
\]
\item For all $x \in [2k-1,n]$, since $(x-k+1)(x-k) \geq 0$, $\left|\frac{s_1(x)}{(x-k+1)(x-k)}\right| \leq n^{40k}$ and $|s_2(x)| \leq n^{-40k}$,
\[
(x-k+1)(x-k) - s(x) = (x-k+1)(x-k)\left(1 - s_2(x)\frac{s_1(x)}{(x-k+1)(x-k)}\right) \geq 0.
\]
\end{enumerate}
\end{proof}
Thus, we have an SoS proof of degree $O(\sqrt{kn}log(n))$ that $(|x|-k+1)(|x|-k) \geq 0$.
\subsubsection{Constructing the polynomial $s_1(x)$}
We now construct the polynomial $s_1(x)$.
\begin{lemma}
For $n\in \mathbb{N}$ and all $k \in [n]$, there exists a polynomial $s_1(x)$ such that
\begin{enumerate}
\item $s_1\left(\sum_{i=1}^{n}{x_i}\right)$ has a degree $O(k)$ sum of squares (modulo the Boolean axioms) certificate.
\item For all $x \in [k-1,k]$, $\frac{s_1(x)}{(x-k+1)(x-k)} \geq 1$.
\item For all $x \in [0,k-1] \cup [k,2k-1]$, $\frac{s_1(x)}{(x-k+1)(x-k)} \leq 1$.
\item For all $x \in [2k-1,n]$, $\left|\frac{s_1(x)}{(x-k+1)(x-k)}\right| \leq n^{40k}$.
\end{enumerate}
\end{lemma}
\begin{proof}
For $k = 1$, we can take $s_1(x) = x(x-1)$ so we can assume that $n \geq k \geq 2$. For $k \geq 2$, we use the following construction.\footnote{Definitions~\ref{def:g_k} and~\ref{def:s_k} are only used in the current section, Section~\ref{section:SoSRankForSQFs}.}
\begin{definition}\label{def:g_k}
For all natural numbers $k \geq 2$, define $g_k(x)$ to be the polynomial
\[
g_k(x) = x^{16k}(x - 2k + 1)^{16k}\prod_{i \in \{0,\ldots,2k-1\} \setminus \{k-1,k\}} (x-i).
\]
\end{definition}
\begin{definition}\label{def:s_k}
Given a natural number $n$ and $k \in \{2,3,\ldots,n\}$, we define $s_1(x)$ as follows:
\begin{enumerate}
\item If $k$ is odd, then we define $s_1(x) = \frac{g_k(x)}{g_k(k-1)}(x-k+1)(x-k)$.
\item If $k$ is even, then we define $s_1(x) = -\frac{g_k(x)(x+1)(x-2k)}{g_k(k-1)k(k+1)}(x-k+1)(x-k)$.
\end{enumerate}
\end{definition}
We verify the desired properties. We first show that $s_1\left(\sum_{i=1}^{n}{x_i}\right)$ is a sum of squares (modulo the Boolean axioms). If $k$ is odd, then since $g_k(k-1) > 0$, $\prod_{i=0}^{2k-1} \left(\left(\sum_{i=1}^{n}{x_i}\right)-i\right)$ is a sum of squares (modulo the Boolean axioms), and by~\cite[Lemma 4.4]{LeePWY16}, \[
s_1\left(\sum_{i=1}^{n}{x_i}\right) = \frac{\left(\sum_{i=1}^{n}{x_i}\right)^{16k}(\left(\sum_{i=1}^{n}{x_i}\right) - 2k + 1)^{16k}}{g_k(k-1)}\prod_{i=0}^{2k-1} \left(\left(\sum_{i=1}^{n}{x_i}\right)-i\right)
\]
is a sum of squares (modulo the Boolean axioms). If $k$ is even, then since $g_k(k-1) < 0$, $\left(\sum_{i=1}^{n}{x_i}\right) + 1$ and $\prod_{i=0}^{2k} \left(\left(\sum_{i=1}^{n}{x_i}\right)-i\right)$ are sum of squares (modulo the Boolean axioms),
\[
s_1\left(\sum_{i=1}^{n}{x_i}\right) = -\frac{\left(\sum_{i=1}^{n}{x_i}\right)^{16k}(\left(\sum_{i=1}^{n}{x_i}\right) - 2k + 1)^{16k}}{g_k(k-1)k(k+1)}\left(\left(\sum_{i=1}^{n}{x_i}\right) + 1\right)\prod_{i=0}^{2k} \left(\left(\sum_{i=1}^{n}{x_i}\right)-i\right)
\]
is a sum of squares (modulo the Boolean axioms). Finally, to argue about the degree, note that by~\cite[Lemma 4.4]{LeePWY16}, $\prod_{i=0}^{2k-1} \left(\left(\sum_{i=1}^{n}{x_i}\right)-i\right)$ has a sum of squares (modulo the Boolean axioms) certificate of degree $2k$ and thus, for all $k$, $s_1\left(\sum_{i=1}^{n}{x_i}\right)$ has a sum of squares (modulo the Boolean axioms) certificate of degree $O(k)$.
For the fourth property, observe that for $x \in [0,n]$, every term in the numerator (except for $(x+1)$ when $k$ is even) has magnitude at most $n$, every term in the denominator has magnitude at least $1$, and there are less than $40k$ terms in the numerator.
The second and third properties follow immediately from the following lemma.
\begin{lemma}
For all natural numbers $k \geq 2$, $g_k(x)$ satisfies the following properties:
\begin{enumerate}
\item For all $x \in [0,2k-1]$, $g_k(2k-1-x) = g_k(x)$.
\item For all $x \in [k-1,k]$, $\frac{g_k(x)}{g_k(k-1)} \geq 1$.
\item For all $x \in [0,k-1] \cup [k,2k-1]$, $\left|\frac{g_k(x)}{g_k(k-1)}\right| \leq 1.$
\end{enumerate}
\end{lemma}
\begin{proof
Since the first and second properties hold for every term in the product
$$g_k(x) = (-1)^{k-1}\left(x(x - 2k + 1)\right)^{16k}\left(\prod_{i=0}^{k-2}{(x-i)(2k-1-x-i)}\right),$$
they hold for $g_k(x)$ as well.
By symmetry, it suffices to show the third property for $x \in [0,k-1]$. For $x \in \{0,1,\ldots,k-2\}$, $g_k(x) = 0$ and for $x \in (k-2,k-1)$, the third property holds for every term in this product, so it holds for $g_k(x)$ as well.
To show that the third property holds for $x \in [0,k-2] \setminus \{0,1,\ldots,k-2\}$, we compare $g_k(x-m)$ and $g_k(x)$, where $x \in (k-2,k-1)$ and $m \in \{0,1,\ldots,k-2\}$. For this, we decompose $g_k(x)$ as $g_k(x) = a_k(x)b_k(x)^{16k}$, where $a_k(x) = \prod_{i \in \{0,\ldots,2k-1\} \setminus \{k-1,k\}} (x-i)$ and $b_k(x) = x(2k-1-x)$.
\begin{lemma}\label{aklemma}
Let $a_k(x) = \prod_{i \in \{0,\ldots,2k-1\} \setminus \{k-1,k\}} (x-i) = \left(\prod_{i=0}^{k-2}{(x-i)}\right)\left(\prod_{i=k+1}^{2k-1}{(x-i)}\right)$. For all $x \in (k-2,k-1)$ and all $m \in \{1,\ldots,k-2\}$,
$\left|\frac{a_k(x-m)}{a_k(x)}\right| \leq e^{\frac{16m^2}{k}}$.
\end{lemma}
\begin{proof
Observe that
\begin{align*}
\left|\frac{a_k(x-m)}{a_k(x)}\right| &= \left|\frac{\prod_{j=1}^{m}{(x-k+2-j)}}{\prod_{j=1}^{m}{(x+1-j)}} \cdot \frac{\prod_{j=1}^{m}{(x-2k+1-j)}}{\prod_{j=1}^{m}{(x-k-j)}}\right| \\
&= \left|\frac{\prod_{j=1}^{m}{(k-2-x+j)}}{\prod_{j=1}^{m}{(k - x + j)}} \cdot \frac{\prod_{j=1}^{m}{(2k - x-1+j)}}{\prod_{j=1}^{m}{(x -m + j)}}\right| \\
&\leq \left|\prod_{j=1}^{m}{\left(\frac{k+1+j}{k-2-m+j}\right)}\right|.
\end{align*}
We distinguish between two cases.
\begin{enumerate}
\item If $m \leq \frac{3k}{4} - 1$, observe that
\begin{align*}
\left|\prod_{j=1}^{m}{\left(\frac{k+1+j}{k-2-m+j}\right)}\right| &= \prod_{j=1}^{m}{\left(1 + \frac{m+3}{k-2-m+j}\right)} \\
&\leq \prod_{j=1}^{m}{\left(1 + \frac{m+3}{k-m-1}\right)} \leq \prod_{j=1}^{m}{e^{\frac{m+3}{k-m-1}}} = e^{\frac{m(m+3)}{(k - m + 1)}} \leq e^{\frac{16m^2}{k}}.
\end{align*}
\item If $m > \frac{3k}{4} - 1$, then $m \geq \frac{3k}{4} - \frac{3}{4} \geq \frac{3k}{8}$ (as $k \geq 2$). Thus,
\[
\left|\prod_{j=1}^{m}{\left(\frac{k+1+j}{k-2-m+j}\right)}\right| \leq \prod_{j=1}^{k-2}{\left(\frac{k+1+j}{j}\right)} = \frac{(2k-1)!}{(k-2)!(k+1)!} \leq 2^{2k-1} \leq e^{\frac{16m^2}{k}}.
\]
\end{enumerate}
\end{proof
\begin{lemma}\label{bklemma}
Let $b_k(x) = x(2k-1-x)$. For $x \in (k-2,k-1)$ and $m \in [k-2]$,~$
\left|\frac{b_k(x-m)}{b_k(x)}\right| \leq e^{-\frac{m^2}{k^2}}.
$
\end{lemma}
\begin{proof}
Observe that
\begin{align*}
\frac{b_k(x-m)}{b_k(x)} = \frac{(x-m)(2k-1+m-x)}{x(2k-1-x)} & = \frac{x(2k-1-x) - (2k-1-2x)m - m^2}{x(2k-1-x)} \\
& \leq 1 - \frac{m^2}{x(2k-1-x)} \leq 1 - \frac{m^2}{k^2} \leq e^{-\frac{m^2}{k^2}}.
\end{align*}
\vspace{-0.6cm}
\end{proof}
\begin{corollary}
For all $x \in (k-2,k-1)$ and $m \in \{1,\ldots,k-2\}$, $\left|\frac{g_k(x-m)}{g_k(x)}\right| \leq 1$.
\end{corollary}
\begin{proof}
By Lemmas \ref{aklemma} and \ref{bklemma},
$$
\left|\frac{g_k(x-m)}{g_k(x)}\right| = \left|\frac{a_k(x-m)}{a_k(x)}\right| \left|\frac{b_k(x-m)}{b_k(x)}\right|^{16k}
\leq e^{\frac{16m^2}{k}} \left(e^{-\frac{m^2}{k^2}}\right)^{16k}~=~1.
$$
\end{proof}
\end{proof
\end{proof}
\subsubsection{Constructing the polynomial $s_2(x)$}
We now construct the polynomial $s_2(x)$.
\begin{lemma}\label{lem:h_sufficient_cond}
For all $n\in \mathbb{N}$ and all $k \in [n]$, there exists a polynomial $s_2(x)$ of degree $O(\sqrt{kn}log(n))$ satisfying the following properties:
\begin{enumerate}
\item $s_2(x)$ is a sum of squares.
\item For all $x \in [k-1,k]$, $s_2(x) \geq 1$.
\item For all $x \in [0,k-1] \cup [k,2k-1]$, $s_2(x) \leq 1$.
\item For all $x \in [2k-1,n]$, $s_2(x) \leq n^{-40k}$.
\end{enumerate}
\end{lemma}
\begin{proof}
\begin{lemma}
\label{lem:H_polynpomial_properties}
For $C:= e^{8\sqrt{3}}$ and $k \in \{0, \ldots, \lceil n/2 \rceil \}$, $H_k(x) := T^2_{\sqrt{\frac{n}{k}}}\left( 2\frac{x}{n} -1 -2\frac{2k-1}{n} \right)$ satisfies the following properties:
\begin{enumerate}
\item For all $x \in [2k-1,n]$, $H_k(x) \leq 1$.
\item For all $k \in [0,2k-1]$, $H'_k(x) < 0$. \label{prop: 2}
\item $H_k(0) \leq C$. \label{prop: 3}
\item $H_k(k) \geq 1.5$.
\end{enumerate}
\end{lemma}
\begin{proof}
Note that
$H_k(2k-1)=T^2_{\sqrt{\frac{n}{k}}}\left(-1 \right) =1$ and $H_k(n)=T^2_{\sqrt{\frac{n}{k}}}\left(1 - 2\frac{2k-1}{n} \right) \leq 1$, which implies the first property.
%
We prove Properties~\eqref{prop: 2} and~\eqref{prop: 3}. By Lemma~\ref{lem:Chebyshev_1-c/n_properties}, for $k$ such that $4k-2 \leq n$, we have
$$
H_k(0)=T^2_{\sqrt{\frac{n}{k}}}\left(-1 -\frac{4k-2}{n} \right) \leq
\left(1 + \sqrt{\frac{32k-16}{n}} \right)^{2\sqrt{\frac{n}{k}}}
\leq e^{2\sqrt{\frac{32k-16}{k}}} \leq e^{8\sqrt{3}}$$
and for $k$ such that $4k-2 \geq n$, by Lemma~\ref{lem:Chebyshev_1-c/n_properties}, for $c \geq n$, we have
$$
H_k(0)=T^2_{\sqrt{\frac{n}{k}}}\left(-1 -\frac{4k-2}{n} \right) \leq
\left(1 + \frac{12k}{n} \right)^{2\sqrt{\frac{n}{k}}}
\leq \left(1 + \sqrt{\frac{12k}{n}} \right)^{4\sqrt{\frac{n}{k}}}
\leq e^{4\sqrt{\frac{12k}{k}}} \leq e^{8\sqrt{3}}.$$
Moreover, by Lemma~\ref{lem:Chebyshev_1-c/n_properties} we have
\[
H_k(k)=T^2_{\sqrt{\frac{n}{k}}}\left( -1 -\frac{2k-2}{n} \right) \geq \frac{1}{4} \left(1+\sqrt{\frac{4k-4}{n}} \right)^{2\sqrt{\frac{n}{k}}} \geq \frac{1}{4} \left(1+\sqrt{\frac{2k}{n}} \right)^{2\sqrt{\frac{n}{k}}},
\]
where the last inequality holds because $k \geq 2$. Finally, since $n \geq 2k$,
\[
\frac{1}{4} \left(1+\sqrt{\frac{2k}{n}} \right)^{2\sqrt{\frac{n}{k}}} \geq \frac{1}{4}2^{2 \sqrt{\frac{n}{k}} \sqrt{\frac{2k}{n}}} = \frac{1}{4}2^{2\sqrt{2}} \geq 1.5.
\]
\end{proof}
\begin{lemma}
For any constants $a,b,C$ such that $1.5 \leq a < b < C$, there is a sum of squares polynomial $p_{a,b,C}(x)$ of degree at most $8\lceil{C^2}\rceil$ such that the following hold:
\begin{enumerate}
\item For all $x \in [a,b]$, $p_{a,b,C}(x) \geq 1$.
\item For all $x \in [0,1]$, $|p_{a,b,C}(x)| \leq \frac{1}{2}$.
\item For all $x \in [0,a] \cup [b,C]$, $|p_{a,b,C}(x)| \leq 1$.
\end{enumerate}
\end{lemma}
\begin{proof}
We can take the polynomial
\[
p_{a,b,C}(x) = \left(1 - \frac{(x - a)(x-b)}{C^2}\right)^{4\lceil{C^2}\rceil}.
\]
We now make the following observations:
\begin{enumerate}
\item For all $x \in [a,b]$, $1 - \frac{(x - a)(x-b)}{C^2} \geq 1$ so $p_{a,b,C}(x) \geq 1$.
\item For all $x \in [0,1]$, $|1 - \frac{(x - a)(x-b)}{C^2}| \leq 1 - \frac{1}{4C^2}$ so $|p_{a,b,C}(x)| \leq \left(1 - \frac{1}{4C^2}\right)^{4\lceil{C^2}\rceil} \leq \frac{1}{2}$.
\item For all $x \in [0,a] \cup [b,C]$, $|1 - \frac{(x - a)(x-b)}{C^2}| \leq 1$ so $|p_{a,b,C}(x)| \leq 1$.
\end{enumerate}
\end{proof}
We construct the polynomial $s_2(x)$. For $k\in \{2,\ldots, \lceil n/2 \rceil\}$, let
$$
s_2(x):= p_{a,b,C}\left(H_k(x)\right)^{40\lceil{k \log(n)}\rceil},
$$
where $a = H_k(k)$, $b = H_k(k-1)$, and $C = e^{8\sqrt{3}}$ is the constant given by Lemma \ref{lem:H_polynpomial_properties}.
\begin{lemma}
\label{lem:h_k_satisties_all_propoerties}
For any $k\in \{2,\ldots, \lceil n/2 \rceil\}$, $s_2(x)$ satisfies the properties in Lemma~\ref{lem:h_sufficient_cond}.
\end{lemma}
\begin{proof}
We make the following observations:
\begin{enumerate}
\item For all $x \in [0,k-1] \cup [k,2k-1]$, $H_k(x) \in [0,H_k(k)] \cup [H_k(k-1),C]$ so $|p_{a,b,C}(H_k(x))| \leq 1$ and thus
$$s_2(x) = p_{a,b,C}\left(H_k(x)\right)^{40\lceil{k \log(n)}\rceil} \leq 1.$$
\item For all $x \in [k-1,k]$, $H_k(x) \in [H_k(k),H_k(k-1)]$ so $p_{a,b,C}(H_k(x)) \geq 1$ and thus
$$s_2(x) = p_{a,b,C}\left(H_k(x)\right)^{40\lceil{k \log(n)}\rceil} \geq 1.$$
\item For all $x \in [2k-1,n]$, $H_k(x) \in [0,1]$ so $|p_{a,b,C}(H_k(x))| \leq 1$ and thus,
$$s_2(x) = p_{a,b,C}\left(H_k(x)\right)^{40\lceil{k \log(n)}\rceil} \leq n^{-40k}.$$
\end{enumerate}
\end{proof}
\end{proof}
\section{SoS rank upper bound for the MK problem via SQF certification}\label{section:MK_problem}
In this section, we prove an upper bound of $O(\sqrt{n}\log(P))$ on the SoS rank for the MK problem, which, together with the lower bound presented in~\cite{Kurpisz19}, constitutes proof of Theorem~\ref{thm:MK_SoS_rank}.
We first discuss the necessary properties a candidate SoS certificate for the MK problem has to satisfy.
A degree $d$ SoS certificate for the MK problem is of the form
$\sum_{i\in [n]} x_i-1=s_0(\mathbf{x})+s_1(\mathbf{x}) \left(\sum_{i \in [n]} x_i - \frac{1}{P} \right), $
where $s_0,s_1$ are SoS polynomials of degree $2d+2$ and $2d$, respectively.
Through permutation of indices, the existence of an SoS certificate for the MK problem implies the existence of an SoS certificate such that $s_1$ is symmetric, that is, there exists $\tilde{s}_1:\mathbb{R}\to\mathbb{R}$ such that ${s_1(\mathbf{x})=\tilde{s}_1(|\mathbf{x}|)}$ for all $\mathbf{x}\in\{0,1\}^n$. Since $s_0$ is globally nonnegative, $\tilde{s}_1$ needs to satisfy
\begin{equation}\label{eq:necessaryMK}
|\mathbf{x}|-1 \geq \tilde{s}_1(|\mathbf{x}|)\left(|\mathbf{x}|- \frac{1}{P}\right) \qquad \text{ for all } \mathbf{x}\in \{0,1\}^n.
\end{equation}
Thus, $\tilde{s}_1(0) \geq P$, $\tilde{s}_1(1)=0$, and $\tilde{s}_1(x)\leq \frac{x-1}{x - \frac{1}{P}}$ for $x\in\{2,\ldots,n\}$.
We will construct a sum of squares polynomial $\tilde{s}_1$ which satisfies the following slightly stronger conditions:
\begin{enumerate}
\item $\tilde{s}_1(0) > P$.
\item For all $x \in [1,2]$, $\tilde{s}_1(x) \leq \frac{x-1}{2}$.
\item For all $x \in [2,n]$, $\tilde{s}_1(x) \leq \frac{1}{2}$.
\end{enumerate}
We will then observe that these conditions imply that
\[
\tilde{s}_0(|x|) = |x| - 1 - \tilde{s}_1(|x|)\left(|x| - \frac{1}{P}\right)
\]
is positive for all $x \in \{0\} \cup (1,n]$ which is sufficient to show that $\tilde{s}_0(x)$ is a sum of squares modulo the Boolean constraints.
A polynomial $T_{2 \sqrt{n}}(\frac{x-1+r_0}{n}-1)$, where $r_0$ is the smallest root of the polynomial $T_{2 \sqrt{n}}(\frac{x}{n}-1)$, which for $P=2$ satisfies similar
requirements was constructed in~\cite[Lemma 15]{Kurpisz19} using properties of Chebyshev polynomials.
To obtain our polynomial $\tilde{s}_1(x)$, we generalize this construction using three parameters, the degree $d$ of the Chebyshev polynomial, a scaling factor $\alpha$, and an even power $m$.
\begin{definition}
Given an $\alpha > 0$, a natural number $d$, and an even natural number $m$, define
$
\tilde{s}_{\alpha,d,m}(x) := {\alpha}T_d\left(\frac{x-1+r_0}{n} - 1\right)^m,
$
where $r_0$ is the smallest root of the polynomial $T_d\left(\frac{x}{n} - 1\right)$.
\end{definition}
\begin{lemma}
$r_0 \leq \frac{{\pi}^2{n}}{4d^2}$.
\end{lemma}
\begin{proof}
Observe that $T_d(x) = \cos(d\cos^{-1}(x))$ so the first zero of $T_d(x)$ is $\cos\left(-\pi + \frac{\pi}{2d}\right) \leq -1 + \frac{\pi^2}{4d^2}$. Thus, the first zero of $T_d\left(\frac{x}{n} - 1\right)$ is at most $\frac{{\pi}^2{n}}{4d^2}$.
\end{proof}
\begin{lemma}\label{madpropertieslemma}
For $d > \frac{\pi}{2}\sqrt{n}$ the polynomial $\tilde{s}_{\alpha,d,m}(x)$ satisfies the following properties:
\begin{enumerate}
\item For all $x \in [1,n]$, $\tilde{s}_{\alpha,d,m}(x) \leq \min{\{\frac{{\alpha}d^2}{n}(x-1),\alpha\}}$.
\item $\tilde{s}_{\alpha,d,m}(0) \geq \alpha\left(\frac{1}{4}\left(1 + \sqrt{\frac{2(1 - r_0)}{n}}\right)^{d}\right)^{m}$.
\end{enumerate}
\end{lemma}
\begin{proof}
For the first statement, observe that by the Markov Brothers' Theorem, since $|T_d(x)| \leq 1$ for all $x \in [-1,1]$, $|T'_d(x)| \leq d^2$ for all $x \in [-1,1]$. This implies that $\left|T'_d\left(\frac{x-1+r_0}{n} - 1\right)\right| \leq \frac{d^2}{n}$ for all $x \in [1 - r_0,2n + 1 - r_0]$. Since $T_d\left(\frac{x-1+r_0}{n} - 1\right) = 0$, when $x = 1$, $\left|T_d\left(\frac{x-1+r_0}{n} - 1\right)\right| \leq \min{\{\frac{d^2(x-1)}{n},1\}}$ for all $x \in [1,n]$, which implies the result.
For the second statement, by Lemma \ref{lem:Chebyshev_1-c/n_properties}, if $0 \leq c \leq n$ then $|T_d(-1 - \frac{c}{n})| \geq \frac{1}{4}\left(1 + \sqrt{\frac{2c}{n}}\right)^{d}$. Applying this lemma with $c = 1 - r_0$, the result follows.
\end{proof}
\begin{corollary}\label{madconditionscorollary}
If the conditions
\begin{enumerate}
\item $d \geq 3\sqrt{n}$,
\item $\alpha \leq \frac{n}{2d^2} \leq \frac{1}{2}$,
\item $m > \frac{\ln(P) - ln(\alpha)}{d\ln\left(1 + \sqrt{\frac{2(1 - r_0)}{n}}\right) - \ln(4)}$,
\end{enumerate}
are satisfied,
then the following properties hold:
\begin{enumerate}
\item $\tilde{s}_{\alpha,d,m}(0) > P$.
\item For all $x \in [1,2]$, $\tilde{s}_{\alpha,d,m}(x) \leq \frac{x-1}{2}$.
\item For all $x \in [2,n]$, $\tilde{s}_{\alpha,d,m}(x) \leq \frac{1}{2}$.
\end{enumerate}
Thus, $(x - 1) - \tilde{s}_{\alpha,d,m}(x)(x - \frac{1}{P}) > 0$
whenever $x \in \{0\} \cup (1,n]$.
\end{corollary}
\begin{proof}
The first statement follows from algebraic manipulations provided that
$$\frac{1}{4}\left(1 + \sqrt{\frac{2(1 - r_0)}{n}}\right)^{d} \geq 1.$$ To confirm that this holds, observe that $r_0 \leq \frac{{\pi}^2{n}}{4d^2} \leq \frac{1}{2}$. Thus,
\[
\left(1 + \sqrt{\frac{2(1 - r_0)}{n}}\right)^{d} \geq \left(1 + \frac{1}{\sqrt{n}}\right)^{d} \geq 2^{\frac{d}{\sqrt{n}}} \geq 8.
\]
For the second and third statements, we use the facts that for all $x \in [1,n]$, $\tilde{s}_{\alpha,d,m}(x) \leq \frac{{\alpha}d^2}{n}(x-1)$ and $\tilde{s}_{\alpha,d,m}(x) \leq \alpha$, respectively.
To show that $(x - 1) - \tilde{s}_{\alpha,d,m}(x)(x - \frac{1}{P}) > 0$ whenever $x \in \{0\} \cup (1,n]$, we make the following observations:
\begin{enumerate}
\item For $x = 0$, $-1 - \tilde{s}_{\alpha,d,m}(0)(-\frac{1}{P}) > -1 - P\left(-\frac{1}{P}\right) = 0$.
\item For $x \in (1,2]$, $(x - 1) - \tilde{s}_{\alpha,d,m}(x)(x - \frac{1}{P}) \leq (x-1) - \frac{x-1}{2}\left(x - \frac{1}{P}\right) > 0$.
\item For $x \in [2,n]$, $(x - 1) - \tilde{s}_{\alpha,d,m}(x)(x - \frac{1}{P}) \leq (x-1) - \frac{1}{2}\left(x - \frac{1}{P}\right) > 0$.
\end{enumerate}
\end{proof}
We now confirm that
\[
\tilde{s}_0 = (x - 1) - \tilde{s}_{\alpha,d,m}(x)\left(x - \frac{1}{P}\right)
\]
is a sum of squares modulo the Boolean axioms. To see this, observe that since $\tilde{s}_0(x) > 0$ for $x \in \{0\} \cup (1,n]$, $\tilde{s}_0(x)$ must have an even number of roots in $(0,1]$ and no other roots in $[0,n]$. Thus, we can write
\[
\tilde{s}_0(x) = p\prod_{i=1}^{l}(x-a_i)(x-b_i)
\]
for some polynomial $p$ which is positive on $[0,n]$ and some real roots $a_1,\ldots,a_l,b_1,\ldots,b_l \in (0,1]$. Since $p$ is positive on $[0,n]$, $p$ is a sum of squares modulo the Boolean axioms. By Corollary \ref{cor:SQF_SoS_degree_closer_roots_crude_bound}, since $|x|(|x|-1)$ is a sum of squares modulo the Boolean axioms, for each $i \in [l]$, $(x-a_i)(x-b_i)$ is also a sum of squares modulo the Boolean axioms. Thus, $\tilde{s}_0(x)$ is a sum of squares modulo the Boolean axioms.
Finally, we observe that we can satisfy the required conditions on $d$, $\alpha$, and $m$ by taking $d = \lceil{3\sqrt{n}}\rceil$, $\alpha = \frac{1}{2d^2} \approx \frac{1}{18 n}$, and $m = O(\log(P))$, which gives a sum of squares certificate of degree $O(\sqrt{n}\log(P))$.
%
\section{SoS rank upper bound for the SC problem via SQF certification}\label{sec:SC_Problem}
In this section, we refute the Bienstock---Zuckenberg conjecture for the SC problem. We provide a degree $O(\sqrt{n} \log(n))$ SoS certificate for the SC problem on the Boolean hypercube, thus proving Theorem~\ref{thm:SC_SoS_rank}. For this proof, we use the SoS rank for certifying SQFs for $k=2$ in Theorem~\ref{thm:SQF_SoS_degree}. We present an alternative direct proof in Appendix~\ref{sec:SC_second_proof}.
We begin this section with a discussion on the properties necessary for an SoS polynomial $s$ to even be considered as a possible candidate for an SoS certificate for the SC problem.
An SoS certificate for the SC problem is of the form
$$\sum_{i\in [n]} x_i-2=s_0(\mathbf{x})+\sum_{i \in [n]}s_i(\mathbf{x})g_i(\mathbf{x}),$$
where $$g_i(\mathbf{x})=\left(\sum_{j \in [n] \setminus\{i\}} x_j - 1 \right).$$
As opposed to the discussion in Section~\ref{section:MK_problem}, an SoS certificate for the SC problem not only has multiple constraints but also displays a certain type of asymmetry, which is present in the formulation of the polynomials $g_i$ for $i\in [n]$. One could hope to abuse this asymmetry by constructing different SoS polynomials $s_i\in \Sigma_{n,d}$ for certain $d\in [n]$, but for this proof, we proceed in a similar fashion as for the MK problem and instead construct only one symmetric SoS polynomial $s:\{0,1\}^n\to\mathbb{R}$ and look for the certificate of the form
$$
\sum_{i\in [n]} x_i-2=s_0(\mathbf{x})+\sum_{i \in [n]}s(\mathbf{x})g_i(\mathbf{x}).
$$
Through permutation of indices, the existence of an SoS certificate for the SC problem implies the existence of an SoS certificate such that $s$ is symmetric, that is, there exists an $\tilde{s}:\mathbb{R}\to\mathbb{R}$ such that ${s(\mathbf{x})=\tilde{s}(|\mathbf{x}|)}$ for all $\mathbf{x}\in\{0,1\}^n$. As for the MK problem, we are interested in the requirements that polynomial $\tilde{s}$ needs to satisfy such that $s$ constitutes part of an SoS certificate for the SC problem. Let $g(\mathbf{x}):= \sum_{i \in [n]}g_i(\mathbf{x})=(n-1)(\sum_{i=1}^n x_i)-n$ and note that $g$ is a symmetric polynomial; there exists a univariate polynomial $\tilde{g}$ such that $\tilde{g}(|\textbf{x}|)= g(\textbf{x})$ for all $\mathbf{x}\in\{0,1\}^n$. Since $s_0$ is globally nonnegative, this implies that $s$ needs to satisfy
\begin{align}\label{ineq:SCCertificate}
|\mathbf{x}|-2&\geq \tilde{s}(|\mathbf{x}|)\left(|\mathbf{x}|(|\mathbf{x}|-2)+(n-|\mathbf{x}|)(|\mathbf{x}|-1)\right)\nonumber \\
&=\tilde{s}(|\mathbf{x}|)((n-1)|\mathbf{x}|-n)= \tilde{s}(|\mathbf{x}|)\tilde{g}(|\mathbf{x}|) \qquad \text{for all } \textbf{x}\in \{0, 1\}^n.
\end{align}
This implies that $\tilde{s}(0) \geq \frac{2}{n}$, $\tilde{s}(1) \geq 1$, $\tilde{s}(2) = 0$ and $\tilde{s}(x) \leq \frac{x-2}{3(n-1)x - n}$ for all $x \in \{3,4,\ldots,n\}$. We will construct a sum of squares polynomial $\tilde{s}(x)$ which satisfies the following slightly stronger conditions:
\begin{enumerate}
\item $\tilde{s}(x) \geq 1$ for all $x \in [0,1]$.
\item For all $x \in [1,2)$, $\frac{\tilde{s}(x)}{x-2} < 0$ and $\frac{\tilde{s}(x)}{x-2}$ is increasing.
\item $\tilde{s}(x) \leq \frac{(x-2)}{2n}$ for all $x \in [2,3]$.
\item $\tilde{s}(x) \leq \frac{1}{2n}$ for all $x \in [3,n]$.
\end{enumerate}
We will then observe that these conditions imply that $\tilde{s}_0(x) = x - 2 - \tilde{s}(x)((n-1)x-n)$ is positive for $x \in [0,1) \cup (2,n]$ and has exactly two zeros in the interval $[1,2]$, one of which is $x = 2$. We can then use Theorem \ref{thm:SQF_SoS_degree} and Corollary \ref{cor:SQF_SoS_degree_closer_roots_crude_bound} to show that $\tilde{s}_0$ is a sum of squares of degree $\deg(\tilde{s}) + O(\sqrt{n}\log(n))$ modulo the Boolean axioms.
\begin{lemma}
For $d = 3\sqrt{n}$, $\alpha = \frac{1}{18n}$, and $m = 2\lceil{\log_2(\sqrt{18n})}\rceil$ the polynomial $\tilde{s}(x) = \tilde{s}_{\alpha,d,m}(x-1)$ satisfies the following properties:
\begin{enumerate}
\item $\tilde{s}(x) \geq 1$ for all $x \in [0,1]$.
\item For all $x \in [1,2)$, $\frac{\tilde{s}(x)}{x-2} < 0$ and $\frac{\tilde{s}(x)}{x-2}$ is increasing.
\item $\tilde{s}(x) \leq \frac{(x-2)}{2n}$ for all $x \in [2,3]$.
\item $\tilde{s}(x) \leq \frac{1}{2n}$ for all $x \in [3,n]$.
\end{enumerate}
\end{lemma}
\begin{proof}
For the first statement, just as in the proof of Corollary~\ref{madconditionscorollary}, $r_0 \leq \frac{{\pi}^2{n}}{4d^2} \leq \frac{1}{2}$. Thus,
\[
\left(1 + \sqrt{\frac{2(1 - r_0)}{n}}\right)^{d} \geq \left(1 + \frac{1}{\sqrt{n}}\right)^{d} \geq 2^{\frac{d}{\sqrt{n}}} \geq 8.
\]
Hence, by Lemma~\ref{madpropertieslemma}, $\tilde{s}(1) = \tilde{s}_{\alpha,d,m}(0) \geq {\alpha}2^{m} \geq 1$. Since $deg(\tilde{s})$ is even, all roots of $\tilde{s}$ are real and the smallest root of $\tilde{s}$ is $2$, $\tilde{s}$ is positive and decreasing when $x < 2$ so $\tilde{s}(x) \geq 1$ whenever $x \in [0,1]$, as needed.
For the second statement, observe that since $\deg(\tilde{s})$ is even, all roots of $\tilde{s}$ are real and the smallest root of $\tilde{s}$ is $2$, $\frac{\tilde{s}(x)}{x-2}$ is negative and increasing whenever $x < 2$.
For the third statement, observe that by Lemma \ref{madpropertieslemma}, for all $x \in [2,3]$, $\tilde{s}(x) = \tilde{s}_{\alpha,d,m}(x-1) \leq {\alpha}\frac{d^2}{n}(x-2) \leq \frac{x-2}{2n}$.
For the fourth statement, observe that by Lemma \ref{madpropertieslemma}, for all $x \in [3,n]$, $\tilde{s}(x) = \tilde{s}_{\alpha,d,m}(x-1) \leq {\alpha} < \frac{1}{2n}$.
\end{proof}
\begin{corollary}
For $d = 3\sqrt{n}$, $\alpha = \frac{1}{n}$, $m = 2\lceil{\log_2(n)}\rceil$, and $\tilde{s}(x) = \tilde{s}_{\alpha,d,m}(x-1)$ the polynomial
$\tilde{s}_0(x) = x - 2 - \tilde{s}(x)((n-1)x-n)$ is positive for $x \in [0,1) \cup (2,n]$ and has exactly two zeros in the interval $[1,2]$, one of which is $x = 2$.
\end{corollary}
\begin{proof}
We make the following observations:
\begin{enumerate}
\item For all $x \in [0,1)$,
\[
\tilde{s}_0(x) = x - 2 - \tilde{s}(x)((n-1)x-n) \geq x - 2 - ((n-1)x-n) = (n-2)(1-x) > 0.
\]
\item For all $x \in [1,2]$, $\frac{\tilde{s}_0}{x-2} = 1 - ((n-1)x-n)\frac{\tilde{s}}{x-2}$. When $x \in [\frac{n}{n-1},2]$, $((n-1)x-n)\frac{\tilde{s}}{x-2} \leq 0$ so $\frac{\tilde{s}}{x-2} > 0$. When $x \in [1,\frac{n}{n-1})$, both $((n-1)x-n)$ and $\frac{\tilde{s}}{x-2}$ are negative and increasing so $((n-1)x-n)\frac{\tilde{s}}{x-2}$ is positive and decreasing and thus $\frac{\tilde{s}_0}{x-2}$ is increasing. Since $\frac{\tilde{s}_0(1)}{1-2} \leq 0$ and $\frac{\tilde{s}_0(\frac{n}{n-1})}{\frac{n}{n-1}-2} > 0$, $\frac{\tilde{s}_0(x)}{x-2}$ must have exactly one zero in the interval $[1,\frac{n}{n-1}]$.
\item For all $x \in (2,3]$, $\tilde{s}_0(x) = x - 2 - \tilde{s}(x)((n-1)x-n) \geq x-2 - \frac{(n-1)x-n}{2n}(x-2) > 0$.
\item For all $x \in [3,n]$, $\tilde{s}_0(x) = x - 2 - \tilde{s}(x)((n-1)x-n) \geq x-2 - \frac{(n-1)x-n}{2n} > \frac{x}{2} - \frac{3}{2} \geq 0$.
\end{enumerate}
\end{proof}
\begin{corollary}
$\tilde{s}_0(|x|)$ is a sum of squares of degree $O(\sqrt{n}\log(n))$ modulo the Boolean axioms.
\end{corollary}
\begin{proof}
Since $\tilde{s}_0(x) = x - 2 - \tilde{s}(x)((n-1)x-n)$ is positive for $x \in [0,1) \cup (2,n]$ and has exactly two zeros in the interval $[1,2]$, one of which is $x = 2$, we can write
\[
\tilde{s}_{0}(x)= \tilde{p}(x-a)(x-2),
\]
for some $a \in [1,2)$ where $\tilde{p}(x)$ is positive for has no real roots in the interval $[0,n]$. Since $\tilde{p}(x)$ is positive and has no real roots in the interval $[0,n]$, $\tilde{p}(|x|)$ is a sum of squares modulo the Boolean axioms. By Theorem \ref{thm:SQF_SoS_degree} and Corollary \ref{cor:SQF_SoS_degree_closer_roots_crude_bound}, $(x-a)(x-2)$ is a sum of squares of degree $O(\sqrt{n}\log(n))$ modulo the Boolean axioms.
\end{proof}
Thus, there exists a degree $O(\sqrt{n}\log (n))$ SoS certificate of nonnegativity for the SC problem.
{\small
\bibliographystyle{abbrv}
| {
"redpajama_set_name": "RedPajamaArXiv"
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{"url":"https:\/\/electronics.stackexchange.com\/questions\/56345\/zxct1009-as-a-current-monitor","text":"# ZXCT1009 as a current monitor\n\nI am currently using ZXCT1009 high side monitor for monitoring the current consumption on a bus line for an embedded system we are developing. I am currently using tek scope with Labview for automation purpose. Works good at our lab.\n\nNow I am thinking of implementing this ZXCT1009 in the embedded design itself and somehow sensing the voltage across the output resistor.\n\nZXCT1009 data sheet -http:\/\/www.diodes.com\/datasheets\/ZXCT1009.pdf\n\nI am not sure how to move forward along the lines of using ZXCT1009 as a battery current monitor.\n\n## 1 Answer\n\nThe datasheet itself provides the schematic for implementing the ZXCT1009 as a current monitor:\n\n\u2022 Select Rsense such that the expected maximum possible current generates just under 1.1 Volts across Rsense (Rsense = 1.1 \/ Imax) - going by the limits in the first graph on Page 3, not by the 2.5 Volt specified in the table on Page 2.\n\u2022 Select a suitable value of Rout, to give a Vout range suitable to one of the available ADC channels of the microcontroller, for a full-scale Iout of around 10 mA (Rout = 5 \/ 0.01 assuming a full-scale of 5 Volts)\n\nAs the current flowing through Rsense changes, so will Vout. Read this into the ADC, process as required.\n\n\u2022 Wow, that's rough... you have to tolerate a 1.1V drop before your load comes into play... I guess \"Load\" could be a regulator or step-up converter and you'd increase V_in accordingly to use this part. Jan 28 '13 at 16:55","date":"2021-10-28 14:06:07","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\": 0.2729036509990692, \"perplexity\": 2766.882348526579}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"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-2021-43\/segments\/1634323588341.58\/warc\/CC-MAIN-20211028131628-20211028161628-00223.warc.gz\"}"} | null | null |
RTI in Media
Website News & Support
Mumbai: Slums redeveloped into housing society to come under RTI for more transparency
rti activism: Mumbai: Slums redeveloped into housing society to come under RTI for more transparency
By Sajib Nandi, February 7, 2018 in RTI in Media
The slums redeveloped into housing societies under Slum Rehabilitation Authority have been brought under Right To Information Act (RTI) in order to bring more transparency. The state Information Commission has declared these to be public authorities under 2 (h) of the RTI act.
On 19 December, 2017, the Chief Information Commissioner of Maharashtra had passed an order stating that all the societies built under SRA are public authority. The order also stated that the SRA authority are required to appoint a public information officer as well as the First Appellate Authority (FAA) under RTI. This order was passed after an application was made by Jayprakash Page on the said date. He had sought details of the total number of flats in his society.
Read more at: Mumbai: Slums redeveloped into housing society to come under RTI for more transparency | Free Press Journal | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 4,094 |
Talking Cinema: Conversations With Actors & Directors, published in 2013, takes a look into the reel lives of film personalities. This book tries to answer questions about how actors prepare themselves for specific roles, and what is their intellectual and emotional state of mind. The author has documented conversations with some of the film industry's most famous stars. It provides an insider's view and insight, and makes readers understand that movies are beyond designer clothes, makeup and glycerine teardrops.
Talking Cinema: Conversations With Actors & Directors is divided into four sections. An Actor Prepares focuses on how a performer readies himself or herself for a role. Character Speak is the second section, and takes a look at the research that has gone into developing some of the most critically acclaimed characters that have appeared on Indian movie screens. The next portion of this book shifts its focus away from the performers, and deals with filmmakers. Directors Cut takes a peek into the mind of such personalities. The Specialists is the final section of Talking Cinema: Conversations With Actors & Directors. The author tries to analyze why a director or actor associate themselves with a particular genre of films or characters. Further, readers have the opportunity to figure out how similar or dissimilar these roles or themes really are.
Talking Cinema: Conversations With Actors & Directors introduces readers to the efforts and skills that are required in order to make a movie.
Bhawana Somaaya is an Indian film critic, columnist, journalist, designer, and writer. She has written Cinema: Images & Issues, Salaam Bollywood, Hema Malini: Authorized Biography, and many other books revolving around cinema. She has done a trilogy on Amitabh Bachchan, which includes The Legend, Bachchanalia, and Amitabh Lexicon. Somaaya started her career as the Chief Reporter of Cinema Journal, and then became a Special Correspondent for Super. She later joined Movie, and became its Joint Editor. In 2012, the author was made the Editor Chief of Screen Magazine of The Indian Express. She has also been a member of the Central Board of Film Certificate's Advisory Panel. She has written articles for The Hindu, Sandesh, The Observer, The Hindustan Times, The Indian Express North American Edition, and many other newspapers and magazines. Somaaya has also designed outfits for Shabana Azmi in movies like Kamyaab, Masoom, and Bhavna. The author is currently Radio Channel 92.7 BIG FM's Film Expert and also does reviews of films for BBC Online. | {
"redpajama_set_name": "RedPajamaC4"
} | 8,951 |
Over the weekend, Saturday to be precise, my brother challenged me to 30 days of "water only drinks". That means for me, no morning coffees before my first lectures, no green smoothies (however I can still have green nicecream and smoothie /bowls/. I just can't enjoy consuming it out of a cup/straw), no hot mugs of tea and no protein shakes/pre-workout. My goal also is to always drink at least 2L of water. I usually do but there are some days where i'm just like "nope, not today". This is day 3 of that challenge. I'm hoping to lose a little body fat (lose that gut that I developed from all those animal by-product treats) and to have overall mental clarity and clearer skin.
I performed the 21 and 9 thrusters without rest but I had to break the 15 into two sets of 8 and 7. Overall i'm happy with my results. If this was me one month ago, I would probably not have finished that workout in 17 minutes! I still need to work on my 400m runs though.
Today I felt like dressing like someone who isn't a slob. Sometimes I feel like I want to get into OOTD and fashion and all that jazz but then I remembered that I have no sense of fashion and i'm not very photogenic... Anyways i'm quite into dresses with a jumper over the top and my heeled boots at the moment.
I woke up at 5.15AM due to my alarm but I didn't get out of bed. It was then that I decided to skip my two lectures (9-11AM). I figured that the 2-hour travel time is not worth the 2 hours of lecture time? Maybe... I'll see how productive I am today. If I find that procrastination was overpowering in today's stay at home then i'll definitely be at uni on Tuesdays.
The workout intended for three rounds of the last two movements but I took a really long time on my snatches. I'd be doing them one at a time and for the last few reps, I pushed out two sets of 3. Anything that requires the bar to go over my head is mentally hard.
For this week I've been having overnight oats for breakfast. It's not messy, doesn't require heating and is absolutely delicious! Every time people tell me that they hate oats or that they tried a recipe and it was gross, I always respond with "maybe you just made it wrong". Here's an idea of how to start with the ratios (everyone's ratios are different) - My basic easy-as-ABC overnight oats recipe!
A handful or two of fruits, nuts, seeds, anything you want really!
Okay here's the hardest part... Find a jar, mix everything together and store it in the fridge. In the morning, you just grab it and go go go! Or if you're staying at home, you can eat it right from the jar or pour it in to a bowl and turn it in to an insta-worthy shot (don't take reference to the above image... it's far from insta-worthy as i've just chucked everything on top - but i'll still probably post it haha). | {
"redpajama_set_name": "RedPajamaC4"
} | 3,122 |
5 Essential Elements For best edm news site
May 6, 2018, 1:56 pm / remingtonkfzuo.bloguetechno.com
Chickens who make sick drops can be much more in-demand from customers and high-priced these days, but a superb mixed omelet will never head out of fashion.
An function won't be extra if we can't uncover an Formal website confirming the function. Connection submissions constantly help, specifically for recent bulletins.
…and he's gushing about what he phone calls "his best album yet". Enlisting artists like Birdy, Emeli Sande, Ms. Dynamite Swedish singer/rapper Elliphant, John Legend and in some cases a classical orchestra, this new LP is like nothing you've listened to ahead of and most surely absolutely nothing like Guetta's previous get the job done. The globe well known DJ phone calls it "his strategy for reinventing himself although wanting to appease supporters and silence critics".
In just two weeks of intensive fighting, Pakistani forces in East Pakistan surrendered into the joint command of Indian and Bangladeshi forces adhering to which the Individuals's Republic of Bangladesh was established.[28] This war noticed the highest range of casualties in any of the India-Pakistan conflicts, together with the greatest number of prisoners of war due to the fact the next Environment War after the surrender of greater than 90,000 Pakistani army and civilians.[29] Inside the terms of 1 Pakistani writer, "Pakistan missing 50 percent its navy, 1 / 4 of its air pressure and a third of its army".[thirty]
THIS is the woman fighting for life immediately after becoming pinned down and drilled in The pinnacle in an alleged homophobic assault.
I like listening to CBC news and radio programming. I do not normally agree... and sometimes I believe you job interview people who don't need to be listened to, but besides that it is the best We've.
The niece of Norwich City's Justin Fashanu has spoken of her delight once the stadium which her uncle used to grace hosted news on edm a Event celebrating LGBT-helpful football.
In their brief Trade, the alleged sufferer was pressed To learn more and was also requested, "What's it that you simply're looking for?"
I'm not an early riser so Really don't pay attention to the early morning exhibit . I do pay attention to the afternoon application and take pleasure in the hosts , their camaraderie and repartee , and customarily take pleasure in the subject areas . The host of t...he midday call in display has a tendency to audio exasperated and can be prickly . I've listened to her sighing and sounding impatient . There was a superb male host filling in for her some months in the past and I actually appreciated him.
"I will having said that under no circumstances Permit go of music but I've decided this 2016 operate might be my previous tour and final shows. Let us make them go out having a bang!"
If EDM is recognized for anything, it's for developing physically and mentally-transferring compositions that may be felt all over the world.
Right here we go yet again. Its not even lunch however plus the Serious T-storm watches are previously in place which includes #yeg #CBC
"Many people, once we were being developing up, could hardly ever have imagined pursuing a occupation in electronic music in India," he suggests. "I believe it's a very important reflection of a brand new India of sab kuch milega
All those plays are again as the highest 32 performs deal with off in head-to-head Competitiveness until a winner is in the long run decided. We are going to regularly set two plays up from each other and It is your choice to decide which one will advance on to the following spherical.
Comments on "5 Essential Elements For best edm news site" | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 1,224 |
'use strict'
var fs = require('graceful-fs')
var path = require('path')
var mkdirp = require('mkdirp')
var osenv = require('osenv')
var requireInject = require('require-inject')
var rimraf = require('rimraf')
var test = require('tap').test
var common = require('../common-tap.js')
var pkg = path.resolve(__dirname, 'gist-shortcut-package')
var json = {
name: 'gist-shortcut-package',
version: '0.0.0',
dependencies: {
'private-gist': 'gist:foo/deadbeef'
}
}
test('setup', function (t) {
setup()
t.end()
})
test('gist-shortcut-package', function (t) {
var cloneUrls = [
['git://gist.github.com/deadbeef.git', 'GitHub gist shortcuts try git URLs first'],
['https://gist.github.com/deadbeef.git', 'GitHub gist shortcuts try HTTPS URLs second'],
['git@gist.github.com:/deadbeef.git', 'GitHub gist shortcuts try SSH third']
]
var npm = requireInject.installGlobally('../../lib/npm.js', {
'child_process': {
'execFile': function (cmd, args, options, cb) {
process.nextTick(function () {
if (args.indexOf('clone') === -1) return cb(null, '', '')
var cloneUrl = cloneUrls.shift()
if (cloneUrl) {
t.is(args[args.length - 2], cloneUrl[0], cloneUrl[1])
} else {
t.fail('too many attempts to clone')
}
cb(new Error())
})
}
}
})
var opts = {
cache: path.resolve(pkg, 'cache'),
prefix: pkg,
registry: common.registry,
loglevel: 'silent'
}
npm.load(opts, function (er) {
t.ifError(er, 'npm loaded without error')
npm.commands.install([], function (er, result) {
t.ok(er, 'mocked install failed as expected')
t.end()
})
})
})
test('cleanup', function (t) {
cleanup()
t.end()
})
function setup () {
cleanup()
mkdirp.sync(pkg)
fs.writeFileSync(
path.join(pkg, 'package.json'),
JSON.stringify(json, null, 2)
)
process.chdir(pkg)
}
function cleanup () {
process.chdir(osenv.tmpdir())
rimraf.sync(pkg)
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 8,147 |
Review: "BlackWolf: The Hunt" - Sea of Tranquility - The Web Destination for Progressive Music!
Highly anticipated debut album from this much touted five piece, The Hunt look set to propel BlackWolf along the same path currently being enjoyed by the likes of The Answer, and indeed the pair will be touring the UK together throughout March. As you will have no doubt deduced BlackWolf are all about the classic retro soulful rock n roll revivalist style without forgetting that all important contemporary edge.
It is fair to say that there are a number of similar sounding bands around at the moment but what sets BlackWolf apart is that they have great songs to match the swagger and attitude. Bursting out of the blocks with 'Mr Maker' with enough power to light up an arena they rarely take their foot off the gas. Vocalist Scot Sharp has a voice that possesses that all important soaring quality set against the background of an abundance of hooks and licks that groove, shimmer and shake. The album has consistency right the way through although notable highlights include insistent new single 'Keep Moving On', the pounding throb of 'Sea of Merry' and urgent 'Dragging Ghosts'. A great start. | {
"redpajama_set_name": "RedPajamaC4"
} | 7,888 |
Derby teenager warned he could face jail for having a hunting knife
The 15-year-old went to a police station to tell them the weapon, which Derbyshire police officers found on the back seat of a car they stopped, belonged to him
Martin NaylorCourt Reporter
A 15-year-old Derby boy has been warned he faces jail after admitting to possessing a hunting knife in the city.
A court heard how the teenager went to a police station to tell them the weapon, which they found on the back seat of a car they stopped, belonged to him.
The teen, whose identity is protected by law and whose offence puts him in breach of a crown court suspended sentence, was arrested, charged and has now pleaded guilty to possessing a bladed article.
The knife was produced at Southern Derbyshire Magistrates Court and District Judge Jonathan Taaffe ordered that it be brought back to the same court when the youngster is sentenced next month.
Pictured is Southern Derbyshire Magistrates' Court
He told the teen: "This is not a knife that can have any legitimate use. People who carry knives need to be made aware that, if they do so, and I say this time and time again regardless of their age, they face custody.
"The public rightly need to be reassured that any court that sentences for an offence like this takes the matter very seriously. And, when you are sentenced, whoever is dealing with you needs to see that knife so I order that it is brought to court that day."
Lynn Bickley, prosecuting, said officers from Derbyshire police tried to pull over a car.
She said it was being driven by a man who reversed away from the officers but was followed and stopped. Officers discovered the knife in the back seat and arrested him.
The man pleaded guilty to failing to stop when directed by the police, was fined £250 and ordered to pay £85 costs and a £30 victim surcharge.
Allenton benefits cheat defrauded Derby City Council out of £2,000
Miss Bickley said: "A week after, the 15-year-old went to the police station and told them the knife belonged to him. He said he had kept it in his man bag and that is must have slipped out and on to the back seat of the car.
"He said to the officers: 'You will find my DNA on the knife'."
The teenager will be sentenced on August 18 at Derby Youth Court.
David Cusack, for the teen, said his client voluntarily went to the police station to hand himself in and tell them the knife belonged to him and not to the man. He said: "He even told them they would find his DNA on the knife."
Judge Taafe told the teen: "Let me tell it plainly to you I have my doubts in relation to this matter in terms of the rights and wrongs of what happened here.
"However, you have entered a guilty plea on the instruction this was clearly your knife."
Derbyshire Police | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 1,253 |
GOOD NEW!! This membership will valid until our shop last!!
- Earn your Reward Point from online/showroom shopping for your next purchase.
**As we will use the e-mail and phone number as the registration information for membership, no alteration can be made after the VIP membership valid. | {
"redpajama_set_name": "RedPajamaC4"
} | 6,487 |
Q: Why does my bool method return true but then not return true when called from other scripts? I'm working on a project with a player character and enemy characters that have a public float variable called "hp" in a class called "DamageDetector". Variable hp decrements based off of the damage of an attack. In the same "DamageDetector" class I also have a bool method "IsDead()" that returns true when a character's "hp" is less than or equal to 0:
`//Method for detecting if the character is dead or not
public bool IsDead()
{
//Return true if hp is less than or equal to 0, otherwise return false
return hp <= 0;
}`
In a separate class called "EnemyGroup" I call upon the "IsDead()" method from class "DamageDetector" to check if an enemy has died so that I can remove it from a list of GameObjects called "enemies":
`//A public list to store enemies in a contained group
public List<GameObject> enemies = new List<GameObject>();
//Called every frame
private void Update()
{
//For each enemy in the group
foreach (GameObject enemy in enemies)
{
//If the enemy is dead
if (enemy.GetComponentInParent<DamageDetector>().IsDead())
{
//Remove the enemy from the list
enemies.Remove(enemy);
}
}
}`
When I attach to unity to debug, "hp" depletes as expected from attacks and the "IsDead()" method returns true in the "DamageDetector" class. But for some reason the "IsDead()" method does not return true in the "EnemyGroup" class when checked by the if statement in the foreach loop. I noticed that it also doesn't return true when checked in other classes.
Any help would be much appreciated,
thanks.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 971 |
Q: Have a single useEffect hook after any component has been rendered So I have my routes that render a component:
const Layout = () => {
return (
<InitLayout>
<Switch>
<Redirect exact from='/' to='/home/recent' />
<Route path="/home/:category" exact component={Home}></Route>
<Route path="/about" exact component={About}></Route>
<Route path="/help" exact component={Help}></Route>
<Route path="/users/:userId" exact component={UserProfile}></Route>
<Route path="/ask" exact component={AskQuestion}></Route>
<Route path="/review" exact component={ReviewPost}></Route>
<Route path="/posts/:postId/review" exact component={ReviewPost}></Route>
<Route path="/users/:userId" exact component={UserProfile}></Route>
<Redirect from='*' to='/home/recent' />
</Switch>
</InitLayout>
);
};
In any of these components I would theoretically set the following effect:
useEffect(() => {
if (!isSsr) {
fetchPosts();
}
setSsrState({ isSsr: false }); // ==> Here
}, []);
This code will basically set an SSR state, to prevent the client to re-request data from the server when it has already been preloaded from the server.
Now this state needs to be set from any of the components, but I don't want to duplicate this code in all components. Forgetting to put it will result in bugs, so that is definitely a bad idea.
Is there a straightforward way to define an effect once, and have it called in every of the route's component?
A: After speaking with Trace, the issue was able to be resolved by wrapping the layout component with an HOC, which sets the SSR state to false.
Interestingly enough, by wrapping the component inside an HOC, this sets off the child components first before the HOC component. That way, we are able to first check on the child component level if the SSR is set. After the child component useEffect is ran, the HOC useEffect is then ran, which sets the SSR flag back to false.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 1,688 |
Q: How to show all the names of three or less authors in text? I am using the article document class and the natbib package. When I cite 3 or more authors, this is shown as FirstAuthor et al. I want to change this such that when I have one, two or three authors, all their names are shown in text, while if I have 4 or more authors, this would then be shown as FirstAuthor et al.
Is there a simple way to change the truncation of authors?
A: You would like to print the full author list, thus use citations with star *, such as \citet*, citep* under the package natbib. See below for more info.
\citet #textual citations, print the abbreviated author list
\citet* #textual citations, print the full author list
\citep #parenthetical citations, print the abbreviated author list
\citep* #parenthetical citations, print the full author list
\citealt #the same as \citet but without any parentheses.
\citealp #the same as \citep but without any parentheses.
A: I suggest you use biblatex with these options:
\usepackage[natbib, maxcitenames=3, mincitenames=11, style=apa]{biblatex}
The natbib option is for compatibility with natbib commands.
Note the default backend for biblatex is biber. You may specify in the options backend=bibtex but you'll lose some functionalities.
A: Try to use these command: \citet*{} or \citep*{} and for more extended citation you can use \citealt*{} or\citealp*{}.
According to natbib documentation, these commands show all authors and not just the abbreviated one
Natbib Documentation
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 1,760 |
Foot.ie > Clubs > Premier Division > Bray Wanderers > The Cup!!!
View Full Version : The Cup!!!
Green&whitearmy
I thought the team would have put in a it more effort last night, now we have nothing to play for at all, out of the cups and we're safe in the league...
What was Quigley thinking of last night??
How did that PR!CK of a ref not see that mitchell got the ball??
And why did dannny have to start screaming after it, the PR!CK wouldn't change his mind ever??
They talk about respect for the ref but how can you respect them when they do decisions like that...
superfrank
I haven't seen the game but the players need to control themselves, no matter if the ref's right or wrong. That's a needless ban for Doc now.
I thought that the penalty decision was wrong - thought that it should have been a corner and the linesman had a perfect view of it.
It was ironic that Danny should have been sent off given the amount of fing and blinding that Pat Scully was doing about 10mins before for everyone to hear! - although Danny should know better - but straight red is a bit harsh no matter what a captain says to the ref??
While we werent great i thought limerick were also very poor - hardly got out of their own half until the last 15mins. WE had about 10 half chances and just didnt take them - we were the masters of our own downfall.
Ref was very poor in the second half - 3 mins stoppage time - i would have been very upset if we were only 1 goal down at that stage!
It was an awful game and anyone who says Limerick were the better side is wrong. Both sides played very poorly but un til the sending offs Bray just about shaded it and didn't deserve to be 1-0, but What Quigley was doing is a mystery. Couldn't make out of Mitchell got the ball or man or both from were i was but i did see Danny run 30 yards to have his say at the ref, he got booked and then when back for more... one word - IDIOT ! for doing what he did. The game was then over with 9 men. I think the management also have to take a lot of blame for the team sent out and the tactics deployed. They got it completely wrong against a very average 1st division side
Doesn't say much that we lost 4-0 does it when Limerick were poor. The ref, the linesman, the ref, the linesman, the ref, the linesman!
"If" the Ref / Limeman did get the peno / sending off decision wrong then people do have a right to moan and complain because it 100% changed the game, Bray were well on top at that stage and were pushing for an equaliser. I suppose we will be able to say more about it later when we see the highlights of the game.
bluewhitearmy
Going by MNS your moaning about the pen is ridiculous..
Oh and the very average 1st division side was missing 11 players.
Stevo Da Gull
Haven't seen MNS yet, but I'll watch it when it's on the player and maybe I'll have to eat some harsh words. The camera was at the far side of the ground though. I had pretty much the same view as the linesman and saw a fantastic tackle. If the MNS footage shows this tackle to be poor, as I said, words will be eaten. If sky sports only had one camera at every ground there would never be any moaning about refs on TV. Sometimes you see a fair tackle on TV from 4 different angles, and when you see the fith angle you think 'ouch, should be a red'.
As for how many players you were missing. Makes a good win a great win for your team. It was a very poor game of football at 11-v-11. Both teams looked very ordinary.
I think that the MNS footage was far from conclusive. I have watched it several times and could not be certain one way or the other.
From my angle at the match which was much better than the camera, Mitchell played the ball out for a corner.
He came in the opposite way to where the ball went and went through the back of Quinn even if he got the ball it was a clear pen for going through the back of him.
Going by the footage which I watched a dozen or so times, looks like he takes the man first, but I wouldn't say that it's clear-cut. You can't tell from the angle if he makes contact with the man or the ball first. If I was the ref, I would have given the pen too. If I was the linesman, I would have disagreed. Penalty would have remained. Also, the lino did call the ref over to say something after the two cards were issued, so it's possible that this is what happened. In which case, I feel awful about the dogs abuse the lino received from myself and others. | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 106 |
<div class="search" ng-class="{focus: hasFocus}">
<label class="fa fa-{{ icon || 'search' }}"></label>
<input placeholder="{{ placeholder }}" type="text" ng-blur="handleFocus($event)" ng-focus="handleFocus($event)" ng-keydown="handleKey($event)" ng-model="ngModel">
</div>
| {
"redpajama_set_name": "RedPajamaGithub"
} | 9,752 |
package org.elasticsearch.action.fieldcaps;
import org.elasticsearch.action.ActionRequest;
import org.elasticsearch.action.ActionRequestValidationException;
import org.elasticsearch.action.IndicesRequest;
import org.elasticsearch.action.ValidateActions;
import org.elasticsearch.action.support.IndicesOptions;
import org.elasticsearch.common.ParseField;
import org.elasticsearch.common.Strings;
import org.elasticsearch.common.io.stream.StreamInput;
import org.elasticsearch.common.io.stream.StreamOutput;
import org.elasticsearch.common.xcontent.ObjectParser;
import java.io.IOException;
import java.util.Arrays;
import java.util.HashSet;
import java.util.Objects;
import java.util.Set;
import static org.elasticsearch.common.xcontent.ObjectParser.fromList;
public final class FieldCapabilitiesRequest extends ActionRequest implements IndicesRequest.Replaceable {
public static final ParseField FIELDS_FIELD = new ParseField("fields");
public static final String NAME = "field_caps_request";
private String[] indices = Strings.EMPTY_ARRAY;
private IndicesOptions indicesOptions = IndicesOptions.strictExpandOpen();
private String[] fields = Strings.EMPTY_ARRAY;
// pkg private API mainly for cross cluster search to signal that we do multiple reductions ie. the results should not be merged
private boolean mergeResults = true;
private static ObjectParser<FieldCapabilitiesRequest, Void> PARSER =
new ObjectParser<>(NAME, FieldCapabilitiesRequest::new);
static {
PARSER.declareStringArray(fromList(String.class, FieldCapabilitiesRequest::fields),
FIELDS_FIELD);
}
public FieldCapabilitiesRequest() {}
/**
* Returns <code>true</code> iff the results should be merged.
*
* Note that when using the high-level REST client, results are always merged (this flag is always considered 'true').
*/
boolean isMergeResults() {
return mergeResults;
}
/**
* If set to <code>true</code> the response will contain only a merged view of the per index field capabilities.
* Otherwise only unmerged per index field capabilities are returned.
*
* Note that when using the high-level REST client, results are always merged (this flag is always considered 'true').
*/
void setMergeResults(boolean mergeResults) {
this.mergeResults = mergeResults;
}
@Override
public void readFrom(StreamInput in) throws IOException {
super.readFrom(in);
fields = in.readStringArray();
indices = in.readStringArray();
indicesOptions = IndicesOptions.readIndicesOptions(in);
mergeResults = in.readBoolean();
}
@Override
public void writeTo(StreamOutput out) throws IOException {
super.writeTo(out);
out.writeStringArray(fields);
out.writeStringArray(indices);
indicesOptions.writeIndicesOptions(out);
out.writeBoolean(mergeResults);
}
/**
* The list of field names to retrieve
*/
public FieldCapabilitiesRequest fields(String... fields) {
if (fields == null || fields.length == 0) {
throw new IllegalArgumentException("specified fields can't be null or empty");
}
Set<String> fieldSet = new HashSet<>(Arrays.asList(fields));
this.fields = fieldSet.toArray(new String[0]);
return this;
}
public String[] fields() {
return fields;
}
/**
* The list of indices to lookup
*/
public FieldCapabilitiesRequest indices(String... indices) {
this.indices = Objects.requireNonNull(indices, "indices must not be null");
return this;
}
public FieldCapabilitiesRequest indicesOptions(IndicesOptions indicesOptions) {
this.indicesOptions = Objects.requireNonNull(indicesOptions, "indices options must not be null");
return this;
}
@Override
public String[] indices() {
return indices;
}
@Override
public IndicesOptions indicesOptions() {
return indicesOptions;
}
@Override
public ActionRequestValidationException validate() {
ActionRequestValidationException validationException = null;
if (fields == null || fields.length == 0) {
validationException =
ValidateActions.addValidationError("no fields specified", validationException);
}
return validationException;
}
@Override
public boolean equals(Object o) {
if (this == o) return true;
if (o == null || getClass() != o.getClass()) return false;
FieldCapabilitiesRequest that = (FieldCapabilitiesRequest) o;
return Arrays.equals(indices, that.indices) &&
Objects.equals(indicesOptions, that.indicesOptions) &&
Arrays.equals(fields, that.fields) &&
Objects.equals(mergeResults, that.mergeResults);
}
@Override
public int hashCode() {
return Objects.hash(Arrays.hashCode(indices),
indicesOptions,
Arrays.hashCode(fields),
mergeResults);
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 9,665 |
Collegio elettorale di Bollate – collegio elettorale uninominale del Regno di Sardegna
Collegio elettorale di Bollate – collegio elettorale uninominale della Repubblica Italiana per l'elezione della Camera dei deputati
Collegio elettorale di Bollate – collegio elettorale uninominale della Repubblica Italiana per l'elezione del Senato della Repubblica | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 3,045 |
Q: Trying to speed up finding solutions of quadratic form related to the weight of a matrix Say I have an integer matrix of size $5 \times 5$ - I am trying to find the solutions to the equation $n^4 wtM = n w^2 + x1^2 + x2^2 +x3^2 +x4^2 + x5^2$ subject to the constraints $x1+x2+x3+x4+x5 = 0$ and $w>0$ where, in this case $n=5$ and $wtM$ is the weight of the matrix i.e. $n^4 wtM$ is just some integer - typically with values in the range one thousand to five thousand.
Now I am using the Mathematica function PowersRepresentations to solve $n^4 wtM - n w^2$ for w ranging from 1 until $n^4 wtM - n w^2$ is still positive.
This gives me a list of lists $w,x1,x2,x3,x4,x5$ for each w. I then combine all these solutions together which I call $reps$ in the following code.
Now PowersRepresentations only gives positive values. I need to allow the $x1,x2,x3,x4,x5$ to be positive or negative subject to the constraint $x1+x2+x3+x4+x5 = 0$
So I take each list $w,x1,x2,x3,x4,x5$ and multiply it by vectors of permutations of plus and minus 1 (always having the first element in the vector 1 so as to keep w positive). I don't bother with vectors of all 1's or all -1's as this would automatically violate my summation constraint.
I then select the cases using a compiled function $cf1$ that makes sure I still obey the constraint $x1+x2+x3+x4+x5 = 0$. I also have some other constraints that I apply (via some other compiled functions) such as $x1\le x2 \le x3 \le x4$ and $x1 \ge 0 \space x2 \ge 0 \space x3 \ge 0 \space x4 \ge 0$.
Now the code I have written tries to make use of parallelisation but for anything above $7 \times 7$ takes a very long time to run.
I have perused many articles on here but I am still unsure of the various methods I have employed. The code works but I am concerned I am missing some tricks that would allow much faster execution. I have used Mathematica quite a bit in the past but primarily in using NDSolve and the like but not parallelising and compiling to C.
Any recommendations and pointing out speed increases (and memory usage reduction) would be much appreciated. As I said the code takes a long time and uses a lot of memory for $n \ge 7$. Notice I am not even saving the solutions but just counting them.
The example used below was for $n = 7$ and $wtM = 54/49$ giving $n^4 wtM = 2646$
One that runs in about 12 seconds is $n = 6$ and $wtM = 4/3$ giving $n^4 wtM = 1728$
n = 7;
wtM = 54/49;
progressreporting = True
ClearAll[results1, results2, results3, results4, data1, data2, data3,
data4];
ordering1 = "";
Do[ordering1 =
StringJoin[ordering1, "#[[" <> ToString[i] <> "]]+"], {i, 2,
n + 1}]; ordering1 =
ToExpression[StringJoin[StringDrop[ordering1, -1], "==0 &"]];
cf1 = With[{ordering = ordering1},
Compile[{{triples, _Integer, 2}},
DeleteDuplicates[Select[triples, ordering]],
RuntimeAttributes -> {Listable}, Parallelization -> True,
CompilationTarget -> "C", RuntimeOptions -> "Speed"]];
ordering2 = "";
Do[ordering2 =
StringJoin[ordering2, "#[[" <> ToString[i] <> "]]<= "], {i, 2,
n}];
ordering2 =
ToExpression[StringJoin[StringDrop[ordering2, -3], " &"]];
If[n == 2, ordering2 = ordering1];
cf2 = With[{ordering = ordering2},
Compile[{{triples, _Integer, 2}}, Select[triples, ordering],
RuntimeAttributes -> {Listable}, Parallelization -> True,
CompilationTarget -> "C", RuntimeOptions -> "Speed"]];
ordering3 = "";
Do[ordering3 =
StringJoin[ordering3, "#[[" <> ToString[i] <> "]]>=0 &&"], {i, 2,
n}]; ordering3 =
ToExpression[StringJoin[StringDrop[ordering3, -2], " &"]];
cf3 = With[{ordering = ordering3},
Compile[{{triples, _Integer, 2}}, Select[triples, ordering],
RuntimeAttributes -> {Listable}, Parallelization -> True,
CompilationTarget -> "C", RuntimeOptions -> "Speed"]];
DistributeDefinitions[cf1, cf2, cf3];
AbsoluteTiming[
reps = Join @@
Table[
Map[Prepend[#, i] &,
PowersRepresentations[n^4 wtM - n i^2, n, 2]], {i, 1,
IntegerPart[Sqrt[(n^4 wtM)/n]]}];
vc = Map[Insert[#, 1, 1] &, Take[Tuples[{-1, 1}, n], {2, 2^n - 1}]];
ParallelEvaluate[foo1 = {}]; ParallelEvaluate[foo2 = {}];
ParallelEvaluate[foo3 = {}]; ParallelEvaluate[foo4 = {}];
sow[x_] := (foo1 = {foo1, x};); sow2[x_] := (foo2 = {foo2, x};);
sow3[x_] := (foo3 = {foo3, x};); sow4[x_] := (foo4 = {foo4, x};);
ParallelDo[
temp = Extract[reps[[j]], 1]; temp2 = Drop[reps[[j]], 1];
test0 = Permutations[temp2];
test1 = Map[Prepend[#, temp] &, test0];
lst = {};
lst = Table[
Map[Times[#, test1[[i]]] &, vc], {i, 1, Length[test1]}];
test2 = Join @@ lst;
test3 = cf1[test2];
test32 = cf2[test3];
test33 = cf3[test3];
test34 = cf3[test32];
sow[Length@test3]; sow2[Length@test32]; sow3[Length@test33];
sow4[Length@test34];
, {j, 1, Length[reps]},
ProgressReporting -> progressreporting,
Method -> "ItemsPerEvaluation" -> 1000];
results1 = Join @@ ParallelEvaluate[Flatten@foo1];
results2 = Join @@ ParallelEvaluate[Flatten@foo2];
results3 = Join @@ ParallelEvaluate[Flatten@foo3];
results4 = Join @@ ParallelEvaluate[Flatten@foo4];
Print["\!\(\*SuperscriptBox[\(n\), \(4\)]\)wtM = ", n^4 wtM];
data1 = Total[results1];
Print[data1, " solutions in Z with no ordering"];
If[n > 2, data2 = Total[results2];
Print[data2, " solutions in Z with ordering"]];
data3 = Total[results3];
Print[data3,
" solutions in \!\(\*SubscriptBox[\(N\), \(0\)]\) with no \
ordering"];
If[n > 2, data4 = Total[results4];
Print[data4,
" solutions in \!\(\*SubscriptBox[\(N\), \(0\)]\) with \
ordering"]];] // First
n^4wtM = 2646
342611822 solutions in Z with no ordering
584282 solutions in Z with ordering
169915 solutions in Subscript[N, 0] with no ordering
556 solutions in Subscript[N, 0] with ordering
1688.18
A:
It's not an answer but a long comment.
Without understanding your code, these are some improvements just by using built-in functions:
*
*ordering1
You'd used string concatenation to build your expression, which could be improved in both readability and performance?
(* use *)
Plus @@ Take[#, {2, n+1}] == 0 &
(* or *)
Total[Take[#, {2, n+1}]] == 0 &
(* instead of *)
ordering1 = "";
Do[ordering1 =
StringJoin[ordering1, "#[[" <> ToString[i] <> "]]+"], {i, 2,
n + 1}]; ordering1 =
ToExpression[StringJoin[StringDrop[ordering1, -1], "==0 &"]];
(* example: #[[2]]+#[[3]]+#[[4]]+#[[5]]+#[[6]]==0 & *)
*
*ordering2
like ordering1, just use the power of built-ins
OrderedQ[Take[#, {2, n}]]&
(* instead of *)
ordering2 = "";
Do[ordering2 =
StringJoin[ordering2, "#[[" <> ToString[i] <> "]]<= "], {i, 2,
n}];
ordering2 =
ToExpression[StringJoin[StringDrop[ordering2, -3], " &"]];
(* example: #[[2]]<= #[[3]]<= #[[4]]<= #[[5]]<= #[[6]] & *)
*
*ordering3
AllTrue needs version 10
AllTrue[NonNegative[Take[#, {2, n}]], TrueQ] &;
(* instead of *)
ordering3 = "";
Do[ordering3 =
StringJoin[ordering3, "#[[" <> ToString[i] <> "]]>=0 &&"], {i, 2,
n}]; ordering3 =
ToExpression[StringJoin[StringDrop[ordering3, -2], " &"]];
(* example: #1[[2]] >= 0 && #1[[3]] >= 0 && #1[[4]] >= 0 && #1[[5]] >= 0 && #1[[6]] >= 0 & *)
*
*lst
Outer[Times, test1, vc]
(* instead of *)
Table[Map[Times[#, test1[[i]]] &, vc], {i, 1, Length[test1]}]
*
*Also, you can use PadLeft instead of Map[Prepend.../Map[Insert[...,1,1] ...
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 1,578 |
Ellison's Battle Royal Essay
Reader ResponseEllison's "Battle Royal"In Battle Royal, Ellison shows us various things to bring our attention to the painthe minority group suffered. In doing this Ellison shows us relationships between thetorment they felt to our feelings for them. When the boys enter the boxing ring, they areshown off like animals. The woman dancing represents the sick pleasure derived from theboys' torture. Ellison shows us a picture of the human mind, in seeing something to lustafter then watching young men being beaten nearly to death as a form of entertainment.He does this to show us a view of human nature.In oppression to the torment the boys developed a sort of counter attack. Theboys were so eager for the the fake money that they suffered electric shocks to grab it. Ithink this sort of surprised the audience, beings that the boys never gave up the fight. Itwas as thought giving up would have meant giving up much more than money or a boxingmatch. It would have been a loss of dignity and pride, none of them wanted to lose that.Also, by the time the boys were given the chance to chase the money, they were numbfrom pain. I don't think the new torture methods were really affecting the boys. Theirbodies became somewhat immune to the blows after awhile.My battle royal was a little bit different from the boys in the story. I did not reallysuffer from outside torment. The battle I faced was mostly inside myself. People didn'thave to say anything and I would be judging myself and putting myself down. Like theboys in the boxing ring fighting one another, I would have to fight with my own feelings toovercome things. Each time I made a decision I had to be critical about what was goodand bad for myself. Even if I didn't do anything wrong I blamed myself for things thatwould go wrong.My battle with low self esteem was an ongoing problem. It pretty much got to thepoint where I didn't even realize I was doing it to myself anymore. The words I said,although not all true, I believed completely. I had put myself down so much, thatcomplements were never taken seriously. I tried to break my habit of putting myself downby setting goals for myself. This helped a little but I honestly don't think I wanted helpback then.Finally it got to the point where I knew I had to do something. This was the timewhen I felt most powerless. I didn't think I had any control over how I felt. Half the timeI couldn't decipher whether I was happy or sad. I began to scare myself because of it. Iwould think, does this make me happy. I couldn't even think of an answer, it was thestrangest feeling I have ever had. Not knowing if you are happy or sad, seems odd Iknow.One day I came to the...
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"redpajama_set_name": "RedPajamaCommonCrawl"
} | 5,332 |
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"redpajama_set_name": "RedPajamaCommonCrawl"
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\section{Introduction}
Optimal transport seeks the mass preserving map $T$ between two probability distributions that minimizes the expected value of a given cost function, the \emph{transportation cost} between a point and its image under $T$ \cite{Vil}. The minimal cost defines a metric in the space of probability distributions, the \emph{Wasserstein distance}. Beyond providing a metric, the optimal map $T$ itself has broad applicability, which this article extends through the development of conditional optimal transport.
Consider as a specific example the evaluation of the effects of a long-term medical treatment (alternatively of a habit, such as smoking or dieting). Optimal transport can be used to quantify the changes in probability distribution of quantities that characterize the health state of a person (blood pressure, blood sugar level, heart beat rate) in the two scenarios: with and without treatment. Data typically consist of independent measurements of these quantities in treated and untreated populations. Yet the distribution of these quantities depends on many covariates beyond the presence or absence of treatment, such as age, weight, sex, habits. Hence one seeks the effect of the treatment as a function of these covariates.
Motivated by this and similar applications, this article develops a data driven procedure to compute the optimal map $T(x, z)$ between two conditional probability densities $\rho(x|z_{1},...,z_{L})$ and $\mu(y|z_{1},...,z_{L})$, with covariates $z_{i}$. In the example above, $y = T(x, z)$ estimates the value $y$ that the quantity of interest would have under treatment if, without treatment, its value were $x$, under specific values of the covariates $z_l$. The procedure is data driven, as it uses only samples $\left\{x^i, z_1^i, \ldots, z_L^i \right\}$ and $\left\{y^i, z_1^i, \ldots, z_L^i \right\}$ from $\rho$ and $\mu$. Notice that we do not seek a pairwise matching between $\left\{x^i, z_1^i, \ldots, z_L^i \right\}$ and $\left\{y^i, z_1^i, \ldots, z_L^i \right\}$: typically these two data sets do not even have the same cardinality. Instead, we work under the hypothesis that these samples are drawn from smooth conditional densities $\rho(x|z)=\rho(x,z)/\gamma^x(z)$, $\mu(y|z)=\mu(y,z)/\gamma^y(z)$ and covariate distributions $\gamma^x(z)$ and $\gamma^y(z)$, and hence we seek a map $y = T(x, z)$ that is a smooth function of its arguments.
The need for conditional optimal transport is particularly apparent when the distributions for the covariates $z$ for the source and target distributions are unbalanced, i.e. when $\gamma^x$ and $\gamma^y$ are different. Consider as a particularly telling example a situation when the treatment has no effect, i.e. $\rho(x|z) = \mu(x|z)$, so we should have $y = x$, yet $\gamma^x \ne \gamma^y$:
$$ \rho(x|z) = \mu(y|z) = N(z, 1), \quad \gamma^x(z) = N(-1, 1), \quad \gamma^y(z) = N(1, 1),$$
where $N(a,b)$ denotes the $1$d normal distribution with mean $a$ and variance $b$.
Then
$$ \rho(x) = \int \rho(x|z) \gamma^x(z) \ dz = N(-1, 2), \quad \mu(y) = \int \mu(y|z) \gamma^y(z) \ dz = N(1, 2).$$
It follows that, if one would not look at the covariate $z$, one would infer incorrectly that $y = x+2$, i.e. that the treatment does have a significant effect. We will see in section \ref{sec:treatment} an instance of this phenomenon appearing in the more complex setting of a biomedical application, where conditional transport provides critical aid.
Conditional transport provides a very flexible toolbox for data analysis, as the choice of which variables are conditioned to which others is left at the discretion of the analyst. In anticipation of the application of this principle to color transfer problems in section \ref{sec:lightness}, we illustrate it here with a simple example. Consider a covariate $z \sim N(0, 1)$ and two dependent variables $x \sim N(z, 1)$ and $y \sim N(-z, 1)$ (see Figure \ref{fig:syntexample} for a sketch relative to this problem). Since the marginals $\rho(x)$ and $\mu(y)$ are identical, performing optimal transport between them yields the identity map $y = x$, while conditioning to $z$ yields $y = x - 2 z$, effectively rotating the joint distribution $\rho(x, z)$ clockwise, and performing two dimensional transport between $\rho(x, z)$ and $\mu(y, z)$ yields an irrotational map \cite{Vil}. Finally, if in a thought experiment we would identify $x$ and $y$ and switch the roles of dependent and independent variables, conditioning the transport in $z$-space to $x$, we would obtain $z_2 = z_1 - 2x$, effectively rotating the joint distribution $\rho(x, z)$ counter-clockwise.
\begin{figure}[!htb]
\begin{center}
\begin{tabular}{ccc}
\resizebox{45mm}{!}{\includegraphics{Figures/SyntExmpl/zx.pdf}} &
\resizebox{45mm}{!}{\includegraphics{Figures/SyntExmpl/zy.pdf}}\\
\resizebox{45mm}{!}{\includegraphics{Figures/SyntExmpl/x-y.pdf}}&
\resizebox{45mm}{!}{\includegraphics{Figures/SyntExmpl/z-z.pdf}}
\end{tabular}
\caption{Upper row: source (left) and target (right) distributions. Lower left: optimal transport of $x$ conditioned on $z$, the arrows indicate that the lower left branch and the upper right branch of the source distribution are mapped respectively to the upper left branch and the lower right branch of the target distribution. Lower right: optimal transport of $z$ conditioned on $x$, in this case is the upper right branch of the source distribution to be mapped to the upper left branch of the target distribution.}
\label{fig:syntexample}
\end{center}
\end{figure}
\section{Conditional optimal transport}
\label{sec:COT}
Conditional optimal transport between two conditional distributions $\rho(x|z)$ and $\mu(y|z)$ can be defined simply as the map $T(x, z)$ that performs optimal transport between them for each value of $z$:
\begin{equation}
\label{eq:OT0}
\forall z \ \begin{dcases}
\min_{T(:, z)}\int c(T(x, z),x)\rho(x|z) dx\\
T\#\rho(:|z)=\mu(:|z),
\end{dcases}
\end{equation}
where $c(x,y)$ represents the cost of moving a unit of mass from $x$ to $y$ and the symbol $\#$ indicates the push forward of probability measures, i.e. if $x$ has distribution $\rho(x|z)$ then $y = T(x, z)$ has distribution $\mu(y|z) = T\#\rho(:|z)$. Since $T(:, z)$ decouples under different values of $z$, we can multiply the cost by the distribution $\gamma^x(z)$ of the covariates $z$ in the source and integrate over $z$, yielding
\begin{equation}
\label{eq:OT1}
\begin{dcases}
\min_{T(:, z)}\int c(T(x, z),x)\ \rho(x, z)\ dx dz\\
\forall z\ T\#\rho(:|z)=\mu(:|z),
\end{dcases}
\end{equation}
where $\rho(x|z)$ denotes the conditional and $\rho(x, z) = \rho(x|z) \gamma^x(z)$ the joint distribution of $x$ and $z$.
We need to reformulate this problem in a way that is implementable in terms of samples $\left\{x^i, z^i\right\}$ and $\left\{y^j, z^j\right\}$. As is stands in (\ref{eq:OT1}), two immediate problems emerge: there are not enough samples for each value of $z$, typically none or one for continuous covariates, to characterize the corresponding conditional distributions, and it is not clear how to enforce or verify the push forward condition. The first problem is at the very heart of the need for conditional optimal transport: even though the objective functions for each value of $z$ decouple, one thinks of a commonality across $z$ that makes samples from each conditional distribution be informative on the others. In the case of continuous covariates $z$, this can be posed as a smoothness condition (in $z$) on $\rho(x|z)$.
In order to address the second problem, we interpret the push forward condition in terms of relative entropy:
$$ T\#\rho(:|z)=\mu(:|z) \iff D_{KL}(T\#\rho(:|z), \mu(:|z)) = 0, $$
where
$$
D_{KL}(\rho_1(x|z) || \rho_2(x|z) ) = \int \gamma_1(z) \int \log \left( \frac{\rho_1(x|z)}{\rho_2(x|z)} \right)\rho_1(x|z) \ dx dz
$$
is the conditional Kullback-Leibler divergence between $\rho_1$ and $\rho_2$ (\cite{cover2012elements}). Since this is non-negative, we can rewrite the problem in (\ref{eq:OT1}) as
$$
\min_{T(: ,z)} \max_{\lambda \ge 0} \left[ \int c(T(x, z),x)\rho(x, z) \ dx dz + \lambda D_{KL}(T\#\rho(:|z), \mu(:|z)) \right] .
$$
Instead of maximizing over $\lambda$, it will be convenient to fix a value of $\lambda$ large enough that the push forward condition can be considered satisfied for all practical purposes (it is straightforward to prove that, as $\lambda \rightarrow \infty$ the solution with fixed $\lambda$ converges to the true minimax solution. In our implementation below, $\lambda$ grows at each step of the algorithm.) Then the problem above becomes
$$
\min_{T} \left[ \int c(T(x, z),x)\rho(x, z) \ dx dz + \lambda\ D_{KL}(T\#\rho(:|z), \mu(:|z)) \right], \quad \lambda \gg 1.
$$
For any $\rho_1(x, z) = \gamma_1(z) \rho_1(x|z)$ and $\rho_2(x, z) = \gamma_2(z) \rho_2(x|z)$, we have the ``chain rule'' for the relative entropy (\cite{cover2012elements}),
$$
D_{KL}(\rho_1(x|z) || \rho_2(x|z) ) = D_{KL}(\rho_1(x,z) || \rho_2(x,z) ) - D_{KL}(\gamma_1(z) || \gamma_2(z) ).
$$
Since the map $T$ acts only on $x$, it has no effect the last term, so we can write
$$
\min_{T} \left[ \int c(T(x, z),x)\rho(x, z) \ dx dz + \lambda D_{KL}(T\#\rho(x, z), \mu(x, z)) \right], \quad \lambda \gg 1.
$$
This formulation improves over the one in (\ref{eq:OT0}) by consolidating an infinite set of problems, one for every value of $z$, into a single one. Yet it is not clear yet how to enforce the push forward condition in terms of samples, as the definition of the relative entropy involves logarithms of $\rho$ and $\mu$. To address this, we invoke a variational formulation of the relative entropy between two distributions \cite{donsker1975asymptotic}:
\begin{equation}
D_{KL}(\rho, \mu) =
\max_g \left[ \int g(x) \rho(x) dx - \log\left(\int e^{g(x)} \mu(x)\ dx\right) \right],
\end{equation}
which involves $\rho$ and $\mu$ only in the calculation of the expected values of $g$ and $e^g$, with a natural sample-based interpretation as empirical means. Then our problem becomes
\begin{equation}
\label{theor_COT}
\min_{T} \max_g \int c(T(x, z),x) d\rho(x, z)
+ \lambda \left[\int g(T(x, z), z) d\rho(x, z) - \log\left(\int e^{g(y, z)} d\mu(y, z)\right) \right]
\end{equation}
or, in terms of samples,
\begin{equation}
\min_{T} \max_g \Bigg[\frac{1}{n} \sum_i \Big(c(T(x_i, z_i), x_i)\rho(x_i, z_i)
+ \lambda g(T(x_i, z_i), z_i)\Big)
- \lambda \log\left(\frac{1}{m} \sum_j e^{g(y_j, z_j)} \right) \Bigg].
\label{sample_COT}
\end{equation}
This adversarial formulation has two players with strategies $T$ and $g$, one minimizing the cost and the other enforcing the push forward condition, providing an adaptive ``lens'' that identifies those places where the push-forward condition does not hold: for any $T$, the optimal $g$ in (\ref{theor_COT}) is given by
$$ g = \log\left(\frac{\rho(T(x,z)|z)}{\mu(y|z)}\right) + \log\left(\frac{\gamma^x(z)}{\gamma^y(z)}\right) ,$$
where the first term is furthest from zero in those places where $\rho(T(x,z)|z)$ and $\mu(y|z)$ differ the most.
\section{Parametrization of the flows}
\label{sec:Flow}
In order to complete the problem formulation in (\ref{sample_COT}), we need to specify the family of functions over which the map $T(x, z)$ and the test-function $g(y, z)$ are optimized. These families should satisfy some general properties:
\begin{enumerate}
\item be rich enough that $g$ can capture all significant differences between $\rho(x|z)$ and $\mu(y|z)$ and $T$ can resolve them,
\item not be so rich as to overfit the sample points $\left\{x^i, z^i\right\}$, $\left\{y^j, z^j\right\}$. For instance, a $g$ with arbitrarily small bandwidth would force the sets $\left\{T(x^i, z^i), z^i\right\}$, $\left\{y^j, z^j\right\}$ to agree point-wise, an extreme case of overfitting that is not only undesirable but also unattainable when their cardinality differs. Moreover, the dependence of the functions on $z$ should be such that, with a finite number of samples, it should still capture the assumed smoothness of $\rho(x|z)$: functions that are too localized in $z$ space effectively decouple the transport problems for every value of $z$, for which there are not enough available sample points,
\item be well-balanced: if one of the two players has a much richer toolbox than the other, the game would be unfair, leading not only to a waste of computational resources but also possibly to instability and inaccuracy, and
\item be apt to robust and effective optimization.
\end{enumerate}
These conditions leave space for many proposals, such as defining $T$ and $g$ through neural networks. Instead, the examples in this article are solved with the two approaches detailed below. Both share the feature that $T$ is built on map composition: at each step $n$ of the mini-maximization algorithm, an elementary map $E^n$ is applied not to the original sample points $\left\{x^i\right\}$, but to their current images:
$$ T^n(x^i, z^i) = E^n\left(T^{n-1}(x^i, z^i), z^i\right). $$
This way, simple elementary maps $E$ depending on only a handful of parameters can give rise through map composition to rich global maps $T$. The two proposals differ in that one builds nonlinear richness through evolving Gaussian mixtures, while the other builds complex $z$-dependence through an extra compositional step. In this article, the first method is applied to a lightness transfer problem, and the second to the effect of a medical treatment, as the latter is linear in $x$ but has complex, nonlinear dependence on many covariates $z$.
\subsection{Evolving Gaussian mixtures}
We adopt as elementary map the gradient of a convex potential function: $E(x, z) = \nabla_x \Phi(x,z)$, with $\Phi$ built from a quadratic form in $x$ with coefficients that depend on $z$, plus a combination of Gaussians in $(x, z)$ space, and similarly for the test function $g$. By having the centers and amplitudes of these Gaussians evolve, we can approximate quite general functions $\Phi$ and $g$.
Notice that the gradient of a radial basis function kernel with bandwidth $d$,
$$
G_d(x,x') = \exp \left( - \frac{||x - x'||^2}{2d^2}\right),
$$
is bounded by $ \pm \frac{1}{d\exp(1/2)}$, and its second order derivatives by $ \frac{2}{d^2 \exp(3/2)}<\frac{1}{2d^2}$. It follows that $ \frac{1}{2d^2}\frac{||\mathbf x||_2^2}{2} \pm G_d (\textbf z,\textbf m_{z_i})G_d(\textbf x,\textbf m_i)$ is convex, so we propose
\begin{multline}
\Phi(\mathbf x,\mathbf z) = (\mathbf c^T_0 + \mathbf z^T \mathbf c_1 ) x +
\frac 12 \mathbf x^T \mathbf C_2(\mathbf z)\mathbf x
+ \sum_{i=1}^K a_i^2 \left(\frac{||\mathbf x||_2^2}{4d^2} - G_{d} (\mathbf z,\mathbf m_{z_i}) G_d (\mathbf x,\mathbf m_i) \right) + \\
\sum_i b^2_i \left( \frac{||\mathbf x||_2^2}{4d^2} + G_{d} (\mathbf z, \mathbf m_{z_i}) G_{d} (\mathbf x, \mathbf m_i) \right), \
\mathbf C_2(\mathbf z) = \mathbf C_{2,0} ^T\mathbf C_{2,0} + \mathbf z^T \mathbf C_{2,1}^T \mathbf C_{2,1} \mathbf z,
\nonumber
\end{multline}
with $\mathbf C_{2,0}, \mathbf C_{2,1}$ lower triangular.
In order to start the map at every step at the identity, the initialization must satisfy
$$
\mathbf C_{2,0}(i,i)^2 + \sum_i^K \frac{1}{4d^2}( a_i^2 + b_i^2) = 1, \quad a^2_{i} =b_i^2,
$$
so we propose
$$
a^2_{i} =b_i^2 = \frac{4d^2 \delta}{ 2 K },\quad \mathbf C_{2,0}(i,i) = \sqrt{1-\delta}, \quad \delta = \frac{1}{2},
$$
with all other parameters starting from zero.
The bandwidth $d$ is chosen via $d = quantile(pdist([y; z]),1/K)$,
where $pdist$ is the pairwise distance function. With this choice there are approximately $1/K$ points in the effective support of each Gaussian.
For the test function, we propose
$$
g(\mathbf x,\mathbf z) = \sum_{i=1}^K \alpha_i G_{d} (\mathbf z ,\mathbf m_{z_i}) G_d( \mathbf x, \mathbf m_i) + ( \mathbf \beta_0 ^ T + \mathbf z ^T \mathbf \beta_1 ) \mathbf x + \mathbf x^T ( \mathbf \beta_2+ \sum_i \mathbf \beta_{3,i} z_i ) \mathbf x,
$$
with each iteration starting at the parameter values from the previous step.
The Gaussian centers are treated differently in the test function $g$, where they are extra parameters to ascend, and in the potential $\Phi$, where they are fixed at their values from $g$ in the prior step. The underlying notion is that $g$ locates those areas where the distributions do not agree, and then $T$ corrects them.
\subsection{Extended map composition}
This second methodology considers maps given by rigid translations and test functions that capture the conditional mean $\bar{x}(z)$:
$$ T(x, z) = x + U(z), \quad g(y, z) = V(z) y + W(z), \quad x \in \ensuremath{\mathbb{R}},$$
with general, nonlinear dependence on $z$. To build these, we define a composition function
$$
F(\mathbf a, z, v, u) = (a^1_0 + \sum_{i=1}^L a^1_i z_i + a^1_{L+1}u ) + (a^2_0 + \sum_{i=1}^L a^2_i z_i + a^2_{L+1}u ) v,
$$
in terms of which the test function at each step is given by
$$
g^{n+1}(y, z) = v^{n+1} y + w^{n+1} ,\quad v^{n+1} = F(\mathbf \beta, z, v^n, u^n), \quad w^{n+1} = F(\mathbf \eta, z, w^n, 0),
$$
and the map by
$$
T ^{n+1} (T^n, z) = T^n + u^{n+1}, \quad u^{n+1} =F(\mathbf \alpha, z, u^n, v^n).
$$
These maps are initialized at $u^0=v^0=w^0=0$. Before each each step, $\alpha$ is set to $0$ (as $T$ is reinitialized every step to the identity), and so are $\beta$ and $\eta$, except for $\beta_0^2=\eta_0^2 = 1$, which makes $g$ evolve from its value at the previous step.
\section{Examples}\label{sec:examples}
We illustrate the procedure with two applications: determination of the effect of a medical treatment and lightness transfer. In order to solve the problem (\ref{sample_COT}) we use the general procedure for mini-maximization described in \cite{Minimax}.
\subsection{Effect of a Treatment}\label{sec:treatment}
We apply conditional optimal transport to determine the response to a treatment of a variable $x \in \ensuremath{\mathbb{R}}$ in terms of covariates $z$. We use data from the ACIC data analysis challenge 2017 \cite{hahn2019atlantic} (\url{https://arxiv.org/pdf/1905.09515.pdf}), considering the first of their 32 generating models, with 8 covariates: 6 binary and 2 continuous. We divide the data set into two groups: the untreated ($x$) and treated ($y$) patients, with samples drawn from distributions $\rho(x, z) = \gamma^{x}(z) \rho(x|z)$ and $\mu(y, z) = \gamma^y(z) \mu(y|z)$, having the property that
$$ \mu(y|z) = \rho(y-\tau(z)|z), \quad \gamma^x(z) \ne \gamma^y(z). $$
It will be important for the analysis below that $\tau$ (the ``effect'' of the treatment) depends only on the binary covariates, but the marginals $\gamma(z)$ depend also on the continuous ones. We compute the optimal map $T(x, z)$ using only the first of the 250 batches of data provided, each referring to the same 4302 patients, i.e. the same values of $z_i$ under different realizations of the noise. The middle panel of Figure \ref{fig:Treat1} displays the untreated values $x_i$ as a function of the expected value that they would have under treatment given the values ${z^s}_i$ of their covariates:
$$ E(x|z^s, 1) = \int \left(x + \tau(z^s)\right) \rho(x|z^s) \ dx, $$
while the right panel displays similarly the treated values $y_i$. The left panel of Figure \ref{fig:Treat2} displays the map $T(x_i, z_i)$ obtained using only the discrete covariates, which are the ones that the true $T$ depends on. However, because of the unbalance between $\gamma^x$ and $\gamma^y$ (see the left panel of Figure \ref{fig:Treat1} for $\gamma(z_7)$), the results are biased, much as in the synthetic example in the introduction. The middle panel shows that, when all covariates are considered, this biased is resolved. For a specific patient, the right panel compares the application of the map $T(x, z)$ to all untreated instances in the full 250 batches to the histogram of the response $y$ for all treated instances of the patient.
\begin{figure}[!htb]
\begin{center}
\begin{tabular}{ccc}
\includegraphics[width=43mm,height=45mm]{Figures/Treatment/covariate7_histogram.pdf} &
\resizebox{40mm}{!}{\includegraphics{Figures/Treatment/E_source.pdf}} &
\resizebox{40mm}{!}{\includegraphics{Figures/Treatment/E_target.pdf}}\\
\end{tabular}
\caption{Left panel: Unbalance in the distribution of $z_{7}$ between the source and the target data set. Center: Response variable $x$ for patients before the treatment VS theoretical expected value of the same patients undergone the treatment. Right: Response variable $y$ of treated patients VS theoretical expected value of the same patients.}
\label{fig:Treat1}
\end{center}
\end{figure}
\begin{figure}[!htb]
\begin{center}
\begin{tabular}{ccc}
\resizebox{40mm}{!}{\includegraphics{Figures/Treatment/E_reduced_map.pdf}}&
\resizebox{40mm}{!}{\includegraphics{Figures/Treatment/E_full_map.pdf}}&
\includegraphics[width=43mm,height=45mm]{Figures/Treatment/samples_full/sample_1.pdf}
\end{tabular}
\caption{Left: numerical value of map $T(x_i, z_i)$ obtained using only the discrete covariates, which are the ones that the true $T$ depends on. The result is biased due to the unbalance between $\gamma^x$ and $\gamma^y$ for $\gamma(z_7)$). Middle: numerical value of map $T(x_i, z_i)$ obtained using all the covariates. Right: comparison between the application of the map $T(x, z)$ to all untreated instances in the full 250 batches to the histogram of the response $y$ for all treated instances of the patient.}
\label{fig:Treat2}
\end{center}
\end{figure}
\subsection{Lightness transfer}\label{sec:lightness}
Next we apply conditional optimal transport to lightness transfer. Consider the first column of Figure \ref{fig:StrTarg}, corresponding to two flowers photographed under different light conditions. We seek to transform the first photograph so as to present it under the light conditions of the second. This goes beyond merely changing lightness uniformly, since for instance at sunset certain colors are perceived as having become darker than others.
An image can be represented in the three dimensional CIELAB (L*a*b) space whose coordinates are the lightness $L$, the red/green contrast $A$ and blue/yellow contrast $B$. The right column of Figure \ref{fig:StrTarg} shows the images of the flowers in this L*a*b space, where each point corresponds to a superpixel, defined through a clustering procedure to introduce information about the geometry of the image \cite{rabin2014adaptive}. We follow \cite{tai2005local} to define a similarity metric by means of Gaussian kernel, map the obtained superpixels with our procedure, and use a TMR filter after the map to recover sharp details \cite{rabin2011removing}.
Figure \ref{fig:red_flowers} shows the result obtained changing lightness in three different ways. First (left column) we use one-dimensional optimal transport (with quadratic cost) to map the $L$ coordinate, ignoring the values of $A$ and $B$. The L*a*b diagram shows that this results in a nearly uniform shift of $L$ towards smaller values. The third column shows the effect of mapping the starting image to the target image through 3d optimal transport in the full L*a*b space. In this case the point clouds overlap to a much better degree, yet we observe that the color of the lotus has been changed too much towards the color on the poinsettia of the target image. The second column is obtained performing optimal transport of $L$ conditioned on $A$ and $B$. Contrasting to the other two results, here the lotus has kept its original color, and the lightness has changed to a different degree for the lotus than for the background leaves.
This is a general advantage of conditional optimal transport: unlike its unconditional cousin, it does not need to preserve total mass (in this case, transferring fully one color palette to the other), but only the mass for each value of $z$. This point to an additional application of conditional optimal transport: its capacity to address possible unbalances between source and target by parameterizing the transfer map by means of convenient labels $z$. In work in progress, we expand on this notion, finding those latent covariates $z$ that help resolve unbalances optimally.
\begin{figure}[!htb]
\begin{tabular}{cc}
\begin{minipage}{0.5\textwidth}
\includegraphics[width = 0.7\textwidth]{Figures/weight_small/image_initial_full.pdf} \\
\includegraphics[width = 0.7\textwidth]{Figures/weight_small/image_target_full.pdf}
\end{minipage}
\begin{minipage}{0.5\textwidth}
\includegraphics[width = 0.5\textwidth]{Figures/weight_small/data2_initial.pdf}
\end{minipage}&
\end{tabular}
\caption{\label{fig:StrTarg} Left column: initial (top) and target (bottom) image. Right column: L*a*b coordinates for the initial (in red) and the target (in black) image}
\end{figure}
\begin{figure}
\subfloat[1D OT]{\includegraphics[width = 0.35\textwidth]{Figures/weight_small/image_1DOT_full.pdf}}
\subfloat[COT]{\includegraphics[width = 0.35\textwidth]{Figures/weight_small/image_COT_full.pdf}}
\subfloat[3DOT ]{\includegraphics[width = 0.35\textwidth]{Figures/weight_small/image_3DOT_full.pdf}}
\subfloat[1D OT result in LAB]{\includegraphics[width = 0.35\textwidth]{Figures/weight_small/data2_1DOT.pdf}}
\subfloat[COT result in LAB]{\includegraphics[width = 0.35\textwidth]{Figures/weight_small/data2_COT.pdf}}
\subfloat[3DOT result in LAB]{\includegraphics[width = 0.35\textwidth]{Figures/weight_small/data2_3DOT.pdf}}\\
\caption{Left Column: image obtained performing one dimensional optimal transport for the Luminosity (L) coordinate ignoring the A and B coordinates. Second column: image obtained by performing optimal transport on luminosity conditioned on color. Third column: plain three dimensional optimal transport in L*a*b space.}
\label{fig:red_flowers}
\end{figure}
\newpage
\bibliographystyle{plain}
| {
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{"url":"https:\/\/math.stackexchange.com\/questions\/2023654\/use-mean-value-theorem-to-show-fy-fx-nabla-fxty-x-int-limits-0\/2030796","text":"# Use Mean Value Theorem to show $f(y) = f(x) + \\nabla f(x)^T(y-x) + \\int\\limits_0^1 t(y-x)^T\\nabla^2 f(x+\\xi (y-x))^T(y-x) dt$\n\nClaim: Given a $C^2$, convex function $f$ and vectors $x,y \\in \\mathbb{R}^n, t \\in [0,1]$ Suppose that\n\n$$f(y) = f(x) + \\nabla f(x)^T(y-x) + \\int\\limits_0^1 (\\nabla f(x+t(y-x))^T-\\nabla f(x))^T(y-x) dt$$\n\nThen\n\n$$f(y) = f(x) + \\nabla f(x)^T(y-x) + \\int\\limits_0^1 t(y-x)^T\\nabla^2 f(x+\\xi (y-x))^T(y-x) dt$$\n\nwhere $0\\leq \\xi \\leq t$\n\nI think the proof relies on the mean value theorem\n\nSpecifically, $$\\nabla f(x+t(y-x))-\\nabla f(x) = \\nabla^2 f(x+\\xi (y-x))^T(x+t(y-x)-x) = \\nabla^2 f(x+\\xi (y-x))^Tt(y-x)$$\n\nWhile this has structural similarity compared to the first order mean value theorem, I am not sure how this can be proved and searching the literature up and down I just could not find a so called higher dimensional mean value theorem. Typing in mean value theorem + hessian returns no good results.\n\nCan someone please provide a reference to a higher order, generalized, mean value theorem which involves the gradient and the Hessian and was used in this proof?\n\n\u2022 You can derivate this from taylor expansion, I guess. Or using the standard multivariante MVT just for the expression in the integral. \u2013\u00a0user160069 Nov 21 '16 at 2:47\n\u2022 Does $\\xi$ depend on $t$ (which would imply that $\\xi$ should be replaced with $\\xi(t)$ under the integral)? \u2013\u00a0gerw Nov 21 '16 at 12:44\n\nLet us define the function $h:[0, 1] \\rightarrow \\mathbb{R}$ given by \\begin{align} h(t)= \\nabla f(x+t(y-x))^T(y-x). \\end{align} Assuming $f \\in C^2$ implies $h$ is continuously differentiable. For any fixed $t \\in (0, 1]$, we apply the mean value theorem to see there exists $t^\\ast \\in (0, t)$ such that \\begin{align} th'(t^\\ast) =&\\ h(t) - h(0)\\\\ =&\\ \\nabla f(x+t(y-x))^T(y-x)- \\nabla f(x)^T(y-x)\\\\ =&\\ [\\nabla f(x+t(y-x))-\\nabla f(x)]^T(y-x). \\end{align}\nNext, let us compute $h'(t)$. Observe \\begin{align} h'(t) =&\\ \\frac{d}{dt}\\left[\\nabla f(x+t(y-x))^T(y-x) \\right]\\\\ =&\\ \\frac{d}{dt}\\left[\\sum^n_{i=1} \\frac{\\partial f(x+t(y-x))}{\\partial x_i} (y_i-x_i) \\right]\\\\ =&\\ \\sum^n_{i=1} \\frac{d}{dt}\\frac{\\partial f(x+t(y-x))}{\\partial x_i} (y_i-x_i) \\\\ =&\\ \\sum^n_{i=1}\\sum^n_{j=1} \\frac{\\partial^2f(x+t(y-x))}{\\partial x_i \\partial x_j} (y_j-x_j)(y_i-x_i)\\\\ =&\\ (y-x)^T\\nabla^2f(x+t(x-y))(y-x). \\end{align} Now, combine everything will yield the desired result.\nRemark: The Hessian matrix is symmetric which means $H^T = H$. Also, this result doesn't require $f$ to be convex.\n\u2022 Why is it true that there exists a $t^*\\in (0,t)$ instead of $t^* \\in (0,1)$? \u2013\u00a0Carlos - the Mongoose - Danger Nov 26 '16 at 2:45","date":"2019-07-19 07:58:19","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\": 3, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.9941828846931458, \"perplexity\": 719.1642885099208}, \"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-2019-30\/segments\/1563195526153.35\/warc\/CC-MAIN-20190719074137-20190719100137-00553.warc.gz\"}"} | null | null |
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how to become a book curator
Education: While most curator positions require a master's degree in art history or museology, smaller galleries may only require a bachelor's degree in art or art history. A curator is an important person in the art world. Our curators only get paid when the submission they have reviewed is approved by the team and accepted by the publisher. Questo libro raccoglie vari interventi sull'arte della curatela. In Becoming a Curator, Brubach reveals the path to becoming a curator in today's ultra-competitive art world, from education to exhibition. Becoming a Curator: Brubach, Holly: Amazon.sg: Books. Become a curator book. The Art Career Project is here to help you learn the skills you need to excel in the arts and … Becoming a Curator book. Cart Hello Select your address Best Sellers Today's Deals Electronics Customer Service Books Home Gift Ideas New Releases Computers Gift Cards Sell. In Becoming a Curator, Brubach reveals the path to becoming a curator in today's ultra-competitive art world, from education to exhibition. A step-by-step guide to every aspect of putting on an art exhibition, with tips from a range of influential curators. All Books Children's Books School Books History Fiction Travel & Holiday Arts & Photography Mystery & Suspense Business & Investing Books Education Studies & Teaching Become a Book Series Curator Common Ground Research Networks is looking to expand our Book Imprints to include thematically-oriented book series. Buy Books. An illuminating guide to a career as a curator written by acclaimed journalist Holly Brubach and based on the real-life experiences of an expert in the field— essential reading for someone considering a path to this challenging, yet rewarding profession. The group of five professors, artists, and curators—including moderator and Jewish Museum deputy director Jens Hoffmann—were more or less unanimous in their answer: No, a curator can get by just fine without one. The market is competitive, and academic standards are very high. As curators have become stars of the art world, a number of courses and degree programs have sprouted up, taking a global perspective. Business Bestsellers; 4.0 all the way through school. ... Careers for Book Lovers. The 'traffic light system' used to review the books is the best way to allow me to ascertain which books are suitable for my students. Right now, the highest paying states for Curators are DC, NJ, NY, MA and CA. Developing the awareness needed to become a goodness curator isn't easy. Prime. Go behind the scenes and be… Its courses are intended for conservators, antiquarian book sellers and collectors, archivists, rare book librarians, and curators. It has a track record for launching careers and educational paths in this field. In Becoming a Curator, Brubach reveals the path to becoming a curator in today's ultra-competitive art world, from education to exhibition. In Becoming a Curator, Brubach reveals the path to becoming a curator in today's ultra-competitive art world, from education to exhibition. Start your free career test. Originally founded in 1983 at Columbia University by Terry Belanger, the Rare Book School moved to the University of Virginia in 1992. Login with email. And like a good art curator, the information curators should have intellectual curiosity, good taste, and willingness to invest time do the necessary research. Sit in on acquisition meetings, plan a splashy new show, go on a studio visit with an up-and-coming artist, and attend an opening at … How to Become an Archivist, Curator, or Museum Worker. Sit in on acquisition meetings, plan a splashy new show, go on a studio visit with an up-and-coming artist, and attend an opening at … I would like to thank you for the wonderful magazine, But that proved to be just the beginning of a wide-ranging conversation about what it takes to be a curator today. Sit in on acquisition meetings, plan a splashy new show, go on a studio visit with an up-and-coming artist, and attend an opening at … As you thoughtfully curate your spaces, they come to reflect the individual character of … Pay I recall, during the year I almost quit teaching, deciding to focus on the good the moment I stepped into the school. The kids become your partners in curating, and then they practice becoming the curators of their own lives. To become a curator at a national museum, a PhD is required, as is about five years of field experience. 4. Account & Lists Account Returns & Orders. Archivists, curators, and conservators typically need a master's degree in a field related to their position. 1. In Becoming a Curator, Brubach reveals the path to becoming a curator in today's ultra-competitive art world, from education to exhibition. Check your registration email for an automatic login link. Sit in on acquisition meetings, plan a splashy new show, go on a studio visit with an up-and-coming artist, and attend an opening at … This course will provide you with an essential tool kit with which to become an independent curator. The 2019 Porchlight Business Book of the Year. One of the easiest ways to increase your salary as a Curator is to move to a higher paying state like DC. Some employers prefer that curators have a doctoral degree, particularly for positions in natural history and science museums. Go behind the scenes and be mentored by the best to find out what it's really like, and what it really takes, to become a curator. 2. Within the first 30 seconds of entering the building, I heard a student scream perversely and … Skip to main content.sg. Read reviews from world's largest community for readers. Kelly Richman-Abdou is a Contributing Writer at My Modern Met. He offered me several options: I could work full-time, or I could work part-time, or I could take a sabbatical summer off and become Curator of Rare Books. How to Become a Curator Curators most earn a minimum of a Masters degree, however you will first need to earn a bachelor's degree in order to move own to earn a Masters degree. The Curator's Handbook is the essential handbook for curators and curatorial students, mapping every stage of the process of putting on an exhibition, no matter how traditional the venue, from initial idea to final installation. Or, login below if you've set a password in the past. I want to become a curator! Most museums require curators to have a master's degree in an appropriate discipline of the museum's specialty—art, history, or archaeology—or in museum studies. Try. All Hello, Sign in. Fluent French and English with more language fluency. A curator (from Latin: cura, meaning "to take care") is a manager or overseer. An illuminating guide to a career as a curator written by acclaimed journalist Holly Brubach and based on the real-life experiences of an expert in the field— essential reading for someone considering a path to this challenging, yet rewarding profession. Useful graduate degrees include restoration science, curatorship, art history, history, chemistry, and business administration. Just like every museum is different, each of our homes will look different. Page 1/2. In Becoming a Curator, Brubach reveals the path to becoming a curator in today's ultra-competitive art world, from education to exhibition. Sit in on acquisition meetings, plan a splashy new show, go on a studio visit with an up-and-coming artist, and attend an opening at … The course is designed to help you think critically about the role of the curator and for you to identify and establish your own curatorial approach. Larger organizations typically require a master's or doctorate in art or art history. However, we regularly offer rewards such as discounts on books and merchandise, invitations to readings and fairs, and access to our community for our curators. 3. Most employers would prefer you earn a degree in museum studies, art, history, … You'll find the most recent quizzes on all these topics, easily browsed in one location. How To Become A Good Curator of Information. Read 3 reviews from the world's largest community for readers. An illuminating guide to a career as a curator written by acclaimed journalist Holly Brubach and based on the real-life experiences of an expert in the field—essential reading for someone considering a path to this challenging, yet rewarding profession. Go behind the scenes and be mentored by the best to find out what it's really like, and what it really takes, to become a curator. books for Primary school children. An art historian living in Paris, Kelly was born and raised in San Francisco and holds a BA in Art History from the University of San Francisco and an MA in Art and Museum Studies from Georgetown University. Museum technicians typically have a bachelor's degree. PHD in Art History from top university, preferably French , specializing in one of the areas the Louvre exhibits. A book is likewise offered for a DIY guide that could help you out tremendously as a starting artist. Sit in on acquisition meetings, plan a splashy new show, go on a studio visit with an up-and-coming artist, and attend an opening at … Experience gained through an internship or by volunteering in archives or museums is helpful. Read more. There are hundreds of curators that you could also submit your music to. Next: How to Become a Curator. How to Become Jobs Education Master's ... Take the CareerExplorer test to get a detailed breakdown of why you may or may not make a good curator. "Like … Kelly Richman-Abdou. If you are interested in serving as a book series curator we ask that you submit a proposal for the direction of the book imprint. Coursework should focus on art history and include a wide range of periods and styles of art and architecture. Explore hundreds of art careers, find top art schools, jobs, inspiration, and more. L anding his current job was not exactly part of a masterplan for Julien Parsons, head curator and senior collections officer at Exeter's award-winning Royal Albert Memorial Museum (RAMM). Make sure you submit the correct genre for each curator. However, a higher pay at DC doesn't guarantee that you will make more because the living expenses at DC might be twice as high than where you are currently at now. Sporcle curators choose excellent quizzes across all the subcategories on Sporcle. Congratulations to Don't Be Evil by Rana Forhoohar, a "penetrating indictment of how today's largest tech companies are hijacking our data, our livelihoods, our social fabric, and our minds."
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how to become a book curator 2020 | {
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{"url":"http:\/\/mathhelpforum.com\/trigonometry\/159183-prove-trig-question.html","text":"Thread: Prove trig question\n\n1. Prove trig question\n\nProve question\nShow that\n(cot^2)X\/1+(cot^2)X = (cos^2)X\nCan you guys help me solve this question please?\n\n2. Originally Posted by mike789\nProve question\nShow that\n(cot^2)X\/1+(cot^2)X = (cos^2)X\nCan you guys help me solve this question please?\nHint: what is $1 + \\cot^2 x$ ?\n\n3. Originally Posted by mike789\nProve question\nShow that\n(cot^2)X\/1+(cot^2)X = (cos^2)X\nCan you guys help me solve this question please?\nit is (cosec^2)x\n\n4. yes.\n\nso you now have cot^2x\/csc^2x.\n\nwrite down cot in terms of cos and sine, and also write down csc in the form of sin to complete your problem.","date":"2016-09-01 02:09:16","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\": 1, \"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\": 0.9135012030601501, \"perplexity\": 4397.622077132878}, \"config\": {\"markdown_headings\": false, \"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-2016-36\/segments\/1471982956861.76\/warc\/CC-MAIN-20160823200916-00214-ip-10-153-172-175.ec2.internal.warc.gz\"}"} | null | null |
# Copyright
This book is a work of fiction. Names, characters, places, and incidents are the product of the author's imagination or are used fictitiously. Any resemblance to actual events, locales, or persons, living or dead, is coincidental.
_Die Legenden der Albae: Tobender Sturm_
Copyright © 2014 by Markus Heitz (www.mahet.de)
Represented by AVA international GmbH, Germany (www.ava-international.de)
Translation copyright © 2019 by Sorcha McDonagh
Excerpt from _The Wolf_ copyright © 2018 by Leo Carew
Excerpt from _The Winter Road_ copyright © 2018 by Adrian Selby
Cover illustration by Alan Lathwell
Cover copyright © 2019 by Hachette Book Group, Inc.
Hachette Book Group supports the right to free expression and the value of copyright. The purpose of copyright is to encourage writers and artists to produce the creative works that enrich our culture.
The scanning, uploading, and distribution of this book without permission is a theft of the author's intellectual property. If you would like permission to use material from the book (other than for review purposes), please contact permissions@hbgusa.com. Thank you for your support of the author's rights.
Orbit
Hachette Book Group
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New York, NY 10104
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Originally published 2014 by Piper Verlag GmbH, Germany
Published in August 2019 by Jo Fletcher Books, an imprint of Quercus Editions Ltd
First U.S. Edition: August 2019
Orbit is an imprint of Hachette Book Group.
The Orbit name and logo are trademarks of Little, Brown Book Group Limited.
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Library of Congress Control Number: 2018965544
ISBNs: 978-0-316-48934-8 (trade paperback), 978-0-316-48938-6 (ebook)
E3-20190615-JV-NF-ORI
# Contents
Cover
Title Page
Copyright
Dedication
Epigraph
Prologue
Chapter I
Chapter II
Chapter III
Chapter IV
Chapter V
Chapter VI
Chapter VII
Chapter VIII
Chapter IX
Chapter X
Chapter XI
Chapter XII
Chapter XIII
Chapter XIV
Chapter XV
Chapter XVI
Epilogue
Discover More
Afterword and Thanks
Dramatis Personae
Extras
Meet the Author
A Preview of _The Wolf_
A Preview of _The Winter Road_
By Markus Heitz
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_It is said that they are crueller than any other known tribe._
_It is said that their hatred of the elves, people, dwarves and all other creatures flows black through their veins and is revealed when their eyes are exposed to sunlight._
_It is said they have devoted their entire lives to death and art._
_It is said they are masters of black magic._
_It is said they are immortal..._
_Much has been proclaimed about the älfar tribe._
_Now read the tales that follow and decide for yourself what is truth and what is not._
_These are tales of unspeakable horror, of unimaginable battles, the greatest evil, magnificent triumphs and devastating defeats._
_But also of courage, sincerity and valour._
_Of friendship._
_And love._
_These are the legends of the älfar._
Author unknown
Foreword from the banned, truth-twisting books
_The Legends of the Älfar_ , undated
# Prologue
_It's not long since I wrote these words down._
_Some events are touched on in the Forgotten Writings; some facts now appear in a new light. It's odd how everything is connected after all, even if many divisions of unendingness separate things._
_It seems the era of false gods is over. They declared themselves superior beings and failed. That was the end of the Inextinguishables._
_But the creature they left behind for us behaved very differently. Dutifulness, humility, self-sacrifice—it's barely expected of mortals and not at all from the son of gods, something he was entitled to consider himself._
_Aiphatòn was on the march to keep danger at bay, moving from one stormy battle to the next. The storms became more and more powerful until he encountered the most powerful one of all._
_And me?_
_I'm still in the eye of the hurricane, enjoying a rest after so many moments of roaring and noise, of screaming and death._
_I can't say how long this calm will last or whether the wind will then tear me to pieces._
_If my notes should end, at least I'll have left a legacy that will outlast me._
_What irony: to live on, an immortal älf needs thin paper!_
_Read and understand._
Excerpt from the epic _Aiphatòn_
chronicled by Carmondai, master of word and image
Tark Draan, Älfar realm of Dsôn Bhará, formerly the elf realm Lesinteïl, 5452nd division of unendingness (6491st solar cycle), early summer
_Just as I thought: they waited because they don't dare attack us at night._
With the pale rays of the rising sun, Daitolór could clearly see the pathetic band of foes marching towards them across the plain. _We'll kill them one way or another._
Dust rose up from underneath their boots—the dry spell had made the earth around the crater sandy. Because there was no wind blowing, the telltale brownish clouds curled up into the air, easy to spot even from far away.
"They're coming across the plain from the northwest yet again. About a thousand of them. Half of the barbarians are dressed like warriors, the others farmers," Daitolór cried down from his lookout point, not sounding worried or nervous. "What they all have in common is that none of them has any sense."
Soft laughter rang out at the benàmoi's words.
The älf, who had stuffed his dark hair underneath his helmet, jumped down from a piece of abstract art made of clear varnished bones and rusty iron. He landed neatly in front of the twenty warrior-women and warriors who were wearing toughened, black leather armour.
Daitolór pointed at the approaching enemy. "Load the smooth arrowheads and pull the strings back as far as they go. Every arrow must run through at least three of the enemy and kill them. It will save ammunition."
Having taken their longbows from their shoulders, his soldiers nodded silently.
"As soon as this senseless lot have come within two hundred paces, we'll release two full volleys, then each of you is to look for targets directly in front of you. Off you go."
The small unit darted behind the many artworks that had once served to make an impression on visitors, with their composition, their strangeness and their uniqueness.
Daitolór's lookout point three paces in the air was resting on a solid pedestal. With its carved bones bound by silver wire, it was modelled on the Inàste's Arrow constellation with all its heavenly bodies, both large and small. All told, the artwork was four by four by four paces; crystals of various sizes on it symbolised the stars and sparkled beautifully in the light of the sun and moon. You could climb some steps up to the top of the pedestal and find yourself in the middle of the replica constellation.
Daitolór's favourite piece, which he stole glances at from time to time, was around ten paces to his left, surrounded by a crowd of statues made from gold, tionium and polished steel. Its simplicity was what marked it out as different and made it eye-catching. A torso seven paces tall had been formed out of bones to look like it was hauling itself out of the earth. The bones were intricately painted and inlaid with precious stones that glimmered and twinkled.
In its right hand, the figure brandished a weapon fitted with eight blades and mounted like a wind-turbine so that the mildest gust of wind could set it moving. When the rune-inscribed blades cut through the air, they whirred and hummed; and the faster they spun, the more hypnotic the overall pattern of sparkling gems became. Daitolór had often caught himself staring and listening to it for too long...
_Just like right now._ He tore his eyes away from the spectacle. _It's a disgrace that the artworks are being used as cover to take the brunt of this._
The benàmoi watched the warriors in his unit taking up their positions as he loosened the feathered arrow shafts in the quiver slung around his hips. Although each and every member of the unit carried fifty rounds, enough to obliterate the enemy, nobody knew how long it would be until more lunatics launched their next wave of attack. _For every bolt that hits an artwork, I will have my revenge and make the archer pay._
Daitolór had stopped counting how many dead carried his name.
And yet, things weren't looking good for the northern älfar's realm, no matter how much scum they were killing off.
The power structures were starting to shake but he had no doubt they would triumph. For the benàmoi, it was just a question of arrow supply.
The älfar had ruled large parts of Tark Draan for twenty divisions of unendingness. At first there were just the Dsôn Aklán—the triplets Sisaroth, Tirîgon and Firûsha—as well as the survivors from the Phondrasôn caves. Together they had built Dsôn Bhará and expanded their rule with every sunrise.
Aiphatòn, the son of the Inextinguishables, had come along later with a band of wild älfar who had no sense of decency or appreciation of art, and he had seized full control over the älfar tribe because of his parentage. The magic he commanded bolstered his claim and literally pulverised any resistance. In the north, they hid their hatred of him and his second-rate entourage behind a mask of haughty politeness.
At long last, the triplets had been able to win over the groundling folk from the Thirdling tribe as allies, and this represented a huge step. It meant that they could tackle the complete conquest of Tark Draan and especially the protection of areas they had captured.
Daitolór remembered the good times that had ended when Tungdil Goldhand turned up. The hero of old, he had led the courageous tribes against the älfar and all the other conquerors the triplets were already fighting a running battle with: from the magus Lot-Ionan to the dragon Lohasbrand and the monster kordrion.
_They'll be close enough very soon._ Sadly Daitolór couldn't turn a blind eye to the fact that there were hardly any more warrior-women and warriors from his tribe left to hold out against the waves of scum surging towards them. The barbarians attacked the capital relentlessly, spurred on by successes in Dsôn Bhará's hinterlands as well as the rousing words of the elves, groundlings and self-declared heroes with ridiculous names like Mallenia or Rodario.
The commanders obviously kept quiet about how many casualties the attackers had sustained so as not to discourage the barbarians.
There usually wasn't enough time to disembowel the corpses and scour them for the right bones for new artworks. Most of the bodies were dragged away at night by carrion-feeders so the barbarians couldn't work out the true scale of their losses. Sometimes there was just the slightly sweet, acrid stench of rotting flesh hanging in the air from the surrounding foxholes.
The small crowd of barbarians was approaching across the plain at the double. Whatever was making them come here and look for conflict, Daitolór doubted that their impetus was courage. Barbarians usually carried out the greater deeds from greed. There was no doubt that the älfar's wealth was known about in Tark Draan. _The glittering of the artworks will attract them._
Apparently the so-called southern älfar, who had been commanded by Aiphatòn, had all fallen in battle against Lot-Ionan, along with their emperor. The only son of the Inextinguishables belonged to the past, and Daitolór did not shed any tears over him. The benàmoi was sceptical that Aiphatòn could have killed the all-powerful magus and dragged him into death with him.
Even the Dsôn Aklán, who to him were the true rulers of the älfar, suffered a painful loss: it was said that Firûsha died a long time ago in a battle with a maga and nothing had been heard from her sibling commanders Tirîgon and Sisaroth for a long time. No doubt they were fighting the scum in Tark Draan somewhere. As long as both brothers stood by them, nothing bad could happen.
_They led us out of Phondrasôn to one of our biggest victories. They will definitely lead us through the hard times too._
Their enemies exploited the northern älfar's vulnerability and the chaos: just as the troops were going to assemble quickly to defend the capital, rebellions suddenly broke out all over Dsôn Bhará. So the älfar were forced to rally against sparks of resistance in many places at once, extinguishing them with blood.
As Daitolór had learned in the meantime, the groundlings from the Thirdling tribe terminated the alliance pact and charged into battle alongside the rebels. _We will crush them too. And punish them like we have never punished any tribe in Tark Draan before._
The tramping of boots and the rattle of poorly made armour rang out. They even had cavalry in their small, shabby army. Around a hundred of their soldiers were on horseback, holding long lances upright with colourful pennants fluttering from them.
_No groundlings?_ The älf scrutinised the whole line as they approached. _I hope, Samusin, that we kill some traitors again._
"Get ready!" he cried and resumed his elevated position. There was a gap between the artwork's intersecting and interlinked bones, and it was through this that he would fire the shots accurately at the enemies.
Daitolór took one of his extra-large black arrows that even thin metal couldn't block and placed it on his bowstring.
The troops started running—but to the astonishment of the benàmoi, none of the attackers drew their weapons. The cavalry trotted casually behind the infantry, the archers having hung their crossbows on their backs.
_They don't know that we're lying in wait here!_ This thought flashed through the älf's mind and a contemptuous smile formed around the corners of his mouth.
The barbarians were probably in a hurry because they could already see the crater and wanted to get into the Black Heart of Dsôn Bhará quickly to tear it out of the kingdom's breast and destroy it.
_Because they didn't send a scout on ahead, they're running blindly into our shower of arrows. Oh, they have truly lost their minds. And soon they'll lose their lives too._ "Ready?" he called, pulling his bowstring back a long way and aiming at the cavalryman with the shiniest armour, the rising sun reflecting off it. He was asking to be shot. "Fire!"
His fingers released the thin cord, and he immediately followed up the arrow aimed at the horseman with another one.
The twenty-one projectiles were still whirring through the air when the next ones followed.
The first hail of impacts and screams was immediately followed by a second. More than a hundred foes fell to the dusty ground mid-movement and some were trampled by the ones who came after them. It seemed as though the army initially didn't grasp what was going on.
_Your death is named Daitolór._ He saw his barbarian target in the shimmering armour slump abruptly in his saddle and slip off his horse; the rider behind him yelled out and clutched his chest, while a third let go of his lance and fell off. Meanwhile the barbarian to his left lurched backwards out of his saddle and the rider behind grasped his visor, writhing.
_Only five?_ Daitolór wasn't happy with his spoils. _It ought to have been six or more. Since when have they been using thicker iron? Surely they didn't learn?_
Enraged, he fired one arrow after another at the pitiful army which had come to a standstill, making it an even easier target for five or six heartbeats before the cleverest among the simple-minded lot raised their shields.
But the älfar's war arrows ran effortlessly through the shields, piercing one or two more bodies beyond them. Anyone who didn't fall down dead immediately sustained terrible injuries.
Once Daitolór had used up half of his ammunition and scarcely more than forty heartbeats had gone by, not one single member of the barbarian troop was left standing; even their steeds were lying on the ground.
The älfar stopped their bombardment.
Their wounded foes crawled over lifeless bodies, looking for a place safe from the arrows. The benàmoi saw a flurry of movement behind some of the horses' corpses.
_The cowards think they're safe there._
"Advance," he commanded. "Keep your bows to hand until we're close enough, then take your lances and kill every barbarian who still looks like they have anything resembling life in them."
Daitolór left his elevated position and strode towards the bloody chaos of barbarian and horse corpses with his twenty warrior-women and warriors.
The älfar didn't encounter any resistance. Not one bolt flew at them.
Deathly afraid and unable to form a coherent thought, the injured fled for their lives much too slowly rather than putting up a fight.
_What a pathetic lot._ Daitolór's nose was filled with the smell of spilled blood, and the whimpering, agonised screams disgusted him.
He ordered three of his warriors to guard the unit with their bows; he had the rest continue the slaughter to make sure that none of their enemies survived and made off during the night. The long-shafted lances belonging to the slain cavalrymen were perfect for cutting the enemy's throats open without sullying themselves with their blood.
In ten cases, they found barbarians hidden among the fallen soldiers, hoping to escape the älfar's keen eyes. Swift stabs put an end to those cowards; the same went for the ones crouching behind the dead horses who literally begged for mercy. They died under the warriors' disdainful gaze.
The sun wasn't quite at its peak when Daitolór and his defending forces from Dsôn took the lives of the last barbarians.
"Gather the intact arrows wherever you can," he ordered his troops and removed his helmet from his dark hair to cool himself down. "Then we'll return to camp and await the next targets. We'll hardly be out of practice!"
Soft, evil laughter rang out again.
"What about the dead, benàmoi?" asked one of the warriors. "I still need a few nice teeth—I want to resole my boots with them."
"The entire sole?"
"Yes. They make a wonderful, musical sound when you walk on stone."
Daitolór raised his hand as a signal of permission to disembowel the bodies. "I've got to see these boots with tooth soles," he remarked.
"I'll show you them as soon as I'm done."
"Benàmoi, a retinue from Dsôn," came the cry from one of the archers still on guard.
Astonished, Daitolór turned around and made out a band of ten älfar riding towards them on night-mares. His surprise grew when he saw the blood-red runes on the pennant fluttering in the wind on one warrior's lance.
_The symbol of the Dsôn Aklán!_ The benàmoi's heart beat faster. _Is that... Firûsha?_
Indeed there was an älf-woman in the middle of the band wearing eye-catching black tionium armour with exquisite inlay. Because the group was tracing an arc as it approached, the extra protective iron ridge along her spine was coming into view. A very long, narrow sword hung at an angle by her night-mare's flank, the massive crossguards jutting out and gleaming.
_That's her! She's alive! Oh, Inàste, that is..._ Daitolór's thoughts raced, his joy threatening to overwhelm him. He took a few steps away from the field of corpses and glanced at his boots to check if the leather was sullied with barbarian blood. _What can she want with us? To congratulate us on our victory?_
The riders stopped in front of him, their snorting night-mares churning up the ground with their lightning-surrounded hooves.
Daitolór bowed slightly. His gaze fell on the double-edged daggers affixed to the armour on her thighs, as well as the iron discuses the size of palms on the metal splint armour on her upper arms. "Dsôn Aklán," he greeted her. "We have held the north of the town once again." He caught a glimpse of her face through the visor and saw she was incredibly attractive.
His troops looked at the älf-woman as if she were a ghost.
Firûsha's piercing black eyes, in which he thought he could detect a hint of blue, were fixed on him. "You have served us well, benàmoi. As long as my brothers are at war with Lot-Ionan and the rebellious barbarians, they will not be able to devote time to Dsôn's security." She nodded first to him and then to his small unit, before finally pushing up the visor of her helmet. "Thank you. Stand your ground."
_She is beautiful. Just like people say._ "We need more arrows, Aklán," Daitolór ventured to suggest. "We are so outnumbered by barbarians that we..."
Firûsha smiled and swept a strand of her black hair to the side. "Send one of your people to my quartermaster in town. He's to supply you with the best ammunition." The älf-woman pointed southeast. "Meanwhile we will ride towards the enemy and slaughter anything that stands in our way, to allow you a break. Your arms must be tired from the relentless shooting."
Daitolór couldn't stop staring at her. _She_...
Firûsha took a breath. "Like so many others, you thought I had passed into endingness, didn't you?"
He nodded almost imperceptibly, although that wasn't exactly what he was thinking. "Forgive me. People said that you had fallen into the hands of a maga and were lying at the bottom of a lake in Weyurn," he answered truthfully. "Seeing you in front of me now is the most wonderful present that the Creating Spirit has given me in the last few moments of unendingness."
A wind sprang up, blowing southwards. It played with the black hair that jutted out from underneath the älf-woman's helmet and fell to her shoulders. It gave off the refreshing smell of fresh confidence; it was unsullied by decay or barbarian blood.
With one hand, Firûsha grasped the hilt of her two-handed sword. "And I will ride into battle again. A barbarian-woman cannot rob me of immortality, regardless of whether she's a maga," she said. "All of you," she addressed the troops, "hear this and carry it in your hearts: I, Firûsha, one of the Dsôn Aklán, walk among you and march out to bring death to enemy ranks. Together we will transform the impending doom into victory!"
Daitolór lifted his blood-spattered spear. "We will not let the enemy advance any further than this point," he solemnly swore. "No barbarian, no groundling and no creature other than an älf will set foot in our town."
The wind picked up a little more and set the artworks moving.
The crystal stars of Inàste's Arrow bobbed and sparkled, the bones gently rubbing against one another and the thin wire creating a high-pitched murmur that sounded like whispering; the eight blades belonging to the figure breaking out of the ground started rotating faster too, and a whistling hum resounded.
A cool shudder ran down Daitolór's spine, despite the heat from the sun. Without meaning to, the benàmoi turned around and let his gaze wander. Something seemed off, and an ominous feeling spread through him.
The night-mares also seemed to sense a change was taking place. Snorting, their red eyes rolled; they thrashed around restlessly and their nostrils flared.
_Would monsters secretly try and approach Dsôn? But where would they be coming from?_ Try as he might, Daitolór couldn't explain his misgivings.
Firûsha reined in her frisky stallion. "Look at them! They want to sink their teeth into barbarians," she cried out, laughing and getting guffaws of approval in return. "We're better off riding out before they get so wild that they..."
A powerful gust of wind made a low-pitched whirring sound as it swept through the group of älfar, churning up dust and earth. In the blink of an eye, the steeds disappeared along with the troops behind the grey-brown clouds of dirt.
The rapidly fluctuating sounds from the artwork's eight spinning blades drifted over to the benàmoi, but now they didn't seem fascinating or soothing. On the contrary, they seemed to intensify and fan the flames of his anxiety.
_The god of wind seems to want to have some fun with us._ Daitolór tightened his grip on his spear, tiny granules grinding between his teeth—then he felt the prickling all over his skin.
This time it wasn't a vague premonition, it was the consequence of powerful magic suddenly appearing all around him.
_What could..._ Before he could let out a warning cry, a shrill crackle cut through the whirring of the wind. In the middle of the dust, dark green finger-sized runes lit up.
Then death cries rang out.
The night-mares were neighing wildly. Daitolór heard the clicks of their teeth snapping shut, followed by loud, dry cracks. Someone or something was breaking the mighty animals' spines.
Then warm fluid from the haze of dirt sprayed at the benàmoi. The smell told him it was blood.
Älfar blood.
"Aklán!" he shouted, brandishing his spear at the invisible foe attacking under cover of dust. "Watch out!"
"Get out of here," Firûsha shouted frantically from somewhere in the sandy haze, profound fear in her voice. " _He_ is here!"
_He?_ Daitolór made out the galloping sound of approaching night-mare hooves, mingling with the renewed hissing as magic was unleashed. _Lot-Ionan!_
A beam of emerald light as thick as an arm made a crackling sound as it shot past him and hit the nearest älf, ripping him apart with its force. Blown-off body parts rained down on the benàmoi, and he was sprayed with blood again.
He panted as he knelt down and peered around, his heart racing, his fingers around the now sticky shaft of his weapon.
The loud, discordant sounds of the eight blades wouldn't stop. For the first time, Daitolór wished they would be silent.
The wind toyed with the clouds of dust, gradually dispersing them as if Samusin wanted to reveal the horror confronting the älfar.
The Aklán and four of her companions were riding in the distance. They could not stand up to the superior magic of a Lot-Ionan.
Bloody scraps lay beside and in front of the crouching benàmoi—it was only the pieces of armour that identified them as älfar limbs. Two riderless night-mares were stomping around and snorting, getting their bearings in the dropping wind.
The artwork went silent.
_Where is the magus?_ Daitolór felt he knew what his mission was: he had to make sure the Aklán had time to reach safety so that she could command her surviving people. A spear was not enough to kill the magus, the älf knew that, but it would definitely be enough to distract it. With Inàste's aid, a miracle might happen.
Out of the mist emerged the silhouette of another älf-warrior whom Daitolór didn't know. _He must have been one of the Aklán's guards who had fallen off a night-mare._
Without looking around or taking any other precaution, the unknown soldier went over to one of the black horses and swung himself into the saddle to follow the queen.
"Where are you going?" came the sound of a sonorous voice from the last of the grey-brown clouds. Then, less than five paces from Daitolór, there appeared a thin, bald figure holding a long staff in his left hand.
The benàmoi ducked even lower, ready to throw his spear. _I might manage it if the magus is distracted._
The älf on the night-mare spurred his stallion so that the huge beast lunged at the magus and—
Steed and warrior were enveloped in green light mid-leap. They were flung to the ground as though they had been struck by a giant fist. The night-mare's legs broke with a crack and the älf warrior was pinned down by the black horse's heavy body. Because the suffering, raging animal was snapping its jaws shut in all directions, the warrior was forced to kill it with a swift blow to the neck before the lethal teeth could get him.
"That's how quickly an attack can turn to defeat," the sound of the magus' voice rang out, speaking excellent, almost archaic älfish.
Daitolór stayed still, not letting the enemy out of his sight as he calmly approached the pinned rider.
The last of the dust clouds dispersed—and he saw his error.
_Aiphatòn!_ Although the benàmoi had never set eyes on him before, he knew immediately that the emperor had come to Dsôn.
No other älf looked like him. Most of his chest, stomach and lower abdomen, as well as his shoulders and upper arms, were covered in plates of armour sewn into his flesh. The metal, people said, consisted of a special alloy that absorbed and stored magic energy. That explained his powers, which rivalled those of a magus. He was bald, wore heavy armoured gloves and a black, wraparound skirt-like garment around his hips.
The pinned warrior pointed the sword covered in night-mare blood at Aiphatòn. "You're a traitor to your own people," he said, groaning. "First you bring that scum out of the south, now you want to kill the Aklán. And all the while you are the son of the Inextinguishables!" He clenched his teeth together to suppress a cry of pain. "Think, Aiphatòn!" he continued. "Ally yourself with..."
The bald älf threw his head back and roared with laughter. "You're just about to pass into endingness and you're trying to talk _me_ into an alliance with the Aklán? I am your _emperor_ , älf!" he thundered, pointing the narrow tip of his spear at the prone man. "You ought to obey me without asking a single question, just like the Aklán should! Instead they carried on with their intrigues, sought to depose me and saw themselves on my throne. Do you think I'll be so kind as to forgive that crime? A crime against me, the son of the Inextinguishables?"
Daitolór didn't dare move.
By now he seriously doubted he would be able to do anything to stop Aiphatòn. Anyone who could simply fling a night-mare to the ground as it galloped would laugh when faced with a conventional spear. He saw his warrior-women and warriors lying around, dashed to pieces, torn apart by magic as if they were battle debris, deemed worthless. _But what will I do?_
"The Inextinguishables abandoned us back then," snapped the pinned man. "We were stuck in that hole, in the middle of the Grey Mountains, waiting for news from Tark Draan. But it didn't come. It _never_ came! Without the Dsôn Aklán, we would have been wiped out in Phondrasôn."
Aiphatòn scrutinised him with eyes like dark black holes that gave his narrow, symmetrical face an extremely sinister look.
It was said his eyes never revealed their true colour, not even at night when älfar eyes usually did. As the child of Nagsar and Nagsor Inàste, he was a shintoìt, the highest and purest being. He was invariably recognisable as one, even without the armour woven into his flesh.
"It would have been better for you all," Aiphatòn declared in a whisper and stabbed the prone warrior in the neck. "And for Girdlegard. But know this: _I_ will make up for my mistake."
The injured man's breath rattled as he grasped the rune-embellished spear-shaft with one hand and tried to pull it out, his sword bouncing off it ineffectually.
"The Aklán will be the next ones I dispatch into endingness. Then I will return and set your beloved Dsôn alight. I am their emperor and the älfar will meet their downfall at my hands, just like I promised an old friend of mine they would. The realisation came late, but it did come. Your death is named Aiphatòn," he said solemnly. "I will take your immortality from you and leave your remains to the carrion-feeders. Isn't it funny that you have that in common with the common _barbarians_? Thus the differences end."
Gurgling, the älf died beneath the night-mare, blood running from the open wound at the corner of his mouth and dripping onto the ground. His body went limp.
Daitolór didn't move. _He must not see me._ Having heard what he had, the benàmoi had reached a decision.
Motionless, he watched as Aiphatòn pulled the narrow spear-tip out of the warrior's flesh and cleaned it on the man's clothing. Then the emperor ran off, apparently hard on Firûsha's heels.
Daitolór, whose whole unit had been taken from him in the blink of an eye by this älf, saw that the shintoìt was not wearing boots, but had taken up the pursuit barefoot.
Only once the enemy had moved further away did he stand up and throw his spear carelessly to the ground. With an adversary like Aiphatòn, wood and steel were no use.
He thought his people were fully capable of getting rid of a magus, but when the son of the Inextinguishables was against them, they were in great danger. And they would remain so until the last älf was wiped out as he had promised.
_I've got to warn the Aklán. She and her brothers will find a way to stop him._
Daitolór went over to the remaining night-mare and grabbed hold of the harness, soothing the animal with a few murmured words and swinging himself into the saddle. There was no special art to reading the tracks, the hooves left clear imprints in the earth. Unfortunately, Aiphatòn had seen them just as easily.
From the black horse's back, he cast an eye over the mound of corpses, then glanced at the rim of the crater a mile away where the town and the palace towered up into the air _. Hold your ground, black heart, and every time you beat, bring endingness to our enemies._
He had to abandon Dsôn against the wishes of the Aklán because that was the only way for him to protect Firûsha from entering endingness. The warrior-women and warriors holding out in the valley, around fifty of them or so, would be able to defend Dsôn long enough. Even without him.
_Samusin, come to our aid. And I beseech you, Inàste, do not allow a shintoìt of all people to be our downfall._ Daitolór felt unspeakable hatred for the emperor; the slight twinge in his face immediately told him that anger lines had formed on it.
He turned his head—and saw Aiphatòn standing right next to the night-mare. _Where did you...?_ Daitolór's eyes widened in fear. Before he could even move his hand to the hilt of his sword, the narrow tip of the spear was thrusting towards him.
"Why so angry, benàmoi?" said Aiphatòn with an icy cold smile. The blade penetrated through the night-mare's neck and then through the hardened leather into the warrior's chest. "Go join your unit and let them know _who_ dispatched them to endingness."
The runes on the shaft lit up a dark green; a high-pitched crackling sound rang out, becoming louder and louder until it was the only sound in Daitolór's ears. His last thought was that there was now nobody to warn the Aklán about her deadly pursuer.
# Chapter I
_I have seen all kinds of characters during my life._
_I have seen those who made an effort to achieve something and I have seen those who squandered their talents for nothing._
_Worst of all were the ones who didn't behave well and were also unable to do anything of worth. Because they wanted to achieve a lot without putting in the effort, they were capable of the most repugnant things._
Unknown author
collected by Carmondai, master of word and image
Ishím Voróo, Älfar town of Dsôn Elhàtor, 5452nd division of unendingness (6491st solar cycle), early summer
"I couldn't help hearing the last few words you said. Incidentally, I do _not_ think that Dsôn Dâkiòn needs to be destroyed." Modôia was wearing a floor-length black dress with a train two paces long inwrought with silver and she was holding a crimson crystal goblet in her left hand. Her long blonde hair was braided into a crown to stop it getting windswept. "You're always so quick with the destruction, my dear Ôdaiòn. Please be a little considerate. It did take a while for that town to be built." From her tone it was clear that she was teasing the älf whose remarks she had just interrupted.
Some of her guests on the enormous terrace of white marble clapped quietly and politely, which caused even more älfar to turn around so that they could follow the unfolding entertainment better.
The sun had long since passed its zenith. The wind had made the temperature more pleasant and the taut white silken cloths protected them from the direct force of the setting daystar.
A sea breeze was coming from the west, carrying the smell of salt and freshness but also quiet, extremely repetitive drumming. This didn't bother Modôia or the nearly forty well-dressed guests in her enormous harbour house.
Ôdaiòn, a young älf in a slim-fitting, dark blue garment gave a slight bow. "Oh, I'm familiar with your leniency, Modôia, and even I appreciate mercy towards those who are weaker. But you're wrong." He swept his mid-length brown hair back and placed one hand on his back, standing up straight and looking her directly in the eye.
"Is that right?" Modôia treated him to a scornful smile. _You're angling for a duel?_ "Just so we're talking about the same facts, my dear fellow: when we talk about Dsôn Dâkiòn, are we talking about the town many, many miles away from our island?"
"That's right."
"The same town that's very far inland?"
"I can't deny that, either." He smiled a crooked smile.
Modôia took a few steps around the young älf, brandishing her crystal goblet as she did so without letting a drop of wine spill over the rim and drip onto the pale stone; her train rustled softly across the marble. "So you're calling for the destruction of a town far away that absolutely cannot become a danger to us and is also full to the brim with älfar?" She burst out laughing. "That would be like smashing a tiny egg because an insignificant little bird could hatch out of it that could potentially fly over one's head some moment of unendingness and... well... bestow a little grain-sized mess on one's gown." The älf-woman stopped in front of him. "And even _if_ that were how it turned out: I can wash my gown. Leave the egg in peace."
The guests laughed and gave another round of applause in support of Modôia. The breeze toyed with the numerous suspended wind chimes made from carved tubes of bone with silver fittings. A randomly generated, delicate melody rang out, reverberating quietly beneath the applause and the drumming.
Ôdaiòn cleared his throat, strolling around her now in his turn. "What you failed to mention is the river. And I'm not talking about a little trickle," he elaborated, with a note of haughtiness, "I'm talking about a full-sized waterway, around sixty to eighty paces wide and deep enough to carry heavy ships."
"You mean the Tronjor," an älf-woman chipped in from the edge of the terrace.
"The very same, darling." Ôdaiòn raised his glass in her direction gratefully. "This river, this Tronjor, flows into the sea not all that many miles from us." He looked at Modôia. "Sorry, but I'm sure you know how far it is better than I do?"
"Twenty-three miles," she said, precise about the details. She feigned cheerfulness but it was clear from looking at her that she was getting increasingly annoyed. _He is good. I know what he's trying to get at._
Ôdaiòn smacked his forehead. "How could I possibly forget? After all, we teach it to the youngest schoolchildren, don't we?" he cried with fake contrition which earned him the guests' laughter this time. "And have we not had a situation where that town set their allies on us before?"
"That was a misunderstanding," exclaimed Modôia.
"Of course. A misunderstanding. Like a mistakenly fired arrow that still hits the bullseye, to use a timely analogy," Ôdaiòn cut in immediately.
Yet more laughter broke out.
"It didn't hit the bullseye, although it may have been flying in our direction when we smashed it to pieces in the air," she countered.
"I accept that argument." The älf tilted his head. "But back to _your_ imagery: how do I know that a... dragon or... the embryo of a horrific monster won't hatch from the tiny egg instead of a little bird?"
"Because we know that Dsôn Dâkiòn is allied with us in a... special way... in a friendly manner. So the egg would have glass walls. We would know what would be inside," Modôia shot back. "And we would be able to see it was harmless." _That should do it._
This time she received the applause and toasted the crowd.
"Because we believe the visible embryo wouldn't change. But what about when it came into contact with the air?" Ôdaiòn wasn't giving up, which was making the älf-woman dig her heels in. "Let's take a tadpole, for example. Who would think a tiny black dot could turn into an animal many times its size that looks completely different?"
_Now I've got you._ "By that reasoning, you think the town will turn into a great big ship, hundreds of paces wide and long, that will descend from the mountain, glide into the river and come to wipe us out?" Modôia drank a sip of wine. "Well, my dear Ôdaiòn, I would go so far as to say that you're drunk. Go home before you fall over the balustrade and plunge into the harbour."
The guests laughed loudly now, clapping for a long time.
Ôdaiòn smiled and raised his glass. "I surrender, but only for this splinter of unendingness. My own analogy led me into a trap I couldn't get myself out of."
Modôia granted him a look of approval. "You're getting better every time. I've got to be on my guard, otherwise you might find too many supporters in Dsôn Elhàtor after all."
He nodded gratefully and grinned.
Modôia was about to raise her hand to place it on the young älf's shoulder but a searing pain ran warningly down her spine. The old pain was setting in much too early. _I should use this opportunity and withdraw before..._
"It's starting!" came a joyful cry from the balustrade. "They'll be here very soon."
_And the moment has already passed._ Modôia and Ôdaiòn plunged into the stream of festively dressed guests as they moved forward to look out over the white-painted stone handrail at the sea. At first the sculptors had tried to make the handrail using skeletons, but the sun and salty air quickly made the bones porous and fragile. Before any fatal accidents could occur, they had been replaced with painted granite hewn from the walls of the island's extinct volcano.
The sea spread out before Modôia and her guests, barely a wave on its surface and glittering picturesquely. It would be the perfect moment to head to the harbour for a swim—if the onwú fleet wasn't coming towards the mouth of the harbour.
From the terrace high above the surrounding buildings, they had an unimpeded view of what was happening.
"I count twenty-one ships," Ôdaiòn said by her side and leaned forward, resting his elbows on the railing. His aftershave smelled of pepper, of lilies and nutmeg. "That must have taken them a lot of time. And gold."
"The most expensive floating firewood currently at sea," Modôia remarked, helping herself to one of the canapés being offered by the waiters. Smoked shellfish had been paired with mild gado fruit. The fruit's sweetness and freshness went wonderfully with the taste of the fish. "You should use less aftershave or you'll attract bees."
Ôdaiòn smiled, looking straight ahead. "I only attract what I like." He gestured discreetly towards a young älf-woman in a white dress. "Describing _her_ as an insect would not do her justice."
The drumming was drifting up to them more clearly from the decks of the enemy ships. Orders were being barked out, sails reefed and dozens of oars lowered.
While the majority of the onwú fleet fell back, two armoured models were gathering way. They had long, iron, naval rams mounted on the bows, aimed at the big fence in front of the mouth of the harbour.
_They are making an effort in terms of strategy._ Modôia looked down.
The harbour wall was crawling with älfar. They had gathered to watch the spectacle, as if the onwú were dropping by in battleships for a joint party. There was food and laughter while children sat on the stones between the battlements to get a better view.
Modôia noticed some älfar on the wall and the terrace were placing bets. It wasn't about who would win. The question was how long the enemy would stay afloat or which of the ships would hold out longest. _I wouldn't bet on the two out in front._
"Would you like to share what it is we're about to see?" asked Ôdaiòn eagerly. "Will our war fleet swoop out of the secret exits and surround the onwú by any chance?"
Modôia clucked her tongue scornfully, and even this caused her pain. But there was no going back, as so often before. "Don't be impatient. You're about to see." She climbed onto a small platform that had been brought out and erected on her orders, then tapped her glass with the tionium signet ring on her middle finger. All attention turned to her. "My dear guests, could I please ask that you listen for a few minutes. It will fall to me in due course to explain what the renovations in the last few moments of unendingness were for. Please keep watching the harbour to see for yourself."
Everyone looked back to where the onwú fleet had gathered.
_They will be surprised._ Modôia forced herself to smile and drank some more of her wine, winking at Ôdaiòn and waiting for her cue as the conversations on the terrace temporarily fell silent. The tension grew. People were desperate to find out what the scholars had come up with.
The blonde älf-woman swallowed her fears as best she could, letting her gaze sweep over all the houses built right the way round the protected bay and stretching as far as the crater cone. _Samusin granted us such luck in reaching this island._
Very much in the tradition of their people, the designs of the buildings were ornate yet elegant, some straight lines here, some wavy ones there. Awnings broke up the hard edges, while flags and banners fluttered in the wind.
Due to the strength of the sun, the walls and flat roofs were painted white with delicate accents of black curved lines, runes, patterns of spots and paintings. Occasionally the decorations stretched across entire streets and created an enormous image that could only be appreciated from the sea and from very far away.
At night, hundreds of lights flickered on the terraces and flat roofs as if the town were a mirror of the stars.
The very steep streets, as well as the steps and arched bridges, were inlaid with little tiles of bone; the roughened surface prevented people slipping and falling when it was wet. As soon as they were too badly damaged by heels, soles, sun and salt, they were replaced.
Roughly ten thousand älfar lived in Dsôn Elhàtor, the älfar realm that, just like Dsôn Dâkiòn, was nothing more than a big town.
_A sanctuary after the many divisions of unendingness I lived through in Phondrasôn and Tark Draan._ Modôia closed her eyes and tilted her face towards the sun which was now shining past the silk cloths. Ever since surviving her adventures in Tark Draan and the Grey Mountains, she loved intense warmth more than anything else; it also helped with her pain.
_I've changed so much in the last twenty divisions._ She sighed. _We've all changed so much. Who would have thought that Ishím Voróo might have something good in store for us if we just travelled far enough?_
"The onwú's ram-ships will arrive soon," she heard Ôdaiòn's voice next to her. "Isn't it about time something happened?"
"The cîani are ready to step in if necessary," she replied without opening her eyes. "But I trust our architects' skill." Modôia opened her eyes and looked at the harbour. "My dear guests, pay attention," she said loudly. "Keep an eye on the towers on the right and left."
The two armoured vessels ploughed through the gentle waves, displacing the water with their low-lying bows. Foam sprayed high into the air, hitting the armour-plating that was mounted above the oarsmen to protect them from missiles.
"New iron pipelines were laid from the volcano's extinct crater down to the harbour," Modôia said. "The seawater that's sucked up by pumps there and then stored, shoots downhill with great force, which the pipes can now finally withstand." The blonde älf-woman took a deep breath. _It will start very soon now._
The naval rams were less than twenty paces from the fence when the thin white jets shot out of the lower third of the towers. Instead of striking the ships from above like stones or arrows, the concentrated water sliced through the ship's side planks at the height of the oars and shot through the slots for the rudder stocks.
Wherever the jets of water hit, the wood caved in and split. Splinters flew inside the ships and the screams of the injured and dying oarsmen were audible from far away. Clouds of foam sprayed up, glittering and making rainbows.
Meanwhile Modôia was proudly explaining, "The further the water flows downwards, the more constricted the pipes become. This increases the force with which it shoots out of the swivelling nozzles set into the towers."
Since the powerful ships couldn't simply be brought to a stop, the hulls were sliced open along their entire lengths. The vessels were being torn apart more and more.
_The architects are keeping their promise._ Modôia watched as the barbarians plummeted into the churned up waters from the upper deck and the rowing decks.
One jet severed the naval ram on the right-hand ship with perfect precision. Falling to pieces, the wreckages reached the fence and smashed into it.
The älfar on the wall cheered and clapped. Even the guests on the terrace joined in the jubilation, and someone ran away after losing a bet.
"The pipes were laid all over the island," Modôia cried over the furore. "We can strike in different places and if necessary, have extra pipelines laid, so that it's even easier to defend our homeland." She raised her goblet, the sunlight catching it and making the wine glow. "To Dsôn Elhàtor, the Magnificent! That it may remain undefeated as it has done for the last twenty divisions of unendingness."
"To Dsôn Elhàtor, the Magnificent," her guests cried.
"And to Modôia," said Ôdaiòn and held his glass out to her. "Remain our guiding star and shine on in well-deserved splendour! Nobody could lead us better."
Applause rang out once more, full of excitement and confidence this time as it echoed across the terrace and down into the town.
Modôia gave a very small bow. "No, that's enough. This is too much praise," she humbly rebuffed the adulation. "Especially when it's my own son calling for it."
The crowd laughed.
"He was just quicker than me, monarchess," an älf called out. "But you certainly deserve it, Modôia. A thousand times over."
She climbed down from the platform with a perfect, charming smile, Ôdaiòn offering her a helping hand as she did so. "I like competing with you," she murmured, "but stop demanding admiration for me."
"Why, Mother?" The brown-haired älf grinned. "What kind of son would I be if I didn't keep seeing to the status you deserve?"
Modôia sighed again. "I won't be able to forbid you from doing it."
"That's right." Ôdaiòn hadn't let go of her slim hand and was about to guide her back into the crowd, but she stopped. "What is it?"
"I've done my bit," she replied gravely. The pain wiped the smile off her face. "Now it's your turn." Modôia pointed to the harbour. "Whatever happens now, it's up to you to give explanations. I want to conduct the transfer of power soon, and the more present you are, the sooner they'll accept you as the future monarch of Dsôn Elhàtor." She was aware of her influence on the island town's residents, which could practically be described as supernatural. _He will find it difficult, despite his sharp mind._ "By the way, that shouldn't happen again." She took her hand away from him.
"What do you mean?" he asked, perplexed.
"You letting me win. It was very obvious that you deliberately let yourself be driven into a corner during our debating contest." Modôia placed her hand on the back of his neck, drew him towards her and kissed him lightly on the forehead. A blessing-like gesture. "Rule her well." Then she turned and withdrew, to the sympathetic applause of her guests. The monarchess had fulfilled her duty.
Nobody had noticed how difficult it was for her to do so; she appeared to be feeling fantastic. But she was fit to burst with the pain.
Modôia returned to the house, holding herself upright as long as she was still within sight of the älfar, but after rounding a bend, she collapsed.
She quickly leaned against the white wall decorated with mosaics and pressed her lips together to stop herself screaming. Her spine burned, sending pain into every corner of her body.
_The medicine is wearing off more and more quickly. I should have gone for a higher dosage._ She was not the only person in Elhàtor who had had to pay this price for a new homeland, and yet it seemed to her that she was suffering the most from the consequences. No cîani could help her—on the contrary, using magic made her agony worse. The sun helped. The sun and the essences she got from her most trusted confidante, Leïóva.
With some difficulty, she dragged herself into her bedchamber where a concerned face awaited her.
"It's getting stronger," was Leïóva's assessment. She was wearing a simple white dress, her black hair flowing down over her strong shoulders. She met Modôia and supported her as she guided her to the bed.
Leïóva picked up the bottle of elixir that had been set out, holding it to Modôia's chattering lips. "I warned you about too much exertion."
"I thought I..." The pain robbed Modôia of the power of speech and she sank onto the bed. After just one mouthful, her mind drifted away into soft black cotton wool.
"You have fulfilled your duty. Leave the land to your son. I'll watch over you," she could still hear Leïóva's soothing words and feel her cooling fingers stroking her temples.
Then Modôia drifted off, floating in pleasant sensations, far from all pain.
Tark Draan, Human kingdom of Gauragar, in the foothills of the Grey Mountains, 5452nd division of unendingness (6491st solar cycle), early summer
Aiphatòn stopped at the crossroads and let his gaze wander over the stony paths. _Where did you make a turn off?_ As he couldn't tell anything from a quick glance, he crouched down, leaning on his spear.
The unique älf had dashed through a flourishing Girdlegard, jogging steadily, and followed the tracks that Firûsha and her little entourage had left in the ground. The night-mares' shoes and the slight scorch marks stood out unmistakably in the soil.
Hurrying along, he ran through sprouting fields of grain and across meadows with gnarled old fruit trees. He raced down roads and paths, rushed through thick woods and soon he was back in great expanses of grassy plain.
His legs constantly rose and fell. He leaped over obstacles, hurrying through sunshine, rain and storms. He took food from people's pantries along the way without asking, or picked ripe fruit. He kept breaks to a minimum.
The hem of his long black trouser garment, which went from his hips to his toes, was tattered, the fabric extremely dirty by now, but he didn't care. His wiry torso had tanned in the unrelenting sunshine.
The spur that drove him onwards was hunting down the dangerous älf-woman.
He had also already dispatched the southern älfar—who had made it to Girdlegard because of him—to certain death using insidious poison. That didn't mean he could wash away the guilt he had incurred in the previous cycles, but he could eliminate any more threats to Girdlegard.
Meanwhile Ireheart and the armies of the dwarves and humans in conjunction with the maga Coïra would triumph over Tirîgon, Sisaroth and Lot-Ionan. Aiphatòn had no doubt about that—and for that very reason he needed to catch the Aklán, who had a very specific goal when she fled. There was a reason why Firûsha wanted to get to the north and enter the Grey Mountains. He was sure of it.
_Nothing to be found._ No matter how hard he tried, he couldn't make out any tracks this time. It seemed like the rock was in league with the Aklán. He straightened up. _How can that be?_
The night-mares moved with incredible speed. Even on a reliable horse Aiphatòn would not have caught up with the flesh-eating creatures. He hadn't passed a farmstead with outstanding steeds yet, so he had kept on running. It gave him greater agility.
Aiphatòn turned his black-eyed gaze to the mountain slopes that soared into the air up ahead, an increasingly leaden grey.
He saw steep, sharp-edged rock faces that would hurt you as soon as you touched them, as well as cloud-wreathed peaks in strange shapes that the dwarves had given appropriate names. Shadowy ditches miles long and filled with snow and ice ran along the sides, making climbing extremely dangerous. There were also porous ledges and fragile overhangs, narrow treacherous paths and storms that picked up quickly and spelled death to any inexperienced hiker.
_What can they be doing there? There's no way out._ There was nothing for it but to follow each of the four paths for quite a few paces, perhaps even for miles, until he found reliable tracks. Once again, that would mean him losing time, which was lucky for Firûsha.
_All right then._ Aiphatòn chose the northern road, which was wide enough to allow two carts to pass each other.
He shouldered the rune spear and balanced it so that the spear didn't slip or tilt to one side as he jogged along. The älf liked to have his hands free.
His thoughts wandered, but he kept his gaze riveted on the rock underneath him.
This hunt shouldn't actually have been taking place, because Firûsha ought to have been dead. During an attempted attack, she had been struck by Coïra's magical charge and had plunged many paces deep into the sea.
He still couldn't understand how the älf-woman had managed to return from the bottom of the ocean. _Ireheart sounded so convinced when he had spoken of her death._
But as Aiphatòn was all too aware, almost anything was possible when an Aklán was involved.
She and her brothers had led many älfar out of Phondrasôn and into Girdlegard, conquering mile after mile using cunning, magic and phenomenal combat skills, before he and his älfar invaded from the south. _She won't evade endingness a second time._
Aiphatòn's guilt was constantly on his mind, with every step he took, from the moment he woke up till the moment he fell asleep. And even in sleep it didn't spare him—the memories and images pursued him into his dreams: the vanquishing of Girdlegard, his merciless troops, the enslavement of the tribes, his title of the "emperor of the älfar" and the ruthless hunt for elves.
But with Tungdil's return came the realisation—no, the _awakening_ —that he had become the monster he had never wanted to be.
_What demonic frenzy did I succumb to, that I acted in the past as if I were depraved like my parents?_ Besides, he had once sworn to the dwarf never to become like that.
Evil dwelt in him and occasionally it was able to gain the upper hand.
_That must never happen again. Henceforth, no älf in Girdlegard can be allowed to live._ His own death was a foregone conclusion. His death, and before that, the death of every last älf.
The road climbed sharply upwards and was leading him towards a town with two guards standing in front of its gate, as he could make out after a few bends in the path. Carts rattled along ahead of him carrying barrels and wooden beams.
To avoid drawing attention to himself, he hid in the shadow of the rock face. And there, in some dried lichen close to the edge of the path, he saw half a horseshoe print that matched the night-mares' shoes.
_They rode along here._ Aiphatòn looked at the unfamiliar town.
He dismissed the idea that the group surrounding Firûsha had dispersed. They hadn't separated before now, why would they start now?
_Is this ordinary town their destination? What could be of interest to the triplets there?_
He couldn't let anybody notice his arrival; he wanted to avoid a commotion. He could forget disguising himself as a beggar in rags—the perpetually black eyes that he had inherited as a shintoìt and his slightly pointy ears gave him away as an älf. The news of his arrival would spread swiftly and reach Firûsha and then the element of surprise would be lost.
_But I could get inside if I was in one of the barrels._ Aiphatòn took the spear off his shoulder and silently caught up to the nearest cart, jumped onto the loading area and crouched down to check what was inside the containers.
From the bung holes on the tops and sides it was clear that a liquid was inside, and judging by the faint smell, it was wine.
He quickly tapped the side opening of one barrel and let a considerable amount of liquid run out. The pale wine flowed onto the street behind the wagon, the splashing sound lost in the creaking and clattering of the wheels. He stopped up the hole with dirt and resin he had scraped from the slats of the carriage.
Aiphatòn hid his spear underneath one of the rolled-up tarpaulins, hoping that would be enough to escape the guards' notice. _Otherwise I'll draw a lot of attention when I invade the town._
It took some skill for him to get the top open so that he could ease himself into the fermented grape juice and pull the lid back over the opening.
He didn't find the wine's aroma all that pleasant, and with every pebble the cart jolted over, the swill sloshed over his face and bald head. He refrained from taking a mouthful of it.
Aiphatòn couldn't help grinning. _No doubt Ireheart would have lapped it up until he could stand up in it without drowning_.
The wagon jolted onwards before slowing and coming to a stop. It seemed they had reached the gate.
"I'm bringing the wine for the mayor," he heard the cart-driver's voice, muffled by the wood.
"We know that. We've been notified about you," came the bored reply. "You can..."
"Hey, what's this here? One of these barrels is leaking," a second guard interrupted him, his voice coming from the rear of the cart and therefore very close to Aiphatòn. "The side bunghole doesn't seem to have been sealed properly."
The driver cursed. "They'll take that out of my wages. And I told them they should check the stoppers. That bloody jolting!" Judging by the rumblings that ensued, the driver was preparing to climb up onto the loading area.
"Get going, you old sod," the other guard ordered him, laughing. "You're blocking the gate on us and I can see the extra-long wagon with the timber down there."
Something scratched at Aiphatòn's barrel, followed by a firm smack. "There, the cork fits nice and snug," called the guard. "This way, at least you'll get as far as the mayor's wine cellar without losing any more."
Aiphatòn exhaled as the cart rolled on.
It would have been easy for him to leap out of his hiding place, overpower the watchmen and violently force his way into the town, but he would rather be discreet. If the Aklán and her entourage were still here, he wanted to ambush them.
_I have no idea what this town is called._ He hadn't spotted any signposts along the way. It was either insignificant and small or so big that everyone knew how to get there. _In any case, the boss likes wine. A lot of wine._
It was a long time before the wagon stopped again.
Then the driver ran around the loading area, murmured something, hummed a song and hit the sides of the barrels, probably with a hammer, so that he could tell from the sound whether he had lost any more grape juice. His checks complete, he jumped down off the cart and called out that the delivery for the mayor had arrived.
There was silence.
Aiphatòn pressed cautiously against the lid—and nothing happened.
Just as he was starting to assume the wood had become stuck, he heard a soft laugh outside.
"We know you're in there," he heard a man's voice. "You're surrounded by my best crossbow archers."
Aiphatòn summoned up his magic powers, but waited.
"My name is Kerjan Münzler and I'm the mayor of Güldenwand." He heard the man again. "In the name of the Dsôn Aklán, I'm arresting you, Aiphatòn, self-proclaimed emperor of the älfar. If you don't come out, the bolts will penetrate through the wood. We can shoot you dead even in your hiding place."
_This just gets better and better._ He toyed with the thought of tasting some of the wine after all. "In case you didn't hear," he answered loudly, "the triplets' reign is over. Girdlegard is making every effort to defend itself from them. You no longer have to prove any loyalty to Firûsha, unless she's standing next to you with a sword."
"She's not. And she has informed us about the uprisings against the Dsôn Aklán," replied the mayor. "But Güldenwand remains loyal to the triplets. My family swore loyalty to Firûsha once and I am abiding by that oath. We owe her too much to abandon her now."
_Ah. Well, well, well. That explains them making their way to Güldenwand. A safe area._ Aiphatòn took some deep breaths and had to suppress a cough. The fumes from the wine were tickling his throat and making him feel slightly light-headed. _Firûsha is, or was, here: so I can learn more from Münzler._ But first Aiphatòn needed to get out of the barrel. _I'll act submissive and lull him into a false sense of security._ "Can I come out?"
"Yes. But if you look for your spear, you're not going to find it. _I_ have it." Kerjan laughed. "Come on, get out so that we can put you in chains."
Aiphatòn thumped the barrel walls to his left and right at the same time and it broke open; the rings hit the loading area with a rattle and the pale wine slopped out of the cart and onto the ground.
"Here I am." Slowly, he stood up and looked around.
The cart-driver had brought the wagon into a huge barn that could withstand the heavy mountain storms and protected everything stored inside. A vaulted ceiling stretched over the älf's head as well as some rafters with hooks, ropes and pulleys dangling from them. The windows were too small to escape through.
Just as Münzler had claimed, the men stood in a circle around the cart. Aiphatòn counted a dozen archers and two dozen armoured guards armed with spears, shields and swords. The pairs of eyes looking up at him from behind their helmets were mostly extremely alert, although some also looked anxious. It was clear they were afraid of what he was going to do next. He spotted some grain scattered in the corners. So the barn was mainly used as a granary.
He recognised the mayor straight away. The brown-haired man stood out with his sumptuous clothes, his ostentatious wealth resplendent on his fingers and around his neck. He had commissioned rings and necklaces in every kind of precious metal in existence.
Aiphatòn's lip curled. _He must weigh ten pounds less without his jewellery._ "I surrender."
Münzler, who couldn't have been all that old, laughed as he brandished the iron chains and shackles in his right hand; in his left hand he was holding the rune spear which looked hopelessly incongruous in his fingers. "That's more sensible than the Aklán predicted. She warned us you would double-cross us." He threw the chains to one of the guards. "Put them on him."
The man caught the metal shackles and walked slowly towards the älf.
"What's going to happen to me?" Aiphatòn remained calm and jumped down off the wagon, landing right in front of the armed guard who flinched and tentatively lifted the handcuffs to put them on the prisoner.
Münzler stroked the forlorn, thin, dark beard on his chin. "The Aklán wants us to detain you here and keep you in our dungeon until she and her brothers secure peace. The rumour is that the älfar from the south have been wiped out. Or rather: that you poisoned them, you traitor." He ran one finger along the shaft of the spear, pressing a fingernail into the runes. "Your fate is to be decided later, although I would be more than happy to execute you on the spot."
"All right," Aiphatòn held his fists out to the guard in resignation. "Where was the Aklán headed?"
Münzler laughed, a gold molar glinting. "That's not your concern. You're going to stew in our jail and wait." He scrutinised the confiscated weapon. "I like this spear. The runes are exquisitely crafted and... Is it made entirely of metal? It seems very light to me if so."
"It's the same alloy my plates of armour are made from," the älf explained calmly. "It could be mistaken for tionium but it's more than that."
The soldier placed the iron rings around the prisoner's wrists and realised they didn't fit securely. "His arms are too thin, sir," he informed the mayor, out of his depth. "He could just take his hands out." He slid the pointless handcuffs off to demonstrate.
Münzler sent one of the guards to get chains and padlocks to tie the prisoner up with. He gripped the spear and lifted it up, examining the shaft. "An alloy harder than steel?"
Aiphatòn nodded. "You've acquired a one-of-a-kind trophy there."
The mayor tried to swing and twirl the weapon, then did a playful stab in the älf's direction, his ostentatious necklaces jangling. It looked very clumsy. Münzler obviously did not often find himself in the embarrassing position of using a weapon himself.
The älf suppressed a laugh and looked at the soldier who was still standing hesitantly in front of him with the handcuffs, unsure what to do.
"It feels very well balanced," Münzler said, claiming to appreciate the mastery of the spear and put the blunt end back on the ground.
Aiphatòn decided to turn the tables. He had hoped that the mayor would blab, but he didn't seem willing to share any more information about Firûsha. _At least not voluntarily._ "And another thing I don't want to keep from you," he began. "You can make the runes light up."
"Because of that alloy you talked about?" Münzler peered at the weapon. "Do you have to leave the spear in the sun for that, so that it stores up its power?" He looked thoughtfully at Aiphatòn. "No, with you people I'm sure it's the moon that makes the runes light up. Am I right?"
"It's magic, actually." Aiphatòn made a small gesture and leaped vertically upwards as quick as a flash, hiding among the rafters from the impending crossbow bolts; cries of surprise came from his captors' mouths. At the same time, he stretched his hand out.
The symbols on the shaft and the blade gleamed and the spear slipped out of Münzler's fingers to fly to its true master. As it did so, the weapon ran through the guardsman who was meant to put the shackles on the älf and snatched him up into the air with it. The handcuffs fell to the ground with a clanking sound as the archers finally recovered from their stupor and shot at the escapee.
The thick metal tips studded their own man all over, but his screams of pain stopped abruptly.
Aiphatòn twisted the spear shaft, making the corpse slide off. It fell down and hit the loading area and the wine barrels with a bang.
He jumped down after it into the midst of the guards while the crossbows weren't yet ready with fresh rounds. The archers died first, killed by swift stabs and slashes.
Then the älf threw himself at the guards who attacked him with their swords. But they couldn't find a way to hurt an enemy who wouldn't keep still: he ducked, dodged and jumped relentlessly, whipping around, launching himself off bystanders' shields to wield his bloody spear with double the force.
_You've had so much time to study my people's tactics and you've learned nothing._ Aiphatòn didn't even need his magic, or darkness or fear, to hold his own against a superior force that just surrendered. _Nothing at all._ With one blow from the blunt end to the neck, he floored the last of the soldiers, who fell face first into a pool of blood.
Münzler was already at the exit about to escape.
"Wait." Aiphatòn hurled the spear after the man. "I have another question for you."
The blade penetrated his forearm and nailed the mayor firmly to the door. Shrieking, he tried to pull the blade out, but it was stuck fast in the wood. "There was nothing I could do," he whimpered, tears in his eyes.
Aiphatòn went over and fixed his black eyes on him. For the man, it must have been like being observed by pitch-black precious stones shimmering weakly in the light. "What exactly does your family owe the Aklán?" he asked quietly.
" _What?_ That's what you want to know?" Münzler screamed at him and spat. He bit his lips until they bled. The pain must have been severe, the spear had definitely gone through the bone. "Is that..."
"I'm trying to understand why you are _so_ grateful that you would willingly rush towards death for her. Because of gold maybe?" Aiphatòn interrupted softly. "Were you really so stupid as to think that you and your guards would arrest me?"
Münzler gulped and looked away from him, staring blankly at his arm where the expensive fabric was turning red as it became drenched in his blood. "The Aklán told us you had as good as lost your power," he whispered. "My ancestors... she made one of my forefathers on the council into the mayor and since then our family has..."
"So you'd give up your life for a job?" Aiphatòn ran a hand over the jewellery around the man's neck. " _And_ for wealth." He pointed one outstretched finger of his armoured right hand at the dead guards. "They died for you. For a fool."
"Please, I... I can tell you where she was headed." Münzler seemed to have grasped, despite the pain and shock, that the situation had changed and that he depended on the emperor's mercy. "She wants to go up to the Jagged Crown."
"And she told you that?"
"No. But I'd bet my life on it."
"Which is in my hands anyway," the älf added, laughing. "What is the Jagged Crown?"
"A mountain half a mile to the north of Güldenwand," spluttered the brown-haired man, his face contorting in pain. His blood was trickling gently out of the fabric and splashing onto the floor. "Apparently the Aklán sent a troop of her best veterans up there many cycles ago. But they never came back."
"How long ago might that have been?"
"Around... two hundred cycles ago," he stammered.
"What's up there?"
Münzler was breathing faster, the colour visibly draining from his face. It wouldn't be much longer till he lost consciousness. "I don't know. But there's a persistent rumour that there was a passage. Out of Girdlegard." He slumped, but was kept upright by the spear which made him gasp out.
_She wants_ _to flee and leave her brothers behind?_ Aiphatòn couldn't believe this outrageous theory. "A mountain pass?"
"I don't know!"
_No. There must be something else more valuable to the Aklán up there. An artefact perhaps? Brought from the depths of Phondrasôn and too unpredictable to use under normal circumstances. Just like the demon who helped Sinthoras and Caphalor in the conquest some time ago._ Aiphatòn needed certainty. "How do I get there?"
In just a few whispered words Münzler described where the way up to the path was located. "But you'll never manage it. The Aklán won't either," he groaned. "Nobody comes back."
Aiphatòn placed a hand against the spear and the runes lit up, then he pulled the blade out of the wood and flesh as easily as if it had been stuck in butter. The mayor fell at his feet. "Then Girdlegard can consider itself lucky that the Aklán and I will both go missing there." He gave the man a disgusted look. "You, on the other hand, will not get anything out of it." Aiphatòn raised his foot and kicked.
The outer edge of the braced sole hit Münzler in the back of the neck and cracked the vertebrae in half.
_Nobody who supports the älfar should remain alive. People like you enabled them to wield their power._ Aiphatòn took two cloaks from the dead guards and threw them round his shoulders, then grabbed himself a pair of boots before leaving the stone barn by a side door.
More soldiers approached him, but nobody stopped him because he was wearing the guards' cloaks and masking his real build from view. Besides, because of his dip in the barrel, he stank of wine like a terrible drunkard. Nobody suspected he was an älf, let alone the former emperor, underneath.
Aiphatòn wanted to stay in the town long enough to steal all the equipment he'd need for the climb, and then he wanted to hunt down the Aklán.
He was sure Münzler had not lied to him and Firûsha really had ridden up into the mountains. _But what is she looking for up there?_
# Chapter II
_It is better to feign ignorance than to announce dangerous knowledge._
Wise saying of the Älfar
Collected by Carmondai, master of word and image
Ishím Voróo, Älfar town of Dsôn Dâkiòn, 5452nd division of unendingness (6491st solar cycle), early summer
Irïanora stepped onto the north tower's wraparound observation deck. Three paces wide, it ran around the upper third of the outer wall like a horizontal collar. It was the second highest point of a town built entirely on a wide mountain in the middle of a rolling plain. _What an awful summer. Not even a breath of air here._
The pale clouds looked like they were glued to the sky, not budging an inch. The building that towered up behind the young älf-woman did cast some shade but there was no escape from the stifling heat. Even though she had thrown on just a thin, blue linen dress, sweat was running down her slim body.
An älf with short red hair was standing with his back to her, using the gap between two battlements as a table and spreading a map out on it. His pale torso was bare—he was wearing nothing but knee breeches and wide, flat, leather shoes. More scrolls peeked out of his shoulder bag.
_The great Bethòras. Punctual and exemplary._ Irïanora smoothed her long blonde hair back and approached him. "Sorry I'm late, but my uncle wanted to discuss a few pressing matters."
He nodded before turning around. "I was enjoying the view and I took the opportunity to check the accuracy of the map."
They gave each other a lingering hug in greeting.
Irïanora noticed his fresh aftershave and took a deep breath in to smell as much of it as possible. She saw compasses, a ruler and optical instruments lying on top of the drawing. Next to that lay a coal-dust pencil and a sheet of paper with notes all over it. "Revisions need to be made?" She let him go.
Bethòras smiled. "Nothing major. A few trees were added and the riverbed over there"—he lifted his arm to point towards it—"extended eastwards. If we were to rely on judging by eye, we would be no better than the barbarians and monsters and, like them, we'd be surprised when something got trapped or stuck."
"My uncle knows why he made you the master architect and cartographer." Irïanora looked around to check if they were still alone.
"Nobody was following me," the älf said, taking a folded drawing out of his pocket, opening it up and placing it on top of the map of the town's surrounding areas.
They didn't waste any time admiring the beauty of Dâkiòn, which they were very familiar with.
It became clear to newcomers that the town had already existed in a different form before the älfar arrived, but it had been derelict and unfinished. It was built on a mountain, but a ravine separated the upper and lower parts of the town—there was just one wide stonework bridge stretching across it. Nobody knew whether the original builders had created the chasm on purpose to protect the upper town more easily in case of attack; the footbridge could simply be demolished.
Legend had it the original inhabitants and architects were enormous creatures. This was evident from the fact that the floor plans of all the houses, palaces, streets and other buildings looked four times too big. The average home had ceilings twelve paces high or more, and the sovereign's palace looked as if it had been constructed so that giants could do gymnastics in it.
The älfar had completed the buildings, all of which were made of black stone, and added elaborate extensions to the massive structures; they had decorated them with the artistic attributes of their tribe, from bone carvings to specific types of stone, ornaments, precious gems, paintings and runes.
Its scale gave the town its epithet: the Majestic. The roofs, the towers, the supporting arches and pillars reached far into the sky, making it clear that it was unconquerable. There was only one footbridge to the upper town. Nobody in their right mind would dare to attack—but there was a legend that some day, the giants would return at dawn to demand their town back.
The two young älfar had other demands on their minds: preparations for war.
Bethòras pointed to the lines that represented a ship, with details of the length, width, draught, mast height and much more. "I made a start on a little draft."
Irïanora pored over the blueprint, her heart beating loudly in her chest with excitement and joy. "How many warriors can that take?"
"It depends what equipment they're carrying," said Bethòras, avoiding the question. "In the light armour that I recommend for this kind of mission, it would be around fifty. On top of that, there would be smaller catapults on deck and the necessary cargo, as well as the crew." He pointed at the corresponding parts on the sketch each time he explained something.
Her brow furrowed. "How much time and money would it take?"
"As soon as we have the wood, it will take sixty moments. Our carpenters are good enough and quick enough to implement the plans I give them." Bethòras pointed to the wide river two miles away that flowed past the town. "There are two spots where the shipyard could be built without having to clear soil away. I've studied the frekoriers' sketches which had exact descriptions of how..."
"Aren't we having some wonderful weather today?" came the sound of a cheery old voice from the doorway. "But I do hope a storm will relieve us of this mugginess. You barely take a step or two and your clothes are soaked through with sweat."
Irïanora and Bethòras did not turn around straight away because they knew who had come to pay them a visit, unasked and unannounced.
"Not a word," the blonde älf-woman whispered to the cartographer and picked up the drawing of the boat, folding it with calm but swift movements and sticking it underneath her dress. In the space of a heartbeat, she had plastered a winning smile on her face. "Uncle," she said loudly and turned round to him.
"Are you enjoying the view?" Shôtoràs walked towards them, his right hand leaning on a walking stick made from silver, tionium and bone inlay. He was the sovereign of Dsôn Dâkiòn and undoubtedly the oldest älf living in Ishím Voróo.
There was a distinct clack every time the end of his stick touched the stone flags, as if the älf was trying to awaken something living in the ground beneath their feet.
Like most älfar, he wore a black robe wrapped around his broadly built body. His right leg dragged slightly, as it had done ever since blood poisoning had nearly cost him his limb. In terms of physical strength, he was still a match for every warrior in the town's army, but as Irïanora knew, he was not as quick as he once was.
His most powerful weapon, which he knew how to deploy so well, was his mind. And that was the very thing she feared.
"Not only are we enjoying the view, we're working. I asked him to check the map of the surrounding area," she lied and gave a small bow. Bethòras followed suit.
"What did you find out?" Shôtoràs had reached them and was smoothing back the thick, light grey hair that reached the nape of his neck. A thin beard glinted around his chin.
"There were minor details to be corrected," the young älf explained, clearing his throat. He turned to the side, revealing the papers; he briefly outlined what had been going on two miles from the mountain.
"Trees. How they grow and stretch upwards," mused Shôtoràs and looked over at the river Tronjor, "as if there was something for them to capture or prop up in the clouds." He smiled contentedly. "Wasn't it lucky our Creating Spirit brought us to this place?"
" _You_ brought the survivors here, Uncle," Irïanora corrected him kindly. "And for that, Dsôn Dâkiòn owes you its thanks above and beyond death."
The sovereign burst out laughing. "My _mortality_. How little I think of it. And yet I probably should. I've been alive for so many divisions of unendingness." His expression grew more solemn, his gaze pensive. "How painful it was for me to see Dsôn Faïmon fall. And how much it hurt to lose so many of my tribe's little towns to the barbarians and monsters after we thought we were safe from the nomadic towers. And why did we lose? Because we didn't have unity."
_Not again._ Irïanora knew what was about to come next: a discourse on what had been experienced and endured, which she herself knew only from stories. The banishment by the Dorón Ashont; the lengthy trials and tribulations through Ishím Voróo; how the numbers of älfar kept dwindling and finally Shôtoràs had led a small band far into the north to settle on this mountain in the enormous ruins of the fortress and consolidate a realm of their own. _He's_ _too old._
Shôtoràs stamped his stick on the ground, making a banging and rattling sound all at once. "From the black ruins, left for us by long-departed giants, we created our new homeland, entirely free of the Inextinguishables. Now we live undisturbed and safe. Because we are of _one_ mind, united. The other town states remained susceptible to attacks by the beasts because of their own disputes." He laughed bitterly. "Wars between the älfar. _Wars!_ Just imagine it, the chaotic and horrible times we used to live in."
Irïanora groaned with boredom. "We know about the sensitivities and long-standing hostilities between the families and their political opponents," she said with a long-suffering undertone. "Uncle, you've told me so many stories about..."
"Only two towns survived that chaotic bloodbath. Us—Dsôn Dâkiòn, the Majestic—and Dsôn Elhàtor, the Magnificent," the old älf went on, ignoring her objection.
Bethòras leaned against a battlement, listening to the sovereign's remarks out of politeness.
"Neither of these towns has ever been conquered. Although I don't trust Modôia and her son, I do respect her," Shôtoràs was speaking to himself. "Despite her young age and the fact that she comes from Tark Draan."
"People say she's from Dsôn Sòmran, actually, which was once located in the Grey Mountains," Irïanora interjected and dropped her smile. He had interrupted their meeting to babble away, because he clearly felt lonely in his palace. _An incredible test of patience._
"Apologies." Shôtoràs finally seemed to notice that he was boring them with his monologues. He lifted his stick and tapped the handle, which was modelled on a bird of prey's beak, against his bearded chin. "How did I get onto that?"
"The trees," said Bethòras, eagerly coming to his aid.
"Ah yes. The trees." The grey-haired sovereign sighed. "That reminds me of life in the old Dsôn, when I was still a member of the Constellations—one of the älfar with power over the Inextinguishables—" he told the red-haired cartographer as if he needed to explain it to him, "who were against expanding the kingdom. Unlike the Comets." He turned his black eyes to the treetops. "Now that I really think about it, we could equally have called ourselves _Trees_ : with deep roots, powerful and strong, braving and surviving the storm in order to preserve the land where we were born."
Irïanora gave a slight but deliberate cough. The heat and twaddle were making her impatient and assertive. "Uncle, don't be cross with me, but Bethòras and I would like to continue our walk and check the map."
Shôtoràs clucked his tongue. "Of course. I've started telling stories yet again." He turned on his heel; as he did so, the hem of his billowing robe caused a slight draught, enough to lift up the map.
The thin paper slipped off the stone and threatened to glide into the abyss.
"Watch out!" Bethòras rushed forward and reached for a corner of the drawing to stop it sailing down into Dsôn Dâkiòn's streets where he'd have to painstakingly search for it.
Meanwhile Shôtoràs continued pivoting on the spot. The curved handle of his stick hit the young älf out of nowhere between his bare shoulder blades, shoving him over the wall with some force. As Bethòras disappeared, screaming, into the abyss, the metallic beak swooped down and pinned the map to the spot.
"Take it," he commanded Irïanora harshly. She was staring at him in horror.
"You... you've..." Trembling with fear and fury, she took the paper out of harm's way.
Shôtoràs used the handle to thrust directly into the fold of her blue dress where she had hidden the drawing of the ship. The sharp, curved beak made of tionium pierced the paper and scratched her skin. One jerk and the sovereign had got his hands on it. He ignored the gash in the älf-woman's skin and the tear in her robe.
_Bastard!_ Irïanora took a breath in, the scratch burning. She was familiar with that cold expression on her uncle's face so she remained silent as a precaution.
The first distant screams of the älfar who had discovered Bethòras' body dashed to pieces in the street rang through the quiet air.
"Unity," repeated Shôtoràs and held up the folded drawing to underscore his words, her blood spattered on it. "That goes for our town too. I cannot tolerate my own niece pursuing plans that run counter to what I consider right and what is necessary for our survival."
"I just wanted to build a boat to travel along the Tronjor and..." Her voice quivered and she balled her hands into fists.
"You," he interrupted, hissing at her, "would like to build a _fleet_ to travel down the river and the coast as far as Elhàtor and attack the island."
"It's just a small _ship_ ," she protested.
"It's a _start_ ," Shôtoràs snapped at her. "A start that will end in war and lead to the downfall of both towns. Look around you: what happened to the other settlements? They quarrelled with each other and fell. Do you think"—he took a limping stride towards her—"that I can allow that?"
"And what if I had a plan to bring Modôia and her followers to their knees?" Irïanora jutted her chin out.
"You haven't got a plan. If you're alluding to your childish attempts to incite the onwú and other maritime tribes against Elhàtor, I'm telling you now: let it go, niece."
"Think of the power we'd have if Elhàtor was under tribute to us. Their fleet is undefeated and unrivalled." She gulped, excited. "And we could finally have our revenge for Modôia enticing so many of our residents away from us... on the way to the sea when she..."
As quick as a flash, Shôtoràs grasped his stick and hit her hard in the side so that she crumpled with a cry of pain and slid down the wall to the ground. "Don't you dare try it again," he threatened her. "Next time, I'll hit you with the beak. Two towns, bound by respect and cautious regard. There will be nothing more than that."
He tore the sketch of the ship into tiny scraps in front of her and threw them over the wall. The little pieces spread like snow and spun away, scattering as they flew through the air and seeming to melt like flakes in the heat.
"There, they're following their creator. Now I'm going to find a new cartographer. This one wasn't as careful about integrity as his job required." The sovereign limped back to the doorway and disappeared through it. "Anyone who succumbs to your way of thinking will suffer the endingness," his voice echoed hollowly from the tower.
_Miserable, old, repulsive_... Irïanora breathed in and out several times then let out a short, piercing cry filled with her fury, her sense of powerlessness and her disappointment. The anger lines flashed across her face, her skin warmed up and an ache masked the pain in her side for two or three heartbeats.
Finally she got up, groaning, and looked down over the battlements.
A hundred paces away she saw Bethòras' mangled body lying on the street between the black stone houses, älfar crowding around it. The unmistakeable red stains and smears on two roofs told her that the cartographer had hit their sturdy surfaces during his fall, before his body ended up on the road. _A hideous death. And undeserved._
Two watchmen hurried over and attended to the fallen man. One man raised his head and looked up at the tower.
Irïanora automatically drew back.
They couldn't have recognised her. Besides, the sovereign would attest that it was an accident caused by carelessness while they were checking the maps.
_I must never underestimate him again._ The young älf-woman walked over to the steps that led down from the tower. She didn't use the lift, even though it was quicker. She wanted—or rather, needed—to stretch her legs.
As Irïanora hurried down step after step, her defiance returned: she would send a boat down the river. _Or at least a handful of scouts, and then I'll get my war_ — _and it will end in Dâkiòn's triumph._
Her hands instinctively balled themselves into fists once more.
Yes, her uncle was old.
Very old.
And ready for endingness.
Then she would see what Dsôn Dâkiòn said about a war against Elhàtor.
Tark Draan, Älfar realm of Dsôn Bhará, formerly the elf realm Lesinteïl, 5452nd division of unendingness (6491st solar cycle), early summer
_... I assume, based on the aforementioned reasons, that the battle of T versus G took a different course than has been claimed and no shapeshifter was involved._ Carmondai put down the quill he had written these last lines with.
His back hurt but he was trying to ignore it. The aching in his finger joints was either from the chilly damp in his accommodation or the meagre rations he was allowed.
Carmondai read through his notes again in the greenish-yellow light from the phosphorescent moss. They contained his theories on the events that took place during the exile of the Dsôn Aklán. The duel that Tirîgon supposedly fought single-handedly against a shapeshifter was, in his telling, overflowing with discrepancies.
Carmondai did not believe everything the triplets had told him without doing his own research.
For that _very_ reason, he had been stuck in this spartan room—probably underneath the siblings' palace—for what felt like a hundred divisions of unendingness.
The aged älf with long, brown hair had experienced and endured a lot, from the thick of battle and the lightning-swift cûithones, to sea voyages, a long stay in Phondrasôn and dangerous journeys through Tark Draan during the period of the Inextinguishables.
Rarely had he found himself in the predicament of having to sit around waiting.
But on returning to Tark Draan with the triplets, fate had turned against him—or else Samusin was suddenly demanding a sacrifice in return for everything good that the älf had been granted: Carmondai had spent the last cycles, or more specifically, tenths of divisions of unendingness, under lock and key.
He constantly had to turn over the hourglass standing on his desk because it was the only means he had of telling whether it was night or day above ground.
He seemed to be ageing fast down here, as if radiation was hastening his physical decay. _I cannot remember my eyes ever burning or feeling tired before._
Treated kindly by the Aklán at first, they later arrested him because of the unrelenting, probing questions he was asking the northern älfar. They had him thrown into an almost forgotten, dusty room, with his books, writings, notes and sketches thrown in after him. The respect for his words was too great to just destroy them, but nobody was going to see them again.
_Obscurity—that is the fate in store for writers and writing._ Carmondai sighed and looked at the window he had painted for himself on the thinly plastered wall. _Even_ _Phondrasôn was nicer than this._ The motifs that looked like they were beyond the window pane were ones he sketched out on paper and changed according to his mood.
His eyes flitted over the old Dsôn Balsur that he had built for the Inextinguishables. He had committed every detail to paper, from the Bone Tower to the palaces and temples; at the bottom of the page stood Caphalor and his lover.
_That was so long ago._ Carmondai rubbed the back of his aching neck. _They're long dead, and I ought to be too._
He was supplied with rations, ink and paint, occasionally with clean clothes, but the Aklán did not allow him anything else. He was not allowed to see the sun or take little excursions under guard. He lived and wrote by the light of phosphorescent moss. The brown linen robes the guards left for him were cut simply; they scratched his skin and still had stains from their previous wearers that wouldn't wash out.
_I'm too old to starve in here._ Carmondai put aside his notes, which he had written in a secret language so that his thoughts could remain private for the time being. He really hoped his stories were still being recounted.
_They probably spread a rumour_ _that I had died._ He stood up and walked his usual route between his desk, door, wardrobe and bed, eight paces in between each one. _I won't give them the satisfaction._ His writing was stacked up on the shelves and new work was constantly being added.
Carmondai threw off his rough shirt because he was starting to sweat, then changed direction; after a few more laps, he did some quick jumps, press-ups and chin-ups. The warrior blood in him refused to lapse into complete physical inactivity. It also wouldn't accept the excuse of a cell or the occasional pain in his old joints.
He may not have had any weapons, but he used two long rulers to practise dagger combat for at least a splinter of unendingness every day. He wanted to be prepared for anything.
He wasn't going to contemplate escape until he could figure out how to take his writings with him, but he would defend himself if the Aklán ever made an attempt on his life.
_I used to be quicker._ Panting, he put the rulers away and wiped off his torso with a cloth, unable to help smiling as he looked down at his skin. _I've got wrinkly. The young älf-women gave me more pity than attention._ He looked at the washbowl with the near-empty carafe next to it. Food hadn't appeared for two turns of the hourglass either.
Carmondai went to the door and kicked it several times to draw attention to himself but there was no response. The slide on the little hatch stayed shut.
_Has the time come? Am I going to die of starvation and thirst?_ He took one look at the carafe and decided to save the rest of the water. He sat down at the table again and started to write. But his precarious situation was visibly troubling him.
_They'll hardly have forgotten me_ , Carmondai reflected.
The door couldn't be forced open, not even if he were to put the wooden shelves together and use them as a battering ram. There were three horizontal iron bars on the outside holding the door securely in place.
His minders had brought him here blindfolded, but he remembered the three hundred and eleven steps down. So he was underground, surrounded by solid rock. _Before I could dig my way out, I'd die of thirst._
Another idea occurred to him.
Carmondai looked at the blank pages. _That would be an option. But it's dangerous. Both for me and everything that I've created in this cell._
He got to his feet and picked up a pile of papers, went over to the closed door and tried to slide a page through the gap between the wood and the stone floor.
It worked.
_If the Aklán force my hand, I'm going to risk it._ Carmondai slid more pages underneath the door and tore additional sheets into tiny little scraps and piled them loosely on top until they formed a little mound; on top of this he crumbled his pencils made of compressed coal dust. Using a metal quill and a piece of stone he had broken off the wall, he struck sparks onto the thing until tendrils of smoke were curling upwards.
_Now then._ The älf blew carefully until little flames flared up and spread along the door.
The sheets of paper pushed halfway under the door caught fire and he hoped they would spread the blaze to the other side.
Carmondai kept adding paper, crumpling up blank pages and throwing them onto the gentle flames, then he smashed some shelves into wood splinters and put them on too, wedging them under the frame where possible.
_Come on!_ He couldn't help inhaling the smoke and it was making him cough. It was accumulating on the ceiling of his cell. It wouldn't be long till the älf suffocated.
The lower section of the door was turning black, smouldering and toying with the flames, but still the wood would not burn properly.
Carmondai fanned it, keeping an eye on the rising sparks so that fire wouldn't break out anywhere it wasn't useful to him.
Finally the little flames danced along the bottom edge of the door and slowly started to eat their way upwards.
Carmondai held a cloth over his nose and mouth and looked at the ceiling where the gathering smoke was gradually darkening. _I have my own storm cloud_ , the thought flashed across his mind, and he couldn't help smiling. _A flash of lightning would be genuinely helpful._
The fire climbed upwards, but as it did so, it gave off more smoke than he had expected. The älf had to lie on the floor to avoid the swirling blackness.
_Where exactly were the three iron bars positioned?_ Carmondai looked at the carafe then poured the remaining water into the bowl. He tipped in every non-flammable paint and ink he could find after it. He soaked his housecoat in the liquid, wrapped it around himself and took a run at the door.
After ten or eleven short, quick strides, he threw himself flat on the stone floor, sliding feet first.
The soles of his feet crashed into the blazing wood in the lower section of the door—and broke through it in a hail of sparks.
Carmondai had enough momentum to get into the hallway up to his chest, then he turned over and used his arms and feet to crawl commando-style backward out of the room.
His face was glowing and there was a smell of scorched hair, but he managed to get through the gap into the adjoining hallway.
_A fat orc would not have been capable of that._ Carmondai got to his feet and took a step away from the burning, crackling door.
The hallway was lit by oil lamps and the smoke was drifting through it in pale-coloured, grey streaks. Nobody came to check on the cause of the fire.
_What is going on here?_ Carmondai took his damp coat, which had stained his linen clothes a strange colour, and threw it at the flames, but they wouldn't go out. _I need water._ Hoping against hope, he hurried on.
He passed empty cells until he reached the passage to the guards' common room. Two chairs stood neatly at the empty table. The logbook was open, the names of every inmate crossed out without comment. _Apart from mine._
_They must have needed the imprisoned älfar_ , Carmondai speculated. _If they were merely killing them, they could just as easily have done it down here._
He went through a second door and up the three hundred and eleven steps and found himself in a second guards' room.
There were pieces of armour strewn about the floor as if they had been cast aside, and swords and daggers of various sizes lay on the tables.
_The other älfar were taken upstairs_ _and prepared for the battle_ , he deduced and to be on the safe side he slipped on some plain armour. Next, he wanted to bring the fire in front of his cell under control before everything inside was lost. _How desperate must they be if they're pardoning criminals and sending them into battle?_
To his right stood an orc-sized water amphora with a tap in it. Next to that were three buckets and he filled them with water one by one.
Carmondai was just about to hurry downstairs with them when he heard a quiet, steady rumbling like a prolonged rockfall in the distance.
Torn, he paused.
With some effort, he chose a sword and two wide daggers with bent-up crossguards before peering cautiously out the door. He had to make sure that he would not be in immediate danger while putting out the flames downstairs.
The palace's enormous reception hall, made of dark grey marble, stretched out in front of him, and there were white statues towering up on all sides covered in little tiles of white bone.
_Nobody in sight and not a sound to be heard._ Carmondai crossed the hall quickly and found himself in a high-ceilinged dark passage with walls covered in lengths of crimson fabric.
The constant rumbling and banging sounds could no longer be ignored. And they were coming from _inside_ the crater.
After walking the length of the corridor, he went out and stood in front of the huge building and looked down the mountain. He was in the open air a mile above ground and was briefly dazzled by the evening sun. A staircase stretched out in front of him leading downwards and at its foot was Dsôn Bhará—but it no longer looked the way he remembered.
The countless sculptures that used to line the streets and the squares in the black caldera no longer existed—and the majority of the elaborate buildings lay in ruins. More than two hundred houses had once been built, in black and white, with pointed and sloping roofs, some with straight walls, some plain or even adorned with little hexagonal towers.
Someone or something had violently torn them all down.
Catapults made of blackwood taken from the beams of the destroyed roofs rose up out of the rubble as well as from the landings on the staircase. The slingshots—at least a hundred paces high—and their ammunition were trained on the tower behind the palace.
Carmondai ducked his head as the shells shot almost vertically upwards and flew over him, hitting the towering building. _Not one defender in sight? The Aklán must have been defeated!_
He couldn't tell if the attackers were Aiphatòn and his southern älfar, or troops from Girdlegard or even another army entirely. He was too far away.
The round crater wall was about five miles away, but he could see that the edges were being tampered with, broken off to try and fill the three-mile deep hole with rubble. That was where the elf realm of Lesinteïl had once had its Moon Pond.
_That will take them cycles, if it's even possible in the first place._
A catapulted stone went astray and whirred on.
The impact, in the middle of one of the many landings on the staircase below where Carmondai was standing, pulverised one of the fountains—red water burbled up out of it. It was made of the same grey marble as the steps.
The shell bounced upwards, levelling the extraordinary polished stairs encrusted with crystals and diamonds. The cut jewels flew, glittering, through the air along with the red droplets. Finally, it rumbled on to the right and came to rest in the gushing blood-coloured stream.
The sound of a horn rang out from the catapults. Figures of different sizes were gathering among them and looking up the broad staircase at Carmondai. His appearance was clearly not unexpected.
_Those are groundlings_ , he gaped. _Groundlings and barbarians and..._ An armed woman who seemed to be dressed entirely in white towered over the rest of them. _An elf-woman?_
Even he, who was used to coming up with the most fitting of words, couldn't think of any way to describe his shock. In his busiest times as emperor of the älfar, Aiphatòn had savagely hunted down his sworn mortal enemy and wiped out the last of the tribe.
That's what everyone had believed.
_Either they had entered Girdlegard from outside or they were able to hide from the emperor and the Aklán._ Carmondai could scarcely believe it but at the same time he knew what it meant for him. _And thus_ _I've become game for a hate-filled huntress._
Fittingly for what he was thinking, the fair-haired elf-woman and some soldiers swung themselves onto their horses and rode up the steps.
Carmondai slowly shrank back, but didn't know where to flee. The only thing on the whole two-mile wide mountain was the oblong palace made from dark grey marble.
He turned round and looked up at the large tower that rose hundreds of paces in the air behind the palace. The awning wires that had stretched taut from the top of it across the town as far as the edge of the crater were nowhere to be seen. The destruction of Dsôn Bhará was well underway. _Only idiots would flee up there._
The black glass dome that had once arched over the centre of the palace had been destroyed by a boulder.
Carmondai's gaze flitted over the marble façade—all kinds of skeletons had been affixed to the walls. _No barbarians, elves or groundlings will have any sense of the beauty in that._ Or the beauty of the bone-segment-adorned portal, the rounded fronts of skulls belonging to all the races and monsters of Girdlegard jutting through the gaps. _All the races apart from älfar._ He looked over his shoulder at the long staircase; the enemy was still climbing up it towards him. _They'd probably like to stick my head up there too._
The catapults kept on firing, not letting up. The stones in the lower section of the tower and the palace were cracking. Something that had taken countless slaves four divisions of unendingness to create, and which they had given their lives to, was gone in no time, turning into ruins and threatening to vanish.
Carmondai weighed up his remaining options.
He could forget about a battle; he would be no match for the stronger side. Fleeing into the tower, which was being shaken by renewed rounds, or into the dungeons, didn't make any sense.
_I ought to get out of the crater and fight my way to... probably to Ishím Voróo._ The thought of the writings he had to leave behind was unspeakably painful to him. _How can I save them? I can hardly take them with me._
The elf-woman and the soldiers had covered two-thirds of the distance. They stopped and went the last few paces on foot; they left their steeds on the landing of the staircase.
_I need a horse. With a horse I'd have a slim chance of getting away._
"Hey, you cowards!" Carmondai brandished his sword at the attackers. "I'm going to nail your skulls to the wall where you belong." He burst into peals of laughter and ran back to the palace. _That should provoke them into chasing me as fast as they can._
A heavy shell crashed into the façade, crushing numerous bones into a fine powder that fell to the ground along with the marble that was blasted off.
He hurried inside the building through the haze of white dust. Cracks had formed all over the walls and they reminded him of anger lines. They looked like they were revealing their hatred of intruders before they shattered and crumbled.
After going down the dark corridor, he turned off into the reception hall and hid behind a statue to let his pursuers pass by; he threw one of his daggers across the room so that it landed in front of a door to lay a fake trail.
He silently congratulated himself on keeping physically fit in the dungeon. He didn't have the heart for battle, so escaping the enemy—who had every right to try and kill an älf—would be a question of speed.
The soldiers ran through the corridor as though out of their minds, before stopping and standing indecisively in the hall—until one of them spotted the dagger and the troop raced off towards it. In the blink of an eye, they dashed through the doorway and disappeared.
_They must all have been barbarians._ Carmondai waited impatiently.
The elf-woman didn't appear.
Shell after shell rained down on the palace, the first clouds of dust wafting into the hall now too. Sections of the ceiling panels came loose from their fixtures and the slabs of bone smashed onto the marble. The missiles had blown the roof off, wreaking more and more havoc every time they struck.
Carmondai didn't want to wait any longer; it was getting dangerous inside and the soldiers were sure to come back soon. He darted off down the corridor, sword and dagger ready to defend himself. He tried to stop thinking about the books he'd had to abandon.
He ran outside, ducking as he sprinted across the small forecourt and down the steps. The elf-woman had obviously taken a different turning in the palace; she was nowhere to be seen.
The horses were on the landing, waiting patiently for their riders to come back. The troops on the ground didn't see the älf as they continued the constant reloading and firing of the catapults.
Carmondai reached the animals and approached the elf-woman's chestnut horse, who lifted his head and snorted suspiciously. "Easy, I'm not going to hurt you," he soothed the animal.
"But I will hurt you." The white-armoured woman emerged from behind the fountain. She was pointing two long swords at him. "I thought you'd run away," she said with satisfaction, her gaze taking in his spotless blades. Her voice was laced with a slight elven lilt which lent even the common language of Tark Draan a certain melodiousness. "The soldiers are still alive?"
"I didn't lay a finger on them." Carmondai's thoughts were racing. "What has happened in Dsôn Bhará and what happened to the triplets?"
The elf-woman raised her delicate eyebrows. "What do you mean by asking such an absurd question?"
Carmondai listened out for potential footsteps ringing out behind him, alerting him to the arrival of the warriors who'd been led astray. "I was a prisoner. I've been locked in a dungeon underneath the palace for many orbits. I escaped and..."
The elf-woman laughed as the sun bounced off her white palandium armour. "A pretty story to wash your hands of any responsibility." She swung the swords. "But there are no innocent älfar!" She stabbed the sword in her right hand forward and slashed horizontally from right to left at head height. "You are the spawn of the devil!"
Carmondai parried the high strike with his dagger, catching the enemy sword in the massive crossguard; he dodged her stab with a swift turn of his body, then rammed his elbows at the elf-woman's face. But his opponent ducked and headbutted him with her helmet.
_I used to be much quicker._ Stars flashed before Carmondai's eyes and blood spurted out of the cut on his forehead so that he couldn't see anything.
Blinded, he staggered backwards into the agitated, snorting horse, wresting one of the elf-woman's swords away from her with his dagger by chance; it clattered to the ground. Using quick, short slashes, without being able to see his opponent, he kept her attacks at bay and rubbed at his face with his upper arm so that he could see again.
Then he was flung backwards by a remarkably powerful kick to his middle.
He tried to regain his balance but failed and tumbled down the stairs.
The armour protected him from broken ribs but Carmondai was forced to let go of his weapon to make sure he didn't injure himself with it. With every somersault, he wondered again how many steps the stairs had.
When he finally came to a stop, he could feel the tip of the sword at his throat before he could even move. Dizziness raged through his head, and his right arm and leg were throbbing alarmingly like they were broken.
"You are one of the last älfar in Girdlegard. Anyone who escapes me and my fellow warriors will be hunted by the dwarves," he heard the elf-woman's voice. "To put it in your own terms: your death is called Fiëa."
Carmondai was too dazed to sweep the sword aside with a desperate shove at the broad edge, particularly as the blade had already penetrated the skin. _At least I'm not dying in the dungeon, I'm dying in the open air_ , he thought cynically.
"Stop!" came the sound of a loud cry from a powerful, throaty voice.
The point dug deeper into his throat.
"Why?" the elf-woman called back, perplexed. "He's an älf, the..."
" _That_ is Carmondai," the man interrupted her. "The writer who penned all those stories." Heavy, brisk steps were approaching from above him.
"Ah, the one who celebrated the supposedly heroic feats of his people," Fiëa retorted scornfully. "Then it will give me great pleasure to chop off his hands before I behead him."
Carmondai's dizziness was subsiding, the spinning world coming to a stop.
The elf-woman was standing over him, the sword pressed underneath his chin.
"Just wait, I'm telling you!" A smaller figure appeared next to her. Its body was encased in black leather armour fortified with tionium plates, but the runes had been scratched off them. A skirt-like garment made of little tiles of blackened iron covered the legs, and a black leather close helmet decorated with numerous rivets and silver wire hid the head.
Gloved fingers pushed up the visor and a blackened face with a cropped beard came into view. "Yes," said the dwarf, nodding. "That's Carmondai."
The älf was not yet sure if it was a good thing to have been recognised. It was possible someone might enjoy torturing him even more than they would a normal warrior.
Judging by the groundling's appearance, he was a zhadár, one of the Invisibles who formed an elite unit from the ranks of the Thirdlings. Transformed by Sisaroth's potions and trained in älfar magic, they were a powerful weapon against the triplets' enemies.
_They've switched sides._ Carmondai slowly raised his painful arms.
"So what?" Fiëa shot back. "What reason could there be to spare his life?"
"We could force him to write down _our_ history this time. How _we_ hunted the älfar and what atrocities _they_ carried out and that kind of thing." He placed his left hand on the hilt of his sword-like weapon. The lower part of it was wide to parry powerful blows but the upper part was shaped into a long thin point so that it could penetrate through gaps in armour. "The victors determine what will be written from this point onwards. And he is good. I read a lot of his stuff before he vanished all of a sudden."
"I was the triplets' prisoner," Carmondai said. "You'll have found my cell." He remembered the fire, which was surely still raging. "Would it be possible to save my writing, the papers I wrote while I was locked up?"
Fiëa upped the pressure and Carmondai's face distorted in pain. "And he thinks he's going to be spared."
"At least until he's done some writing." The groundling scrutinised him. "Think about it: he's very useful, Fiëa. He was there when Dsôn Balsur began and knows many of the Akláns' secrets."
"Well then, we should interrogate him."
Carmondai could already see himself being tortured and was still nervous about his hands. "I promise to tell you everything and answer all your questions."
The groundling crouched down next to him and grinned. "That you _will_ , black-eye." He pushed the elven sword tip away. "That you _absolutely_ will."
The sudden, powerful punch to the chin dispatched the älf into darkness.
Tark Draan, Human kingdom of Gauragar, Grey Mountains, 5452nd division of unendingness (6491st solar cycle), early summer
Aiphatòn had to abandon the steady jog that had got him through Girdlegard and into the north so quickly.
In all kinds of ways, the Grey Mountains put him in his place: treacherous ground, very thin air and extremely unsettled weather.
Coming up against these kinds of barriers was a new experience for him.
Mayor Münzler had been telling him the truth. Aiphatòn had little trouble finding the steep path. What he noticed immediately were the muddy rivulets coming towards him and softening the trail wherever it didn't consist of solid bedrock. The intensifying sun was also thawing ice and snow in the upper regions.
_At least the_ _Jagged Crown is unmistakeable._ Aiphatòn looked at the faraway, oddly shaped peak that looked like it was formed of upright obelisks. _It's bound to take eight orbits to get there. Or even more._
The white stretches on his route worried him. He had read about the mountains' countless pitfalls. Besides the thin mountain air, in the upper regions there was also permanent frost and several fathomless ravines in the bedrock, hidden under thin firn, which he might smash through thanks to the heavy equipment in his rucksack.
Aiphatòn looked ahead, keeping an eye on his surroundings. He hoped that Firûsha had just as little experience of the climb as he did.
He might encounter her soon—or an ambush by one of her warriors. Four veterans had been accompanying her since he deliberately let her get away in Dsôn Bhará. He wanted her to reveal her secrets to him or maybe even lead him to her brothers.
From what he knew of the Aklán, he thought she would very likely have had two of her warriors lie in wait to kill him while she herself kept moving.
Aiphatòn didn't believe there was a mountain pass or tunnel leading away to Tark Draan. A secret like that could never have lasted so long.
And yet he was inwardly worried there might be a kernel of truth to it.
He was more willing to accept the existence of a magical artefact than a passageway. But ever since it had become common knowledge that the foothills of Phondrasôn reached underneath Girdlegard, the utmost vigilance was necessary. Because a passageway or a sunken lane would be perfect for avoiding the existing five entrances. The dwarf tribes usually stood watch at them for anyone coming in or out.
Anyone who snuck past the fierce, short-statured, brave defenders via a different path through the mountains could smuggle in an army—or a worse threat—unnoticed and attack the country. It would take place in secret and probably be just as successful as Sinthoras and Caphalor had been in the past with their conquest of the Stone Gateway. It ranked as one of the dwarves' greatest defeats and it had led to the extermination of the Fifthlings tribe.
But Balyndis and huge numbers of volunteers had resettled the dwarf kingdom since then and Aiphatòn knew they kept watch. Once again, the stony mountain ranges surrounding the people's, elves' and dwarves' kingdoms were considered impassable for hikers, carts or any kind of carriage. Even the expeditions dispatched by the Smith's children either turned back or were presumed missing in the sea of basalt and granite.
Aiphatòn's instinct had not let him down when he had held off on shooting Firûsha among the artworks in Dsôn. It seemed she and her brothers had worked out a plan to stave off the älfar's impending defeat. To achieve it, she needed to get to the Jagged Crown.
_Whatever the reason: I'll find out._ Leading Girdlegard and even Aiphatòn to believe the Aklán had died turned out to be an extraordinarily good move. An enemy everyone thought was dead could strike all the more cruelly and savagely.
_That way, they surprise us._ He walked on, the spear balanced freely on his shoulder. _It's Samusin's providence_ _that I encountered them._
Aiphatòn had no doubt Ireheart and the band of heroes were defeating Lot-Ionan and the älfar already. He would help them as soon as he had killed Firûsha.
_The time is ripe to break free of the shackles of all foreign powers. Soon the inhabitants will rule over their own homeland, free from the influence of a vile magician or the dragon-worshippers of Lohasbrand and most definitely free from the tyranny of the älfar._
He stopped and took a deep breath to get some air into his shrivelled-feeling lungs. _And free of me._
Aiphatòn remembered the conversation he'd had with Tungdil on the ship some time ago. _Never strive to be like the Inextinguishables._ Still, despite every good intention, his self-control had slipped away. _My past words will finally be followed by actions._
His gaze swept across the countryside that stretched out in the valley to the south of him.
Little white clouds drifted across the blue sky, some dancing around the smaller peaks as if they wanted to stroke the rock and make it slightly less harsh. The sun shone, bringing the plains the warmth they desperately needed to allow the summer crops to ripen.
It seemed to Aiphatòn as if he had woken from a dream in which evil, hunger for power and unhappiness prevailed.
He had let himself get carried away, hunting the elves even more successfully than the Inextinguishables before him. He almost wiped them out, despite the fact he once named himself after their life star.
_What a mockery._ His ever-black eyes turned to the blueness high above him. _So many things I'll never forgive myself for doing._
It was still too early to see the first stars twinkling.
His gaze kept returning to the same place, but at night only a dark mark was visible there. The elves' life star could no longer be made out. With every death of a member of their tribe, it had darkened further. _I really hope I see it shine again one day._
Aiphatòn resumed his slow march and recalled the promise he had made to Tungdil the last time they met. _I swear I will never return to Girdlegard unless someone invites me._ That's what he'd said, and he'd meant once the battles were over. After the great, deadly slaughter.
But, in fact, he hoped he would pass into endingness with the last of the northern älfar. Until then, his hunt would continue, his next five opponents awaiting him.
Aiphatòn knew he was superior to them in terms of fighting skills. Besides, he had magic within him, stored in the rune-inscribed plates stitched fast into his skin. He used this energy intuitively, without reciting any spells. Five älfar warrior-women and warriors represented at most a _minor_ challenge. He was thoroughly justified in this hint of arrogance.
He reached a plain that was practically designed to enjoy the view to the north.
He didn't know the names of all the peaks and mountain ranges that had towered up since time immemorial as if to prove his own insignificance, and which would continue to do so after he'd gone. Ireheart or one of the new Fifthlings would surely have been able to tell a story about every single mountain.
No particular imagination was required to pick out specific shapes, like a sword or a dragon's head. On closer inspection, a wall with a ridge jutting out of it became the back of an enormous monster disappearing into the rock, its last vertebrae just visible as it vanished.
_If Vraccas really did create these mountains then he has shown a flair for variety._ Aiphatòn smiled and shielded his eyes from the daystar in order to observe the beauty without the glare.
He didn't feel any kind of urge to translate the view into a painting, sculpture or ballad. Even this proved to him how much he differed from his people.
During his years as emperor, the idea of sitting down at a canvas because of a whim or emotion had never even crossed his mind. Although he had tried his hand at it many times out of a sense of duty, it didn't do anything for him.
He valued art without being an artist. And sometimes he valued it when things stayed as they were, and kept their own uniqueness.
To his astonishment, Aiphatòn didn't miss anything. He didn't miss his palace or servants or anything else that came with his title of emperor and his once-powerful kingdom.
_Things in Girdlegard ought to go back to how they were before Caphalor and Sinthoras' invasion_ , he mused. _And then that's how they should stay._ He felt a duty to the inhabitants and would do anything to protect them. Sighing, he looked out over the mountains. _I should never have got carried away like that but that's behind me now._
The hiss of the arrow and the soft sound of the string snapping back into place were unmistakeable in the silence.
It told Aiphatòn where the archer was.
He grabbed the spear resting on his shoulder, turning round as he did so and flinging it in one fluid movement.
The blade made a whirring sound and hit the tip of the black arrow whizzing towards it, breaking it and destroying its shaft.
Continuing its flight, the spear plunged through the hardened leather armour and into the chest of the warrior who had taken up a good shooting position on an overhang thirty paces above.
He dropped his bow, sank to his knees and stared in bafflement at the shining runes filling with his blood. The stricken älf tilted backwards and came to rest on his back, the projectile sticking out of him like a thin flagpole.
Tiny fragments of the arrow clinked harmlessly onto the stony ground, one dark feather floating slowly towards the earth.
A warrior-woman stepped out of a dark niche in the rock and came towards Aiphatòn, holding one long sword and one short one with a serrated blade.
"Your journey ends here," she announced firmly. She was wearing the black armour too, dark blonde hair peeking out from underneath her helmet. She lifted the hand holding the smaller weapon and pointed it at his solar plexus. "Know this: you were _never_ our emperor. And the moment we send you into endingness is long awaited."
"That moment has not yet arrived, however. Not for me. But your own end might put a stop to your agonising wait." Aiphatòn scrutinised her. "You ought to know that I'm in full possession of my powers, in case the Aklán told you something different to reassure you." He lowered his head a little so that a shadow fell across his finely chiselled features. "I'll give you the chance to walk past me and jump into the abyss. With no pain, no injuries. A small step, a fall during which you can curse the Aklán or pray to a god and then there'll be nothing more to worry about." With a jerky movement, he threw off his cloaks along with his pack and revealed his bare torso with the stitched-in rune plates; the symbols shimmered, green and menacing, as if they were waiting for an opportunity to be allowed to prove their power. "Anything else will cause you pain. I will show no mercy."
"Your death is called Tanóra and I..." the älf-woman began.
" _My_ death does not have a name yet," Aiphatòn interrupted her and closed his armour-encased hands. He felt the magic within him as a gentle warmth flowing through his body. "And if it does come my way, it will have a nicer sounding name than yours."
Tanóra launched her attack, lashing out with swiftly alternating kicks and punches, which he dodged with expert twists. When he needed to, he used the large metal fittings on his armoured gloves to block the blades; metal sang as it clashed with metal.
Through careful observation, Aiphatòn saw his opponent's weak spot: just before the attack with the long sword, she lifted her shoulder slightly, giving herself away.
When Tanóra, panting with exertion, went to deliver another horizontal blow, he took a swift step towards her, knocking the attacking short blade aside and punching the älf-woman in the upper lip and nose.
A loud crack rang out as bone and tooth shattered.
Blood spurted out of Tanóra's cracked lip and smashed nose, the redness running down her chin and dripping steadily onto her armour.
She staggered backwards to put some space between them again so that she could use her blades.
But Aiphatòn stayed an arm's length away and rained down punch after punch on her face, the runes on his armoured knuckles glowing more and more with every hit. Five blows landed on target in the space of a heartbeat. Then he wound his arms right back and launched a double attack on the dazed woman, using both fists on her armour.
A dazzling explosion discharged.
His knuckles smashed through the hardened, reinforced leather and undergarment, where they met vulnerable flesh. There was a loud hissing sound and Aiphatòn knew that her pale skin had gone black.
Tanóra shrieked and was simultaneously flung upwards, her swords clanking down onto the stony ground.
The magical-physical attack flung her straight out over the edge of the mountain until the momentum subsided and she plunged downwards, still screaming. As she fell she suddenly started to burn, a dark cloud of smoke drifting out behind her.
_You could have made it less excruciating for yourself._ Aiphatòn watched her descent until Tanóra finally got too close to the mountainside and was torn to pieces, pulverised on the rugged surface. Only once almost nothing was left of her did the flames go out.
"Your death is called Aiphatòn," he murmured as he picked up her weapons and threw them into the abyss. "As I predicted."
He raised his hand and his spear extricated itself from the corpse of the first slain älf and flew to its master, landing neatly in his open hand.
He quickly looked for the two veterans' equipment but couldn't find any.
That meant that they had fully expected to kill him and return to their group. At this altitude, running fast was exhausting so he reasoned that Firûsha could not be far away.
He put his cloaks and pack on again, placing the blood-spattered spear on his shoulder as before. With no regard for himself or his well-being, he started jogging. His body would just have to endure the strain.
Aiphatòn caught up with the group towards evening.
They may have decided against a fire, but he could hear their quiet conversation coming from a small, sheltered recess.
He threw off his rucksack and cloaks again so that he could move more easily. He crept cautiously towards the recess and noticed at once that it was just _one_ älf, who was disguising his voice as he spoke, quickly switching between voices.
_So at least one of them must be lying in wait out here for me._ Aiphatòn presumed that the Aklán was sacrificing the last two veterans to stop him. He could not ignore them and leave them on his heels. He knew that, and Firûsha did too.
He looked around, searching for positions where an archer could easily hide.
_Up there perhaps?_ There was a groove four paces above the ground, as if a giant troll had cut a notch into the rock with an axe.
He took the spear and threw it on the off-chance, making the runes at the front of the shaft light up as well as the runes on the blade.
The greenish light from the symbols dragged an astonished älf-woman partially out of the darkness. She had been waiting at her post with a bow at the ready, wedged inside the rock face.
_There she is._ Aiphatòn cut his weapon's flight through the air short and made it hover menacingly in front of the warrior-woman. The tip was pointed at her face, the shimmering reflected off the gleaming blade, casting the light onto the rock even more intensely.
"Climb down," he called. "And you, sitting in the recess: show yourself."
The älf-woman in her raised hide stood up, casting her bow and arrow aside, and jumped out of the crevice, landing elegantly on the rock. A warrior came out of the entrance to the little cave, a spear in his right hand and a square shield in his left.
Aiphatòn let his weapon float downwards, bringing it between himself and his opponents. "You think you'll make it out of this alive, but you're mistaken. I'm giving you just one chance to choose a swift death instead of agony." He drew himself up. "Tanóra did not make a wise choice. You may have heard her screams? The mountains carry echoes quite some way."
The two älfar watched him over the spear, their eyes brimming with hatred.
_You're not going to surrender either._ "A swift death is yours if you go to the edge and—"
The älf-woman went to stand behind the shield-carrier who immediately held the shield in front of him, hurled his weapon at Aiphatòn and then charged forwards; as he did so, he ducked so low he almost disappeared completely behind the shield, so as not to offer Aiphatòn a target.
It wasn't difficult for the shintoìt to dodge the missile. At the same time, he forced his own hovering spear to attack magically.
The blade penetrated the shield's thin metal coating and the wood underneath, then penetrated the älf's arm along with his helmet and skull.
Before the warrior-woman could even realise the enemy weapon was unstoppable, the tip bored into her shoulder and flung her to the ground, along with the dead älf; she was sprayed with the blood of her companion. Skewered, she lay underneath the motionless warrior, moaning with pain. Every attempt she made to free herself from the spear failed and ended in an agonised, furious cry.
_As I thought: they didn't want to surrender._ Aiphatòn approached her slowly, stopping two paces away from her. "What's your..."
She reached for her belt, drew a throwing knife and tossed it at him.
Aiphatòn turned so that the blade hit one of the sewn-in plates of armour on his torso. It shattered against it with a dull clatter. "What's your name?"
She spat.
"I left it up to you to decide," he said, "what kind of death you wanted. And look: you're in agony." Aiphatòn cast a glance at the dead body. "He was lucky he kept his head ducked right down." He crouched next to her. "The Aklán let you and your veteran friends pass into endingness. Did she tell you I had no power left too?"
The warrior-woman's eyes flicked right and left. "You are the worst thing that could have happened to our tribe," she shot back, groaning. "You brought the scum to us."
" _Every_ älf is scum. Dangerous scum that threaten the unity and harmony of a peaceful world," he said thoughtfully. "Where would Girdlegard be if it hadn't been for all of you? If _I_ hadn't existed? The people, elves and dwarves..."
The älf-woman laughed scornfully. "You think they'd be living in peace? We were what first enabled them to unite. We throw them into the dust, give them the enemy they need in order to stick together. They were too foolish to pool their forces and skills of their own accord." She groaned, then fixed her gaze firmly on him. "End it now, _scum_ ," she said, grinning maliciously. "I can call you names now, and what's more, I'm entitled to do it."
_It's not going to be that simple._ Aiphatòn placed his index finger on the shaft of the spear and the runes lit up.
Slowly but surely, the metal warmed up as magic flowed into it.
Smoke was rising from the warrior-woman's shoulder and she clenched first her lips and then her teeth together hard.
"You still owe me your name."
The älf-woman was sweating, droplets glinting on her forehead and rolling into the blood spatter. She lowered her head and gave a loud shriek, anger lines forming across her face.
"I promised you pain. And I don't think we'll be done any time soon." Aiphatòn placed his hand on his weapon and lifted it up slowly, bit by bit.
The dead body slipped down the shaft onto the female veteran, pinning her with its weight. She wailed and tried to sit up without making the pain worse.
"Vonòria," she gasped. "My name is Vonòria."
"Now tell me: what does Firûsha want on the Jagged Crown?"
The älf-woman's breathing was jerky and she seemed determined not to say anything more.
" _What_ does the Aklán want on the summit, Vonòria?" he repeated his question, making more energy flow into the spear.
The smoke thickened, and there was a smell of roasting flesh. Burn blisters appeared around the edges of the wounds.
"The Ten. She wants to get to the Ten," she said in a high-pitched gasp, imploring him with one arm outstretched. "Stop!"
Aiphatòn dimly remembered the story but couldn't recall it fully. He let go of the spear so that the pain wasn't being unleashed for the moment. "Who are the Ten? Do they live up there?"
Vonòria gulped; she needed to take several breaths before she could go on. "The Ten were a unit of female and male veterans dispatched by the Aklán to search for the mountain pass reputed to run from the Jagged Crown to Ishím Voróo. Apparently elves were fleeing from the Dsôn Aklán via this route, unnoticed at first."
_Elves?_ "When was this?"
"Soon after the beginning of their reign in Tark Draan." She sneered at him. "You didn't know everything, you wretch. There was a _lot_ you didn't know about what the rulers were doing and setting in motion, from the zhadár to..."
_Could this be true?_ Aiphatòn hit the spear and she fell silent with a groan. "What are the Ten doing at the summit?"
Vonòria was gasping for breath. "I don't know," she panted. "We were to accompany the Aklán but she didn't let us in on her plans."
_A passageway and apparently it leads away from here._ Aiphatòn placed a foot against the warrior's corpse and pulled the spear out of a moaning Vonòria and then out of the dead man, before pushing his body off her. Using some magic, he warmed up the weapon and made the blood on it evaporate.
He pointed the spotless, gleaming tip at the älf-woman, blood oozing out of her shoulder. "Do you at least know what she was planning to do _after_ she'd visited the Ten?"
Vonòria lay still on her back, her eyes closed, seeming to be waiting for the pain to subside. She shook her head feebly.
"Then I don't need you anymore. Your death is called—"
A pebble skittered across the ground behind Aiphatòn but the warning wasn't enough.
A powerful blow hit him in the back, the blade of a heavy sword striking the plates as well as his bare skin.
The älf was thrown forwards by the force of it and, without meaning to, he rammed his blade through the front of Vonòria's neck and right up into her skull. _You'll pass into endingness before me._ He ducked instinctively.
The sword hissed as it sliced over his head and an älf-woman cursed loudly.
Aiphatòn did a foot sweep to take his opponent's legs out from under her, turning as he did so—and saw the black tionium armour of the Aklán in front of him.
Firûsha staggered but kept her balance. She immediately started hacking at him, the long blade coming down like a guillotine.
Aiphatòn whipped his arms up into the air and crossed his armoured fists to block the sword before it could plunge into his head and cleave him in two. There was an unpleasant ache in his back and he could feel his own warm blood running over his skin from a cut.
The two-handed, powerful blow flung him to his knees and the soles of Firûsha's boots were already poised to kick him in the face.
Fiery smoke flashed before Aiphatòn's eyes. He flopped backwards, grasping her blade with his armoured fingers as he did so and trying to pull his opponent with him.
But the Aklán let go of the hilt and immediately took two polished discuses out of the holders on her forearms and hurled them at Aiphatòn, who with some difficulty managed to deflect the missiles with the sword he had seized. He had no time to summon his own spear.
"You're going to die, you self-proclaimed emperor," she cried and lifted the dead warrior's spear to stab him. "Here, in the wasteland!"
_I'll be okay, even without a spear._ Aiphatòn rolled aside and escaped her attack, getting up on one knee and swinging the long sword by the blade like a heavy hammer; the hilt was aimed at the älf-woman's skull.
Surprised by the unexpected attack, she was still trying to pull her head away when the polished sword guard slid through her helmet at the height of her ears.
Firûsha's strength suddenly deserted her. She collapsed in a heap in front of Aiphatòn. Writhing, she panted and opened her eyes wide.
"I... can't feel my body anymore," she murmured in abject terror. Her blue eyes darted around searchingly. "What... where am I?"
_She won't reveal anything to me voluntarily. But if her mind is sufficiently disoriented by the injury, she might reveal something after all._ He knelt down next to her. The visor on her helmet wouldn't open so he leaned close to her to ensure she could hear and understand him. "You're here, with us. With the Ten."
"With the Ten?" Firûsha was breathing so hard that she had to pronounce each word separately.
"At the summit of the Jagged Crown, yes."
The älf-woman must have been smiling, judging by the crow's feet he could see, although fear radiated from her pupils. "I can't see the settlement. Is it as beautiful as I heard it was?"
_A settlement?_ Aiphatòn had to check himself to make sure he didn't give away the trick he was playing on her with a careless word. "Yes, it is. Now that you've found us, Aklán: what should we do?"
"The älfar need you," she murmured. Firûsha looked relieved for a heartbeat. "You... you must rally the resistance against the scum from Tark Draan. Look for our far-flung people!" Her eyelids fluttered. "We mustn't give up. The settlement is our new cradle and in one division of unendingness, I'll lead you back so that we..."
Her ribcage suddenly stopped moving and her pupils clouded over. The blue of her eyes dulled and became streaked with endingness.
Aiphatòn watched the transition from life to death. "Thus you pass on without fame, without fuss, without becoming a legend," he whispered to the Aklán who could no longer hear him. "You wanted to execute me in the wasteland of the Grey Mountains, but instead you're passing into endingness."
He pulled the sword's crossguard out of her head, blood and slimy grey brain matter clinging to it, then peered closer.
Horrified, he recoiled at the sight of her face. _That's not her! The features are similar, but that's not her._
He quickly released the chin-strap and tore the helmet off her mop of hair. He smelled a strand of it and noticed the scent of pnia root, which was used to dye fair hair black.
Astonished, he sat down, his gaze fixed on the älf-woman.
_I've been taken in by an imposter. Along with everyone else who believed her._ Then Aiphatòn burst out laughing. _What a con! This warrior-woman passed herself off as an Aklán to rally as many warriors and warrior-women as possible to her command._ He could feel the pain in his back but was ignoring it as much as he could. _In any case, she did delay her death._
He lifted his head and looked at the Jagged Crown, glowing in the light of the stars in the night sky.
If the con woman had stayed silent and passed away without uttering those mysterious words about the settlement, he would undoubtedly have travelled back to Girdlegard immediately and would have helped to raze Dsôn Bhará to the ground or hunt dispersed älfar-units.
_But now I've learnt too much not to look into it more closely._ Aiphatòn believed there really was a secret surrounding the strangely shaped peak.
And he would find out what it was.
# Chapter III
_If a creature is without wisdom and danger, beauty is wasted on them._
Wise Saying of the Älfar
Collected by Carmondai, master of word and image
Ishím Voróo, Älfar town of Dsôn Elhàtor, 5452nd division of unendingness (6491st solar cycle), early summer
A steady rustling woke Modôia from her slumber.
She opened her eyes and looked out the open, floor-length window at the rough sea; thin white curtains fluttered in the warm wind, dancing for the monarchess.
But it wasn't the waves making the soothing sound.
Dark veils of mist hung from the low-lying grey clouds, covering the sea and the island with rain.
The fat drops pelted down on the balcony, the cane chair and the little table, bursting on them and slowly running off. The first big puddles had formed on the floor outside the room.
_As if the sea needed watering._ Modôia smiled and slid one arm underneath her head and used the other hand to sweep her long blonde hair back. _Who would guess_ _what's hidden from us in there, growing and sprouting?_
She knew a whole moment of unendingness had gone past. The elixir that Leïóva mixed put her to sleep for a long time and helped her recover. Meanwhile, Dsôn Elhàtor had to manage without her and rely on her son's judgement.
For a little while longer, Modôia enjoyed the sight of the rain and the clean smell that was streaming inside.
Far in the distance the cloud cover was already scattering and the sun was forging its way through, its rays glittering on the waves.
Amid the gently rising and falling waters, many black silhouettes appeared under full sail.
Modôia narrowed her eyes and sat up. _Sails!_
All of a sudden she realised that the First Fleet was expected today. It meant there was a huge amount to be done at the marketplace.
Eagerly anticipating all the goods and new sights, she got out of the bed with its embellished frame made of polished basalt and glass, making sure not to move too fast. Her body was still shattered. Incurably so.
Modôia threw a dark red brocade coat with black and gold embroidery over her white nightdress and opened the double doors from the bed chamber into her study.
She wasn't surprised to find Ôdaiòn at the carved whale-bone table. Surrounded by balled up sheets of paper, he was just writing something down only to cross it out immediately with a despairing groan. The dark blue robe suited him very well and he had sandals on his feet. The whiteness of the floor-to-ceiling bone shelves made the room look bright and welcoming. The papers relating to decrees, laws and events lay in stacks on the floor.
She looked at her son with a smile—he hadn't noticed her coming in. _He is really working hard._ "What are you working on?"
Ôdaiòn looked up at her, seeming embarrassed that she had caught him trying unsuccessfully to do some writing. He was using the tincture that stopped the white of the eye clouding over in daylight, so the radiance of the deep-sea blue was clear; it went very well with his clothing. This invention would have been invaluable in Tark Draan around the time of Sinthoras' and Caphalor's invasion. Modôia herself didn't think much of it.
Ôdaiòn shuffled the balls of paper together with his foot, to make it seem like there were fewer of them. "I'm trying my hand at writing to the sovereign of Dâkiòn. It's time for a few more little white lies," he explained. Breathing heavily, he put the silver ink-pencil he had been writing with to one side and tore up the latest draft. "How do you manage it, Mother?" He threw the scraps onto the bone tabletop with a flourish.
"I'm older than you and have more experience. That helps a great deal," she replied. "And Leïóva's elixirs make me very calm."
They both laughed.
Modôia went over to him and leaned against the edge of the table. "So has someone written us a letter?"
The älf, who looked remarkably like his father, nodded. "It came at dawn. It's the usual, the pleasantries we're used to." He gestured towards the blank page. "And even though I'm just as familiar with the niceties, I can't seem to arrange them in a way that still sounds genuinely friendly, despite their triviality." He ran a hand through his shoulder-length hair, brushing the unruly brown strands out of his face.
Modôia picked up the letter from Dâkiòn.
The sovereign, Shôtoràs, was a seasoned politician to his core, as well as a vehement advocate of the Constellations. He was undoubtedly one of the oldest in his tribe and he came from the days when Dsôn Faïmon was a strong and feared kingdom, when the radial arms were at the height of their powers and nobody could beat the älfar.
Under no circumstances would Modôia underestimate him. While _she_ spoke about experience in comparison with her son, Shôtoràs was unassailably superior to _her._
She knew the old älf hated her. Profoundly and irreconcilably. Her emergence from Tark Draan as if out of nowhere was reason enough. But on top of this was the fact that back then, she had convinced hundreds of älfar to follow her further north, where the sea awaited them.
The monarchess firmly believed that these inhabitants of the Majestic who had been enticed away were the reason why Shôtoràs refrained from attacking Elhàtor: the sovereign dreamed of getting his lost älfar and their grandchildren back. The fragile peace was founded upon it, the peace that was about as buoyant as a plank floating in water: it would founder at the slightest pressure.
Modôia skimmed the message overflowing with friendliness. _And Shôtoràs has been aiming for restraint until now._ "These are the usual pleasantries," she confirmed her son's impressions. "We should reply in a similar way."
"Just out of curiosity: how would it go if you wrote it?" Ôdaiòn tried to sound somewhat nonchalant.
"My dear Shôtoràs," she dictated with a self-satisfied smile because he wanted to make her do the work again. "I was delighted to read your letter. I too assure you as ever of my friendship and goodwill. The town and its residents are well. One of our fleets has just returned from a trading voyage, and there are such delicacies coming up out of the holds." Modôia looked out the window at the rapidly approaching sails. There were two enormous ships and five smaller auxiliary boats, just like they had learned from the frekoriers. With them, any unit was unbeatable. She cleared her throat and looked at her son. "At that point you could put in everything that you'll see down at the marketplace." She put the letter from Dâkiòn back down and stood up. "Just like that or along those lines, is how it would go if I wrote it."
"What about the question in his brief second message, Mother?" Ôdaiòn picked up a small piece of paper and passed it to her.
The blonde älf-woman took the piece of paper and her brow furrowed. The lines in her smooth skin deepened as she read aloud:
" _My dear Modôia,_
_We once agreed that no ship from Dâkiòn would travel more than four miles downriver. However, how would you feel if we at least permitted our fishermen to go as far as the estuary and within a mile's radius of it? The fishing grounds upstream have been exhausted and you wouldn't want our residents to starve, would you? Plenty of their relatives live in your town._
_It's time this permission was granted as a gesture of solidarity and mutual respect._
_Please use the bird which brought this message when you answer. He is more reliable than all the others._ "
_Extremely odd._ Modôia lowered the sheet of paper, thought it over, then picked up the first message and held one on top of the other to compare them.
Ôdaiòn laughed softly. "I had the same thought. And I think the writer went about imitating Shôtoràs' handwriting extremely skilfully. It must be someone who has access to his papers."
"And the instruction to use the same bird too," murmured Modôia. "No doubt the message was never supposed to get to Shôtoràs." Her stomach grumbled—it was about time she ate something. She couldn't make any decisions before breakfast. "We won't answer this for now. Since it wasn't written by the sovereign, it can wait." She handed the sheets of paper back to her son. "Keep them both safe. Leïóva will be waiting for me with the food. She gets angry if I don't eat."
Ôdaiòn nodded. "May I also say that you did well against the onwú, in case Shôtoràs has changed his mind about the peaceful coexistence of the towns?"
"Are you referring to the letters?"
"I was thinking and it occurred to me: isn't it also possible that Shôtoràs did actually write both?"
Modôia was taken aback. _What a strange thought._ "You think the sovereign wants us to believe there's someone double-crossing him, but in reality he's behind the message?"
"Wouldn't that be an obvious strategy? He could safely gauge our reaction to the request and then easily talk his way out of it by blaming treacherous älfar in his circle." He leaned back in his chair and pondered to himself, gesticulating, his eyes fixed on the white bone shelf in front of him. "And if we _were_ to allow it, he could use the fishing boats for espionage. It wouldn't be long until one of them happened to get lost along our coast. Badly damaged by a storm, of course, so that it seemed credible."
She smiled mischievously. "That would be like Shôtoràs. And kudos to you: you're already thinking like someone who had to operate in the snake pit of the old Dsôn among Constellations and Comets."
Ôdaiòn looked at his mother. "Ah, what a great compliment." He bowed slightly.
"Don't get too full of yourself. And don't forget to go to the market. Our ships should have come into port just this splinter of unendingness." Modôia left the study and entered the short corridor adorned with mosaics—it had three other doors off it made from opaque, very thin sheets of rock.
At the end of the corridor, she entered a very spacious, bright room which, with its extremely broad glass façade, offered an unimpeded view of the sea at its far end. The delicious hot and cold dishes arranged on the table were giving off delightful aromas.
Chandeliers made from delicate fish bones hung from the ceiling and gave off a lovely light in the evenings. Gold and silver splashes and streaks clung to the whitewashed walls as if the precious metals had been thrown at the walls in a liquid state before hardening.
The rain had subsided and the sun seemed unrestrained, casting its rays on Dsôn Elhàtor and forcing the grey clouds apart.
Modôia noticed the slight twinge as her eyes turned black. Her confidante's essences meant it often took longer, and sometimes the clouding over didn't happen at all on overcast days. That didn't have anything to do with the tincture that her son used but was a side-effect of her own remedies. That's probably why she hated that trendy elixir.
Leïóva was standing at the window with her back to her, dressed in a floor-length silvery white skirt and a chest wrap in the same colour that revealed her willowy physique and brown skin. The sun couldn't bleach the black hair that reached down to her behind. "I hear the First Fleet is returning from its voyage," she said in greeting. "We really need to check what they've brought with them."
"We will."
"After some refreshments," Leïóva added pointedly, without raising her voice. She radiated gentleness and elegance in all that she did. Even when she was killing someone. "You need your strength and something in your stomach, otherwise my remedies will eat away at your insides."
Modôia sat down at the table. "I know," she responded with a sigh.
Leïóva stayed by the window and crossed her arms underneath her bosom, the muscles across her back and powerful shoulders glistening in the sunlight as she did so. "I was in the grotto earlier. Work on the ships is coming along well. The only difficulty that may arise is the ships' draught. If the catapults we plan for the upper decks are too heavy, we could run aground."
"I'm aware of that." The sovereign helped herself to some of the thin milk soup, scattered some dried fruit into it and then stirred in little pieces of twice-baked spice bread. She always forced herself to eat.
Her spine was sending out a weak pain impulse, which was making its way into the furthest corners of her body. Modôia stopped moving briefly. _The remedy is wearing off_ _again already. Oh, Inàste, what I wouldn't give if it would only stop getting worse._
Leïóva didn't seem to have noticed. "Sailing upstream will be a challenge for the helmsmen," she said quietly.
"It's possible that we'll be putting out to sea earlier than we thought a few moments of unendingness ago." She ate spoonful after spoonful, barely enjoying the taste that spread across her palate. The frekorian and älfar cuisines complemented one another extremely well, the art of meticulous spicing crossed with careful preparation.
"What do you mean?" Leïóva was still standing serenely at the window.
Modôia told her about the two messages and the suspicion her son had mentioned. "Either way, it seems like someone doesn't want to stick to the agreement that the Majestic and the Magnificent's spheres of influence remain separate," she finished, scraping the remaining food in her bowl together. "Besides, the onwú didn't come up with the idea of sailing in our direction by themselves."
"So our preparations have turned out to be spot on." Leïóva laughed drily. "I knew it! Till his dying breath, the old älf will not be able to get over the fact you took residents away from him and that you transformed Elhàtor into a strong naval power within the space of just a few cycles."
"We achieved it _together_ ," the blonde älf-woman corrected her.
"As far as the outside world is concerned, it was _you_ and that's how it's going to stay," Leïóva insisted and took a deep breath. "So after our meal, I'll go back to the grotto and tell the architects to come up with a way to reduce the draught." She turned to the side so that Modôia could see her beautiful, regular profile. Her hair looked like it was made of silken black threads. "We need something to make the ships lighter and increase the buoyancy."
"Maybe a specific kind of wood with air pockets?" Modôia offered and beckoned her over. "Keep me company. We see each other rarely enough without being interrupted."
Leïóva walked across to her, every step looking easy. Easy and pain-free. She sat down and helped herself to a slice of the dark bread; she sliced some cheese and poured tea, adding milk and ground spices to it. "That's true. But hasn't it always been that way?" She gave Modôia a warm, affectionate smile and placed one hand on hers. Her eyes were clear and white, not a trace of discolouration visible; there was an amber glow around the pupils, although the colour turned greenish depending on how the light fell.
"Your tinctures to block the colour change are incredible," the sovereign remarked and winked.
"Aren't they? They're selling very well, although not everyone responds to it equally well. Anyone island-born can tolerate it much better than newcomers descended from the old älfar realms." Leïóva laughed. "You could mistake half of the townspeople for elves. Shôtoràs would die at the sight of them."
Modôia joined in the fun and also ate some bread and cheese, with greater relish this time. The presence of her confidante gave her a lift.
They told each other the latest gossip, none of which had anything to do with politics or disputes. Town life in Elhàtor always had something new in store, bringing couples together and separating them again. Sometimes this happened spectacularly, sometimes quietly and with barely any fuss.
From time to time, Modôia's friend put a drop of elixir in her tea. Without the dose of reddish-brown medicine, she could barely get through the day without screaming.
After a good splinter of unendingness, Leïóva got up. "Now, if you'll excuse me. The fleet must have sailed into the outer harbour by now."
"Say hello to your daughter from me." Modôia nodded to her and drank the rest of the tea in one go under the watchful eye of her friend. "And Ôdaiòn sends his very best too."
The slim woman smiled knowingly. "You and your son would be so pleased if our friendship was carried on into the next generation through their marriage."
"My son likes her. As far as I know, he's already told her as much."
"And as far as I know, she informed him that she holds him in high regard. But as commander of the First Fleet, she isn't looking for a long-term relationship." Leïóva nodded to Modôia and walked towards the door. "I'll give her your best."
"Thank you very much." Modôia propped her elbows on the table and clasped her hands together; she watched her friend leave, then turned her head towards the window.
Her thoughts returned to Shôtoràs and the two messages as she watched the waves and their foaming crests. _The mystery will be solved._
Tark Draan, Älfar realm of Dsôn Bhará, formerly the elf realm Lesinteïl, 5452nd division of unendingness (6491st solar cycle), early summer
Carmondai woke to find his wrists in iron handcuffs. _A prisoner yet again._ He sat up.
All of his armour and clothes had been removed apart from his loincloth. From one ankle shackle there was a chain tethering him to a ruined sculpture in the middle of the crater. The sun beat down on him, the skin on his face felt tight and he was hot. His overriding feeling was thirst.
_It's the simplest form of torture._
"Black eyes and red skin. That looks funny." In the shadow of a tent, holding a bottle of water in his hand, sat the black-armoured groundling who had saved his life. "You really haven't been outdoors in a long time, judging by how quickly you burnt."
"Cheers," Carmondai replied, scraping dried blood out of the corners of his eyes.
"For letting you roast in the sun?"
"For saving my life." No matter what position he was in, he couldn't escape the scorching rays. What little remained of the artwork was no use.
"Well, you've heard what I expect in exchange." The mysterious dwarf took a mouthful of water and the älf's mouth suddenly went drier at the sight. "Will you do it?"
"You're a zhadár who has switched sides," Carmondai realised and shielded his eyes with one hand. Dust crunched between his teeth. "Did you all do that?"
"We never served the triplets with our hearts. Even the admirers were waiting for the orbit when they could drop their masks like all Thirdlings and wipe out the älfar." He drank some more. "Until recently I was called Balodil. And yes, I'm the last zhadár created by the älfar. And it's specifically _your kind_ that I'm going to hunt until I've driven the last one out of hiding. I know all the secrets you thought were safe."
"What are you called now?"
The groundling laughed wickedly. "What would you call me?"
"It would probably be an älfar name."
"That would probably be appropriate, especially as"—he looked down at himself—"I'm still wearing my old armour, although without the Aklán's runes." He poured some water over his furrowed, black face. The drops trickled down off his thick beard and onto his armour. "Think it over, writer. In the meantime, I'll tell you what you missed when you were locked up down there and time moved on without you."
"Have you saved my papers?"
"Quite a lot of them, yes. The fire had already spread. The sparks were to blame, I'm afraid. But escaping from the cell like that was a good idea." The groundling looked up at the palace, a loud explosion audible from it. Shortly afterwards the earth shook slightly beneath them. "That was the tower," he explained. "Caved in, right in the middle. That was it."
Carmondai swallowed, feeling like his tongue was swelling in his mouth. "What are you planning?"
The zhadár made a soothing gesture. "One thing at a time. In broad brushstrokes, the situation is that Girdlegard is free of every insidious threat, from you lot right through to Lot-Ionan, the kordrion and the dragon Lohasbrand. All crushed and stamped out." He stamped his foot on the ground once. "When the uprisings against the älfar broke out, Ilahín and his wife Fiëa turned up, having been deep in the woods, hiding from Aiphatòn's hunt. Under their command, an army of humans, dwarves and magicians marched, destroying huge swathes of Dsôn Bhará, and they didn't leave Phôseon Dwhamant unscathed either, or Âlandur, to give it its ancient elven name again. The people in these areas ensure that nothing remains as a reminder of the älfar's existence." The groundling shook the water bottle enticingly, and there was a splashing sound. "Have I forgotten anything?"
Sweat ran down Carmondai's brow and trickled into the cut which instantly started to sting. "Quite a lot has been going on," he murmured, trying to take in everything that had happened.
"Oh yes! The elves will return. Ilahín and Fiëa started preparing the Golden Plain for resettlement by their people. For some reason, they're convinced the elves will settle down in Girdlegard again."
_A plague on them._ Carmondai laughed nastily. "Whatever they've promised you, if I were in your position, I would make sure that no pointy-eared creature sets foot in it. They cannot be trusted."
"An _älf_ certainly cannot trust them," the groundling retorted. "The rest of us can, though."
Carmondai sighed heavily. "And _that_ is coming from a _dwarf_. These really are new times."
"And that's coming from a zhadár." He threw the water bottle to him and watched the älf snatching for it. "As far as the two of us are concerned: I'm going to go hunting, and you are going to come with me. I've read some of your stories and I liked them."
Carmondai didn't ask what would happen if he refused. _Better than boiling and roasting._ "And the elves have agreed to this?"
"Yes. They know your death has not been called off completely and that instead you've been given a postponement before endingness." He grinned. "You'll have the chance to clear your name."
"Of what? I didn't spread any lies."
"You described the älfar as your people saw themselves. But now you'll see what they did to Girdlegard." The zhadár watched as the älf greedily sucked the last drops out of the bottle. "I know three places where the Aklán constructed secret hide-outs. Aiphatòn is travelling through Girdlegard with the same objective as me. But I know he won't find all of you. You'll be a witness to those I track down in the hide-outs."
Carmondai slowly lowered the bottle, looking astonished. "Why was the emperor, of all people, spared?"
"Because he helped to defeat Lot-Ionan in the Blue Mountains and led his southern älfar to their doom without causing any casualties on our side." He pointed into the crater. "This hole is going to disappear. The catapults are razing the palace to the ground and when the last few threats to the tribes in Girdlegard have been eliminated, the magicians will come and use spells to fill the crater in. A wood will grow over it and its roots will hold prisoner something that will never again be allowed back to the surface: the last few remnants of your race."
"I see." Carmondai realised that so many things had happened during his imprisonment that he could have filled countless books with it all. _The most important thing is my survival. Everything else will become clear on the journey._ "I will go with you and I'm excited, genuinely so, about what I'll see on the way."
"So be it." The groundling placed a hand on the hilt of his unusual sword. "If you don't follow my instructions, I will kill you. If you try to escape, I will kill you. If you try to kill me, I will kill you. If you write anything but the truth, I will kill you," he rattled off calmly. "Those are the conditions for our journey together."
"They are very simple and consistent," Carmondai commented wryly, wishing he had ten more bottles of water to quench his thirst. _I won't make it that easy for you._ "Know this: I'm putting my life in your hands."
"What do you mean by that?"
"Since you won't allow me any weapons, I presume, you will have to protect me. The humans are vengeful." Carmondai tossed the empty container to him. "And without me, there are no beautifully written stories about the end, only second-class attempts by humans and groundlings that don't captivate anyone and come across as clumsy. You need me, my dearest new friend."
The zhadár laughed. "You're a true älf, just with a bit more subtlety. I'm putting you in chains, which will allow you a certain freedom of movement to dodge pitchforks and projectiles. If the people attack you, I'll stop them slaughtering you. We'll make sure you look sufficiently worse for wear, which will keep their anger at bay."
"You're too kind." Carmondai gave a cheerless laugh. _From the master of word and image to a clerk of the decline._ "When do we set off?"
"As soon as the palace has fallen." He looked at the älf. "So what about my name?"
Carmondai was silent, his gaze fixed on the once-imposing building.
The entire tall marble façade tipped slowly forwards, raising clouds of dust as some parts crashed onto the mountain and some parts onto the stairs, wreathing the mountain in grey clouds. Some rubble tumbled down the staircase, destroying the steps and tearing down the fountains on the landings. The red water in the streams and ponds splashed into the air and turned a dirty brown.
_All those beautiful skulls and skeletons. Orcs couldn't wreak worse havoc._ "Carâhnios," he muttered. "That's what I'd call you: the exterminator."
"Sounds good." The zhadár nodded, pleased. "See you tomorrow morning." He got up and left the shadow of the tent to make his way to the catapults.
"Are you going to let me roast? I'll lose my head! **"** Carmondai blinked in the bright daylight.
"See it as preparation for your journey with me. You're going to have to get used to all kinds of headaches." Carâhnios walked away, laughing. "Especially when my constant teasing starts to do your head in."
_Groundling humour._ The älf turned his attention to the Dsôn Aklán's collapsing stately home, just a few of its walls still standing. _A symbol of what is happening to us._
An entire side wall several hundred paces long began to sway, and after a shell struck, it slid down the mountain. Disintegrating, it crashed to the ground and set off a fresh round of quaking through the earth. Clouds of dirt rose up and spread across the surrounding area.
But this time the ground didn't stop shaking.
_What have they started?_ Carmondai heard the first agitated cries coming from the siege equipment and saw an extremely heavy, enormous catapult tilt to one side and disappear downwards. The troops ran in the opposite direction.
That's when he realised: the bombardment was not going to plan.
Tark Draan, Human kingdom of Gauragar, Grey Mountains, 5452nd division of unendingness (6491st solar cycle), early summer
_This beats all of my expectations!_ Aiphatòn was standing at the upper edge of the valley, looking down at the lush greenery surrounded by craggy rock faces, thick sheets of ice and permanent snow. _You could mistake it for a magical illusion._
But as he didn't feel a twinge or prickle warning him of magic, it had to be real.
Aiphatòn reckoned it was two miles long and half a mile across. Terraces had been built and the trees growing on them bore fruit that did not look ripe enough to eat yet. Amid the tree trunks different types of grain grew wild, as if either their seeds had been mingled when they were being sown or the fields had long since been left to their own devices. A wide, babbling waterfall came gushing out of the mountain at the far end of the valley and plunged into a small lake.
On the ground, he could make out the ruins of stone buildings. Their charred walls and rock faces made it clear that a fire must have raged here a long time ago. Just two buildings seemed to have been built more recently.
Aiphatòn walked cautiously down the steps towards the abandoned basin-shaped valley; he was holding his spear in his right hand.
On one point, in any case, Firûsha's doppelgänger had not lied to him: there _was_ a settlement—or at least the remains of one.
He had reached the Jagged Crown several orbits ago and from the summit he had noticed this idyll a few miles below and to the north, eye-catching with its vivid colours in the midst of white and grey.
_It would be an ideal place to rally the resistance, just like the älf-woman said. It wouldn't occur to anyone to look here._ A warm draught of air was blowing at him, streaming steadily out of the many holes, large and small, in the rock face. That was why the ice couldn't damage the plants and the inhabitants. Aiphatòn noticed a mild sulphurous smell.
He stayed on his guard, but the further he went down the stairs, past the overgrown fields and trees, the more certain he became that nobody lived in this safe, secluded spot anymore.
_Least of all any älfar warriors._ Aiphatòn reached the ground. Once he had taken off his cloaks and rucksack, he jogged over to the two houses that had been built from the remains of other homes. He could see traces of the fire that must have ravaged the valley on the stones and beams that had been used.
Around the lake, and also to the right and left of the waterfall, he could see metal suspension systems that must once have supported something heavy, something big.
_Mill wheels, perhaps?_ From the durable foundations and last iron remains, he figured there must have been equipment there and it had succumbed to the flames. The former settlers might have had mechanical systems far superior to Girdlegard's from a technical point of view.
_Who used to live in this valley?_ Aiphatòn walked around the first building and after straining his ears briefly, went inside. Whatever had happened here, it was a long time ago.
The furniture seemed very sparse to him and was reminiscent of the elves' tastes. Even the decor had elements that could be traced back to the älfar's mortal enemies; however, he recognised utensils here and there with dwarf runes emblazoned on them. From the different sizes of the mugs, knives and handles on containers, it was clear that dwarves as well as humans and elves had used them.
_That's odd. It's as if they were all here at the same time._
In the middle of the only room was a table that also had scorch marks on it. A series of wooden boards lay stacked in a pile on the table.
Aiphatòn picked up the top one and cast a glance over it: the characters carved into it were älfar.
His confusion knew no bounds. _Elves, älfar and dwarves in one place—did they live here together? Did one of them invade the others?_
Aiphatòn sat down on the floor and focused his attention on the letter that had been left prominently enough that a visitor couldn't help but find it. And someone had been absolutely certain that the visitor would be an älf.
_My name is Modôia,_
I serve Dsôn Aklán Firûsha and came here on her orders to pursue the elves who fled Tark Draan because of us.
When we set out there were ten of us, but the elves were lying in wait and attacked us deviously. The elements and other imponderables also whittled down the size of our party.
In the end I was the only one left and I made it to this settlement.
According to my investigations, groundlings and elves once lived here together, whatever their reasons for deciding to do this might have been.
I'm not staying here long—I'm going to continue the Dsôn Aklán's mission to locate a route past the groundlings' kingdom and stronghold west of here. It's called the Stone Gateway.
I will find a way to Ishím Voróo so that I can look for more älfar there, unbeknownst to anyone else, and lead them back to Tark Draan as reinforcements. If needs be, common beasts who follow my orders will do.
One way or another, the arrival of new troops will surprise everyone and lead the Aklán to victory.
Last but not least, I'm pursuing the last elf-woman. Northwards.
I will leave markings along the way that will be impossible for älfar eyes to miss.
If whoever finds my letter can only read and understand the language of my tribe, it will not be of any use to them.
If the finder is not an älf but an ally of my people, then here are your orders: bring the boards to the Aklán or their successors. You will be rewarded for it.
I don't know whether I will find a path through these wretched mountains.
I desperately hope and wish to catch up with the elf-woman and dispatch her into endingness.
Thus I place my fate in the hands of Samusin. The god of balance has the power to decide what I experience and endure along the way.
Whoever follows me and walks in my footsteps, pay attention to the ground and forge ahead with courage!
Aiphatòn placed the boards to one side and stared at the fireplace where cooled ash had lain for so long. _After me, nobody will find this message again._
He swept the ashes aside, building a small tinder pile out of wood chips lying around and placed the thin little wooden boards on top, one by one. With flint he got out of his rucksack and a few powerful blows, he set the thing alight. The little flames crackled as they engulfed the dry wood.
_Whoever you were, Modôia, your self-sacrifice was for nothing._ Aiphatòn waited until there was nothing left of the message. It was possible there were rumours in Dsôn Bhará of the existence of this place full of promise high in the Grey Mountains. _If that is the case, they will not find anything to help them sow terror throughout Girdlegard again._
He took the rucksack and spear, stepped out of the hut and surveyed the slopes surrounding the valley. He dismissed the idea of setting the fields and trees on fire too. The smoke might attract more attention than was necessary.
Then Aiphatòn turned northwards.
It was possible the veteran hadn't got more than a mile away.
Perhaps she had frozen to death after twenty minutes.
Or she had caught up to the elf-woman and they had both died in the struggle.
One possibility after another occurred to him.
But _one_ possibility made Aiphatòn particularly uneasy: with a lot of help from Samusin, through luck or some such, she might have managed to walk to Ishím Voróo. _And left telltale_ _markings behind._
In his mind's eye he saw Modôia, whom he didn't know at all, recruiting new armies, training them and leading the troops on a narrow path through valleys and along mountain passes towards them.
A fresh stream of starving, revenge-seeking älfar could pour into Girdlegard, which still had a long way to go to recover from the impact of the oppression and battles.
_She set out two hundred cycles ago. What could have happened to her?_ Aiphatòn contemplated the sky and the glowing sunset bathing the rocks in a warm golden light he had never seen on the plains before. He put it down to the air being thinner up this high.
The moon was out, clear against the night sky, and the most valiant stars were twinkling, almost winking at him.
His gaze wandered to the spot that always remained dark and empty.
Then a shiver of pleasure ran down his spine, despite the warm gusts still flowing out of the holes. _That's the elves' life star! I can make it out again!_
That could only mean one thing—that the battered people were slowly recovering and even announcing births.
Aiphatòn gave a small smile. _I'll sleep better tonight than I have in a very long time._
He knew what he needed to do at dawn: this twist of fate had changed his mission and might lead him back to his parents' homeland to look for älfar there—they were a greater danger than the Aklán's remaining troops. He would look for them and the path that the last of the Ten may have discovered.
_Truly, the mountains are full of wonder._
Ishím Voróo, Forty miles north of the älfar town Dsôn Dâkiòn, 5452nd division of unendingness (6491st solar cycle), summer
"You know the old man will kill us for this?" Gathalor kept looking around as he pulled up the cord with the coloured markings.
_Miserable ditherer._ "The depth?" Saitôra replied, unfazed.
"Eight fathoms," he grumbled, ready to do another measurement right away.
Sitting an arm's length away from him in the bow of the fishing boat, Saitôra noted down the number. "Only if he finds out what we're up to—and how would he do that?" She remained the picture of calm and glanced over at Iophâlor who was in charge of the steering, keeping them in the middle of the river the whole time. "Width?"
"The heaving line measurement hasn't changed. For the last two miles it has maintained twenty-eight paces," he reported, and the älf-woman wrote it down.
The river Tronjor drifted along with the three of them, at its most calm. Their little boat had already weathered two rapids—the most dangerous points of their reconnaissance trip so far.
The young älfar were wearing Dâkiòn fishermen outfits as disguise: brown shorts and sleeveless white shirts. They had brought nets as well as mooring lines with hooks on them. If they met people from Elhàtor, their excuse would be that their boat broke adrift and that they found themselves fleeing swamp creatures using a damaged oar.
Their armour and weapons were stashed in the bow compartment under a pile of empty sacks. These were only there in case someone wanted to harm them. After all, they could run into monsters living in the nearby swamp.
_I wouldn't have brought Gathalor with me, but Irïanora insisted. I know all too well why._ Saitôra was a good friend of the älf-woman whom many considered the future successor to Shôtoràs. As Saitôra was always game for an adventure, she had taken Irïanora up on her suggestion to measure the river as far as the estuary in secret. The up-to-date map was intended as a gift for the eccentric sovereign's new architect and cartographer. The last exploratory trip had taken place quite a few divisions of unendingness ago and the Tronjor had changed.
Saitôra grinned. _I'm having an adventure._ The black-haired älf-woman had to make numerous notes on the old sketch. The river was the only link to the sea—to its right and left stretched miles and miles of moorland and marsh. The Tronjor was the safest route through it.
The reedy embankments gave way to dizzyingly sheer rock faces, then the terrain became open again and practically boundless until woods and thickets loomed into view. Now their boat was gliding past stony banks with a lush green, grass border rising up beyond them. The blades of grass infused the air with the pungent smell of leeks.
Gathalor fed the string into the water again. "Eight fathoms," he announced, sounding like he was about to burst into tears.
_White-haired moaner. He's only doing this to impress Irïanora._ She nodded and made a note.
According to her calculations, they were at most just one moment from the estuary. As soon as they reached the sea, they would set sail, travelling back upstream to Dsôn Dâkiòn.
It sounded easy when they had discussed it, but the rapids and shallows they had passed through worried her. Iophâlor knew how to sail, and in the places where it was sixty to eighty paces wide he would be able to tack against the current. But they didn't have a reliable plan if there was no wind in the narrow points or the gorges that hadn't been sketched in yet. Disembarking, abandoning the boat and walking didn't seem like a good idea.
Saitôra looked down at the box beside her containing the half dozen pigeons she'd brought. She could use them to send messages to the town in case anything happened to them on the journey or she had important discoveries to share that couldn't wait.
Her favourite was the bird with the golden yellow feathers. A pre-prepared message was on his foot, only intended to end up in Dsôn Dâkiòn in case of extreme emergency: their three wills, succinctly and clearly written.
The pigeons cooed, waggling their heads and looking startled.
_This isn't the right way for you to travel._ Saitôra slid into a more comfortable sitting position.
"Will we make it through the rapids?" Gathalor asked uncertainly and wound up the cord as if he had heard her thoughts.
"No," replied Iophâlor from the stern, steering the boat around a piece of driftwood and adjusting their course so that they were back in the middle of the river once again. "We'd be better off swimming back." He gave a broad smile.
"What?" Gathalor went pale.
"He was making a joke. It depends on the wind," Saitôra chipped in. "Let's pray to Samusin not to forget us." She looked down the Tronjor and saw the narrow point that was also marked on the map. It didn't seem to have got any wider.
The riverbed narrowed to barely eight paces here. The flat, pleasant banks were gone and rock faces loomed up menacingly. There was no escape now. The water sloshed, foaming, against the obstacle in its path and eddies formed on its surface—a warning sign of a whirlpool.
The boat was gathering speed.
Worried, Saitôra looked at the towering walls either side of the Tronjor. _Our boat is going to wreck against them if Iophâlor doesn't hold his course._ She gulped and couldn't help looking over to the helmsman again.
The dark-haired älf behind her laughed. "I'm not about to let us crash into them," he reassured her.
"Twelve fathoms," Gathalor reported in astonishment. "It's getting deeper?"
"Because of the current. The eddies wash the sand away." Saitôra made a corresponding note. "Keep measuring."
The rushing water got louder and the hull began to bob in the waves. Droplets sprayed up and sprinkled the passengers.
Saitôra cursed. She needed to be careful that the map didn't suffer any water damage.
Iophâlor's expression had closed off. He had both his hands on the helm now to make sure the boat didn't veer off course.
"Twenty fathoms," Gathalor cried anxiously. "And... here, there isn't enough string anymore." He turned to the älf-woman, looking horrified. "The bottom is more than twenty fathoms below us. And the Tronjor is powerful. It's literally yanking at the line like there's a heavy fish hanging off it."
"Calm down," she snapped at him, barely managing to make legible entries anymore. The boat swung from right to left, then suddenly the bow dipped down, scooping up a deluge of water that swept over the deck.
This inadvertent braking made the stern swing round and their course changed. They weren't heading towards the gap between the boulders anymore.
Saitôra jumped up in horror and held the map close to protect it. "Iophâlor!"
"I see it," he replied in a choked voice and braced his feet against the side of the boat to swing the helm around with all his might.
But the Tronjor defied him.
Gurgling and burbling, the water surged around them, the bow making straight for the wet, black wall.
Saitôra could only guess how fast they were going. _It would definitely rival a swallow in flight._
"Gathalor, come here," Iophâlor shouted and leaned his upper body right out over the side of the boat. "I can't do this alone."
"I knew it! I knew it!" The white-haired älf staggered awkwardly towards the back and threw his body weight against the thick handle now moving slowly but surely to portside.
"If we drown, you'll have no need to be afraid of Shôtoràs anymore," Saitôra remarked. _Irïanora will have to explain to me why I have him with me. He's useless._ "Go on, put some effort into it! This is taking too long."
Both älfar were screaming with the strain, their muscles bulging. The wood of the helm groaned and creaked under the stress but they managed to make the boat turn back into the current so that they were speeding towards the gap.
Saitôra was taking deep breaths, wiping the spray off her face. "Well done," she praised them loudly over the roaring of the Tronjor.
The boat headed for the gap between the boulders and the bow was racing through it when there was a deadly jolt and their journey ended abruptly.
Saitôra toppled forwards and lost her balance. She fell flat on her face on the deck.
The impact as she hit the planks was very painful, but the älf-woman didn't let go of the map. The deck was bucking and rocking beneath her so that she struggled to get to her feet.
Huge amounts of water washed over the stubborn boat as it turned very slowly and began to present its broadside to the current more and more. A loud cracking and splintering sound underneath the soles of their feet made it clear that the timbers were breaking and being torn apart.
_Wrecked on a bloody rock!_ Saitôra was furious and only just about managing to keep her balance. She shoved the map into the waistband of her shorts. If Gathalor hadn't been needed for maintaining their course, the accident could have been prevented with just one glance.
But then the älf-woman heard, amid the roaring of the river, a soft rattle mingled with the cracking of wood.
_Is that..._ Her gaze flicked right and left. She could make out rusty iron rings in the rock fitted with a chain that ran underneath the surface—that's what they had crashed into. _What on earth..._
At the same moment, the Tronjor hurled itself at the boat and pushed one end down.
The capsizing hull was pushed against the chain along its entire length and split against it, breaking into separate pieces.
Saitôra fell into the torrential river, got caught by the current and was pulled downwards.
It got suddenly colder; the water was like liquid ice. The älf-woman lost track of which way was up and which way was down in the gushing water.
The Tronjor pushed her forwards and her head and face were dragged along the rock, making her cry out in pain—and swallow water that tasted metallic and coppery from her blood.
All at once everything brightened.
Hands grabbed her by her black hair and shoulder; two voices were shouting over each other, then Saitôra was pulled roughly out of the water and across soft sand as she retched and vomited.
_Rescued._ She propped herself up on all fours. She vomited surges of river water several times, and she was trembling and coughing. Her right cheek burned and she could feel the blood running down it. The wound must have been deep.
When there was no more water to come out of her lungs and stomach, Saitôra knelt back on her heels. She had grazes all over her arms and legs, redness oozing out of them. The map was gone from her waistband.
She had expected to see Iophâlor or Gathalor, but found herself instead facing four älfar wearing green, light leather armour that made them difficult to spot among woods and grassland. Even though Saitôra was still gasping and could barely think straight, she grasped that her rescuers were not warriors from Dsôn Dâkiòn.
She brushed her dark, wet hair out of her face so that she could see better. "Who are you? How dare you string up a chain and... we're fishermen who..." She retched again but didn't vomit. "Where are my friends?"
The unfamiliar älfar silently exchanged looks. Then one of them raised his hand and pointed at the map he held with her blurred notes on it. "Simple fishermen would hardly have something like this with them," he replied frostily.
"You're forbidden to travel more than four miles down the Tronjor," another of them chipped in. "You would have avoided the shipwreck if you'd adhered to our pact."
Saitôra tried to pull herself together. _They're scouts from Elhàtor._ "You have just as little right to be here," she said, trying defiance and accusation. "It's more than four miles from here to the mouth of the river."
"I could claim that we didn't use a boat," retorted the warrior who had spoken first, splitting hairs. "Hence we're not breaching the agreement. We're just safeguarding what we and the monarchess are entitled to: protection from Dsôn Dâkiòn. Who would deny us that? How do I know what you've had installed further upstream as protection from us?" He took a step to one side.
The älf-woman saw Gathalor and Iophâlor lying further up the beach. Their eyes were closed, but her friends were breathing. _At least there was that. Nobody was hurt._
"You're spies!" The unfamiliar älfar tapped the map. "You've measured the river again to find out which ships you could sail down it as far as the sea, to attack us." He nodded to his people, at which signal they grabbed Saitôra and dragged her to her feet. "You're coming with us to Elhàtor. The monarchess should interrogate you herself."
"No!" she cried indignantly. _That_ was too much of an adventure for her. "No, it's not like that!"
"The monarchess will be the judge of that." The commander looked at Gathalor and Iophâlor. "Bash in their heads and throw them back in the river. We only need the girl."
Struck dumb with horror, Saitôra watched as two of the soldiers picked up huge boulders and dropped the stones multiple times on her companions' skulls and backs of their necks. The twitching bodies of the young älfar were shoved into the gurgling, swirling waters with boot-clad kicks, and then were washed away.
Saitôra had her arms bound behind her back, then two warriors set off with her while the others stayed behind at the bottleneck.
Listless, she let them do as they pleased.
# Chapter IV
_A timid hand on the bowstring violently jerks the simplest shot._
Wise saying of the Älfar
Collected by Carmondai, master of word and image
Ishím Voróo, Älfar town of Dsôn Elhàtor, 5452nd division of unendingness (6491st solar cycle), summer
Modôia entered the gallery. From it, you could look down into the large, austere basalt hall. The only embellishments were the runes chiselled into the walls. The monarchess was followed by Khônatá, the top cîanai of the fine art, who wore her hair tucked underneath a coil of colourful cloth. The monarchess felt the painful prickling on her skin. _It smells of blood, and the air is charged like it is before a storm._
Below them, half a dozen älfar were practising combat, being instructed by both warriors and cîani at the same time, in order to combine their skills to become invincible in battle; the shooting pains from the constant release of invisible energies reached them where they stood.
There were no flags or pennants hanging down or anything that could go up in flames or get entangled—just pure, fireproof basalt which could withstand very high temperatures.
_Who would have thought it?_ Fascinated, Modôia watched as the students combined the sword and spear attacks with magic in a supremely confident way.
A house-sized cloud of the blackest darkness formed in one corner of the hall despite it being broad daylight. Modôia just caught a glimpse of the attacker hiding inside it. The edges of the cloud rippled like mist and expanded, edging its way forward.
"So you can spread them out?" the monarchess asked, wearing a deep red, floor-length silk robe with black and silver embroidery on it.
"The girl is capable of plunging the whole building into darkness," Khônatá explained. "Her sister is able to create mirages and apparently move everything: walls, doors, windows."
One young älf got ready to jump and then shot far up into the air, covering a distance of fifteen paces without visibly making any effort. He pulled off the landing as easily as if he had just done a little hop. As he landed, he used a short sword to split a tree trunk as tall as a man in two, right down to where it was clamped to the floor.
Then there was an älf-woman sitting on the floor, rotating five short swords around herself so quickly that no blades or arrowheads could get near her.
_A shield made of_ _dancing blades._ Modôia nodded almost imperceptibly. "And they were all born on Elhàtor?"
Khônatá came and stood next to her. She had chosen a high-necked, brown robe that allowed enough air onto her skin through slits. "The youngest generation, monarchess, and yet the strongest that I've ever trained. They have all absorbed the magic of the island without suffering from it." Her sympathetic glances did not go unnoticed by Modôia. "They even manage the spells more easily than anyone else to date. I've never seen our tribe produce anyone like them."
_Only a hundred of them and all of Tark Draan would have fallen to us._ "How strong are they?"
"The real question is this: how strong are they capable of becoming?" Khônatá placed her ringed hands on the railing, black ink stains on the fingers of her right hand. "And if you _were_ to ask me that question, I couldn't answer it for you. The älfar have not had cîani of this quality before."
_That was for sure._ Modôia pursed her lips and reflected. "So we need magical spells to develop their skills further."
Khônatá bowed. "And the necessary teachers. Our older cîani may have been exploring our powers and possibilities in Dsôn, but very few of them managed to go beyond the innate skills." She pointed at an older cîanoi with a brisk gesture. "Take Olòndôras, for example. He's able to influence the weather if he concentrates hard. But afterwards he has to lie down for ten moments, on the brink of death."
"The old guard from Dsôn?"
"Correct. Like me, he is able to use the magic of the island but it causes us pain. Or rather, the energy field is not very pleasant." Khônatá turned her face towards her. "I heard that you were doing worse, although you're not weaving shadow around yourself or..."
Modôia raised a hand to deter her. "My troubles have not worsened here. And you can save your sympathy too. Elhàtor has become my home and I'll gladly pay the price for us all living here in safety." She smiled down at the students. "They've got it better than we do already. Can you imagine how life will be for their descendants one day? What power they will possess and how confidently they'll use it?" The monarchess sighed happily. "This island, Khônatá, will never be conquered." _My people are protected from all harm._
"That is my firm assumption." The cîanai drew a folder out of her white shoulder bag. "I took the liberty of writing down some remarkable new advances in detail, so that you can study them at your leisure in your chambers. Soon we'll be able to deploy two cîani on each of our ships instead of one."
"And that's not counting the magic-wielding warriors and warrior-women in this hall?"
"I'm only talking about cîani of Olòndôras' ilk. Soon the fleet will no longer be dependent on temperamental winds and treacherous ocean currents in order to..." Khônatá broke off and stopped herself saying any more.
_So you're one of them._ Modôia knew that the chief cîanai had come within an inch of mentioning an attack on Dsôn Dâkiòn.
Quite a few of the islanders agreed with her; they wanted to get rid of the latent threat and focus on new goals. Before starting a new war, end the old one, so the saying went.
_But war hasn't even broken out. At most, we have a war of words and we're sinking ships belonging to tribes who are deceived or stirred up._ There had not yet been any proof that the sovereign Shôtoràs was involved in these attacks in the past. Modôia was relieved by this, because she really would have to start a war if he was.
"Well, that puts paid to the last of our worries, doesn't it? What can stop us in the future if we command the winds?" Modôia chattered away coolly, clapping her hands once before taking the folder. "Thank you for your thoughtfulness and your time." She rested her left hand on the cover. "I am going to read this thoroughly and let you know what magic I want to see improved."
Modôia turned around, sighing softly as her spine sent scorching heat into all of her bones. She swallowed and moved more slowly, but still steadily, towards the exit of the gallery and the basalt building. She wouldn't have been able to endure it any longer without fainting.
Being in a place where the magic was concentrated caused her a huge amount of pain, which she had tried to combat by taking a double dose of elixir in advance. _Leïóva needs to change the formula of the concoction or soon I'll barely be able to leave the house._
Khônatá saw her out and the älf-women said their goodbyes.
Her gait stiff, Modôia went down to the harbour to enjoy the wind and look at the wares the merchants had on display.
The further she got from the academy, the more the pain subsided.
Khônatá once tried to explain the discomfort with an analogy. The magical field, palpable across the whole island, affected the älfar from Ishím Voróo like a thin spike. For some, a poison flowed out of the spike, for others it was an invigorating substance.
Khônatá attributed the fact that Modôia suffered more than anyone else to the fact that the monarchess had been in Tark Draan, where a different kind of magical energy prevailed. Her body had grown accustomed to one kind and was rejecting the new kind. The youngest generation, however, was born with none of the foreign magic at all, and enjoyed the advantages of the island's version.
_I wonder if they would be in as much pain as I am if they were to go to Tark Draan?_ Modôia walked stiffly on, as if she were in the cold winds of the Grey Mountains, her limbs and muscles nearly frozen solid.
The cries of the locals rang out ahead. The merchant fleet had brought an array of goods to be given away and bartered. No coins were used on Dsôn Elhàtor; the locals bartered for things they needed.
Along the coasts and on some of the islands in the area, the älfar did use gold as a currency, because the inhabitants liked to hear it clinking in their purses, but the abundance of wealth on Elhàtor made all currency redundant.
Modôia strolled through the narrow alleyways, enjoying the shade, the wind and the hubbub of voices growing louder. Children raced along the cobbled streets and played tag. _The young generation that no longer needs to put up with any disadvantages._ She waved to the boys and girls and they returned her greeting cheerfully and effusively. _Innocent and perhaps more powerful than the Inextinguishables ever were._
There was no cult surrounding Modôia and nobody worshipped her as they did Nagsor and Nagsar Inàste. She was the monarchess and nothing more. If her death came, the people expected her son to follow her into office. Her clever Ôdaiòn was very well suited to it, he was good-looking and aware of how things worked despite not being island-born. _He's still finding it difficult, but he's learning._
Modôia had reached the harbour, which was protected by an enormous wall and the fence.
The remains of the ships that had attempted the ramming attack and been smashed to pieces by the concentrated jets of water had left sculptures on the quay and turned them into works of art; the dead body parts in them served as food for small crabs. They plucked the flesh meticulously off the bones.
_A work of art that constantly evolves._ Modôia nodded approvingly as she strolled past the artworks, admiring and marvelling at them like some other locals.
Her thoughts turned to Leïóva, who was overseeing the construction of special ships that could be used to travel the eighty miles up the Tronjor and disembark outside her hometown.
Dsôn Dâkiòn would be surprised by their arrival and their cîani's skills would shock old Shôtoràs and his guards even more. The river may be two miles from the Majestic but that could be factored into their plans. Magic was swifter than any arrow or night-mare.
But there was as yet no well-thought-out plan incorporating the exact sequences of events in their military campaign.
Modôia thought about the two messages she had received, one from Shôtoràs and the shorter one from an unknown hand. Unlike Elhàtor, other places seemed to be preparing.
_Was it a mistake not to be making these kinds of invasion plans?_ Modôia stopped in front of a sculpture without really taking it in. _How quickly could the sovereign drive his troops downstream?_
She placed one hand against the rotting wood which was held in place with gold, silver and tionium wire. She could clearly feel the warmth radiating from its porous, rough surface.
A new thought occurred to her: had Shôtoràs already sought out allies? Would some coastal towns potentially make their boats available so that Dâkiòn did not even have to come down the river, but could just walk to the coast?
But the moorland between the town and the coastline was considered impassable. An eighty-mile strip of land inhabited by monsters, diseases and mosquitoes that attacked hikers in swarms and killed them. Even marching along the riverbank was too risky—there were quite a few areas of swampland and quicksand.
Modôia sighed again. _I just wanted to stretch my legs and get away from the pain. Instead I'm brooding over what I should do._
If Leïóva had her way, the grotto would already be full of the long, narrow boats that fit through the narrowest parts of the river.
They could glide up the river with their diamond-shaped sails. The lack of woods around Dâkiòn would not prevent a conquest: straight after landing, the ships could be dismantled according to a detailed blueprint so that ladders and catapults could be built from them. The fixing bolts were prefabricated, the parts carefully marked. The scholars had thought of everything.
_And yet I don't want that. There have been too many wars._ Modôia was looking ahead to the marketplace with its spices, the barrels full of goods and fabrics, and the news the sailors had to report. _One more alley and I..._ Then she noticed the shadow falling next to her own.
As if out of nowhere, the black-haired Leïóva was standing next to her looking very solemnly at her. "You've got to come with me." She was wearing the white skirt and matching chest wrap. She didn't seem bothered by the heat; there wasn't a drop of sweat on her tanned skin.
"Did I miss a meeting?" She looked around in astonishment. "I was with Khônatá and..."
"We've taken a prisoner," the slim woman interrupted her. "In the area around the estuary, at the bottleneck our scouts are safe-guarding."
"Why have the warriors brought them to Elhàtor?" Modôia's thoughts were struggling to keep up. First, she had to shake off what she had just been thinking, which fit unfortunately well with this news.
"For interrogation. She's a spy," Leïóva replied brusquely.
That got Modôia's attention. "Proof?"
Her confidante handed her a crumpled, tattered map with the river sketched on it. The paper must have been in the water, but it was clear amendments and annotations had been made to it.
_Now I've got the proof I never wanted._ Modôia put the map away and motioned for Leïóva to walk on ahead of her.
They crossed various bridges and smaller footbridges before reaching one of the closely guarded and secured entrances to the grotto.
The lightly armed guards let them pass and soon they were descending a wide staircase into the cavern hidden below the surface of the island.
The air temperature was noticeably cooler and felt damp. It smelled of wet stone, algae and mussels.
The sea cave they entered was a mile wide and had four entrances; the ceiling was high enough to accommodate the fleet despite the height of the masts.
Modôia had had the heavy stalactites cut down and made into missiles for catapults to prevent any harm to ships and crews. If the large and small vessels weren't in the harbour to unload goods, they were steered into the grotto. The commanders were able to set sail at any time and in any direction via the tunnels.
Leïóva led Modôia past the long harbour wall—from which long footbridges led to the waiting ships in the grotto—and towards the empty prisoner wing.
Anyone who did something wrong in Elhàtor—and that happened extremely rarely—ended up here after a good beating. If they didn't learn their lesson, they would be put out to sea in a boat with no oars. If they found their way back to the town, they were pardoned.
But with spies from Dâkiòn, Modôia would show less mercy.
They entered the large space that had been hewn out of the rock, the place where the punishments were meted out; at the sight of the älf-women, the two warriors waiting there wearing the green armour of scouts rose to their feet and greeted them respectfully.
The prisoner had been stripped and was standing with her arms forced above her head in the middle of the room. Her wrists were in iron handcuffs bound to the ceiling via chains. They had refrained from tying her to one of the upright wooden stakes where the beatings took place.
"Monarchess, we detained the boat at the strait we were guarding," one of the two scouts began their brief report. "This one survived. She wouldn't tell us her name."
Modôia dismissed the scouts with a nod and walked slowly up to the black-haired prisoner; she took the creased map out as she did so. "You measured the river," she said pleasantly. "Give me _one_ good reason why I should _not_ assume that your intentions were related to war."
The naked älf-woman looked past her at Leïóva and remained silent.
"Do you want to tell us your name, little girl? It'll be easier to speak then," the monarchess suggested, taking in the side of her face that had cracked open as well as the raw skin on her scalp. "That looks bad. I've got good healers who will take care of you. Afterwards too, once I've finished your interrogation. But only—" she rolled up the sheet of paper and forced the prisoner's chin upwards with it—"if you tell me what you were trying to do."
"An attack, what else," grumbled Leïóva in the background. "Width and depth are marked, and in the most minute detail too. I..."
Modôia raised her other hand and her friend fell quiet. "Would you bring me my whip?"
"Of course." Leïóva hurried out.
"I'd like to warn you that the pain I inflict on you will not be out of malice, little girl," she said apologetically. "You could spare yourself all this by speaking to me."
The unfamiliar älf-woman gave her a searching look, then raised her pale grey eyes to the ceiling and acted indifferent.
"Ah, you're a warrior, of course, and you think I can't scare you." Modôia put the map away and turned to the door just as Leïóva was returning with the coiled whip. "After the first blow, you'll see that you overestimate yourself." She removed the protective caps and jerked her arm to unfurl the weapon.
The three straps slid to the floor and looked like they were creeping forwards like snakes; there was a soft clanking sound. At the end of each strap was a blade sharpened on both sides; a thick wad of wire wrapped around the leather protected it from the sharp edges.
"My son and I are only ones who know how to use this without cutting ourselves to pieces." Modôia enjoyed the sight of the blades twitching as if they were alive. "I don't use it often. I used to be able to slice the limbs off a full-grown barbarian and cut his throat in just one blow. Since you're not wearing any armour or even any clothes as protection, you're making it very easy for me."
The prisoner swallowed. Goosebumps formed on her bare skin.
"It takes skill and a good eye to swing this vicious weapon in such a way that you hover between death and agony." The älf-woman lifted the whip and cracked it gently.
The straps hissed straight at the terrified prisoner—and changed direction at the last moment. The blades shaved three long strips off the wooden stake right next to the trembling captive.
"You haven't lost the knack," Leïóva remarked and laughed quietly.
Modôia nodded approvingly and ignored the pain in her shoulder, her spine warming up. "That ought to give you an idea of what is about to happen to your flesh. I will slice out little sections all over your body. Then I'll continue with the bones," she explained politely. "My healers will stop you dying on me and then..."
"Saitôra," she blurted out. "My name is Saitôra." She strained furiously at the chains.
Leïóva emitted a disappointed sound. "Now we'll both miss out on our fun, monarchess."
"Be patient." Modôia moved her arm, flicking the three straps at the ground in front of her feet with a jingling sound. "Now, Saitôra. You measured the river..."
"Your warriors murdered my friends Gathalor and Iophâlor," she shouted, enraged. "They bashed their heads in to make it look like an accident."
"It was an _accident_ that you encountered my scouts. Because you and your friends were not allowed to be there in the first place. Let's leave it at that. And you ought to be glad you escaped the _accident_. It could just as easily have been you getting eaten by crabs and fish." Modôia spoke like a scolding mother. "Did Shôtoràs dispatch you to the _accident_ , to use your term?" she asked, condescending now. "How far did the preparations for the attack get?"
"I don't know anything about an attack."
"So you measure the river as a way of killing time, make notes on the map out of boredom and breach the agreements between our two towns on a whim?" Modôia made the leather lashes twitch, the blades sliding towards Saitôra's bare feet. "One more time: who sent you?"
The älf-woman stared at the blades, petrified. "Irïanora. My friend and Shôtoràs' niece.'
"Ah, so it is true!"
"No, nothing to do with a war. She wanted to give the map to the new architect as a gift!"
Leïóva laughed in disbelief. "Somebody thinks you're more stupid than she is herself."
_We'll see._ Modôia struck as quick as a flash.
The straps with the blades whistled as they darted forwards and Saitôra screamed in fear of her life. Her courage vanished as quickly as it had come.
But the monarchess had planned the blow in such a way that the leather wrapped itself around the upper arms and torso of the prisoner without the tips piercing the skin. "One last warning, Saitôra. My next blow"—she undid the straps which left dark blue welts on the älf-woman's grazed skin—"will go deep and it's going to be bloody."
Saitôra was panting hard. "I swear I don't know anything else," she said, weeping. Modôia simply gave the whip a crack and the prisoner screamed as though out of her mind. "I swear! Please, I just wanted to have an adventure."
Leïóva came forward, approaching Modôia, who was looking indecisively at Saitôra. "I get the feeling," she murmured, "we have the wrong person in chains."
"So do I. Your friend Irïanora should have a taste of my whip." _If she was ever truly a friend._ Sending this young älf-woman down the Tronjor without even hinting at the danger it put her in showed an extreme ruthlessness on Shôtoràs' niece's part. Modôia turned to Leïóva. "Might Irïanora have written the second message, do you think?"
"We could let Saitôra have a look at it. She may recognise the handwriting." She left the room at a signal from the monarchess.
"Tell me about your friends," Modôia said on the spur of the moment.
"They're dead," Saitôra spat.
"Yes, slain in an _accident_ that Irïanora is responsible for." She relaxed her painful shoulders and this alone was enough of a threat to make the prisoner start whimpering. "Who were they?"
"I didn't know Gathalor, but Iophâlor... he was a good warrior and swimmer. He served in..."
"Did they come from prominent families?"
Saitôra looked at her in astonishment. "I... don't know. I doubt Iophâlor did."
"Think!" Modôia lifted her arm and thrashed the whip in one fluid movement, despite her own pain.
The blades leaped into the air, whirring away and burying themselves in the post in a vertical line; the tips sank deep into the wood and wouldn't come out again when she tried to pull them out with a jerk.
_This was always its flaw._ Modôia swore inwardly. _Luckily Ôdaiòn has mastered another method._ She went to the large stake and, with some effort, pulled the blades out one by one.
"Did you see how easily..." She turned to Saitôra who was hanging limply from the chain beside her. Modôia couldn't help laughing: the young prisoner had fainted in fear.
Tark Draan, Älfar realm of Dsôn Bhará, formerly the elf realm Lesinteïl, 5452nd division of unendingness (6491st solar cycle), early summer
Cracks formed in the earth beneath Carmondai's bare feet as the ground continued to shake unrelentingly. He couldn't crawl away; the chains were holding him in place near the remains of the statues with steely indifference. _I mustn't stay here._
"Carâhnios!" he shouted.
Next to the mountain, the crater was subsiding even further. The sides of the banked-up mound collapsed and slid into the opening. The edge of the opening was coming closer to the älf with every heartbeat. The catapults vanished into the hole one after another.
The shaking under Carmondai's feet was not letting up. There was still no sign of the groundling.
"Zhadár!" Unlike the others, he guessed—or rather he _knew_ —what was happening. They were standing in the oldest part of Dsôn Bhará, where the Moon Pond had been—it was through here that the triplets had led the älfar out of Phondrasôn. After the Aklán arrived, the marshy pool had run dry and caved in.
Nobody had ever reckoned on this phenomenon happening again.
_There was too much heavy siege equipment in one place. Along with the palace's land collapsing, the weakened crater floor gave way._ At Carmondai's feet the earth sank by two or three hands' widths, but it didn't cave in altogether.
The quaking ended.
Then the groundling appeared by his side. "Ah, you haven't left yet," he cried, grinning. "Just stay there then."
_Never._ "Untie me!" Carmondai demanded fiercely, noticing more fissures forming beneath him. He suspected the destruction could start again at any moment. "I'm meant to be recording the decline. This event is part of it."
"Not in the way I had intended, but all right, fine," Carâhnios agreed. He took a key out of his pocket and detached the foot shackle fixture from the chain. "Your hands stay in the cuffs. You'll have to remember what you see. We've got nothing to write with here."
Carmondai followed the zhadár. His skin was noticeably tight, the sunburn making itself felt despite his agitation. He tried to ignore the fact he was wearing nothing but a loincloth so as not to feel too ridiculous.
Right next to the palace mountain, which had lost a whole chunk out of one side, a hole had formed with a diameter of a hundred paces. Terrible clouds of dust were rising up out the hole, as if rainclouds and thunderclouds were being created in the abyss and making their way towards the heavens.
The people and the elf-woman stood at the edge and looked cautiously downwards. From time to time they leaped backwards when smaller pieces broke off.
Carmondai reached the edge with the zhadár, and both of them looked into the darkness.
It looked like a wide well shaft had opened up. Along with the catapults—whose remains could be seen at the bottom of the abyss—the palace and mountain debris had smashed through multiple layers of rock.
Near the bottom there were clearly discernible holes and signs of cave entrances in the walls, which suggested there were passageways down there and that beasts could appear through them at any moment.
"An entrance to Phondrasôn," Carmondai murmured. _Just as I thought._
"What do you think?" Carâhnios looked at him.
"The Moon Pond was once in this spot, and beneath it were the foothills of Phondrasôn, the place of exile. I escaped from there with the Aklán more than two hundred cycles ago," he summarised. "The elf-woman may still remember the Moon Pond." He felt a shooting pain at the back of his neck, partly because of his old bones and partly because of his burnt skin. And he was still parched. "Pray to your god Vraccas that the collapse didn't create any openings that will allow monsters to escape."
"That's all we need," Carâhnios grumbled. "Vraccas, hurl glowing coals into this hole and burn it out."
Fiëa spat into it. "The älfar's gift to us. We defeated them and in return they fling open the gateway to Tion's kingdom."
"Blame the advisor who had the catapults built," Carmondai said. "There was no earthquake while the Aklán lived and ruled here." He looked at the elf-woman. "In my dungeon, I would have noticed it immediately."
"What do we do now?" asked one of the soldiers, at a loss.
"Scrape the loose earth away from the crater and push it inside," Fiëa replied anxiously. "Ideally before the monsters realise they have a path to freedom."
"You should be quick about it," Carâhnios remarked. "And until the passageways that we can make out down there are blocked off again, we should also have pots of boiling pitch and tar lined up so that we can tip them out over any attackers climbing up."
"Hear hear," Carmondai agreed in an undertone.
"You ought to be pushed in, black-eye!" a soldier said menacingly. "As a sacrificial offering."
"The dwarf is right." Fiëa looked out over the ranks of her volunteers to the right and left. "Prepare cauldrons and then send for more workers from the surrounding kingdoms." She turned around, fixing her gaze on the mountain. "Chip away at the sides more and push the ruins of the palace downwards. That will get us part of the way there anyway."
The captains passed on the instructions and Carmondai was silent so as not to draw any more attention to himself.
"Four good men have fallen in. We should climb down and look for them," one warrior said.
Fiëa shook her head, her fair hair bouncing. "Nobody is setting foot into it."
"But they..."
"They are dead or so severely injured that they will be dead by the time you've risked your life and made it down," she cut across him unsympathetically. "We will remember them but it's more important that everyone helps stoke the fires underneath the cauldrons and fill in this hole." Fiëa waved her arms over the pit in a blessing. "May Sitalia receive their souls and take care of them. Our responsibility is to the living." She pointed one hand at Carmondai, her index finger extended in accusation. "Get rid of him, zhadár. I can't bear him near me so long as one spark of life remains in him."
Carâhnios turned to the älf, snarling. "All right then. Our trip is going to start a little earlier than planned." He set off, making straight for the only house in the crater still standing. "Let me pack up my gear while you count your lucky stars, because you're going to travel through Girdlegard with me killing älfar."
_Better than lingering in the vicinity of the elf-woman._ Carmondai followed him, holding his cuffed hands loosely in front of his stomach. "Something to write with would be a good idea. And clothes. But water is even more important."
"We will get our hands on that. Stay out here." Carâhnios disappeared through the doorway.
Carmondai couldn't wait anymore; he saw a horse trough and stuck his head into it. The water tasted stagnant and he saw little bits of straw floating in it, but he lapped it up anyway. Warm yet exquisite, it sloshed around inside him. He swallowed and swallowed until he emerged spluttering and gasping for breath. _Better, much better._
He looked at the mountain again, a hundred troops scaling it via the remains of the badly damaged staircase.
Despite the sunburn he suddenly felt ice cold: there was a gaping hole where his dungeon used to be. You could see inside the prison like it was a crushed ants' nest.
_If I hadn't escaped, I would be dead and my notes would have been lost in the hole._ He thanked Samusin for his mercy.
Carmondai didn't for a moment wish the appearance of monsters upon Tark Draan, or at least not as long as he was in the crater. _After that, whatever happens, happens._ He leaned back against the wall of the house. His face burned even though he was standing in the shade. With a cupped hand, he scooped more water from the trough and poured it over himself.
Carâhnios did not reappear for quite some time.
When he did, he was carrying a large bag which he fastened to a white pony, as well as four saddlebags which he tied to a horse. A soldier brought out some shabby clothes and Carmondai put them on awkwardly. His handcuffs were taken off briefly so that he could do so.
He was getting even hotter now; his skin felt like it was glowing and the fabric about to burn. To add insult to injury, the trousers and shirt were too short and the boots were too wide. _I look like an idiot._ The humiliations continued.
"I'm bringing rations and some sheets of paper as well as quills and ink," the zhadár announced and shooed the älf towards the horse. "Mount."
_Ink. It will fade and run and leave blots._ Carmondai thought wistfully of his smashed, burnt pencils made from coal dust. "Was nothing saved from my dungeon?" He swung himself into the saddle and every one of his joints hurt. The daystar seemed to have penetrated right through to his bones.
"Some stuff was. But I didn't manage to get my hands on anything else just now." Carâhnios put the handcuffs on him and attached them to a chain that he passed underneath the horse's belly and secured with a padlock. "For your sake, I hope you can ride. Because jumping off is not going to work for you." Laughing, he strode over to his pony and mounted it. "If you start to slip, let me know straight away."
"So that you don't miss it, I take it?"
"Absolutely! It's going to be hilarious to see." Carâhnios howled with laughter.
Carmondai cursed inwardly. He used to be extremely skilled at riding, racing into battle at a gallop brandishing his lance. _Nobody forgets how to do it, but it will take a while for me and the nag to get to know each other._ Disappointed, he inspected the horse. "Is there a night-mare that I could use, maybe?"
"No. Most of them have been killed." Carâhnios set his pony trotting. "If we see unicorns along the way, you can make yourself one. But something tells me you'd die in the attempt."
Sighing, Carmondai followed him to the winding paths that led out of the basin-shaped valley and up to the plains. _This is going to be the hardest journey I've ever undertaken._
Quite apart from becoming a witness to a zhadár killing one älf after another, the spectre of his own death hung over him constantly. Either in the form of angry locals who wanted to take revenge for oppression and abuse, or at Carâhnios' hand when his mission was complete and there was nothing left to hunt or for Carmondai to record. What's more, he doubted whether the elves could restrain themselves from demanding his life much longer.
_I'll need to have a plan by then._
Escape or become indispensable, those were the options.
He didn't have much faith in an escape.
_What could I offer them to avoid endingness?_ Carmondai rode after the groundling. _Knowledge. That's the advantage I have._
Now he needed the people and the groundlings to ask the right questions about his knowledge—then he would be allowed to keep living.
_Only the living get options._
Ishím Voróo, Älfar town of Dsôn Dâkiòn, 5452nd division of unendingness (6491st solar cycle), summer
Irïanora was looking anxiously at the two bedraggled pigeons that had turned up in the pigeon loft just a few moments before.
Pecking and cooing, they walked back and forth on the landing board, their heads bobbing as they went over to the water bowl and drank in small sips.
_No message for me._ The älf-woman left the cramped coop on the roof of her house and looked at the river. She traced its course until the trees got too high and she could no longer make out even a flash of it.
Irïanora could vividly imagine why there was no scrap of paper, but she didn't dwell on the explanation for how the pigeons had got away: the boat carrying Gathalor, Saitôra and Iophâlor had had an accident, either in the rapids or because of driftwood, or another unfortunate series of events. The cage had smashed in the accident and these birds had found their way home; the rest of the carrier pigeons had probably sunk to the bottom of the river.
She didn't dare speculate whether her friend Saitôra was still alive.
And Irïanora was equally unsure whether she ought to wish the gods came to the aid of the trio and that they found a path back through moorland and swamp teeming with vermin and snakes. Not even monsters ventured into the woods either side of the river.
_Even our best scouts don't get more than half a mile in before having to retreat. Not one of the three of them is capable of fighting their way through that terrain._ So many thoughts were racing through her mind, and none of them good ones.
Assuming they managed it nevertheless, Saitôra, Gathalor and Iophâlor's return would obviously be noticed straight away, no matter what state they were in. Plenty of questions would be asked if inhabitants of Dsôn Dâkiòn disappeared and then suddenly turned up outside the gates.
_They will not be able to wriggle out of it with talk of getting lost._ Irïanora felt like having a large glass of wine.
The trail would inevitably lead to her, the niece of the sovereign, and that meant she would be in huge trouble with her uncle. But all she had wanted was to have a map of the river, an up-to-date one, so that she could discuss her ideas with like-minded people, of which there were quite a few in Dâkiòn.
_I should have allowed for an accident in my plans._ She walked over to the narrow staircase down to her living quarters.
She quickly swapped the grey shawl she always put on before she went up to the pigeons for a bright red dress. A few feathers came loose and floated through the room with its ten-paces-high ceiling.
Irïanora took a pitcher of wine out of the cabinet, poured herself some and diluted it with water. The alcohol ought to do the trick somewhat. Maybe then she could come up with a plan for how to explain the whereabouts of the missing trio.
But short of sending out a second group, she was stumped.
_Would that be wise?_ Hesitant, she poured herself a second glass and this time didn't add the water. _No, I can't do that. It will attract even more attention._
On her third glass of wine, Irïanora decided that the pigeons had simply escaped. An accident hadn't necessarily happened, and the little group might be on their way back already. In complete secrecy so that nobody found out anything about it.
If the three didn't turn up within seven moments of unendingness, their families would send out a search party. And as soon as that happened, an expedition could potentially be sent down the Tronjor after all.
_I'll just say that they wanted to go fishing._ Irïanora took a deep breath, and another sip. _It will work out. I'll get my map. And maybe more. I didn't send that idiot Gathalor along for nothing._
There was a knock on the door downstairs and her maid, Zelája, answered it. After a loud argument that came closer and closer to the room, the door to her chamber opened.
An armed man stood on the threshold wearing the insignia of her uncle's bodyguards.
_This seems like perfect timing for bad news._ Irïanora sipped her wine. "I didn't invite you to come inside." Offence was the best form of defence and it suited the sovereign's niece very well.
"I request that you follow me." His eyes were alert and fixed on her, his expression hard. He would not stand for any arguments or excuses. "I have been sent by Shôtoràs."
"On what business?" She made an effort to look nonchalant although she was rattled.
"My task is to accompany you to the sovereign. I don't need to know any more than that." He unblocked the doorway, which was a clear command.
Irïanora decided against playing any more games and walked to the warrior's side; she polished off the wine as she did so and handed the empty glass to the waiting Zelája.
"Have dinner ready just after sunset," she ordered as she passed by. She appeared unfazed.
They left the house, walking through the neatly laid out streets and over the bridge into the second, larger part of Dsôn Dâkiòn. The majority of the residents lived there.
In Irïanora's district, some buildings had stood empty ever since so many älfar moved to Elhàtor with Modôia. The generations that followed were too small to fill the gaps and bring back the old hustle and bustle.
Irïanora used this walk, which she was trying to make last as long as possible, to examine her hometown in the radiant sunlight.
Due to Dâkiòn's position, perched on top of the mountain with its impassable, steep slopes, the Majestic was impregnable. This was what Irïanora firmly believed as she walked over the ravine between the upper and lower towns and looked down into the abyss.
Nobody knew what had happened to the giants who had built their fortress on this spot in earlier times. A few bones had been found and they stood in the squares as works of art, reminders that the älfar owed their sanctuary to the transience of their predecessors.
_They must have been wiped out by an epidemic. A fever from the moor_ , Irïanora thought and after the bridge, she turned onto the path that led to her uncle's palace.
The warrior escorted her in silence, not revealing what he was thinking.
Soon they were standing in the Hall of Entreaties, as the locals had taken to calling this auditorium with cross vaulting and a ceiling thirty paces high. Artists had decorated the walls, and the ceiling was panelled with slivers of bone while the arrises were plated with silver. Multiple chandeliers hung low to provide light.
_Ah, I'm to lend the old man a hand._ Irïanora moved towards the chair to the right of where her uncle sat whenever he heard suggestions, entreaties and complaints every forty moments of unendingness. She had been present at the last session, bringing him wine and correcting the scribe if he made a mistake when recording the cases.
"Stop." The warrior held her by the arm. "You're to wait here."
With a mixture of disbelief and bewilderment, she stood still.
_Now I'm the one who's to be heard?_ Anything was possible. Maybe it was repercussions from the onwú or maybe it was probing questions about the boat she had had designed. _For the first time, I'm on this side of the hall._ The älf-woman had a bitter smile on her face.
The side door swung open and Shôtoràs entered without deigning to look at her; for once he was tapping the end of his walking stick down softly.
He ascended the platform and took a seat behind the balcony-like desk. He shooed the guard out with an impatient gesture.
The door banged shut behind the älf, setting off an echoing rumble like a thunderstorm.
The sovereign rubbed the back of his neck with one hand and tossed back his thick, pale grey hair. One hand rested on the metal crow's beak, the other lay on the little desk. His eyes were fixed on the dark wood for now, his mouth pressed into a very thin line.
Irïanora sensed it was smarter to wait, although it took some effort.
Suddenly Shôtoràs tapped the desktop quickly with the tip of his index finger, drew breath and emitted nothing but a loud exhalation. He seemed to feel the words that occurred to him were inadequate.
Without warning he reached into the pocket of his robe, took something out and threw it at her. Pale feathers twirled across the room.
Irïanora was hit by a dead golden pigeon that must have fallen into the clutches of a bird of prey.
The animal fell at her feet with a muffled rustling sound, one of its wings splayed out; red spatters were clearly visible on it.
Irïanora understood within half a heartbeat and she started to feel hot. Beads of sweat formed on her back and forehead. She needed to come up with something right now. Neither of her plans had foreseen that her uncle would receive news first.
"I, Gathalor, declare that my worldly goods should go to Irïanora," he quoted from memory, reciting the words as if they were a poem. "As she already possesses my heart, may she also, in the case of my death, be given my assets."
The sentences echoed across the high ceiling and took a long time to fade away.
_You mustn't make any mistakes now_ , Irïanora warned herself and conjured up an expression of shock on her face. "Gathalor is dead? How terrible!" She looked at the battered pigeon. "Why does the news come to us like this?"
Shôtoràs leaped up and banged the walking stick on the desk; the bone inlay rattled as it shattered and then skipped along the stone floor. "Try again," he thundered.
Irïanora tried to work out from his furious expression what he already knew and what he was still figuring out. She admired his composure. If he were any other älf, the black lines on his face would long since have become visible.
"So he has put into action what he used to tell me about so often," she began cautiously. "He dreamed of travelling down the river."
Shôtoràs sat down very slowly and didn't say a word.
"He, Saitôra and Iophâlor had made firm plans. They wanted to explore the Tronjor and see what adventures there were to be had along the way. Life in Dsôn was too boring for them and didn't offer any excitement," she said, concocting an explanation in which she was ultimately the least to blame. "I tried to dissuade them. Our last conversation about ships was still fresh in my mind. Poor Bethòras."
Shôtoràs shifted his probing gaze away from her and stared at the high ceiling with its little tiles of bone; his right hand remained on the handle of his stick. The reflection of a beam of light from one of the silver arrises fell right across his face, as if he had a glowing scar.
"Since absolutely anything can happen on a trip like that, I asked Gathalor to take some of my carrier pigeons with him so that they could summon help in case of an emergency," Irïanora continued, feeling slightly more sure of herself. _He knows less than I feared, otherwise he would have interrupted me long since._ "I gave them an old map to take with them so that they could get their bearings and not be at the mercy of every set of rapids."
"When did they set sail?" he demanded in a husky voice.
"I couldn't say exactly. They just wanted to take a simple fishing boat and..."
Shôtoràs' head jolted to face her, his pale grey hair slipping forwards. "Why did you keep it secret from me?"
"Because it's not my expedition," she dared to protest slightly. "If Gathalor and his friends are prepared to take the risk, why should I stop them? I'm not allowed to, but at least they can try." Irïanora cupped a hand over her mouth and cleared her throat. "Uncle, I bear no responsibility for their deaths."
The sovereign took his time before answering. "Yes, you do. And I cannot absolve you of it. Because if I had heard about it, they wouldn't even have boarded the boat in the first place." Shôtoràs lifted his stick, the tip pointing towards the domed ceiling. "We are able to imagine who built these enormous halls. Who stacked the ashlars one on top of the other, the ashlars that are twice as thick as an älf is tall, and yet they were defeated by something. An illness, a plague, magic—who knows?" Suddenly the tip was aimed at her. "And what I _very much_ suspect is this: you had a hand in their _adventure_."
"Uncle, I..."
" _You_ sent them out, _you_ gave them the map and _you_ sent them to their deaths!" he shouted at her, getting to his feet. The anger lines shot across his face now. The stick shook and his knuckles stood out, white. Shôtoràs clasped the handle with unbridled strength. "And all that you're giving me is this made-up story?" He leaped down from the platform and rushed at her, the tip still pointed at her chest like he was going to bore a hole through it at top speed. "I warned you!"
Irïanora shrank back in fear. "I didn't lie to you," she cried. Then the stick whizzed downwards and caught her in the hollow of her knee so that she collapsed in front of him. "No, please, I..."
Shôtoràs beat her, battering her shoulders, her back, the nape of her neck, head and arms until the skin changed colour and cracked in several places. Blood oozed through her clothes, dripping onto the floor of the hall in multiple places.
Panting, the sovereign at last let her be, tossing his dishevelled hair back. "Stand up."
Irïanora struggled against the dizziness. The pain overwhelmed her, and with every heartbeat another stabbing pain went through her body. She tried to rise but her legs wouldn't obey her.
"Stand up!" Then the sharp crow's beak was hovering in front of her eyes. "Or I'll help you up with _this_."
The älf-woman struggled first to her knees and then to her feet but couldn't keep upright.
"I have received a message from Dsôn Elhàtor," she could hear her uncle was keeping his voice in check with some difficulty; it cracked from the restraint. "They wrote to me asking how I could explain that a boat had been captured with three spies from Dâkiòn on board. And why equipment for accurately measuring the Tronjor had been found?" He grabbed her by the throat. "And they would like to speak to an älf-woman called Irïanora who was accused by the spy Saitôra of being the instigator of the plot!" Shôtoràs shook and choked her at the same time.
"She's lying," gasped Irïanora, "or they forced her into it."
His laughter echoed. "They forced her to give _your_ name? How would that happen? Does the monarchess just know you from hearsay because you've performed so many glorious deeds and she's dying to get to know you?" he sneered and tossed her across the room. "Or because the onwú mentioned your name?"
Irïanora flew a good distance across the hall before crashing into a pillar and sliding down it, moaning. None of her thoughts could be pinned down, the excuses slipped through her hands.
"You stupid idiot! With your lust for war you've already ensured that poor Bethòras didn't survive a fall from the highest tower. How much further does your destructive impulse go?" Shôtoràs planted himself in front of her again, then slowly crouched down and grasped her by her mop of fair hair so that she was forced to look at him. "You knew how fond I was of Gathalor. So I'm sending _you_ to Elhàtor so that you can explain to the monarchess how this could have happened. You will apologise and accept any punishment that this älf-woman metes out to you so that this does not end in war between the towns." He let go of her hair. "Bring me back Saitôra, Gathalor and Iophâlor. Don't you dare show your face to me again with excuses."
Irïanora was too weak to reply so she just nodded. Blonde strands of hair covered her face.
Shôtoràs limped over to the platform and returned with a sealed casket which he threw into her lap. "You're to hand that over to Modôia. Nobody else is allowed to accept it or open it. My personal apology to her is inside. I can only hope that it satisfies her."
"Yes," groaned Irïanora, wiping away the blood running into her right eye from a wound on the top of her head. _I must not underestimate the old bastard anymore. That was my last mistake._
"The healers will tend to your wounds, but not too much, so that the monarchess can see that I've disciplined you," Shôtoràs informed her. "Oh yes: and I keep my word."
Before Irïanora could ask what he meant by that, she felt a blow to the ribs followed by a diabolical stabbing pain and rupturing.
Without any input from her, she was lifted up like a doll, feeling like she was hanging on a hook.
She looked to her side, screaming, and realised that her uncle had rammed the tip of the beak into her side and pulled her to her feet by it.
"I told you I was going to choose the _other_ end next time," she heard his chilling words. "Bring me back my three älfar. Alive! I've lost too many to Modôia already." He pulled the metal out of her and Irïanora fell to the floor again, whimpering.
She saw the sovereign's broad back limping away from her. So the älf-woman dared, despite the pain, to grin furtively as the blood gushed down over her eyebrow and her side burned like fire. _Sending me to Elhàtor will be your downfall._
Ignoring the excruciating agony for a moment, her plan was far from doomed.
# Chapter V
_One can hang a barbarian even on the most crooked tree._
Wise saying of the Älfar
Collected by Carmondai, master of word and image
Tark Draan, Human kingdom of Gauragar, Grey Mountains, 5452nd division of unendingness (6491st solar cycle), summer
_There's another one._ Aiphatòn was climbing the adjacent rock face, his movements feeling clumsy and slow. Although he had walked several orbits at altitude, his body couldn't seem to acclimatise to the conditions. He still needed to pause and get his breath back every fifty paces.
_Good thing this kind of pursuit doesn't depend on speed and my targets are fixed in the rock._
The gusts were tearing at his cloaks as if the wind was trying to strip him, but his armoured gloves dug too firmly and securely into the small number of crevices for him to be in any danger. _It's getting even colder. Without sunshine I'm going to freeze as soon as I stop walking. I'll need to give up the night search completely soon and make a stop by a fire._
The markings the unknown älf-woman had left behind for him had been done in a colour that an älf could only see if his eyes were clouded over by the daystar. She must have got the extract from the plants in the valley. No other creature would have been able to identify them.
Aiphatòn's unusual feature as a shintoìt was the fact that, due to the permanent pigmentation in his eyes, he was identifiable as an älf even after sundown. _Finally there's a perk to being the son of the Inextinguishables._
He had reached the marking about five paces from the ground and two arms' lengths wide. It was in the shelter of an overhang so that it couldn't get covered up by swirling snowflakes.
Petrol had turned out to be the most effective antidote. He had brought some from the hollow in a leather pouch to kindle fires on his journey. But the fluid had run low two orbits ago so Aiphatòn had to scratch the surface carefully with his spear or gloves. If he pressed too hard, the runes would be immortalised as an engraving, visible to all eyes.
He wasn't using his magic anymore either because he didn't know how much of a supply the alloy armour had stored in it. There were no signs of a magical source in the Grey Mountains.
_The stone is soft_ , he noted to his relief, gripping tightly with one hand. _This will be quick._ He carefully rubbed one hand across the rock.
He looked around casually to see if anyone was watching, which was of course highly unlikely. But carelessness had sent more lives into endingness than the most hideous diseases.
Once the sun had set and its indirect, blood-red light reflected off the slopes, he finished his task.
_Another one down._ Aiphatòn looked to the ground and let himself drop. The thick snow muffled the impact. _Tomorrow, the work continues._
He picked up his rucksack and the holder he'd built to carry his spear on his back when he climbed.
What he didn't have was somewhere to spend the night.
By now he could tell from the cloud formations what was in store for him and the small, seemingly harmless scraps in the sky signalled an advancing storm front he did not want to face out in the open.
_A recess in the rock would be more than enough for me._ Aiphatòn adjusted his cloaks and cursed the fact he didn't prepare for his adventure properly. It had been impossible to say in advance how long it would last. _A fake Firûsha, a mysterious settlement and a search for runes._ He ran a hand over his skull where black hairs were sprouting. _Still too short to keep me warm._
He set off, paying close attention to the rock face further ahead. The älf-woman, whose name he'd already forgotten, generally left her markings at one-mile intervals and was careful that they caught the eye without needing to look for them too hard.
The light was fading, which was not a problem for Aiphatòn—however, the swiftly descending cold was, despite the double layer of cloak fabric and magic.
Hoping to find shelter, he marched onwards.
He walked along a narrow, ice-covered path, not knowing if there was a ravine or solid rock under it. As the ground got steeper and steeper, he needed to use his spear on it to stop himself slipping and falling.
Suddenly the next rune glowed on a cliff two hundred paces away. Something was written underneath it.
_That's new._ Aiphatòn was still too far away to make out the sentences but his curiosity compelled him to run to the marking despite the pain in his legs and heart. There was no cave or niche anyway.
The path suddenly fell steeply away and turned into a channel of ice. The glittery coating evenly lined the sides of the narrow pass.
Aiphatòn stopped and looked ahead. _Fate seems to decree that I slide down._ He took off one of his cloaks and laid it with the rough side face down so that he didn't hurtle too quickly down the sheer ice. _At least it'll be easier for me to breathe down there._
He sat on the pelt and pushed himself off, using the spear so that he at least had the illusion of being able to steer as he slid.
Aiphatòn flew downwards, faster and faster.
The rune was clearly visible and the writing underneath it said...
The cold wind brought tears to the älf's eyes and it was difficult for him to make out the small symbols.
_I've got to stop, one way or another._ He drove the tip of the spear into the ice behind him, and with a loud scraping sound, tiny ice chips sprayed up in a shimmering white fountain.
But he wasn't slowing down.
_Soon I'll have gone past it._ Aiphatòn infused his weapon with a pinch of magic.
The runes shimmered green, and now the blade plunged into the layer of ice as far as the beginning of its shaft, creaking as it carved through it. Cracks darted out from the groove in every direction and streaked to the edges of the iced-covered pass.
Aiphatòn came to a stop directly beneath the rune.
_Now for a spot of acrobatics._ He worked the spear free without taking the magic out of it and threw it into the sheet of ice right underneath the markings.
Straight away, he leaped after it and landed on the shaft. He skilfully kept his balance and read.
_Here ends_
_what I have left for the älfar._
_That could_
_be for many reasons._
_You must discover_
_the truth_
_for yourself._
_But I doubt_
_you will_
_find it_
_and still be alive._
_Endingness_
_is more free from_ _fear_
_than you think._
_What does this mean?_ Aiphatòn read the lines over and over again. _This must be a riddle. Or there used to be more here._
He rubbed a hand carefully over the wall, but he couldn't make out any traces of paint.
With a loud crack, a large chunk of the icy path cracked and sank downwards, as the älf saw at a glance over his shoulder. More fragments were following suit and hurtling into a chasm so deep that no explosion or crash signalled their impact.
Stunned, Aiphatòn sat on the spear and watched the disintegration progress. It must have been caused by the long cut he had made. The path was turning into a gaping abyss. The ground was literally being taken out from under him. _Along with my second cloak._
Then he saw lights approaching from higher up the slope, where he had just come from.
He strained his eyes.
A troop of armed figures draped in pelts and carrying torches and lamps in their gloved hands were on the upper section of the slope—which wasn't too steep—when it was suddenly struck by the growing cracks in the ice. They were pulling a sled in their midst with a modest wooden sarcophagus three paces long lying across it.
_Things are going to turn out badly if they don't go back the way they came in time._ "Hey," called Aiphatòn to attract their attention, although he didn't think they could see him in the darkness.
"Get back!" he shouted in various human dialects. "Get away if you don't want to lose your lives."
Not that he cared about the fate of these strangers especially, but he thought that they deserved to be warned about the impending disaster he had caused.
The troop stopped and the fissures darted beneath their feet. There were loud shouts when they realised what was happening.
Two of them tried to push the sarcophagus back, while five masked figures raced up the crackling path and tried to outrun the destruction; four others thought they could cling to the edges of the walls.
The collapse continued at top speed.
In the upper section, however, the ravine underneath the ice sheet was only just beginning, so that the pieces only fell one pace and shattered on the rocks underneath.
As a result, the sarcophagus fell, then shot downhill almost vertically, rumbling over the heap of broken ice.
Some of the figures couldn't keep clinging to the rock face and fell into the depths where the abyss lurked; two of their comrades rolled down after the wooden casket screaming but soon fell silent.
_They must have broken their necks._
Only four of the masked figures were in the safe area, which had only caved in by half a pace. They were holding the torches and lanterns down to shine the light into the ravine and look for the survivors as well as their cargo. Their muffled voices drifted over to Aiphatòn.
_Quite interesting, what you come across in the mountains._ The älf was looking for a way to climb down and look at the sarcophagus and the bodies. It didn't solve the puzzle the älf-woman had left for him, but the clothing down there was better than what he had. _And there were rations._ And besides, he could light a warming fire using the wood of the casket.
With his armoured fingers, he found purchase in the rock, then took the spear out of the ice and slid it into the holder on his back. The runes went dark and he became an invisible shadow.
Aiphatòn climbed down, hanging by his hands, the exertion warming his muscles and hence his whole body. As he descended he mused that he could give up the search for more runes.
The älf-woman had started her journey into the Outer Lands a long, long time ago along the ice path. Since it no longer existed thanks to Aiphatòn, every other traveller who came from Girdlegard from this orbit onwards would have to take a different route. Nobody could stumble across any other potential signs anymore.
The torches and lamps were quickly approaching the ground too. The armed troops had to jump down between the lumps of ice despite their heavy furs and weapons. The fact that they were taking this risk meant they were trying to get to the sarcophagus quickly because it had some special value to them. They didn't even stop to call or look for the injured.
_Maybe they stole the coffin from the dwarves? That would be brazen and very courageous._ Aiphatòn started to descend more quickly.
But the strangers reached the floor of the ravine before him. There were large and small mounds of ice lying around.
They hadn't noticed him so he was able to get closer using the milky, opaque blocks as cover without revealing his presence.
The strangers weren't worried about their own casualties. They wore scarves over their mouths and noses because of the cold and the only thing they seemed to be worrying about was the casket they were examining from all sides with their lamps. The weapons hanging from their belts and on their backs looked heavy and bulky. One of them held a shield in his right hand.
Aiphatòn could hear their voices better now. _What are you going to do now that you have it back again?_
The troop spoke a human dialect, and one of them stank of orc. That could be because he had seized a monster's armour and buckled it on—or because he actually was one of the green-skinned beasts. They were all broadly built and their clothes would be too big for the älf.
_You are an unusual bunch._ When he focused, he could understand what they were discussing, so he stayed in the shadow of a lump of ice the size of a cottage to concentrate on their words.
"A big fat sacrifice to every fucking demon: the thing is still intact," one of them cried out in relief.
"Gricks and Tratshka aren't," interjected the smallest one, who was still probably as tall as Aiphatòn, with a bleating laugh. "Man, did they go flying! Squealing the whole time!" He did an exaggerated impression of his comrades' dying screams.
"Did any of you see who called out to us before the path caved in?" the stoutest one interrupted, running a hand over the sarcophagus. "Ah, the wood has cracked here, but the charm rune wasn't damaged at all."
"It was like that already. And so what? He's in shackles." The smaller one bent double with laughter, the sight of his dead comrades seeming to delight him. "Now that's a box! I should have sat on it and used it as a sled! I would never have thought I'd start sweating in an ice chamber. It's this stupid jumping around." He wiped the sweat off his brow. "How do we get him out of the ravine, my friends?"
"The first sensible thing you've said," the stout one praised him, before turning to the tallest member of the group. "What do you think, Cushròk?"
A figure more than two-and-a-half paces tall turned aside slightly and pulled his scarf down, showing Aiphatòn his hulking great face, which bore orc and troll characteristics in equal measure.
_It hardly gets uglier than that._ The älf did not want to imagine how the creature had come to be.
"Let's get him out of this," Cushròk ordered in a deep, grating voice. He revealed pointy, stained teeth when he spoke. "Then we'll take it in turns to carry him."
_With those molars he could crush nuts in their shells,_ Aiphatòn supposed.
"But we're carrying the sarcophagus with us specifically to prevent him moving and to keep him safe," the smaller one countered.
"We've put steel clasps around him. What could he do to us?" Cushròk placed his enormous hand on the edge of the sarcophagus, underneath the lid. "Are you afraid of an opponent who weighs barely a quarter of what you do and whose muscles are nowhere to be seen?"
The other masked figures laughed softly and nastily.
Aiphatòn still could not work out the exact races of the figures hidden beneath the thick clothes and the scarves. _Could they possibly be monster and human half-breeds?_ He was familiar with the south side of Ishím Voróo, where he had found älfar who had turned out differently. He knew that creatures and things existed that were beyond the imagination of anyone in Girdlegard. _Even after the events of the last three hundred cycles._ The same went for peculiarities in the north.
Cushròk tensed his muscles, which were big enough to rival the hind leg of a night-mare, and grasped the top of the coffin.
But instead of the lid coming off, the entire sarcophagus lifted up.
His companions burst out into guffaws of laughter, enjoying his failure. This made the ringleader yank all the more furiously on the sarcophagus—to no avail.
Eventually he lifted the casket and roared as he tossed it at the rock face.
It crashed into it, bounced off and flipped over as it landed among the creatures who puffed and panted as they jumped out of its way.
"What a piece of demonic shit!" shouted Cushròk and stared at them all, eyes wide and angry. "Keep your big mouths shut! All of you!" He pointed to one of them. "Nrashq, you try it."
Nrashq, who beneath his scarf looked like the ugly brother of the ringleader, gazed at the sarcophagus. "Not a single new crack or a scratch." He passed a hand across the runes. "I think we can save ourselves any more attempts. This is powerful protective magic."
"So we drag it after all? You're so good at that, of course," joked the smallest one to Cushròk, who simply grunted and panted with exhaustion.
The stout one shoved Nrashq aside and placed both hands on top of the lid. His lips moved swiftly and silently while the älfar symbols on it glowed brighter and brighter.
_Keep what's in here hidden_ , Aiphatòn read what the letters said. _Freed, it spells great trouble. Destroy what escapes. It will kill as long as it breathes._ He couldn't help an icy shiver running down his spine. _They should take this warning seriously. Too bad they don't understand it._
He took off his one remaining cloak. Since he didn't want the ignorant beasts dragging him to his doom with them, he had to take action. He was also curious about where they came from and _what_ they were transporting.
Aiphatòn stepped out from behind the block of ice, holding his spear in his left hand. "Whatever you're doing," he said to the stout one, "you should stop. Immediately."
Cushròk turned his head with a grunt, already holding his morningstar in his right hand. Apart from the stout one, his companions all drew their weapons and pointed the ends of them at the newcomer. "The voice in the night," snarled Cushròk.
"He deliberately made the path collapse; I bet he wanted to rob us," the smallest one said to stir things up, the largest sword in his hand.
"He's a black-eye," Nrashq observed, wielding a lance as long as a leg. He held his shield protectively in front of both the casket and his stout comrade, who had not allowed the challenge to distract him from conjuring spells over the sarcophagus.
"And an odd one at that. Since when do they sew the armour into the skin and since when do their eyes look like _that_ when the sun has long set?" Cushròk added, scrutinising Aiphatòn from head to toe. "Why should Obko stop what he's doing?"
"Because the runes warn against it. I can read them, unlike you." He had been standing still since the ringleader had pointed at him. "The contents will kill us." He didn't reveal that he had been observing the group earlier. _One of them will blab._
"The contents are harmless," Cushròk contradicted him calmly, but his glittering eyes the size of hands glinted with suspicion. "What exactly do the runes mean?"
The älf revealed what they said.
"And how do I know that what you're saying is true?"
The warning didn't seem to have made much of an impression on any of his fellows, although they must have known what was in the sarcophagus.
Aiphatòn took his spear in both hands and wrapped his armoured fingers around the metal shaft with a click. "I will stop your comrade, and if I have to kill you to do it, then that's how it'll have to be. Is my determination proof enough?"
Cushròk contemplated Aiphatòn, maintaining eye contact as his eyes narrowed more and more, gradually becoming slits—then he let out a sound; his breath shot out of his lips in a white jet and expanded into a cloud.
Nrashq immediately launched an attack.
He took a step towards Aiphatòn and dealt an arching blow with the edge of his shield; Aiphatòn drew his head back, dodging the shield. At the same time, Nrashq's other arm thrust the long lance diagonally upwards from below, directly at Aiphatòn's throat. The attack with the shield had just been a diversion.
_For a creature this size, he is surprisingly quick._ With one judicious arm movement, Aiphatòn jerked the spear around so that his opponent's weapon was knocked aside. His armoured right hand jolted forwards over Nrashq's shield as swiftly as a snakebite, gripped his throat and crushed it with a cartilaginous crack.
Groaning, his enemy sank to the ground, clutching at his disfigured neck, but he could not stop the suffocation.
"It would be easier," Aiphatòn said, "if you stopped setting your people on me. Otherwise you'll end up having to carry the sarcophagus yourself."
Cushròk remained angry but called a halt to any more attacks. "Leave it, Obko."
"I—I can't," the stout one replied, clearly trying to take his hands off the lid. The runes' glow was spreading over the entire coffin. "It's got me." Obko looked from one companion to the next in desperation. "It won't stop anymore! It's draining me!"
Cushròk's broad, high brow furrowed and he nodded to his smallest mate.
But the underling didn't dare get any closer to the shimmering sarcophagus. "Oh no, I'm giving _that_ one a miss," he said, refusing to obey. " _I_ didn't tell Obko to cast a charm. And besides, we were forbidden to."
Aiphatòn could feel the magical radiation as a tingle on his skin. _This is... like nothing I've ever felt_ _before!_ He had opposed Lot-Ionan and found out what it meant to get into a fight with a magus. The armour and his own powers had protected him from the might of the old magician. But this radiation signified something else: it was both familiar and alien, powerful and uncontrollable.
Aiphatòn automatically took a step backwards, away from the sarcophagus. _The runes are right!_ "He's got to stop or I'll kill him," he murmured absently.
"What?" Cushròk's lips retracted, showing his teeth and puckering the bridge of his nose.
"Leave it," the älf commanded Obko, raising his spear to throw it.
"I can't! I... But you're a black-eye. Help... me!" stammered the stout one, squirming. "It—it hurts!"
_It can't be helped._ Aiphatòn hurled the spear.
Obko couldn't raise his hands to defend himself or dodge the missile. The blade came whizzing towards him and he screamed out in terror—until the tip plunged through pelt, armour and clothing, through skin and bone and into his heart. The runes on the shaft of the spear flashed.
The stout one immediately fell silent and collapsed next to the casket. As his life stopped, the symbols on the sarcophagus stopped glowing too.
Aiphatòn could clearly feel that the magical radiation had lessened in strength. _But it's still there._ "You should be grateful to me," he said to Cushròk. "I saved your life." He extended his arm to summon the spear back. The weapon flew out of the corpse and landed in his metal hand. "Now tell me: what's in that casket that cannot be taken out?"
"This is truly the first time I've seen a black-eye like you." The ringleader could not be rushed, even though he had just witnessed the death of his comrade. He still seemed convinced he could hold his own against this opponent. "You read the runes, you're an expert in magic and you're capable of tricks with your spear that I'd like to be able to do too."
_The first time?_ This phrase did not bode well. "How many älfar do you know?" Aiphatòn suspected there must be more of his people in the north. He had heard the stories about the downfall of the älfar realms Dsôn Faïmon and Dsôn Sòmran, but he had always feared there were survivors. _No matter how many there are: I must find them and exterminate them._ "Did you steal the sarcophagus from them?"
The other masked figure laughed. "This black-eye is not from here. Or he was trapped in the ice and then thawed out. We should take him with us too." He pointed at the casket with his sword. "Preferably in there. Then he won't cause any trouble."
Aiphatòn found it admirable that they were both ignoring how effortlessly he had picked off two of their team. He leaned on his spear. "Yes. Take me with you. I'm looking for my tribe."
Cushròk's laugh boomed out and he clapped a hand against his thigh. "It just gets better and better with you, black-eye." He wiped tears of laughter from the corners of his eyes.
"Take me with you," the smaller one imitated him and copied his posture. "I'm looking for my tribe."
Cushròk's cheerfulness evaporated swiftly and all of a sudden he was holding another morningstar in his other fist, and it seemed weightless to him. He attacked the älf with both weapons and the smaller one set upon him from the side.
Only an inexperienced warrior would have let themselves be fooled by their trick of good humour and let their guard down. Aiphatòn leaped over the smaller one and past the whirring, spiky iron balls, landed on the sarcophagus and used his spear to stab Cushròk from behind between the dorsal vertebra.
The thick pelts acted like a cushion to stop the blade plunging deep enough to kill the monster.
Cushròk bellowed and turned around, the balls whizzing closer. The smaller fighter swung his extra-long weapon down vertically.
Aiphatòn let the short chains of the morningstar wrap around the shaft of the spear, then yanked it and intercepted the blade slicing towards him with the taut iron links.
The heavy sword bounced back and hit the small one on the forehead, who staggered aside, dazed, and fell. "Dirty black-eye!" he howled.
"Come over here!" Cushròk tugged on the morning star handles and pulled Aiphatòn towards him.
"You want my weapon? Here, I'll give it to you." The älf let go of the spear and tried to throw himself at the ringleader to get at his broad back and floor him with blows to the skull.
But it didn't go as planned.
The jolt made the spear turn slightly and the blade inadvertently sank into the wooden lid of the sarcophagus—directly into a rune.
All of the symbols on the spear and the casket gave off a blazing light and there was a loud clap of thunder. Aiphatòn had to close his eyes.
The warm air suddenly smelled of burning fields and ripe cherries, of tobacco and a westerly wind carrying the smell of iron and earth.
Then Aiphatòn was struck by a violent blow that hurled him onto the sarcophagus.
Ishím Voróo, Forty miles outside the älfar town Dsôn Dâkiòn, 5452nd division of unendingness (6491st solar cycle), summer
_Having an uncle like him is such a pain._ Irïanora watched from the bank as the älfar pulled ashore the boat in which they had travelled down the Tronjor as far as the strait. _The old bastard should have killed me. I would have preferred that to grovelling in front of the scum._
She had disembarked via a plank with her servant Zelája and one of her uncle's warriors and had sat down in the shade of a weeping willow that functioned as a parasol with its low-hanging branches and dense foliage. The tree got its name from the translucent petals that closed once they'd withered and lay on the ground like tangible tears; but the willow was still in bloom.
The warrior kept watch while the servant gave loud instructions to the crew about which pile to leave which piece of luggage on. An impressive, varied wardrobe was important on a mission like this.
Irïanora watched the crew at work as if through a billowing curtain and rearranged her black and yellow dress.
They had stopped on the grass-green bank before the bottleneck where Gathalor, Iophâlor and Saitôra had presumably come a cropper. Rushing and frothing, the river hurled itself furiously against the large rocks further down, gurgling as it squeezed between the boulders, only calming again several paces downstream.
_How could Saitôra have survived this?_ Irïanora looked around and spotted an älf on top of the boulder on the right-hand side, wearing a pale green wrap over his armour. His helmet was covered in the same coloured fabric, while the trousers made from light brown leather and the rest of his camouflage clothing meant he as good as disappeared in front of the trees.
_And there they are, the watchful eyes of Elhàtor._ If the älf hadn't moved, Irïanora would not have noticed him. She took a deep breath and instantly groaned; her side hurt where the spike had bored into her ribs. _Who would have guessed they'd conceal scouts at this spot?_
Since the measuring expedition had failed, she would have to make the best of the scraps that providence threw her. _There's nothing else I can do._ The young älf-woman couldn't find a way to sit to avoid more pain. Her whole body had been beaten black and blue and the healers had refrained from using healing magic on her. The monarchess was supposed to see what Shôtoràs had done to her in his fury and cunning.
By now, the boat had been pulled up the slope and the crew were throwing themselves into the tall grass and relaxing. Bread, sausage and cold meat was shared around, there was wine; they scooped water out of the river.
Nobody saw the enemy scout still standing above them—apart from Irïanora.
But instead of pointing him out to her companions, she picked up the casket entrusted to her by Shôtoràs which she had placed in direct sunlight. His wax seal was resplendent on it, keeping the lid shut.
_Jewellery to make amends, maybe?_ She shook the box back and forth but couldn't hear anything. _Or an insulting letter?_
She didn't like the thought of carrying something around that might put her in a difficult position with her enemies. There were stories of messengers carrying a note saying that the recipient was to kill the bearer immediately. That would not fit in with any of her plans.
Irïanora tested various places on the piece of wax that had warmed up in the heat of the daystar. _That should be enough._
She pulled her small knife out of a fold in her dress and carefully eased the thin blade underneath the edge of the seal and pushed cautiously until the whole disc of wax came away from the lid and the front of the box with a sticky sound.
The älf-woman carefully opened the box. It would be child's play to glue the supposed safeguard back on before she got to Elhàtor then pretend she knew nothing about the contents.
Irïanora was smiling as she lifted the lid—and found herself looking at a message fixed to the inside.
Her good mood evaporated.
_I guessed you would try and gain access to the contents._
_See it as another test you have not passed._
_One of your companions is carrying my message to the monarchess. They would have_ _taken the box away from you before reaching the town._
_What can I say about your attempt to circumvent my orders?_
_Inàste must hate me that YOU have to be my flesh and blood._
_As your uncle, I must confess you are an unparalleled disappointment. Your mother was so much better than you and departed from us far too soon._
_Be a worthy successor to her at long last!_
_For her sake, I desperately hope you will be successful._
_Otherwise I don't know what to do with you on your return._
Irïanora shut the lid, her face getting warm.
She could quite clearly feel a rage line forming above her right eyebrow and then creeping across her face in jagged strokes. It moved gradually and tentatively, as if exploring the älf-woman's skin and facial features.
_I will be successful if I achieve_ MY _goal, not yours!_ She raised her arm and flung the casket in a high arc through the branches of the willow and into the river. Green leaves snapped off and fell onto the grass, while blossoms came loose and floated down far too slowly.
The current swept the light wooden container away.
Irïanora watched as it collided with a boulder and smashed into several pieces; some fragments were sucked downwards, some drifted away in the Tronjor.
_What a pointless test_ , she thought. _What did he mean by it? That he thinks he knows me?_ The blonde älf-woman felt the wax seal with her uncle's symbol on it in her fingers. _He's in for a surprise._
She pocketed the little disc, making sure not to break it or put too much pressure on it. It could come in handy to blame an action or gift on Shôtoràs and put him in a tricky position.
Irïanora smiled coldly but even that caused her pain. _He underestimates me, as I do him._
And yet she would have been so glad to know he was on her side, although his past as a Constellation seemed to make this impossible. But a war and conquering the satellite town meant everything to the blonde älf-woman and her supporters.
Her mother had not passed into endingness as her uncle's wording implied **—** she had been one of the ones who moved to Elhàtor, leaving everything behind to risk a new start.
Since then she had been dead to Shôtoràs. Irïanora had the same profound hatred for her mother that she did for the älf-woman who had taken her mother from her. Her father had raised her alone before succumbing to a fever. Some people even thought he never got over being separated from his wife and perished because of it.
On his deathbed, Irïanora had promised him she would do everything she could to defeat Elhàtor and its monarchess because they had unleashed misery on Dâkiòn a hundredfold, and even worse on her family.
Irïanora looked at the river. _I will not ask after my mother. I couldn't care less about her now, just like she couldn't care less about me when she left me._ Maybe her traitor of a mother would give her a hug and pretend she was delighted to see her. _If that happens, I'll stab her, Father._
Shouts started to ring out—the boat crew had noticed the scout.
The älf from Elhàtor climbed down to them and two more approached from the adjacent forest. Although they had been hiding right next to the group, nobody had noticed the scouts till now.
_They are dangerously good._ Irïanora wrenched herself away from her musings about her past and wondered how many of these spies were dotted across the land surrounding Dâkiòn with a view of the town at all times.
That would put her plans at risk too.
_I can occasionally get away from my uncle but what if they're watching me and my preparations?_ The älf-woman lapsed into unpleasant brooding once more. _I will have to take countermeasures._
The warrior from her uncle's bodyguard, whose name she kept forgetting, pushed the branches aside with his spear and came to her underneath the weeping willow. "The delegation from Elhàtor is here. They're going to take us in their boat from here," he reported.
"Is it big enough for all of us then?"
"They're only taking you, your servant and me with them," he replied and prompted her with a nod. "Our crew will wait here. If the trip drags on, I'll send a message to Dâkiòn to have the crew turn back."
Irïanora got up carefully with his help, clenching her teeth and suppressing any cry of pain. She didn't want to give the bodyguard any opportunity to laugh mockingly at her. "It's a miracle anyone can camp here at all."
"It's the only place for a radius of forty miles," the scout said. "The creatures and animals who live in the swamp don't dare approach as long as there's a fire burning." The warrior glanced around, looking for something. "Where's your little box?"
"The river knows where it is," she responded nonchalantly, picking one of the translucent blossoms off her dress.
He looked at her, aghast. "The present for the monarchess of..."
"Save yourself and me the farce," she countered acidly. "Show me to the boat taking us to Elhàtor."
His brow was furrowed, which she could only just make out because of the helmet, but he was silent.
Irïanora strode towards the three enemy scouts as best as the ground and the pain throughout her body would allow, making an effort to look as arrogant as she could.
She had actually planned not to come face to face with any of the seaside town's älf-women or älfar until their conquest was complete and she was receiving the surrender from the survivors. _I'll regard this as practice for the big moment._
The Elhàtor soldiers' annoyed expressions made her certain: she had passed this test.
Tark Draan, Blue Mountains, Kingdom of the Secondling dwarves, 5452nd division of unendingness (6491st solar cycle), summer
"King Boïndil: I said, we've removed the last of the corpses." The dwarf in a coat of chainmail and leather trousers waited in vain for the monarch to turn to him. In the end he bowed and left the room. The room's only function was to serve as a reminder.
_He was my scholar._ Wistful, Boïndil Doubleblade from the clan of the Axe Swingers was still looking at the little box made of pure vraccasium that held some of the ashes of Tungdil Goldhand.
The preliminary sketches etched onto the walls of the room showed the intricacy of the reliefs the stonemasons were due to carve to honour the memory of the dwarf people's great hero. Various episodes from the recent past appeared as well as the first time Goldhand met the twins.
But there was still plenty of other work to be done in the Blue Mountains, apart from carving images in stone, applying gold leaf and encrusting ornaments with precious gems. Decorating the memorial chamber would have to wait.
The powerful fingers on Ireheart's right hand played with his black beard, silvery grey hairs shimmering in it. His advanced age had brought them on, and they appeared in the long, black plait that dangled down to his belt too; he wore the sides shaved so that the coronet-like crown sat a little looser.
In his mind, he found himself in the assembly hall in the fortress at the Black Abyss, where he had received the little box with his share of the remains. Contrary to tradition, every tribe and the freemen and freewomen had kept a part of the best, the most heroic and simultaneously most controversial high king, in the form of ashes.
Ireheart sighed and rearranged the thick belt he wore on top of his coat of chainmail.
The container should really be placed in a statue but there had not been time to arrange it yet. He preferred the idea of this room, where you could come to think and remember anyway. _It would have appealed to him more than a likeness that wouldn't have done him justice, no matter how large and magnificent it was._
After the death of the magician Lot-Ionan and the liberation of the Blue Mountains, the home of the Secondlings, the surviving dwarves had to deal with disposing of the corpses of the southern älfar poisoned by Aiphatòn. The cadavers lay decaying in the passageways, polluting the otherwise fresh mountain air.
Ireheart contemplated the little box. _Or are the sceptics right after all?_
He turned his head towards the door and started to respond to the dwarf until he realised there was nobody there anymore.
Sighing, he left the memorial chamber to make his way through his kingdom which lay in the south of Girdlegard overlooking the Stone Gateway. Aiphatòn had once got through the gate with his älfar, and it was from here that the magus directed his reign of terror.
That was over, the clearing up had begun.
Ireheart placed his free hand on the stone wall and ran his calloused fingers over it. _It belongs to us again now. This time, nothing will drive us away from here._
He strolled on, smelling the faint scent of decay. The dead bodies of the black-eyes had lain here for too long. It would be some time before the stone could be purged of the decomposition fluids. Despite cleaning and scouring, the smell remained as if it was the final rebellion of the villains and an attempt to remain from beyond the grave.
Deep in the south, the fortress had to be completely rebuilt. All the equipment and retractable bridges had been destroyed. The good thing was that during this time, beasts couldn't cross the ravine anymore either.
_This cursed restlessness is back._ Ireheart shouldered his weapon with its long shaft. At one end it was double-sided, with both a heavy, flat head and a hooked spur the size of a forearm. His brother, Boëndal Hookhand, used to carry it into battle and now Boïndil owned it. Nothing could withstand the crow's beak—every target was either drilled through or smashed to pieces.
Ireheart walked and walked.
He saw all the destroyed dwarf runes on the walls of the halls and corridors, damaged indiscriminately by the magus and his famuli during their training. The runes had been target practice for their evil magic. _A disgrace._
The dreaded restlessness was accompanied by an unquenchable thirst that frightened the dwarf. Ever since he had been forced to drink the secret zhadár elixir to escape death, he had sensed his addiction to it.
_Distilled elf blood and all kinds of strange substances._ Ireheart felt nauseous. _But without the potion I would have died of the scorpion bite._
He was glad he had consigned the last mouthful to the flames and thus destroyed it. He was nonetheless tormented by the fear of becoming a zhadár himself and losing his dwarfness by gaining älfar powers. He had drunk the concoction more than once.
_Vraccas, protect me._
Ireheart went through a small portal into a beautifully laid out ravine garden where squat trees grew and sheep and goats grazed on the meadow. It smelled of honey as bees buzzed and flew the pollen to the plants for the sweet, liquid gold. Exquisite mead could be made from the honey. _Perhaps I'll find some peace here._
He sat on a wall, leaned back against the gnarled old tree behind him and closed his eyes; he put the crow's beak down next to him.
The rustling of the leaves and the tranquil buzzing made his heart beat more slowly. He dozed off into a half-waking, half-sleeping dream filled with chaos.
In this dream, he even saw the dwarf who had supposedly been the real Balodil. He watched him attacking the älfar.
_Balodil._ Apparently, Tungdil had dropped his son into the river while drunk. A current had carried the little dwarf to humans who kept him as a slave until he ran away when the älfar invaded. After spending some time in Toboribor, where he had allegedly lived a life of pillaging, it was said he ended up in a zhadár's house and that's how he had joined up with that strange unit.
Ireheart didn't believe that was how things had happened. The zhadár had been having some fun with his well-crafted story.
But when the king woke up, he did so with the crazy idea of setting out to look for Tungdil's only legitimate son, the truly missing one.
_Because the scholar isn't here, it would be all the more important to have the son of this great hero for support._ The King of the Secondlings looked at the sun through the ceiling of green foliage. _It's pure fantasy. I wouldn't even know where to begin looking. He could easily be dead._
Ireheart cursed the daydream that had got his hopes up that there was a part of his dear friend he had not lost after all. He was overwhelmed by despair. _Ashes in a vraccasium box. What am I meant to do with them? What should the dwarf tribe do with them? We need him. Alive._
"King Boïndil?"
He turned his head. A dwarf in a simple brown and white leather robe was walking around the large garden, looking for him; the animals were running away from him, bleating, as if he were a walking affront on two legs.
"Over here." Ireheart reached for the crow's beak and waved it. "What is it?"
The red-haired dwarf came towards him with two documents in his hand. It was Baromir Goldenstein and his job was to collect all messages in the newly rebuilt Secondling Kingdom and pass them on to the relevant people. "There's been some news." The three braided parts of his beard shook as he spoke, the tiny silver hair clips knocking against each other.
The pages changed hands and inquisitive bees buzzed over the words, as if they could suck sweetness out of them.
Ireheart read the message written by the elf Ilahín which described in detail how the demolition work in Dsôn Bhará was going—and it said that by a stroke of bad luck, a hole had appeared in the crater.
It seemed that a passage to Phondrasôn had been opened up. Ilahín's wife had taken some precautionary safety measures, so that nothing escaped from the hole into the weakened Girdlegard. However, he was requesting a small division of Secondlings to keep guard.
"That's all we need." Ireheart groaned as he sat up straight. His exhaustion, thirst and despair were forgotten for now. "We barely have enough warrior-women and warriors to clear up and guard the Blue Mountains."
"That's what I was thinking." Baromir frowned. "Shall we decline?"
"With a heavy heart, yes." Ireheart reckoned that at best the Thirdlings would have enough soldiers and hoped Hargorin would send some.
His gaze scanned the next lines without taking in what they said. He was still preoccupied by the opening to Phondrasôn, as the älfar called the place.
It crossed his mind that many people assumed that the Tungdil Goldhand who had returned and died was a doppelgänger, created by dark forces and the älfar. Was something like that possible?
Ireheart was breathing faster. _If the scholar was still down there, how would we find him? People say it forks endlessly._ He dismissed the notion as too obscure and far-fetched. _We could travel for a thousand cycles and not find even a trace of Tungdil._
Only now did he grasp the rest of the message.
Ilahín wrote about an älf who had supposedly been locked in a dungeon in the triplets' palace but was overlooked during the initial search because they thought all the cells were empty.
The älf in question was Carmondai who had previously helped to build Dsôn Balsur and had returned from exile with the Aklán.
The letter said he was currently travelling through the country with Balodil, who was now calling himself Carâhnios, to document the deaths of the last älfar. The zhadár was interrogating him from time to time and sending all the information to the royal courts of the humans, elves and dwarves.
"Hurrah!" Ireheart exclaimed, jumping to his feet in excitement and heaving the crow's beak onto his shoulder with a flourish. _So I do have an älf who has been there before!_ "That's the solution."
"The solution?" echoed Baromir in bewilderment.
"We'll take the black-eyed braggart as a guide who will lead us through Phondrasôn to the place where he last saw Tungdil before leaving," he spoke swiftly, placing one hand on his forehead as if needing to stop his ideas bubbling out. "A troop of fifty dwarves from across all of the clans."
Baromir blinked in surprise. "Tungdil is dead."
"The creature we thought was him is dead."
"But didn't you say yourself you were convinced he was the real deal?"
Ireheart hesitated. _Am I giving in to an illusion? Is this illusion caused by withdrawal_ _from the black remedy of..._
The next brainwave was already coming to him.
_This Carmondai used to live with the Aklán. Maybe he knows the potion's formula and how to counteract the withdrawal symptoms!_ Ireheart started running. He would never have dared to dream that a black-eye could be the key to two big puzzles at the same time. "Come with me," he commanded the dwarf, barely able to keep his excitement in check. "Send the message to Dsôn Bhará and Ilahín at once."
"What message, King Boïndil?"
"They must stop filling in the hole immediately. We need a way in," he said as he ran. _They'll all think I'm crazy, even Goda and my children._ "They are to get the black-eye to me in the Blue Mountains."
Baromir looked sideways at him in astonishment and clasped all of the silver clips in his beard in one swift movement. "King, I can put it like that in the message, but many questions will be asked." The way the dwarf spoke, it was clear he was among those who doubted the king's sanity.
Ireheart smiled at him. "On the contrary. _I_ have many questions. And this Carmondai needs to answer them all for me."
# Chapter VI
_Dance and combat are fuelled by the same fire._
_Hence bad dancers fall first in a duel._
Wise saying of the Älfar
Collected by Carmondai, master of word and image
Ishím Voróo, 5452nd division of unendingness (6491st solar cycle), summer
Aiphatòn crashed into the sarcophagus just as everything around him lit up a blazing white and blinded him. _What kind of magic is this?_
He was buffeted by wind that tore at his trouser garment, then he fell to the ground and pressed his body flat against it to stop himself getting wrenched away by the violent gusts; his metal fingers clung to the rough stone.
As abruptly as it had come, the storm died down again.
Bit by bit, Aiphatòn started to be able to see again, but the world was just a blur. _Is it over?_ He opened his hand and summoned the spear.
It took a little longer than usual, but the weapon obeyed his wordless command. He had been afraid the accidental magical discharge had damaged it.
He felt the prickling straight away. The spear must have been in contact with enormous energy stores in the sarcophagus runes. He felt barely capable of conjuring up those kinds of effects. _The alloy must have discharged during the encounter._
Aiphatòn got to his feet, blinking as he looked around, holding his weapon loosely at the ready.
The mighty slopes, the steep, craggy rock faces and the peaks of the Grey Mountains were—gone.
The älf found himself in a flat landscape that smelled of sewage gas and moist earth. Trees towered up out of the dark brown earth at irregular intervals and marshy pools with brackish water gleamed in between them, slick and menacing.
Far into the distance, several white towers rose up with smooth, white walls. Most of them seemed to be in ruins; two of them were ablaze, as if they were mainly made of wood and not stone. Clouds of dense smoke rolled lethargically and languidly towards the heavens, the smoke seeming sluggish and heavy.
_Is that a mirage?_ Aiphatòn took a breath and felt sweat break out all over his body.
The weather was muggy and swarms of midges were flitting by in whirring black clouds, looking for fresh blood.
_Or I'm dead and..._
He turned around and saw the sarcophagus lying in ruins less than two paces behind him.
Underneath the broken fragments was a figure that could certainly have been an älf.
Inàste had made Aiphatòn's race particularly skinny, but there was barely any weight to this specimen. He was sheer bone with thin parchment skin and just a hint of musculature. He was pure white from head to toe.
His emaciated rib cage slowly rose and sank, the prominent deep blue veins on his neck and stomach pulsating in time with his heartbeat. Old scraps of material had been wrapped around his stomach, but otherwise he wore no clothing.
The steel clasps the monsters had spoken about lay around the stranger, smashed to pieces; just one clamp was still tight around the upper body, keeping his arms pressed firmly against his body.
_Cushròk was right about the prisoner's condition._ Aiphatòn pushed the pieces of the wooden coffin aside with his spear to get a look at the älf's face.
A black-metal mask covered the lower half of the face, from the chin to the cheekbones. Level with where the mouth would be was a thin hole with a slide in front of it—at most a narrow straw could fit through it. His eyes remained closed, and his curly hair was a messy jumble on his head.
Aiphatòn found it difficult to identify the colour of his hair. _It's like glass._
He carefully examined the runes on the metal shackles. When he reached his hand out towards them to wipe away the dust so he could read them more easily, he felt magic within them too. _What kind of älf are you, that you are so feared?_
He was familiar with these types of half and full masks, used on the mentally disturbed so that they didn't spit, bite or assault anyone around them. The shackles also indicated an immense danger that Aiphatòn could not fathom at first glance. This was why he didn't immediately stab the masked figure to death. There was a mystery to investigate, and it might prove useful.
_And where have we ended up?_ He straightened up and looked around again.
No matter how hard he tried, he couldn't even see the foothills of the Grey Mountains.
He presumed he had been brought to this deserted place by a magic spell. So Aiphatòn looked through the rubble, searching for the rune that had been pierced by the tip of the spear to unleash this charm.
After a lengthy rummage, he found what he was looking for.
_That is the älfar symbol for swift return_ , he realised in surprise. Soldiers used these signs to give each other rapid instructions on the battlefield by brandishing flags and some explorers carried them in coin form as talismans for longer journeys. _A return to this place? Or did my spear make the spell go awry?_
Aiphatòn couldn't come to a clear-cut conclusion, but there was one hypothesis left and it might be correct or as far from the truth as he was from the Grey Mountains.
_On the other hand, did I not want this? Did I not want to get away?_ In any case he had taken the markings away and made the ice path collapse. Ireheart and his friends could deal with the rest in Girdlegard themselves.
His black eyes swept around, finally coming to rest on the burning towers. He might find someone there who could explain to him where he was.
_It doesn't look like things are peaceful_ _over there._ Aiphatòn shouldered the spear. _But who should I be afraid of?_ he thought, looking down at the unconscious figure. _What shall I do with you?_
Until he had solved the mystery of the unknown madman, he would hold off on killing him.
_Maybe he can tell me if there are any more älfar in Ishím Voróo that I need to kill to eliminate another swathe_ _of the villains_ _from the face of the earth._ He picked up the unconscious figure and was astonished at how light he was. He couldn't have been more than eighty pounds and that was while still wearing the clasp and the half-mask.
_A miracle that he didn't pass into endingness from exhaustion. It's possible the magic of the sarcophagus protected him from that till now._ With the spear on his right shoulder and the älf over his left, Aiphatòn set off through the flat landscape towards the towers.
The ground beneath his boots was springy and squelchy, and the stink of excrement and sewage gases worsened.
Here and there, the rotting bones and corpses of monsters and humans jutted out of the earth, and in between lay filthy, trampled standards and flags. Rats and carrion birds hopped around the remnants, insects and maggots crawling over the mortal remains. He couldn't make out any älfar among the victims.
_A battlefield that has already seen much conflict._ Aiphatòn walked down into a shallow dip and the ruined, burning towers disappeared from view; the only sign of their presence was the smoke.
_It's not a good idea to go any closer._ He glanced at the overcast sky. Through the haze and thick smoke he glimpsed the sun—a small, dim disc shining dully and feebly.
_It must be around noon. So the south is approximately that way_ , he decided and pivoted to the west. _They can fight without me. It's not my business. I'll make my enquiries elsewhere._
The dip, which might once have been an anchor trench, screened Aiphatòn from view and he advanced a few miles undetected. The ground was still strewn with the remains of bones, twisted armour parts and shreds of banners; the odd barely legible symbol on fabric and chainmail meant nothing to him.
Then he passed the ruins of homes that must have been in bad condition even when they were still inhabited.
Whoever had produced them did not seem to have a sense of craftsmanship—they looked haphazardly nailed together, piled up lumps of rock quickly encased in clay and held together by prayer.
Disintegrating, rotten planks broke beneath his feet. The decayed wood seemed to have been used in place of a road.
The recess in the ground ran straight through the middle of the abandoned settlement. The scorch marks on several walls told the älf that the residents had not left voluntarily.
_Who settles down in a swamp like this... or... did it form in the first place because they were here?_ Aiphatòn didn't feel any fear, but a sense of unease had become his constant companion.
The area didn't resemble anything he'd seen in Girdlegard or the southern wasteland. It was full of repulsiveness, unleashing wave after wave of disgust in him.
_Could it have been the work of demons?_
The dip got shallower and shallower. Soon he could peer over the edge and see what was on the other side of the former embankment.
The towers were now diagonally behind Aiphatòn and looked like finger-high chimneys spewing out smoke. Directly in front of him, at the edge of the dip, the remains of another tower soared three paces into the air. It must have been destroyed a long time ago.
The white paint was flaking off the outer walls and creepers twisted around the ruins, as though trying to pull the charred scaffolding, beams and cladding into the earth, to obliterate every reminder of it.
_The towers are not solidly built._ Aiphatòn suspected that the buildings only partly consisted of the precisely hewn stone blocks that were strewn about. The rest were support structures made of wood, false ceilings and painted outer walls with metal fittings. _They were not made to withstand a siege._
A shot from a small catapult could make a hole in it. Three shots and the tower would collapse. This led him to conclude that the towers could be assembled and disassembled for transport. A more comfortable, showy alternative to a tent.
If he had ever had any doubts he was in Ishím Voróo, they were now gone. These things didn't exist in Girdlegard with all of the upheavals and catastrophes it had experienced in recent cycles: he would have known about it.
_And yet it seems familiar. Have I read about it?_
His prisoner suddenly groaned and started to stir.
Aiphatòn quickly laid him on the ground and crouched down next to him as the prisoner's veiny, parchment-like eyelids flicked open. The black eyes stared at Aiphatòn and he could see astonishment in them.
"My name is Aiphatòn," he said. "I am an älf like you and I freed you from the clutches of thieves whose ringleader was called Cushròk. They were carrying you through the Grey Mountains in a sarcophagus with älfar runes on it." He placed an armoured glove on the clamp that was radiating magic just like the half-mask. "Can you let me know who you are and how I can release you from your shackles?" _It would mean he'd be even more in my debt and would reveal information more willingly._ He was mentally preparing a story he could tell to win the prisoner's trust.
The stranger lay still, examining Aiphatòn's face. Then he turned his head frantically right and left as if he wanted to make sure that they were alone and his captors were gone.
"Do you understand me?"
The moon-pale älf nodded slowly and relaxed slightly. It seemed he was only just starting to believe what his rescuer was saying.
Aiphatòn reached out a hand to the little slider in front of the prisoner's mouth. "It's best if I take this mask off you, so that we can speak..."
The älf shook his head in fear and uttered some muffled sounds, pressing his heels into the soft ground and trying to creep away from Aiphatòn.
"All right, I'll leave it then," he reassured him. "What about the clamp? It's magical, I felt it. Is there..."
Calm now, the älf nodded and angled onto his side so that he could reach the earth with one finger. He sketched runes in the soil with his fingertip, then scooted aside and kept drawing.
"Is that the order I need to touch the runes in?" Aiphatòn attempted to make sense of them.
The stranger bowed his head in agreement.
Aiphatòn didn't feel completely at ease as he reached out his right hand and tapped one symbol after another in the given sequence with one armoured index finger. Anything might happen next—the älf could even attack him. _But otherwise, I'll never find out who I'm carrying round with me and what he knows._
The runes he touched glimmered and didn't extinguish again. On the last one, there was a distinct click and the link rattled as it came away. The clamp opened a crack.
Aiphatòn got up and held his spear at the ready. "Break free. But don't you dare try to attack me or try any other tricks."
The wan älf pulled his thin arms out of the clamp and held them out, although this took visible effort; his muscles were trembling like they were at the limits of their endurance already.
He sat up carefully, panting hard through his mouth and nose, the half-mask turning it into a sinister, hollow sound. Condensation dripped onto the ground from underneath the metal on his chin. Nevertheless, he wrote on the ground again with one dirty finger, then pointed to himself.
"You are Nodûcor." Aiphatòn pointed at the mask. "How do we get that off you?"
Nodûcor shook his head once more and his glassy hair whipped around but didn't break. He drew the words in the earth again.
_A tedious way of communicating._ "There's no way. There are safeguards, both magical and mechanical," Aiphatòn read in bewilderment. _Why go to so much effort?_
A soft crack made both älfar look over at the ruins of the closest tower at the same time: someone had stepped on a shard of glass or a roof tile.
"Might be an animal just scavenging for carrion," Aiphatòn murmured. He took the spear and crept towards the ruins, noticing out of the corner of one eye that Nodûcor was burrowing in the ground for a rusty old dagger. _If it's not, he'll be food for them._
Crouching down, Aiphatòn started to work his way silently around the ruined building—and spotted two lightly armed beasts sitting on a rock in the shade on the far side of the tower's ruins, sharing a piece of rotten meat.
They looked like orcs but without the greenish or black skin. They cut off slice after slice of meat, stuffed them into their gobs, devouring them without enjoying them; their movements looked jerky. Cloudy juice ran over their lips and trickled down their cracked, scabbed skin.
Aiphatòn thought their gazes strangely vacant and fixed, as if they were sleeping with their eyes open. They didn't exchange a word during their revolting meal, and they didn't behave in that rowdy, showily loud way he was used to beasts behaving.
_Have they taken a drug that's clouding their senses?_ White runes stood out on their armour but they weren't älfar in origin and seemed too curly and ornate to have come from an ungainly clawed hand. _Or could those runes be charm runes?_
All of a sudden, another figure emerged from inside the ruins, moving just as silently as Aiphatòn. He approached the two monsters and they ignored him. His filthy armour was made up entirely of replacement parts and was loose on his slim body; his straggly brown hair with grey mud clinging to it came down to his shoulders, and a sword dangled at his side. His gait was swaying and unsteady.
Aiphatòn only realised he was an älf once he turned around. The same white runes glowed on his forehead.
_Is he the commander? But then why is he wearing that dreadful armour?_ Even the sword wasn't right for an älf.
Breathing heavily, the unidentified man sat down next to the beasts and stared in revulsion at the putrid meat—then raised his hand.
He rested his fingers on the hilt of a dagger stuck into his entrails. After it had been thrust into him, someone had wrenched it up to the base of his ribcage. With a tug and a scream, he pulled it out of the wound and, reaching over to the beasts, he used it to cut himself off a chunk from their meat, gagging as he stuffed it into his mouth and chewed.
Aiphatòn couldn't grasp what was happening before his very eyes. The blood was gushing out of the älf's wound as he tearfully chewed; the beasts didn't even glance at him—they kept on eating just as silently as before.
_I'll need to ask questions if I want to understand._ He stepped out from his hiding place. "Who are you and whose symbols are you wearing?" he demanded in a firm voice.
The monsters may have been moving sluggishly until now, but suddenly they lost all their ungainliness and got to their feet quick as a flash, whipped out their weapons and launched themselves at their enemy without a sound.
Aiphatòn brandished his spear. The tip plunged through the knee of the attacker on the right and severed the joint from all the muscles and tendons. He fell down mutely.
The other beast came at Aiphatòn with a sickle-shaped sword and a light cudgel with spikes, and he was extremely skilled.
_You're quicker than a human._ He dodged and parried the attacks, the blade and metal spikes clinking as they glanced off the shaft of the spear. There was considerable force behind the blows.
The unkempt älf in the cobbled-together armour was still sitting on the rock, chewing and bleeding, his black eyes riveted on the fight.
_Could they be zombies?_ Aiphatòn rammed the bottom of his weapon into his opponent's face, and his enemy snapped at it as if that might stop it. When the älf yanked the shaft back in one tug, shattering and wrenching the beast's teeth out of its mouth, it wasn't bothered. _It seemed that way._
The blade of his forcefully wielded spear cut the attacking monster's right throwing arm in two at the elbow.
The sickle sword fell and was sprayed with blood—but the enemy was undaunted, continuing to attack him with the cudgel until Aiphatòn penetrated his eye socket and kept pushing until he had forced the tip through the brain and out the back of the skull.
The beast collapsed and lay still.
Aiphatòn looked over at the chewing älf, who had the black lines on his face now. He walked over to the first, fallen attacker and, with one swift movement, his blade sliced through the cringing, injured beast's back into his heart. He too slumped to the ground and died.
He brandished the bloody spear-tip at the älf. "Tell me what's going on."
"Are you from Elhàtor or Dâkiòn?" he groaned, but didn't stop chewing the lump of meat.
"What are they?"
"Our towns, the..." He rolled his eyes, writhing. "You must warn them. About the botoicans." He panted as he spoke and spat out chunks of meat. "They—it... will attack. We're not protected anymore... Surrender... Complete surr..."
_Of course!_ Aiphatòn remembered why the outline of the building looked familiar. It reminded him of an old story he had read. _It was in Carmondai's writings._ "I can bandage your wounds and—"
"No," screamed the horrified älf. "No, I _must_ die! I _want_ to die! I did it myself when the control..." His upper body shook. "I'm escaping the madness," he murmured contentedly. "Save the towns! Warn them."
"Where do I find them?"
"Further northwest. Further towards..." The injured älf let out a terrible scream and fell forwards, twitching, his feet shuffling in the dirt as if they were trying to run away. "End it!" he screeched shrilly. "Put an end to this!"
"I will." Aiphatòn leaped onto the rock in front of him, forced the unnamed älf into an upright position with his foot and, facing him, stabbed him in the heart with the spear. His body stiffened immediately. "Your death is called Aiphatòn," he said. "I will find the towns—and destroy them _before_ the botoicans reach them. Is that a consolation to you?"
The dying älf opened his eyes wide, then he passed away and the blackness disappeared. What remained were cloudy, greenish eyes.
_Who would have thought: two towns. Elhàtor and Dâkiòn._ He jumped back onto the ground and walked around the ruins to look for Nodûcor. _At least I'll have_ _something to do in Ishím Voróo. And I thought the death of the Dsôn Aklán meant that the evil had been wiped out._
The emaciated, wan älf had not moved. He held the dagger pressed against his body, as if he had to protect the weapon instead of using it to defend himself.
Aiphatòn smiled at him. _He must come from one of the two towns. I'll take him along for now and ask him about_ _it. Every piece of knowledge is important for me to be able to destroy the towns more easily. I can kill the bag of bones_ _any time._ "On your feet," he ordered and held out the armoured fingers of his right hand to him. "We're moving on."
Nodûcor nodded hesitantly and grasped the outstretched hand, letting himself be pulled to his feet. He tentatively grasped the dagger and bent down to pick up the clamp.
"Round the corner you'll find clothes better than those rags, at least, and weapons," Aiphatòn explained to him. "Then we'll move on and look for a straw you can suck some water through." _He won't be able to eat anything but gruel._
Nodûcor hobbled away slowly, and Aiphatòn followed.
When they walked round the ruins of the building, they saw to their surprise that a massive army was approaching from the west less than half a mile away, marching silently across the marsh. They were quite clearly making for the towers.
Just as many warriors were approaching from the towers, however, as was evident from the pennants and lances reaching up into the air.
But Aiphatòn could not make out a formation or even an attempt at battle array in either army.
_Is this a merger rather than_ _a battle?_
"Choose something for yourself. Quickly," he urged Nodûcor and climbed the ruins to get a better view from three paces up. He was careful not to be seen by the armies as he did so.
The warm, putrid wind carried the soft sounds of the soldiers' armour and weapons jangling and clinking.
The warriors were marching in silence, trudging through the mud as it splashed up among their bare feet and boots. While the first row was still making good progress, the ground would have turned to thick sludge after the twentieth or thirtieth soldier, which did not seem to slow them down.
Aiphatòn shook his head as he watched.
Monsters from all kinds of races, known and unknown, from orcs to trolls to hybrids, were walking shoulder-to-shoulder with humans. Foot soldiers with long pikes trotted along next to sword-bearers, while bow and crossbow-archers were marching elsewhere in the pack. Among them rode warriors on horses and oxen and there were even ordinary carts trundling along with warriors gathered on them.
The crowd reached as far as the horizon; far away an enormous banner fluttered in the air, probably so the troops could tell where their commander was. Aiphatòn's vantage point was not high enough to have a clear view of everything. _This is an unparalleled mess. This cannot be the build-up to a battle._
Everyone's heads were facing forward, and not one person in the armies spoke.
_Like the beasts during their meal._ The älf was astonished. He now vaguely recognised the white runes painted on bare skin, on pelts and on armour. It looked like everyone was wearing them. He could see less armour than might have been expected of an armed force. And the number of weapon-bearers seemed low too—the rest of them would need to fight with their bare hands.
_There are thousands upon thousands of them. They could form ramps with their bodies just like crabs and scale walls._ If the armies joined forces, Aiphatòn estimated the number of warriors at just under two hundred thousand.
"We should get going," he called to Nodûcor who had stocked up on clothes without taking his eyes off the crowd trudging along. It seemed this was new to him as well.
When the first rows of the factions came within twenty paces of each other, they suddenly started to rush at each other—without uttering a single scream.
Ishím Voróo, Älfar town of Dsôn Dâkiòn, 5452nd division of unendingness (6491st solar cycle), summer
Shôtoràs walked across the bridge that linked the two parts of Dsôn Dâkiòn and stopped exactly in the middle, then moved to one side so he wouldn't be in anyone's way.
The strong wind whistling constantly through the groove in the mountain tore at his black robe which was embroidered with old Dsôn Faïmon patterns. He made no secret of his origins and was proud of his past.
_I've experienced and achieved so much in the last divisions of unendingness._ He looked back and forth between the river two miles away and the ravine below. _For so long I've managed to avoid anything that would force us into a dispute with the Elhàtor scum. And now this!_ From time to time he turned around and watched the residents crossing the footbridge.
Shôtoràs silently cursed his niece. _She may be cunning, but she is remarkably foolish all the same._ He couldn't comprehend her desire to provoke outright war. _What is she thinking?_ Irïanora didn't even have a specific strategy. Surprise alone was not enough against the Magnificent.
_The battles would last too long._ The monarch shook his head and fixed his gaze on the Tronjor once more as it meandered along steadily, a sparkling blue in the sunshine. _The only ones who would be pleased are the tribes in the surrounding areas. This means they'd either be rid of us_ _or they'd attack us because they knew we were weakened._
Shôtoràs shut his eyes and listened to the rushing of the air; he could feel his beard and hair fluttering.
The past came rushing at him, conjuring up certain images.
They had gathered near the Black Heart, which had been corroded by acid. They had seen the land caving in and knew that the nomadic towers were prowling through the area and the Inextinguishables had fled rather than coming to their aid.
_Fled_. Shôtoràs snorted in disdain. _Traitors to those who had been loyal to them for so long._ He of all people, a glowing Constellation, was among those who led the survivors northwards to find a new home.
But the harmony didn't last long. The älfar scattered and that's when the defeats started. The dying. The endingness.
_But not in my town._ In his mind's eye he saw Dsôn Dâkiòn being built under his leadership and guidance. Thousands of älfar daring to enter the enormous ruins, searching and securing them, always vigilant about the return of their most recent inhabitants; marvelling at the gigantic towers and buildings and wondering what race of beings had erected this monument; building on the old foundations, constructing new buildings from the ruins and upholding traditions.
Even though there were quite a few older residents like Shôtoràs, time could not be stopped. New generations brought new ideas and thoughts.
This didn't make things worse, although it often required a lot of effort on the monarch's part to accept and agree to these changes. There were no slaves anymore, älfar served älfar now. Different classes had arisen out of the different professions and it took a huge amount of energy to make sure none of them looked down on any other class.
_Anyone who rejects the_ _pressure to change will crumble._ Shôtoràs placed his hands on the sun-warmed stones of the parapet.
Ishím Voróo changed so many things. Even the älfar themselves.
At first, nobody noticed; it was accompanied by mysterious deaths that were put down to fevers and other illnesses of the wasteland—until the cîanai and cîanoi among them suddenly grew stronger.
_It might be because of the stones._ Shôtoràs thought about how the basalt ashlars apparently came from the island where the Magnificent was. A considerable number of cîani had left Dsôn Dâkiòn with Modôia long ago. _May Tion devour the soul of that blonde villain!_
He hated the monarchess. From the bottom of his heart, desperately and with a real passion. She had come from Tark Draan down at heel and over the hill, accompanied by dishevelled älfar she had picked up along the way like cattle. Then she claimed to have previously lived in a town called Dsôn Sòmran in the Grey Mountains. And she had supposedly been in service in an älfar realm in Tark Draan.
_Ridiculous!_
Hundreds followed her flattering words and her promises of a better town. They had once owed their existence to Shôtoràs.
_To me!_ He breathed deeply and opened his eyes.
He didn't think Irïanora was capable of—to use a coastal town metaphor—calming the troubled waters. It was possible Modôia herself was waiting for the chance to start a war.
The king looked back at the river, the greatest danger facing his town. At the same time, it supplied plenty of fish, the necessary water for the surrounding fields and enabled trade with the areas upstream.
There were reports that the monarchess was secretly having a fleet built with the sole purpose of sailing up the Tronjor. Boats with minimal draught, very well-balanced but with capacity for huge quantities of military equipment and soldiers. Apparently dozens of these boats already lay at anchor inland on the island.
_Oh, my foolish niece. It looks as if you're in agreement with her and you're trying to provide her with a pretext for having the ships put out to sea._ Shôtoràs smoothed down his pale, tousled hair. He had been brooding long enough. He had made a decision now and he wanted to put it to his two closest confidants.
They would not be able to talk him out of it, but they could help by fleshing it out.
Because his word was law in Dsôn Dâkiòn, undiminished despite the innovations and changes. Anyone who opposed his word crumbled.
"This is the starting position." Shôtoràs had summoned Pasôlor and Horgôra to the hall where Irïanora had recently been given a taste of his stick. They were two of his best friends and were able to say things to the sovereign that other residents would receive severe punishments for.
The älfar were standing around the big desk with the map spread out showing the town and a surrounding area of just under forty miles. That was as far as the area claimed by the Majestic extended. Anyone who wanted to cross this land or settle down on it had to pay a fee. The marsh was exempted from that, but nobody tried to build a settlement there.
Shôtoràs pointed to the Tronjor. "The river has barely changed in our region, the riverbed just got slightly wider. So Elhàtor's ships would come within two miles of us, as before."
"Reminds me of my last game of Tharc," Horgôra replied, bouncing up and down on her tiptoes. "I'll take the blue army." The black-haired robe-maker, who was generally good-humoured and fond of jokes but also had a very sharp and agile mind, turned aside and poured grape juice from the carafe into three glasses. Her bright flame-coloured coat with its sophisticated cut showed her expertise in handicraft.
"If we could be a little more serious, please," Shôtoràs chided her. "So?"
"We've heard the rumours about the fleet," Pasôlor murmured and placed his hands on his back. He had had his hair shaved off and now wore caps that he changed as often as other people changed their underwear. The bald älf had conceived of the bridges that led into the town and was considered a prudent strategist. "There are only two places where we could lie in wait to ambush the ships."
"Probably," Horgôra agreed, pensive, "but they'll send scouts on ahead to secure the bank as much as possible."
"They would suffer huge casualties because of the quicksand, insects and monsters," Pasôlor shot back immediately and placed one hand on the woven silver-wire belt fastened around his dark green robe at hip height.
"Better than losing the fleet. _I_ would do it like that and discover the ambush." She held one hand to her chin and reflected. "Tell me: what makes you so sure Modôia is going to attack us?"
Shôtoràs leaned on his walking stick to relieve his painful leg. "She comes from Tark Draan—the älfar there had to be hell-bent on conquest to survive in that prison and they became scum themselves. You don't just shake off a trait like that."
"Might it not be the case that _you_ would like her to attack?" Pasôlor ventured to remark.
If it were any other älf, Shôtoràs would have knocked him to the floor immediately with one blow, but he allowed his closest friends to speak openly at all times. "How could I wish for an attack?" he answered. "Älfar would die. Our tribe has been decimated enough already and we certainly do not need a war with our own kind."
"But you hate them. Because they cost us some of our residents," Pasôlor persevered with his suggestions undaunted. "It would suit you very..."
"A war will cost us even more residents. I would immediately set a zhartài on her to dispatch her into endingness if the infamous assassins were still around," admitted Shôtoràs, grumbling. "And if he were to ask for all of my riches, my artworks..."
"... even if he demanded your high office?" Horgôra added, challenging him.
"Yes," he exclaimed and clenched his teeth. "But we're not here because of my darkest desires." He shifted his weight and used the stick as a pointer; the silver tip was directed at a valley eleven miles west of Dâkiòn. " _That_ is my solution."
Pasôlor exhaled contemptuously, "A parade?"
The sovereign grinned wickedly which was a clear _no_.
"This valley is half a mile from the river." Horgôra tilted her head slightly, her black hair flowing like ink over her shoulders and hanging down as far as the table. "Crazy, the thought that just crossed my mind—but perhaps it's the same thought that occurs to you?"
It took Pasôlor less than half a heartbeat to catch up with what they were thinking. "That is just _too_ crazy. And besides..."
Shôtoràs held up his free hand in his defence. "The fact that barbarians live there is not important. We'll have the little men dig the canal. The brats and womenfolk will have enough time to get away. If they don't do that, then that's their lookout. I'll warn them and nothing more." He nodded to his friends and smiled. "I see you agree with me?"
"You know that we don't need to give our opinions," Pasôlor said.
"Or that you don't need to have them anyway," Horgôra corrected him in a mocking voice. "And yet he wants to listen to us. I think he is unfailingly noble. The power hasn't gone to his head." She took her hand away from her chin. "We divert the river into the valley, fill it up and the old riverbed dries out. So Elhàtor's ships—provided they have some—don't reach us because the water needed to travel the remaining miles upstream is missing." Her eyes narrowed. "I see one significant danger in this: it would mean an army and all manner of monsters could reach us on foot."
"We could flood the old riverbed at regular intervals," Pasôlor suggested and pointed to various points on the map. "We make the barbarians build a second, narrow canal fitted with a large dam. Open the sluice gate, the trash is washed away and swept into the sea to be devoured by fish."
Shôtoràs hammered his applause on the little desk with his cane, the rumbling echoing for a long time. "You've grasped my plan quickly."
"Because it makes sense. I think it's elaborate and grandiose," Horgôra added, "but it's good."
"I'll take it even further." The sovereign pressed down so hard on the map at several points along the riverbed downstream that he left marks. "We'll station warrior-women and warriors here, in troops of ten. We'll give each post a hundred barrels of petrol which we can also use to flood the dried-out riverbed." The tip of the cane traced the bends in the Tronjor. "It's not enough to produce a sustained surge, but it is enough to set monsters and Elhàtor's army alight. It only needs to roar towards them ablaze at ankle height and we'll be rid of them."
"It could be mixed with the water, if needs be," said Pasôlor and nodded approvingly. "If this were a game of Tharc, our opponent would give up before we had even started because they would be forced to acknowledge our superiority." He looked delightedly at Horgôra. "Is that not right?"
"Exactly: that is _not_ right." The älf-woman placed her right hand on the extensive swampland in one delicate movement. "Doing that would mean we also dry _this_ out. _Therefore_ the most dangerous section—the quicksand, moorland and swamp—becomes passable much too soon. _Therefore_ the monsters can escape in all directions. Not to mention: Elhàtor could launch its troops at us on a broad front. Eighty miles—a quick-moving army could cover that in two or three moments."
Pasôlor laughed. "We're talking about ten or twenty divisions of unendingness, that's how long it would take to dry out the moor. If not more."
"No. Canals run along there, water seeps into them and gets diverted. Our initial scouts told us about them—in case anyone at the table has forgotten," she countered, enjoying being able to make a significant contribution. "Within forty or fifty moments, you could march through the natural barrier using certain pathways." Horgôra looked back and forth between them. "What's the point of winning a battle if it doesn't settle the war?"
Shôtoràs' expression darkened. "You're ruining my plan. I still liked you until just now."
"I'm pointing out the weakness to you, before monsters and Modôia do it. Be grateful to me, sovereign." She laughed cheerfully. "Don't look so bitter. Think further ahead, like I've already done."
"A continuous supply line," he replied after a brief reflection.
"A trickle that keeps the swamp wet enough. Superb!" Pasôlor shook his head, baffled. "Sometimes the simplest solutions remain out of reach."
"I'm happy to help," she said, laughing, and drank some of her juice. "Not bad for a robe-maker, eh?"
Pasôlor bowed to her. "I will never play Tharc against you."
"I knew there was a reason I listened to you two." Shôtoràs pulled his stick back to lean on it again. His confidence and satisfaction had returned. "Let's do it exactly according to this plan then."
" _You'll_ do it that way, monarch. We are simply honoured to have been allowed to help you and our homeland." Horgôra bowed to him and Pasôlor followed suit.
Shôtoràs accepted the obeisance because he knew it was purely intended to tease him. "Yes, yes," he mumbled. "Make fun of me."
"I would never dare do that." The älf-woman winked at him. "And as your chief robe-maker, I can tell you: you've lost weight, sovereign. Drop by and have your clothes taken in. You could do with it."
Pasôlor was still looking at the map, lost in thought as he retraced the waterways. "I agree, there's no other plausible possibility."
There probably were some. But the monarch didn't like to consider those.
_I would not like to send our budding cîani out into the wasteland to fight against the monarchess' ships._ Shôtoràs was aware that the town was educating around a hundred talented pupils.
Thirty of them were advanced enough to be deployed in battle because they had a good enough command of their spells to cast them under great stress. But in the face of a hail of arrows or brandished swords, the beginners would lapse into stammering or lose focus. _No, they're staying put. They will back us up in case the Elhàtorians do manage to get right up to the steep cliffs._
"Some may take this remark badly, but there's still _one_ thing I'm hoping for above all else," Pasôlor interrupted Shôtoràs' thoughts. The two other älfar looked expectantly at him. "That we take every possible precaution and don't need them." He pursed his lips and looked back at the map with a steady gaze. "May the gods give Irïanora enough sense to placate Modôia and convince her to forgive Irïanora for her absurd idea."
Shôtoràs didn't know what to say in response, though his first thought was: _Then bring me a zhartài who will finish off the scum_. He truly did not want a war with the Magnificent, just the death of the monarchess. But who could carry out that assassination?
_I would need a warrior, an älf, who is not from this town. A hitman._ Shôtoràs was sorry the zhartài were no longer around. They would have come in useful on occasion, and nobody would have been able to trace anything back to him.
"May the gods see to it," Horgôra agreed.
"And if they don't hear our prayers—no matter if it's Inàste or Tion or all of the rest of them, for all I care—then we will be prepared and settle this dispute for ourselves," Shôtoràs said absent-mindedly; a part of his brain was still occupied with other thoughts. "I swear to you, friends, that I will eliminate Modôia and only Modôia. Afterwards the Magnificent and the Majestic can live in unity and peace." His fingers clicked as they closed tightly around the handle of his stick, and he was breathing faster. "Her dead body will lie before me and I will have it disembowelled by my best artists. It will be scattered in tiny pieces all over Dâkiòn so that everyone understands we can never trust the scum from Tark Draan."
"Strictly speaking, she's from Ishím Voróo like we are," Horgôra interjected. "Her town was located..."
"Regardless! She divided a powerful town and brought us discord." Shôtoràs was panting as if he had just done a long, strenuous jog. He quickly wiped the sweat back off his brow and into his pale grey hair. "You understand me, don't you?"
Pasôlor and Horgôra looked at the old älf.
"We do," the robe craftswoman answered sympathetically for both of them. "You are our sovereign. And our friend."
Shôtoràs stretched his broad back and then stretched the rest of his body. "I will order the relevant decrees then. As early as tomorrow, our warriors will travel into the valley and set the barbarians to work." He felt incredibly thirsty and simultaneously exhausted. _I've got to rest._ "Let's believe in the gods and trust ourselves most of all." That's how he had achieved his greatest successes so far.
He turned around and limped away from the balcony-like platform and into the hallway.
# Chapter VII
_Garnish a rumour that revolves around you with obvious lies. The lies will be detected and the rumour will no longer be given any credence. Even if it was true._
Wise saying of the Älfar
Collected by Carmondai, master of word and image
Ishím Voróo, Älfar town of Dsôn Elhàtor, 5452nd division of unendingness (6491st solar cycle), summer
Irïanora wiped away the water that was intermittently hitting her in the face in thin veils and tasted the drops. _Saltier than tears_. She hoped the foam wouldn't leave any white ring marks on her yellow and black dress, but the place she was standing was just too tempting.
They were travelling towards the Magnificent in a three-masted ship and the young älf-woman was standing at the bow.
The sea was practically still, not one sail was hoisted and the oars were pulled into the belly of the craft. But the little waves were being carved in two by the hull as it glided along, without any magic coming into play.
Irïanora could see the thick, taut cables that ran through a narrow opening next to the anchor chain then disappeared beneath the surface ten paces from the front of the ship.
Her bodyguard was approaching, wearing the leather armour with the insignia of the bodyguards to Dâkiòn's sovereign. He was walking so defiantly across the deck it was as if he wanted to challenge the men from Elhàtor to a fight.
_Or he's not capable of moving normally on board ship_. Irïanora smiled disdainfully at him. "And what were you able to find out about how our journey seems to progress as if by magic?" _Arthâras, that was his name_. She was forgetting it less often, but it gave her fiendish pleasure to ask him his name constantly, to show him how utterly insignificant he was to her.
The bodyguard, a veteran of eleven divisions of unendingness, came and stood next to her. He wore his fair hair short and the air couldn't mess it up. "With this calm weather, the crew is using an undersea current so that they don't have to row in this heat and work themselves into exhaustion," he explained. "Lazy bunch!"
"I call that _clever_. I think they're doing it to try and impress us." Irïanora looked towards the island where the white town rose up into the sky. Patterns were becoming visible on the roofs and, taken together, they formed images yet to become fully clear.
She knew the monarchess had received help from the frekorian soldiers: boat-building methods, navigation and the various ways of travelling at sea. All of that knowledge had been passed on to the älfar. "How does it work?"
"If there isn't enough wind and you don't have any oars or you want to spare the crew, you lower weighted objects shaped like fishing pots to a precisely calculated depth," Arthâras explained. "The currents seize them and pull them forwards. That's how we're making headway."
_Clearly there's a particularly strong current between the coast and Elhàtor._ Irïanora was still experiencing pain throughout her body, which meant her hatred for the sovereign was as strong as ever. "My calculating, oh-so-cunning uncle," she muttered contemptuously and thought of the casket he had used to play a nasty trick on her. _Why does he have to go on living?_
"What about the sovereign?" Arthâras asked.
"I was just mentally admiring his foresight," she said aloud.
The bodyguard laughed softly. "Yes, he's well capable of that. That's why our homeland still exists and wasn't destroyed like all the other älfar towns. By scum, by barbarians or by beasts." He followed her gaze, his hand moving to the hilt of the long dagger he wore strapped to his thigh. "A very large town. I can barely see any defensive fortifications. There are just the two towers at the harbour." He pointed at the ship. "But I see why their fleet is considered invincible. The hull of this main ship that we're travelling on is eighty paces long and around twenty across, but the draught is very low."
"They won't get through the bottleneck on it."
"Not on this. They'll have other boats built for that type of plan." Arthâras couldn't hide his admiration despite his dislike. "These are made for living at sea. Multi-storeyed, with fish ponds and crops growing during the voyage; they even have hen coops," he reeled off. "It's a warrior settlement on the sea."
"That someone could sink," the blonde älf-woman cut in.
"That would be difficult. I couldn't see much, because they won't let me get into every corner, but I think there are compartments in the hull that could be separated by bulkheads. If there were a leak, this ship won't go down straight away, it will continue to deliver lethal strikes."
Irïanora looked at the three large masts and the two narrower ones close by on the foredeck. The enormous ship was accompanied by four smaller, easily manoeuvrable sailboats that served as extra back-up. They had also joined forces with the undersea currents via the fishing pots and were being towed along.
Arthâras placed one hand on the railing. "The frekoriers knew how to remain undefeated and Elhàtor has perfected it. We could do with this fleet."
"You'd like to go into battle against Elhàtor," Irïanora said in astonishment, when she recognised the expression on his face. _The pride of a veteran._
"Possibly."
_A kindred spirit._ She lowered her voice. "But my uncle will never allow it. He wants to keep the peace."
"That's why I'm bringing you to the monarchess," he said. "It's his will. As you said yourself: he has foresight and he made sure that Dâkiòn grew strong and survived. _My_ thoughts are irrelevant here." He laughed suddenly.
"What's so funny?"
"That you're genuinely trying to work out whether I'd come over to your side. First me, then maybe the guards and then, some moment of unendingness in the future, you'll consider a rebellion against your uncle," he guessed what she was thinking. "Don't you think he has already considered _that_ too?" Arthâras pointed to the emblem on his armour. "I'm as loyal as they come. Sticking together makes us strong. Without him the Majestic is lost."
Irïanora felt her damp blonde hair, which was slowly going frizzy from the effects of the saltwater and the sun. She was annoyed about the insolent bodyguard as well as the fact that her uncle was at the head of another battalion. "Oh, you've got it all wrong. I wasn't thinking that," she lied—and had a brainwave. "I was thinking about the casket."
"Oh?" He smirked as he turned towards her. "What about it?"
"My uncle wrote a note in it that one of you two was carrying the real message for the monarchess."
The hull jolted forwards slightly; the undersea sail must have been caught by a powerful current. The bow rose up a little and then sank down deeper.
The commanding officer was giving loud orders and from the lower deck came the sound of the windlass rattling. It was clear the length of the ropes was being audibly adjusted.
Irïanora raised one hand to protect herself from the glittering droplets flying up from the hull. Some of the spray hit her anyway. "He knew I'd open it."
"He probably did, yes." Arthâras laughed gently. "Now you're wondering which of the two of us is carrying this message: me or your maid, Zelája?"
Irïanora joined in the laughter and hit him lightly across the right shoulder. "Of course not, Arthâras. Quite the opposite." She left her hand on his armour and traced the inlaid work in the leather.
The bodyguard was confused now. " _The opposite_ means what exactly? That you don't care either way?"
"No. It would make the situation simpler if I knew."
Arthâras looked astonished now, but he was still laughing. "You're talking nonsense, Irïanora. You do care, and yet..."
The rattling underneath their feet stopped. The ropes slackened and the bow rose slightly.
The älf-woman had been expecting the upward movement. While Arthâras was still shifting his weight to counterbalance the rocking, Irïanora suddenly pushed him hard in the shoulder so that her shove and the movement of the ship coincided.
The bodyguard's hip struck the railing and he was catapulted over it; meanwhile Irïanora acted fast and stole the falling man's dagger.
Arthâras had the physical control of a warrior and he rotated as he fell. He grabbed hold of one of the fishing pot ropes with his right hand.
Irïanora cursed and looked around quickly.
Nobody had noticed anything.
She bent down and drew her own knife. She needed to save the bodyguard's weapon.
"Your uncle will never forgive you for this. An _attempted murder_!" Arthâras was staring up at her and was about to get a firmer grip to pull himself up the cable.
"You're wrong: this is a _murder_ he will know nothing about," she countered and hurled the knife.
In the position he was in, the älf couldn't dodge it. The blade plunged through the hand he was clinging to the rope with. The tendons were severed and his fingers were forced open. He couldn't regain his grip quickly enough.
Arthâras fell into the sea in front of the bow and with a dull sound its planks smashed into his forehead. The water turned red instantly but momentarily.
_I'm rid of him._ Irïanora straightened up and hurried across the deck. She tucked the stolen dagger away in a fold in her clothes as she did so. "When do we arrive in Elhàtor?" she called to the commanding officer who, like his crew, was wearing a simple linen shirt and calf-length trousers. His rank was clear only from the insignia on his right breast and his red headscarf. "I want to freshen up a little and I need to start in good time."
The crew laughed.
"In a splinter, I'd say," he answered.
She nodded. "Thank you. Then I'd probably better get started." Irïanora ran down the broad staircase and hurried into the small cabin she had been assigned. _My dear uncle, you don't understand me as well as you think you do._
When she entered the compartment her maid Zelája was just picking out different dresses and hanging them in a row. She was putting them on wire hangers, then hanging them from the hooks jutting out of the ceiling intended for lamps or hammocks. "Which would you rather wear: dark blue, dark red or dark green?"
Irïanora took the dagger out of the fold of material, went over to the unsuspecting woman and drove the long, thin blade up through her neck, pressing Zelája against the wall of the cabin with her own weight. "As I just told the late Arthâras: I don't care _which_ of you two has the message for the monarchess," she whispered icily. "Because neither you nor he will reach Elhàtor."
She wrenched the dagger out, avoiding the blood spurt and stabbing the älf-woman in the heart straight away to make absolutely certain she killed her.
Zelája slumped.
Irïanora let go and the body slid down the wood, landing at her feet. _From this splinter on,_ I _am the message, the slight difference being that I can now invent what my uncle would no doubt have wanted to be communicated._
Breathing hard, she took a quick look around, then searched the body as it bled out. But she didn't find a message to the monarchess.
_As I said: I don't care._ She heaved Zelája's corpse into a chest along with Arthâras' dagger and covered them with a dark green dress. The fabric was thick and absorbent enough to soak up the blood. _I never could stand that design._
Irïanora pushed the chest over the large stain on the wooden floor and waited a while before going back on deck and complaining loudly that her servant was missing.
"Is this her?" The commanding officer was on the upper deck, standing over the open chest with the blood-stained dress and maid inside.
When there was still no sign of Arthâras and the maid after they docked, he had ordered a search of the ship. They found the traces of blood in the cabin during the investigation and shortly after that the corpse of the unfortunate älf-woman with the bodyguard's weapon in her heart.
Irïanora was suitably shocked. "Oh, how horrific! That's Arthâras' dagger!" She spoke haltingly about a supposed relationship between the maid and bodyguard and how they had argued many times on the voyage. "Now he's gone and killed her." She shook her head in dismay. "I'm sure he'll try and swim ashore to get to Dâkiòn or at least to the strait."
"He won't manage it." The commanding officer ordered the chest to be closed and brought ashore. "The predatory fish are quicker than he is."
_This couldn't be going better._ "Predatory fish!" Irïanora was delighted to hear this. "In that case, the murderer will get the punishment he deserves." She pretended to pull herself together and placed one foot on the ramp that led to solid ground.
The dark blue silk and velvet dress was a good choice—she wasn't sweating in it, but she wasn't too cold either. She wasn't wearing jewellery and she couldn't get her blonde hair under control without a maid so she had simply put it in a triply braided plait.
They had put up towering canvas screens everywhere and they blocked Irïanora's view of the town and its fortifications. All she glimpsed was a brief flash of the mouth of the harbour and she didn't glean much from that.
A detachment of armed warriors on night-mares was waiting at the harbour wall with a carriage and a servant showed Irïanora into it. The windows were completely covered on the outside to prevent any light getting in, so that she was shielded, sitting in the dark.
It didn't surprise her to see the black horses with glowing eyes on the island. _They come from Dâkiòn,_ she thought angrily. _Good animals, that these scoundrels also wrenched away_ _from us in the old days. What good are they on an island? We need_ _them much more urgently._
The journey began. Irïanora could only imagine what her surroundings looked like. At least the carriage had good suspension and was comfortable to sit in. She had expected to have a stinking sack pulled over her head and to be driven through the streets while the locals mocked her. This kind of travel suited her better.
The wheels rattled uphill, then crunched through gravel or what she took to be little pellets of bone.
Finally the carriage stopped and the door was opened.
A ghostly hand helpfully reached inside, and soft rays of sun fell on the interior of the carriage.
"If you would like to come out, Irïanora?" came the voice of an älf.
She was too dazzled to be able to make out anything clearly. She grabbed the soft but strong fingers and climbed out of the carriage.
"Welcome to Elhàtor," the älf greeted her. He was wearing an incredibly elaborate blue and silver outfit, with an upturned collar and cuffs. "And I am pleased to see: colour-wise we complement each other very well."
Irïanora could see again properly now.
She was under an awning to shelter guests from the weather when they arrived. Directly behind the young älf were four steps up to a double door with four armoured warriors on guard in front of it.
_Their armour is much lighter than ours._ "Thank you so much..."
" _Sir_ ," the älf with the mid-length, brown hair interrupted her in a friendly, instructive way. "I've heard that one cultivates less of a sense of politeness and manners in Dâkiòn, but on Elhàtor, I request, _madam,_ that you observe the etiquette." He bowed slightly. "My name is Ôdaiòn."
_The son of the monarchess._ Irïanora kept her composure and inclined her blonde head. "I will make an effort to please you and your mother, sir." She was absolutely amazed he didn't have black eyes despite the sunlight. _How does that happen? A freak of nature?_
"You please _me_ already, madam." The young älf gave her a mischievous grin, the interest in his eyes unmistakeable. He escorted her to the portal which opened for her as soon as she had climbed the steps. "I was very curious about you, Irïanora. The niece of the monarch pays us her respects."
"What could have triggered this curiosity?"
"Apart from your insubordination and plans to incite a war?" Ôdaiòn sounded extremely amused. "People say you're very pretty."
Irïanora was taken aback by his frankness. "I don't quite understand..."
"Your friend told us about you, madam. And based on what I heard, it wasn't difficult to work out your true intentions when you sent those poor souls down the Tronjor to make them measure it." He laughed and gently kissed the back of her hand. "Measuring, absolutely priceless! You are genuinely gifted. You should come over to our side."
Irïanora didn't know what to think. Here she was on her way to report to the monarchess of the Magnificent, and at the same time her son was trying to make her turn her back on her homeland. _A test, I presume._
"Should I? Not a bad idea at all. But only if the rumours about your fleet are true. Apparently it's hidden somewhere on the island," she shot back sweetly. "I'm used to being on the victorious side."
Ôdaiòn stopped walking, let go of her hand and gave a slight bow, clapping silently. "You're enchanting," he conceded. "Shrewd, attractive _and_ quick-witted. And that business with the two murders on board the ship—unbelievable."
Irïanora grew hot and felt disconcerted. She remained silent as he grasped her fingers again and continued walking. _He... cannot know._ She gave him a quick sidelong glance. _He's still testing me._ "I thought it was appalling," she replied.
"Is that so?" And he left it at that.
She breathed a sigh of relief. _He wanted to frighten me like you might frighten a flock_ _of birds at a hunt._ Irïanora smiled in relief. _Not on my watch._
They entered a hall where enormous fish bones served as pillars and turned into a passageway that had been modelled on an open clam.
"Before I forget: your mother has asked me to say hello from her."
Irïanora flinched. "My uncle says my mother is dead."
"She's not. I met her just yesterday in the market square. You look very similar, did you know that?"
She breathed in, unable to quash the various feelings that rose up within her and formed a chaotic mass she couldn't deal with.
Ôdaiòn waited several heartbeats. "Please excuse my joke, madam. Of course I didn't meet her. But you can do the joke on anyone who comes here from Dâkiòn—it works every time. It's fascinating to watch the reactions."
_Another test._ Before Irïanora could even deliver a slick retort, they strode through a black curtain made to look like a tapestry of algae and seagrass and into a small room where a cosy suite of white leather armchairs stood by a fireplace. Waterlilies looked like they were growing out of the walls, and it smelled of flowers and the sea. Small, black birds hummed through the air and sucked nectar out of the roses.
_It looks so different from home._ Irïanora noticed that the plaster was made of very fine fragments of bone and sharp teeth that must once have belonged to predatory fish. Here and there, tiny tiles of gold and silver gleamed in the plaster.
The monarchess was on her feet and waiting for them, having pinned up her long, blonde hair and adorned it with shimmering strings of pearl and amber. The white dress suited her extremely well and she wore sandals on her feet.
At the arrival of the two newcomers, servants brought out dishes of fruit and carafes filled with various juices and wines, setting them down on the table.
"Keep in mind the correct form of address," Ôdaiòn murmured to her again. "Mother," he cried cheerfully. "Look who I've brought you. Our guest has just arrived." He let go of her hand so that she walked the remaining paces by herself.
Irïanora didn't let her unease show. _It feels like they're indulging in a game with me._ She approached Modôia and dropped a deep curtsey. "I stand before you, monarchess, at the command of my uncle, Shôtoràs, sovereign of Dâkiòn, to speak with you about the incident at the strait and to beg for my friends' freedom."
Modôia laid both her hands against her flat stomach and nodded to Irïanora. "I'm delighted to hear that our towns are seeking a solution that does not end in war." She gestured with an elegant motion to the armchair opposite her. "Sit down, Irïanora." She herself sat down on the chaise longue and put her feet up. Her son chose the seat next to her. "Pick out whatever you'd like and point to it," she said, indicating the table. "My servants are swift."
Irïanora smiled and sat down.
The monarchess' black eyes, which looked surreal in the midst of the otherwise white room, rested intently on her, scrutinising her and seeming to penetrate her thoughts. "I hear you had a murder to deal with?"
"Yes, it turned out there was an unfortunate death." Irïanora briefly explained and asked for bite-size pieces of cut fruit to be handed to her on a bone saucer. The spine of the creature they'd used to make the plate must have been wider than three älfar. _What creature living_ _in this sea has bones like that?_ "But I was surprised by my maid's killing."
Modôia nodded and was sympathetic. " _Surprise_ , that's the key word for me." She had a glass of water handed to her. "Because _you_ in turn surprised me—to put it mildly—rather a lot. Sending your friends to certain death, that is... extraordinarily calculating. You are a strategist and a gambler."
"And you overplayed your hand," Ôdaiòn added with a chuckle.
Irïanora found this exchange annoying. Even more annoying, however, was their unwavering politeness combined with their bluntness. _My uncle would have been shouting long before now._ She gave a little cough. "I did not intend to kill my friends. All that was planned was a measuring expedition for the new cartographer because, as you know, the courses of bodies of water change. So there was nothing malicious about it, it was just meant to prevent any unpleasant surprises," she said, without pausing to draw breath. "The monsters could have made use of the time to build a fortress on the Tronjor—how else would we have been able to spot it? And the river isn't part of the sea..."
"But we have an agreement that you are not allowed to go there," the monarchess interrupted her. "It was much more than the four miles downstream."
"Hence the chain at the bottleneck too," her son agreed. "A precaution we took because we expected someone from Dâkiòn to hit upon the idea of breaching the treaty at some point."
"Even your best excuses won't protect you from punishment." Modôia took a little sip of her drink. "A breach of a treaty is still a breach, regardless of the reason. Even if you'd been trying to save hundreds of lives: I couldn't care less." The blonde älf-woman asked for a crystallised red fruit to be handed to her. "You won't be able to tell, but I am incensed." She smiled as kindly as if she and Irïanora were the best of friends, just chatting about old times.
"You can tell I'm... astonished," she replied. "Again, I merely wanted to have a map made."
"Those are _your_ words, my dearest Irïanora." Ôdaiòn leaned forward eagerly. "Now let's hear what message your uncle gave you for the monarchess. I'm expecting an apology from the sovereign and an offer of reparations."
"Possibly seeds or..." Modôia shrugged her shoulders. "Well, there's no limit to your uncle's imagination, is there?" She laughed and reached behind the chaise longue. Suddenly there was a rolled-up triple-strapped whip in her hands, its ends fitted with blades. She removed the safety sheaths from the blades without uncoiling the weapon.
Irïanora gulped. At the sight of the gleaming blades, she could feel fear wrapping its claws around her heart. "Don't blame _me_ if my uncle's words aren't to your liking," she pleaded. Metal clashed against metal with a soft jangling sound, reflecting the sunlight.
She had heard tell of the weapon capable of causing excruciating pain. Some detached part of her couldn't help but wonder what her red blood would look like on the white leather. Drops, smears, pools, long spatters. She could see there was something very artistic to the idea, despite what it would ultimately mean for her.
"No, we won't blame you at all." Ôdaiòn pulled a small piece of paper out of his sleeve. "Look, _this_ message from your uncle reached us three moments ago." He smiled coolly. "You weren't to know that there are carrier pigeons that can fly back and forth between the Magnificent and the Majestic when a matter is urgent."
Irïanora drank her wine, her hand trembling slightly. _That old bastard! What else will I need to come up with to outsmart him?_
Meanwhile Modôia got up and let the three straps slide to the floor, the blades clinking as they hit the marble. They hung from the blonde älf-woman's hand like thin, black snakes.
"You get three chances to tell us exactly what your uncle's message to us says," Ôdaiòn continued. "Since you have it in your head, as you say, you just need to say it out loud. For every mistake, you'll feel how creatively my mother"—he reached down the side of the armchair and also picked up a whip—"and I are able to handle these."
_Two of them?_ Irïanora felt sick; she was fighting the urge to vomit. If she didn't guess the words right, it would not matter. Three blows with those weapons was tantamount to a death sentence. _The first blow alone could tear me to shreds._
With a conspicuous lack of haste, Ôdaiòn held up the little scrap of paper. "We're on tenterhooks, sweet Irïanora."
Tark Draan, Human kingdom of Idoslane, 5452nd division of unendingness (6491st solar cycle), summer
Carmondai was perched on the horse in a slumped position. The shackles didn't allow him to move his hands much. It was not really riding, but he could hold the reins himself; the steel rings clinked softly every time the animal took a step.
Carâhnios, on the other hand, sat upright on the white pony, its colour particularly accentuated by his black leather and tionium armour. One hand resting on his hip, he was humming a sombre song to himself that sounded like a traditional dwarf tune. Apart from the luggage, he was carrying enough weapons for them to go into battle against a thousand orcs.
Carmondai looked up at the swallows performing their breathtaking, zigzagging flying manoeuvres high in the sky. _That is freedom._
It was inevitable that he was now mulling over an escape plan, though he wouldn't try and escape from the zhadár any time soon. He understood the level of transformation and training the extremely skilled warriors of the Thirdling kingdom had received from Sisaroth.
_I would be no match for him in my condition._ Plus there were the magical powers the zhadár possessed. _The last one of them left, and I've got to accompany him._
Besides, he wouldn't know where to turn even if he did manage it. The whole of Girdlegard hated älfar and the passageways were manned by dwarves—there was no escaping. _But living a never-ending life in hiding?_
Time and Samusin would tell how things would go and perhaps his immortality worked in his favour. He hadn't escaped the Aklán dungeon only to launch himself into one last, desperate battle that would prove his downfall out of some false sense of pride. _Only the living get options._
"Where are we riding to?" Carmondai might have had paper and ink, but on the horse's lurching back it was impossible to write a sentence or start a sketch.
Carâhnios kept humming.
"Did you hear..."
The groundling raised one hand, uttering some final notes and holding the last one for a particularly long time before sniggering. " _Now_ you can talk to me. And if you speak during my song again"—he looked menacingly over his shoulder, the short, black beard scraping bristle-like over the leather armour and tionium reinforcement—"you'll be sorry."
Carmondai made an apologetic gesture. "Our destination?"
"Where are we?"
"In Girdlegard."
"Shrewd, black-eye. More specifically?"
"If I've got my bearings right, we ought to be in Idoslane."
"Aha. Despite being locked up in a dungeon, you've still got the knack." Carâhnios clapped far too quickly and far too loudly.
"I know Girdlegard very well," the älf replied, not without a trace of wistfulness. "And I've known it _longer_ than you have."
"Ah yes. I keep forgetting that you founded Dsôn Balsur." He stroked the pony between its ears. "Tsk, tsk, you black-eye. The human women are jealous of you all. You age but nobody can tell how many cycles there really are on your face."
Carmondai knew that his age was very obvious. "Inàste was kind to me."
"That makes one of her then!" Carâhnios guffawed with laughter at his own joke.
Once he had settled down again, he pointed through a thicket at a ruin that must once have been a temple. About eleven miles away from them, it clung to the little hill it was on as if for support.
It was overgrown with creepers and the toppled pillars lay piled up on top of each other, which made them dangerous traps. Even if they had held up for a hundred cycles, one gentle nudge and they could still tumble downhill and bury an unsuspecting visitor.
" _That_ is our destination?" Carmondai couldn't imagine an älf living there.
"You'll see, it only looks like an old shrine. The runes inside it refer to gods who have not been worshipped in Girdlegard for a long time. Nobody is going to go inside." Carâhnios pulled up the pony. "We'll camp behind the bushes and go in once night falls." He dismounted, the small blackened iron tiles of his skirt-like robe rubbing together silently.
Carmondai brought his horse to a halt and slid out of the saddle, looking as clumsy as a drunk while doing so thanks to his shackles. He was desperate for a bath, clean clothes, a mirror to shave with and a meal. A good meal.
Carâhnios chuckled and detached the chain from the iron handcuffs so the älf could move away from his steed.
Carmondai looked through the undergrowth at the hill and the ruins. _The hideaway is inside the hill._
The groundling tied the horse and pony to a tree and sank down into the grass, then put his arms behind his head and looked at the clouds.
"We zhadár know every castle and every fortress in this kingdom. We spied on all the dwarves, on all the people, invisible as shadows in the darkness," he said solemnly but grinned as he did so. "And since our hearts were never in it when we served the älfar, we collected _their_ secrets too. Sisaroth made the mistake of believing his concoction made us stupid and submissive." He looked at Carmondai expectantly. "How come you're not writing?"
"Just a minute." As the handcuffs allowed only minimal movement, he dragged paper, an ink bottle and a quill out of his saddlebag with his hands bound. He settled down next to the groundling and scribbled a few notes on what he'd heard. On a second sheet of paper he made a sketch of the landscape including the ruins.
Carâhnios waited a while, plucking a stalk of grass out of the meadow and putting it in the right-hand corner of his mouth. Grass seeds sprinkled into his clipped black beard. "It's terrible to betray your own people and have to incur the hatred of Girdlegard, just to prepare for the orbit when you ambush the enemy. So many cycles, and we've endured so much suffering." He made the stalk of grass seesaw up and down.
"Was it worth it?"
"Are the älfar still in their palaces?" Carâhnios retorted cheerfully. "Without us, Girdlegard would never have been freed from the black-eyes so quickly."
Carmondai noted these words down. _And not just from the black-eyes._
He remembered passing hanged bodies dangling from the trees during their journey. If anyone had made common cause with the älfar or declared themselves rulers or lords, the humans strung them up on the spot.
It's true that the queens and kings tried to stamp out these unauthorised killings and set up special courts to execute lawful punishments. But the anger of the oppressed could not be stemmed.
_No matter how many laws you have posted on bridges and the walls of houses._
It had been dangerous for Carmondai on their trip too. They had ridden past a town with a market taking place outside its walls. When the people saw the älf, they wanted to kill him, but Carâhnios made it clear that only he could touch his prisoner. The incident repeated itself when they met a group of volunteers who were on their way to a garrison to enlist in the army. On this occasion, the groundling actually had to knock one of the strong men to the ground to make sure the others didn't get too brave.
Carmondai was surprised that Carâhnios didn't just order him to use his älfar powers of fear or use his own. _He's bound to have his reasons._
The seesawing stalk came to an abrupt standstill. "I don't trust them."
"Who?"
"The two pointy-ears who came crawling out of the woods recently and wanted to flood the Golden Plain with new pointy-ears." The zhadár sounded contemptuous. "I don't know where these new elves are supposed to have come from unless..."
"From outside?" Carmondai suggested.
"Smart arse! Of course they came from outside. But then shouldn't they have put in an appearance to save Girdlegard sooner?" Carâhnios pressed his lips together and spat the stalk out in a high arc.
"How could they have? The gates were locked and the bridges were torn down."
"Pah. As if that would stop them! The pointy-ears are the most cowardly people I know. Popping up once the bloodthirsty, tough part is done, saying a few unctuous words. And everyone looks up to the glowing elf-lets like they're gods. To hell with them and their Creating Spirit." He spat a gobbet of saliva to his right. "Write that down! To hell with them."
"I am." Carmondai put this abiding hatred of the elves down to the changes caused by the älfar elixir. _Deep-rooted, unrelenting hatred. Sisaroth's remedy still works as well as ever on that front._
Carâhnios reached a hand to his belt and took a metal vial out of a leather holder. He opened it, put it to his black-stained lips and tipped one drop onto his dark tongue. His face relaxed slightly. He grinned an evil grin, then carefully put the vial away again.
Carmondai presumed this was the remedy made by the triplets which gave the zhadár their unique powers. "I heard it was distilled elf blood," he remarked.
"Did you hear that?" The groundling giggled again. "Well, it _was_ once." He tapped the leather holder with the flat of his hand. "It will last for some time yet, I hope."
"And what will serve as a substitute?"
The zhadár's dark eyes turned to focus on him, and his wrinkled face took on a furtive look. "What do you think?" he murmured menacingly. "I'll give you a clue: this source is also dwindling more and more in Girdlegard."
_That's why he's hunting the älfar._ Carmondai swallowed. "You're capable of making the same remedy as the Aklán?"
"We had eyes everywhere, even in Sisaroth's laboratories." Carâhnios smacked his lips. "I can't say if it's the same, but I hope it'll do the job." He shut his eyes again. "You're safe, scribbler."
Carmondai sensed the zhadár was lying and not even making much of an effort to do so. _I'm not safe from anything or anyone in Girdlegard._
The älf had rarely felt so alone as he did in that moment. _Not even in Phondrasôn._
The groundling's slowing breaths were infectiously sleep-inducing.
_He's dozing, as if he were in his own safe bed in a tunnel._ Carmondai had to hand it to him. _Either he's crazy enough that he doesn't care where he nods off or he's counting on his warrior instincts to warn him of any dangers._
He decided to get some rest too.
The älf put the paper and ink aside and stretched out in the soft, dark green grass beneath the tree. He had to keep his hands together lengthways because they were bound by the shackles so he lay his head down on top of them.
He felt like he had barely fallen asleep when a kick struck him in the side.
Carmondai winced and sat up with a bolt, only to see a grinning Carâhnios standing in front of him.
Night had fallen during his nap and a delicate mist was rising off the grass.
"Here we go," the zhadár whispered. "Let's check if there are any black-eyes holed up inside the hill."
With extremely mixed feelings, Carmondai got to his feet and walked over to his horse to follow the groundling.
Ishím Voróo, 5452nd division of unendingness (6491st solar cycle), summer
Aiphatòn was just about to jump down from his lookout point to move further north-westwards with Nodûcor when the battle broke out. _I've got to see this._
With no shouts, no signals from trumpets or pennants, the two crowds suddenly rushed at each other and merged into one. The clash of swords rang out and the first death cries echoed over to him. _They're not mute anyway._
Aiphatòn watched the deadly skirmish with around a hundred thousand beasts and a hundred thousand people fighting each other. _Who is in command? I can't make out any captains or military signals._
The draught animals were being driven onwards by coachmen, thundering straight through enemy lines with their carriages to crush as many opponents as possible under their wheels. There was fighting, mutilation and death everywhere. Lances and spears were flying, arrows hissed to and fro.
Aiphatòn realised there was no letting up. The enemies worked their way deeper into each other's armies, hacking and thrashing, as if there were a reward on the other side. Any soldier they encountered along the way was attacked until they succumbed to enemy bites, punches and weapons.
_They're tearing each other limb from limb with their bare hands!_ He could make out an ogre-like creature sweeping through the opposing army with long strides. Its long, hairy arms darted left and right; its claws ripped heads off and shredded armour, while intestines and severed body parts flew through the air. Red and dark-coloured drops of blood glittered.
Soon even the big beast fell to the ground, after two orcs and eight gnomes had clung to its legs. All its rolling about and lashing out was no good: the orcs and gnomes dug their hands into the enormous beast's flesh and stripped it from the bone. Their fallen enemy had hardly lain still when they picked themselves up, drenched in blood, and hurried on towards enemy lines.
All over the battlefield, scenes of unparalleled brutality were playing out.
A lightly armoured warrior with a copper-coloured, close helmet caught Aiphatòn's eye. He was burrowing forwards ruthlessly, tearing apart anything that offered him resistance with powerful movements, like he was cutting through thin material. He was the furthest into the ranks of the enemy.
_This is the most appalling battle I've ever seen._ Aiphatòn shuddered. "We're going," he called down to Nodûcor again, who had helped himself to the corpses' clothes and was wrapping up the body clamp as if it were a talisman. It was vital that they investigate what the dead älf had said about the towns of Dsôn Elhàtor and Dsôn Dâkiòn.
With one last look at the bloodbath, he saw there were älfar fighting on one side too, throwing themselves into battle. They may have been using swords and spears, but they weren't behaving the way he expected his tribe to either.
_It must be the power of the botoicans._ Aiphatòn leaped back onto the ground and landed next to Nodûcor. They hurried away together.
They couldn't escape the constant screams and shouts, the roars and metallic clashes from the bloodbath.
Aiphatòn reflected on how little he knew about the botoicans. _If only I had remembered Carmondai's stories better. It would come in handy now._ He had a vague recollection that an älf was usually immune to mind-control spells because they themselves possessed magic. _Or am I getting confused?_
Nodûcor just shrugged his shoulders when he asked him about it.
Aiphatòn was not satisfied yet. As soon as they had put enough distance between them and the battlefield, it would be time for him to question his companion more, starting with his own lot in life and covering the towns too.
Aiphatòn had in fact been expecting to find barely any traces of surviving älfar in Ishím Voróo. But the challenge he faced was now expanding many times over.
The älfar in the botoican army didn't worry him. They were already doomed and would die sooner or later.
_But the two towns represent a danger to Ireheart and Girdlegard. I swore to wipe out all älfar._ He glanced at Nodûcor. _My vow stands, even if it takes me ten solar cycles or more._
Aiphatòn stopped himself speculating any further about the size of Dsôn Elhàtor and Dâkiòn. He was relying on his magic, his wits and his speed.
_If I reveal myself as the son of the Inextinguishables, they will have to look kindly on me_ , he thought, forming a rough plan. _That kind of audacity will probably get me further than anything else._
If they were to go so far as to crown him as their ruler due to his lineage and his status as a shintoìt, it would be child's play to lead them to their doom, just like he'd already done with the älfar from the south of Ishím Voróo. _At least then something good would come of my existence._
Aiphatòn and Nodûcor ventured on north-westwards, slowly but steadily.
Time and time again, they had to rest because the weak, pale älf couldn't walk any further in the scorching sun. He used a reed to drink with, sucking the water out of puddles that looked cleaner than the sludge in the marshy pools. They may have looked deceptively clear, but the acrid stench promised nausea and vomiting.
Their surroundings only started to change towards evening. The flat swamp with its sea of reeds gave way to a grassy landscape they could take in at a glance. The temperature became more pleasant and when the stars shone in the heavens, the wind blew. It carried the scent of fruit, dew and ripening grain to the älfar.
The landscape's atmosphere changed and became peaceful and pleasant, as if it was trying to make up to Aiphatòn and Nodûcor for what they'd seen, and allow their minds to rest.
They pitched camp underneath an old apple tree that spread its foliage over them protectively like a roof. The lights from a small village they were deliberately avoiding glowed nearby.
They didn't need a fire. The night was mild and the ground having retained the heat from the day, now gave off the warmth from the sun.
Aiphatòn picked some fruit and pounded them down into a fine pulp using stones. The extremely feeble Nodûcor was able to suck the pulp up through a straw. When he sensed the sweet flavour on the roof of his mouth, he groaned with pleasure and a tear of joy ran down from the corner of his eye.
He took Aiphatòn's hand and placed his forehead against it, his glassy hair touching Aiphatòn's arm and seeming to crackle softly.
"You don't need to thank me," Aiphatòn said, not allowing himself to feel any sympathy. _How do I know what crimes he has committed? He's an älf. He must have killed hundreds and he'll kill again if I let him._
Nodûcor stood up, his gaze falling on Aiphatòn's face—and he froze. Huge shock and immense awe were etched on the masked älf's face, and it wasn't long before he bowed and then stayed there in that humble pose.
"No, that's not necessary." _He has noticed my black eyes._ No ordinary älf kept this pigmentation once the sun had gone down, so Nodûcor realised he was in the presence of a shintoìt. "At the most you can be grateful to me for preserving your immortality, but nothing more. I didn't accomplish anything to receive my lineage."
Nodûcor looked up and nodded hesitantly.
_It's time to find out more about him._ "How did you end up in the sarcophagus?"
The ashen-skinned älf picked up a little stick and used it to write in the loose sand. "I was following the runes I found in the mountains. They guided me." Every so often he wiped the sentences away after Aiphatòn indicated that he was finished reading. "I wanted to escape from this wasteland where there is nothing but fear and stupidity. To me, the runes promised älfar who were interested in art. And a new home."
_These must have been the signs that Modôia left behind._ "How long have you been travelling for?" He observed his companion's face carefully to see if he was trying to lie. But his gratitude to him seemed to be coming in handy. Aiphatòn could not detect any signs of dishonesty. _He suspects it would be a death sentence._
"I wasn't counting the moons. Then I noticed I was being followed and before I knew what was happening, Cushròk and his people grabbed me, put all of that stuff on me and bundled me into the coffin." He pointed at his scrawny muscles. "I was too exhausted to fight back.' But believe me, I'll be more than capable of fighting as soon as I get my strength back." Nodûcor was smiling underneath his half-mask, the smile obvious from the little wrinkles around his eyes, which were the same shimmering colour as his hair.
"Where were they trying to take you?"
"I don't know."
"Why did they guard you like you were the deadliest warrior in existence?" Aiphatòn could no longer recall the inscription that Cushròk had not been able to translate but great trouble had been mentioned.
"I don't know," Nodûcor drew in the sand.
Aiphatòn was sorry not to be able to hear his voice. Telling a lie was easier if you were writing it down. "The sarcophagus had älfar runes and words on it, and it was the same on your shackles. I don't think they were Cushròk's handiwork. So were they trailing you on the orders of an älf?"
Nodûcor underlined his sentence twice.
"Did you live in one of the towns?"
"No. I roamed around looking for a place where I could find beauty. Beauty and peace. Preferably solitude and nothing but the companionship of the wind," Nodûcor answered. "In the mountains, I thought, that's where I'm most likely to find all of that. Then I noticed the älfar runes and followed them." He gave Aiphatòn a scrutinising look. "How did you get to this side from there?" he wrote in the soft earth.
"I was following the runes too," Aiphatòn shot back, thus avoiding a lie as well as the truth, and he looked sharply to one side. _There's someone there!_ He had made out a movement in the meadow and heard hasty footsteps; a flag was fluttering softly in the wind.
Nodûcor also peered into the darkness—älf eyes could easily see in the dark so long as a star was twinkling.
They both saw a very muscular, extremely large man in dark brown leather armour that looked almost black in the gloom; the white, precisely drawn runes on it gleamed in the starlight.
His boots rose and fell in a steady jog and leather trousers protected his legs from dirt and the elements.
_The monsters and the älf we met at the ruins of the tower were wearing those symbols. But I can't make sense of them._ Aiphatòn could see the pale banner the lone runner was carrying on a long pole fixed to the back of his armour. The broadly built man's head was hidden underneath a simple, polished helmet with an intense metallic sheen; slits had been made in it, level with his eyes, mouth and nose.
_Isn't that the warrior from the battlefield who fought his way to the most advanced position?_
The runner was headed straight for the village, his arms swinging forward and back in a steady rhythm.
_No. That other warrior wasn't carrying a banner around. And the armour runes were missing._
Suddenly the armoured man stopped and clouds of dust rose up from underneath the soles of his feet.
Very slowly, he turned his head and the eye slits fixed on the älfar under the tree as if the armoured man could see them in the darkness.
Aiphatòn picked up his spear. _What is he doing?_ Before he could even decide to throw the spear, the man turned to face forwards again and continued on his way. _Did he spot us?_
Aiphatòn weighed up whether he still needed Nodûcor, given that he didn't come from the towns. But an älf without a family? With no origin? That didn't exist. His companion was still harbouring too many secrets that he needed to get to the bottom of. _He could still be useful to me, and I'm going to exploit_ _his gratitude._
"We're moving on," he murmured to Nodûcor and helped him to his feet. "I think he's a scout or a go-between. I don't want to be here when the army follows."
Nodûcor nodded and got to his feet. The food and the brief rest seemed to have done him good and he was looking more healthy.
They took a few more pieces of fruit for the journey, left the shelter of the apple tree and walked briskly and silently north-westwards.
After half a mile, Aiphatòn couldn't help but notice they were being followed: when he looked over his shoulder, he could make out ten silhouettes on their heels and they were rapidly catching up to them. At the same time, it looked like a ragged-edged black cloud with a wide front was dragging itself across the grassy plain and drifting towards the village.
_The vanguard of the army._ He stopped and pushed Nodûcor behind him.
He wished the people in the village all the best. If he had been in Girdlegard, he would have intervened on their behalf, but not in Ishím Voróo. He had just one duty: destroying the älfar towns.
"I'll get the shadows off our backs," he said quietly and walked towards the silhouettes. This wouldn't take long.
# Chapter VIII
_Death conquers all. Except art._
Wise saying of the Älfar
Collected by Carmondai, master of word and image
Ishím Voróo, Älfar town of Dsôn Elhàtor, 5452nd division of unendingness (6491st solar cycle), summer
Irïanora sat in her white leather armchair as though rooted to the spot, her arms on the armrests. _The blades are going to carve me up like a_ _sponge cake._
She stared anxiously at the piece of paper in Ôdaiòn's well-groomed hand. On it was her uncle's message to the monarchess and it needed to match what she said. Otherwise the whips would fly at her.
"Go ahead, my dear." Modôia towered above the chaise longue, the black whip looking out of place in the hand of the elegant älf-woman in the white dress, surrounded by yet more whiteness in the high-ceilinged room. The little birds flew tirelessly from lily to lily on the walls, making the scene even more surreal with the sound of their swift, droning wingbeats. "You know the message. Don't keep me in suspense. It's dampening my good mood." She smiled coldly. "You would sense that straight away, at my first blow."
Irïanora's lips were moving but she couldn't think. "Before you stands my niece," she said falteringly.
Modôia's left eyebrow shot up. The blow followed so quickly that even an experienced warrior would not have been able to dodge it.
Irïanora saw the blades glinting right in front of her, the tips heading straight for her middle—before they switched direction with a crack. The three straps jerked to the side, then her shoulders and neck started to burn.
The älf-woman screamed first in fear and then, shortly after that, in pain. The whips were pulled back again, the wet, red blades leaving thin lines on the white stone floor. The top half of her dark blue dress slipped down and warm blood trickled over her skin. The monarchess had cut through the fabric and made just a few minor incisions in her skin.
"I've always thought clothing doesn't show off the effect of the whip properly," she remarked. "Besides: you are very attractive and have nothing to hide, if you ignore the bruises."
"She could be the model for a statue of Inàste. Perfection from head to waist, madam, and perhaps we'll see the rest too," Ôdaiòn agreed with his mother and looked down at the piece of paper. "You'll have realised that those were _not_ the correct words." He got up and his whip uncoiled as he did so. "Someone should paint this, the way you're sitting there, surrounded by cleanliness and blood, the immaculateness fading more and more because of your inability to hit upon the correct message." He moved his whipping hand and the straps jerked. "Ah yes: _hit_."
Another barely perceptible movement and the blades were whirring towards her.
Irïanora screamed when they made contact on her right and left sides and again on her neck. Her dress fell open to her navel after this attack, but she didn't move to cover up her nakedness.
She stared Ôdaiòn in the face **—** and detected desire in his eyes.
When she saw this she realised, quick as a flash, that the älf would never severely injure her because he was still planning to have some fun with her.
Irïanora held his gaze and stayed seated bolt upright, as if she was trying to offer the whip an easy target.
Ôdaiòn lifted the piece of paper again. "Now, the second attempt," he commanded her. A ray of light fell so that it hit the thin paper in his fingers and shone through it.
Irïanora saw that there was nothing written on it. _My uncle didn't send a message. They're playing a game with me. They want to frighten me, humiliate me. Is that my punishment?_ She slowly got up from her armchair, blood pearling across her skin, tracing red tracks down to her navel and seeping into the fabric.
"The piece of paper you're holding in front of you is blank, sir," she said in a firm voice. "My uncle couldn't have sent you a message because he thought it was a better idea to send me to speak with you instead."
Modôia's gaze became furtive. "Why did you try to guess the words at first, if you knew the truth?"
"You were making such an effort to frighten me, I didn't want to ruin your fun, monarchess," replied Irïanora, putting on just as convincing an act of being fearless as she had of being terrified at the sight of her dead maid. She gave a small bow. "Now, if you'll excuse me? I'd like to put on a different dress."
Ôdaiòn burst into peals of laughter and Modôia joined in.
"Just go. My maid..."
"I'll go with you," her son said quickly, carelessly tossing the whip onto the armchair. "You'll love the rooms I've picked for you."
"You're too kind, sir." Irïanora bowed again. Small, red drops were pouring off her skin and falling onto the marble with a soft splashing sound.
Modôia seemed to have enjoyed herself. "Freshen up then, pick out a new outfit and I'll be expecting you at dinner."
Ôdaiòn took Irïanora by the hand and led her out.
The älf-woman didn't even consider adjusting her ruined dress. The son of the monarchess ought to enjoy the sight of her. She wanted to arouse his desire and make an ally of him as soon as possible. _Who knows what plans his mother has for me._
Irïanora was led through corridors and galleries decorated in pale blue and white.
The bone art on Elhàtor was confined to working with enormous bones and fish skeletons. There was no sign of the skeletons of barbarians or other beasts. Two jellyfish-like creatures four paces wide had been recreated with the help of fabric and looked like they were floating across one hall—lanterns inside them made it look like they were glowing.
Sea air made the curtains billow constantly and occasionally Irïanora caught a glimpse of the waves off the coast of the island.
After quite a few sets of stairs they entered the tower room where all of her trunks of clothes already stood, apart from the one containing the corpse of the murdered maid. A bath had also been prepared and there was a scent of lavender and citrus fruits from the warm water.
Without asking, Ôdaiòn undressed Irïanora.
In Dâkiòn she would have had the pushy älf thrown out, but luring him in like a big fat fish was part of her plan. So she bit her tongue as her cuts and scratches stung in protest.
Smiling, he helped her into the bathtub and picked up a sponge to wash the blood off her gently. "Don't worry. Our healers will make the wounds disappear later, along with these bruises which no doubt came from Shôtoràs," he said, his voice like velvet. He wrung out the sponge at the nape of her neck. Warm water ran down her back and she shuddered with pleasure. "Forgive my mother for the little game, but she felt you needed to be punished for what you'd done."
"You didn't?"
"I saw you, madam, and knew I couldn't harm you in any way," he whispered in her ear and gently kissed her bare shoulder.
Irïanora laughed coldly. "The words trip off your tongue so easily."
"I say them to every beautiful woman," he replied with a smile. "Because they're true."
"But your whip struck me anyway."
"It scratched you," he corrected her. "Not one of my blows would have done anything more than scratch you, unlike my mother's lashes." Ôdaiòn kissed the wounded area on her neck. "She tends to be cruel. You can tell she lived in Tark Draan for a long time."
"So I've had my punishment and I can go back?" Irïanora placed a hand on his cheek and it felt soft and well-groomed. _Come, my little fish. Get into my net._ "Or can I keep you company a while longer?"
"I would be delighted, even though you'll try and spy for your uncle." He winked at her and ran his wet fingers through his mid-length hair.
"I hate him," she blurted out too quickly.
Ôdaiòn laughed. "Then you're doubly welcome to Elhàtor. We gladly accept älfar who renounce the sovereign, which has been something of a rare occurrence lately. They could potentially unleash a wave of emigration." He kissed the palm of her hand as he wrung out the sponge on her throat so that the water ran down over her breasts. Then Ôdaiòn leaned forwards, his lips gently coming to rest against Irïanora's.
She returned the caress without much desire. _I certainly won't fall in love with him_ , Irïanora thought. _Play with him, yes. But not the other way round. He is my fish._
When the älf got up and left her apartment without turning around, she ducked underneath the surface of the water, hoping it would wash away and drown any potential feelings.
Towards the evening, Ôdaiòn came to fetch her and bring her to the meal. His fondness for dark blue and silver was in evidence again and despite its opulence, his robe was light-weight.
Earlier, two guards at her door had put paid to any attempt to explore the palace when they made it clear that Irïanora was to wait in her chamber.
Most of the windows had been covered with fabric from the outside so that the älf-woman could only see a narrow strip of the coast and the sea. So the splendid Dsôn Elhàtor, the Magnificent, with its streets, houses, the harbour and the fortifications, remained hidden to her for now. There could just as easily have been crooked huts and ugly stone hovels underneath her bedroom, she wouldn't know.
Irïanora had spent her time watching the waves and writing down her impressions. Two healers appeared at intervals and made all of the wounds and marks on her body disappear using magic.
"You look wonderful, madam." Ôdaiòn kissed her hand. "How could anyone not fall in love with you?"
"Is that what you're doing right now?" she teased him and bowed slightly. The red dress accentuated her figure particularly well and she had braided her long, blonde hair into a wide plait. Attempting anything else would have been pointless in the damp, salty air.
He placed his free hand on his heart. "Oh, you don't feel it then? From the splinter of unendingness when I helped you out of the carriage, you entered my heart." Ôdaiòn flung open the door to the dining room she'd seen earlier. "Let's enjoy the jolly part of your visit. I really hope"—he stepped to one side to allow her to enter—"you're pleased to see the familiar face you didn't ask after once. Just like you didn't ask after either of your other two friends."
Irïanora looked at the dining table where the monarchess was sitting with a brunette älf-woman Irïanora didn't know who was wearing a short, white leather dress, and Saitôra. Her friend from Dâkiòn was wearing a simple robe in various shades of blue, interwoven with silver and white, as if she had married Ôdaiòn in the meantime. She got up when they entered and nodded to Irïanora.
"Saitôra!" cried Irïanora gladly and hurried over to her, not forgetting to bow to the monarchess, who was now wearing a black dress embellished with pale blue. "I was so worried."
Ôdaiòn went to his mother's side. "We're all here now," he said, giving her a light kiss on the crown of her blonde head. "Let the meal begin."
Saitôra leaned over to her friend. "Gathalor and Iophâlor are dead," she blurted out quietly. "They killed them. Back at the strait!"
Irïanora's mouth was drying out more and more with every heartbeat—but not out of anxiety. _It's a pity about Iophâlor, but good thing Gathalor died... That is... wonderful!_ She didn't let on to Saitôra about her sudden good mood, but quickly gripped her hand and pressed it to feign dismay and seeking support. _The murder of Gathalor will upset my uncle so much, he'll fly into a rage. And a peaceful Constellation will turn into a burning Comet hurtling towards Elhàtor. The whole of Dâkiòn must have heard about the murders. Oh, I..._
Her plans ground to a halt: the task she had been given was to bring all three of the missing älfar back. Alive.
Her failure meant she was in danger from the old man too.
The servants entered and Modôia gestured to them to begin serving. "We're starting with a seafood soup," she explained. "The broth contains the best marinated crabmeat, unlike anything you'd find anywhere else." She picked up her spoon and looked around. "So I hope our guests enjoy it."
Irïanora tasted it cautiously and found the flavours of fish, herbs and salt very pleasant. And the taste of the crabmeat was very good too. "The cuisine is more sophisticated than ours," she remarked loudly and looked at Saitôra who was eating a little more slowly. "I think it's exquisite."
Modôia smiled. "I'll let my chef know."
Ôdaiòn leaned back suddenly. "What bad manners," he cried in surprise and tapped two fingers on the table. "I completely forgot to introduce the great Leïóva. What a faux pas."
Irïanora nodded to her.
"She is Mother's closest confidante. She even shares some worries with her that she keeps secret from me." Ôdaiòn sat up straight again and went on spooning up his soup with a wink. "Even though I find it hurtful to be belittled like that."
Irïanora surreptitiously scrutinised the älf-woman and took an instant dislike to her. _Something is off about her._ It wasn't because of her pretty face or her physique or posture. _Her perfume?_
"Leïóva's daughter commands one of our largest merchant ships," Modôia elaborated. "She is the best commander we have." She pointed at her son with her cutlery. "She and my son..."
"... are friends, Mother. Nothing more," he interrupted her with an air of amused light-heartedness. "But that's an area of my life our guests will find boring." He looked back and forth between Irïanora and Saitôra. "How I'd like to tour you around and show you both the beauty of Elhàtor. But so long as we haven't settled on how to proceed from here, I've got to hold fire," he explained with that friendly arrogance in his voice.
Saitôra looked at her friend. "What does that mean? I'm allowed to go back to Dâkiòn, right?" The young älf-woman looked at the monarchess. "I told you everything that I..."
"Hush," Modôia said kindly, putting her spoon aside. "Don't worry, my dear. That decision will be made by just _one_ person at this table."
The servants cleared the soup away and brought out plates with prised-open crab shells, various kinds of mussels and a piece of crayfish whose insides had been fried until they were crispy. The monarchess refrained from explanations this time.
Irïanora couldn't take her eyes off Leïóva. _What is it about her?_ "Excuse me," she addressed her, "don't I know you from Dâkiòn? Do you have family there? Can I pass on any..."
Ôdaiòn snorted, Leïóva and Modôia looked amused.
"Did I say something stupid?" Irïanora didn't know what to make of their reactions.
"No," answered Leïóva simply and kept eating.
"So you're not a former resident of Dâkiòn?"
"No."
Irïanora felt uneasy and embarrassed by her ignorance. "So are you a descendant of the älfar who stood their ground in the wasteland after the fall of Dsôn Faïmon and came to the island some time later?"
"I came here after my people were as good as wiped out, yes," Leïóva agreed coldly. "Our enemies pursued us relentlessly, murdered women and children and didn't even baulk at hunting down pregnant women who wanted nothing but to live in peace."
"Oh, so you escaped from Dorón Ashont?" Saitôra was spellbound.
"For me, there are more appalling enemies. The Acronta don't frighten me." The älf-woman in the white leather dress carved up a crab shell. "After a very eventful escape, I met Modôia. And although we hated each other from the bottom of our hearts at first, we overcame our dislike."
"And survived." The monarchess pointed to her son. "Without Leïóva he wouldn't be sitting here today."
"Without Modôia, my daughter would have been doomed." The black-haired älf-woman's gaze was fixed penetratingly on Irïanora. "Do you know any friendship like ours, profound enough to be capable of overcoming hatred?" She pointed at Saitôra with her knife and did not shift her gaze, but the muscles in her shoulders started to stand out. "Are you two linked by a similar bond, given she was ready to die for you?"
These words were followed by a deathly silence.
_No, I can't stand her._ Irïanora took a drink of water. "Yes," she replied and touched Saitôra's foot under the table to show her how serious she was. She turned her attention to the monarchess. "I beg you: when you make your decision about Saitôra's fate and mine, please consider..."
Modôia raised her hand and the älf-woman fell silent. "There's been a misunderstanding, my dear. When I said earlier that there was just _one_ person at this table who would make the decision, I meant _you_ , Irïanora."
Saitôra laughed with relief. "Oh, then send us home," she muttered loudly enough for everyone to hear.
Modôia, Leïóva and Ôdaiòn laughed pleasantly.
"It's not that simple," the monarchess admitted. "As that first trip down the Tronjor took such an unfortunate turn—not that you, Irïanora, could have predicted how tragically it would end—I thought to myself that it would be a good thing to leave the decision up to you this time."
"You killed them," Saitôra hissed in the monarchess' direction.
"We agreed it was—" Modôia looked to her son for help.
"An accident," he stepped in immediately.
"What decision?" asked Irïanora uncomprehendingly. "I thought I was allowed to make up my mind?"
"Just as the river and your decision caused an _accident_ that claimed victims' lives, there can't fail to be victims this time either." Modôia had some wine poured out for her and Leïóva took out a vial and tipped three greenish drops into it. " _One_ of you is allowed to return to Dâkiòn." She raised her glass to Irïanora. "You, as the niece of the sovereign and the higher ranking of you two, will decide who that will be." She emptied her glass in one go.
"And the other person?" whispered Saitôra.
"Will stay. As a hostage. If even _one_ boat from Dâkiòn approaches the strait, my whip will do the talking for as long as it takes. Until there is nothing but little scraps of the hostage left which I will send to Shôtoràs." Modôia looked at her plate. "I don't want to let myself be embarrassed or provoked any longer. Not by your uncle, by you or by any other älf who rules Dâkiòn in the future. That's the end of it." She cleared her throat and clasped her hands together expectantly. "So, my dear: who will go?"
Thoughts raced through Irïanora's head, from her uncle's threat and her hatred of him, to her hatred of the monarchess and the barely concealed desire of her son, the little fish in her net that she wanted to exploit.
New possibilities were opening up, old ones bowed to the inevitable and were dismissed, all within the space of a few heartbeats.
It all led to a strategy that fit excellently with her plan.
" _Who_ "—Modôia could make her voice crack like her whip—"will go?"
And Irïanora answered.
Tark Draan, Human kingdom of Idoslane, 5452nd division of unendingness (6491st solar cycle), summer
Carmondai placed a hand on the pillar lying diagonally across another pillar and pushed to see if it would hold. When there was no creaking or wobbling, he continued on according to the zhadár's instructions, ending up in the centre of the ruins.
Carâhnios got a kick out of sending Carmondai on ahead. "So the black-eye will think he's being given some help," he'd said with a grin when they parted.
So Carmondai was running along in the clothes that were now too small and threadbare. He was upright and easy to see in the moonlight as he moved through the ruins of the temple while the groundling took care of the security, moving furtively and as silently as an älf.
_This is not how I pictured the mission._ Carmondai's wrists were still shackled, which Carâhnios had thought made his pretence of being an escaped prisoner look more plausible. He also stumbled now and again as he'd been ordered to do, so that he could be heard. He could not work out the purpose of the large glass bottle the zhadár had pressed into his hand. There was a thin layer of silvery fluid along the glass bottom of the bottle.
Eventually, Carmondai was standing in the middle of the temple and behind him were the remains of a wall four paces high, with colourful glass windows decorated with unfamiliar symbols still preserved in it. The panes of glass turned the moonlight different colours and gave his tanned skin an unfamiliar tint. Five pillars as wide as a man and criss-crossed with cracks towered up in front of this, forming a semi-circle.
_What now?_ He had made an effort to be loud and conspicuous.
Carmondai still didn't know what to do if it came to a fight. Carâhnios had made it very clear what awaited him if he were to go against the groundling's instructions. But if the fortunes in a battle were to tilt and there was a chance of shifting the advantage more in favour of an älf... _And then what? I'm more or less in enemy land._
He forced himself, despite the humiliation, to stick to the agreed plan for the time being and stay close to the zhadár.
There was a quiet click behind him.
Carmondai turned around and stepped backwards to be on the safe side because he thought one of the pillars was collapsing or a piece of rubble had broken off and was falling down on him.
To his astonishment, a door had opened in the column to his right and a black-haired älf in tionium armour was standing inside it holding a long sword. Instead of paying any attention to the interloper, he strained his ears and carefully scanned the ruins. "Stay where you are," the warrior murmured to him.
Carmondai waited, taking time to relish his surprise. _Carâhnios was right_. The entrance to the hideaway—which was indeed inside the hill—was through the pillars that looked dangerously dilapidated.
The älfar stranger emerged slowly from the doorway. "You're alone," he said in a normal voice and put the sword away. "Forgive me for the unfriendly welcome, but times have changed for us. The barbarians might have been using a trick to lure me out of the hideaway."
Carmondai held out a shackled hand to him. "I get it."
"Who are you and how did you know about the ruins?"
The truth would be the most convincing. "I'm Carmondai. The Dsôn Aklán told me about all of the hideaways they built so that they could go to ground."
" _You_ are the master of word and image?" The stunned älf gave a small bow. "I adore your works! I praise Inàste for sending you to me and that endingness passed you by. My name is Ostòras."
"I thank you too, for showing yourself. It saves a lot of trouble. It would have taken me a long time to find the opening mechanism," he replied, feigning friendly solidarity.
"Then come inside with me so that we can take your shackles off." Ostòras looked genuinely pleased they had met, although the circumstances left a lot to be desired, of course. His dark red eyes were fixed on the glass bottle. "Is that valuable? Why are you carrying it around with you?"
Suddenly Carâhnios leaped out of the darkness of the shadows, holding the sword in his right hand and pointing it accusingly at Carmondai. "Don't believe him! He's an elf in disguise—they sent him as bait," he shouted menacingly and looked around hurriedly as if he were being followed or was expecting an attack. "You've walked right into the trap!"
Ostòras almost attacked the groundling but he immediately realised he was a zhadár. He turned this way and that, on his guard. "I knew it," he shouted. "You were much too loud to be an älf."
Carâhnios burst into gales of laughter. "This is too good! I use one black-eye to trick the other and I pull a fast one on you twice!"
It took Ostòras several heartbeats to realise he had fallen victim to a trick with a deadly ending. "This is how you both die!" He went to draw a dagger out of the holder on his back.
As soon as the armoured älf's arm moved backwards, the zhadár pounced.
Carmondai couldn't help but admire the agility of his movements. They were beyond the skills of an ordinary dwarf.
Ostòras dodged the blade, whipped his knee upwards to hit Carâhnios in the face then drew his own sword.
But the groundling dodged the attack. He parried his opponent's sword with his own weapon above his head and used his helmet to ram the älf in the solar plexus with all his might.
Suffocating, Ostòras sank to his knees despite his armour. The tip of the zhadár's weapon thrust vertically downwards through his armour into his collarbone. He dropped his sword and dagger with a clatter.
Carâhnios was still clasping the handle undaunted.
_The duel lasted less than three heartbeats. He took the warrior completely by surprise._ For Carmondai, not even the slightest opportunity to take sides had arisen, although he wouldn't necessarily have considered it.
Groaning, the kneeling Ostòras hung from the weapon like a fish on a harpoon.
"Now you're utterly confused," Carâhnios guessed and sniggered. "Yes, I _am_ a zhadár, and that _is_ Carmondai. We've set out to track down the last of you in the most secretive hideaways. Because I know every last one of them."
Ostòras cursed him. "One day you're going to come across one of us who doesn't fall for your trick," he predicted. "And then you'll die. Miserably and agonisingly."
"Not like you anyway. That's for sure." The zhadár drew his dagger and stabbed the älf in the neck, hitting the artery. "Carmondai, the bottle."
The älf handed it to him.
Carâhnios held the mouth of the bottle to the wound to collect the blood that spurted against the transparent walls in time with the heart's rhythm. His other hand rested around the hilt of his sword, fixing Ostòras firmly to the spot on his knees—he was moaning but didn't move so as not to injure himself more severely.
_He's taking the blood to distil the essence from it._ Carmondai wished he'd brought along something to draw with. _The former allies, joined in a deadly struggle. The älfars' creature triumphs over its masters._
"Let's play a game, my black-eyed friend," Carâhnios announced. "Your wounds are not yet fatal, and I could let you go."
"A traitor is not going to turn me into a traitor," Ostòras replied with hatred and contempt. Anger lines flashed across his face and it looked like his face was glowing in multiple colours because the coloured moonlight was falling on it through the panes of glass. "I'd rather pass into endingness. But know this"—he looked at Carmondai with eyes that were now black—"we are everywhere and yet nowhere. We will go into hiding, we will strike from the shadows and kill the kings of the barbarians, the pointy-ears and the groundlings. Girdlegard will descend into fear and chaos." He laughed and coughed. "And every time a hero rises up to bring unity, we will be there. We are the darkness!"
Ostòras leaped to his feet and drew a rasping, painful breath as Carâhnios' sword plunged down as far as his lungs, carving up his entrails and severing his arteries. Then the älf fell slowly forwards. Surprisingly little blood came from his two wounds, as if it was pooling internally.
The zhadár only just managed to keep hold of the glass bottle of blood in time. "He almost cost me my yield," he grumbled and gave the corpse a kick. "Dumb black-eye."
Ostòras' threat had made an impact on Carmondai because he knew it would come true if the groundling didn't manage to check all of the älfar's hideaways in time. _And he won't._ The great and the good of Tark Draan were all in danger. _This is the stuff of great dramas._
Carmondai could see it now: wise kings rising out of the human and dwarf tribes and getting cut down by a black älfar arrow at the peak of their powers, making the country descend into discord. His mind was already beginning to devise an epic.
Carâhnios held the container up to the moonlight to check it. "Very good. That's at least three units. The best way to collect the blood is when the heart is pumping it out. Once they've been run through with a sword it's no good anymore. There could be impurities and that ruins the elixir."
Words failed Carmondai; he could barely tear himself away from his thoughts about the epic but at the same time he was fascinated by the groundling's mercilessness, his coldness. _What did the Aklán create when they formed that unit?_
The zhadár calmly put a cork in the bottle and looked around. "Everything is still quiet. Looks like there was only one of them. Such a pity." He took a step through the doorway in the pillar. "Come on. Let's take a look at this." Then he smacked his forehead. "I almost forgot: go to the horse quickly, get yourself something to write and draw with, then come back here. Write down your thoughts and record what we find. Hurry up!"
Carmondai nodded and hurried through the ruins to their steeds. _He's letting me go by myself._
After the lightning-quick defeat of Ostòras, he knew exactly why Carâhnios was not worried about sending his prisoner off: Carmondai wouldn't get far on his horse. His presence as history's memory didn't protect him from the zhadár's anger and sword. _Besides, he needs my blood. He will never let me go._
Sighing, Carmondai reached the horse, found what he needed in the saddlebag and hurried back through the remains of the temple to where the skirmish had happened.
_I'm really, really intrigued about what we're going to see._
He still could not imagine the ritual in which Carâhnios was going to transform the blood into the distillate that truly kept him strong.
He wanted to be a witness to this miracle too.
Ishím Voróo, 5452nd division of unendingness (6491st solar cycle), summer
Aiphatòn saw the white runes gleam on the armour of the ten enemy combatants in the starlight: four orcs, three humans, two gnomes and an unfamiliar beast with an ugly mug like a wolf.
The six familiar specimens of monster were racing purposefully towards him, drawing their weapons as they ran. The wolf-beast and the humans went round him to get to Nodûcor.
Aiphatòn didn't ask himself what they wanted and beat them to the attack: he threw his spear at the two gnomes who were running in a staggered line, one behind the other, and penetrated their upper bodies; they fell to one side screaming and perished.
Aiphatòn launched himself at the closest orcs, smashing his armoured fists into their ugly mugs with such force that their facial bones caved in with a cracking sound. Blood gushed out of their noses, muzzles and eyes.
Squealing and gurgling, the enemies fell backwards onto the next two beasts and knocked them off their feet.
Aiphatòn landed behind the fallen orcs, dodged their whirring blades and summoned the spear which extricated itself from the dead gnomes and flew into his hand. He used all his might to ram the blade horizontally through the neck of one of the orcs who had been knocked down and carved up its blood-spurting throat.
The last orc got to its feet and swung its sword at Aiphatòn's chest with a slanting blow.
The älf blocked the attack and suddenly pulled the blade of the spear downwards and straight through its hideous head, then immediately thrust the tip into the shrieking enemy's belly and shoved him backwards. After his third staggering step he fell over the corpse of one of his own kind and lay still.
_You're all so easy to take down._ Aiphatòn looked at Nodûcor who was shrinking away from the humans and the wolf-beast. He was brandishing the serrated dagger at them with the courage that comes of desperation. But given his thin arms and his weakened state, he did not present much of a challenge to his opponents.
_Now for all of you._ Aiphatòn started running and hurled the spear at the armoured wolf-creature's back—he was the enemy he deemed the most dangerous. Its furry ears twitched; they detected the sound of the thrown spear. The monster dodged the missile with a rapid pivot—and made a grab with its right hand: its claws wrapped around the metal shaft of the spear. Enraged, it turned round to face the älf, holding the weapon it had seized at the ready.
By this point, the men were attacking Nodûcor and he was lashing out in every direction, trying to keep his opponents at bay.
Aiphatòn smiled at the slobbering wolf-beast as it bore down on him, holding the spear in both its hands now, planning to run his enemy through with it. _It won't be any use to you._ He moved towards the beast.
A brief jolt of magical energy made the runes on his weapon glow. There was a hissing sound when the symbols heated up so quickly they burned into the creature's skin; howling, it dropped the stolen weapon.
Aiphatòn came over and with his right hand he dealt the creature a direct punch to the centre of its chest, crushing the armour. The runes on his glove lit up and released a flash from the knuckles that blasted the armour open and carved a hole in the flesh underneath. A cloud of blood and bone fragments flew out of the wolf-beast's back as it shot backwards eight paces and took one of the men's feet out from under him. It landed in a smoking heap on the ground and didn't move; the man under it twitched once before going still.
Nodûcor exploited his attackers' confusion and stabbed upwards at one of the men's chins with the dagger.
But his opponent moved his head back and the tip of the dagger slid uselessly over his coat of chainmail. One kick to the stomach sent the pale-skinned älf flying to the ground.
"It's my turn first." Aiphatòn sprinted towards them, hunched like a beast of prey, as the spear flew into his left hand and the runes went dark.
The first man attacked him with two short swords and the other one drew his double-bladed axe, which must once have belonged to a lumberjack, and waited.
_This is taking too long._ Aiphatòn swept the swords aside with his armoured right forearm, the symbols gleamed and the massive blades shattered like fragile glass. His left hand jolted forwards, driving the spear at his opponent's heart and killing the man.
By now, the last enemy had put one foot against Nodûcor's throat and the broad, right axe blade was resting at the älf's neck. "Surrender, älf," he said, his gaze vacant. "You and your friend will accompany this warrior to my army."
_It must be the botoican speaking to me._ Aiphatòn wished he had Carmondai's knowledge or that the tale-weaver himself would appear—he was so much more than a gifted storyteller. "So that you can enlist me like those wretches?" He gestured at the corpses. "Find someone else to hound to death for your collection."
"That's what I'm doing. I've heard there are towns to conquer, large towns with älfar living in them. I'll see if I feel like it as soon as my preparations are complete," the warrior replied. "But you are something unique, I feel. That makes you all the more valuable in the battle against my foes." He heaved the blade at Nodûcor's mask and a metallic clang rang out. "If you refuse, _he_ dies first. I can't allow you to fall into someone else's hands."
Aiphatòn looked around quickly, but couldn't make out any other enemy fighters.
The mob that had reached the sleeping village half a mile behind them thronged the spaces between the houses and huts, storming into every building they found. Screams cut quietly through the night air.
Aiphatòn felt no sympathy. This was Ishím Voróo, not Girdlegard. Aiphatòn did not feel responsible for the lives of these locals. He had no doubt the people would soon be incorporated into the botoican's army against their will. _They'll be hauled in front of him and then..._ He realised he knew nothing about these magicians' methods. They wove spells so vastly different from that of a Lot-Ionan. _What then?_
Nodûcor groaned, the axe blade cutting into his skin. Blood ran from the superficial wound.
"It's time, älf," the man said in a hollow voice and drew a throwing knife. "Turn around and go to the army in the village so that they can tie you up and guard you. Once you're down there, the warrior will follow with your friend."
_A trick will be more useful than speed right now._ Aiphatòn nodded, dropped the spear and walked off slowly; his arms dangled loosely at his sides. Now and again, he turned around.
The warrior grabbed Nodûcor and got him to his feet, pushing him on ahead. He had placed the heavy axe head on the älf's shoulder so that one jerk would be enough to sever the prisoner's skull from his torso.
_Oh, that makes it easier for me. I was having misgivings._ Aiphatòn was ready.
The warrior passed the spot where the spear was lying in the long grass but didn't check for the weapon. He felt safe at a distance of fifty paces.
"Watch out," Aiphatòn cried in älfar, still facing ahead. He simply opened the fingers of his right hand.
The spear whirred into the air and travelled in a straight line towards its master.
His opponent was struck in the spine and the weapon lodged there. It seemed like the power of the magic and hence the momentum of the spear was waning.
Nodûcor lifted his hands up quickly and held on tight to the blade of the axe; he tilted his shoulder so that the cutting edge didn't slip and accidentally hurt him after all.
Aiphatòn laughed nastily and ran back. "Are you all right?" he called to the älf.
Nodûcor nodded and took two paces away from the warrior who was standing there leaning sharply backwards. The end of the spear's shaft had bored into the ground and now functioned as an inadvertent prop so that the man didn't fall over.
The dagger and axe handle slipped out of the enemy's hands and his eyes flicked back and forth between the two of them. "You won't get away from me," he promised, his voice breaking. "And you, you strange älf, will reveal your magical secrets to me as soon as I've broken your will." The man's arms sank limply to his sides, his head tipped back. "The Nhatais will take what they are entitled to. And I am entitled to _you_ , just like I am to all of your tribe, wherever I find them!" the dying man whispered. "No matter whe—" The threat faded away with one last breath. Death came more quickly than the botoican's message.
Aiphatòn kicked the body onto the ground and pulled the spear out of the vertebra. He looked at the village where some dots were already breaking away from the black mass and racing towards them. "Let's get going. The botoican will lose interest in us as soon as he has created enough other toys."
He let Nodûcor link his arm and hurried away, carrying the light älf more than he was supporting him. Aiphatòn marched on relentlessly, leaving the vanguard behind them to fall back.
They walked throughout the night.
He crushed apples for Nodûcor with his glove and had him suck up the pulp so that he stayed relatively strong. From time to time they quenched their thirst with clear, cold water from streams.
They didn't rest until the break of dawn at the foot of a gentle hill covered in trees.
Nodûcor could not take one more step and his eyes closed immediately. Aiphatòn scanned the grassy landscape that lay behind them. _They've given up or were called back by the botoican._
He too sank into the soft green carpet and closed his eyes. The scent of the grass, the pure soil and the fragrance of apples coming from his glove pervaded his nostrils.
Yet he could barely relax.
He couldn't imagine how powerful a spell needed to be in order to control a hundred thousand warriors at once and make them fight and commit murders in the most gruesome way. He thought about what he'd heard.
_Are the botoicans at war with each other and gathering as many soldiers around them as they can?_
The fatigue settled into his limbs like lead and finally drove even these thoughts away.
His breathing slowed and Aiphatòn slipped into sleep as the sun came up over the hill.
# Chapter IX
_The imagination allows some people to travel in the hopes that they come back educated._
Wise saying of the Älfar
Collected by Carmondai, master of word and image
Tark Draan, The Golden Plain, 5452nd division of unendingness (6491st solar cycle), late summer
Barefoot and topless, Ilahín stepped out of the first house in the emerging elf settlement on the Golden Plain in the middle of the night and looked up at the stars.
The life and destiny star of his people was visibly glowing more boldly and cheerfully, which brought a smile to his slender features. _The Firstlings will come soon._
He and his wife had made the building they were sleeping in with their own hands. They had carved and painted, hauled materials and built walls, put in balconies and layered up materials until the roof could be thatched with reeds and the inside was protected from the elements.
At the appearance of the special star, Ilahín offered up his prayers to the Creating Spirit of his people that Sitalia and Elria received their oblations.
Afterwards the elf wove a rare spell that only becomes truly powerful when the heavenly bodies shine.
_I've had to wait a long time for it to be possible._
The charm sent nothing more than an inaudible but palpable signal through the world and it reached elves wherever they were. From then on they would know that there was enough space in Girdlegard to settle down in safety.
Ilahín tied back his long, almost black hair and watched the nearby river that promised so much life. _Many houses will spring up_ _along the bank, like how it used to be. We will bring the people a noble attitude and make sure the älfar are forgotten._
"What are you doing out here?" Fiëa walked up behind him and leaned her head against the back of his neck. "You've already said the magic spell." She was wearing a transparent, white night-gown made of cool silk.
He was pleased she had joined him and not left him alone with his brooding thoughts. She was visiting him here on the Golden Plain but would head back to the crater the next morning. "I wanted to see whether our star was still visible."
She wrapped her arms around his waist. "Were you afraid it would go out again?"
Ilahín took his time in answering. "So much has happened."
"And so much of it in our favour. Our worst enemies are as good as wiped out. After so many cycles of hiding and fear, it's we who survived."
He turned to face her slowly and she didn't relax her embrace. He stroked her long, white hair. "Even though this crazy zhadár is hunting them, there will always be a few more left," he told her gravely. "They too can do what we were capable of doing. There is enough shadow in Girdlegard to make sure they're not seen. It's only their evilness that causes them to refuse to stop their slaughter." He kissed her on the forehead. "They will be the black thorn in the flesh of the kingdoms."
"Why do you think that?"
"I don't think it. It's a certainty."
"But even Aiphatòn will leave, and the dwarves are guarding the passageways so that no more älfar can get to us." Fiëa caressed his face. "Trust our Creating Spirit."
"I do. With all my heart and soul." Ilahín smiled weakly. "What's happening with this hole that opened up in the crater? You didn't say much about it."
"There's not much to report. We are filling it in as quickly as we can get our hands on soil and debris," she said, seeing right through his attempt to change the topic before a fight could start. "The guards are vigilant in carrying out their duties. It's been quiet so far. Not one monster has been sighted."
But the elf could tell she was worried. "You're afraid that it can't be filled in fast enough?"
Fiëa drew closer to him, her head resting on his bare chest. "It's because of the writings."
"I don't understand."
"Carmondai's work, which we didn't find in the palace at first." Her mood changed audibly. "I should have killed him," she said softly. "But that crazy dwarf stopped me."
"A task has been found for Carmondai that makes him harmless and even useful."
"No älf is harmless or blameless. And the same goes for his writings. They are more than just easy-to-read events described excellently well." She lifted her head and looked at him. "We've got to destroy them, otherwise they could potentially foster affection for the black-eyes."
" _Affection?_ " Ilahín laughed at her. "After what they did to Girdlegard?"
"I'll put it a different way then: understanding, fascination, an emotion that negates their terror and brutality. He makes heroes of them. But they're demons who plagued us. He twists the truth." Fiëa was trying to find a justification. "We've got to tackle it." She looked pleadingly at him. "One thing from the writings has already leaked to the humans and dwarves which I would have liked to have avoided."
He looked at her in astonishment. "Who was able to translate the älfar?"
"The black-eyes have ruled long enough that their language and script spread to quite a few humans. They wrote their instructions to allies and deserters in their own language sometimes." Fiëa closed her eyes. "How I wish," she murmured angrily, "that I had killed Carmondai!"
"I'm still waiting for you to give me the bad news."
She took a deep breath. "The village in the Grey Mountains, near the Jagged Crown."
Ilahín knew what she meant straight away. He was silent for a while. "There has been a rumour ever since Leïóva and her people climbed up there and a group of älfar followed her. It will die down soon."
The two of them would never have travelled there to escape the älfar. They would sooner have died than go to the place where their tribe's turncoats were trying to befriend the dwarves in the name of working together.
Ilahín had never understood why the elf rulers had allowed this splinter group to exist. Even when they returned from the Grey Mountains and tried to live on the Golden Plain again, in Âlandur and Lesinteïl, they had not been turned away. But after many cycles of denunciation and occasional friction, the splinter group left the community again and stayed in the mountains.
"The difference is this: it has been written down, it's out there in the world. And the news is already spreading like wildfire in Girdlegard." Fiëa's concerns were far from over. "One thing leads to another: as soon as the dwarves hear it, they will check how much of it is true. And the more truth there is in the älf's writings, the more status they'll gain."
"Then someone might assume that the lies in there about our people are true or at least that there's some truth to them," he finished her thought process. "You're right. Could you potentially, after the fact..."
"Luckily some parts went missing when the palace and its mountains collapsed, but the rest were passed to various scholars who began to translate them." Fiëa let go of her husband. "There can only be so many accidental fires."
"No, that would be too obvious." Ilahín looked up, staring at the elves' life star. "Let's try for truth and reason: we'll convince the queens and kings of the danger of the dishonest writings," he said slowly, formulating his plan as he spoke. "I'll work on a speech that will ensure they're more afraid of the papers than the black-eyes themselves."
"You'll have to hurry though. Once anything gets into anyone's head, it can never be removed again."
"I will." He kissed her reassuringly. "By the way, I haven't been able to find out what happened to the former emperor of the älfar."
"Nobody knows where his hunt took him." Fiëa walked slowly back to the house. "He is to be feared just as much as the impact of Carmondai's writings. Will your speech achieve that?" She didn't think Aiphatòn was capable of leaving Girdlegard willingly.
The same was true of Ilahín. Aiphatòn had hunted the elves for almost two hundred cycles before he awoke from his madness and led his own people to their doom.
_But that doesn't diminish the guilt he brought upon himself._ "It ought to." He followed Fiëa back into the house. _Or we'll kill him as soon as he turns up._ That would be a fair punishment.
Ishím Voróo, Several miles outside Dsôn Dâkiòn, 5452nd division of unendingness (6491st solar cycle), summer
"It seems we chose the right route." After several orbits of Aiphatòn and Nodûcor walking through hilly grassland, a mountain now loomed far in the distance with a town on it. Long walls ran along the precipices and they would be impossible to climb with conventional equipment, which made conquest out of the question.
_You would need dragons to attack it from the air. Who knows what Ishím Voróo has to offer in comparison with Girdlegard._ Aiphatòn estimated the summit was about five hundred paces high. The densely packed homes stretched around the peak and stopped a hundred paces above the walls. As far as he could make out, two wide bridges were the only ways to access the town. A deep ravine also ran through the mountain, spanned by just one footbridge. _Gigantic structures. The älfar who live there like things big._
"Is that Dsôn Elhàtor or Dâkiòn?" he asked Nodûcor.
Compelled to remain mute, the älf made a helpless gesture. His skin had not browned or reddened in the sun, as if stubbornly refusing to betray any sign of life; his hair looked the same as before.
_Either he's lying or he's less help than I'd hoped. At least he's putting on weight so I don't need to worry that he could die on me before he becomes useful._ On the journey, Aiphatòn had fed him porridge with fruit pulp or meat mixed in, often heavily watered down so that Nodûcor could suck it up through the straw. But in the black half-mask he still made a bony, terrifying sight. _Death_ _in älf form._
As they walked across the plain they spotted a solitary flagpole as wide as a man, with a yellow älf rune on a black silk flag fluttering in the wind.
When they came closer they saw an iron plaque that had been fixed to the pole at chest-height with long nails.
"Well, this is polite," Aiphatòn remarked and scanned the message that had been engraved into the metal in various languages.
_Wanderer,_
_if you're coming to Dâkiòn,_
_be advised_
_you will have levies to pay_
_as decreed by law._
_Anyone who roams this land_
_will pay on request_
_a coin of gold_
_apiece_
_or a jewel of the highest quality._
_Should you not possess either,_
_make a detour of forty miles._
_Or pay_
_with your_
_mortal remains._
"That solves that mystery. Dâkiòn is up ahead." Aiphatòn looked at the town. "A forty-mile sovereign territory? The älfar in Ishím Voróo have become modest with the size of their kingdoms, in any case. Unlike the structures they build." He could make out several villages in the plain, as well as paddocks and cultivated fields and small patches of woodland. "The yield from those crops would never be enough to feed the residents for a whole cycle. They must do trade or rely on compulsory levies."
Nodûcor pointed to the words _gold_ and _jewel_.
"Yes, they're definitely rich," Aiphatòn agreed and rested his spear on his shoulder. "We'll likely have to pay with our mortal remains, if they catch us." He laughed and set off.
Nodûcor followed hesitantly. He was still carrying around the clamp that had been on his upper body, even though it exhausted him. It was just peeping out of his rucksack.
At first, Aiphatòn had toyed with the idea of tying up the pale älf in a hiding place and leaving him behind so that he could do an initial reconnaissance by himself. But Nodûcor's weakness and the approaching botoicans stopped him doing that. He didn't want Nodûcor killed by a band of orcs out of hunger or hatred before he could solve the puzzle of the half-mask and its origins. And his conviction that the pale älf would somehow be useful to him had taken root.
By the afternoon, they had covered a third of the distance to Dâkiòn and had walked through the first large village. It was not much different from the settlements in Girdlegard in terms of architectural style or local clothing trends. It seemed humans looked the same everywhere. Aiphatòn saw älfar runes painted or engraved on the homes, but no signs of altars to the gods or statues placed in niches in the houses for protection. It was clear whose favour was prioritised around Dâkiòn.
Nobody paid them particular attention. Nodûcor's mask provoked the odd look of surprise but no sustained interest.
"Either they think we're townspeople or they know they're under the protection of Dâkiòn and we cannot harm them," Aiphatòn said to Nodûcor, glad that there were no glances coming their way: no anxious, shy or hate-filled looks. Life was rather different in north-western Ishím Voróo; it was practically relaxed.
The locals weren't running away from them or following them. If they had seen Aiphatòn's plate-covered body, the encounter might have gone differently. But as he was wearing a robe over them, nobody noticed. _This is unusual. Incredible._
As night fell, they reached another village, also populated by humans.
The two älfar were walking along the high street. Nodûcor's posture betrayed the stress he was feeling. He didn't trust the tranquillity.
Aiphatòn stopped abruptly in front of a half-timbered building with a tankard dangling over its open door. The smell of cooked food and the hubbub of conversation drifted out to where they stood.
"This'll be a bar. And I feel like a drink that doesn't taste of water." He grabbed Nodûcor by the arm and dragged him into the pub, his spear lowered.
Aiphatòn was astonished all over again that nobody cared about the newcomers. The men and women's conversations continued uninterrupted; there was no commotion.
The barman, a tubby little man whose beard and hair were unkempt, looked up, nodded to them and pointed to the right where there was a small table free.
The älfar crossed the room and sat down; they put their luggage and spear on the floor.
The balconies inside the building had been painted a dark brown and the walls were white. Candles and lamps burned in various niches and poorly done paintings of the town hung on the walls for decoration, along with several different flags. Two tables away, some men were singing a rowdy tune and a woman was dancing to it. Swathes of tobacco smoke wafted about and irritated the älfar's noses.
"I can hardly believe it." Aiphatòn remembered Girdlegard. If he and Nodûcor had walked into a village when his tribe was in power, everyone would have thrown themselves to the floor and asked what they wanted, immediately begging for mercy so as not to have their bones removed for artworks.
The barman, whose leather pub apron harboured an overpowering smell of beer and sweat, brought them two earthenware goblets and a carafe of wine. "I hope you like it," he told them in älfar with a very human accent and an unfamiliar emphasis.
Aiphatòn laughed in surprise. "Am I dreaming?"
Nodûcor shook his head, looking equally perplexed, if not more so.
The barman eyed him with a friendly expression on his face. "Sir, you're not dreaming. I can tell from your clothes that you don't come from Dâkiòn. Therefore you must have completed a long trek to see the sovereign and become new residents of the town." He pointed to the wine. "The local älfar are particularly fond of this one. It's light, fruity and it comes without too much sweetness."
"We don't have any money."
"A gift. Accept it, sir. You're welcome to eat as well."
"Well, I'm dreaming after all." Aiphatòn picked up the goblet and poured some wine for himself, raising his glass to the barman and Nodûcor. "To you, my good man."
The barman bowed and put one hand on his chest.
"Yes, yes, the kind-hearted Joako," came a voice by the door, followed by a chorus of laughter. "Likes to make friends he might make use of later."
Aiphatòn looked toward the doorway. _Apparently the money-collectors are here._
An älf with dark blonde hair was towering over the threshold. He wore black lamellar armour under a white tunic with the familiar yellow rune and another symbol emblazoned on it in green. There was a silver-plated black helmet in his right hand and iron batons in holders on his thighs.
"Greetings to the travellers," he cried and entered the room. "You noticed the sign at our border?"
Business carried on as usual in the tavern, the singing just got a little quieter.
Outside the window, Aiphatòn could see three more warriors chatting, not looking worried. They were holding curved bows made of horn, the quivers full to the brim with long, black arrows. _They're like us on that score._ "Yes, we noticed it."
"My name is Vailóras," he introduced himself and sat down opposite them at the table. "Joako, fetch me a goblet too," he said, turning to the barman; as he did so the long dagger at his belt became visible. "What's wrong with your eyes?"
"They take a long time to lose their blackness," the shintoìt said, playing it down. "It's bothered me since birth."
"Ah. Now then: I'm the one you need to settle your debt with," Vailóras smiled calmly. "You choose the currency: gold, jewels or your mortal remains?"
"We have neither the first nor the second and we still need the third," Aiphatòn replied politely. "I'd like to go to Dâkiòn."
"And so you can. As soon as you pay." Vailóras seemed to have these conversations rather frequently. He sounded aloof, but there was a certain menace in his voice. "If you think you can slip away from me, you'll be asked for the fee—at the latest—at the gate if you can't present the receipt that I issue after payment."
"Could you advance me two coins then?" Aiphatòn suggested. "I'll be sure to pay you back double as soon as I've spoken to the sovereign."
"Me lend you something?" Vailóras raised his eyebrows. "Nobody has come up with that idea before." He grinned and in the end couldn't help but laugh. "But no. And no jewels either."
"Your mortal remains then?" Aiphatòn followed this with a wink. "You'd get those back too."
"Even less likely," Vailóras replied, amused. "You're a real joker." Joako brought the goblet and the warrior drank from it. "What ruined town do you and your friend come from? And what's with the half-mask?" He drank and waited. "Does he bite?"
"He tends to be a bit rude. A mask of disgrace," Aiphatòn lied. "He even spits if he gets too worked up. He's trying to break the habit at the moment."
Vailóras pulled a face. "Ah, I see. Another funny story. And what about your origins then?"
"Girdlegard," he responded evenly.
_"What?"_ The warrior did not understand.
"You probably call it Tark Draan, if the Dsôn Aklán informed me correctly," he elaborated and was amused to see Vailóras' jaw falling open in shock. "That's where I come from anyway. I rescued him from the clutches of a mob on the way."
Vailóras polished off his wine in rapid gulps. "Then count yourself lucky you came across me," he said; the cheerfulness had vanished from his voice and face. "The sovereign doesn't like älfar from Tark Draan. You can turn back and I'll forget I ever saw you." The dark blonde älf placed his hands flat on the table to show he meant no threat.
"Why is that?"
"That's just the way it is. And I can't bring you to him to ask him yourself because you don't have the coins."
"Well, thank you for your candour." Aiphatòn nodded slowly. "But if I've absolutely _got_ to see the sovereign?"
"Then you and your friend owe me gold coins, jewels or mortal remains, the same as before. We're going in circles," said Vailóras, not giving in. "Unless there was a good reason why I _needed_ to bring you to Shôtoràs."
"Like for the good of the town, for instance?"
"A good reason." Vailóras inclined his head in agreement. "But how could that be dependent on you?"
Aiphatòn grinned. "I can only tell the sovereign himself that." He raised his glass to him. "Do you want to be responsible for Dâkiòn being in danger, all because you didn't bring me to him?"
A smile played around the corners of Vailóras' mouth. "You're smart. But I'm still not convinced. Give me more."
"How about botoicans?"
The warrior wiped dust off his lamellar armour. "Nobody is afraid of them. We crushed one of their armies."
"Well then, what about magic?" Aiphatòn made the spear runes light up and the symbols on his armoured gloves glow.
"We've got cîani who can do a lot more. How else could we have crushed one of the botoican armies?" Vailóras remained unimpressed and got to his feet, readjusting the white tunic he wore over the dark armour. "I'll give you one last chance. Otherwise"—he drew the right-hand baton out of the sheath on his thigh—"I'll remove the nicest bones from the pair of you."
Aiphatòn stood up slowly too. Using the armoured glove on his right hand, he slipped off his robe so that the warrior could see the pieces of metal sewn into his body; with his left hand he summoned the spear and made the runes on the weapon, the gloves and the plates glow with a dazzlingly bright light.
Silence fell across the room now. Apparently this was a rare sight even in Ishím Voróo.
"My name is Aiphatòn. I am the son of the Inextinguishables who once ruled Dsôn Faïmon, cradle to us all, and before whom perhaps even the sovereign Shôtoràs once bowed his head," he said, speaking so loudly that nobody could fail to hear him, even the älfar outside the window. "What I have to say to the sovereign concerns him and only him." He pointed at the exit with his glowing blade. "Now take me to Dâkiòn!"
Vailóras eyed him with a look that betrayed neither awe nor respect, only hostility. "Hence the eyes." He turned round. "Let's go then," he ordered briskly and rudely as he walked out.
_Let's go then—is that it?_ Aiphatòn was utterly baffled. By now at the latest, he would have expected demonstrations of respect and bended knees. Nodûcor rolled his eyes. _Everything is different in this wasteland. Even the älfar._
They quickly picked up their luggage and left the bar. The mutterings started as they left.
The archers were already sitting in the night-mares' saddles. Through the medium of extended arms, it was communicated to Nodûcor and Aiphatòn that they were to mount behind. Just a few heartbeats later, they swung themselves up behind the riders.
"Ah yes: it's possible that I'll demand the levy at a later point," Vailóras informed them, making his black horse trot with a gentle kick to its flanks.
His warriors laughed softly, in anticipation of watching them suffer.
They covered the final miles to the town in the dead of night underneath the starry sky. The trot turned into a breakneck gallop that required utmost concentration from the night-mares. The earth trembled beneath the stamping hooves as they trampled the ground, bolts of lightning flashing around their ankles.
But the real spectacle was happening ahead of them: the moon shone down on Dâkiòn and made the whole town glow.
The bright, painted roofs cast the light far into the countryside, jewels and diamonds glittered and sparkled all over the walls; the large connecting bridge gleamed, golden in colour. All kinds of artworks fixed to the dormer windows and looming up between the houses were moving and drifting in the gentle breeze.
A quiet, barely audible glockenspiel rang out from the town. The melody touched Aiphatòn's soul, although the wind was rushing in his ears and distorting the notes. _What must the original be like, if I could hear it correctly?_
Runes loomed into view on the enormous defensive walls. They praised Inàste and asked for her protection against attackers.
_Save us from new enemies and old masters_ , Aiphatòn read.
It didn't sound to him like they had been longing for the return of the Inextinguishables or one of their offspring.
Ishím Voróo, Älfar town of Dsôn Elhàtor, 5452nd division of unendingness (6491st solar cycle), summer
Standing with Saitôra at the quay wall, Irïanora hugged her friend, then set one foot on the ramp up to the ship. "I'll pass on your messages," she said glumly and held up the folder full of letters to emphasise this. Ôdaiòn had checked the contents in advance for any information about their defences. "We won't forget you."
Step by step, she climbed backwards up the gangway, nearing the deck.
Irïanora didn't let Saitôra, who despite her luxurious silver-blue dress was an unparalleled heap of misery, out of her sight. The wood gave way slightly under her, rising and falling with the rocking of the ship and the waves. _She's going to break down any moment now._
The canvases in the enormous frames that had been put up around the little group stretched taut in the wind. The fabric meant she couldn't get a glimpse of her surroundings; however, she had a clear view of the sea, the mouth of the harbour and the large ship.
Ôdaiòn, in his lavish, sophisticated blue clothes as always, was waiting with five lightly armed soldiers a small distance away and watching the departure scene.
The black-haired Saitôra was close to tears. "Tell your uncle never to give in to those who want war," she pleaded, her voice choked up. "And you... please don't send anyone else down the Tronjor. Otherwise..." She wrapped her arms around herself and lowered her head, her shoulders shrugging. Her composure was gone. "Irïanora! I don't want to die. Not here. And I don't want to be alone, away from my family," she sobbed and sank to her knees. "Think of me," she cried, weeping. "Oh, Inàste!"
Irïanora stopped on the ramp, swallowed and quickly came back down. She took her friend in her arms and embraced her. "I can't do this to you," she said, deeply moved. " _You_ will travel to Dâkiòn and tell everyone why I stayed."
"What?" Saitôra stared at her with swollen eyes, and her disbelief turned to overwhelming joy. "No, this cannot be! You're the niece of the sovereign!"
"And hence all the greater an obstacle for the warmongers if they try to incite our town to fight," Irïanora added loudly so that the monarchess' son could hear and stroked Saitôra's black hair. "I'm staying. My decision has been made." Her gaze shifted over Saitôra's head to Ôdaiòn, who was looking intently at her and smiling slightly. Then she hugged her friend again, reaching into the fold of her dark red dress as she did so, secretly taking out two letters and slipping them to her. "One is for Shôtoràs, the other is for a good friend. His name is Anûras. You'll find him in the Death-dancer," she whispered hurriedly. "Go."
"You... planned this?" Saitôra's pale grey eyes opened wide, sparkling and damp. She was also using the tincture to preserve the whiteness during the day.
"It's the only way I could write messages that Ôdaiòn _didn't_ check. Tell our people how brutally they murdered Gathalor and Iophâlor. Their deaths must be atoned for," she whispered. Then she picked Saitôra up off the ground and put her onto the ramp. "Tell my uncle I love him," she called loudly, wiping away hastily faked tears.
Saitôra staggered up the slope and laughed in relief while Irïanora threw her friend's now useless messages into the harbour basin. "I will let everyone know about your heroism! They will sing songs and tell stories about you!" She blew her a kiss and placed one hand over her heart. "I owe you my life, Irïanora. I will do everything I can to make sure nothing happens to you on Elhàtor." Waving, she disappeared on deck where the crew immediately met her and led her inside.
The ropes were untied and the ship put out to sea. Two smaller sails unfurled with a flutter, the bow swung around and headed for the mouth of the harbour.
Ôdaiòn came and stood next to Irïanora. "So we've got ourselves a little heroine," he said and laughed kindly. "I have great respect for you. That was noble and selfless." He took her hand and kissed the knuckles. "If I were to claim your presence didn't suit me, I'd be lying."
"To be frank"—Irïanora dropped him a small curtsey to give him a view of her cleavage—"I _hate_ my uncle. And when I saw poor Saitôra, how heavy her heart and soul became, there was nothing else for it. I got her into this situation so it was up to me to get her out of it." She waved farewell to the ship with her other hand, as if her friend could see her. "Besides, this way the risk of a war will be ruled out. Nobody wants to put the life of the sovereign's niece at stake."
"You escape the great Shôtoràs and become the self-sacrificing friend. Well played." He reached into his pocket and pulled out a black cloth, stepped behind her and put the blindfold on her. "By the way, my mother is of the opinion that you're nothing more than a spy. A very cunning spy but still one who ought to be killed straight away."
Irïanora let him have his way. She smelled his aftershave and felt the warmth of his body. "Or maybe I fell in love with you, which reinforced my decision to stay?" It was time to lure the fish again but more intensely.
Ôdaiòn laughed softly. "That's flattering. A symbolic marriage between us would create a firm bond between Elhàtor and Dâkiòn." He took her by the hand and guided her along. "But you should know that my mother would like to see me in the arms of Leïóva's daughter."
"The commander of a merchant ship?" Irïanora protested incredulously. "That's... verging on the ridiculous!"
"The two woman are blood sisters, my dear Irïanora. And in order to carry their friendship on into the next generation, this marriage would make sense." There was a click as he opened a carriage door, then she was guided into the coach where there was a smell of fresh flowers. She heard Ôdaiòn getting in after her. The door closed with a clack and the vehicle jolted forward.
"Can I take the blindfold off?" The blonde älf-woman breathed in the sweet aroma—and suddenly felt his lips on hers.
She didn't hesitate to reciprocate his tender kiss, clasping his face in her hands and pulling him closer. _That worked better than expected._
As he was such an excellent kisser, she didn't mind returning his caresses. It was a lovely diversion. It was some time before they separated, breathing heavily.
Ôdaiòn removed the cloth and smiled, fascination and desire in his eyes. "I think the wedding to Ávoleï can wait." He stroked the älf-woman's lips with his thumb. "Or be called off entirely. She doesn't like me anyway."
"And a wedding would make my uncle even more furious. Fantastic!" Irïanora kissed his finger. "He hates the monarchess. But that's nothing new."
Ôdaiòn laughed. "No, that's nothing new. Because of their past in Tark Draan. And because she allegedly stole his residents from Dâkiòn."
_What do you mean allegedly?_ Irïanora had to bite her tongue to stop herself responding with anything that would startle her fish. Her hatred for the Magnificent had to remain hidden for her plans to flourish. She smiled at him instead. "That old fool."
Ôdaiòn threw himself down onto the cushions as the carriage raced along. He gazed at her face for a long time, looking pensive. "It's not a good idea to develop feelings for someone," he said in a measured voice.
"Because you can be disappointed," she took up where he left off.
"Because you become vulnerable," he added and cocked his head.
"So what shall we do?" Irïanora's chest rose and sank. "Do we reject our feelings and deny love?" _Was that too much?_
The brown-haired älf looked taken aback. " _Love?_ A word for poets. Right now, we feel attracted to one another." He took both of her hands in his and covered them with tender kisses. "We will spend plenty of time together to find out what else we have in common. We come from different cultures, although we belong to the same tribe."
Irïanora nodded. _You are going to fall under my spell even more._ _I'll make sure of it._
She saw through his performance very easily because she was better at it. She had learnt Ôdaiòn was well-known as an älf who had numerous affairs—for one thing, he was outwardly handsome and for another, he had an inherent status that made him attractive. He was the future ruler of Elhàtor and her female rivals would be taking up their positions to push her out, the pretty hostage from Dâkiòn. Or take her out.
"It's up to you. But since I'm assuming I won't leave the island again, may I move around a bit more freely?" Irïanora treated him to another smile full of promise. "I'm so keen to see the beauty of my new home with my own eyes and not just in sketches."
Ôdaiòn winked at her and pulled back the carriage's curtains.
Sunlight flooded the coach and blossoming trees stretched out all around them. They were driving down a road along the coast.
"Welcome to your first little tour. You'll see our humble woods, fields and vine-covered slopes." The älf gave instructions to the coach-driver, then pulled out a drawer underneath the bench. Inside were two glasses and a sealed earthenware jug.
"You guessed I would stay after all?" Irïanora was looking at the drink.
"Oh, it was intended for consoling your friend on the pain of being separated. But it's more suitable for this fortunate turn of events." He opened the jug and poured the fizzy liquid into the receptacles, holding one out to Irïanora. "As soon as night falls, we'll go back into town." He clinked glasses with her. "Ask me anything you'd like to know. You deserve at least _some_ answers."
Irïanora gave him a kiss before she drank. It tasted sweet, prickling on her tongue and going straight to her head. "What's this called?"
"It's a mixture of fermented apple juice and new wine. Refreshing and it livens the spirits." Ôdaiòn looked contentedly out the window and pushed the pane down so that the wind rushed in. "Isn't it splendid on Elhàtor?"
"Indeed." Irïanora took another sip. _How soon will I be able to change that?_
She was pleased that this was going better than her initial plan.
The chances of war with the hated sea-town had rarely looked so good. Saitôra was carrying the letters with the fiery remarks and would willingly spread news of the murders of Gathalor and Iophâlor far and wide. She had seen the sustained outrage in her friend's eyes. That, combined with Anûras' activities, would provide the sparks to unleash the blaze.
_Gathalor, my uncle's darling, slain like vermin._ The älf-woman smiled. _The fire of war will break out and be constantly stoked. And I'll make my contribution on this awful island._
Ôdaiòn looked at her and wrongly believed her good mood was down to him. "You are wonderful!" He leaned forwards and gave her a long, tender kiss.
Irïanora returned the caress. _That will not protect you from endingness._
Ishím Voróo, Älfar town of Dsôn Dâkiòn, 5452nd division of unendingness (6491st solar cycle), summer
The place where the sovereign received them looked to Aiphatòn more like a courtroom than a stately residence, as would have been fitting for the son of the Inextinguishables. What's more, the _Hall of Entreaties_ , as Vailóras announced it was called, didn't sound quite as hospitable as the barman's behaviour had led him to believe it would be.
_It's like they want to condemn us._ The inscriptions on the battlements had already made him wary. The balcony-like platform with the desk on it, where those seated looked down from above, reinforced the impression that justice was administered in this immense vaulted hall, and no heartwarming balls or glamorous banquets took place here.
During their swift ride over the bridge and through the streets, the dimensions of the town had looked different. Giants had clearly founded it before being chased away. But he did like the way the älfar had taken the long, enormous buildings made of black basalt blocks and made them their own. _So different from home._ The Majestic was appropriately named and the nobility of this town and people were obvious in the hall too.
Nodûcor stood diagonally behind him. Vailóras and half a dozen warriors in a semi-circle guarded them.
Aiphatòn waited patiently and listened to his own body. Another thing—apart from the nature of the town—had struck him and it only seemed to affect him. His whole body was prickling so much that it was almost painful. He rubbed his arms several times, but it didn't help at all.
The runes on the alloy plates and the spear flashed from time to time without him ordering them to. Either there was a magical field under Dâkiòn or it was linked to the stones. The runes appeared to be invisible whenever he was particularly near the blocks of stone or where they closely surrounded him.
_It's no surprise they have cîani in their ranks._ He was sure that their spells would cause difficulties even for him. In northern Ishím Voróo, many things were very different but an älf was still an älf and still evil. _This town will fall._
A side door eight paces high swung open, the wood creaking.
To Aiphatòn, Shôtoràs was simply a limping, broadly built älf using his right hand to lean on a tionium stick with a skeletonised crow's head on it; its tiny inlaid tiles of bone had been damaged and not yet repaired. His black robe had runes and decorations on it that had long since been forgotten in the älfar realms of Girdlegard.
He was followed by a heavily armed warrior with two swords on his weapons belt as well as a young, red-haired älf-woman who was wearing nothing but tight-fitting shorts and a skimpy top; her nail-like daggers were mounted on tionium forearm guards. Intertwining tattoos of runes shimmered all over her skin, mainly done in black and grey. Glittering precious stones had been affixed to her skin in a number of places.
Bringing up the rear was an elderly älf who favoured a pale purple robe and wore a thick curb chain made of silver, bones and diamonds. His head was covered by a helmet-like cap of white leather.
_Clearly a welcoming party._ "I would have expected a little more pomp and ceremony when the son of Nagsor and Nagsar Inàste is standing in front of you," said Aiphatòn boldly. "You're not even having musicians and singers put in an appearance to praise my name?"
The pale-grey-haired Shôtoràs dropped into the armchair behind the desk and placed his stick on top of it, while his companions spread out onto the chairs around him. Their heads and hands could just about be made out from below. None of their expressions were friendly and in the redhead's gaze he could read the thrill of the chase.
"I take it you're disappointed, from your accusatory greeting," replied the sovereign haughtily.
"He's a pure shintoìt," the älf in the robe remarked offhandedly. "The eyes aren't just dyed."
" _Dyed?_ " Aiphatòn banged the end of his spear once to give weight to his feigned outrage. The inlaid symbols flashed of their own accord, but it suited his gesture. "You're acting as though the closest descendant of the Inextinguishables stood before you at sunrise every day."
Apart from the sovereign, the älfar from Dâkiòn all broke into loud laughter.
"No. There haven't been all that many times," Shôtoràs announced, smoothing his thin grey goatee. "It's possible, of course, that the Inextinguishables have produced more than one like you. They've had time enough. In their lovely Dsôn-whatever."
"They passed away. A long time ago," Aiphatòn informed them.
"We're delighted to hear that again from an authoritative source. I certainly do not extend my sympathies to you. We've already celebrated the happy occasion," sneered the elderly älf, looking contemptuously at him. "What do you want? To fall back on your heritage and demand control of the town with a straight face?"
Vailóras and his troops laughed quietly, and the redhead grinned.
_That's exactly what I would have done. But I can discard that plan._ Aiphatòn thought it smarter to be less arrogant in his choice of words from now on. But he noticed the älf in the robe looking over at Nodûcor from time to time and trying to conceal his curiosity. _That is more than interest. That is badly disguised knowledge. Is he a cîanoi?_ "I thought I would at least have accommodation and a seat of honour bestowed on me."
"Why so?" snarled Shôtoràs.
"You used to bow your head to the Inextinguishable siblings and follow their orders. I am their offspring..." he began.
"As far as I'm concerned, you might as well be Inàste's son. Or Samusin's. Or Tion's," the powerful sovereign interrupted him harshly and tossed his silvery fair hair back. "They would _all_ have been more welcome than you, Aiphatòn, son of cowards." Shôtoràs propped his muscular forearms on the desk and leaned forwards. "Your parents fled to endingness _the_ splinter their people needed them most. They abandoned the survivors while they set off into the lovely new world to build a new Dsôn. They forgot us."
Aiphatòn was silent. He had not expected hatred towards the Inextinguishables. More like a cooling off of veneration **—** or yes, their longed-for return. But a complete rejection—never.
Shôtoràs snorted disdainfully. "Do you know what we would do to them if they stood outside our gates?"
"I'm guessing not invite them inside, if I've understood correctly."
"Rain missiles down on them," the armoured warrior replied firmly.
"Burn them to ashes with magic," the robe-wearer added in a low voice, still easily heard due to the way the hall was built.
"So that Samusin blows them away and rids us of them," the redhead finished smugly.
_That was unequivocal._ Aiphatòn waited in silence.
Shôtoràs sat up straight. "In departing for Tark Draan, they became traitors in our eyes. Traitors to those who remained loyal to them." He pointed to himself. "I grew up in Dsôn Faïmon, I fought many battles for them—and _that_ was how they repaid me? They turned their backs and didn't care. No news, no messenger reached us." He banged the stick against the surface of the desk. "For those of us in Dâkiòn, they passed into endingness as soon as they marched through the Grey Mountains. They snuck away, secretly. Just like cowards do, instead of bracing themselves for their fate."
Aiphatòn took a breath. _What do I do now?_ He hadn't formulated a new plan yet, much less could he predict what was going to happen in the hall next.
"You're at a loss now." Shôtoràs spun the stick, the metal bird of prey's head twirling around. "You thought we would wrap you up in golden robes or carry you through our town on a sedan and that we'd be under your command from then on."
His companions and the guards laughed again.
"Why did _you_ leave Tark Draan?" the redhead asked sharply. "Was it cowardice once your parents were no longer alive? Are you looking for a place to hide away, little shintoìt?"
The älf in the heavy armour bent down to Shôtoràs and whispered something to him, upon which the old älf spread his arms; his expression was both pleased and surprised.
"Oh, Tanôtai does you an injustice! You were a ruler _yourself_! That Tark Draan scum that turned up here about twenty divisions ago mentioned your name. My friend has reminded me of it: _Aiphatòn_ , the powerful _emperor_ of the älfar of _Tark Draan_!" After a dramatic pause he burst into peals of laughter and everyone joined in.
"If that's the case, powerful emperor, did _your_ kingdom fall?" Tanôtai said with feigned sympathy amid their amusement. "Did you want to talk us into moving to the Stone Gateway with you and wiping out the wicked dwarves and the terrible barbarians and the demonic elves?"
"I'm sure you would stab them to death with your sharp tongue." Aiphatòn gave a small bow. "I left Tark Draan because the era of the älfar was coming to an end there and..."
Shôtoràs leaned back in the armchair. "Just like his parents," he told his companions, turning his head right and left. "His kingdom is falling and instead of going down fighting with it, he flees and wants to get into the ready-built house." He fixed his eyes on Aiphatòn.
It was on the tip of Aiphatòn's tongue to say that the sovereign had come into a ready-built house himself, but instead he said nothing.
"You will get _nothing_ here, neither sympathy nor control over the town. We've learnt from the past. No matter who wants to conquer Tark Draan, we would not lift a finger. Not even to exterminate elves. Those are all absurd reasons for a war." Shôtoràs lifted the stick and traced a kind of circular shape with it. "We're doing fine here. You might find an audience and refuge more easily in Elhàtor."
_They have changed. Completely. Not a hint of desire to conquer._ Aiphatòn could tell that every word the sovereign spoke was true. Judging by his mentality, he suspected Shôtoràs had belonged to the Constellations—the älfar who were against the conquest and ultra-expansion of realms. Still—Aiphatòn had taken a vow of destruction.
Shôtoràs gestured out the window. "Follow the Tronjor downstream as far as the strait. There are scouts there who will no doubt take you to their monarchess. She will be glad to see you. Trash mixing with other trash." Shôtoràs' gaze grew hard. "Dâkiòn dismisses you, Aiphatòn."
"He still owes us the levy," Vailóras interjected from the back.
"I am exempting him and his companion from it." The sovereign got up with a suppressed gasp and leaned on his stick. "Now throw them out!"
Aiphatòn's thoughts were racing. He was thinking above all about the botoicans and the advancing army who wanted to seize Dâkiòn before he could stir up enough unrest in Elhàtor and unleash a war against the sovereign. _I cannot allow them to be conscripted._ "One thing," he raised his voice. "What are you doing about the botoicans?"
"Why would I do anything about them?" Shôtoràs was climbing down from the platform step by step and his companions were getting to their feet.
"Because there are troops on their way to Dâkiòn. Their commander told me he wanted to capture the town." Aiphatòn was watching the älf with the white leather cap and the pale purple robe who could no longer take his eyes off Nodûcor. He whispered to the scantily clad älf-woman then beckoned the warrior over. _Either Nodûcor is from here and lied to me or they know more than they will ever let on._
Caution told him they needed to make themselves scarce extremely soon.
Apparently an älf-woman from Girdlegard ruled Elhàtor. _I'll be able to incite her to war more easily._ "But if you insist we go, we'll look for an audience and safe refuge somewhere else."
Shôtoràs froze on the steps. "What is the commander's name?"
"He spoke to me through one of his men. I don't know it," replied the shintoìt.
Nodûcor touched Aiphatòn's sleeve and drew him letters in the air that everyone could see.
"Nhatai?" the älf in the pale purple robe blurted out, aghast, and placed one hand on his thick chain as if he could to use it to keep himself on his feet. "Was his name really _Nhatai_?"
"We saw two armies tearing each other to shreds, commanded by botoicans. Then one marched on further northwest and attacked a village," Aiphatòn reported succinctly. "And if memory serves, their commander swore to enslave every älf he could get his hands on as soon as he had overpowered his enemies."
Shôtoràs and his companions were exchanging glances now.
"The botoicans are overestimating themselves as always. The Nhatais are considered to have been exterminated, having perished in family feuds and internal conflicts. And I'm even more surprised that your friend claims to have heard that name, emperor." The sovereign limped on, reaching the floor of the hall and then making for the exit. "We will defeat them just like we've done before."
_There it is, that old arrogance of my race. If they hadn't been_ _botoicans, I wouldn't have warned them._ "There are a hundred thousand of them," Aiphatòn pointed out, "or maybe even more. There are even some of our tribe serving in their ranks."
"You're mistaken," the älf in the robe said in disbelief and walked down the stairs. Behind him came the redhead and the warrior who were laughing quietly and uncomprehendingly. "They can't break our will. Our magic will protect us."
"I killed an älf who asked me to kill him, just so that he could escape the enslavement of the Nhatais," Aiphatòn protested. "How could I be mistaken?" _Is he a cîanoi or even their commander-in-chief?_ On closer inspection, he noticed that most of the runes on the chain resembled the ones on Nodûcor's half-mask. _Did he order the abduction or is that a coincidence?_
Shôtoràs stopped again, his hand resting on the door handle. "We will check. And if what you say is true, I'm not afraid. We're protected by the precipices, our catapults are loaded and our cîani are extremely well prepared."
"Darkness and fear won't stop them." Aiphatòn was angry that he needed to warn Shôtoràs, whom he thought a miserable end would serve right—if the älfar weren't to become a danger to others. _It's one of Samusin's cruel tricks that Inàste's children lost interest in subjugating other tribes and precisely because of that, they represent a danger to them._
The sovereign pushed the door handle down. "Lethòras, show him why we're not scared. Then throw them out at long last." Shôtoràs left the Hall of Entreaties.
"Look at this." The älf in the robe was standing next to the stairs. He did two brisk moves and uttered two syllables, then a flash of lightning shot out of the palm of his hand and sped towards Aiphatòn.
The intended display of superior magical power happened too quickly for Aiphatòn to be able to call out a warning to the cîanoi. The spell had barely started to fly towards him when his alloy responded with a counter-discharge, redirecting the energy back at the sorcerer with greater force. The dazzling white lightning turned green in the air.
Lethòras was struck by the beam. A frantically invoked defensive charm did glow around the cîanoi, but the spell was not strong enough to stop the impact.
He uttered a terrible scream and was hurled against the wall as if a troll had thrown him. Blood sprayed on the stonework around his head like a halo. He stretched his arms and legs out, then fell on the stairs and lay still. Strands of hair, pieces of bone and brain matter clung to the brickwork.
The armoured warrior stooped down and tended to the cîanoi while the tattooed redhead stared at Aiphatòn in horror.
_I won't be able to ask him about Nodûcor's abduction anymore._ "We're going," Aiphatòn whispered to the ashen älf and dragged him away. "They don't want us here anyway."
The guards and Vailóras shrank back from them; the terrifying impression they had made clearly ran deep. It appeared Dâkiòn's magic had met its match.
Only once Aiphatòn and Nodûcor were back outside on the street did a loud cry go up from the hall.
The warriors came running after them. "Halt!" Vailóras ordered the pair.
"There was nothing I could do," Aiphatòn shot back and didn't even consider obeying his order. "That's what will happen to anyone who attacks me using magic."
"That's not what this is about. Pasôlor wants to speak to you," cried Vailóras and stopped. "It's possible the sovereign is wrong and you could actually enrich Dâkiòn."
"Enrich it? He probably just wants to enrich himself off me." _First they throw us out, then they want us to stay._ Aiphatòn shook his head, jogging towards the first bridge with Nodûcor. He wanted to take a look at Elhàtor first. _I know what they're worried about. Having seen my power, suddenly they're afraid we could be of use to the other town._ "We are not wanted here and we ourselves no longer want to seek refuge," he replied. "These two things complement each other very well in my opinion. Farewell! And I'll definitely pay next time."
They ran through Dâkiòn under cover of darkness, taking the broad main road that ran in a straight line eastwards to one of the bridges and out of the town.
Again there was no opportunity to study the artworks, statues and ornaments in detail as they rushed past. Aiphatòn felt smaller than a child, surrounded by the gigantic, imposing houses. The unpleasant prickling was getting worse. _Maybe my alloy reacted more violently than usual because of it?_
There came the sound of hoofbeats, pursuing them and catching up.
Vailóras and his troops had set off on their night-mares and now they continued to escort them but didn't pester them.
"Come on, wait! Pasôlor is one of the sovereign's most trusted advisors. He is very keen that you stay at least till morning so that he can work on Shôtoràs," the dark blonde älf tried to persuade them, his white tunic shining in the starlight. "He thinks you're an asset."
"Oh, I would have been. But I'm taking the sovereign up on his recommendation and I'm going to pay a visit to Elhàtor. If I don't like it there, I'll come back." Aiphatòn suspected they hadn't been surrounded only because reinforcements were massing in great secrecy. _A hundred of them will probably be waiting at the gate._
They were racing across the large, bright golden bridge over the wide ravine between the two parts of the town.
Aiphatòn's gaze fell on the sides that fell sharply away. Climbing down would take too long. He gripped his spear more tightly. _It ought to work with this._
Vailóras urged his night-mare on; snorting, the creature's muzzle and sharp teeth came closer. "I'll say it one last time: stay tonight, shintoìt." His warriors were loading arrows on the strings in their horn bows. "Or never see another."
Without warning, Aiphatòn grabbed Nodûcor around the waist and leaped onto the railing of the bridge, fired himself off it and flung the spear diagonally downwards as he did so.
The runes lit up and the tip bored into the stone.
Still holding onto Nodûcor, the älf landed on a narrow ledge on the slope and immediately continued sliding further into the abyss, straight towards the shaft of the weapon that was jutting out.
The landing was successful—but their escape didn't end there.
Aiphatòn used the spear as a springboard so that he and Nodûcor were carried into the air, then he summoned the spear which came away from the slope and whirred into his hand.
He hurled it into the wall below him as they started to fall downwards and landed on it again. In this way they swiftly reached the floor of the ravine while the shimmering gold bridge above them meant they were not easy targets for the archers. _I could hardly have wished for a better shield_.
"To the wall," Aiphatòn commanded and let go of Nodûcor who immediately broke into a run beside him.
It was a few hundred paces from the ravine to the bulwark. The long allures weren't manned because there was no imminent attack. The lamplight in the watchtowers a long way off was the only sign of guards, who were passing the time reading, playing cards and observing the plain in front of the town.
Nobody was looking inwards. This made it easy for the escapees to scale the nearest narrow staircase and stare down onto the next steep precipice from the battlements.
Approximately a hundred paces below them was solid ground and the river shining like a silver ribbon in the moon's glow.
Aiphatòn was panting. The magical exertion was slowly exhausting him; he barely had any strength left. He looked at the armoured glove he was using to lean against a battlement. The runes flickered of their own accord again. _Was my hunch wrong? Are the black stones leaching energy from me?_ He pointed to the Tronjor. "That's where we need to get to."
Nodûcor nodded and looked doubtfully into the chasm.
A metallic, glassy sound rang out on the allure, then a faint breeze sprang up and it smelled of red-hot iron.
They turned around and were staring at Tanôtai, the scantily clad red-haired älf-woman with the tattoos.
Her runes shimmered and pulsed, the jewels on her skin sparkling mysteriously. "My master said that your friend with the glass hair has to stay." She was holding her needle-thin daggers in her fists.
_How did she get to us so quickly? A spell?_ Aiphatòn stood in front of Nodûcor to protect him. "Your master is dead. Save yourself from the same fate." He pointed the tip of his spear at her. "Magic is no use against me."
Tanôtai copied his threatening movement with the dagger in her left hand. "So I've seen. It will be enough if my weapon is magic." The älf-woman lowered her head slightly and blinding white flames encircled her round blade. "Let me see how they fight in Tark Draan, little emperor."
Aiphatòn went on the attack immediately—and swung his spear through nothing but air.
Tanôtai had anticipated his attack and shot upwards right in front of him, wrapping herself around him like a seductive dancer and swinging behind him underneath his arm. The magic she was radiating made the prickling inside him worse; her skin felt red-hot.
Aiphatòn whirled around, lashing out.
But again she was no longer there. His blade sliced through the air with a whistle and Nodûcor leaped back a pace.
"I," the älf-woman whispered in his right ear, "am Tanôtai, the death-dancer. Nobody has beaten me before, and you will be no exception." She laughed mockingly.
Aiphatòn tried to hit her with his elbow, but this attack sliced through empty space too. _I'm quicker than any warrior. How is she pulling this off?_ He assumed that the runes drawn on her skin wove a permanent spell around her that made her supernaturally quick.
The red-haired älf-woman appeared in front of him and stabbed at him with the glowing dagger. "Here I am, emperor!"
He deflected the glowing tip more out of reflex than in a well-thought-out parry.
"I have another one for you, little emperor," whispered Tanôtai.
Aiphatòn couldn't hold off the second dazzlingly bright blade anymore: it struck one of his plates directly, and orange sparks sprayed up like a volcano exploding in his chest.
The eruption of energies hurled a blinded Aiphatòn through the air.
When he did not hit the flagstones of the allure or the rock face within the next four heartbeats, he knew: _I'm falling down the cliff-face!_
# Chapter X
_Bear in mind that decisions always entail consequences. Including unintentional ones._
Wise saying of the Älfar
Collected by Carmondai, master of word and image
Tark Draan, Human kingdom of Idoslane, 5452nd division of unendingness (6491st solar cycle), autumn
Intrigued, Carmondai watched as the älf blood—fresh and fluid—ran down the walls of the glass bottle as soon as he shook it. _That must be the silvery substance that had been added. It stops it coagulating._
He was sitting at the rough table in the kitchen of a deserted farmstead, whose owners had either wanted to start again somewhere new or had been among the triplets' unfortunate victims.
The zhadár stoked the fire in the man-high, dwarf-wide hearth, throwing another four logs on top. "I need a really high temperature," he explained.
During a quick search, Carmondai had found clothes that fitted him better than the much-too-tight and by now filthy garments he had been wearing. At this stage he looked more like an älfar farmer than an artist, but his circumstances didn't allow for such sensitivities.
He felt childish to have been so delighted to find the piece of ash soap among the washing utensils. It might not have been as good as a bath in a tub but his next wash would be more thorough than ever.
Due to the wrath of the people, they avoided staying the night in villages and towns. It was impossible to predict whether the inhabitants would suddenly be overcome with anger and daring in equal measure. Carâhnios didn't want to deploy his powers and those of the älf against the innocent.
Carmondai put down the bottle, reached for his quill, dipped it into the ink pot and recorded his thoughts on the waiting paper. _An Ode to the Soap. Oh what times, oh what customs._
Carâhnios got up and came over to the table where Carmondai was sitting. He had spread out various jars, vials and caskets over the stained wooden tabletop. "I stole them from their laboratory. In Bhará." He sat down and giggled as he opened each in turn. "I secretly watched Sisaroth so many times."
"Did you _see_ the right thing then?"
"You think I can't prepare the remedy?" Carâhnios tapped the small lid of one mother-of-pearl casket against the bottle and it made a low clinking sound. "I'll admit I don't have any experience with _älf blood_ because Sisaroth distilled it from the blood of elves. I am my own test subject as it were." He looked at the various receptacles, strange smells and aromas streaming out of them from time to time. Here and there, thin wreathes of smoke curled upwards. "Good. It's all here."
"And what are these ingredients?" Carmondai was drawing a quick sketch of the kitchen on the piece of paper beside him. The nib scratched softly across the paper, accompanying the crackling of the burning wood. "Can you tell me their names?"
To his astonishment, Carâhnios shrugged his shoulders. "I never found out. Sisaroth had a vast supply of ingredients for his drinks and demonic elixirs. I'm pleased I discovered _which_ ones he was even using."
"Aha. Well, that's brave. Daring." _Not to mention thoughtless. It's just like you._ Carmondai swept the quill along his chin. "What are you going to do if you run out of these ingredients? How are you going to know what you're missing and how to source more of it?"
"I'll think of something. And anyway, I've stockpiled a small supply. Since there are no zhadár left apart from me, it will last for a while." He checked on the fireplace where the fire was still blazing high and sending the flames shooting up the chimney. "It will take a while before the heat is right for distilling, but I can get to work on the mixing now."
Carmondai was in awe of the nonchalance with which the zhadár fished spatulas and little spoons with different markings out of a pouch and placed them in front of the receptacles, then fitted together the component parts of a pocket-sized set of healer's scales. "This is not the first time you've done this."
"No. I've gone over the sequence many times, but today there will be a yield at the end of it for the first time." Carâhnios balanced the scale pans, nodded and measured out the ingredients precisely, using a different spoon for each one. "Some of the ingredients react if you combine them in their dry state or even if the tiniest pinch is mixed with something. Then the distillate would be ruined."
One substance after another passed through the neck of the bottle and into the dark, almost black, blood, its surface a shimmering silver.
_A novelty, even for me._ Occasionally, Carmondai saw a glow when the zhadár added a new ingredient and carefully tilted the container to mix them; St. Elmo's fire swirled over the surface.
Outside, the first severe storm of the autumn howled across Idoslane, testing the resistance of the stalks in the last unharvested fields. Strong winds shook the farmstead, making the beams groan. The flames in the chimney even dropped occasionally, but the gusts of wind could not extinguish the fire.
Carâhnios closed the jars, vials and caskets, dismantled the scales and meticulously tidied everything up. "This will go into the fire very soon." He put a glass stopper fitted with coils into the mouth of the bottle. On the end of this, he put a tapering porcelain tube that had a sharp bend to the right and ended in a thin outlet that could be opened with an adjustable screw.
Carmondai pointed at it with the quill. "How much yield will there be?"
The zhadár again had to admit he did not know. "If we could get one small dishful out of approximately four units, I would be happy. It would be enough for me for one cycle." He took the prepared bottle along with its contents and set it down ready next to the hearth.
Carmondai alternately wrote and drew like a man possessed, so as not to miss anything and to capture the atmosphere in the kitchen as accurately as possible. _Never has anything more unusual been prepared here._
As he drew, his thoughts wandered to Ostòras' hillside hideaway in the purpose-built ruins.
Disappointingly, it had been empty and there were no indications of any other inhabitants. Their enemy didn't seem to have been living there long. There were just a few barrels and jars of supplies, bandages along with weapons and a small forge for repairing armour and swords.
Carâhnios looked very unhappy about it too. He had been expecting more älfar.
_And more blood._ Carmondai believed Ostòras when he'd said the remaining älfar would hide away and sow terror in Girdlegard through ambushes.
The zhadár never dreamt of informing Girdlegard, or at least the monarchs and monarchesses, about the threat because he felt it would lead to uncertainty—and hence the älfar would have achieved their goal before the first death.
Carmondai saw it differently, but it might as well have been all the same to him. He was a prisoner only pretending to be docile.
Carâhnios smashed the last charred piece of wood with the poker and it fell apart, glowing and emitting sparks. He put the bottle on the pulsing, dark red embers and crouched down. With his forearms resting on his knees, he watched eagerly.
Carmondai got up and joined him in watching the process that would produce a remedy from the blood of an älf and other ingredients—a remedy containing and conferring incredible powers.
He suppressed his fear that a small disaster might take place, like an explosion or a deflagration that would badly injure the älf and groundling or even cost them their lives. _That would be a belated satisfaction for Ostòras._
At first, nothing happened apart from the St. Elmo's fire, its greenish-blue flames turning dark blue and flitting here and there as if delighted by the heat.
_Or it's trying to escape it._ Carmondai sat on the uneven stone floor and started drawing again in order to capture the different phases.
"It's still all right," murmured Carâhnios, fascinated. "If I say: _run_ , black-eye, you're going to run."
_Just as I thought._ The älf stayed bravely where he was.
Above the surface, a thin, greenish smoke formed that was iridescent in the glow of the embers, occasionally looking gold.
And from one heartbeat to the next, the blood started simmering and foaming black. The stopper may have stayed firmly inside the glass rim, but the aggressive hissing was unmistakeable, as if the elixir was trying to corrode its way out of its transparent prison and descend on them.
But since Carâhnios didn't move, Carmondai stayed calm and kept drawing.
The smoked turned white and climbed up into the glass coil where it condensed in the lower part as caramel-coloured drops.
The fine webs that made it as far as the bend looked more like a pale black. Just before it percolated into the little porcelain tube, it took on a light, cloudy colour that Carmondai had never seen before in his whole life. _How am I meant to describe that?_
The simmering and boiling continued, the foam climbed higher and blocked their view.
Carmondai noticed the pungent smell. The glass stopper was leaking somewhere. The next time he drew breath, he had an attack of dizziness so he crawled two paces away from the bottle.
"That," remarked Carâhnios, coughing, "is not good." He reached out his gloved right hand to check the fit of the stopper.
When he increased the pressure on the neck of the bottle, the bottom of it shattered. The viscous contents poured all over the bed of glowing coals and the hissing got louder.
Carâhnios removed the little porcelain tube with apparent calm, then turned to Carmondai. "Run," he said and dashed out of the room. As he rushed past, he grabbed the bag of ingredients.
Cursing, the älf snatched up his pages, got to his feet and staggered out of the kitchen. The fireplace was getting dazzlingly bright, as though the sun and moon had been able to unite for the first time. As a precaution, he pressed himself against the wall in the adjoining room, hoping the brickwork was thick and would protect him.
There was no bang, no explosion to make the farmstead collapse. Not _one_ spectacular sound and yet the light continued to radiate.
Carmondai tried to make out what was going on in the kitchen, but he couldn't look into the light. It was terribly painful to his eyes.
The wall where he had crouched down for protection from the expected blaze was heating up more and more quickly. The alchemical reaction that the zhadár had unleashed was still happening.
Carâhnios was kneeling on the floor a few paces away, pouring the contents of the little tube into a second vial. "Better than nothing. It got me a few precious drops," he announced. "Let's get out of here. Our enemies are waiting for us at the next hideaway."
"What happened?" Carmondai still had the pungent smell in his nose.
The groundling grinned and jumped up. He slipped his cloak on over his black leather armour. "No idea. But I think we're lucky it didn't kill us."
They ran out to the stables where the pony and the horse were tethered and waiting for them. The restless animals were quickly saddled and the journey continued in spite of the howling winds and impending thunderstorm.
One look back at the farmstead told Carmondai that this had been a good idea: behind the window panes there was a dazzlingly white glow and flames were pouring out of the windows and already spreading to the rest of the building.
_What weapon has he concocted?_ Carmondai thought he was seeing things, but in that moment he could have sworn that even the stone building blocks were on fire. _Ostòras would be delighted._ Even after death, an älf remained bent on destruction.
Ishím Voróo, 5452nd division of unendingness (6491st solar cycle), summer
Aiphatòn was woken by the gentle, steady rise and fall of the surface he was lying on.
It evoked memories of a very special encounter.
He opened his eyes and found himself back on the deck of a ship. The stars sparkled in the night sky above and the air was cool and pleasant.
He turned carefully and got his bearings. The sails on the large mast had filled out and they were moving quickly over the waves; from time to time sea spray spattered on the bow but it didn't reach him.
On top of a knee-high rope pulley, he spotted a squat figure sucking on a pipe. Grey smoke drifted across the otherwise deserted deck like mist. "Ah, my friend has woken up," he heard the friendly, deep voice of a dwarf.
Aiphatòn hauled himself to his feet and peered over the side of the ship, looking out for land but not finding it anywhere. "Where am I?"
The dwarf, whose face lay in the shadow of the mast, puffed several times in a row. "My home," came the amused answer.
"How did I end up on the ship?" He looked at his arms, his stomach and legs, and they seemed unscathed. "I was falling down the cliff-face and... am I dead?" He knew humans who believed that their souls would be brought to the kingdom of the dead by a ferryman. _Could they be right?_
The dwarf laughed and leaned forwards so that starlight fell on his features. He wore his brown beard cropped very short and there was a mischievous twinkle in his eye. A gold mark glittered on the hand that held his pipe. "Then I would be too," he retorted and laughed softly. "Which I would find very inconvenient, I must admit." He placed his other fingers on the handle of his axe whose blade was made of diamonds on one side and long, stone spikes on the other. "I've got a few more things planned."
Aiphatòn's eyes widened. "Tungdil?" He walked over to his friend. By now he had recognised the ship whose planks he was standing on: he was aboard the same boat he'd met the dwarf on long ago in order to find out more about himself and the Inextinguishables. "Are we travelling across Weyurn's lakes?"
"So you might think, yes." Tungdil sucked on the pipe again. "Or we are figments of our imagination because I'm actually somewhere else." He looked around. "What can it mean?"
Aiphatòn lifted his shoulders slowly. "Did the gods send us back in time so that we could decide things differently from how we once decided them?"
Tungdil puffed away at his pipe and pointed at him with the mouthpiece in agreement. "Oh now _that_ would be fun all right!"
"It truly would be. I would not bring the älfar to Girdlegard," he said bitterly. "I would go back to the Blue Mountains alone and would not waste any time in killing Lot-Ionan. Finally, I would pounce on the Dsôn Aklán and annihilate them."
"Good plan, my friend!" The dwarf smiled at him. "I'd come to your aid and I'd be more on my guard against the triplets."
A large breaker from starboard crashed against the hull and hit them both with a deluge of water.
Aiphatòn was knocked off his feet and slid over the wet planks to the other side. He quickly grabbed at a rope to stop himself plunging into the suddenly rough sea.
"Tungdil!" he cried. "Where are you?"
Another wave came crashing down on top of him, filling his mouth with salty water. His eyes burned and he had to close them.
"Hey!" screamed Tungdil.
He wanted to answer the dwarf, but a burbling sound was all that came out of his mouth.
"Hey!" came the cry again, but the voice had changed, becoming higher and more girlish.
Aiphatòn coughed and opened his eyes—and was looking into the face of an anxious, black-haired älf-woman.
Bewildered, he noticed that drops of water were rolling off his face and that the ground was rising and falling as before. _I'm on a ship and... in the next dream?_ The last thing he could remember was falling over the parapet and tumbling down the rock face in Dâkiòn.
She was looking at him with yellowish-green eyes. "Finally awake?" She straightened up, revealing as she did so her light leather armour with a red symbol and a white shirt underneath. She wore linen trousers and sandals. "Get yourself ready. We're landing soon. And my advice is: have a good story ready for my godmother, or else you'll fall from the cliffs a second time." She stepped back.
She was replaced by a bald älf in a pale robe who held out a mug of foul-smelling liquid to him, which Aiphatòn was presumably meant to drink. His eyes were black, as they were meant to be.
"How long have I been sleeping and how did I get on board? Where are we going?" Even more questions flashed through his mind. "And _who_ are _you_?" He sat up carefully in the swinging hammock and almost fell out. He was not accustomed to lying like this.
"I am Ávoleï, commander of the _Mistress of the Sea_. My godmother is Modôia, the monarchess of Elhàtor, which is where we're going to land within this splinter of unendingness, although the sea is stormy. You seem to be churning up the elements." The älf-woman nodded to the mug. "You're going to drink that. It will give you your strength back. A magical healing was too dangerous. After you nearly barbecued my cîanoi in your sleep, I didn't allow another recovery spell to be applied."
"I'd manage it on a second attempt," the bald älf interjected. "I could feel where the magical abutment started." He gestured towards the plates. "A more than unusual job. Unique."
_He could feel it?_ "My apologies, but it's rarely under my control," Aiphatòn tried to explain.
"We noticed that." She smiled but it didn't look friendly. "As soon as you feel able, come on deck." Ávoleï went to the door. "Oh, and you were asleep for eleven moments so you missed the whole crossing."
_Modôia? Where have I heard that name before?_ Aiphatòn took the potion and knocked it back.
The healer and cîanoi watched him as he did so and took the empty mug back. "The external wounds are mostly healed," he explained and pointed to the bandages on Aiphatòn's thighs. "The broken bones, well, you'll have to see for yourself. It's possible those places have knitted together." He gestured towards Aiphatòn's chest. "A blacksmith will have to repair that, although I wouldn't know how they'd do it."
_My armour!_ He lowered his head.
In the place where the death-dancer's dazzling blade had hit him, a hole the width of a finger gaped in the plate. Underneath he saw pink skin that looked freshly healed.
Aiphatòn placed his hand on it. _She could have killed me,_ he realised to his shock. _The first opponent to have put me in that kind of danger._ If not for the fall from the battlement, he would have died at her hands, as far-fetched as that sounded.
"Do you know what happened?" he asked the healer quietly.
"Ávoleï will explain it to you," the älf replied and got up. "I'm forbidden from exchanging too many words with you because you're a prisoner. But don't worry: Elhàtor will deal with you fairly."
"And will throw me off the cliffs if necessary, I hear." Aiphatòn remained silent and moved his toes cautiously, not feeling any pain in his legs. _I'm afraid I'm going to have to quiz the älf-woman._ Very slowly, he placed one foot after the other on the creaky planks that trembled at intervals with the force of crashing waves. "It seems the potions worked miracles," he announced to the healer and stood up, only to realise that they had undressed him down to his loincloth.
"You have a remarkable constitution." The älf was ready to offer him his hand as a support.
"Where are my spear and robe?"
"You didn't have a weapon on you when you were brought on board. And your... robe was as good as non-existent."
Aiphatòn cursed. "Then Dâkiòn can expect another visit from me," he muttered grimly. _Preferably with an army from Elhàtor. And if I'm already there, I can thank Shôtoràs for his hospitality. In my own way. Which he will not survive._
The healer handed him trousers and a shirt that reached down to the knee and Aiphatòn put them both on. "What is wrong with her eyes?"
"Because they're not black?" The healer grinned. "We use tinctures to preserve the white. It came into fashion to emphasise the beauty of the eyes. But I dare say it wouldn't be any use to you."
_That's deceitful. There would be no better way to pass yourself off as an elf in Girdlegard._ Unsteady on his legs, he walked barefoot across the cabin to the door, went out and climbed the broad staircase whose steps were wet with spray and waves.
Cool, moist wind howled through the hatch and the waves hurled themselves against the deck, crashing dully. Snatches of bellowed orders reached his ears; sails were being reefed.
Aiphatòn stepped into the open air and the wind threatened to knock him over. He was familiar with storms from Girdlegard, he was familiar with seas that you crossed by ship, but a sea in such turmoil was another new experience. He tasted salt on his lips.
Ávoleï was standing tall at the helm and shouting her instructions over the thundering as if she were leading a battle against the elements.
Only one part of the sail was hoisted on the yards; the three main masts looked like dead trees. The wind whistled and screeched in the rigging.
The _Mistress of the Sea_ careened to the side and performed a sharp turn that set them on course for the mouth of the harbour.
Aiphatòn saw four smaller escort ships surging over the crests of the waves to their right and left, racing ahead of them into the calmer dip.
The rain pelted steadily down on the crew. The thick haze from the clouds stopped him getting a good view of the town but the island looked bigger than he had imagined it would be.
_And we thought there were practically no älfar left in the northern wasteland._ Aiphatòn thought about Shôtoràs' remarks. He understood his attitude and his hatred of the Inextinguishables. _They just had no incentive to show off or conquer. Now we want to hear how..._ Suddenly the penny dropped. _Modôia! The monarchess of the town is the älf-woman whose message I found in the deserted settlement and whose runes I destroyed! The sovereign mentioned that she had come from Girdlegard._
Aiphatòn walked across the swaying deck to the stairs to the upper deck where Ávoleï stood. She needed to tell him more before he met her godmother.
The _Mistress of the Sea_ entered the harbour and the rocking instantly eased off. The waves were significantly smaller than on the open sea, crashing against the harbour wall in clouds of spray.
You could feel the crew's tension easing. The almost-hundred-pace long ship seemed sturdy and reliable but a voyage always remained a risk.
Aiphatòn approached the älf-woman who gave some final instructions to the helmsman and then turned to him. "Oh, excellent. So your broken bones have healed nicely?"
"Yes, they have." Aiphatòn held on tight to the railing of the upper deck and noticed how far they were from the ground. _How many storeys has this monstrosity got?_ "Would you please tell me what happened? I can only remember the fall over the battlement."
Ávoleï laughed. "I wasn't there when they picked you up, but the warriors report that at first, they thought Shôtoràs had fired a burning sack of petrol at them that wouldn't fly properly." She examined his body. "A miracle, truly. And of course we're rather used to sorcery in Elhàtor. You must have shot down the rock face glowing like a comet and kissed the stone several times." She reached out a hand and ran it over the scratches on his plates of armour. "Your magic checked your fall, I'd assume. I've been told countless runes on this lit up. You did hit the ground, but you were still alive. The warriors dragged you away before the rockfall that followed. They brought you to the river and so to me. We were just dropping off a hostage from Dâkiòn there in our dinghy and I decided to take you with us." She winked. "Anyone who is thrown out of the town like that can only be a friend of ours."
Aiphatòn had no choice but to believe her explanations as he had no memories. "Then I owe my life to you," he said thoughtfully.
"That you do." Ávoleï seemed pleased by this. "I'll claim my reward at some point." Now, her gaze looked different than before. "And you are a shintoìt, as the cîanoi suspects?"
"Yes." Lying was pointless, his eyes gave him away sooner or later.
"Then you must be Aiphatòn, the emperor of the älfar. My godmother will be pleased to hear your story and why you turned your back on Tark Draan." The statement sounded neutral. "If you've come to seize control..."
"No," he interrupted her immediately. "And that was also not the reason why I was thrown off the walls."
"Shôtoràs doesn't need a reason. You come from Tark Draan and to him you're dirt. That's enough for the old fool." Ávoleï gave some quick orders and the _Mistress of the Sea_ came alongside the harbour wall and dropped anchors at the bow and stern before being tethered. "But did he know who you are?"
Aiphatòn nodded. "Yes."
The älf-woman was watching the ship's landing very carefully, looking visibly pleased with how it was progressing; from time to time she wiped the rainwater out of her eyes. A ramp was placed between dry land and the ship's wall to allow everyone to disembark easily. "Then he must think you're dead."
"My spear will be a memento he won't be enjoying for very long."
"You want to go back?" Ávoleï looked at him in surprise and walked towards the steps to the lower deck. "Come on. They'll have dry clothes for us in the palace. My godmother will be glad to see you."
"I hope so. I can't rely on surviving falls from cliffs forever," he replied and followed her. "My spear is too special and too unique to leave in ignorant hands."
"Believe me: Shôtoràs will find a warrior who knows how to fight using your weapon."
They walked down the ramp side by side and stepped onto the harbour wall which was humming with activity. The crews from the escort ships were unloading cargo. The wall of the _Mistress of the Sea_ soared up imposingly behind them.
"What is this kind of ship called?" He just had to ask.
"It's a rònke, frekorian in origin," explained the commander. "We improved its performance and changed its appearance to suit our tastes better. When it's in formation with the four sailing boats you see over there, it's unbeatable. You don't need to know any more than that."
A carriage rolled up and they got in.
"To come back to our original topic: the spear obeys nobody but me. It's forged from the same alloy as the plates." Aiphatòn sat down and touched the armour.
"And yet I see a hole in it that I presume wasn't there before," Ávoleï countered, no malice in her voice as she took a seat opposite him. She didn't seem concerned that she was wet through to her undergarments. "You're in a part of Ishím Voróo where magic is incredibly strong. Let that be a warning to you. Our cîani are varied and they are blessed with gifts that would make a magus or maga from Tark Draan look like a schoolchild."
Aiphatòn pictured the death-dancer with her glowing needle-dagger blades that had burnt through his armour. Just the thought of it was enough, the prickling spread through him again. "Someone could have told me that earlier," he murmured to himself. He stuck his little finger through the hole and clenched his teeth when his fingertip touched the soft, pink flesh. _It must have been a deep wound._
The carriage started to roll along.
"Let's consider it a merciful act of Samusin that my people were just off Dâkiòn at the instant you literally fell at their feet... or should I say: into their hands," Ávoleï said and threw him a blanket so that he could dry himself off. "Don't worry: you're my guest and because I saved your life, it belongs to me."
"And what does that mean?"
The älf-woman took a second blanket and rubbed her head with it. "It means my godmother can only throw you off the cliff once I've given her my permission." She laughed to show him she'd been joking.
Aiphatòn joined in, dabbing the water off his face as well as his short, black hair which had grown back during the course of his adventure.
He thought the commander was more attractive than any other älf-woman he had met in the past solar cycles and yet she radiated something undefinable that he found confusing.
Ishím Voróo, Älfar town of Dsôn Dâkiòn, 5452nd division of unendingness (6491st solar cycle), summer
Shôtoràs was awoken in the early hours by a servant standing next to his bed and gently shaking his shoulder.
"What's happened?" he asked and was immediately wide awake. Under ordinary circumstances, nobody dared rouse him from his sleep.
"Saitôra is back from Elhàtor," answered the underling and bowed apologetically. "She brings news of your niece."
" _Only_ Saitôra?"
The älf nodded and held out the black housecoat for him which Shôtoràs slipped into as he clumsily got up. "She came alone. The Elhàtorians dropped her off at the strait and our people brought her up the Tronjor."
Shôtoràs reached for his walking stick and had his black leather, embroidered shoes put on his feet before limping out of his chambers in a hurry. He entered the Hall of Entreaties where just a few splinters ago he had received that ridiculous emperor of the curs. He swept his silvery grey hair back but didn't waste time combing it. There were more important things to do.
Saitôra was standing forlornly in the middle of the room as he limped up the steps to the platform and sat down at the desk, beckoning her over impatiently as he did so. She was wearing a blue and silver dress with an Elhàtorian pattern woven into it.
_She should have been allowed to get changed._ "Come closer," he said. "And don't be afraid. I know that Irïanora dispatched you and the other two on a flimsy pretext."
The young älf-woman nodded in relief. "I feel so stupid, sovereign." She took an envelope out of her dress, glanced at it and held it in her right hand.
"And so you should. Letting yourself be exploited by my niece to provoke a war is the most foolish thing I've been forced to witness in recent divisions of unendingness," he replied. "What have you got there? And where are the rest of you river sailors?" He extended his hand.
Saitôra passed the envelope up to him. She had to stand on her tiptoes; her fingers trembled. "Gathalor and Iophâlor are dead. The scouts from Elhàtor killed them after pulling them out of the water unharmed," she told him, her voice cracking. "In front of my eyes, they smashed their skulls to pieces." She swallowed. "Irïanora stayed on the island in exchange for me. Sovereign, I was never in favour of the war, but the way they..."
"Silence," he ordered quietly and icily.
The colour had drained from his face and he only just managed to stop the anger lines. _Gathalor—dead? Inàste, keep my soul from shattering!_
He opened the sealed message that was addressed to him in his niece's hand.
_Dear Uncle,_
I stayed in Elhàtor to allow Saitôra to travel home and so that I could send you these words. This message has been smuggled past the vigilant rulers so that you could learn the truth. Gathalor and Iophâlor are dead, murdered by Modôia's vile scouts.
And my life will end too if an inhabitant of Dâkiòn travels past the strait, downstream to the sea.
In the eyes of the monarchess, I am the supposed guarantor of peace between the towns—but I ask this of you nevertheless: attack! With everything our warriors and our cîani are capable of.
They have built a fleet that they keep hidden in a grotto in the middle of the island. Saitôra has seen it with her own eyes.
Modôia is deceiving you and all inhabitants of Dâkiòn about her true intentions. The pretence of a peaceful co-existence has been exposed. She will attack us!
It can't be much longer now.
I know you never thought my behaviour was good and that you believe enough älfar blood has already been shed. But if you don't spill it, the monarchess will start to, and she will have an answer for everything that you throw at her.
I would gladly give my life for this.
I'm thinking of you and Dâkiòn and extend my condolences to you!
Don't let Gathalor and Iophâlor have died in vain.
_Irïanora_
Shôtoràs ripped up the letter and placed the scraps in a neat pile, Saitôra watching on wide-eyed. _You're the one who has been exposed, niece. Even with this pain that you inflict on me, you're ultimately hurting yourself._
"Don't be fooled by her," he told the young älf-woman. "Irïanora stayed because she was afraid of what I would do to her. I sent her to bring all three of you back home unharmed. I vowed she would receive the severest punishment if anything happened to just one of you." That wasn't completely true but it was enough to make his action look reasonable.
"But the fleet!" Saitôra protested.
"Who said you could read the letter?" he thundered, and she flinched. "Have you seen the fleet?" Shôtoràs knitted his eyebrows. "Did you stand in this grotto my niece has written about and see the countless ships the monarchess wants to use to come here?"
The young älf-woman hesitated.
_Another Irïanora lie_. That was enough of an answer for him. "You can go." The sovereign looked at the scraps of paper. "And remember: the scouts from Elhàtor did not kill Gathalor and Iophâlor, it was Irïanora. She sent you out and made you breach the agreement," he added quietly. "I will adhere to the peace treaty and I will not fall for this trap from my niece and her warmongering friends. _You_ shouldn't either." His piercing stare embarrassed Saitôra. "Go back home and be glad that you were allowed to leave the island, but keep quiet about your adventure. That is an order! Irïanora will be very resourceful. She's cunning." _And if the Elhàtorians kill her, so much the better._
Saitôra bowed and walked away, striding through the doorway and vanishing.
Shôtoràs shook his head slowly. _As if these whiny, heroic words would hold any sway with me._ He would never embark on open warfare.
He looked at the window. The first strong rays of sunshine were falling through it and his eyes were turning black. _I'm not afraid of the scum from Tark Draan._
His thoughts revolved around the countermeasures to be taken if this secret fleet really existed.
Work on the canal was coming along well. By the time winter came, the final touches would be complete and the weirs to dam the Tronjor and allow it to flow the way it needed to would be in place.
The soldiers and barrels of petrol were already making their way to selected sites along the bank so that the flammable liquid could be deployed against the attackers' ships if needed.
_Besides, we also have our cîani. Elhàtor will never reach our walls._ Shôtoràs placed his lame leg on the desk and massaged the thigh. Over the last few moments of unendingness the pain had worsened. For some unknown reason, the nerves were rebelling against every kind of treatment, from compresses to magic.
He thought about the warning from the self-proclaimed emperor about the botoicans' army. _A hundred thousand. That would be vast._
He wanted to dispatch Vailóras and four of his best warriors to scout out whether there was any truth to the unwelcome guest's claim. He wasn't afraid of the disorganised packs and hordes the mind-meddlers' armies went into battle with. _As long as no botoican has had tactical training superior to mine_ , Shôtoràs mused.
The feuds between families and within the inner circles of the magicians were not revealed to any outsiders.
Shôtoràs had heard that over the last few divisions of unendingness there had been unrest in their ranks and that war had been raging for around a hundred moments. But as to who was lining up against whom, he had no idea. They remained a closed unit, split up into families who fought bitterly.
_Destroy us? Ridiculous. The Nhatai family is far too small to achieve that._ His gaze wandered to the large red stain and spatters on the wall next to the stairs—they had really seeped into the plaster due to the effect of the magical discharge. _My best cîanoi, destroyed by his own spell._
Shôtoràs pictured the impact of the reflected spell and the älf's horrified face. The heat surged towards the sovereign, followed by the smell of charred flesh and spilt blood.
In spite of the closed windows and doors, a light breeze blew steadily, carrying the scent of red-hot steel.
He smiled and faced straight ahead again. He saw Tanôtai standing in the Hall of Entreaties, her sinewy hands clasped at her belt, her slender but strong arms hanging down loosely. "Have you found him?"
"Not yet," answered the red-haired death-dancer. "The little emperor has been missing since he fell over the battlements. I think he's under the piles of rock."
Shôtoràs couldn't help grinning because as soon as talk turned to Aiphatòn, everyone referred to him using the most noble title as an insult. "Can you rule out him having used magic to save himself?"
Tanôtai looked hesitant. "We've seen what he's capable of. That explosion when my magic met his was unparalleled."
Shôtoràs remained quiet because he had been expecting the discovery of a body, not this at all. "It would have been good to get hold of him. I would have been so pleased to cut those pieces of metal off his body and have a weapon forged for you out of them."
She smiled gratefully. "You do me too much honour."
Shôtoràs took his leg off the wooden desktop. "It was a mistake to try and chase him," he told her and got up, leaning on his stick. "We should have allayed his suspicions and sent him to Elhàtor. He could have killed the monarchess and her son for us. We would have been free of all suspicion and could have blamed an old feud between them. The filth from Tark Draan would be history." He limped slowly down the steps.
"That would still leave Leïóva and her daughter."
"The elf-woman is still alive only because she is Modôia's confidante. Without her protection, she'd be cast out by the Elhàtorians along with her brat. And then the inhabitants would come to us, to Dâkiòn, looking for help, which I would offer." Shôtoràs placed one hand on her bare shoulder, the tattoos feeling warmer than the untattooed skin. "But I've let this opportunity slip through my fingers. I expect the emperor has saved himself with a spell by now."
Tanôtai pulled a sour face. "I'm having the cliff searched carefully anyway. The men will abseil down and the cîani will go out looking with floating spells. It's possible he's hanging from a ledge that we couldn't see at night. And there's always the mountain of debris."
Shôtoràs squeezed her shoulder gently and then drew his hand back. "Before that happens, go and shadow Saitôra. If she tries to talk to someone about her time on Elhàtor and stir up the inhabitants of my town, silence her."
"Would she do that?" The very slender, red-haired älf-woman did not look convinced.
"When she gave me the message from my useless niece, I saw she was carrying a second envelope, hidden in a fold of her dress. Since she didn't mention it, I'm afraid Irïanora has come up with a plan to set the residents against me and make loud calls for war. I cannot allow that."
"I see. The murder should take place secretly, I take it...?"
"In complete secrecy. Throw the body off the large bridge."
Tanôtai bowed and in the blink of an eye, she had vanished with that quiet sound that the spell made every time. The death-dancer's powers were one-of-a-kind. The breeze she unleashed sprang up suddenly and blew the scraps of paper off the table.
Spinning and whirling, they rained down on the flagstones, some falling with the letters facing up and some face down. They lay at his feet in no discernible pattern. Just two little shreds floated towards the ceiling as if the sunbeam streaming inside was pushing them.
_We've got Nodûcor now, but he's no use to us at all._ Annoyed, he stepped over the scraps and limped out of the room and down the corridor to the kitchen to have his breakfast. _He falls into our laps like this by Samusin's providence, and shortly afterwards the only cîanoi who could have taken that damned half-mask off him dies!_
Shôtoràs passed through his palace without taking any pleasure in the artworks and interior decoration.
When he had heard from a merchant that there were unpredictable winds raging and howling through the mountains all of a sudden and that they seemed to be blowing from every direction at the same time, Shôtoràs had sat up and taken notice. The legends of the wind-voice had always been his favourite stories and suddenly it sounded as if there might be a grain of truth to them.
So he had his best cîanoi build a transportable container that was impossible to escape from, as well as making shackles and a mask to prevent the wind-voice being able to unleash its power.
_The emperor must have freed him_ , he mused.
But since neither Aiphatòn nor Nodûcor knew who was really behind the abduction, they came to Dâkiòn unsuspectingly. To the people who had ordered it.
Shôtoràs walked slowly down the staircase. _I desperately need him. He would be perfect for literally blowing the arrogant botoicans away. And of course the unworthy Elhàtor with its traitors, the scum, the elf-woman and its frekorian mercenary roots._
Surely there was more than one half-breed älf among the residents of the island—the sovereign would have staked his life on it.
_I'm just a lock, a pinch of magic and a little metal away from my greatest victory—and nobody would ever suspect a thing._
Having reached the ground floor, Shôtoràs was following the smell of toast drizzled with melted lard, topped with a thin layer of egg and a scattering of fresh herbs. There was nothing better for his stomach and his mood of a morning.
He _loved_ giving the impression of being the peacekeeper.
Under no circumstances did he want to hand Modôia a reason to steal a march on him with an attack. Although his preparations were going well, he felt uneasy at the same time. A battle could always take a different course from the one the strategists and his dear friend Pasôlor had planned in advance.
_It won't be long until I know more._
Shôtoràs entered the kitchen and was greeted warmly by the servants.
He went over to his seat by the window, through which he had an excellent view over Dâkiòn, and his meal was served. He ate with relish.
On his orders, four cîani were looking into a way of neutralising the protective spells on the half-mask.
_Assuming Cushròk captured the right älf, he will unleash a storm for me, a hurricane even, that will churn up the sea and tear Elhàtor apart._ The sovereign took a bite of the crispy, delicious sandwich as he gazed at the pale roofs of his town. _The waves will rage over the island until nothing is left standing and the rabble have perished. The survivors might find refuge with us but I will be extremely selective._
One of his cooks served him a tea made from fresh mint and herbs, and Shôtoràs nodded pleasantly to him.
Nobody would be able to tell from his demeanour what thoughts and images were currently going through his mind. He had led the life of a cunning politician too long for that.
The wind-voice represented the solution to every problem.
But if Nodûcor was just an älf with no special gift, he would have him killed and send a new battalion out on the hunt. _Until I've got my wind-voice. It's in Ishím Voróo somewhere._
Making Nodûcor compliant was possible, he had no worries on that score.
_Wave after wave will break over them, whether they're on the river or in Elhàtor. Irïanora can drown, as far as I'm concerned. That's her punishment for Gathalor's_ _death by negligence._ Shôtoràs smiled with satisfaction. _Nature can be cruel._
_Especially when someone is commanding it to be._
Saitôra hurried through the ravine-like streets, making her way towards the Death-dancer.
She knew the institute where they taught you how to move to become one of the exceptional warrior-women or warriors.
Her own cautious attempts had not ended in success so she had dropped out before her first magical tattoo was due to be inked. This procedure could be fatal—the energy had to be infused into the poisonous ink very carefully. If the needles pierced too deep, you died an excruciating death.
Saitôra reached the locked door that had been set into the access gate. She was still wearing the dress gifted to her in Elhàtor. She would take it off later; she wanted to be sure she carried out her tasks first. Anûras was apparently one of the experts who gave lessons, although she didn't know him.
"It's probably still too early," she murmured and took a step backwards to look up at the windows. "Hey, can anyone hear me? I have a message for Anûras," she called loudly and clearly.
She waited a while and repeated her words.
Eventually a window opened and a sleepy älf stared down at her; his long, grey-black hair fell onto his bare torso where colourful runes had been etched. "What do you think you're doing?" he said, irritated. "The sun is just coming up and if you..."
"Are you Anûras?"
"I am, and I'm grumpy too."
"Prove to me that you're Anûras."
"I can wake up other älfar who will give you a beating while they confirm to you that I'm me," he replied.
Saitôra reached underneath her cloak and took out the envelope Irïanora had given her. "From a mutual friend," she replied softly. "Meant for your eyes only."
"Could this not have waited?"
"Her name is Irïanora," she cried, hoping he would hurry up. She was angry that the sovereign refused to declare even a small threat against Elhàtor. Two murders were two murders. _Irïanora could never have wanted that._ She looked around before adding conspiratorially: "It's about Elhàtor and how things are taking a turn for the worse." She didn't want to imply any more; her heart was beating rapidly.
"I'll throw on some clothes quickly." The corners of Anûras' mouth clenched, and he disappeared from the window.
Saitôra found the idea of the älf not wearing any clothes thrilling and couldn't help smiling mischievously.
"Did the sovereign not order you to keep your silence?" whispered the silhouette near her. "You know your punishment."
_A spy!_ As she turned around, Saitôra drew her dagger and stabbed at her pursuer.
Tanôtai pirouetted around her and dodged the attack with elaborate grace, the needle-dagger gleaming white in her hands, which were covered in tattooed tendrils. "You've got to be quicker than that to kill me," she murmured.
She avoided every one of Saitôra's attacks that followed by writhing like a snake, using swift sequences of steps as though she were dancing to a tune; she swung her arms nimbly as she did so and drew shapes in the air with the glowing blades. The gleam of the light was still visible for a few heartbeats before new lines flared, criss-crossing the old ones.
The lock on the small door clicked.
"Dâkiòn ought to know what I've seen," Saitôra panted with exertion and missed Tanôtai for the umpteenth time. Tanôtai suddenly wrapped a hand around the back of Saitôra's neck as if they were dance partners.
"Perhaps it should." The red-haired älf-woman suddenly pulled her towards her, looking like she was stealing a kiss. A thin, dazzling blade shot through Saitôra's neck. "But _you_ will not be announcing a thing."
Tanôtai expertly intercepted her collapsing, gasping opponent, spun underneath one of Saitôra's arms, then heaved her onto her back, picked the envelope up off the ground and vanished into the shadows with the dead body.
Then the door opened.
Anûras, wrapped in a pale-yellow cloak, looked out but couldn't see the messenger. "Hey!" He stepped into the street and looked around, searching for her. "Where are you?"
But Saitôra had vanished.
# Chapter XI
_Anyone who makes the same mistake twice must love pain._
Wise saying of the Älfar
Collected by Carmondai, master of word and image
Tark Draan, Human kingdom of Gauragar, 5452nd division of unendingness (6491st solar cycle), autumn
"As soon as night falls, let's see who's holed up in this hideaway." Carâhnios gave an evil laugh. "You know how this goes now, black-eye."
Carmondai grimaced and brushed his long, brown hair back with his fingers. Every bone in his body hurt; travelling like this did not agree with him. "I take it I pretend to be the loud, clumsy älf again?" His gaze swept over the picturesquely colourful, autumnal landscape that stretched out in front of them.
There were no more gentle hills here, apart from the one they were standing on, which had an entrenchment-like path leading down from it. The zhadár had guided them to an area where the woods grew more thickly than in any other region. The mixture of different deciduous and evergreen trees created an unparalleled array of colours.
Carmondai was profoundly sorry he was not able to capture this splendour on paper. With ink, it would remain a uniform black or at most grey. "What have the Aklán come up with this time to make sure their refuge is somewhere nobody would willingly set foot? Another temple?"
"Much more sophisticated than that: a _legend_." Carâhnios chuckled. "I can tell you were thrown into that dungeon, otherwise you would have written it down long ago."
"And what is the legend?"
"I'm not a storyteller like you so I'll avoid showing off with embellished details." The zhadár pointed to the section of woodland where nothing but black firs grew. "A creature lived there who devoured the best warriors and warrior-women of the älfar—the ones who set out two hundred cycles ago to destroy the creature. Four charcoal-burning villages fell victim to the creature so they decided to abandon the area." He set the pony to trotting.
Carmondai sighed. "That was the legend?"
"Yes. That was it."
_No, he's no storyteller._ "And that deters humans from venturing into the area?"
"Like any legend, it contains certain truths. The charcoal-burning villages were killed by the älfar themselves, the people were butchered, the pieces scattered brutally all over the place. Even along the street," Carâhnios said, pulling his helmet off. Short, black hair emerged from underneath. He looked like a dwarf shadow brought to life, having snuck away from its master; the fact he was sitting on a white pony reinforced this unusual quality. "Of course travellers and merchants noticed this and combined with the relevant legend that I've just told you..."
"That wasn't a legend. It was a summary," Carmondai interrupted him, cursing the chains and the rocking and the ink. _I will have to memorise it._ "How long will the legend last now that there are no älfar left to make it look like the beast is still alive?"
"As soon as just one brave soul goes inside, it won't be long till they are found torn into nice little pieces."
"So there are mechanical devices then?" Carmondai guessed.
Carâhnios wedged his helmet under his arm, clapping too hard and too long, and chuckling in his crazed way. "The Aklán have had clever traps laid—they reset themselves after they've been triggered. The last murder by the supposed beast was eighty orbits ago. That time, all that was left of a woodcutter were shavings."
Carmondai was following the zhadár. "Where exactly is the hideaway?"
"In the centre of the four villages. The entrance to it is in the trunk of what looks like a dead, old fir tree. But it's made of painted granite and it's protected by even more traps." He winked at him. "Are you excited yet?"
"Very."
In silence, they rode along the path southwest towards Oakenburgh until Carâhnios steered his pony to the right through the undergrowth and away from the road; he put his helmet back on as he did so.
_It looks like things are getting dangerous._ Carmondai stayed close behind until the zhadár stopped on the bank of a small stream a mile later and dismounted.
"Let's wait here. The first village is half a mile away." He watered his steed and removed his prisoner's chains.
The älf slid out of the saddle and stretched. The densely packed firs gave the sunlight a greenish tinge, and there was a strong smell of moss, resin and earth. Needles crackled under their feet. The deciduous trees were harder to spot. _As if they wouldn't venture into the darkness._ "A beautiful wood."
"If you're an elf." Carâhnios chuckled. "But why do you like it? Is it kinship with the pointy-ears that's making you feel that way?"
Carmondai led his horse to the water to let it drink too. "My way of seeing things is not necessarily the same as everyone else's." He breathed in the cool air that smelled of mushrooms. He quickly scooped up some of the gushing water and washed his face with the little piece of soap that he guarded like a treasure, then drank plenty of water. _Cold and delicious._ "A wood is a beautiful thing."
"Even if it's not on fire?"
Carmondai smiled. "Is that the zhadár in you speaking or the groundling?"
"Someone who doesn't like woods," Carâhnios replied pensively and pointed upwards. "You have to keep an eye on the ground as well as on all the branches above you to spot dangers. _That_ is what I don't like about them."
They unsaddled the animals and then each lay down on a blanket.
While the groundling fell asleep straight away despite still having his helmet on, Carmondai used the opportunity to fill page after page with sketches of his impressions of the wood; his thoughts wandering all the while.
Carâhnios still hadn't told him how many hideaways there were. He was really hoping there were more than a dozen, preferably scattered all over Girdlegard, although he himself thought that was out of the question. That way he would have more time to devise his plan of escape.
Together with the Thirdlings, the älfar had ruled in Idoslane, Urgon and Gauragar. Therefore his tribe's secret refuges were in these realms, where residents were overjoyed by the freedom they'd gained.
After the end of the occupation and foreign rule, the people had elevated a young woman called Mallenia to be their queen. The warrior-woman of Ido descent had made a name for herself in the previous cycles as a freedom fighter against the Aklán. The reward for her life-threatening service was the throne.
As far as Carmondai had been able to make out in the last orbits, a descendant of Rodario the Incredible ruled over Urgon, because even the actor had taken part in decisive battles and played an important role.
_Actors as kings. That's what we've come to. Mere barbarians can do it too. A fool on the throne ensures laughter, but never order._ Carmondai's gaze darted towards the snoring zhadár. _Unfortunately he's not a source of more_ _detailed information._
He took a break from the drawing he'd begun of a withering leaf caught in a spider's web. He was desperate to know what the young sovereign Mallenia looked like. Apparently she was blonde, tall, a true warrior-woman and good-looking—by human standards, anyway.
Carmondai remembered her ancestor, the hero and prince Mallen of Idoslane, so he drew a feminine, slightly altered version of his face.
After a while, he looked critically at the result. _I wonder if she looks like that?_
A stifled scream made Carmondai jump. He only just managed not to tip the ink pot over his version of Mallenia.
He looked over at Carâhnios—the noise had come from his throat.
The groundling was sitting on the blanket, the vial with the newly acquired elixir in his right hand. He seemed to have licked a drop of it off the index finger of his left hand. His gaze was fixed, his eyes were open wide. His breathing was very irregular, stopping for several heartbeats only to start again far too fast.
Carmondai looked at him in a calculating way. _If he were to die now... or if I kill him..._
Bolts of light flashed underneath the zhadár's black skin, an outright storm brewing on his face. No emotion was discernible on it.
The älf looked at the tempting dagger that Carâhnios carried at his side. _Should I risk it? But what would happen afterwards?_
Then the zhadár uttered a low sound, and at the same time the tension eased and his body relaxed. He gasped for air as though he'd done a strenuous run, staring at his index finger. "It was just one drop," he whispered hoarsely. "Just _one_ drop, but..." He swallowed and put the vial away with trembling hands.
"So the remedy works?"
Carâhnios ignored him, his Adam's apple bobbing up and down. First he closed the visor, then his eyes, and lay down again.
_There it was, my chance._ But Carmondai didn't worry for long. Now that he knew what the reaction to taking it was, he was going to be prepared the next time. _We'll see if your next drop is also your last, zhadár._
He picked up the page with the beginnings of the dying leaf drawing and completed it by the time darkness fell—it descended quickly on the travellers in the wood.
His vast knowledge of the älfar was in fact his greatest treasure and his most valuable asset. _I've got to get rid of him without them throwing me into a dungeon and torturing me._ Carmondai felt more than capable of suitably manipulating a person. _All I need now is the opportunity._
Mist was rising off the moss and creeping up the tree trunks like the tide of a ghostly sea. The haze rippled and broke, swirling, on the trees; the temperature dropped significantly.
Carmondai wrapped the pages in wax paper before the moisture could get at them. _Pity. I would have loved to draw this scene._ He could feel a thin film of moisture forming on his shabby cloak.
Carâhnios had got up and seemed to be his old self again. "Let's go." He found one of the familiar bottles with a dash of the silvery substance in his luggage and pressed it into the älf's hand. "As I said: you know how this goes. But watch out for traps."
"How about you warn me?"
"And let the black-eye know there are two of us?" He snorted derisively. "Plus it makes your escape more convincing if you fear for your life and have to struggle." He pointed into the wood. "Onward, my unwilling ally. But woe betide you if you let the bottle break." The zhadár grinned demonically from inside his helmet. "If you do, I'll take _your_ blood, you know!"
Carmondai didn't doubt that. He set off down the path, picking up his rucksack and a bundle of pages first.
The mist, which was up to his thighs at this point and had looked picturesque until just now, turned out to be treacherous: he couldn't see the ground at all, let alone whether a snare, sword or harmless moss was in store for him. So he moved slowly, feeling his way forwards with the tips of his boots.
He soon reached the village, which was nothing more than a small cluster of dilapidated huts that couldn't have looked much different even when they were inhabited. The wood had already reclaimed large sections of them. Small trees rose up in the middle of the settlement, pushing the buildings sideways as they grew, smashing roofs or forcing them apart. Here and there lay bits of bone that had been bleached by the sun or were overgrown with moss like greyish scabs.
_Now what? Keep going straight?_ Carmondai looked around and couldn't see the zhadár anywhere. With a bit of imagination it was possible to interpret whirls in the haze as clues to where the groundling was sneaking along.
As he was not getting any whispered instructions, he walked cautiously on, through the village and into the steadily rising mist that now enveloped him up to his waist.
Carmondai was feeling increasingly tense and he was sweating. The closer he got to the hideaway, the more likely it was that he would encounter a trap.
Then he spotted a weather-beaten tree trunk just under five paces high that looked like the top had snapped off.
If Carâhnios had not told him it was painted granite, Carmondai would have walked unsuspectingly past.
_How loud do I have to be for someone to hear me?_ He didn't think stamping his feet was a good idea because of the traps, and falling over or fake limping were out of the question too. His thoughts revolved less around his opponent than around the deadly mechanisms. The wood-cutter had been found in _shavings_.
Carmondai stood motionless in the mist.
_I could have been just about to reach it._ He stooped, groping through the ephemeral whiteness for a branch or stone he could throw.
His fingers caught hold of a piece of wood, he picked it up—and there was a click.
Ishím Voróo, Älfar town of Dsôn Elhàtor, 5452nd division of unendingness (6491st solar cycle), summer
Aiphatòn left the chamber Ávoleï had shown him to. He was wearing a skirt-like robe of pale silk that went from his hips to his feet and reminded him strongly of his own clothes that he had worn in Girdlegard.
It was warm enough for him to skip wearing a shirt so the armoured plates on his skin were visible; he wore open-toed sandals on his feet. He was not used to having to go without his spear—the armoured gloves were the only weapons he had left. A servant had given him a shave and had cut the black hair on the nape of his neck level with his ears.
"Can I appear before your godmother like this?" he asked Ávoleï.
She scrutinised him hard and walked round him once, her yellowish green eyes looking him up and down. She herself was wearing a shirt and trousers underneath the armour with the commander's insignia. Her black hair was pinned up in a clasp. She was pleased with what she saw. "You can. It may not be the usual fashion in Elhàtor, but she will be able to overlook that in the case of a guest and especially an älf from Tark Draan." She pointed at his covered fingers. "You couldn't take off the gloves?"
"They're bonded to me like the metal. Besides, there hasn't been any reason to do so."
"No reason?" Ávoleï sounded astonished. "Do the älf-women from your homeland like it when you touch them with iron?"
Aiphatòn did not respond.
"We are expected." She took the lead through the palace and he looked around as he followed a pace behind.
Although he hadn't seen much of Dâkiòn, he noticed striking differences in the architectural styles and choice of decoration. Bones and bone segments had been used as ornamentation on the walls and ceilings, but they were all animal in origin. The few bones that came from other beings could be counted on one hand.
The palace had been built in a style that allowed light and air to stream through it, so that the sea wind could blow the heat of the orbit from the rooms. The predominant colour was white, while black was used only to pick out window frames, benches or unusual features in a room. He also saw many symbols that were not älfar.
_Completely different from the Dsôns in Girdlegard._ Aiphatòn did not yet know what he was going to tell Modôia about Girdlegard and the Dsôn Aklán. Ultimately, he feared triggering her desire to take revenge for the triplets' death and starting a war. _She will have plenty of questions for me._
The prickling he had felt in Dâkiòn earlier had followed him to Elhàtor. His hope that this pain would stop if he moved away from the gigantic town proved false. He glanced at his armoured gloves, the runes on them flickering occasionally. _Could there be one of those fields here too?_ He wanted to ask about it at some point.
Ávoleï turned right and led him into a courtyard covered by a vaulted glass ceiling with raindrops falling gently on it. Four bone fountains were gurgling in the corners, and in the middle was a platform and a suite of furniture around a low table. The water gave off a blossom-like, earthy scent.
They were expecting them.
"The älf-woman in the middle wearing the white dress is my godmother," Ávoleï explained quietly. "Directly to her right, wearing the blue cloak of a dolled-up dandy, that's Ôdaiòn, her son. The woman next to him, who is already imitating how he dresses, is Irïanora, a hostage from Dâkiòn and the niece of its sovereign. To the left is my mother, Leïóva."
Aiphatòn tried to memorise the names.
They had reached the platform and were climbing onto it.
Ávoleï gestured towards the unoccupied thick cushion. Once the älf had lowered himself onto it, she made her way to her mother's side. "I bring you the emperor of the älfar from Tark Draan," she announced with a smug undertone. "We picked him up when he was thrown off the highest cliff in the town by Shôtoràs' warriors."
Laughter rang out, Ôdaiòn laughing loudest of all.
Aiphatòn put up with it. "I came to Ishím Voróo by following your runes, Modôia," he explained, not mentioning that he had removed them. "My route took me straight from the settlement below the Jagged Crown to Dâkiòn where my journey took an... unpleasant turn and I lost my spear."
"And a bit of your pride," the monarchess' son chipped in.
"I don't need pride," replied Aiphatòn politely. "I leave pride to those who require constant reassurance."
Modôia's gaze had become distant. "My runes," she repeated softly. "I forgot that I'd painted them on the slopes."
Leïóva, a slightly older version of her daughter, poured him some water. She favoured a delicate, white skirt and a top that emphasised the muscles in her bare shoulders. "How did you find the settlement? It's well hidden. And nobody knows about it either."
"That's not quite true. Carmondai wrote an unfinished _Ode to the Ten—_ the Ten who had been dispatched by Aklán Firûsha to get to the bottom of the rumours about the village beyond the Jagged Crown," he contradicted her. "I followed a few criminals who were hoping for refuge there." Aiphatòn had decided not to reveal anything about the incidents in Girdlegard for now. "After I knocked them to the ground, I wanted to find out which parts of it were true." He looked at the blonde monarchess as he picked up his glass. "You and Leïóva were among the Ten."
Ôdaiòn cleared his throat. "With regard to the form of address, emperor, we prefer to use titles."
Aiphatòn eyed Ôdaiòn scornfully. "With regard to _my_ address, there are so many titles you would need to mention that I'll permit you to disregard them. Therefore I will stick to my own ways."
Ôdaiòn's lips thinned, but he did not venture to protest.
Ávoleï laughed and started to speak but was silenced by a gesture from her godmother.
"I was a member of a troop of veterans who accompanied Firûsha and she dispatched us to find runaway elves and their settlement in the Grey Mountains," Modôia recounted. "I discovered a village where the elves and dwarves had lived together. Inspired by the ambition of catching the last elf-woman, I went north, followed her tracks and came here." She placed one hand on her son's back. "Samusin was merciful in allowing my destiny in Ishím Voróo to turn out well." She turned her gaze to Aiphatòn. "The emperor himself followed my runes—what for? You have thousands of älfar at your command."
"Who is in charge while you're away?" Ôdaiòn cut in inquisitively. "Do you have enough confidence in them?"
"Everything is in order," he answered evasively but without lying.
"Well." Modôia's smile was ambiguous. "Now, due to your rescue from Dâkiòn's warriors, you owe me your life, emperor."
"I owe it to Ávoleï. It's already been agreed that she would like to come back to me on that issue." In thanks, Aiphatòn bowed his head in her direction, looking as mischievous as possible. "Elhàtor is beautiful, or what I've seen of it so far, at least. So there would be no reason for you to return to Girdlegard?"
Modôia looked astonished. "Is that meant to be a veiled request? Bear in mind: you're not an emperor on this side of the mountains. You may be the son of the Inextinguishables but as Shôtoràs has made clear to you: their words count for nothing now." She called the servants over to the table with the food to begin the meal. "Dâkiòn and Elhàtor are home to the last of our people in Ishím Voróo. Our towns maintain a fragile peace."
Irïanora lowered her head in shame.
"We simply want to live in harmony, devoting ourselves to art and not to quarrels of any kind between ourselves—or with anyone else, if it can be avoided." Modôia's face suddenly distorted and she had to lean back into the cushions as if she had become exhausted in the blink of an eye.
Leïóva immediately tended to her, the women talking quietly to each other.
"When my mother came to Shôtoràs, she saw that she never wanted to live under his strict rule. Together with other älfar who felt the same way, she made her way to the sea and agreed a pact with the frekoriers who lived on this island," her son took over the story. "The mercenaries gradually died out, but we are carrying on the knowledge we inherited and are even refining it." He raised his head slightly. "Nobody from Elhàtor wants to march into Tark Draan and contest your right to the throne, emperor of the Älfar. Go back there and announce to our tribe that we exist. And I advise you to allow anyone who wants to move here to do so. That's all there is to say."
Aiphatòn could tell that Ôdaiòn was to become the successor and was already enjoying the role. _His mother looks sick._ "I think I will." He believed the assurances that neither Dâkiòn's nor Elhàtor's rulers felt like making their way south and invading the weakened country; besides, he was happy to let them keep believing the Aklán were still alive.
_All the same, Girdlegard will only be safe once the älfar are wiped out. Who knows what will sprout from the next seed? They might have passed their thirst for conquest on to the next generation._ "I ought to head back soon then," he said, tasting dish after dish of the food on the table. _Fragile peace. That sounds perfect. I will know how to destroy it._
Leïóva had got up and taken a small vial out of her pocket, opened it and handed it to the monarchess. "And don't be tempted to have your army march against us," she said. "Perhaps you haven't felt it yet, but Ishím Voróo changed us, those of us who've lived here a long time and those who were born on this soil. Our cîani are strong."
"I've had a foretaste of the new magical talents, thank you very much," Aiphatòn replied and looked at Modôia. _That's what it is! A magical field that made anyone from Girdlegard unwell._ He toyed with the thought of getting himself some of the remedy that eased the monarchess' symptoms. But he could still tolerate it for now.
"Oh, our sorcerers know their craft better than the amateurs from Dâkiòn," Ôdaiòn interjected pompously. "No offence, Irïanora." He pointed to the hole in the plate of armour. " _Our_ cîani would have done a thorough job. Then there wouldn't _be_ an emperor anymore."
"Possibly." Aiphatòn let the young älf brag so that he could marshal his own thoughts and find a way of setting the towns against each other. He glanced at Irïanora. _Killing the hostage? Would that be a reason for the sovereign to start a war?_ He couldn't come up with anything off the top of his head, but perhaps something would emerge as the conversation went on.
"I've often mused with Mother about whether the Inextinguishables knew that the älfar would gain magical power if they pushed further into the north." Ôdaiòn helped himself to delicious-smelling meat and sprinkled extra spices over it. "The magical fields outside the old Dsôn had a transformative effect on us, on our innate gifts and also our magical power. Nearly every young älf in Elhàtor can do small tricks or make things float. _Without_ any training." He dipped each morsel into a dark brown gravy with a nutty aroma. "I've come to the conclusion that the Inextinguishables were deliberately preventing an expansion of the kingdom. Out of fear for their power, which could certainly have been endangered." He gave Aiphatòn an appraising look to gauge his opinion. "Were your parents ultimately just ordinary älfar who had spent long enough in the north and came back strengthened? Hence couldn't _anyone_ have become an Inextinguishable?"
Aiphatòn ate some of the flatbread deep-fried in hot, flavoured oil. "I wouldn't put it past them." He would not say any more than that. _Could I talk him into an alliance with me? He seems so hungry that he could be made to cast the first stone at Dâkiòn. His mother and Leïóva might want to keep him in check. But once the stone is soaring through the air..._ He chewed and swallowed. "Before I go back, I've got to pay Shôtoràs a visit and reclaim my spear that he's withholding," he said, beginning the cautious process of sounding them out. "It's an excellently crafted piece and responds to my magical commands. It's a symbol of my power and I wouldn't like to turn up in Girdlegard without it. There would be stigma, you know."
"I wish you the aid of all the gods in that," said Modôia, sitting up straight once more. The remedy Leïóva had administered was having its soothing effect.
"Well, I thought you could send a few good cîani along to accompany me. Or warriors. I just need a bit of a diversion to get into the town." Aiphatòn looked innocent. "It could be the beginning of a pact with Tark Draan and me. Think about it: more trade, more residents for Elhàtor, more security..."
"No," the monarchess said immediately. "You'll have to get the spear alone."
"Even if Shôtoràs' power could become a danger to Elhàtor?" Aiphatòn looked to Irïanora.
But she shrugged her shoulders. "My word won't be much use. My uncle hates me."
"How much danger are you talking about?" Ôdaiòn gestured for him to go on. "Let's listen to more of what the emperor has to say, Mother. I can imagine paying a visit to Tark Draan some time and doing an exchange."
"I said _no_ , Ôdaiòn!" his mother responded curtly. "What would we want with foreign-born älfar? Just so they can die miserably like me and all the others because the magical radiation affects them too badly?"
"Fine. Let's just leave Tark Draan out of it," her son promptly changed his tune. "Our scouts have reported on a dam that Shôtoràs is having built and a canal that leads straight to the Tronjor and a large valley," he said. Irïanora looked astonished at his words. She had clearly had no idea how well informed they were. "We could use the opportunity to try and get insights into his plans. The emperor would be the best diversion for us because everyone would assume that he was searching the rooms for his spear. The sovereign would not be suspicious of Elhàtor. And if Aiphatòn makes off with his weapon, the old chap won't be using it."
_Well, those sound like preparations for war in Dâkiòn after all._ Aiphatòn struggled not to grin broadly. He had judged the monarchess' son correctly. _I'll find a way of using this._
Leïóva looked to Modôia and the pair of them communicated without words this time.
Aiphatòn could see how clearly the rejection of this daring plan was written in the black-haired confidante's eyes. _Her word carries more weight than the son's._ If he didn't convince Leïóva, he might as well be talking to a brick wall. "Besides," he added quickly, "the sovereign is still holding a poor guy prisoner and I'd like to free him."
"Where does this generosity come from, emperor?" Leïóva looked at him scornfully—and he felt the same confusion with her as he did with her daughter. They had the same intimidating aura. "Is he a friend of yours?"
"To be honest: I first came across him in Ishím Voróo."
Leïóva looked surprised. "Wouldn't the fate of a random älf be all the same to you?"
"Absolutely. However, I rescued him from a band of thieves who were carrying him through the area in a sarcophagus. That oughtn't to have been in vain," he told them, seeing the stirrings of emotion on Modôia and Leïóva's faces. "A secret surrounds him that may also concern Elhàtor. I would need your opinion on that." Aiphatòn fed them some more details. "I found him shackled, bound with magical clamps I was able to remove. A half-mask over his face was the only thing I couldn't take off and it had runes on it too. We had to crush fruit into a pulp just to feed him."
The table remained suspiciously silent after his final words.
The älfar from Elhàtor looked at each other in turn while Irïanora's brow furrowed.
"That cannot be," Ôdaiòn eventually blurted out in bewilderment, running a hand through his brown hair. "How did he find him?"
"I should have believed Cushròk when he told me about it," whispered the monarchess, turning pale. "It's happened now!"
" _What_ has happened?" Irïanora understood just as little as Aiphatòn did and she gave vent to her astonishment at the top of her voice. This saved him asking the question. "Who is this prisoner?"
"It has happened, the thing I have feared every division of unendingness since I arrived on Elhàtor," said Modôia and looked to Leïóva for support. Her confidante lowered her head very slowly, seeming, in doing so, to agree with what the monarchess wanted to announce. "I must order war against Dâkiòn."
"What?" Irïanora leaped to her feet in horror. "But my uncle hasn't done anything to justify that!"
_All it took was one story?_ Aiphatòn had to suppress a loud cheer; at the same time, he noticed that the hostage's alarm was very clumsily feigned. _She's glad about the impending conflict too. How interesting._ "Well, I feel honoured that you've changed your mind about helping me. But I wonder if an army needs to be dispatched immediately just because of this?" he asked, to give off the appearance of being calming.
Leïóva fixed her eyes on him. "Is he still wearing the mask?" she demanded to know.
"Yes. I couldn't undo the protective spell." Aiphatòn grinned. "And the cîanoi who appeared to have the relevant knowledge died at my hands." _Should I have kept that quiet?_ he immediately thought, uneasily. _Not that the danger has been averted now._
"Good. So we still have time to dispatch the fleet." Ôdaiòn looked at Ávoleï. "You know the Tronjor best. You'll lead them upstream."
"Who," Irïanora shouted, "is this prisoner of my uncle's? A war is being started over him without hesitation. Do you not even want to look into what the emperor is saying?"
Leïóva turned to look at the young älf-woman. "He has many names, but he is known as the wind-voice, provided the stories are true and Cushròk found the right creature. He is able to unleash storms that churn the sea up into such devastating waves that not one stone of our homeland will be left standing. Shôtoràs will use him against us to force us to surrender, there's no doubt about it."
_This is perfect! Samusin, you have given me a better weapon than I could have dreamt of._ Aiphatòn had to be careful because he was afraid his face might give him away.
"There's no time to investigate and the description was clear-cut. Particularly since I was aware of Cushròk's mission. Who could have guessed it would be successful? We cannot delay." Modôia gazed round at all of the älfar's faces. "Elhàtor is going to war."
None of those present rejoiced.
Ávoleï fixed her yellowish-green eyes on Aiphatòn. "And you, emperor, will help us. Thus will your debt to me be paid."
"Gladly. I suggest that I lead an advance party right away, returning secretly to Dâkiòn to thank Shôtoràs for the way he treated me."
His words drew applause from Ôdaiòn. Aiphatòn gave a slight bow. "And another thing: I'm getting my spear back." He smiled. _No älf will survive this war. I'll make sure of that._
Ishím Voróo, Älfar town of Dsôn Dâkiòn, 5452nd division of unendingness (6491st solar cycle), late summer
_That's him apparently, the wind-voice._ Tanôtai contemplated the moon-pale älf who was being kept in a magical sleep.
Nodûcor was lying on a very large bed in a beautifully furnished room in the sovereign's palace with a ceiling eight paces high. Little staircases led to suspended ceilings and open-plan levels with libraries and sleeping facilities. Through the enormous windows on every floor there were magnificent, ever-changing views over Dâkiòn. The fragrance of incense purified the air, cleansing it and leaving an aromatic smell behind.
Were it not for the four cîani, who had spread their books and rolls of parchment out all over the tables, chairs and windowsills, one might think Nodûcor was a privileged guest of Shôtoràs.
His glass hair caught the sunlight, his bare, sinewy chest slowly rising and falling. The magical slumber was deep.
_He looks unusual anyway._ Tanôtai looked over at the magic experts who were arguing quietly while leafing through their notes occasionally, looking for symbols and approaching the black half-mask to inspect it closely.
Many moments of unendingness had passed in this way.
_And you can command the wind?_ It was Tanôtai's job to stay close by in case Nodûcor managed to wake up and try to escape. The death-dancer would be able to grab him more easily than the cîani since most of them had less muscle than the thin prisoner. _I'm intrigued by what your voice sounds like._
The door opened.
Shôtoràs entered; they had all heard his stick clicking beforehand. "How do things stand?" he asked, full of energy and confidence. "Have we got to the bottom of the puzzle that Lethòras left for us?" He nodded to Tanôtai in greeting and limped over to the bed. "He's still wearing this mask?"
The cîani in their robes bowed to the sovereign, their unease visible on their faces.
"The situation is this: Lethòras used a spell made up of different parts that are each encrypted in turn," one of them explained. "He fit, if you like, a series of spells one inside the other, to stop anyone opening the lock without a lot of effort."
"I see." Shôtoràs touched the black metal and felt the warning tingle. "And he took this knowledge with him into the endingness."
"Unfortunately, sovereign."
"How long will it take you to solve this puzzle?"
The cîanoi made no secret of his own ignorance and that of his fellow guildmates. "We deciphered the first four spells but then we reached a point where we have to be particularly careful. This particular rune symbolises death." He reached behind him and snatched up an open book where he had marked the relevant part with a ribbon. "If we make a mistake, this next symbol will unleash a flash of lightning that will destroy the half-mask. Along with Nodûcor's head."
"Good thinking by the cunning Lethòras, but bad for us." Shôtoràs lifted the stick and tapped it against the metal, the sleeping älf's head wobbling slightly. "We are so close to being able to call the most powerful weapon our own. After that there will be nothing left for us to fear." He looked at the cîani. "Will it be difficult to bend his mind to our will?"
"No. We've already woven a spell to, firstly, make him sleep and, secondly, ensure that he takes orders—just like a dog takes orders from his master. As soon as we wake him," one cîanai explained, "he will obey your every word. Your image is fixed firmly in his mind."
Shôtoràs nodded absent-mindedly and turned to leave. "Work faster," he commanded.
"It's possible," Tanôtai interjected cautiously, "that we've got the wrong one, sovereign."
The cîani stared at the death-dancer as if profoundly offensive insults had passed her sensual lips.
"Don't look so surprised. We have no guarantee that he truly is the wind-voice." Tanôtai pointed to Nodûcor and a diamond on her wrist flashed. "Apparently Cushròk captured him, as Aiphatòn told us. But we will only know whether he unleashes storms once he starts to speak."
Shôtoràs smiled. "I'm very sure. That's enough." The silver end of the stick was pointed towards the door. "See me out. You seem bored, and boredom leads to dangerous thoughts. I've got a better use for you than keeping watch over someone who looks dead."
Reassured, the cîani turned back to their papers and the runes.
The sovereign and Tanôtai left the room and walked through the vaulted corridor and down the steps to the first inner courtyard. Vailóras and four of his warriors were waiting there, sitting on night-mares; one other black horse had been saddled.
"I'd like you," Shôtoràs told her, "to ride with them. You will be looking for Aiphatòn on my behalf. I'm sure he's somewhere in the vicinity so that he can get his spear back."
Tanôtai screwed up her mouth. It pained her that she had not managed to kill the emperor. Anyone who could survive her dagger and that fall had proved they were extraordinary but that hardly made her failure any better. "I'm glad you've chosen me to accompany them."
"No doubt he has received support and care from unsuspecting locals. Spread the word that Aiphatòn died trying to kill me and seize power for himself," he instructed Vailóras and his warriors. He stroked a night-mare fearlessly, and it approved the affection with a snort. "If you do that, the locals ought to give you the updates you need to find him."
"We'll do that, sovereign." Vailóras turned his black night-mare around.
_Inàste, lead him to me. Then I will burn my name into his plates of armour._ Tanôtai mounted and they rode out through the narrow gate, across the wide main road and immediately left Dsôn Dâkiòn via one of the bridges.
The benàmoi guided his night-mare towards the southeast. "That's where the closest village is," he told the death-dancer. "It's possible he dragged himself into one of the barns. The locals may not necessarily be aware that he is hiding in their village. So we'll be friendly," he ordered his warriors.
_I won't be._ Tanôtai saw the huts, and to the side the enormous hay and grain silos looming up in front of the riders.
The crops were stored in the silos temporarily before being transported to the town's storage towers. The farmers were left with enough grain and straw to make it through the winter and they got the seeds from the sovereign in the spring. In this way the älfar stopped the residents fleeing.
"A good place to hide," she said as they approached. "It will take a long time to crawl over every last nook of it."
"The farmers will do that for us," said Vailóras. "Nobody wants to think there's a traitor under their roof who wanted to kill Shôtoràs."
Tanôtai grinned. "You know how to make others take on the work and still feel like a hero during the slog."
"I've travelled this land for a long time. I know every individual within a radius of forty miles and I have made sure that they appreciate the mercy of the sovereign. From generation to generation." Vailóras reined in his night-mare outside the first hut and its door opened immediately. The residents had noticed the troops and were coming to ask what they wanted. "Who would have thought that our people would be loved instead of feared?"
" _I_ am feared, benàmoi." The death-dancer leaped down from her saddle and walked up to the astonished villagers. "If the barbarians are too slow, I'll show you why."
After four splinters of unendingness, which they spent waiting and doing their own searches in the village, they were forced to move on empty-handed. Aiphatòn had not been hiding there.
They continued unrewarded for quite a few more moments and neither Tanôtai's unfriendliness nor Vailóras' knowledge helped. They spent a long time travelling and making inquiries, which the death-dancer did not enjoy. She found it at least as awful and boring as guarding a sleeping prisoner.
They rode through the villages in a strict sequence, beginning with the most likely ones, but they didn't find any leads on the missing emperor.
The residents of Dâkiòn's territory were horrified that someone had tried to kill the sovereign. Their anguish, as the red-haired death-dancer could clearly tell in every conversation with village elders or mayors, came from a profound sincerity: nobody wished Shôtoràs dead.
As they sat in the parlour of an isolated farmstead on the western outskirts of Dâkiòn country one evening, Vailóras toyed with the thought that Aiphatòn had started his journey home. "In his position, it's the best solution. He knows we'll kill him as soon as we track him down. And he has already lost his spear."
Tanôtai couldn't stand the idea of not finishing the duel she had started with the shintoìt. She touched the dagger on her right forearm guard. "If I lost one of these, I would be desperate to get it back," she replied. "They're one-of-a-kind, like the spear."
"Actually, what's the news on that?" interjected one of the warriors.
"As far as I know, a cîanoi is examining it. They want to uncover the tricks to the magic stored in it. It's extremely different from ours," Tanôtai was repeating what she'd heard while guarding the sleeping älf's bed. "Lethòras was reputed to be the best of our magically gifted, but he didn't know how to resist this kind of inverse charm."
"Yes, the magic," grumbled Vailóras as more wine was poured for him by the farmer's wife, which he acknowledged with a polite nod. "I deliberately stay away from that." He rubbed his black lamellar armour to remove a stain he'd got during his meal. His helmet dangled from the back of his chair and his dark blonde hair was plastered to his head.
"Surely you don't mean you don't use it?"
"I've never had reason to yet," he admitted. He looked at his batons resting in their holders on his thighs. "I've made the handful of defaulters pay the levy in my own way. From gold to bones, we've collected everything for the sovereign."
His men laughed cruelly.
_A squandered gift. He ought to pass it on to me if it's possible._ Tanôtai stayed away from the fermented grape juice. As a death-dancer, she preferred her head to be clear at all times so that she could deploy her talents without any unsteadiness.
What's more, her magic worked differently under the influence of alcohol. She tried to perform a dance drunk once, and the consequences were embarrassing. It had given her a broken arm and she'd needed five moments of absolute bedrest to recover.
_I want to catch him. Aiphatòn must die at my hands._ Tanôtai traced the lines on the side of her thigh, feeling the ink just underneath the skin—it was ink and so much more.
It was made from plant sap extracts, distilled and magically treated before being inserted with the needle. When combined with the correct movements, they released the magic—which could happen while both fighting and dancing.
Tanôtai was aware of cases of self-inflicted injuries or even explosions, poisonings and suffocations because the steps weren't right or the necessary precision was lacking, resulting in alterations to the magic spells.
_Magic is unforgiving._
The red-haired älf-woman tore off some brown bread and dipped it into the pot of cream still on the table from the meal, enjoying the mild sweetness and freshness.
While Vailóras, the country folk and the warriors chatted about the harvest, her thoughts returned to the evening when she had struck Aiphatòn directly in the chest.
_What did I do wrong? He ought to have died._ She contemplated her right hand, whose fingertips had turned black after the explosion and had been prickling ever since. _Should I be glad I survived—unlike Lethòras?_
Hurried footsteps approached the main building and the door was thrown open at the same time as a knock resounded.
Everyone turned to the door and saw a panting barbarian boy, sweat running from his temples and forehead.
"We've seen him," he uttered breathlessly. "The conspirator. He was running west beside our fields and my father sent me to fetch you immediately."
Vailóras stood up; his warriors followed suit and grabbed their helmets from where they had hung them on the backs of their chairs. "Are you sure?"
The boy nodded. "Father said he's absolutely certain. He said he'd never seen an älf like him before." The farmer's wife handed him her glass of water, and he drank greedily. "West," he repeated. "Following the constellation of the Ishtainor."
"Let's look into it." Vailóras walked past and stroked his head, and another warrior pressed a coin into his hand.
Tanôtai brought up the rear. The inks in her skin were warming up; her heart was beating faster and waking the magic from its slumber. _Thank you, Inàste!_
The night-mares were swiftly saddled, then off they went.
"Form a line," Vailóras commanded as he rode, "so he cannot evade us."
The group fanned out, the black horses galloping through the night at intervals of fifty paces. Their red eyes gleamed, their hooves flashed as they hit the ground.
Tanôtai looked up at the stars guiding them. Her excitement was growing all the time; the wind caught in her red mane and made her look like a blazing fire. "He belongs to me," she screamed to her right and left. "It's my right to take his life."
Vailóras laughed. "I will not refuse a death-dancer her wish, otherwise you'll invite me to lead off a dance with you."
"Over here," cried the warrior on the left flank of their formation. "Tracks in the sand. They lead into the woods."
The älfar turned slightly and made for the woodland, which looked like one big black mass looming up in front of them.
The route between tree trunks would mean the night-mares would have to slow down, but Tanôtai saw to her relief that the trees were still relatively far apart and there was practically no undergrowth.
_You will not shake us off_ , she thought grimly and raced into the wood before anyone else. She briefly wondered why Aiphatòn was supposedly fleeing westwards when the passage to Tark Draan lay to the southeast of Dsôn Dâkiòn. _Because he wants to get his spear._
Thin branches cracked on either side of her under the horseshoes, the little explosions around the beasts' ankles flashed brightly, casting such bright light on the tree bark that it looked like a storm was raging in the middle of the copse.
Tanôtai saw the tracks up ahead of her left by their prey. _The armour is making him sink into the moss._ She urged her night-mare into a trot, gazing alternately upwards and downwards.
Then she saw a reflection up ahead. A figure was scurrying forwards under the cover of the trees.
"Up there," she called to the troops and dug her spurs into the stallion's flanks so that he started to gallop with a roar, catching up with the fleeing figure. The silhouette disappeared for several heartbeats every now and then, before reappearing again.
Tanôtai drew the needle-dagger from her left forearm guard. _I will slaughter you_ _from my saddle like a bull running wild. My magic will make the nape of your neck explode and make your skull fly through the air._ She would only embark on a dance if he dodged her initial attacks. _But that will not happen._
The red-haired älf-woman lost sight of him again for an instant. _Damn!_ She swung the galloping night-mare around to take him past a dead tree stump—when the figure suddenly stepped out from behind the stump and planted itself directly in front of the black horse.
The collision happened almost simultaneously.
But instead of knocking the emperor to the ground and trampling him with its hooves, the animal seemed to crash into an unshakeable pillar.
Bellowing, the night-mare fell forwards, was spun around and pressed its head deep into the soft ground; with a loud crack, its neck broke. The bones poked through its black coat and the red glow in its eyes went out. Its hindquarters jutted up into the air.
Thinking quickly, Tanôtai wrenched her feet out of her stirrups. In a high arc she flew over the motionless, blood-spattered figure, who was still standing there as if the heavy stallion had been a light, harmless fly.
Tanôtai thought she saw a copper-coloured helmet on her opponent's head as well as brown leather armour and a broken flagpole on his back.
Realising this was not the emperor they were looking for, she wasted no time getting into the low-hanging branches without injuring herself.
The red-haired älf-woman held on tight to one branch, slid down the foliage and hurtled towards the ground, although with a graceful spin, she turned this into a safe, catlike landing. The magical lines on her skin pulsed and heated up.
_What was that? How is he able to survive that without any trouble?_ She hurried back to the place where the collision had taken place, the needle-daggers in her hands.
But her opponent was no longer there.
It smelled of the blood flowing out of the animal, of resin and earth. The dead night-mare had visibly churned up the soft ground and the footprints of the enemy looked deeper than usual.
_Magic._ Agitated, Tanôtai listened to the sounds of the wood and picked up the noise of thundering hooves, saw the flashes and heard the alarmed cries of Vailóras and his warriors who had not realised what had happened to her.
The death-dancer ran off after the troops. "Watch out! That is not the emperor!" she cried over and over. "It..."
Suddenly she realised one explanation for the crash as well as the strange behaviour of the figure they were following. The scorching heat inside her intensified.
"Careful! Oh gods! Careful!" she shouted and made the blades light up so that she could be seen by her team. "It's a ghaist! A ghaist!"
Then there was a loud crashing and smashing and an enraged night-mare whinnied—and fell silent.
_Those damned botoicans. I thought the sovereign had made it clear to them they had no business being in our territory._ Too late, Tanôtai remembered the scouts the mind-controllers dispatched to look for villages and towns they could conquer with their mass magic.
A ghaist, as the cîani explained it, consisted of magic and many souls bound together in a fake human form. The copper helmet with runes on it was a distinctive feature of this unarmed creature, who could not be stopped by anything but immense heat. The warmth made the symbols melt and deformed the copper so that the souls could not be kept in their prison any longer.
Not that long ago, the cîani had used magic spells to crush the mob-like army of one of the botoican families as they ran about in confusion outside Dsôn Dâkiòn.
_They are getting cocky._ Tanôtai looked at the nearest dead night-mare and the motionless warrior underneath it who hadn't got his feet out of the stirrups quickly enough. It seemed the surviving mind-controllers had learnt nothing from the defeat. _I'll cure the Nhatais of that, even if I have to go into their dilapidated_ _town and annihilate their families. The sovereign just needs to let me do it._
The death-dancer checked the heartbeat at the jugular but the älf had passed into endingness.
"Vailóras!" she shouted and stood up. "Call off the chase. The cîani will have to take care of it." She listened out for the pounding of hooves to figure out where the riders were.
But the woods had fallen silent.
Completely silent.
"Vailóras?" Tanôtai cried and extinguished the blades so that darkness closed in around her.
From her right came the voice of the dark blonde commander cursing and then there was a swift, repetitive clanking.
_Who is he attacking? Not the ghaist?_ She ran between the tree trunks and spotted the älf facing the enormous fake human-warrior with the leather armour and copper helmet.
Vailóras was showering his opponent with blows from his batons, and his opponent was accepting the attacks without moving.
_Is that blood?_ The death-dancer had reached the pair. Black liquid was running down the ghaist's fingers and forearms, dripping onto the moss and bracken they were standing on.
After a quick look all around her, she realised where it was coming from: among the tall blades of grass she made out the corpses of the other warriors. Their bodies had been ripped apart, arms and legs lying scattered about, one torso looking like it had been prised open at the heart and disembowelled.
Tanôtai started to stumble, assailed by the smell of fresh blood and entrails. Death spurred her on, making her plot revenge and overwhelming her mind. "Wait, I'll be right there!" Finally she could give her powers free rein.
Vailóras turned his head towards her. "Run back and alert the cîani," he ordered her in a choked voice. "This is no ghaist as we know it!"
The creature suddenly yanked its arms backwards and thrust its upper body forwards, the slight ridge of the helmet on its forehead headed straight at the dark blonde älf's face.
Vailóras swept the batons into the air with one crossed over the other, the symbols on them glowing. It seemed he had no choice but to use his magic now. He tried to catch the ghaist by the throat and hold off the attack.
But the ridge of the helmet smashed into the middle of Vailóras' handsome face, crushing the nose guard along with the bones and the delicate flesh. Blood sprayed through the air. Vailóras was hurled backwards and vanished into the speckled bracken.
_No!_ Tanôtai raised her weapons.
The ghaist slowly turned the helmet with the narrow eye slits towards the death-dancer. The blood of the benàmoi ran down over the copper, trickling over the white botoican runes and tracing the lines, until he started moving towards her.
"I don't need any cîani to annihilate you. My magic is strong enough." Tanôtai did a full spin and the needle blades shone like the diamonds and lines beneath her skin.
As she did so, their surroundings suddenly took on their true daylight colours.
The ghaist gave a hollow snort, its muscular arms swinging forward and back. The fresh blood, in streaks and large stains on her approaching opponent's copper helmet, armour, forearms and fingers looked unexpectedly intimidating. The creature exuded unprecedented brutality and mercilessness.
She saw the openings in the polished helmet, nothing earthly hidden behind them; it contained nothing but powerful magic and bewitched souls.
_Vailóras deployed his magic and failed. That will not happen to me._ Tanôtai summoned her focus, went up on tiptoe and spread her arms out slowly from her body. "You will not survive this," she whispered to the ghaist and the light around them increased. "And then I'll come for your master!"
The creature dipped its head and rushed at her.
# Chapter XII
_A spring tide will be stopped by a net before a ghaist is stopped by a weapon._
Wise saying of the Älfar
Collected by Carmondai, master of word and image
Tark Draan, Human kingdom of Gauragar, 5452nd division of unendingness (6491st solar cycle), autumn
Carmondai heard the whirring and felt the draught of air passing directly over his brown hair after the click.
His heart pounding, he straightened up and saw the tree next to him was studded with numerous horn arrows. If he had not stooped down to the stick, if he had stepped on the tripping mechanism while standing up, the trap would have riddled him with holes from his navel to his throat.
_I'm not taking another step._ "Listen to me!" he cried in älfar. "I know there's a hideaway here. The entrance is in the granite tree trunk and I want to come to you and open it. But the mist is too thick. I can't see the tripping mechanisms on the traps."
His voice echoed forlornly through the wood. The clouds of mist rippled and twitched as if his words had reached inside them.
"I'm asking you: show me the way! I didn't escape my captors only to be sent into endingness by the swords of my own people!" Carmondai really hoped someone appeared. He didn't care if crazy Carâhnios died.
A very soft, scraping sound rang out, then a figure appeared at the top of the granite stump.
A fair-haired älf-woman wearing dark plate armour lifted a hand in greeting and looked around. She was holding one of the dreaded longbows in her other hand. "It nearly slit me open when I arrived. But don't worry: I'll guide you." She pointed to the right. "You're less than a thumb's width away from a second tripping mechanism, so do not move your feet without my say-so." She smiled. "What's your name?"
"I'm Carmondai."
"Not _the_ Carmondai?" She sounded just as awestruck as Ostòras.
He held up a bundle of pages. "I'll be happy to show you all the sketches I've drawn on the road despite my shackles, and what I've written too. As long as I survive the last steps to where you are."
"We ought to manage that." She laughed warmly. "My name is Rhogàta. Take three big steps forwards."
He did so. "Are you alone?"
"Yes. You're lucky I was still here." The älf-woman was watching him. "Stop. Now one to the left and five straight towards me."
Carmondai followed her instructions. "Is the hideaway not safe anymore?"
"It's safe. I was going to follow Votòlor to Oakenburgh."
_I know that town._ Oakenburgh was a medium-sized settlement in the south of the kingdom. In his day, there had not been anything special there to make it a destination for an älf to visit. The residents made a living from wood-cutting. The trunks of the rare blackjack oaks were floated upstream and processed in sawmills. _Why go there?_ "Is that to do with the liberation of our people?"
Rhogàta answered in the negative. "Two diagonally to the right, then you've got to crawl five paces forward."
"In the _mist_?"
"In the mist. Unless you'd like to touch the wire." Rhogàta looked around again and listened out for anyone who might have followed him. "No, there are no älfar to be freed from prison. A different mission altogether. You're very welcome to join us if you think you're up to it. I've heard you're capable of more than writing stories." She burst out laughing. "And this way I'll become a heroine in your stories too. As a child I used to dream of my name being celebrated."
"It will be." Carmondai ducked, crawled forward and when he stood up he was less than two paces from the trunk. A shudder ran down his spine when he realised he still had his rucksack on and it could have caught on the wire. "Are you planning an invasion then?"
"Not the usual kind. The barbarian-woman who seized the biggest swathes of our kingdom is due to pay a visit." Rhogàta held up her longbow as a clue. "We are going to send greetings from our people straight into her heart." She gestured around the trunk. "Now just come along this side and I'll open up the door for you as soon as you get here." Then she looked confused. "Is that a bottle in your right hand?"
Before Carmondai could respond, he saw the small figure detach itself from the thick branch six paces above the älf-woman.
Feet first and in free fall, the zhadár swooped down like a bird of prey, his unusual sword raised above his head, poised to strike.
Rhogàta must have heard a noise, because she spun round as quick as a flash with her face turned upwards. Her free hand shot to the hilt of her sword.
Then Carâhnios' sword struck her, splitting her skull vertically and continuing downwards despite the armour. The zhadár's boots crashed onto the little platform, his weapon going down as far as the älf-woman's middle. Now half split in two, she keeled backwards and toppled off the tree stump. Severed strands of black hair fell into the bloody stream.
"Hey, black-eye! I subdued her for you. Look alive and collect her blood." Carâhnios shouted the order from above, followed by sinister laughter.
_What was he thinking?_ Carmondai had to step around the body so as not to be hit by the spray—and there was another click.
A searing pain shot across his heels and took his legs out from under him. He fell head over heels and landed on his back and the rucksack. Somehow he managed to keep the bottle safe as he did so.
"What are you doing down there, scribbler?!" Carâhnios yelled.
"Surviving, hopefully!" Surrounded by mist, all he could see was a thin shadow swooping down from above and he tried to block it with his steel shackles.
The container shattered into pieces due to the impact, the shards hurting him as they hit his face. Sparks flashed as the blade struck the connecting part of the shackles and was brought to a halt.
"Have you found another trap?" the zhadár chuckled.
Carmondai needed all of his strength to stop the blade. It was now pinning him to the ground with a huge amount of unrelenting pressure. If it slipped off the metal of his shackles, it would plunge into the middle of his chest. _It must be a tense spring._
"Some help would be nice." Moaning, he slid down under his hands to get out of the danger zone and slowly release the sword. He saw the curved blade like a claw dangling right in front of his nose. That's apt considering the legend.
Carmondai kept moving, his arms burning and trembling with exertion. _I can release it very soon._
"You'll manage," Carâhnios remarked. "But what made that clinking sound just now? Don't tell me it was the bottle!"
There was a second click.
The hook-shaped blade was suddenly pulled forwards, catching on the connecting part of the handcuffs and dragging the älf face down over the damp, cold, mossy floor until the ground suddenly vanished and he was rolling down an embankment.
"Hey! Hey, come back!" shouted Carâhnios, outraged. "You know what will happen if you breach the agreements. I swear I will find you!"
Carmondai could not speak. His fall ended in a pit full of decayed skeletal remains. One glance was enough to tell him they had been animals.
_That was quite a trip._ Carmondai groaned as he stood up and started removing the splinters from his face before making his way up the slope and following his own trail back to the tree trunk. That hadn't done the aches and pains in his old body any good, he had to limp to relieve the pressure on his right knee with its stabbing pains.
"Good. You've come back voluntarily." Carâhnios was waiting for him in the entrance to the hideaway and, deadly serious, holding out a shard of the bottle to him accusatorily. "What did I vow to you earlier?"
"The platform is swimming with Rhogàta's blood, it's running down the trunk and seeping into the soil. Oh yes, and it's in your beard," he countered. "How was I meant to collect it?"
The zhadár's gaze fell on the iron handcuffs and the grooves the sword had left behind. "Am I seeing things—or did my shackles save your life?" He burst into such peals of laughter that he must have been audible for a radius of more than four miles in the quiet woodland. "Now _that's_ what I call Samusin's work!"
Carmondai briefly described what had happened to him. "I assume that trap is meant to make it look like the victim has been seized and dragged off by the beast."
"Seems that way to me too." Carâhnios sniggered, squeezing the älf-woman's blood out of his facial hair. "I'll admit her death was not intended to be like that. I overestimated the force."
"From six paces in the air? Yes, it really took her by surprise. She literally burst with joy," he remarked cuttingly.
"Let's say this: since neither of us did our best work, I'll forgive you and let you keep your blood. Especially as I know where I can get some more soon." He pointed to the opening in the trunk. "This is the entrance, by the way, but I've already been inside. Disappointing. Barely any different from the first hideaway."
"I'm going to take a look anyway so that I can describe and draw it." Carmondai looked quizzically at the zhadár. "Is the third sanctuary nearby?"
"How did you figure that?"
"Because you said you'd get new blood soon."
Carâhnios pointed south. "If we hurry, we'll make it by daybreak."
The short distances between the hideaways made no sense to Carmondai. "Is there a tunnel between them, why are they so close together?"
"Who said anything about a hideaway? I'm talking about Oakenburgh."
"The attempt on Mallenia's life." He had not considered that. "You'll be a hero if you save the life of the Queen of Gauragar and Idoslane."
"True, true." Carâhnios suddenly smiled that crazy grin he could have impressed demons with. "If it arises, I'll do it. But I'd be content to catch the älf." He pointed to the entrance. "Now take a look, draw like the wind and then we'll get going." He grimaced. "Remind me, I need to go to a glassmaker. The bottles are running low."
_He would allow Mallenia to go to her death. And yet they are allies._ Carmondai was more than a little taken aback and he gave up trying to understand the zhadár. The creature was different from groundlings and älfar, he had both good and evil in him. _The last drop of the new distillate seems to have pushed him much more towards the evil._
He entered the hideaway and found a narrow staircase leading downwards. Phosphorescent moss provided enough light to make out the steps.
His plan to kill his crazy guard soon, before he lost his own life in the hunt for älfar—due to traps, villagers or one of Carâhnios' whims—crystallised. _Take any more of that elixir in my presence and you will die._
Ishím Voróo, Eleven miles from Dsôn Dâkiòn, 5452nd division of unendingness (6491st solar cycle), late summer
The long, narrow boats with their big, triangular sails swept up the Tronjor so quickly that Aiphatòn was astonished. _You'd think they did this every orbit._
The wind was favourable for the attackers and they had passed the rocky bottleneck. Aiphatòn's suggestion to lead a separate party on ahead had been rejected so he was forced to travel with the troops.
The ships were noticeably different from the rònkes and the escort sailboats. They had been invented purely to travel upstream and get to Dâkiòn. It appeared the älfar had had it with keeping the peace. The large three-masters were outside the mouth of the Tronjor awaiting their return.
_We'll get right up to the town in just a few orbits._ Aiphatòn was on the first of almost a hundred vessels and was preparing to be dropped off on land with a small troop. They had been given a special task that would be vital in gaining further ground.
Irïanora was standing less than two paces away from him. The blonde älf-woman was wearing the white armour of the Elhàtorians, but to set her apart, she had been given red armbands. She had insisted on taking part in the venture.
Aiphatòn would have suggested it anyway. For one thing, she knew her way round Dâkiòn, and for another, she would be some useful leverage. _Maybe not for using against Shôtoràs, but with the warriors they met along the way._ The sight of the sovereign's niece could provide the vital hesitation he needed in order to fire the first arrow. What's more, Irïanora had friends in the town who would no doubt want her back alive and would insist on negotiations.
Aiphatòn went and joined her. "Is this how you pictured your return?"
She glanced at him briefly and then looked straight ahead again. The landing manoeuvre was beginning, the right bank drawing closer. "I assumed I'd never see my homeland again," she drawled.
_Now I'll sow a little uncertainty._ He folded his arms across his chest. "I've seen your antipathy towards me and your badly faked horror when the declaration of war was made," he said softly. "I'm telling you: you're _glad_ about it. And you're probably wondering how to lead the troops from Elhàtor into the trap."
"Nonsense," she retorted indignantly. "A lot has changed and..." She faltered. "I've lost my heart to Ôdaiòn. How could I betray the älf I love?"
_We've got a little actress on board._ "And the älf who will enable you to live the life of a monarchess, which you might never have been in Dâkiòn," he continued her sentence and laughed at her. "I may quite clearly be the same age as you, but in terms of experience you're no match for me, Irïanora. You're being toyed with the same way you imagine you're toying with others." Aiphatòn looked over at Ávoleï who was just swapping her white armour for brownish-green armour to stand out less in grassland. "You're a useful playing piece to her. Nothing more. Nobody will hesitate to kill you if the situation calls for it. And Ôdaiòn would be the first to rip your oh-so-loving heart out of your body."
Irïanora was giving him a contemptuous look now. "You Tark Draan scum," she hissed.
"Just like the monarchess of the town, whose son you want to take as a husband," he countered. "You don't fool me. In your shoes, I'd be wary if Ôdaiòn approaches you. Once he's had his fun with you, he'll cast you aside. Pray that you can still seem useful for a long time. Maybe neither your uncle nor the monarchess' son will want you. What are you going to do then?" Aiphatòn was getting ready for the ship to land. _That will have made her anxious enough and lead to mistakes. Let's see what she does._
The flat bow of their ship made its way up the shallow gravel beach.
The crew jumped over the ship's side and made it fast with ropes as well as long iron rods that were hammered quickly into the ground.
More and more of the other vessels came alongside, deliberately running aground. The fleet of a hundred ships temporarily dropped anchor to allow the remaining river ahead of them to be explored and to avoid sailing into the defending forces' traps.
Elhàtor's secret boats could be dismantled and reassembled into scaling ladders and catapults designed to cause trouble for the defending forces. They could also be made into bridges to get across any gaps in case the sovereign ordered the entrances to be demolished. Along with the thousands of warriors, there were cîani who were thoroughly prepared for the conflict.
"Do you think they'll let you return to your subjects in Tark Draan if you get your spear back?" Irïanora whispered.
"Who's going to stop me? You? How? With your gift of bad acting?" He saw that Ávoleï was approaching them, followed by a group of twenty warriors in the camouflage armour; in her left hand she was holding a rolled-up map. "I advise you to get yourself to safety as long as you still can. One of the soldiers will be under orders from Modôia to kill you. She wants to see Ávoleï at her son's side, not you."
"He and the elf-woman?" she spat. "Ridiculous. Ôdaiòn doesn't like her." She turned to the commander.
_Elf-woman?_ Aiphatòn hoped his surprise was not obvious, especially to Ávoleï, who had just joined them. It explained what was making him feel uneasy, no matter how attractive he found the commander.
Ávoleï spread the map out on the railing, with the exact course of the river plotted on it. "We've reached the first safe landing point," she explained.
Irïanora took over the explanations unasked. _Probably to justify her presence and make herself indispensable after his warnings._ Aiphatòn grinned as the blonde älf-woman pointed at various parts of the map. "Those are shallows where whirlpools form quickly. The ships could be pushed sideways and end up with their broad sides to the waves," she elaborated. "I recommend you keep your distance. At least two lengths."
Ávoleï's forehead furrowed. "That's not the issue at all."
"No?" Irïanora looked at her, then at Aiphatòn as if afraid she was about to be attacked by him. "I thought..."
"What do you know about the supplies of petrol that have been stockpiled further up the bank?"
The sovereign's niece swallowed and placed one hand on her stomach. "I'm hearing about it for the first time," she admitted after a brief hesitation.
Ávoleï nodded. "That's what I thought. So it's not for nothing we've had the Tronjor under surveillance for many divisions of unendingness." She picked up a compressed coal-dust pen and marked several bends. "Behind these bends, barrels have been buried in the embankment, each guarded by a platoon of around ten men." The black-haired elf-woman nodded to Aiphatòn. "You go with some of the warriors, investigate the right-hand bank and secure the supplies. I'll take the other side with the rest of them."
He looked at the turns in the river. "A simple option to put the fleet out of action." _And that must be prevented at all costs. I need a huge battle with thousands of casualties. Burnt-out ships are no good._ It was a struggle to hide his continued surprise. _An elf-woman and yet... I would never have suspected it._
Irïanora looked miserable. She had realised that she was no use for the time being. Her knowledge was out of date. "I didn't know anything about it," she insisted.
Ávoleï didn't even look at her as she replied. "You also didn't know anything about the canal that Shôtoràs is having dug that flows into a hollow. We're assuming he wants to dam up the Tronjor in there and drain it. If he did so, our plan could no longer be put into action."
"Then we've come at the right time." Aiphatòn unrolled the paper further, his eyes fixed on the sketch of Dâkiòn, the river in front of it, the outlines of the canal and the weir. "You're right. No boat would have been able to use the river anymore."
Ávoleï rolled up the map. "We'll move along the banks in parallel and maintain eye contact. As soon as we've secured the petrol supply, let's pass a message downstream so that the fleet can follow slowly," she explained. "In complete secrecy, we and our scouts will work our way as far as the small fishing port two miles from the town."
He placed a hand on the map. "But what if Shôtoràs is keeping more barrels of petrol hidden upstream from the village? As a last resort?"
"Then we'll have come far enough to be able to walk the rest of the way through the swamps. I think my warriors are just about capable of that." Ávoleï put away the rolled-up parchment. "Don't go too far from the bank. After more than twenty paces, the bog, swamp or quicksand starts. All three will kill you."
"Let's get going." Aiphatòn turned down the proffered leather armour in camouflage colours and placed one armoured hand on the railing. "Whichever of us gets to Dâkiòn first owes the other one a favour."
He gave Irïanora another look to remind her of his comments on her safety. _I hope she does something rash. Ideally she'll try and attack Ôdaiòn._
He vaulted energetically over the wood and landed on the flat shingle, running off immediately without paying any attention to whether the warriors allocated to him were keeping up with him. _They ought to see how much I want my spear back._
Aiphatòn was following the simple plan of accompanying the attacking troops to start with and then making his way on to Nodûcor alone. The wind-voice signified the end of all worries and fears. Not just for the towns. _With him, I can ensure the definitive safety of Girdlegard. Dâkiòn will fall first, then Elhàtor._
"Not so fast," he heard the quiet but irritated cry from behind him. "Ávoleï still has to cross to the other side."
Aiphatòn slowed his pace and mulled over the sequence of his plan.
With Nodûcor, he would exterminate the älfar all around Dâkiòn with storms and hurricanes, then he would go to Elhàtor and destroy that town wave by wave too. Finally, it would be important to demolish the path through the Grey Mountains that could be used to smuggle the beasts from Ishím Voróo through the valleys and ravines.
_This is going to be a spectacle!_ Aiphatòn pictured rock faces collapsing, peaks sliding down and making new slopes. The winds would give the mountains a new silhouette. _Nobody will travel that path again, the one Leïóva and Modôia took. Not monsters, not botoicans or any other creatures who have come in the hopes of conquest._
He hurried along the embankment; on the other side of the Tronjor he could see through the ferns and creepers a sweaty Ávoleï scurrying along and scowling at him. She had had to hurry to keep pace.
_Eventually I'll kill Nodûcor. And myself._
If Nodûcor were not the wind-voice as everyone supposed, there was always the war between the towns to eradicate the last älfar.
Aiphatòn almost had an attack of conscience about obliterating kingdoms that seemed to have become harmless. But the behaviour, the intrigues, the speed with which they went to war, all triggered the reassuring realisation that the älfar in Ishím Voróo hadn't changed so much that they deserved mercy. Especially not in view of their magical power.
The ten men under Aiphatòn's command dashed through the thicket.
There was a smell of decay whenever the wind from the swamp blew towards them. It was only along the river that they could breathe the air without their stomachs heaving.
Swarms of flies became their constant companions, settling on their skin and stinging them to get at their blood. It hurt, as if they were secreting venom. The bites swelled up and turned red.
_We should be at the first bend soon._ Aiphatòn didn't even consider slowing down, no matter how much he could see Ávoleï gesticulating out of the corner of his eye.
He was glad that the painful prickling was subsiding. Magic fields really did seem to be the reason for the agonies he suffered along with the monarchess and all the other älfar from Tark Draan. _For two hundred cycles._ He couldn't help admiring her self-control.
"The commander wants us to get there at the same time," a soldier whispered angrily behind him. "Go more slowly, aren't you listening?"
Seamlessly, he stopped, grabbed the rebellious warrior by the throat with his armoured glove, lifted him up and pinned him to the ground.
"You," he whispered menacingly, "are under my command. And you will do what I tell you. If you dare try and advise me again, you'll end up in the quicksand." He dragged him to his feet by the neck, let him go and turned around.
Aiphatòn continued running, faster than before, to make up for the lost time that the reprimand had cost him.
This time there was no grumbling, only the soldiers' wheezing coughs.
The bend appeared ahead of them.
The petrol supply was expertly hidden. Aiphatòn couldn't see the barrels or the troops from Dâkiòn who were watching over them, waiting until they saw the fleet to smash the barrels and set the river on fire.
He ordered his warriors to crawl so they could approach unseen and unheard. "I'll go first."
Aiphatòn chose a different route, however: he slid silently into the water and made his way upstream by hanging from the roots, finding that the water was pleasantly warm and reduced the itching from the bites. His armour plates were light enough that there was no risk of him sinking to the riverbed like a stone.
It was only once he was in this position, with his eyes just above the flowing Tronjor, that he could make out the small recess in the steep bank on the opposite side—it lay hidden underneath the dangling ferns, roots and bushes. _They've dug out an old water vole burrow and extended it._
He could make out definite movements inside it.
Aiphatòn's gaze swept along the embankment looking for Ávoleï.
The elf-woman was moving towards the lair, but she was going to pass over it.
_She'll miss them, and they'll be alerted!_ He had to do something. Aiphatòn took a deep breath, then sank down and propelled himself forwards.
He glided along underneath the surface. Swimming underwater was easy with the increased weight from the metal on his body.
The current caught him, but he held his own against the pressure and the dangerous pull and reached the other side of the Tronjor.
He put his head up out of the water cautiously.
The recess was just ten paces upstream—the river had made him drift slightly.
He moved forwards quickly by hanging from the vegetation on the embankment, getting closer and closer to the burrow. He could hear a quiet conversation coming from it about the relief shift being late.
Then the warriors from Dâkiòn fell silent as Aiphatòn skilfully groped his way up to the opening. The fact that the water was hitting him in the chest with a quiet splashing sound didn't attract any attention.
The soft tinkling coming from the recess did, however.
Aiphatòn peered inside and saw ten armed figures sitting in the spacious burrow, all straining their ears; four little strings of bells dangled down in front of them from the reinforced ceiling and every single one of them was shaking. _Trip wires._ Ávoleï and her team had set off the alarm.
Aiphatòn watched as five guards got ready and grabbed their bows, while three others climbed on top of the petrol barrels and picked up chains linked to a series of bungs. The last two got torches and lit them over the little coal brazier.
_Ávoleï will have to see for herself how she deals with those five. I'll take care of the barrels._ He could clearly see that two of the guards had short signal-whistles between their lips. Presumably they blew into them during times of danger, transmitting the sounds to sentries further upriver. _Our plan would be done for. We could just turn back or set the ships on fire straight away ourselves._
The archers left the cave.
Aiphatòn lay flat in the Tronjor like a predatory water lizard, cautiously drawing in his legs so that he could catapult himself out of the river.
When he heard a cry of surprise from the steep bank above him, he sprang out of the river and rammed into the three guards, sending them flying off the barrels. Meanwhile, he put one foot on the chain that linked the barrels as quick as a flash to stop any pressure on the bungs.
One warrior did manage to pull on the handle of the chain as he fell but Aiphatòn's boot blocked his attempt to remove the stopper. The three soldiers fell backwards in between the containers and vanished for the time being.
After a brief instant of shock, the torch-bearers attacked him with the burning ends of their torches.
The blows rained down uselessly on Aiphatòn's wet plates; sparks flew, hissing and glinting.
"You should have used swords." He stood his ground with furious punches from his armoured fists and knocked his attackers to the damp floor with split chins and shattered cheekbones; both of them had swallowed their whistles.
One of the three soldiers had worked his way out from between the barrels and drawn his short swords. He jumped down and attacked at the same time.
Aiphatòn caught one blade in his metal-encased hand and snapped it, and he let the other blade slam into the plates of armour on his chest. The impact made him stagger slightly and he fell to his knees. As he did so, he did one full turn to absorb the force.
He used the momentum to hurl the broken sword fragment at a second älf who had just appeared between the barrels. Struck in the torso, the enemy collapsed, dying, and lay on the container.
Aiphatòn dealt the soldier directly in front of him a punch to the crotch with his armoured left hand, standing up at the same time and slamming his shoulder plate into the groaning älf's chin so that he fell backwards and stopped moving.
_Still one to go._ Aiphatòn took a spear off the wall and looked around.
He found the last warrior wedged between the barrels, wriggling. His armour had got caught.
"Aha. That's inconvenient, isn't it?" He lowered the tip of the spear to the warrior's throat. "You would have done the same." One stab was enough to send the last sentry into endingness. _Now_ _the fleet is safe as far as this bend._
Aiphatòn climbed up the narrow ladder the archers had used to leave their lair—and his head emerged into the open, directly behind one of the enemy warriors.
He pulled his legs out from under him with the shaft of the spear so that the ambushed warrior fell at his feet. Then Aiphatòn broke the warrior's neck by hitting him with the side of his hand.
Aiphatòn was cautious as he emerged fully out of the hole. He could very clearly hear the soft whizzing of fired arrows. _It seems like Ávoleï could do with some help._
The immediately muffled cries of those who had been hit rang out from further away. The archers had let the elf-woman and her troops pass by so that they could kill them from behind.
Aiphatòn crept through the ferns.
Another archer stood less than eleven paces away from him and pulled a long, black arrow back on his bow string quite some way.
_I should have taken more spears with me._ He gauged the distance and threw.
The missile plunged sideways into the shoulder of his enemy's drawing arm and on into his neck where it stuck fast. The archer was dying as he fell among the tall, serrated leaves.
Aiphatòn ran over to him, braced one foot against the dead body and pulled the spear out. He then tossed it in one fluid motion at an archer who stepped out from behind a tree trunk and was aiming at him.
"Here's another!" the voice of his enemy warned, before the lethal tip of Aiphatòn's spear bored into his chest and pinned him to the tree.
_He's calling them over to me. Perfect._ Aiphatòn allowed himself a grin and ducked under the cover of the ferns like he had under the waters of the Tronjor earlier.
He lay still, straining his ears, and drew the dagger from the sheath on the dead body next to him along with a sheaf of arrows from the quiver.
Soon he heard the noise of stalks brushing over leather and clothing. Barely audible, an overstretched string creaked, held taut by the archer.
"There!" whispered someone.
The string whirred. An arrow hit its target nearby and another stifled cry rang out.
_There are two of them._ Aiphatòn raised his upper body, spotted his enemy and sent the dagger flying at the archer, just as he reloaded.
The tip struck him from behind, level with his right kidney. Moaning, he fell to his knees and dropped his bow.
The last enemy had turned away from Aiphatòn and was aiming straight at Ávoleï who was standing between the trees and preparing to throw a sword.
_That's not going to save her!_ Aiphatòn immediately hurled the sheaf of arrows at the soldier and leaped to his feet to give chase.
The momentum of the arrows might not have been enough to penetrate the armour, but a dozen arrowheads pierced his arms and legs superficially. In the end, Aiphatòn achieved exactly what he had hoped for from his attack: one of the blades severed the bow string in the crucial instant before the archer let it go to shoot Ávoleï with an arrow.
Then Aiphatòn was close and smashing his fist into the back of his opponent's neck at top speed so that he was knocked face-first onto the ground and lying motionless with broken vertebrae before he could even utter a scream.
"So my debt is settled then," he yelled at the elf-woman and turned around. _Where did the other one get to?_
The injured enemy was groaning as he crawled commando-style through the ferns and tried to pull the dagger out of his back.
Aiphatòn reached him and pulled him up by his mop of fair hair, yanked the weapon out of his wound and saw the blood and a pale liquid spurting out; the smell of urine spread. "How many people are with the barrels?" he said quietly.
"Die," snarled the warrior and tried to break the grip on his hair with both hands, but couldn't manage it. His dirty fingers slid uselessly over the armoured glove.
Ávoleï came to Aiphatòn's side, pale with anger. She rammed her sword into the injured warrior's stomach and twisted it. "Shooting my men dead from behind like a coward," she whispered, "is not an act of heroism!"
The älf from Dâkiòn uttered a high-pitched sound, his eyes rolled back and his eyelids fluttered.
Aiphatòn felt the warrior go slack. _Dead._ He dropped the body. "How many of your troops died?"
"All of them," she replied, filled with hatred.
_She's a beginner. She won't have called more than a handful of rebellious fishermen or cowardly pirates to account as commander._ "Welcome to war, little _elf-woman_ ," he remarked.
"How did you know...?"
"You mustn't take it to heart if you lose against warriors. See it as a game where you need to budget very carefully."
Ávoleï looked at him in bafflement, remaining silent for several heartbeats. "A game? That's what you call it in Tark Draan?"
"It's like with Tharc. The enemy carry out their job, we do ours. What matters"—he walked over to the tree and pulled the spear out of the trunk and the enemy's corpse—"is that at the end of the battle, we are the victors." He tipped the dead body to one side. "That's the best way to honour the ones who have fallen." Aiphatòn wiped the blood off on the ferns. "I suggest that I continue on with my troops and you. You would only lead new warriors into another trap, after all."
Ávoleï scrutinised him, a bead of sweat running down her right temple. He saw appreciation, awe and fear in her eyes.
_It's time to sow more uncertainty. I started with Irïanora, and I'll continue_ _with Ávoleï._ Aiphatòn smiled calculatingly. "I'll take that as agreement." He took a step towards her.
"What?" The elf-woman shrank back a step.
"This." He moved toward her, grabbing her by the neck and drawing her lips to his.
To his astonishment, Ávoleï did not resist his caress, she breathed faster.
Aiphatòn let her go.
She glared at him, furious and confused. "What was that?"
"Just a foretaste of the favour that I'm going to call in from you." He went to the embankment and waved to his warriors on the other side. "You remember? Whoever reaches Dâkiòn first?"
The stunned looks he was getting from the troops made it clear that they had been watching the kiss.
_Excellent. There will be gossip and then it won't be long until she's no longer trusted. That will weaken the army. And Ôdaiòn ought to hate me even more because it will look like I'm becoming_ _his rival._ "The relief shift is on its way," he told Ávoleï, turning to the surprised elf-woman. "We ought to hurry and intercept them."
She didn't seem to be over her shock yet. She nodded mutely.
"Let's join my platoon." He took a run-up and jumped into the middle of the Tronjor, then swam the remaining paces to the bank.
Although Aiphatòn had not particularly enjoyed the kiss at first, he could still feel Ávoleï's lips on his mouth.
There was no longer any trace of his antipathy, truly _none at all_.
_That_ was not something that could have been foreseen, however.
Tark Draan, Human kingdom of Gauragar, Oakenburgh, 5452nd division of unendingness (6491st solar cycle), autumn
_If I were an assassin, this is where I would lie in wait._ Carmondai was crouching on the roof that Carâhnios had forced him onto during the night. He was looking at the Elria Temple and the wide road that led up to it before making a sharp turn westwards. _The line of fire is clear and it's not too far away. He could fire four times before a bodyguard would be able to respond._
The young queen would take this route to make her entrance to Oakenburgh, if he was correctly interpreting the plethora of stalls pitched along the road.
The small town looked like many others with its half-timbered houses at most three storeys high—with the exception of the mayoral building and the temple—and colourful, painted façades, the brown or white shutters and the simple red clay roof tiles.
_Tranquil_ was the word that came to Carmondai's mind, which was a euphemism for _boring_. _As ever, the barbarians don't let art into their lives, their streets or their squares._
Yet again, he didn't know where the zhadár had got to.
Carâhnios had taken off immediately after they'd arrived and ordered him to stay in the shadows on the roof to get a bird's-eye view of everything. The groundling would draw attention to himself in good time. Nobody was meant to know anything about their arrival in Oakenburgh because that would frighten Votòlor and stop him continuing with his mission.
The residents, full of anticipation, never suspected that certain death could lurk round every corner. Twine had been stretched across the streets and banners hung from it emblazoned with large-lettered greetings in honour of the Ido woman. There was a great atmosphere in the alleyways and streets, the Gauragar standard pennants fluttering in the cool autumn wind. The woodland's blaze of colour seemed to be reflected in Oakenburgh.
Carmondai crawled commando-style to the chimney with whitish-grey smoke billowing out of it and hid. He stifled the urge to cough. His sketching was coming along very well despite his reddened eyes. Carâhnios had even taken his shackles off for this, adding the threat, of course, that he could hunt him down any time. _At least this time his plan doesn't entail me having to hold that bottle. Watch, wait, record._
He was intrigued as to what kind of performance Carâhnios was giving in front of the Gauragarians. The news of the existence of the zhadár had done the rounds. But being changed for the worse by älfar magic and drinks didn't necessarily cultivate a good reputation. No amount of self-sacrifice would help.
Carmondai looked around incessantly, noting details and jotting them down, from the tent stalls and the traders with trays around their necks to the snack bars.
Musicians were rehearsing their melodies on the little square for the fifth time but he thought it would have sounded better with tuned instruments. Small children were being given baskets full of brightly coloured leaves and the last blossoms of this cycle to scatter before the queen.
Carmondai took out the sketch he'd done where he'd tried to get her features right. _I'm excited to see how close I got._
More and more residents appeared, their murmuring and chatting melding together; from his position on the roof it sounded like slowly falling rain. The stirrings on the square and along the road stoked speculation the dignitary was to arrive soon.
The beggars also pushed their way forward to get their share of the Ido woman's generosity and surely the cutpurses were sneaking through the crowds, getting ready to slip their newly acquired riches into their own pockets in one swift, expert movement.
_I'll make a sacrifice to Inàste if I make it out of Oakenburgh in one piece._ Carmondai still didn't think it was a bright idea not to warn Mallenia. If the attack was successful and the älf and the zhadár were caught, the incensed mob would string them both up.
_Provided we let it happen._
He had no interest in a fight against an angry mob, especially as he had no usable weapons on him. Besides, there would be survivors in Oakenburgh; the news would have repercussions in Girdlegard and bring more trouble with it.
Just briefly, his time in the Aklán dungeon seemed temptingly safe.
But the more Carmondai thought about it, the more a plan formed that—if it could actually be put into action—would free him from Carâhnios in Oakenburgh.
Finally a horseman raced down the street waving a banner as he shouted over and over: "They're coming! They're coming! The queen and her entourage are coming!"
Carmondai ventured out of the smoke, staying in the shadow of the smokestack which he intensified using älfar powers. _Will I be able to see you, Votòlor?_
He was undoubtedly an observant onlooker, but it was not easy to spot an älf-warrior if they absolutely did not want you to do so.
There came the sound of multiple hoofbeats, then the first armed soldiers came riding round the bend and turned onto the main street; the flags of the two kingdoms of Idoslane and Gauragar were flapping on their upright lances.
The crosswind and the cloths fluttering everywhere would make it harder for the assassin, but Carmondai estimated three or four shots would be possible.
No matter how hard he tried, he couldn't see Votòlor or make out a conspicuously darker shadow where the assassin could be hiding, lying in wait.
Mallenia of Ido appeared around the corner with her courtly entourage after twenty soldiers. She was indistinguishable from the armed riders around her at first glance.
The tall woman had strapped on light plate armour with the coat of arms of her ancestor, Prince Mallen of Ido, engraved on it. She kept her long, blonde hair back in a braid that dangled down between her shoulder blades. Her thin crown, more like a headband made of silver wire, was not particularly eye-catching. She carried two short swords at her side.
Cheers rang out, the musicians let rip and in their excitement promptly played so badly out of tune that Carmondai grimaced in pain.
At the sight of the symbol on her armour he thought of Mallen of Ido, the brave ruler who had opposed the traitorous magus Nôd'onn and also fought against the eoîl. The young queen made no secret of the fact that she saw herself, like her ancestor, as a warrior and not as a dolled-up, expensively dressed piece of eye candy on the throne.
Carmondai looked back and forth between his sketch and Mallenia. _Not a bad likeness, I'd say. My imagination is reliable._
A glance at the temple revealed nothing unusual and there was no sign of Carâhnios.
_Maybe they've killed each other._ The idea brought a smile to his face, even though that would thwart his own plan.
A delegation from the town broke away from the ranks of curious onlookers. Marching at the head of it was the mayor, as the imposing chain around his neck and chest made clear, and behind him came the representatives of the guilds and the council leaders.
Mallenia's convoy came to a halt, the mounted soldiers forming a passageway through which the mayor could walk to the queen. The flower girls and flower boys were hastily pushed to the front and scattered the mixture of blossoms and leaves, bringing a warm smile to the young ruler's face.
_The line of fire is clearer than ever._ Carmondai thought the two soldiers at Mallenia's side might have been vigilant but by the time they'd have raised their arms with their heavy shields, two black arrows would be lodged in the young woman's heart. The plate armour she had selected was no match for the extra-large älfar arrows. The polished arrowheads that had been designed to be used against this kind of armour would probably come out again on the other side.
"We are delighted, Queen Mallenia of Ido, Ruler of Gauragar and Idoslane, that you are visiting our town on your way through the kingdoms," the mayor cried solemnly, and was handed an oversized key by the guild chief. "Take this as a symbolic gift that our gates are as open to you as our hearts, Queen." He walked at a measured pace with the guild chief through the cavalry's guard of honour.
_As open as our hearts? What a trite image. Surgical instruments would have been an appropriate symbolic gift._ Carmondai was surprised there had not yet been any soft whirring sound. _Carâhnios has probably tracked him down and intercepted him._
He heard the quiet creak of a string growing taut next to him.
He turned in surprise and saw an älf standing in front of the chimney, taking precise aim over the shaft of a black arrow. He was wearing black leather armour, his dark hair tied up in a band at the nape of his neck. The polished arrowhead was presumably aimed at the queen's heart; two more arrows were leaning against the brickwork.
The assassin turned his head to Carmondai and winked once.
That winking—combined with the evil smile—said it all.
_They're meant to think I'm to blame._ He looked at his sketch of the queen and it looked like an accusation already.
Before Votòlor could release his finger from the string, Carmondai swung around and pulled the assassin's right leg out.
The älf recovered from the impending fall but the arrow he had accidentally released misfired.
The projectile whizzed, unnoticed by the locals, through a banner and lodged in a beam a hundred paces away.
Votòlor dropped the bow and drew a dagger out of its sheath, hurling it at Carmondai. "You miserable traitor!"
He was too close to dodge the attack completely. Turning round was only partially successful—the tip of the blade plunged into his left shoulder instead of his heart.
Carmondai fell backwards. _Damn it! But you haven't got me yet._
Nobody in the street noticed the silent struggle on the roof.
The assassin had picked up the bow again, taken aim and fired—just as Carmondai pulled the dagger out of his shoulder and threw it back at him.
The blade struck Votòlor underneath the shoulder, while the arrow whizzed into the chest of the bodyguard next to the queen. The polished tip penetrated the metal easily.
The man slumped forwards very slowly and fell out of his saddle, crashing to the ground next to a terrified flower girl. Shouts started up in the street.
_I am definitely not dying for you._ Carmondai had got to his feet and now threw himself at his opponent, who couldn't pull the dagger out. He dropped his bow and drew his sword.
Carmondai dodged a whirring blow and hit the hilt of the lodged dagger to drive it deeper into his enemy's body.
Screaming, Votòlor pushed him away.
Carmondai toppled backwards onto the roof tiles and only just escaped the next blow, the blade slicing into the fired clay.
"How can you betray your own tribe?" The assassin kicked Carmondai in the head, sending him to the edge of the roof. "I could have killed her!" he hissed and prepared to strike again.
"Not at my expense," Carmondai retorted in a daze.
"You're going to..." Votòlor didn't get any further. With a soft whistle, six arrows struck his upper body, making him stagger. Groaning, he fell sideways and plummeted into the depths.
They missed Carmondai only because he had taken cover. _I'll only avoid death if they all know that I saved the queen's life._
He held up the bundle of white pages and waved it as a symbol of surrender. "Don't shoot," he shouted in the language of the humans. "I foiled the attack on the queen, do you hear? I _foiled_ it!"
"Stand up, black-eye!" came the cry.
_Inàste, think of the sacrifice I'll make for you._ Getting gingerly to his feet, he looked over the edge and spotted ten archers aiming at him. "Here I am."
A healer was already tending to the wounded bodyguard and Mallenia was surrounded by more soldiers. Amid the sudden horrified silence came the sound of many blades being rammed relentlessly into a body. Several warriors were making sure that Votòlor was dead.
"Look!" As proof, Carmondai brushed the paper over his wounds and showed them his blood. "We fought, I pushed him down."
"Come down from the roof," Mallenia commanded, her face a picture of rage. "If you make any sudden movement, my archers will shoot you dead."
Carmondai nodded. "Right away. But forgive me if it takes a while. It's the wounds and my age." Suddenly he noticed a ragged beggar who, unlike the other unkempt people and the rest of the villagers, was creeping surreptitiously through the crowds.
Just three more paces and a powerful leap and the man would reach the queen.
The tale-weaver's blood ran cold. _How did it not occur to us that there could be more than one älf?_
If the second assassin were to attack, the archers would also shoot at Carmondai because they would consider him an accomplice providing a diversion—which he ironically was doing an extremely good job of right now.
_I've got to warn them._ "There's another one there!" he cried and pointed at the beggar who ran away and slipped his cloak off at the same time. Black armour appeared from underneath it, and two slim maces gleamed.
The outcry from the crowd blended with the cries of the surprised warriors and the whinnying of the startled horses.
But it seemed Carmondai's warning hand gesture had been too quick, and the chaos too great: a hail of arrows whirred up at the roof.
He did not have time to take cover.
Ishím Voróo, Älfar town of Dsôn Dâkiòn, 5452nd division of unendingness (6491st solar cycle), late summer
On the evening of the fourth moment, Aiphatòn, Ávoleï and the ten warriors glimpsed the enormous mountain and the contours of Dsôn Dâkiòn through the undergrowth, shining far and wide in the light of the setting sun. The golden bridge was all aglow.
"We've done it." Ávoleï knelt down on the dry border of the overgrown riverbed and wrote some messages that she then floated down the river in inflated leather pouches.
_That was too easy and full of unexplained incidents._ Aiphatòn looked back and forth between the river and the town.
They had made good progress, constantly sending news back to the waiting fleet. They found one cache of barrels after another as well as two chains that had been strung up just below the waterline. The ships would collect the barrels on their way upstream so that the petrol could be used in their attack on the town.
What they did not find, however, were the defending forces and their own scouts. They had not even encountered the expected relief shift.
_Now we're outside the town and we still don't have a logical explanation for it._ Aiphatòn stood up.
"We're waiting until the fleet..." Ávoleï looked up in surprise as he ventured out of the undergrowth below the riverbank and into the open. "What do you think you're doing? Come back!"
"I want to know why there was nobody waiting with the other barrels," he replied and darted across the gravel, which gave off soft crunching sounds. "You should be having the same worries I'm having." Aiphatòn raised his head from time to time and looked over the bank at the town that rose up all-powerful and majestic. With its bridges, battlements and towers, it clearly proved who ruled for a radius of many miles. _Is this a trick by_ _Shôtoràs?_
The älfar from Elhàtor followed him while Ávoleï brought up the rear.
"I _have_ thought about it. And I assume it's to do with the canal and the imminent flooding," the elf-woman answered. "They need every pair of hands to finish it."
"Nobody would ever give up the sole lines of defence they'd had up till then for that. Even if they left just two men in the hideaways." Aiphatòn couldn't see any lights on the allures, on the plains around Dâkiòn or in the buildings in the small fishing port where they were headed. _That means that they are lying in ambush somewhere._ He looked past the warriors to the woodland and the adjoining swamp. "Do you think it's possible they've set up a second garrison in the marshland where they're assembling troops to attack the ships from behind?"
Ávoleï shook her head. "Our scouts would have noticed. They were scattered right around the town and reported every change, no matter how minor, as well as information on the dam and the canal."
_Quite true. But where are they now?_ Aiphatòn stopped, crouched down and took one enormous leap from the bank onto the higher ground, holding the spear in his left hand and brandishing it defiantly. _This is no ploy by the sovereign._
"Madman!" Ávoleï hissed after him, outraged. "You'll give us away!"
Aiphatòn's gaze darted this way and that as he waited for a cry, a bugle call, a blast of fanfare, a cloud of arrows or a platoon of horseback riders bursting out of the ground because they had dug themselves into it.
Swallows screeched as they flew overhead and chased the swarms of midges that were buzzing around; two hares hopped cautiously among the blades of grass and nibbled them while the wind swept over the älf and cooled his skin.
_There's nobody here._ Aiphatòn placed a hand over his eyes, shielding them from the glare and he saw the open gates at the lower entrance as well as at the internal gateways. "The town has been abandoned," he informed his companions.
"That's what they want us to think." Ávoleï pulled one of the warriors back by the shoulder just as he was about to climb upwards. "It's a trick to get us to make stupid mistakes. Come back so that..."
"Let's split up." Aiphatòn walked towards one of the entrance gates, the bridges stretching up gradually beyond them. "You take five warriors and investigate the trench they've started as well as the dam. The others are coming with me."
He couldn't help grinning when he noticed the soldiers joining him and Ávoleï cursed. "Keep an eye on the battlements," he advised the elf-woman. "One of us will give you a signal as soon as we've found anything."
He raced across the plain with his warriors and reached the gate. They didn't waste any time, going straight through the open portal.
Nothing indicated an attack or a battle. There were no bodies, no blood spatters or other obvious signs.
Bridge by bridge, they jogged onwards, infiltrating Dsôn Dâkiòn.
The daystar was sinking rapidly and the sky was turning red and preparing the backdrop for the stars and moon to come out. The wind was picking up, carrying the smell of dust and burnt food.
The vast settlement gave them a silent welcome. The patter of their soles on the stones and the occasional clank of a scabbard hitting a leg or armour were the only sounds, eerily loud in the silence.
"I would never have thought when the sun came up that I would be inside the town in the very same moment," murmured one of the soldiers who was constantly looking around like all the others. Out of incredulity and wariness. Nobody trusted the tranquillity.
At first Aiphatòn expected the defending forces to come charging out of the gigantic basalt buildings or start throwing stones at them from the roofs to kill them, but once they'd reached the edge of Dâkiòn's lower town and were hurrying along the broad street undisturbed, he knew that Shôtoràs had abandoned his Dsôn.
"I wonder if he built his own fleet in the swamp and is sailing to Elhàtor right now?" one of the soldiers suggested.
Aiphatòn thought this was an intriguing idea. "Nobody would have expected that anyway. Myself included." He wheeled round and started to climb one of the tall watchtowers with his troops. "Let's see if we can find out any more from up here." The prickling in every fibre of his body had returned, and it could not be put down to the exertion. The magical field of the town was reacting with his innate magic and the alloy.
They went round and round up the tower until they reached the viewing platform.
The wind was fierce up here and the sky had darkened, accentuating the brightness of the stars.
"Take a look around."
From around seventy paces above the roofs, the houses still did not look small.
They shimmered thanks to the inlay, the jewels and likely some special-effects spells; it was similar to what he'd seen when Vailóras brought him to the sovereign.
But behind the windows it was still dark.
_Not one light, not even a small one._ Aiphatòn looked towards the river, flowing along with its glittering waves. He could make out six figures moving around and spreading out near the clearly distinguishable dam. _Ávoleï has made it too. Good._
The canal for diverting the Tronjor extended as far as the old riverbed. There was less than three paces to go before a large proportion of the river would flow into the valley. Even the flooding mechanism for the second weir was in place. Dâkiòn's architects had done a good job of preventing the fleet from Elhàtor attacking by taking the water away from them.
_The plan was perfect. If it were a game of Tharc and I was the opponent, I would have to yield before the round began because I'd have nothing to counter it with._ Aiphatòn didn't understand what had prompted the sovereign to get it all ready and then not actually put it into action.
"Is it possible that they wanted to lure us into the valley to drown us?" One warrior came over to him and looked at the construction on the river.
"How stupid must Shôtoràs think we are for him to seriously believe that Elhàtorians would get out of their ships to climb into a valley that has a canal leading into it from the river, visible from very far away?" Aiphatòn propped one hand against the tower wall. _Who is depriving me of my war?_
Ávoleï also seemed to assume they were alone now and her entourage lit torches. The glow of the orange flames was visible from a distance away and brought the warriors out of the darkness.
"I think there's someone there!" Aiphatòn heard the faint cry from behind him. "There, in the second part of the town, on the bridge."
They ran over to the soldier who made the discovery and peered around.
_He's right! A decoy?_ Aiphatòn saw the shadowy silhouette of a petite älf-woman that looked familiar; like the last time they met, she was wearing skimpy clothes. _The death-dancer._
"Let's seize her, but be on your guard against her magic. She is nimble and deadly." He involuntarily placed his hand over the hole in the armoured plate—he had not yet fitted it with stuffing or a cover. A serious weak point and an oversight. _I'll have a little plate of iron laid over it later._
They ran down the steps and spread out as soon as they reached the ground so as not to let Tanôtai escape under any circumstances.
The red-haired death-dancer was coming towards them over the bridge and saw them. She stopped in shock and ran back the way she'd come.
Aiphatòn suppressed the impulse to take up the pursuit. "We're going after her slowly," he commanded. "Watch out! Because now it really looks like a trap."
"Could all of the locals be lying in wait for us in the upper town?" one warrior said, trying to sound amused. But the idea that the sovereign's troops were standing silently in the side streets with their weapons drawn, just waiting to charge out and hack them to pieces with their swords was making the soldiers anxious.
Meanwhile Tanôtai was walking along the large road, straight towards the palace where Shôtoràs lived, her long, red hair fluttering behind her. She didn't look round, as if she didn't care whether the intruders were following her.
Aiphatòn started to jog slowly. _She's afraid of us._
The death-dancer disappeared through the open gate into the palace.
"I'm going first." Aiphatòn took the lead and dashed up the five steps to the entrance.
With one enormous leap, he got through the gate that was still ajar and landed in the inner courtyard he had visited once before. He did a shoulder roll and stayed down on one knee, holding the spear at the ready with both hands. _What I wouldn't give to be wielding my own spear._
He couldn't see Tanôtai.
The courtyard appeared empty and gave onto a second courtyard directly beyond another semi-circular passageway.
Aiphatòn spared himself the analysis of carefully devised ambushes. _Anything is possible._ He stood up and moved slowly through the surreally large arch into the second courtyard.
The footsteps behind him belonged to the warriors from Elhàtor who caught up with him to protect him—he knew this without turning around. He recognised the sounds they made.
The walls towered up around him four gigantic storeys high. Large windows and galleries allowed a view of the inner courtyard and hence a view of him too.
_There she is._ Aiphatòn saw the death-dancer standing in the courtyard next to an älfar statue made of marble, bone and steel.
Tanôtai was leaning her tattooed shoulder blade against it and had slung her arms around the stone neck as though it were her lover and she had invited him to a secret nocturnal assignation. Her needle-daggers were stowed in the holders on her metal forearm guards. The lines on her skin looked black, as though poison was flowing through her veins.
_Or anger is spreading throughout her body._ Aiphatòn stopped four paces away from her. "I want my spear back," he said firmly and raised his weapon. "This one isn't up to much."
Tanôtai laughed quietly at first and then worked herself into such a fit of laughter that her whole body shook. "Aiphatòn, emperor of the älfar of Tark Draan, ruler of a kingdom, commander of the Dsôn Aklán, son of the Inextinguishables," she reeled off, sniggering. "You're someone with great power and plenty of titles."
"My spear, Tanôtai," he reminded her. "And what has happened to the town? Where is the sovereign?"
The death-dancer disentangled herself from the statue and slowly raised her arms out to the sides, turning on her tiptoes and gently tilting her head to the right.
With every graceful, elaborate-looking turn, more älfar appeared at the windows and on the galleries, their eyes fixed mutely on the inner courtyard and the pair inside it.
Aiphatòn saw warriors, cîani and plainly dressed townsfolk pushing and shoving each other aside to get the best view. _There must be hundreds of them and they're all unarmed._ He turned around—and saw the first inner courtyard was suddenly filled with Dâkiòners lining up in silence too.
His warriors, on the other hand, had vanished.
The prickling sensation became stronger. "Are we to have a duel? Is that what you're after?" he tried out one explanation for this spectacle. "Is the courtyard going to be our arena?"
Tanôtai paused and slowly lowered her arms, straightened up her neck and stared at Aiphatòn.
A huge, muscular, human-warrior suddenly leaped from the highest gallery wearing a copper close helmet and landed safely next to the death-dancer. Stone shattered under the soles of his boots on impact, dirt swirling upwards.
He was wearing simple, hardened leather armour that was covered in artistic white runes, as was his helmet. Pale, delicate smoke rose steadily out of the eye, mouth and nose slits and dispersed almost as soon as it emerged from the openings.
Aiphatòn changed his grip on the spear so that he could toss it. _I saw someone like that on the battlefield. When the botoican armies charged into each other._ "Am I fighting him then?"
The residents of Dâkiòn stood around stiffly, staring and waiting. From time to time, whitish runes gleamed at their necks.
Tanôtai laughed. "No, you're not going to fight. You're going to _belong_ to me!"
Aiphatòn began to suspect he was no longer speaking to the death-dancer, but to a botoican. "I'm immune to your power, botoican."
The red-haired älf-woman gave a grotesque smirk, her charming features vanishing. "Your tribe is vulnerable to my magic, just like every other tribe. Nobody is immune to me. Nothing and nobody, Aiphatòn."
The warrior with the copper helmet walked towards him slowly.
"Let yourself be touched," Tanôtai purred. "Let yourself be touched like the others and you will be a good servant to me."
"You've incorporated Dâkiòn into your army?" Aiphatòn was thinking through his options for escaping the trap. The quickest route out would be to go upstairs, then onto the roofs via the galleries and on from there. _The war will take a different course from the one I planned but I will get my war._
"Surprising Shôtoràs was a wonderful moment," the botoican confessed through the mouth of the death-dancer. The botoican must have been somewhere nearby. "I sent this beautiful älf-woman to her homeland to have the gates opened for me. And as soon as I was inside the walls, things happened very quickly. My power is spreading like mad." She did a few little dance steps. "She was looking for you, by the way. She and her entourage, who were wiped out by my ghaist. They're incredible warriors, these creatures made of magic and sacrificed souls. Nothing can stop them."
The warrior with the copper helmet had almost reached Aiphatòn and was slowly extending his hand.
"Now let yourself be touched," Tanôtai repeated seductively and showed him her slim silhouette. "I swear I'll treat you well. Because I've got plans for you. Your knowledge will become my knowledge and I'll give you back your spear immediately if you ask for it. Along with Nodûcor..."
"The wind-voice fell into your hands?" _Good thing he's still wearing the half-mask._
Tanôtai sniggered again. "Oh yes, as a bonus in Dâkiòn. At first I didn't know who I was looking at, but I was informed." She tensed her muscles as though preparing for an attack. The tattooed lines glowed weakly, the light intensifying with every heartbeat. "Nodûcor is an obedient little älf now. And the no-less-obedient cîani of this town are putting all their efforts into removing his gag so that I can start storms." She whooped. "And I'll annex Elhàtor, of course. With your help, great emperor. _You'll_ come up with a way of conquering the island, I'm sure. It would be a shame to raze it to the ground with wind and waves. But if I can't have it, it's to be destroyed."
The enormous ghaist's index finger came very close to the älf's solar plexus.
"I do not accept the offer." Aiphatòn thrust the spear at the fingertip but the tip shattered as if it was made of brittle wood.
Cursing, he catapulted backwards and evaded his opponent, jumping up onto the first gallery and running past the silent residents of Dâkiòn as the ghaist lifted his head. The smoking eye slits were fixed on him.
_I've got to warn Ávoleï. The fleet needs to turn around. Otherwise we're bringing the botoican the ships he needs to conquer the Magnificent._ Aiphatòn jumped upwards from one storey to the next, dived onto the roof and looked down into the inner courtyard.
The warrior and the death-dancer were staring up at him.
_The petrol! With petrol, we could torch them all, including the ghaist._ He thought his idea was a good one. _Before he..._
"Catch him!" Tanôtai commanded sharply and pointed one of her daggers at him, the tip of the blade flaring with a dazzling glow. "Catch him _alive_ for me so that he can become one of you!"
And with a collective, greedy cry, all of the älfar behind the windows, on the galleries and in the courtyard started to run, push and shove to get at Aiphatòn.
# Chapter XIII
_There is nothing greater than the power of suspicion stoked by distrust._
Wise saying of the Älfar
Collected by Carmondai, master of word and image
Tark Draan, Human kingdom of Gauragar, Oakenburgh, 5452nd division of unendingness (6491st solar cycle), late autumn
"I want to see him. He's _my_ prisoner!"
_Well said!_ Mallenia of Ido couldn't help but admire the black-clad dwarf for standing as confidently in the stone foyer of Oakenburgh's town hall as if he were a king. She was sitting in a window alcove enjoying the rays of sunlight falling through the glass.
"I'm sure you understand that he's not capable of receiving visitors," she responded politely but firmly. "He was lucky the arrows didn't kill him, but let's just say this: he was close to passing into endingness." She scrutinised the zhadár. The älfarness radiated from every single one of his pores; the aura of evil and danger was more palpable than they were with her prisoner. "I'll have you summoned as soon as he's awake. My healers' sedatives are strong."
The dwarf, who introduced himself as Carâhnios, but who had once gone by Balodil, had appeared during the dramatic orbit in the utter commotion of the second attempted attack. He had fearlessly confronted the älfar assassin who was dressed as a beggar.
Without him, Mallenia had to admit, it would barely have been possible for her soldiers to kill the black-eye making an attempt on her life. _I don't have to like him though._
The guards standing around the queen in the cramped hall couldn't hide their discomfort at the dwarf with the black skin and black hair who had undergone an unmistakeable transformation due to the Akláns' influence.
_A manifestation of night and evil._ Mallenia, who was wearing her armour, tried to smile. But it didn't quite work. "What do you want as a reward, my dear dwarf?"
"My black-eye back." The zhadár glared at her and placed his blackened fingers on his belt. It had been a clever move not to turn up wearing the armour that made him look even more sinister.
"He's not _your_ black-eye. He was caught in Bhará, as far as I know, and you took him with you as your companion so that the stories of what you experienced during your hunt would be written down," she corrected him. "That's how Fiëa reported it to me. And on top of that, the fact is, _she_ overpowered the älf. Correct me if I'm wrong."
Carâhnios took a deep breath. "So I'm not getting him back?" he fumed.
Mallenia said nothing. _Never._
The zhadár bowed his head. "I'm very surprised at you, Queen," he said, his voice deeper than before. "You hate the älfar. They killed your relatives, you fought them relentlessly and swore not to rest until all of them were killed. But now you save an älf's life? Give me a reason that I'll understand."
"You know he's no ordinary älf." Mallenia was prepared for the accusation. "This is Carmondai, who has spent the last few cycles in a dungeon. His name does not appear in connection with any atrocities in the recent history of Girdlegard. He could be accused of being involved in the construction of Dsôn Balsur and creating stories that portrayed black-eyes in a better light than was accurate," she shot back quietly. "But that's all."
Carâhnios laughed bitterly. "Do you hear yourself saying these words? You're defending an älf, Queen. An älf! Prince Mallen of Ido would box your ears for that." After this insult he turned around and made for the door. "I expect you to send me word as soon as he is fit to travel."
"My advice, my dear dwarf, is to move on before word spreads that a zhadár is hunting the älfar," Mallenia replied. "Your intervention was impossible to miss."
Carâhnios left the room without answering.
The queen heaved a sigh of relief. Even the guards around her relaxed, as was clear from the grinding and scraping sounds their metal armour made. _If I put the älf to death, I'd have to have you murdered too. Who knows what crimes you've committed?_
The zhadár appeared to be the more dangerous of the pair. And the fact that he had tried to collect the blood of the mutilated assassin in a bottle after the attack did not improve his trustworthiness.
_He has more demonic knowledge than the tale-weaver._
Mallenia got up from the window seat and went down into the vaults of the town hall with an escort. Along with the wine cellar and the storage barrels, down here was where the dungeons were. They had chained the älf to a camp-bed in one of the dungeons; her healer was taking care of him.
Carâhnios had wounded her with his final words, because they were essentially true: the Idos did not show mercy to any black-eye.
But there were a few things about Carmondai that made the circumstances different and as long as these puzzles remained unsolved, she would hold off on executing him. _Even Mallen would spare him._
Mallenia entered the vault and hurried to the windowless cell where they had imprisoned the älf. Ten sentries were guarding the exit and were under instruction that, at the slightest sign of unexplained fear or darkness or the torches extinguishing, they were to kill the prisoner instantly.
She walked in and saw the healer sitting next to the älf and feeding him soup. His muscular torso was bandaged in various places and his shoulder was also wrapped in a thick layer of pale, sterilised cloth.
_He's awake. Excellent._ "Can he speak?"
"He can," replied Carmondai with a smile. The dried blood was still caked on his skin in a few places, flaking off as soon as he moved. There were reddish-black clots in his mid-length brown hair too. The priority had been to save his life, not his looks.
Mallenia dismissed her healer, who obeyed in astonishment. Then she sat down next to the älf and drew one of her short swords. "Here's a legend who wrote legends," she said thoughtfully.
Carmondai watched her closely, his dark eyes shimmering a brownish colour in the light from all the oil lamps. "You're not known for being a friend of my people."
The queen nodded slowly. "But in dying, would you potentially become an even greater legend?" Mallenia looked at the bandages—they no longer showed any red staining. "Your wounds are closing up fast."
"As I didn't pass into endingness, my body wants to participate in life again quickly, no matter how old it is and how much it hurts when I get up. I'm an old man, I just look like a man of fifty cycles to you." The älf looked searchingly at her. "That's your reason? I shouldn't become a legend? To whom? To the two or three älfar still sneaking across Girdlegard and being hunted by Carâhnios?" He shook his mop of brown hair. "Hardly likely, Queen."
"Well deduced." Mallenia raised the sword. "Your death would be more than welcome but there are circumstances that make you very interesting. There is that zhadár who is collecting älfar blood and wants to have you by his side." She placed the sword against his throat. "I need to find out more about him and his kind because he exudes more evil than one of the Aklán. He needs to be watched more carefully than you do."
Carmondai simply raised his eyebrows to signify his agreement.
"Secondly, I received a letter from Ilahín, one of the last elves in Girdlegard, just after it became known that I had you here in Oakenburgh." She leaned forward. "In it he warns me urgently about your words, and your silver tongue that allows you to twist truths, as you have done in your writings before. Apparently I should do Girdlegard a favour and execute you."
"That doesn't surprise me."
"I'm surprised by the fact he is so insistent on it." The queen looked him in the eye. "You are so old, have so much knowledge and can give us information about so many things regarding the älfar—and we're just meant to destroy that?"
"No doubt Ilahín thinks I'll lie."
"And you would too, and I couldn't blame you for it. But there are means of making even you tell the truth. I don't mean torture." She gestured to the soup. "My healer is a very experienced man. The herbs he mixes in make the truth come to light. Without using any magic." Mallenia smiled when she saw his look of consternation. "The elves were the first to push for your works to be collected and destroyed. Because they were a danger, because they tempted the humans into evil acts. At first I saw it the way they did," she explained. "But their demand is starting to seem too aggressive to me, too mysterious. And that's exactly why I want to hear more from you. If the elves have something to hide, I want to know before they invite even more of their people to Girdlegard."
Carmondai nodded again. "Are all of my drawings, poems and books already lost?"
"A lot was tossed into the flames, occasionally in anger, sometimes with joy but also with wistfulness." Mallenia sat up straight. "I secretly had some compiled instead of destroyed. Reading keeps me busy when I travel. As I know exactly what to think of your words, I can make sure the transformation of your people's deeds into heroic or even good deeds doesn't get to me. And you see: I gain knowledge from it without getting carried away by the älfar style."
Carmondai slowly lifted one arm and reached for the soup as if to prove he wanted to tell the truth. "That is wise of you, Queen Mallenia."
"I just think I'm sceptical. That stemmed from the fight against your people," she replied. "And since the elves are your relatives and they brought ruin to my homeland once before with the eoîl, I'd like to know every little secret the älfar know about them. It is sometimes said: enemies usually know more dangerous things about you than your friends do."
"I'll see to it as soon as I can write." Carmondai spooned up the soup. "I am in your debt, Queen."
"You saved my life. I'd be in your debt for that if you weren't a black-eye." Mallenia realised she was finding the älf more and more fascinating. It was one thing to fight against his people, but it was quite another to have a specimen in front of her who was not consumed by murderous thoughts towards her. _I can already see long conversations by the fire of an evening._ "Let's start right now with some new information for me: what does the zhadár do with the älfar blood?"
Carmondai didn't hold back in explaining how Carâhnios went about things, and also what he was distilling for himself from the blood in order to increase his powers. The herbs ensured that no lie passed his lips.
Mallenia listened intently and found her suspicion confirmed. The last of the zhadár was definitely more dangerous than an älf.
_I don't want him anywhere near me anymore. I'll let him know that and have him thrown out of Oakenburgh. He can go and hunt älfar._ "Thank you," she said and put away the sword. "So Carâhnios has a reason to kill you too then."
"I'm aware of that. He has threatened me with it before."
_Which I must not allow._ "By the way, I hear King Boïndil of the Secondling tribe is desperate to have you visit him. It's about that very remedy that a zhadár..." She hesitated. "The remedy that very zhadár Carâhnios gave him to drink. He wants to know what's in it and what you can take to counteract it."
"I'm your prisoner, Queen." Carmondai drank the last mouthful of soup straight from the bowl. "You decide."
Little by little, Mallenia was growing less certain as to whether the black-eye was putting on an act for her, or his meekness was down to the effect of the food garnished with herbs, or whether he had simply given up because he knew he was safe in her custody. "I suppose so."
The queen thought for a while.
Finally she got up and went to the door. "Once you've recovered, you'll stay at my disposal and be permitted to move freely in my two kingdoms. Nobody will be allowed to kill you or beat you because from now on you are my property: an älf as the slave of a human. How times change," she declared harshly. "If you leave the confines of Idoslane and Gauragar, I cannot guarantee your safety."
He put down the bowl in astonishment. "That is a great mercy."
"You have a vast amount of knowledge about älfar and elves at your fingertips. That is a great opportunity." Mallenia pointed to his wounds. "By the way, they're healing because my friend Coïra stood by your bed and cast a healing spell that also bound you to me: if _I_ die, _you_ will pass on too. That's my protection against any more potential assassins." She gave a brief nod. "And so my debt to you would be settled." She opened the door and went back into the corridor.
"Queen! How are you going to make sure your subjects don't mistake me for an ordinary älf?" he called after her.
"You will be recognised." Mallenia closed the door and sent one of the guards for the jailer as she crossed the vault. The spell supposedly binding Carmondai to her was a lie. _But he believed it._
The jailer hurried over from the guardroom and bowed deeply to her. "Majesty?"
"I'm very pleased with your work," she praised him and pointed to the cell where Carmondai was. "Oakenburgh has its own executioner, doesn't it?"
"Yes, majesty."
"Is he skilled at torture?"
"Certainly, ma'am."
"Is he a drinker or does he have a steady hand?"
The jailer didn't know what to make of all her questions. "Well, I'd say he knows all the necessary methods of eliciting from the black-eye every answer that he refused to give you during the interrogation, majesty."
Mallenia smiled. "He was very open and spoke candidly." She lifted her right arm, the index finger pointing at the coat of arms on her armour. "The executioner is to brand the prisoner with the symbol of my family on both cheeks, because from now on he is my slave."
"I see. A wonderful way of demonstrating the subjugation of the black-eyes, majesty," he agreed, surprised and excited. "I'll go and..."
"Wait," she stopped him and turned off into the guardroom to get some paper and a quill. "After that, the executioner is to get a thin wire, make it red-hot and write the following on the black-eye's forehead." She jotted the words down on the page and pressed it into the jailer's hand. "And shave the prisoner. I want the writing to be good and visible." Mallenia turned to leave. "My new slave is not to suffer pain at anyone's hands but mine."
Ishím Voróo, Älfar town of Dsôn Dâkiòn, 5452nd division of unendingness (6491st solar cycle), late summer
_I've got to get to the river._ Aiphatòn jumped from roof to roof while hundreds of älfar followed him through the alleyways and streets of Dsôn Dâkiòn.
They kept their eyes fixed on him, running and pushing each other out of the way. Anybody who fell was trampled; nobody cared about anyone else. Urged relentlessly on by the botoican's magical command, from that point on this was the only mission on their minds.
Nobody shouted and nobody screamed anything at him, which was the most creepy thing about the scene. The shuffle of feet, the scraping of material, leather and metal, the fall of bodies and the stifled rattling breaths of those who didn't get back on their feet quickly enough, the squelching as they were then trodden over like trash by those who followed behind—there were no other sounds.
_Everyone together and yet each for themselves._ Aiphatòn changed direction again to leave them guessing where he was trying to go. Doing this meant they had not been able to cut him off yet.
The crowd stopped every time.
The pairs of eyes looked around until they made out their prey and started chasing after him again.
_And now to the bridge._ Suddenly Aiphatòn raced off in the exact opposite direction, and leaped from shingle to shingle towards an area where there were only very narrow alleys beneath him. _That will slow them down._
He ran, dropped down onto a canopy and reached the ground. Then he was dashing towards the golden bridge. _If only I knew if it was possible to make it collapse quickly._ He wished he'd spoken to Irïanora for longer now. _She would have been able to give me some advice._
Panting and footsteps pattering, the first älfar appeared behind him. His manoeuvre had gained him a head start of about a hundred paces, but the speed with which they stayed on his heels was remarkable.
_This will not be fast enough to close a gate._ Aiphatòn was running through the lower part of the town, racing towards the bridges that led away from it. He looked at the river as he ran and could make out the torches that Ávoleï and her warriors were carrying. _They are still examining the dam._
"Hey," he shouted as best he could while sprinting; he was running out of breath. "Get away from there! Find a boat and set sail!" Then he had to stop shouting because it was getting too hard to breathe. _It's two miles. They'll hear me but not understand._
He made the runes on his armour light up so that the Elhàtorians could see him and hopefully work out that he was fleeing.
Aiphatòn risked a glance over his shoulder.
His pursuers had caught up part of the way, closing the gap to fifty paces. Eight warrior-women and warriors were running out in front, having thrown off their armour without stopping so that they could run faster. Their faces were contorted; the pain in their legs must have been enormous but the botoican's mental command made them overcome the physical discomfort.
_I wonder if they would still try and catch me with broken legs?_ As he ran past, he knocked over a large oil lamp.
The fluid spread over the stones and made them slippery.
The first two pursuers made it safely across, then the stumbling and skidding began. Hardly had one älf fallen when more of them would trip over the living obstacle until a gigantic teeming cluster had formed in front of the second gate and the lower bridge.
Aiphatòn knew it wouldn't hold up the possessed warriors for longer than a few heartbeats. _But even that could be enough for me to get into the boat and down the Tronjor to alert the fleet._
Having crossed the last bridge, he dashed across the plain to the river. Two miles that threatened to go on forever.
To his relief, the handful of faster älfar warriors had fallen back, one lying motionless on the ground.
Aiphatòn headed for the fishing village and extinguished the runes so that he wasn't so visible to his pursuers.
He was surprised to see not only Ávoleï and her team, but also the five warriors who had accompanied him to Dsôn Dâkiòn. _The cowards fled just in time and deserted me._ "We've got to get away," he shouted at them.
"So it was a trap after all." Ávoleï looked at the advancing crowd and turned pale. She completely misconstrued what she saw. "Holy Inàste! Our plan is done for then. We will have to lay siege to Dâkiòn for a long time."
Two of her warriors loaded arrows onto their strings and fired the missiles at the closest pursuers, who collapsed, fatally wounded.
"No. Shôtoràs and the town have fallen. But not to us." As they hurried to the jetty where fishing boats were bobbing, he quickly summarised what had happened in the inner courtyard of the palace. "And if the brave warriors had stayed by my side, they would have been able to tell you all this already." He looked daggers at the five of them.
"They stayed," replied one of the scolded warriors in a low voice. He drew his sword and stabbed the älf next to Ávoleï in the stomach. "They became part of it."
The stabbed warrior groaned as he fell onto the wooden planks.
The elf-woman wrenched both of her swords out of their holders and pointed them threateningly at him.
The warrior gave a distorted grin, having apparently lost his mind. "Part of the infinite number of creatures who follow my will. Surrender and you will live—or end up like the dead."
_The botoican is speaking through him._ Aiphatòn cursed and hurled his spear at the warrior, who was struck sideways through the chest by the tip of the spear and fell off the jetty into the river.
But the element of surprise was too strong: quick as a flash, Ávoleï and the four other älfar were overpowered by the externally controlled warriors, then wrestled to the ground. Meanwhile the mob of foes surged towards them along a wide front, jumping down off the embankment to get at them.
Before the ledge that led to the jetty, the crowd suddenly stopped as if there was a glass wall there.
Ávoleï was lying on the planks of the jetty. One of her own warriors was kneeling on her back and holding a sword to the nape of her neck to stop her moving.
_There's only one option left._ Aiphatòn was standing right in the middle of the booms, trapped between the enemies. His gaze was fixed on the elf-woman, and he tried to convey to her that he would swim to warn the fleet.
"If you jump," the soldier behind her said, "I will stab the commander through the neck. But if you stay and surrender to me, I will make you my top henchman."
The warrior with the copper helmet forced his way through the glassy-eyed, motionless mob and stepped onto the jetty, placing one foot in front of the other. The wood creaked and rumbled dully under his boots.
"Ávoleï knows she's done for. Death is better than being your servant, botoican." Aiphatòn launched himself off the jetty in a racing dive, flying through the dark night air before plunging into the river.
He glided underneath the surface for quite a few paces before needing to come up for air.
He could barely believe his eyes: the churned up water around him was foaming and splashing from all the bodies that had plunged in and were swimming towards him. _They are not giving up._
Quicker than he'd have liked, two or three älfar had reached him.
"Back!" With swift blows Aiphatòn beat them off and they sank unconscious beneath the waves. He did the front crawl to get away and saw the mob forming a chain in the river by holding hands. The ghaist with the copper helmet was the first one in the chain.
More and more enemies joined in and lengthened the line in the water like an endless cord being unwound.
_What are they up to?_ He again had to beat off several grabbing attackers with punches as he swam.
In the fray, one warrior-woman on the end of the älfar chain missed getting a firm hold on Aiphatòn by a hair. Her fingers slid over his wet shoulder and couldn't get any purchase.
_She almost had me._ Before Aiphatòn could draw his arm back to shake her off completely, it happened: a small bolt shot through him as if he had touched a powerfully magical object.
_That damned energy field._ Aiphatòn didn't feel any different from before and started swimming again to make up the ground. The Tronjor carried him along.
Meanwhile the chain of älfar broke up and they swam to the bank. The warrior with the copper helmet attacked Ávoleï and the four remaining älfar from Elhàtor in turn.
_Thus they've become puppets of the botoican._ Aiphatòn laughed grimly. _But I escaped him. We will burn them to ashes with petrol and..._
His arms and legs were swimming in powerful strokes. But to his horror, he was suddenly moving towards the bank on the right like all the other älfar, to get to dry land and struggle out of the river.
_This... cannot be._ He became a mere observer of his own actions.
Dripping wet, he trudged out of the waves, his legs rising and falling, carrying him towards the fishing village, surrounded by the puppets of the botoican who had no will of their own.
_But I'm able to think._ Aiphatòn's mind seemed to be locked inside an unruly body that was taking him through the area as it pleased.
Nothing in his movements betrayed the fact that he was not in command of them himself; he was not walking stiffly or otherwise behaving unusually. Not even a close friend or confidant would be suspicious if he approached them—until he carried out a murder or an arbitrary atrocity at the behest of the botoican.
He strode through the crowd and stopped in front of Tanôtai, who was standing next to the copper-helmeted warrior.
She sneered repulsively in a way that wasn't like her. "Welcome. You didn't make it easy for me. You needed to be touched to gain power over you," she greeted him. "The transfer is more than sufficient that way."
_I'll find out where you're hiding, botoican, and annihilate you_ , he thought and felt the anger lines forming on his face. But his arms hung loosely by his sides and his body obeyed an enemy's will and made him stand idly by.
_Besides, it doesn't make any sense to kill Tanôtai. The botoican would find himself another mouthpiece and mock me._ Aiphatòn realised the infinite possibilities open to the mind-controller. _He can have me speak on his behalf and make everyone think they're my own words._
"That was an exciting day, wasn't it? We've earned a rest." The death-dancer scrutinised him. "We'll come up with a plan for how you and your girlfriend are going to get your hands on the approaching fleet for me. That ought to be simple, as they think you're allies." She pointed to the copper-helmeted warrior. "Oh, I know: you'll take my ghaist with you as a captive and very soon boat after boat will belong to me." She turned away. "Let's make ourselves at home in the village. First the ships, then Elhàtor," she remarked as she walked away. "Even more warriors for my army!"
The älfar marched off towards the houses, pushing and shoving each other before disappearing inside.
Aiphatòn also followed the unspoken command the botoican conveyed to everyone and entered one of the dwellings. The warriors, cîani, children and adults were curling up on the floor and on the chairs and tables, wherever they found space.
Most of their clothing already looked shabby, showing stains and dirt. He saw tears in some eyes and black lines flared on a few faces, revealing their anger and hatred. _So I'm not the only one who has kept their mind._
But none of them had the power to rise up and resist the spell that had come over them.
_Not even the cîani are capable of doing that._ Aiphatòn's body walked over the figures on the floor, threw two älfar out of the bed and settled down into it.
Nobody came to contest his right to the bed.
Aiphatòn tried to move his lips and say something, but he couldn't manage more than a twitch. _It probably won't work until the botoican is distracted._ His eyelids closed and he was plunged into darkness. _I will find out where the weaknesses of this spell lie._
There came the sound of deep breathing immediately from all around him, occasionally someone coughed. A soothing peacefulness was stealing over the settlement when quiet, suppressed weeping penetrated the silence and would not stop.
A shudder ran through Aiphatòn.
He had never heard anything so moving, despairing and dreadful.
Ishím Voróo, 5452nd division of unendingness (6491st solar cycle), autumn
Suddenly the bow dipped and the narrow ship raced down into the trough of the wave, lurching as it gathered way again. Foam and spray blew across the deck where Aiphatòn was holding his ground like a statue.
To starboard and port, more boats that still had enough rigging followed them, fighting their way through the storm. They had been crossing the whipped-up sea for the last four moments, losing one ship after another, but the will of the botoican was unrelenting in its demand that they get to Elhàtor. Even the bigger, sturdy rònkes and their escort ships struggled but they fared much better in the storm.
_I hope we don't sink._ Aiphatòn held on tight with one hand and counteracted the movements of the hull. _That would put paid to one element of the terror at best._
He still didn't know what he could do to fight the incredible power of the botoican. The plan to take control of the fleet had worked with terrifying ease: they had presented the copper-helmeted warrior as a supposed captive and in less than half a splinter of unendingness the warrior-women and warriors lost their free will. With nobody suspecting anything, the controlling spell spread more quickly than fire through dry grassland.
Dsôn Elhàtor, where they were headed through the raging storm, was no less unsuspecting.
_Thousands live there. Thousands who will have to surrender. Even more warriors for the army._ Aiphatòn still could not understand what the botoican was trying to achieve. To get an insight into his thinking and background, he would need Carmondai, who was more familiar with the stories from Ishím Voróo. _Did he say he was a member of the Nhatai family? How will I find out more about them?_
The ship passed through the lowest point of the waves and rose up again.
The wood creaked loudly under the strain, the overfilled sails looked ready to burst. Lightning darted across the black sky and the rain was thundering down relentlessly on them as if the sea spray and the breaking waves weren't enough to soak their clothes through.
The endingness seemed close enough to grasp but all of the älfar were still going about their work. While their hand movements were swift and precise, there was no shouting or agitation, as might have been expected in the face of the storm and the towering waves.
_Enforced control._ Aiphatòn had more freedom of movement than others, as he had noticed after a few cautious experiments in the last few moments. He was shrewd enough not to show anybody.
Presumably it took the botoican a lot of strength to maintain the spell over the agitated creatures. Or perhaps it was down to Aiphatòn's own energy which was stored in the magical alloy. As long as he hadn't received a specific order that his body was carrying out, he seemed able to control himself to a certain extent. The tiny scrap of resistance he had left. He turned his head and looked around.
On the starboard side, the crest of a breaker washed full force over one of the fragile invasion ships. The deluge of water that poured in smashed the planks of the deck, filled the triangular sail and broke the end of the mast off, which then crashed into the slightly raised look-out platform, crushing the steering wheel along with the crew. The ship instantly broke up and sank beneath the waves.
Aiphatòn looked around and made out numerous boats that looked as delicate and fragile as nutshells amid the incredibly tall waves.
A fair-haired man wearing älfar armour came and stood next to him. There were white runes visible at his temple and his grey eyes remained fixed forwards. "Your mind is capable of greater resistance than the others' minds," he said thoughtfully and reached for a rope to keep himself steady as the hull shot up the waves at a sharp angle.
Aiphatòn was silent—not because he had to be, but because he was surprised by how casually the man spoke to him. He hadn't noticed the man before. _Why would I have? I'd have taken him for a soldier from Elhàtor or Dâkiòn._
"I am Kôr'losôi and I'm a member of the Nhatai family," he explained, "but I'm not the one controlling you. Don't even think about trying to do anything to me." He looked at the shintoìt. "I'm the only one who can help you, emperor. If _you_ help me." One of his hands rested on the älf's forearm and immediately a magical prickling started that was different from the painful stinging that he had felt in the towns. "As long as I touch you, her power is reduced without her noticing. We can talk."
Her _power? A woman then._ Aiphatòn gave up his impassiveness, especially since Kôr'losôi thought his touch was responsible for the freedom of movement. He would keep it secret that he had been able to move of his own free will before. "She will read my thoughts."
"No botoican can do that. We influence living creatures physically, but their thinking remains off limits to us. You needn't worry. At the most, it could be risky if she orders you to tell the truth." He lowered his head to avoid getting a descending deluge of water in the face. "Her name is Fa'losôi and..."
" _Needn't worry?_ " The älf laughed bitterly. "You want to get rid of her so you can seize control of the army yourself."
"To dissolve it and overthrow her," Kôr'losôi shot back. "She is exterminating all of the remaining botoican families and it's clear she'll kill me too as soon as she has achieved her goal." He wiped his free hand over his sea-drenched face. "I command the fleet on her behalf. She sent along her confidant, who oversees me in turn."
"The warrior with the copper helmet," Aiphatòn guessed. "The ghaist."
"Yes. He's not a living creature, although it may look that way." Kôr'losôi used the älf to support himself—the angle at which they were moving upwards was getting steeper. "It's a ghaist, made of magic and souls. Through _it_ , her magic and her will are strengthened. I haven't worked out how she pulls it off yet."
"How do you kill it?" Aiphatòn asked immediately.
"Only with powerful fire. But it is too cunning and too quick." Kôr'losôi gulped as the hull reached the point where the wave broke and they glided downwards with the ship. "She created lots of these ghaist-creatures to have them scour the wasteland for new resources for her army."
Aiphatòn remembered how the human village had fallen to the searchers. "That's how they found Dâkiòn too."
Kôr'losôi confirmed this with a nod. "She is the only one capable of breaking an älf's will. And since you are all regarded as the best warriors, she wants you. You yourself were a bonus she didn't expect." Kôr'losôi looked at him. "You've got to help me! Otherwise she'll create an army that sweeps aside everything that stands in her way."
"Is that not what the Nhatai family want anyway?" Aiphatòn did not feel any sympathy for the botoican who wanted to save himself from his own doom, having very likely bound and abused countless creatures with his spells.
But he recognised the danger brewing for Girdlegard: the botoicans could storm the Stone Gateway.
_Not even the dwarves are capable of stopping the army of creatures with no will of their own. They will not countenance fleeing or retreating._ In his mind's eye, he saw the älfar forming a chain and touching the first dwarf in the defensive line. From then on he would be under the spell of the botoicans. _That must not happen._
Kôr'losôi dodged out of the way of a barrel that rolled towards them after breaking away from its fixings. It knocked two sailors behind them to the floor and broke their legs before going overboard.
The sailors didn't make a sound, clinging instead to the struts of the railing to stop themselves following the barrel overboard. It seemed they were forbidden from screaming so as not to spread any further unease. Or because the shouting annoyed the botoican.
"We botoicans just want to live in peace and protect ourselves with armed forces who obey us unconditionally," Kôr'losôi explained. "It might look odd to you. But we don't understand the ways of the älfar and we don't expect to be understood."
_Show me your weak spot._ Aiphatòn nodded. "Then tell me what we're going to do about her."
"She is in her town, in Tr'hoo D'tak, where she is assembling an army to fight the battle against the last botoican families still standing in her way," he summarised. "We are procuring the most unique warriors in the wasteland for her right now, to ensure her victory."
"How big will the armies be?"
"As big as possible."
"On the way to Dâkiòn I saw forces with as many as a hundred thousand troops. One of them could have belonged to the Nhatais."
"Yes. That was us. We defeated the Xotoina family and destroyed their town." Kôr'losôi could barely hide his pride. "We lost half the puppets in the process and she wants to make up for that."
_Puppets. That's all they are._ "There's no strategy in these bloodbaths?"
"No. There doesn't need to be either, especially as the creatures can't be controlled that precisely. They receive the order to destroy the enemy and they do so. Every creature according to its own ways and however it wishes." Kôr'losôi sounded callous. "What matters is a victory."
Aiphatòn wasn't surprised by such wastefulness. _Since they can create reinforcements at will, they can afford it._ He saw in his mind's eye the images of the brutal battle he had watched, the carriages, the beasts, the enemies being torn to pieces with bare claws and talons. _I could find myself in a similar situation soon._ "So let's bring her the älfar from Elhàtor and Dâkiòn and pretend we're submissive. You make sure I can move however I like at the relevant moment," he outlined his plan. "If I have my spear, nothing will be able to stop me."
The crests of the waves seemed to be flattening out gradually and the rain had eased off too.
One glance at the sky told Aiphatòn that the storm was dispersing. _The elements want me to slay the sorceress and not end my life, apparently._
"Yes. You will take her life. Then the army will dissolve anyway." Kôr'losôi looked at him. "Even if I were lying to you in order to seize control of the countless warriors for myself, it wouldn't work. Her power is _too_ great. No ordinary botoican can control such a huge crowd of creatures from the most diverse races and species."
"You mean we should get ourselves to a place of safety afterwards."
Kôr'losôi pursed his lips, droplets running over them. His pale pink tongue darted out and licked them off. "There are many souls who would like to vent their anger and their joy at being freed from someone else's will. In either case _I_ do not want to be standing right next to them." He went to take his hand away. "Take it as read: we are allies."
Before the botoican could even break the bond between them fully, Aiphatòn regrasped, clutching the botoican's wrist.
Kôr'losôi looked searchingly at him.
"I wanted to confirm that from now on we are allies, before I become a tool of your relatives again," he said pointedly, fixing his black eyes on the man.
"You can save yourself the effort of trying to intimidate me." Kôr'losôi smiled knowingly. "Botoicans are immune to älfar powers unless it's a steady hand holding a weapon." He grinned, confident of victory. "I would have tried it in your position too and I'm going to overlook it."
Aiphatòn let go of him and the prickling stopped. _That's all I needed!_
"Act submissive and let them go on believing they've broken you completely so that you get your spear back," Kôr'losôi urged him. "Inattention is the greatest gift they can give us."
"Nothing can harm the ghaist?"
"Nothing short of complete destruction with fire. We can only take one chance, one that leads to guaranteed success." The botoican fixed his gaze ahead where something was growing larger out of the flattening waves that was not rising and falling in their rhythm. "Is that the Magnificent?"
"It probably is." Aiphatòn didn't feel any kind of external command within himself, apart from to stand still and doing nothing. "There aren't that many islands."
Kôr'losôi turned towards the quarterdeck. "Then I'll begin the preparations. Irïanora and Ávoleï will bring us into the harbour without even one defending warrior suspecting something is off. When the sun breaks through the clouds, Elhàtor will belong to us." He hurried off to look for the älf-woman and the elf-woman. They needed to go to the bow to give the impression of being victorious heroines returning.
Aiphatòn sighed and relished the fact that the planks beneath his feet were coasting more and more calmly over the sea. _A fool like so many others_ , he thought as he watched the fair-haired man go.
He had not for a moment intended to make Kôr'losôi tremble with fear, he wanted to find out whether the influence lessened if he touched the botoican or if it only worked the other way round.
_It works._ There was a reason he was smiling. _I have taken some of his magic for myself._
He still needed a plan to bring about the downfall of the älfar from Elhàtor and Dâkiòn _before_ he killed the botoican-woman. Kôr'losôi could be lying to Aiphatòn through his teeth to turn him into his puppet without any magic. He needed to be on his guard about that.
It was as the fleet, which had been scattered by the storm, headed straight for the mouth of the harbour from all directions that Aiphatòn had the brainwave.
Tark Draan, Älfar realm of Dsôn Bhará, formerly the elf realm Lesinteïl, 5452nd division of unendingness (6491st solar cycle), late autumn
"The crater is up there." Ireheart pressed his heels into the flanks of the white and brown piebald pony to make it trot faster. _No other ride has ever taken so long._
He was followed by a band made up of sixty brave dwarf-women and dwarves from all the tribes and some free people. The rain and the lashing wind couldn't stop them or their shaggy little horses.
At first, Ireheart's request to all the tribes had been rebuffed. Nobody wanted to dispatch a large delegation. But each tribe granted him ten volunteers willing to take the risk of making their way down to Phondrasôn even though Carmondai and Balodil were nowhere to be found. So the dwarf sallied forth as the leader through the highways and byways of the place of exile.
Ireheart and his valiant group claimed to be relying on their unerring instinct for managing better underground than any other tribe. Some of the warrior-women and warriors spoke älfar as well as the language the orcs used. So they could always interrogate captives along the way to gather information on Tungdil.
_Vraccas, if you send us the lost, presumed dead scholar, the Children of the Smith will not know what to do with themselves in their joy._ He found the role of king easier now. The kingdom in the Blue Mountains looked better and better every orbit.
Although his duties as a ruler were piling up and Goda called him an enormous fool and none of his children were able to understand how he could get so fixated on this idea, he _needed_ to lead the volunteers to Dsôn Bhará and pay them the honour of personally bidding them farewell before sending them into Phondrasôn. It was extremely important to him. _Because who knows whether I'll still be alive when they come back to the surface?_
Fiëa had studiously ignored all of his messages and inquiries.
That was another reason to make an appearance and to—in a spirit of friendship—keep a close eye on the elf-woman and what she was up to in the hole in the middle of the former älfar town. _I'm intrigued to hear her excuse._
Soaked through to their undergarments, they hurried down the crater rim via the winding paths. The palace mountain ought to tower up right next to the hole, Ireheart remembered it well. Tungdil had met Tirîgon there and greeted him like an old friend.
But there were no remnants of either the palace or the town.
There were, however, numerous tents in which people had set up camp. Even the mountain that had once been a mile high seemed to have shrunk in size by more than two thirds.
_The elf-woman is really working them hard._ Ireheart saw that they had built enormous diggers out of tree trunks and planks with tin fittings. They were using these to help stack the crater soil into piles with chains, ropes and idler pulleys and pushing it into the hole. As it was descending into the wide opening, the rain stopped dust flying far up into the air.
The very sight of the workers annoyed Ireheart. Had he not let her know that he needed access to the tunnels dug out of the sidewalls?
His misgivings were confirmed when they came riding up to the hole: a third of it was already filled in.
"By Vraccas! What is that pointy-ear thinking?" he ranted and jumped down off the pony to run over to the edge and look down. The soles of his boots splashed through the mud, the dirt spraying up onto his trouser legs.
And worse was yet to come: Ireheart could no longer make out an opening or even the smaller niches in the side walls that had been mentioned in the report. The debris that had been shoved in was already too high. In among it he could see clumps and even whole sheets of burnt pitch, tar, slag and scree. _What has she done?_
"At first glance, you might think the weather would make it more difficult for us. But in fact it makes our work easier—the water softens the ground and our diggers clear away the soft layer more easily," he heard the elf-woman's voice behind him. It was clear she was deliberately adopting this innocent, chatty tone to show him her conscience was clear.
_Well, she's come to the wrong person._ Ireheart rubbed his face to brush the drops out of his eyebrows, eyes and beard, turning round as he did so. "I asked you stop filling it in until we got here."
"I heard that nobody could find Balodil and Carmondai, and the dwarves cannot spare any warriors," she said in apology, smiling. "After two escape attempts by the monsters, I felt waiting was too risky."
"So how many tried to get out?"
"Quite a few." Fiëa remained vague and polite. Ireheart could clearly see in her eyes that she was dancing dangerously close to the line between truth and untruth. She pointed into the hole. "We drove them back with hot slag, then we filled the passageways as best we could with plenty of..."
"You blocked the passageways?" he screamed at her. "I can't even dig down to get into the labyrinth?" Ireheart felt the rage, a wave of heat shooting furiously through his body. "How are the volunteers meant to get to Phondrasôn?"
With a splashing sound, the digger—many paces high and wide—poured a fresh load of sludge into the hole, the grey-brown mass flowing into the tiniest holes and filling them in.
"They won't." The elf-woman was distant all of a sudden. The rain drummed softly on her white armour, the splashes hitting the dwarf in the eyes so that he had to blink. "I've saved the lives of the brave volunteers who wanted to go into the underworld for no reason."
"You disregarded my wishes," he raged, balling his hands into fists.
"I have protected Girdlegard, King Boïndil," Fiëa countered coldly. "Because I am focused on more than the fate of one individual who is in all likelihood dead. I will not allow my homeland, which is yours too, to be plagued by evil creatures yet again."
Ireheart glared at her angrily, feeling as if his eyes were glowing like pieces of coal. _I'd be all too happy to bury you down there._
"And just to warn you, my dear dwarf: don't even think about digging a tunnel somewhere else until you find a different entrance," she said and bent down to him. "I have said that I will protect my homeland."
He took a step backwards to stop himself flying at her throat. "You're always the same," he cried, beside himself. "Acting friendly, as if you invented goodness, but you murder and threaten just as cunningly as the black-eyes." He spat at her feet, the rain immediately washing away the saliva.
Fiëa smiled patiently now, without arrogance. The rain ran through her long, white hair and trickled down her forehead. "I understand your bad mood because you see a hope lying in ruins and now you've got to ride back to the Blue Mountains without achieving anything." She went to place a hand on his shoulder but he dodged her. "Be a king of the Secondlings, take care of the High Gate and hence of Girdlegard, like I'm doing. But leave the dead in peace."
_He is..._ Ireheart didn't know what to think or believe. "I'm angry you haven't followed my instructions," he repeated furiously.
"Whether the tunnels would still be available when you arrived was irrelevant. I would not have allowed your volunteers to climb into the hole because they would have lured the monsters here." The elf-woman straightened up and looked at the warrior-women and warriors from the dwarf tribes. "You heroes! Accept my thanks too, for your noble intentions and your willingness in this undertaking. But for reasons of common sense, it ends here."
"The king must tell us that," replied a dark-haired warrior-woman carrying a double-edged battle axe. "Not you."
Fiëa nodded and slowly moved away from the edge and the group. "Stay tonight if you like. We have space left in the tents." She gave a slight bow. "I'll go and supervise the works. We want to be finished before winter comes and in eight orbits the honourable maga and queen, Coïra, is going to pay us a visit and see what she can achieve with magic." The elf-woman turned and walked away.
Ireheart trudged through the mud towards his piebald pony and got back into the saddle. His anger was slowly subsiding, the rain was cooling his head. _When I think about them repopulating the Golden Plain and how we'll have even more of these know-it-alls, I feel sick._
"We're leaving," he announced loudly. "There's a guesthouse not far from here where we'll stop off and spend the night. I'd rather lie with sixty snoring dwarf-women and dwarves in scratchy hay than near that insufferably posh elf-woman."
The platoon laughed raucously and banged their coats of chainmail and shields for emphasis.
"Let's go! I feel like washing down my anger and frustration with a beer." Ireheart took up the lead of the baggage train and they trotted back to the winding paths.
The dark-haired dwarf-woman who had replied to Fiëa rode up alongside him and looked at him in awe. She had a sturdy build and she carried the double axe on her shoulder in the same way he was in the habit of carrying the crow's beak. "I've simply got to ask you to reconsider your decision, King Boïndil."
"Well, we certainly aren't staying here unless Vraccas appears and demands it of me."
"I didn't mean that, I meant you turning down the position of high king and not wanting to have the election take place for another twenty cycles," she explained. Underneath her leather cloak he could see a blackened coat of chainmail.
"Is that what you mean?" Ireheart looked at her in surprise. "Remind me what your name is? The anger banished it from my memory."
"Beligata Hardblow from the clan of the Bloodshedders, formerly of the Thirdling tribe, now a freewoman." She gave a small bow, revealing a delicate but green scar on her right cheek.
"And why should I change my mind?"
"The tribes and their clans need a high king who stands for loyalty and heroism. _You_ have _both_." She pointed her thumb contemptuously over her shoulder. "They're just two pointy-ears but they've barely crept out of the forests and they're already revealing their old arrogance. A dwarf like you, with your age, experience and history could run against them to be our high king. Otherwise the people will soon be awestruck again and elevate them into gods of wisdom." Beligata bowed her head lower this time. "You'd have my vote." She dropped back into the baggage train.
Ireheart mumbled to himself and started to brood.
_I can't allow bad thoughts to have any space in my heart. Otherwise we'll soon be back where Girdlegard once was._ He clicked his tongue and set the pony trotting. _Beligata is right. Unity. Among the Children of the Smith and all tribes. That is the best way._
Nevertheless, he preferred the inn to the company of the elf-woman this evening.
A little later they had reached the farmstead and handed the innkeeper's family an entire cycle's salary, although it did mean that barrels of beer and provisions were emptied and the cupboards were cleared of sausages and cheese.
In the middle of a beautifully belted out rendition of "A thousand tankards, a thousand drunkards," the door opened and a dwarf entered the room, soaked to the skin. His face was positively glowing with happiness as the whole troop waved their tankards in his direction and seemed to sing in his honour, making the window panes rattle.
He thanked them at the end of the song with a deep bow and had a beer mug pressed into his hands.
Before helpful hands could even push him towards the fire to warm up, he hurried over to Ireheart, who was watching all the fuss, tipsy and tickled.
_Being king like this is fun._ "What have you got for me?" he greeted him and laughed. "I'm sure you're rarely granted such honour on your arrival."
"Not even for the most wonderful or terrible news, my king." The dwarf grinned and bowed to the monarch. "Baromir sent me to you so that I could let you know two things before you arrive at the Blue Mountains."
_Vraccas, no bad news._ Ireheart sat up straight. "What's wrong in the Blue Mountains?"
"Don't worry, everything is running as smoothly as a wagon on a track. The works are coming along." The messenger lowered his voice which made him hard to understand amid the revelry. "It's about the writings of the älf who was rescued from the palace. The human king has decided to ban them because they could lead readers astray. The idea is to prevent anyone starting to pity the black-eyes or understand their views. Only the scholars are allowed to look at them and analyse them."
_They are afraid of the quill, once the sword has been overcome._ Ireheart thought about it. "Well, I don't care, although it's nonsense. After all, anyone in their right mind who reads them knows what and who they're about. I hope the scholars aren't more susceptible than the corruptible readers." He winked as he took a swig of beer. "What else?"
"Here's the most outrageous thing," the dwarf's voice cut through the din of the bar. "There are notes about an elf settlement in the Grey Mountains. One cavalry officer is already on the way to Queen Balyndis from the tribe of the Fifthlings to let her know."
Ireheart almost spat beer all over the messenger. The nape of his neck itched, his facial hair seemed to stand on end. Aghast, he swallowed with difficulty and wiped his sleeve across his lips. " _Pointy-ears_ in the _mountains_?" He set the tankard down on the table with a bang, making the platoon's conversations and laughter fall silent all of a sudden. _Vraccas, that really is enough now! I've understood your signal to me._
Every pair of eyes was fixed on him; the dwarves from the various mountains suspected terrible news was going to be announced.
The stately monarch of the Secondlings tossed his plait over his shoulder, stroked his silvery black beard, climbed onto the table and shouldered the crow's beak. "With Vraccas as my witness," he cried, letting his gaze rest on Beligata a little longer. "Take this message to the dwarf kingdoms: if the tribes so wish, I want to be your high king as soon as possible!" He waved the tankard in the air. "And I'll drink to that."
The whoops of glee this unleashed made the inn shake to its foundations.
Ishím Voróo, Älfar town of Dsôn Elhàtor, 5452nd division of unendingness (6491st solar cycle), autumn
_You fools._ As the locals rejoiced, Aiphatòn trudged through Elhàtor next to the copper helmet who looked as if he had been put in chains. _One touch will be enough to put an end to your free will._
The warrior-women and warriors, who had supposedly been successful in attacking and destroying Dâkiòn, were being given a triumphant victor's welcome by their homeland.
Colourful petals twirled as they rained down on them, cries of joy and fanfare sounded everywhere. Children ran along placing sashes over the fighters and pinning little bunches of flowers to them as they went uphill to the monarchess' palace with their unusual captive.
_Has nobody noticed how blank the homecomers' faces are?_ Aiphatòn's legs were moving of their own accord, driven on by the external will. _Their silence would seem odd to me._
From secret experiments, he now knew that he could often move of his own accord. The botoican-woman thought he was submissive like the rest of the army. That had proved useful not too long before, when he had been busy in the hull of the ship just before being ordered to disembark.
Through the hail of fluttering blossoms they approached the white palace, where banners and flags were flapping in the wind to welcome the army. This was the monarchess' way of paying homage to them.
Aiphatòn could feel the delicate petals on his bare torso, some sticking to the armour and his brown skin. He had to leave them wherever they landed.
Irïanora and Ávoleï were at the front in their white leather armour. Kôr'losôi was somewhere among the troops, equipped with a close helmet so that his human features didn't give him away. The ghaist remained staunchly by Aiphatòn's side as if he suspected how many freedoms the älf truly possessed. _Hopefully he doesn't notice my smell._
The procession had reached the front courtyard, which was lined with crowds of älfar. The town house-like palace towered before them, its façade decorated with whalebone and dark blue marine motifs; the crowd was still clapping and screaming in excitement about the fleet's victory.
Modôia appeared on the large balcony first, wearing a white dress, and her arrival was immediately cheered. Next came her son Ôdaiòn in his ostentatious blue and silver clothes. Leïóva joined them but stayed very much in the background; her black clothes made her look like the consummate älf-woman.
Aiphatòn's legs paused and the copper helmet came to a standstill too.
Some warrior-women and warriors formed a large circle so that they towered up right in front of the onlookers, while the others marched with Irïanora and Ávoleï through the gate to get to the balcony.
_They are getting into position. It's going to happen extremely quickly._ Aiphatòn clenched his teeth in disappointment. _My plan could go awry. But all I need is a small opportunity._
Then his legs started to move; he was following the commander and Shôtoràs' niece. This route took him through the gate in the reception hall and immediately up the stairs to the left. He reached the balcony above the front courtyard soon after the elf-woman and älf-woman.
The prickling was back and it hurt more than it had on his first visit. His magic-steeped body was coping with his time here increasingly badly. _I hope this isn't giving me any permanent damage._
Aiphatòn's legs had stopped and he found himself right next to the black-clad elf-woman, who stayed in the shadows and looked around warily. It seemed the botoican-woman had him in mind as back-up against Leïóva.
When Irïanora and Ávoleï walked to the balcony's railing and joined the monarchess and her son, the frenzy of delight was stoked further and further until Modôia, who looked weak and sickly, raised her arms to make the crowd fall silent. The sun shone down on her and made her blonde hair gleam.
"What a tragic moment of unendingness," she cried, sounding less euphoric than expected. "Our victorious army returns with the news that Shôtoràs and Dâkiòn are history from now on. And Inàste knows that they forced us into it. Many älfar had to die and it hurts deep within my soul. But even the Creating Spirit knows: I had no choice." She took a symbolic half-step to one side. "Tell us what happened yourself and who this mysterious captive is that you bring to us."
Ávoleï stepped up to the balustrade, took a quick breath and then looked out over the silent crowd. Tears welled in her eyes although there was a contorted smile on her face.
_She is resisting the command._
Leïóva watched her daughter carefully, her brow furrowing.
_Is she the only one who has noticed Ávoleï is struggling? They'll mistake_ _it for emotion. As compassion towards the dead._
The locals remained intrigued. Nobody dared order the commander of the successful fleet to hurry up and begin.
More soldiers marched up onto the balcony. They had belonged to the contingent fighting Dâkiòn. Elhàtor's residents thought they were saluting.
_In reality it's about forming a chain from the ghaist all the way up here._
Ávoleï wrapped her fingers around the railing and lowered her head, panting. "We sailed up the river," she began a disjointed story.
Aiphatòn stopped listening to her words. He wanted to use the opportunity he had been given, out of eyeshot of the ghaist. "Intervene," he said softly to Leïóva. "We were put under a spell. Whatever happens, don't let yourself be touched by any of us or the botoican's power will break your will."
The elf-woman glanced at him in shock. "Botoican? What..."
"The creature with the copper helmet waiting patiently on the square, that looks like it's in chains, is a ghaist. It is under orders to conquer Elhàtor and make its inhabitants mental slaves. Dâkiòn has already fallen," he whispered quickly.
"But what about you?" Leïóva didn't seem inclined to believe him.
"Look at your daughter. Do you think she's behaving as a victorious commander should?"
The black-haired elf-woman looked at him, disconcerted now. "It sounds absurd."
_I understand her doubts, but they're no use to me._ "I'm only partly under his spell because I have more magic in me than the other älfar," he explained urgently. "The ghaist is going to attack very soon, then the soldiers will touch you, the monarchess and her son. They will grab hold of the people in the square and with their help they'll form chains and spread the influence spell into every last corner of Elhàtor." Aiphatòn dared to turn his head slightly towards her. "Anyone who escapes him will be hunted down and subjugated later, like they did in Dâkiòn. Like they did to your daughter too."
"What can I do to fight the ghaist?" she whispered, not letting her fear show. He saw her muscles moving underneath her black clothes as she got ready.
"Fire." Aiphatòn carefully turned to face forwards again. "The hottest fire there is."
Leïóva took a few cautious steps backwards. "I'll fetch our best cîanoi. He'll know how to fight a botoican." She gave him a probing look. "If you're deceiving me, emperor, and you're actually behind all this, nothing will protect you from me." The elf-woman disappeared into the corridor without a sound and he could no longer see her.
Aiphatòn hoped Leïóva would pull off a miracle.
In the best-case scenario, the Elhàtorian älfar would take out the ghaist and Aiphatòn could proceed with the plan he had started to form in the hull of the ship; in the worst-case scenario, the elf-woman died, no suspicion fell on him and he would stand by for his next opportunity.
"... we freed the copper helmet from the sovereign's dungeons," Ávoleï cried in a choked voice. "We brought him with us because..." She faltered. "Because... it's a lie! I'm lying to you!" She took her hands off the railing and balled them into fists. "You are all in great danger," she moaned. "We are under a magic spell and have come to subjugate you too."
One of the soldiers on the balcony drew his sword and approached her from behind.
Ôdaiòn tried to stop him with a gesture but the warrior carried on moving towards the elf-woman. To him, the monarchess' son didn't count for anything. "Soldier?"
"Ávoleï?" Modôia came and stood next to her sympathetically, placing a hand on her shoulder. "Child, what's troubling you?"
Aiphatòn's eyes widened. _She's resisting!_ He saw the mistake the botoican-woman had made: _she overlooked the fact she's an elf-woman. The magic works less powerfully on her. Just like with me._
"Hey, soldier!" Ôdaiòn walked towards the armed soldier. "Get back! What do you think you're..."
The warrior brought the sword down at a slanting angle, sliced through the monarchess' son's collarbone and left the collapsing princeling to die. Then the warrior lifted his arm to stab the elf-woman's armoured back.
"No!" Modôia launched herself at him—and the point of the sword ran right through her abdomen. The sword jutted out through her back. The monarchess clung to the soldier to protect Ávoleï for as long as she could.
The locals beneath the balcony were screaming in horror. They rebelled, pressing towards the square and pushing the guarding warriors together.
Ávoleï saw her murderer coming. Her whole body trembled, visibly struggling against the orders being given to her by the botoican. "Run! Run and jump into the boats! Before they get their hands on you, slit your own throats!" She turned her gaze to Aiphatòn. "Otherwise you'll be lower than slaves."
The black-haired elf-woman threw herself over the balcony head first. The impact came straight away, followed by yet more bewildered screams from the crowd.
_Did I scream too?_ Aiphatòn realised his mouth was hanging open.
He couldn't move and meanwhile a revolt was breaking out in front of the palace. The botoican-woman's command over his body meant he couldn't move his legs to get to the railing and look for Ávoleï.
_What was it that had been in her eyes before she jumped? Confusion, fear and..._ His solar plexus ached, suddenly feeling cold.
By now, the soldier had shaken off the severely wounded monarchess, but he was standing around uncertainly because Ávoleï had escaped his attack. There were no more opponents he was meant to be attacking. So he turned into a statue.
The screams from the crowd soon grew quieter, as if the locals were seeking shelter in the houses, but very few had actually left the square, as Aiphatòn could tell from the sounds of the footsteps.
But since the clash of weapons didn't ring out, this meant: the ghaist and Kôr'losôi had set to work.
Aiphatòn turned his head and saw the soldiers march up on all sides and form a chain—they held hands on some silent command. The spell could be passed on as far as the balcony.
Modôia pulled herself up by the railing, her right hand groping for the three-strapped whip she wore on her belt; as she did so, she slipped the protective sheath off the blades and cut herself. She didn't even screw up her face. The blood came gushing out of the gaping wound in her abdomen and drenched her white dress. "You won't get me." Her eyes turned even darker, literally devouring the light. Black lines marked her face and soon her weapon cracked, ripping the head off her son's murderer.
Whirring and unbelievably fast, blow followed blow.
The blades brought endingness, whistling and softly jingling, the leather straps loudly whipping. Body after body fell to the white stone and blood spatter clung to the pale wall, furnishing it with new works of art. A number of droplets rained down on the monarchess, a frozen Irïanora and Aiphatòn. His legs walked backwards until he reached the wall without any input from him; Irïanora soon followed. _Our mistress is taking us to safety._
The botoican-woman had apparently had enough of Modôia: a dozen warrior-women and warriors drew their swords at the same time and charged at the monarchess.
But she dealt out death undaunted. Two opponents had their stomachs slit open, a third had his skull smashed to pieces, and finally the weakened monarchess fell to the ground amid the stabs and punches. Her long blonde hair, the white dress—it was all coloured by her own and others' blood.
Aiphatòn's feet carried him forwards to the railing now so that he could look at the square.
Directly below him, Ávoleï's corpse lay on its back, not a single blemish visible. _She must have broken her neck._
The ghaist was standing tall, his strong, bare arms outstretched and touching two warriors on the shoulder. Through them, the influence spell had passed into the other soldiers and from there into the crowd on the square.
A few hundred älfar stood dumbly in front of the palace, their eyes fixed on the ghaist. Further away, in the streets paved with tiles of bone, others lay dying with their throats slit, having taken Ávoleï's warning seriously and killed themselves before the spell got to them.
But seven chains of älfar were nevertheless moving away from the square through the alleyways to carry the botoican-woman's power deeper into Elhàtor and enslave the town.
_Hopefully lots of them manage to kill themselves. Then I'll have less work to do._ Aiphatòn still did not allow himself to feel pity. He had seen too much suffering caused by his people. _No älf is blameless!_
He couldn't help but gulp as he looked at the beautiful elf-woman. He remembered her last glance, which had been at him, and her lips on his...
A steady jet of fire made a whooshing sound as it shot out of a side street and burned its way through the crowd, completely enveloping the ghaist and the two warriors.
Burning and roasting, everyone struck by it fell to the ground and the chain was broken.
_Leïóva. She has found a cîanoi who has not yet succumbed to external will._ Aiphatòn could clearly feel sensation returning to his legs, although he remained where he was. As long as the ghaist was still alive, he couldn't give up his charade.
The elf-woman rode into the square on a night-mare holding a very large sword with runes engraved on it.
The hissing jet of fire continued relentlessly, keeping the creature with the copper helmet enveloped in flame. Having turned to ashes, the älfar dispersed, the little grey and black flakes swirling away.
The ghaist turned around, looking for the cîanoi whom Aiphatòn couldn't see. The leather armour crackled as it burned, the fake flesh sending tongues of flame and white sparks into the air.
_Will this work?_ Aiphatòn waited to see what would happen. The tremendous heat surged up to where he was on the balcony.
Having just reached the creature, Leïóva swung her sword at his head with a terrible scream; the stream of fire stopped at the same time so the elf-woman wouldn't be burned. The magically formed creature kept burning.
_Too soon! That was too soon!_ Aiphatòn had desperately hoped the sword would split the now red-hot copper in two—but the blade left a deep, straight dent, failing to penetrate the helmet.
The burning ghaist staggered and fell. It was able to get away from the trampling hooves of the night-mare and received more blows from the sword, but the blade did not destroy it. Nothing but little flames darted from the wounds inflicted on it.
"Give him some more of your fire!" Leïóva realised her mistake and moved the black horse back so the cîanoi could finish the job. "Quickly!"
But the ghaist suddenly sprinted off, shooting tongues of flame as it ran towards some corbels and launched itself forcefully off them.
It flew several paces through the air like a comet and then sank towards the ground much too soon. It crashed onto the sloping street between the houses, the impact breaking off small segments of bone that bounced around and came tumbling after the creature. It rolled downwards head over heels and landed with a splash in the harbour.
Leïóva cast a quick, inquiring look at Aiphatòn as if he could tell her whether this was enough to destroy a ghaist.
Then bright flames shot across the water, from the quay wall to the mouth of the harbour, and danced around the rest of the fleet, the smaller ships, the rònkes and escort sailboats and it looked like the sea was ablaze.
The first explosion followed instantly, blowing up the boat that Aiphatòn had secretly bored a hole in so the petrol could flow out of the smashed barrels through its hull. Rigging and sails caught fire, and one ship after another flickered with flames.
_It's working._ His plan was a success. There was no escape for the älfar anymore. The fire would definitely spread throughout Elhàtor now and the residents would be wiped out. _I'll help things along however I can._
Then he would sail back in a boat and kill the botoican-woman herself to get his spear and toss the remaining älfar into endingness with Nodûcor's powers.
A loud curse rang out below him.
When Aiphatòn turned his attention to the square, he saw Kôr'losôi standing close to Leïóva but not touching her.
The elf-woman had just slipped out of the night-mare's saddle, having rammed her own sword through her breast, and was staring straight ahead with pain etched across her face.
_She followed her daughter's advice too._
He looked at the botoican, who couldn't have known how many freedoms Aiphatòn had. _Now I'll kill you._
Then his own torso turned, hips and legs following obediently.
_I... how can this be?_ His feet carried him over the dead Modôia and her slain son to the steps. His soles left red prints in the blood of the dead. Irïanora followed.
And thus it was clear: the ghaist was still alive, the heat had not been enough. The victims and Aiphatòn's plan had all been for nothing.
# Chapter XIV
_Don't believe what you're told. Make up a lie that everyone falls for. Even you._
Wise saying of the Älfar
Collected by Carmondai, master of word and image
Ishím Voróo, Several miles outside Dsôn Dâkiòn, 5452nd division of unendingness (6491st solar cycle), late autumn
Aiphatòn glanced back at the gigantic town's burning buildings, from the smallest house to the sovereign's palace in the upper town. _What a waste._
The clouds of smoke soared into the sky, proclaiming the end far and wide: Dsôn Dâkiòn, the Majestic, thus suffered the same fate as Dsôn Elhàtor, the Magnificent, albeit much later and unexpectedly.
So the town, built by some unknown, giant creatures, perished for a second time, set on fire by its former inhabitants. Nothing from it was salvaged, no artworks or gold or any object that could serve as a memento.
_The botoican-woman wants to make sure that nobody comes back here or resettles it._ Aiphatòn was walking at the head of the convoy, surrounded by the Majestic's warriors. His legs rose and fell, as so many times before, of their own accord.
The ghaist was leading the älfar that remained at his disposal after the suicides and the blaze. They were headed southwest towards the place they planned to stay next: Tr'hoo D'tak, the Nhatai town.
_There ought to be an opportunity to kill the botoican-woman there._
After the fire in the harbour, in which the navy relief forces had all died, the flames had spread to the houses near the quay and from there to Elhàtor, as Aiphatòn had planned.
At first it had looked as though there was no way of escaping the island. But then the grotto with more rònkes was discovered.
They sailed as far as the mouth of the Tronjor in them, and then rowed and sailed as far as possible with the smaller dinghies against the current before getting out at the rocky bottleneck and crawling along the arduous route along the bank, coming out at Dâkiòn.
The marsh had cost them a lot of time and some more lives due to exhaustion. The mosquitoes from the nearby swamps transmitted illnesses and fever wiped out more älfar.
Aiphatòn reckoned they had brought at most seven thousand Elhàtorians with them. _It wasn't worth it for the botoican-woman_ , he thought grimly. _Samusin could make the fever we're carrying spread through her entire army and even infect her. That would be payback._
A loud rumbling noise sounded at intervals from behind him whenever a house collapsed in the doomed Dâkiòn and brought other buildings down with it. When an unusual metallic clanking and creaking mixed in with it, the älf guessed that the golden bridge had collapsed.
The ghaist suddenly started to sprint, moving swiftly away from the troops.
Kôr'losôi came to join Aiphatòn, so close that their shoulders touched; the monarchess' three-strapped whip dangling at his right-hand side.
"Finally," he said, breathing a sigh of relief. "I thought it would never disappear. After that business in Elhàtor, suspicions were running high. I think there was a fear that more elf-women and elves would be found among the inhabitants." The fair-haired botoican looked at Aiphatòn. "I couldn't get to you sooner to make arrangements. That would have put our plan at risk."
The älf nodded and feigned sympathy. He knew he'd been very lucky. The disastrous events in Elhàtor were put down solely to the elf-women's resistance to the control spell; suspicion didn't fall on him. "Where is it going?"
"It's hurrying on ahead of us, either to announce our arrival or because my cousin Fa'losôi has a specific use in mind for it." Kôr'losôi followed the copper helmet with his eyes. "Whatever. As long as it stays away, I feel more at ease."
Aiphatòn thought he saw a white tower looming up in the distance. "Is that where we're going?"
"Yes. Fa'losôi has moved her town to have more space for the huge number of warriors. Our towers can be dismantled," he explained. "They look enormous but they can't withstand more than the average storm." He looked warily at Aiphatòn. "What are you planning?"
He smiled darkly. "I saw the ruins of a residential tower like that one. They must catch fire easily?"
"The proportion of wood is high, yes." Kôr'losôi didn't seem to like this. "But planning to set them on fire is far too risky. They could be salvaged. Your spear must kill Fa'losôi, _then_ it will be a sure thing."
"Then get it for me."
"I can't. Shôtoràs and the others kept it."
"I take it Nodûcor and the älfar from Dâkiòn are already there?" Aiphatòn was constantly worrying about whether the cîani had managed to remove the half-mask. It would fit nicely with his new plan.
"Of course." Kôr'losôi glanced over his shoulder to keep an eye on the stragglers. "We'll lose at least another fifty or more," he estimated. "Malaria. That's what I call irony." He let out a laugh. "Have you ever... oh no, how could you have," he interrupted himself.
"What do you mean?"
"The more powerful an army, the more often a family moves. Most of our towns quickly turn the surrounding area into muddy land, depending on the size of the army and the creatures' excrement. Rain doesn't improve the state of affairs. Before the morass and smell become unbearable, we move on," he explained.
Aiphatòn also turned around briefly to check on the weaker warriors.
There was a cowering figure every hundred or two hundred paces, while on the horizon, Dâkiòn descended into flames and smoke. Anyone who could still move was crawling along on all fours or on their elbows behind the baggage train. The will of the botoican-woman knew no mercy.
"There was a time when the families aspired to build kingdoms like the ones the älfar built before the old Dsôn fell and you were scattered to the four winds," Kôr'losôi told him. "They conquered the most enormous fortresses in just one day. No wall could withstand them."
Aiphatòn thought about the Stone Gateway with its gigantic fortifications. _I've got to find out more._ "Without siege equipment?" he asked incredulously. "I doubt that."
"The tribes they conquered doubted it too at first," Kôr'losôi replied, laughing. "All that a botoican army needs is bulk. Bulk is malleable, flexible, you can stack it up and let it down like a rope, you can even make it build bridges." The botoican grinned. "I know you can't imagine it, but that is its very advantage." He reflected. "The älfar must have had acrobats who performed tricks as entertainment?" he asked.
"They performed art that had to be practised for a long time, not _tricks._ We leave those to animals."
Kôr'losôi waved a hand dismissively. "Well, I'm sure they built towers where someone climbed onto someone else's shoulders and that kind of thing?" When he saw Aiphatòn nod, he clapped his hands. "That's _exactly_ how our armies overcome walls and fortresses. They climb one on top of the other, and very quickly too."
In his mind's eye, Aiphatòn saw two hundred thousand beasts, monsters, people and älfar running up the thirty-pace wide approach road and stacking themselves in front of the closed doors of the portal until they reached up high enough to take the defending forces by surprise. _They don't need to open the gate. They climb over it._
"And then if you've got," Kôr'losôi continued his story, lost in thought, "over a hundred ghaists at your disposal, there's no stopping you."
"A hundred?" Aiphatòn had been confident he could protect Girdlegard if the botoican-woman's hunger for more land and soldiers increased further and spread beyond the wasteland, but that confidence was melting like ice in the sun. "What will happen to all of these creatures if I kill their mistress and free them from her will?"
Kôr'losôi looked pensive. "I've never been there when it's happened. Maybe they win their freedom? Or they die? Or they just freeze mid-motion?"
_We need a lot of petrol. Or the power of numerous cîani._ Aiphatòn saw the single needle-shaped white tower drawing closer. "Do you know where the armies are going to encounter each other?"
"No. We'll find out as soon as we get to Tr'hoo D'tak." Kôr'losôi broke his connection with the älf. "I can't weaken Fa'losôi's power for too long. We're already very close, she might notice." He peeled off from the baggage train and let the älfar march past him. His lips formed the words, _stay patient_.
Aiphatòn laughed inwardly. _Patience._ As an immortal being, he had all the time in the world, the best prerequisite for having the utmost patience.
But right now, time of all things was his greatest enemy.
_What will the botoican-woman do if she notices that I can resist her to some degree?_ Aiphatòn and the head of the convoy from Elhàtor reached the town's outermost foothills where they found strange tents made out of shabby coats, tattered sails and ragged tarpaulins. Gnomes and smaller monsters were scurrying around, bickering and arguing over half-rotten chunks of meat, the origins of which were more than a little dubious.
The stench of excrement that hit them made Aiphatòn feel sick. The swirling smoke from all the campfires couldn't cover it up. Every beast, every man and every woman, every creature in this army seemed to relieve themselves wherever they saw fit.
_But they haven't been in this spot for long._ Aiphatòn suddenly felt an attack of nausea. The soggy ground gave way beneath the soles of his feet as they pressed on towards the pointy white tower. It was emblazoned with green runes, no doubt proclaiming that this armed force was under the command of the Nhatai family.
Soon Aiphatòn realised that the tall structure had been built at the other end of the camp so that the älfar had to march straight through it.
The small tents gave way to shelters made of wood, initially ones with brushwood walls to keep the wind out, then walls made of small tree trunks and finally ones with planks and eventually even foraged stones.
The botoican-woman's power pulled off a miracle: orcs slept next to humans by the campfire, trolls and ogres lay right in the middle because they were too big for the buildings and they rested their ugly heads on their arms. All enemy beings and races squatted down close together without going at each other's throats and flesh.
Admittedly, loud arguments did break out but Aiphatòn could see that as soon as a ghaist appeared, the quarrel ended as quickly as it had flared up. They clearly served as the supervising authority, stepping in and strengthening the botoican-woman's spell with great precision.
_However it is they manage it._ Out of the corner of his eye, he saw one of the copper helmets using his bare hands to tear the head off an orc who wouldn't calm down and then throwing his corpse to his clan, who set about it hungrily. There wasn't even a flicker of protest at the treatment of their relative. Smacking their lips and grunting, they devoured one of their own kind.
The baggage train went on and on, past the familiar and unfamiliar beasts of Ishím Voróo.
Aiphatòn even spotted several oboona who weren't in raptures watching the älfar go past like they ought to have been.
He remembered the stories that Carmondai had told him about them and how Caphalor lost his family to the worst of them. _Now their gods walk past them and they just stare into the fire. They've found a stronger power._
Kôr'losôi appeared next to him. "Don't be surprised if your legs choose a different route soon," he explained, without touching Aiphatòn. This was his way of communicating his cousin's will. "Fa'losôi is expecting us in the tower. But first she wants to make sure that you're washed and changed."
Aiphatòn only just stopped himself responding with a question when he saw the warning look on the botoican's face.
He and Kôr'losôi turned and left Elhàtor's älfar army who hurried on, heading for an area where black tents towered into the air. His tribe seemed to be the only ones in the crowd who, despite all the magic, were trying to maintain a vestige of dignity.
The door to the narrow, white tower—which looked out of place towering up out of the excrement and crowd of creatures—was five paces above the ground but there were no steps up to it. In the doorway stood a brown-haired woman wearing a dark green dress with white embroidery on it.
"Don't be surprised. I hinted at what would happen," said Kôr'losôi.
Particularly strong orcs loitering underneath the entrance suddenly stood still and used their bodies to form a sturdy staircase which Aiphatòn and the botoican climbed up; the pair were hardly inside the building when the beasts scattered and the steps made of broad, armoured orc necks dispersed.
"Welcome, Kôr'losôi. Our cousin is eager to hear what you have to tell her," said the botoican-woman, who wore her hair short and strongly resembled her relative.
"Thank you, Saî'losôi. Have you been a good confidante and aide to her in supervising the army?" He gave her a kiss on the forehead.
She returned his greeting. "She didn't need me. So I just supplied her with food and drink." Saî'losôi didn't look at Aiphatòn.
_She thinks I'm one of the botoicans' normal tools._ He looked around surreptitiously as his legs started moving to follow Kôr'losôi and Saî'losôi.
They passed through a compact corridor which brought them into a narrow shaft with a spiral staircase winding its way up the walls. It smelled of varnish and dry wood.
_That's crazy: this tower is going to burn like firewood._ Aiphatòn started plotting. _It's obvious they've never played Tharc or had to wage a real war._
There was a platform on the ground fitted with a lever mechanism. They had barely stepped onto it when Saî'losôi shifted one of the levers.
Invisible chains unwound, cogs rattled and they kept moving upwards for what Aiphatòn thought was about fifty paces.
"See you soon," Kôr'losôi said in parting. The look in his pale eyes urgently warned Aiphatòn not to do anything stupid.
The älf left the platform and as usual, Aiphatòn's body performed actions without him thinking about it. He went through a door and behind it he found a bathtub with scented water waiting for him. Towels and clean clothes had been laid out.
The bath did him good. It was only now that he realised how badly his own things stank of brackish water, salt and sweat.
He observed himself getting out of the tub, drying himself off and putting on the black robes emblazoned with the runes of the Nhatais. _It's as if I myself were giving orders to my hands._
Then he went out and hurried up the stairs before stopping outside a large door that then opened.
Aiphatòn found himself in an anteroom where Kôr'losôi, Saî'losôi and Tanôtai were waiting for him.
The death-dancer also looked like she had been allowed a bath—she was wearing similar clothing to the shintoìt and didn't have her needle-daggers; the red-haired älf-woman's gaze was vacant and listless.
Together, they all went through the elaborately carved double doors and entered a bright room with numerous candles burning.
Incense smoke filled the air, dispelling even the slightest trace of the stink of excrement. A cosy bed had been made up with embroidered cushions, blankets and pelts, and a low table with food stood in front of it.
Unable to resist, Aiphatòn thought of Ávoleï, of the kiss, of her glance, of his encounter with her, of her scent... Bewildered, he pushed her image aside. _I cannot allow myself any distractions._
Diagonally behind the seats, a ghaist remained slightly in the shadows. The long, deep dent in the copper helmet gave him away—he was the creature who had escaped falling victim to the magic fire and the elf sword by a hair's breadth. His strong arms dangled down with no signs of wounds and his old, burnt armour had been replaced by new armour.
_They couldn't replace the helmet. Because the souls are bewitched_ _inside it._ Aiphatòn's patience was tested again as he walked towards the bed of cushions and blankets, flanked by Kôr'losôi and Saî'losôi as Tanôtai walked ahead of him. Although the botoican-woman was controlling her, her footsteps retained their dancer-like quality and grace. The two älfar took a seat next to one another.
The botoicans sat down opposite them.
"My cousin has brought me a very special guest," a female voice rang out, followed by a metallic clanking sound as something Aiphatòn recognised very well struck the paving stones.
_She has my spear with her._ It took a huge amount of control for him to keep facing forwards like the death-dancer.
A cloud of incense smoke enveloped him, a breath of wind caressed his neck—and he felt the tip of his own weapon at the nape of his neck.
"Aiphatòn, emperor of the älfar and son of the Inextinguishables. A pure shintoìt," said the stranger behind him, impressed. "The magical potential in you must be considerable." She walked around him and went to take her place at the head of the table while Saî'losôi and Kôr'losôi greeted her with slight bows; she placed the spear across her lap. "No, it's _different_. That's the right word. Different from the way it is for the cîani, who brought about the conquest of Dâkiòn and Elhàtor for me."
_Is she commanding the mob?_ Aiphatòn found her very unprepossessing.
She was a petite human woman with a bald head and white Nhatai tattoos on her thin skin, her veins visible through it. A black oval was painted in line with the bridge of her nose, accentuating the affixed diamond chip. Her white and dark green robes looked like they were made of silk and silver chains studded with gemstones in a variety of colours hung around her neck and wrists. "I am Fa'losôi, your mistress. So speak: what are you thinking?"
Aiphatòn suspected she had relaxed her spell. " _That_ is _my_ spear."
The three botoicans laughed at the same time.
"There, you see what happens if you allow the puppets to speak all of a sudden: they say whatever is going through their head," Fa'losôi cried out in amusement, her pale-yellow eyes scrutinising him. "Does that mean you'd like it back?"
"If I had it, I'd be better in battle and stay alive longer," he replied.
"Oh, you're already thinking about combat? A superb warrior!" Fa'losôi slapped her right thigh, her jewellery jangling softly. "Now eat and drink."
Tanôtai moved suddenly, looking in confusion from one to another of the assembled group.
Fa'losôi took a flatbread from the plate and filled it with chunks of cooked meat. "Don't get your hopes up," she said as she did so. "Your magic shackles from the navel downwards will stay in place so that you can't run away on me. But let's pretend you're not my puppets—act like you're my acquaintances and let's chat. It's a long time since I've spent time with älfar." She poured sauce over the aromatic morsels. "I killed most of them with my own hands. The two of you are an exception. In several respects." She took a bite and chewed with relish, then laughed with her mouth full.
Kôr'losôi and Saî'losôi joined in the laughter. They helped themselves to some of the food too.
"Are my people getting food?" Tanôtai asked icily.
"They're not starving if that makes you feel any better." Fa'losôi was chewing so noisily that it made Aiphatòn want to ram the spear through her throat even more. She leaned forwards and raised her goblet. "The best wine, from the cellar of Dâkiòn's sovereign. I took the liberty as he doesn't need it anymore. Your people are making use of the provisions, don't worry." She took a sip.
Aiphatòn didn't touch the food. _One brief pulse and I could summon the spear to me. Would there be enough time?_ There was no way for him to tell how quick she was. "Why did you kill the other älfar?"
Fa'losôi waved her wine. "Would you explain it to him, Saî'losôi?" she asked. "I'm too hungry. As soon as I feel full I'll take over the conversation."
Saî'losôi put her flatbread back down on the plate. "Fa'losôi is the daughter of Sh'taro Nhatai. Our family received a visit from one of your tribe's assassins. He killed her second cousin and simply took the head away with him. Presumably as a trophy. To this day, we don't know who the assassin was," she explained, looking enviously at Kôr'losôi who had carried on with his meal. Her stomach rumbled softly.
Fa'losôi looked at the botoican. "Recite my message, cousin, the one that I used to leave. And make an effort. Älfar like poetry."
Sighing, Kôr'losôi lowered the glass that he had almost raised to his lips; this time Saî'losôi grinned.
_She likes her little power games._ Aiphatòn couldn't find the words to describe the disdain he felt. He would have been so glad to summon his weapon.
Kôr'losôi sat up straight and spoke as if he were reciting a poem:
" _My name is Fa'losôi of the Nhatai family,_
_I declare_
_that the Nhatai family will not rest_
_until the murderer of my kin is found_
_and killed._
_Until then,_
_every älf is_
_fair game for the Nhatai family._
_If this message reaches the murderer of my cousin:_
_give yourself up and save countless älfar_
_lives_.
_Because I will come_
_and seize_
_every one_
_I can get my hands on._ "
"It doesn't rhyme at all," Tanôtai's assessment was disparaging. "Even a stammering child wouldn't have been that bad. The rhythm of the individual lines is awkward and at the end it would have been better if..."
"Yes, yes. I admit it could have been better," an offended Fa'losôi interrupted her. "It wasn't a good idea to try impressing an älf-woman with clumsy words."
"You'll have to command me to be impressed," the death-dancer shot back drily.
Aiphatòn guffawed with laughter—and was the only one to do so.
Kôr'losôi used the opportunity to keep eating fast.
Saî'losôi didn't quite know if she should continue her story. She didn't resume until her disgruntled cousin gave her the signal. "Over time, thinking changed and during her preparations in the battle against other botoican families, she managed to make a capture that she initially regarded as a stroke of luck. Sinthoras and Caphalor..."
"They're long since dead," Aiphatòn exclaimed in surprise. "When is this supposed to have happened?"
"After the conquest of... well, you call it Tark Draan." Fa'losôi relished his shock. "Oh yes, I'm older than you. Much older. As old as Shôtoràs perhaps." She stretched. "I aged better than he did." She had bitten into some bread, but she threw it back onto the plate, seeming to be full. "In any case, they stood before me one day, on Nhatai land, and I had them locked up in my tower."
Aiphatòn didn't believe a word she said. _As a human woman, how could she have lived this long? Even the magae and magi_ _of Girdlegard don't live more than at most two hundred cycles._ He rested his left hand loosely on his paralysed thigh. _It would take me less than a heartbeat to stab her._
Fa'losôi's mouth twisted. "Those two warriors ensured that... let's say... a spell went awry. It cost thousands of lives and it wasn't just simple-minded beasts who died. No, almost all of my Nhatais were killed."
"Only you weren't. What a shame," Tanôtai remarked, disappointed.
_She wants to provoke Fa'losôi into killing her in a rage._ Aiphatòn thought he could see right through the älf-woman.
"Only I wasn't, that's right." Fa'losôi finished her wine and poured herself some more. "I was presumed dead and my enemies tossed me into the swamp. The Nhatais were believed to have been wiped out and the remaining botoicans carried on with their usual childish efforts to outdo each other." The look in her pale-yellow eyes became haughty. "Their cowardly ancestors"—she pointed at Kôr'losôi and Saî'losôi—"surrendered and served as henchmen to the others." She threw her hands in the air, the gemstones jangling against each other. "But then I woke up from my magic sleep after a few years. I fought my way out of the marsh into the open air and escaped death by suffocation." Fa'losôi lifted her bald head and smiled cheerfully. "It took a while for me to understand what had happened. But the unintentional sleep caused by the misfiring spell strengthened my powers." She lowered her arms and grinned as she drank. "I couldn't help but be grateful to Sinthoras and Caphalor for trying to kill me that time. They recreated me. And in turn I rescued these two." She pointed at her cousins again. "Otherwise they would still be serving boy and girl to foreign masters."
"Is serving a mistress you know any different?" Tanôtai chipped in. "You're still slaves no matter what way you look at it."
Kôr'losôi paused in his chewing, Saî'losôi glared spitefully at her.
"The death-dancer has a sharp tongue." Fa'losôi looked amused. "Huh. Why did I used to kill älfar before? I could have had so much fun at mealtimes." She burst out laughing.
"You're going to kill us too. By deploying us on the battlefield," Aiphatòn replied. He could barely control himself any longer. His weapon seemed to be calling to him to free it from the sorceress' fingers.
"Indeed. But at least I've talked to you first." Fa'losôi leaned back against the cushions and placed her hands on the rune-emblazoned spear shaft. "This isn't steel. And the armoured plates are made of an alloy I've never seen in the wasteland before."
"My parents made it. This metal is one of a kind. Like me," he answered. A new brainwave came to him in a flash. _Could I successfully win her trust by stealth? I wouldn't need to rush anything and I'd be in better control of the situation than the one I'm currently in._ He thought of the ghaist that was still in the corner. _An enormous imponderable._ "If you hand over the spear, I'll lead your army from victory to victory."
"I'm victorious anyway," she countered cheerfully.
"But you sustain high casualties. And then the ghaist creatures scurry about looking for reinforcements. That takes time, and your enemy could pounce on you in the meantime," he reeled off the reasons. He thought he'd found her vulnerability. "Do you play Tharc?"
"What's that?" Fa'losôi looked curiously at him and rolled the flats of her hands over the spear, making the tip spin.
"An älfar strategy game. I was the best at it," he lied.
"And how do you plan on commanding my troops when you don't have any power over them?"
Aiphatòn pointed to Kôr'losôi and Saî'losôi. "I'll tell _them_ what the army is to do, they'll implement my instructions and the victory will be achieved in no time. Even against a force that seems greatly superior," he suggested. "So you and your relatives decide what happens."
"Are you certain, even against the _greatest s_ uperior force?" Fa'losôi gave a cunning grin. Her emphasis puzzled Aiphatòn but he could no longer take back his promise without her losing interest. "Why should I believe an älf seriously means what he says?"
"Because I'm immortal and would like to stay that way." Aiphatòn sounded completely serious because that's exactly what he meant.
"And because he's a coward from Tark Draan," Tanôtai angrily snapped at him. "He will stand at the back and watch as others go to their doom on his orders."
He laughed. "That's what all generals do."
The death-dancer uttered a contemptuous noise. "I forgot: you were the _emperor of the älfar._ You never stood where the battle raged." She picked up her glass.
_Is it me she wants to kill now?_ Aiphatòn's eyes narrowed into slits, he turned to face the red-haired älf-woman. "You will..."
"Are there still älfar in Tark Draan?" Fa'losôi interrupted him casually.
Kôr'losôi and Saî'losôi had stopped eating, having taken enough hasty mouthfuls. They waited eagerly for the response.
"No," he answered and turned to the botoican-woman. "They were wiped out by magic and an army that was second to none."
He didn't reveal the full truth. No doubt some of his tribe had still roamed Girdlegard but they ought to have been picked off by Ireheart's crow's beak or the weapons of braver warriors.
"That fills me with a certain satisfaction." Fa'losôi leaned forwards and poured herself some more wine. "Because if I send you and your friends from Dâkiòn and Elhàtor to their deaths, your race will"—she paused, searching for the right word—"pass into endingness. Belated revenge for my kin becoming the victim of an älfar assassin." She nodded, as if she were enjoying the thought of it. "But now you: what drove you to enter the wasteland?"
"Girdlegard no longer belongs to me. The armies are too strong, the defending forces prepared for anything and I was the only älf left. So what business did I still have there? As I mentioned, I'm fond of my immortality," he replied glibly. "I managed to get away from my pursuers. I jumped off the portal on the Stone Gateway and fended for myself. Here..."
Beside him, Tanôtai suddenly smashed the glass in her hand and at the same time stretched her arm out in one seamless throwing motion to hurl the largest fragments at Fa'losôi.
But the petite älf-woman's hand didn't open.
Gasping, Tanôtai stared at her paralysed arm. Aiphatòn looked at her face, fear and disappointment written across it.
"My will is stronger than your thought," Fa'losôi said unsympathetically. " _Quicker_ than your thought."
One finger after another closed around the shards; they crunched as they rubbed together and cut into her flesh.
The death-dancer screamed in pain. Blood dripped, then ran down her arm and hit the cushions. Once the tendons had been severed by the blades of glass, her hand opened, the little fragments flying onto the table or falling almost inaudibly onto the fabric.
"Your flesh is mine," said Fa'losôi coolly.
Aiphatòn was forced to watch what happened next.
Tanôtai leaned forwards and picked up the largest shard, her red blood smeared on it, and raised it to her throat as she gasped. The tattooed lines lit up all over her skin, but the magic seemed useless. Very slowly, the tip scratched her skin, cutting through the colourful lines, and the älf-woman screamed again.
"You're just a puppet. My puppet." Fa'losôi's yellowish eyes were still fixed on Aiphatòn, as if the death-dancer was not worthy of her attention.
"As long as I breathe, I will try to kill you," Tanôtai yelled—and uttered a strangled groan.
Her mouth closed and opened, her nostrils flared but no matter how hard she tried, her ribcage stayed as hard as stone and would not move. Not a breath of air reached her lungs; the glow of her tattoos was dimming.
" _As long as_ you breathe," Fa'losôi repeated softly. "Do you see how quickly I can change that?"
Aiphatòn had no choice but to be the observer who was learning how to avoid becoming the botoican-woman's next victim.
Tanôtai's fury gave way to sheer mortal fear. Her complexion was getting redder and redder, the veins at her throat and around her eyes were swelling. The black anger lines didn't stand out anymore. She was still holding her cut, bleeding hand outstretched, the other resting at her throat holding the shard.
" _My_ puppet," Fa'losôi declared. "Like everyone else."
Tanôtai got up from her seat and started to dance, her legs still full of the grace she had once demonstrated to Aiphatòn. Only once she had so little air left that she was staggering and practically falling unconscious did the botoican-woman allow her to breathe again.
Tanôtai stopped moving and breathed hard, panting like an älf-woman who had escaped death by drowning at the very last moment. Her chest looked like it was bursting, she was pumping air into it so hard.
She dropped the shard, and came back and sat down next to Aiphatòn, gasping as strings of saliva ran from the corners of her mouth. She couldn't speak. The tattoos lost the last of their light.
Fa'losôi was silent at first, looking like she had fallen asleep with her eyes open. Then she flinched. "All right, Aiphatòn. I'm glad to have found an astute commander in you." She looked at Kôr'losôi and Saî'losôi as if nothing had happened. "We'll try what he has suggested." She got up and leaned on the spear. "Kôr'losôi, you go with Aiphatòn and a troop of a hundred beasts to Ultai t'Ruy. A ghaist has located the town and will show you where you need to go. Apparently Ysor'kenôr _is_ there with his allies." The botoican-woman strolled over to a side door. "Attack them. I want to see what you can accomplish against the _greatest superior force._ Seeing as he's such a good Tharc-player." Laughing, she stopped on the threshold. "Oh, as a little incentive: if I'm satisfied, you'll get your toy back. I've heard it's meant to be good for warding off endingness." Fa'losôi left the room.
_I am going to find out whether presenting my suggestion to her really was a brainwave._ Aiphatòn felt the external power taking hold of him, then his arms dangled down.
Tanôtai groaned, her hands lowering. Her wound was still bleeding.
Kôr'losôi grimaced. "Setting out with a hundred beasts," he moaned in a low voice. "Not the best idea, cunning emperor."
Saî'losôi, on the other hand, looked relieved. She looked at Aiphatòn. "Do you also play Tharc with a hundred against a hundred thousand?" She stood up, giving Kôr'losôi an encouraging clap on the shoulder. "And I used to be jealous of your travels." The botoican-woman snickered as she left through the door the group had entered by.
"I sincerely hope," Kôr'losôi practically whispered, "that this game actually exists and that you are as good at it as you fooled Fa'losôi into believing you are."
Tanôtai still could not speak, and she had a faraway, blank look on her face, as she had had at the beginning.
Aiphatòn was about to respond when the copper helmet, whom he had already forgotten about, ran off after the head of the Nhatai family. _I almost gave myself away._
"Since I'm the only one who knows Tharc, I'll win," he whispered when they were alone, barely moving his lips. "It will be enough if we annihilate a few thousand with our hundred monsters before they get crushed."
Kôr'losôi stared at him in horror and stood up. "A vital detail has escaped you, however: the _greatest_ superior force," he hissed. "If you knew what she meant by that, you might not think your suggestion had been so successful. Unless another part of Tharc is forcing your enemy to surrender through _inferiority._ "
Aiphatòn's legs were moving, the botoican-woman was sending him out of the room. Tanôtai was still sitting on the cushions. _Like a puppet._ "It's just a test."
Kôr'losôi came right up close to him and he looked anxious. Anxious and angry. "Ysor'kenôr's army is overwhelmingly made up of mongrels that he bred himself, a mixture of trolls and ogres and giants. He calls them malméners," he revealed. "What do you think these mountain-sized creatures are going to do to our orcs?" He walked past him.
Aiphatòn started to brood. These things never happened in Tharc.
# Chapter XV
_Beware of the shadow that is also visible in the dark._
Wise saying of the Älfar
Collected by Carmondai, master of word and image
Ishím Voróo, 5452nd division of unendingness (6491st solar cycle), late autumn
"It was not a good idea." Kôr'losôi wouldn't stop complaining. "In fact it was the worst possible idea." At the head of a group of orcs a hundred strong, he and Aiphatòn were speeding through the grassland at a brisk pace, the rippling green stalks occasionally reaching up to their hips. The stalks grew as much as a finger's-width thick, the reed-like plants hitting them painfully in the thighs and shinbones. The sap that sometimes seeped out left streaks on both armour and fabric.
They were taking the path south-westwards to where the town called Ultai t'Ruy was located, as they had heard from the ghaist that Fa'losôi used as a scout.
" _Greatest_ superior force." Kôr'losôi cursed and placed a hand on the älf's shoulder.
_His whining is the whining of a coward._ Aiphatòn remained silent. He would not start to worry about his plans until they got close to the enemy camp.
The botoicans hadn't drawn up any maps of Ishím Voróo because they moved around with their armies in a nomadic fashion, settling down wherever they liked. That made preparing for the skirmish difficult.
Aiphatòn felt the botoican-woman was giving him just enough freedom, like a dog on a long but very secure leash that could be yanked on at any time to call the mutt back. "I've never been more relaxed," he admitted to Kôr'losôi.
"What?" The botoican, who was wearing the white armour of Elhàtor because he liked it, cursed again. "You are genuinely crazy. Malméners are enormous. Those hairy brutes! Like three orcs stacked on top of each other. They snap trees between their fingers and twist the trunks to tie them in knots."
Aiphatòn didn't set too much store by these words. They came from sheer fear. "We are on the safer side. All we need to do is find ourselves a cosy spot and direct the greenskins." _But if an arrow were to get you, that wouldn't be such a shame._
The black robe the botoican-woman had given him fit perfectly. If it hadn't been her who had given him the gift, he would have liked the outfit.
"These beasts that Ysor'kenôr created for himself have got keener noses than the most experienced bloodhounds and they detect scents upwind." Kôr'losôi still wouldn't be pacified. "But they're reared to be so obedient that it only takes him one tiny thought to command them. They are perfect. What the last botoican of the Rhâhois lacks in powers, he has made up for with his subordinates."
Aiphatòn was gradually realising why Fa'losôi amassed so many warriors. _And I promised her I'd achieve it with less. She is sitting in her tower right now, sick with laughter at me._
He was sticking to his plan, however: he would pass the test, get his spear and send the älfar into a decisive battle first, to dispatch as many of them as possible into endingness. Then there was the botoican-woman to be dealt with. _She doesn't realise how much magic there is within me and the weapon. And for that very reason, I could overpower her._ He reflected. _Best to wait until the battle is over._
"Do you hear that?" Kôr'losôi turned his head slightly in the wind.
Aiphatòn had heard the quiet rumbling sound coming from up ahead. "It could be falling tree trunks. Maybe they're building catapults?"
The group jogged up a gentle incline to get a better view. Under orders from Aiphatòn, Kôr'losôi made the orcs slowly creep up the last few paces before the summit so that they weren't visible from the other side. The blades of grass weren't as high here, but still provided enough cover so long as they were careful.
Aiphatòn was looking down into a gently sloping crater no more than four paces deep at its lowest point, but with a diameter of two miles. Tree stumps rose up out of the mossy floor, a reminder of the wood that must once have stood there, and it smelled of fresh resin and turned over earth.
The malméners, whom Kôr'losôi had described accurately earlier, were roaming across the cleared expanse as if they were looking for tree trunks that had been overlooked. Their heads were lowered and their eyes, as big as plates, stayed fixed on the ground.
"There are only fifty of them," murmured Aiphatòn, his gaze roving around. _Something is off here._ "That's not even a _greater_ superior force," he couldn't help adding. "Fa'losôi needs all these soldiers just for them?" To the north, he thought he could make out a narrow path. "And where has the botoican got to?"
Kôr'losôi looked confused. "The ghaist said that this was where..." He lifted his head slightly to assess the situation better.
"How intelligent is a ghaist if it's not being directed by its master?"
"That depends. Most of them are about as smart as a dog but if the souls used were particularly clever, it comes close to a human." Kôr'losôi didn't seem to grasp what the älf was trying to get at. "Am I mistaken or are the malméners looking for something?"
A vague explanation for what they were seeing was forming in Aiphatòn's mind. "We need to get closer. I want to know what they're searching for."
"Never!" Kôr'losôi made a defensive motion with his hands. "We'll make the greenskins..."
"They're too stupid." Aiphatòn had to admit that the enemy outclassed them. The orcs would be torn to pieces, and just a dozen of the enemy beasts would be enough to do it.
"You might be a warrior, emperor, but I'm nothing more than a puppet-master." Kôr'losôi looked at the malméners again, who were staggering about like tree trunks brought to life. "We would need all of the älfar to defeat those brutes down there."
"Trust my Tharc skills." He pointed to the right. "Send thirty greenskins back so that they come round the hill and encounter the enemy as if by chance. If these simple-minded giant-beasts are as dumb as you say, the majority of them will attack the greenskins immediately. As soon as that happens, you send the next thirty in from the other side."
"They won't survive for long," Kôr'losôi interjected.
"They don't need to. If the sixty are as good as annihilated, send another twenty in on either side and make them run away immediately so the malméners give chase." Aiphatòn went over his strategy again in his mind.
"What is that meant to achieve?"
"I can go down and take a look around without them pouncing on me right away."
Kôr'losôi scowled as the orcs crept back and positioned themselves at the foot of the hill. Being sent to their deaths didn't seem to bother them. "At some point, you're going to explain this Tharc game to me," he whispered. "So that I can understand whether what you're doing right now is a good idea."
The two of them watched as the greenskins marched around the mound and launched themselves at the enemy with loud roars, as if these were just harmless gnomes whom they could slay with the flats of their hands.
The extremely simple-minded malméners started by storming over to the first group of orcs, then split up when the second detachment of greenskins advanced. Just ten enemies remained on the cleared field, looking indecisively at the ground and over at the skirmish as it calmed down and drew to a close.
_It turned out the way I'd hoped it would._ Aiphatòn gave Kôr'losôi a clap on the shoulder. "Now the final forty." He got ready to run down the hill.
The botoican dispatched the last battalion, instructing them to run away immediately.
The gigantic malméners promptly fled the clearing and chased after them—including the ten indecisive ones who were screaming at each other as if trying to remind themselves of their mission and keep themselves under control.
_I'll be quicker than them._ Aiphatòn ducked, then hurried down the hill through the knee-high stalks.
He reached the outer edge of the crater unnoticed and stayed in a crouched position as he examined the point where forest gave way to grassland.
It was in that exact spot that he noticed a ditch-like indentation, as wide as a forearm and as deep as the blade of a dagger.
Aiphatòn glanced right and left. _That ditch keeps going and stretches right_ _around the missing forest._ When he looked forward again, he saw two malméners coming towards him and spotted some more indentations. _That makes sense._
Aiphatòn got up and started running, right between the two beasts who were moving far too slowly to be a danger to him; symbols branded on their chests showed that they belonged to the Rhâhois. Since he saw no need to kill the malméners, he kept them at arm's length. _There's a favour they're going to do for me._
He jogged across the hollow, looking at the marks and swerving from time to time when the enemies yelled and threw stones at him. These beasts were cut out for the battlefield, not for fighting nimble adversaries like him.
During his inspection, he occasionally noticed a magical radiation being emitted from something in the area, but it was nothing like the torturous magical fields in the towns. He explored the area, trying to pinpoint its exact location.
Aiphatòn grinned as he watched two malméners trudging up the hill. They had probably picked up Kôr'losôi's scent. The white armour meant he was easy to see against the green; he would not be able to escape. The botoican had no more orcs he could summon as a diversion. _That's one less Nhatai. They're doing the favour I wanted them to do for me. A good Tharc player thinks many moves ahead._
The älf scoured the ground as he ran. The more semi-circular and right-angled indentations he found, the more he was convinced: Ysor'kenôr had built a town here as a trick, probably with pictures in heavy frames and thin brick walls and roofs made of hastily bound branches and slats to keep up appearances; and he had a handful of his impressive beasts walk around to boot.
The ghaist-creature had been taken in by the sight from a distance but the botoican-woman hadn't let her scout go any closer so as not to be spotted. That's how the trick worked. _But why go to so much effort?_ Realising he might not be the only one who knew how to play Tharc, Aiphatòn smiled.
_He wanted the Nhatais to relocate their town! A good strategy._ He assumed the enemy army was already on its way to Fa'losôi to ambush her in her own residence instead of seeking conflict in the usual battlefield carnage. _He isn't sticking to the established rules of the game. That makes him even better._
A loud human scream cut through the air.
Aiphatòn smiled. Due to the power of the malméners, Kôr'losôi had stopped being a puppet-master.
He suddenly noticed the magical radiation was unusually concentrated so he stopped and looked around more carefully.
A sparkle in the churned-up moss caught his attention.
_Is that the object the monsters were looking for?_ He stooped down, rummaging in the soft, damp carpet of green until he caught hold of a triangular silver amulet.
He immediately felt a warm but pleasant prickling in the tips of his fingers and the runes on his gloves glowed blissfully.
_This is highly magical._ The runes undoubtedly belonged to the Rhâhoi family. On the polished surface, numerous jewels were glimmering. _No matter what Ysor'kenôr needed it for, he'll have to do without it._
Aiphatòn stowed it underneath his black clothing and jogged on again to get away from the enemy.
Tracing a wide arc, he returned to the path that he, Kôr'losôi and the troops had taken. Their tracks were easy to make out, thanks to the trampled stalks of grass.
The malméners were unable to keep up with his speed despite their long legs and they fell behind straight away.
After half a mile, he passed by where the last of the orcs were being torn into little pieces.
_Thus they've fulfilled their duty._ Aiphatòn stayed a safe distance away from the crazed, gigantic monsters jumping around on the cadavers of the defeated orcs and trampling them flat.
Aiphatòn wasn't worried about his future, despite the defeat. By the time he reached the white tower, he would have thought of a good story to explain Kôr'losôi's death and present himself as a skilled general. On top of the knowledge that Ysor'kenôr might invade their army camp at any time and that he protected them from imminent defeat or at least an attack, his spear was drawing nearer as a reward.
Aiphatòn could feel the amulet underneath his clothing. It rubbed against his tanned skin as if it were trying to draw attention to itself. Nobody knew that he had taken it—neither Kôr'losôi nor any ghaists—so it remained secret from Fa'losôi too.
_I will find out what it does._ He hurried across the grassland, his thoughts returning to the incident in the tower when the botoican-woman had demonstrated to Tanôtai how deft her responses and actions were as soon as someone tried to attack her.
And he suddenly thought about Ávoleï again, which surprised him.
Was it because she had been an elf-woman? His shock at himself continued when the images took him unawares.
He remembered her laugh.
Her kiss.
That look she gave him before throwing herself over the balustrade in Elhàtor to escape the spell.
_Whatever might have happened with her—it didn't happen and never will. It's better like this, although I wouldn't have wished death on her._ Engrossed in memories and strange thoughts, it took Aiphatòn a long time to notice the two black columns of smoke looming straight as an arrow over the grassland. They were both above Fa'losôi's town and a third was just working its way skywards.
Ysor'kenôr had made his next move.
Ishím Voróo, Tr'hoo D'tak, 5452nd division of unendingness (6491st solar cycle), late autumn
Saî'losôi lay in the copper bathtub with her eyes closed and let the water laced with essential oils wash away the dirt the moloch had left on her.
She breathed in the fragrant steam, enjoying the aroma of flowers and spices. And yet she fancied she could still smell the acrid stench of excrement, decaying corpses and fermenting swamp.
She was haunted by the grumbling, panting and roaring. The crowds of älfar made the monsters uneasy because they were afraid of black-eyes. What's more, it seemed the race of tall creatures emitted a weak radiation because of their own innate magic, which made the botoican spell less reliable.
So Saî'losôi had walked around on Fa'losôi's orders, accompanied by two ghaists, and pulled the invisible chains around the beasts' minds tighter while the more powerful botoican-woman and the cîani made an attempt to force Nodûcor's half-mask off.
Saî'losôi hated what her cousin called a town. This village was unwieldy, the paths too wide, the air foul.
And she hated her cousin—something she had in common with Kôr'losôi.
_The time for a decision is drawing near._ Tr'hoo D'tak was a matter of pride only for Fa'losôi, not for her. Not for any of the Nhatais. Saî'losôi had been treated better by other botoican families than by her own flesh and blood.
She thought her cousin was completely insane—lingering in a half-death seemed to have made her take leave of her senses. She was behaving more and more strangely, her actions verging on incomprehensible. Saî'losôi knew that she became dispensable after the last battle—another thing she had in common with Kôr'losôi. _I've got to act before she kills me on a whim._
It appeared her cousin Kôr'losôi had joined forces with the älf, the former emperor, which she thought was a mistake. No puppet was a match for Fa'losôi, the death-dancer's failure clearly demonstrated that. _Not even Aiphatòn will be quicker than her._
The brown-haired botoican-woman wondered how Fa'losôi had managed to escape the marsh she had supposedly been lying in after the älfar, Shintoras and Caphalor, appeared to have finished her off.
That incident took place a long time before she was born. The fact this relative of hers, who was her cousin many times removed, had survived lying in wet earth was a puzzle. It had been a long time since there were any witnesses around who might have been able to confirm the story.
Kôr'losôi had simply accepted her return because he was no match for her and he benefitted from her swift rise to power. Or at least he did at first.
Meanwhile Saî'losôi paid close attention to many little things about her cousin, trying to uncover the secret. Her certainty grew day by day that there was a demon involved, which explained the madness and the volatility.
The wasteland had known more than one such creature to get up to mischief and enter living beings to gain possession of them and control the destinies of entire tribes.
_Even the älfar used one of them when they battled Tark Draan._ Saî'losôi opened her eyes and fished the sponge out of the water to rub it over her rune-adorned skin. _Why wasn't it possible that a demon had taken on Fa'losôi's form?_ That would explain her immense power, if control and influence spells were at work.
Saî'losôi knew there was an antidote to anything and everything.
Even for demons.
Unfortunately, she wasn't an expert in the art of exorcism. Her cousin kept a very careful eye on the cîani, otherwise Saî'losôi would have used some pretext to grab one of them a long time ago. This possessive behaviour confirmed her theories.
_If Kôr'losôi acts oddly and arouses her suspicions by making a pact with the emperor—I'll wait for my chance. And it ought to come soon._
A gentle jolt passed through the bathtub.
There were barely noticeable ripples in the water and the thin foam sloshed up over Saî'losôi's arms and neck.
She stopped moving and listened. _Was the platform falling? Or was it..._
The second jolt made the whole room shake hard, the water flowing over the copper rim.
Saî'losôi cursed and stepped out of the bathtub, wrapping herself in her green dressing gown, wet as she was, to go and check if everything was all right.
She feared an earthquake or that the ground beneath the Nhatai tower was softening. Subsidence could create strain in the beams, which warped and broke easily. She had experienced it once before and that time she was able to stabilise the building before it could fall, with help from a pack of beasts, while the residents had moved their worldly belongings to safety.
_Ideally, I'll be able to see from one of the balconies what's causing the groaning and cracking in the timber frame._ Saî'losôi ran out of the room and along the narrow corridor, opening a door to the open air that was about forty paces above the ground and gave onto a viewing platform.
One glance was enough for her to realise that the ground sinking or even an earthquake would have been less of an issue.
_Ysor'kenôr!_
The revolting town that stretched out in front of the botoican-woman was being attacked from two sides. The surviving member of the Rhâhoi family had had his malméners advance from the south and southwest in wedge formation and they had already cleared two paths.
At the point where the heads of the two platoons met, they formed a cluster, launching carved tree-trunks lengthwise all over the town.
The extremely heavy tree-rolling demolished any and all huts or beasts standing in their way. Two of them had rolled right up to the tower and smashed into the lower part of the stone wall.
_Are those catapults?_ Saî'losôi thought she could make out enemy creatures assembling the roughly hewn components of catapults under cover of the group. The throwing arms were aimed at the tower, stones the size of oxen placed in the slings.
Meanwhile Fa'losôi's army set upon the enemy from all sides in a chaotic tumult. With no rhyme or reason, they obeyed the control spell that ordered them to tackle everything that attacked them or represented a danger to the town.
Ysor'kenôr's army had been recognised as an enemy by their befuddled minds. But since the enormous adversaries were in the middle of their camp, the defending forces themselves were in the way—and they tore through everything that stopped them getting at their opponents.
Orcs trampled gnomes, trolls knocked people down and sprinted over them, and the älfar unit used their cîani's magic fire to burn a path of destruction right through all of the monsters, large and small.
_I've got to sort this out before Fa'losôi intervenes._ Saî'losôi made the gnomes drop back, then the people, to bring the orcs and älfar up towards Ysor'kenôr's group faster. The trolls and ogres acted as marshals in this, creating pathways.
Then she noticed there were two standard flags with Ysor'kenôr's personal coat of arms in different places on the battlefield. Was this to create confusion, to leave the enemy uncertain as to where the Rhâhoi man was, or could the opposing side have more than one powerful botoican?
_Where can my cousin be?_ Saî'losôi didn't dare leave the balcony to look for her because that would make the defending forces descend into chaos again. It was a risk, bringing the älfar's magic radiation close to the orcs and encouraging their wild natures. _But maybe it will upset Ysor'kenôr's power too._
In the meantime, the wedges of malméners had banded together and taken control of a quarter of the town by advancing right and left. In the distance, even more troops were marching closer; Ysor'kenôr made sure they were rolling into the town in waves.
_That son of a bitch!_ The botoican-woman felt an ache in her temples; her exhaustion was making itself felt. The ghaists were desperately needed but their creator was Fa'losôi, therefore she was their only commander. Saî'losôi could only hope that the creatures would step in of their own accord.
The älfar had reached the northern edge of the pack and were launching themselves at the malméners. The cîani used their magic to transform the house-sized monsters into roaring flames, and the archers killed the burning, helpless enemies within a few heartbeats. Two of their siege machines had also caught fire.
The orcs, on the other hand, were doing a much clumsier job of it. Their attacking unit ran at the enemy and got stuck in their ranks, getting killed and trampled on.
The wind carried the sounds of screams and animalistic roars, and the hail of weapons and arrows to Saî'losôi. Never before had she found herself so dangerously close to the fighting.
_It's taking too long._ Her breath caught in her throat as the burning catapults, despite being damaged, fired a first salvo.
Four stones flew in a high arc, spinning as they did so, as if they were trying to show themselves to the botoican-woman from every angle.
One missile whirred past the tower less than four paces from it, at the height of her balcony. Saî'losôi automatically leaned sideways, as if the building would tilt with her and dodge it.
The second stone was aimed far too high, only ripping the roof off.
The botoican-woman shrank back against the white wall to escape the falling debris—and threw herself flat on the balcony when she saw the third shell coming towards her.
Five paces above, the heavy missile thundered through the wall, smashing beams and supporting structures, snapping guy ropes and leaving a hole behind.
This time the tower shook underneath Saî'losôi, who had put her hands over her head. She felt the fourth impact much further below her—it must have torn away sections of the external wall to the right.
_I need to get out of this trap._ She got up, trembling with fear, but managed to keep setting the älfar and orcs on the malméners.
Two catapults went down in flames and a hastily fired stone did not have enough momentum and landed in a pack of gnomes, crushing three dozen of them and rolling through the crowd, leaving a trail of destruction in its wake.
The double rumbles of a wooden swinging arm heralded new missiles. These stones flew straight at the centre and foundations.
As the shells hit the tower and forced it to bend like a reed, Saî'losôi made a handful of trolls run towards her. _I can do this._
She clung to the railing and ordered her approaching rescuers to form a ladder with their bodies against the wall. In this way the botoican-woman managed to keep the swaying under control.
She vaulted bravely over the balustrade and dived onto the highest troll's neck, clinging to his stinking hair and making him jump onto the ground.
At the same moment, new missiles hurtled at them. They scattered the beasts stacked on top of each other and dealt the final blow to the building.
Saî'losôi landed safely on the soft earth with the troll but she needed to get out of the way immediately to avoid the falling building. "To the left, to the left!" she thought and screamed at the same time. The monster obeyed.
With a cracking sound, the tower tilted. The wall panels came away, and masonry rained down stone by stone on the Nhatai troops, crushing humans and pulverising gnomes. Even the ogres and trolls fell to their knees under the weight of debris and were severely wounded.
The swamp quaked at the impact.
Beams and planks shot out and fetid mud sprayed many paces upwards and outwards. The tower collapsed, smoking, and fell onto the mucky ground like a dead, burst mayfly.
The survivors crawled out of it like maggots.
"Cousin!" From the troll's neck, Saî'losôi scoured the ruined building, the different storeys and destroyed floors. _There she is!_
Amid the disarray, Fa'losôi lay trapped, surrounded by various älfar, Tanôtai and some servants. None of them were moving.
_Don't be dead! I need you alive to achieve victory!_ The clouds of smoke blocked Saî'losôi's view of the battlefield. She ordered the monsters to launch themselves at Ysor'kenôr's troops with all their might.
Her troll suddenly uttered a muffled groan and held his side, his knees swaying before he collapsed.
Saî'losôi jumped off in time to avoid getting buried underneath him. She didn't see what kind of missile had killed the creature but it meant that some enemies had got far too close.
"Fa'losôi!" she screamed, as she balanced her way across the rubble and approached her cousin. The sounds of fighting beyond the grey clouds were getting louder and seemed to be moving forward as Saî'losôi did.
Finally, she reached the motionless woman. Her jugular vein was throbbing gently.
Tanôtai groaned and sat up.
_Good! Oh, that's good!_ Saî'losôi commanded the death-dancer to clear away the debris then helped her tackle it. Tanôtai picked up a stick and then swapped it for an iron rod to use as a lever with bigger pieces of debris.
Suddenly the ghaist with the dented copper helmet appeared and started to help. Its supernatural powers ensured that Fa'losôi was quickly rescued from the tangle of beams. Then, as quickly as it had come, the ghaist disappeared again, burrowing down through the ruins of the tower.
_It could be looking for anything down there._
"Cousin, it's me: Saî'losôi," she cried, stroking the unconscious woman's dirty cheek. "Wake up! I'm begging and pleading!"
Her eyelids fluttered, then Fa'losôi coughed and inhaled, her breath rattling. The dust had settled in her lungs. "What... happened?"
Saî'losôi was relieved, although the yelling and shrieking and dying seemed to be just beyond the clouds of dust now. She drew her dagger as if she could halt a superior force with the blade. "You've got to rally the troops and launch a counter-attack. Ysor'kenôr has led his army right into our town. He might even have brought a second botoican with him!"
Fa'losôi touched her shorn, rune-adorned head, a rivulet of blood streaming out of her nose and running red over her lips. "I... can't remember," she moaned. "What troops? Aren't we in Ikârion?"
Saî'losôi felt a chill all of a sudden. "That was almost eighty days ago, cousin!" she replied in a guttural voice, grabbing her by the shoulders and shaking her. "Try and remember! You've got to think straight. My powers are exhausted. You are Fa'losôi, the commander of the Nhatais, and if you don't pull yourself together right now, you are going to die, along with me, unlike the Rhâhois' beasts!"
Fa'losôi looked around in confusion, wiping a hand over the blood under her nose, which was followed by a fresh stream from both nostrils, bigger this time. "My head... is pounding and burning," she said haltingly. "I... do you have anything to drink? I wouldn't mind wine."
"Wine? Is this one all right with you?" Saî'losôi cursed and slapped her across the face. "I'll keep giving you this wine until you remember!" the brunette screamed in terror. "By the ancestors of the Nhatais, I swear I'll kill you myself before one of Ysor'kenôr's people can do it." After three swift, ringing slaps, her cousin wailing as she tried to block them, her gaze changed and seemed to clear. "Oh, do you remember now?"
Fa'losôi gulped and touched the diamond chip on the bridge of her nose. She closed her eyes. "I need to concentrate."
"Good! Great! Now..."
Saî'losôi was annoyed by a powerful, pale-green light that fell on the botoican-woman from one side.
She turned her head to look for the source and brandished her dagger.
"Endingness awaits you." The death-dancer got to her feet next to her. She had taken off the black robe and was wearing nothing but the loincloth. The object that Saî'losôi had thought was an iron rod turned out to be Aiphatòn's rune spear.
All of the symbols were gleaming and illuminating Tanôtai, who was holding the weapon in her uninjured hand; the lines on her skin were glowing too, the jewels sparkling. The long, narrow blade was pointing at the brown-haired botoican-woman—and stabbed at her.
Saî'losôi couldn't parry the spear with the dagger; her weapon slipped over the metal. The thin dressing gown did not put up any resistance and the tip of the spear plunged right into her solar plexus.
She opened her mouth to scream but couldn't breathe.
"That's what happened to me," remarked the red-haired älf-woman, twisting the shaft so that the blade caused greater damage inside her enemy's body. The runes were flickering as if they were exhausted or were overwhelmed by the contact with the botoican-woman's magic; then they went out. "But I'm breathing again. You never will." She yanked the spear out of the dying woman, droplets of blood falling on the woman's gaping robe and skin. "Your death is called Tanôtai," she said in älfar, the dripping red blade swinging towards Fa'losôi, who was still lying there with her eyes closed. "And your death also bears my name."
The slim death-dancer's muscles tensed.
Heat spread through Saî'losôi's stomach and burned into every last nook of her body. This was followed by a second wave, this time of ice. Her eyes were fixed incredulously on Tanôtai, who was taking her time to stab Fa'losôi. _Or..._
"Isn't it a shame that you're failing for a second time?" A smile played around the corners of Fa'losôi's mouth, her eyelids still closed. "So close to freeing your people from my will."
_She's awake at last._ Saî'losôi fell sideways silently, the world swimming and dimming. She guessed what was happening more than she could actually perceive it.
Tanôtai uttered a despairing groan and couldn't move.
"Here we are again, my puppet. Like at dinner when I invited you and Aiphatòn." Fa'losôi opened her eyes, her gaze riveted triumphantly on the älf-woman. She didn't seem interested in either the outcome of the battle or the approaching enemies. "You älfar are a race I will never understand. But why worry about the dead?"
Out of the thinning clouds of dust and smoke, arrows whizzed in their direction.
Saî'losôi felt an impact in her back, next to her spine. But the chill from her mortally wounded solar plexus masked everything.
Fa'losôi stayed on the ground, ducking lower behind the beams. "Well, this is getting annoying now."
Two projectiles struck the upright death-dancer in the thigh and shoulder. Her face was covered in anger lines, but her mouth remained shut. Tears of disappointment and pain ran down her cheeks.
"You would definitely have been a motif for your tribe's painters and sculptors to fight over," Fa'losôi remarked thoughtfully. " _The frozen death-dancer_. That could have been the title of the work they created in your honour."
Another arrow whirred towards them and pierced the red-haired älf-woman's right side.
Tanôtai stayed standing, the tip of the spear still aimed unrelentingly at her opponent. Blood ran from her wounds and painted symbols on her skin, as if trying to cover the tattooed runes that did not have the strength to light up.
"So close to your goal and rashly claiming my death would bear your name." Fa'losôi watched as the red-haired älf-woman was penetrated by two more arrows that plunged into her neck and upper arm. "Your death will have no name," the botoican-woman decided. "Some unknown archer will release the arrow that strikes your heart or goes through your skull." She turned to Saî'losôi. "Can you still hear me, cousin?"
_Yes._ The dying woman managed to make two fingers twitch.
"Then take my thanks with you into the beyond," Fa'losôi bid her farewell. "You have put yourself in danger to rescue me and it has killed you. That was noble." She laughed softly. "Although you needn't have worried, you could have let it be."
Saî'losôi didn't understand what her cousin meant.
Any more thoughts she had froze like ice.
Her body gave up and she did too.
# Chapter XVI
_The best victory is always the next one._
Wise saying of the Älfar
Collected by Carmondai, master of word and image
Ishím Voróo, Tr'hoo D'tak, 5452nd division of unendingness (6491st solar cycle), late autumn
Just as night fell, Aiphatòn approached Tr'hoo D'tak from the east so that he would have a better view of the town away from the columns of smoke. The dwellings were reasonably sturdy here.
He climbed onto one of the huts to take an awed look round. _The tower is gone. And the enemy catapults over there are on fire._
The bloodbath was in full swing and would end in defeat for Fa'losôi's forces.
The bright red flags of the foreign family had already laid claim to the entire western half of the town. The ruined tower lay partially burning, partially smouldering along the town's north-south axis and looked, with its shiny protruding beams, like a gigantic animal with its ribcage exposed. The attackers may have lost the catapults they'd brought, but they had achieved their goal.
_Ysor'kenôr knows what's he doing more than the Nhatais do._ Aiphatòn could still feel the magic shackles, albeit faintly. At least one of the botoican family members was still alive. _I'll change that soon._
The älfar units from Dâkiòn and Elhàtor fought quietly and with a will of iron. Swarms of arrows whirred across the battlefield, carrying death deep into enemy ranks. The cîani were unleashing havoc among the malméners.
It was magic similar to what he knew from Lot-Ionan, but he would never have expected his people would be capable of it. It was clearer than ever before: northern Ishím Voróo and the time that had gone by had both transformed the älfar.
_Girdlegard would have been easy prey for älfar like this. Praise be to all the gods that neither Shôtoràs nor the monarchess had been eager to make conquests._ Aiphatòn could see the ghaist-creatures were tough opposition. With their white flags on their backs, they ploughed through enemy lines, tearing apart every creature that crossed their path. They didn't even shy away from the malméners.
But the Rhâhois' troops were too numerous and too enormous, and they made up for their stout statures and lumbering gaits with their strength.
From where he stood, he could make out two eye-catching banners hovering above the enemy army, far apart from each other. They had the same Rhâhoi insignia on them as the one he had seen branded into the malméners.
_So perhaps they've got two puppet-masters_ , he reasoned. The Nhatais had not counted on that.
The enemy botoicans controlling their contingent had a head for military strategy. The weaker auxiliaries marched along behind monsters the size of trees, stabbing wounded enemies to death. Their certain victory did not make them at all cocky.
And that annoyed Aiphatòn. He would have been pleased to see the Rhâhois advancing in a more frenzied, rash way and suffering more casualties.
The älfar now found themselves at the centre of the devastation. The opposing army seemed to have magicians at their disposal too; the air shimmered with the cîani's jets of flame fizzling out or getting redirected at the älfar troops.
_Ysor'kenôr and his second in command know exactly what they're doing._ Aiphatòn watched the downright one-sided destruction unhappily. They mustn't make it too easy for the Rhâhois.
What's more, he was growing increasingly afraid that the enemy would spare the älfar troops at the last moment so that they could use them themselves after the victory over the Nhatais. That would achieve nothing.
_Things ought to be moving more quickly. I need a quick, brutal battle that does not allow any mercy._ His gaze swept over the swampy plain again, the stink of putrefaction and fresh blood mingling together in a nauseating way.
Aiphatòn assumed that Ysor'kenôr and the second botoican were near a flag with insignia, slightly elevated so as to have a better overview and direct the army.
_We'll see whether there really are two botoicans or if it's a trick._ He planned to put one of them under a little pressure. _Then, out of fear, they'll urge their people to move faster._ After that, he wanted to kill the puppet-master and take another piece off the Tharc board.
As the älf couldn't make out any platform that might have been constructed like one of the catapults, he assumed the enemy commanders were each on the shoulders of one of the enormous malméners.
_They're hardly going to be right in the middle of the densest fray. The danger of falling victim to a charm or an arrow is just too high._
Aiphatòn picked out one of the gigantic monsters towering up out of a crowd of shorter auxiliaries in the southwest and not moving. He couldn't tell if someone was on its shoulders but one of the flags with insignia was fluttering less than fifty paces away. _That's where one of them might be._
He jumped down off the dilapidated hut and kept to the outskirts of Tr'hoo D'tak to avoid going straight through the battle and encountering a ghaist.
The closer he got to the district of the doomed town that had fallen to the Rhâhois, the more often individual enemy fighters or smaller units attacked him.
Aiphatòn didn't waste time on them; he slayed them with his armoured gloves or used their own weapons to kill them. Since he still hadn't got his spear back and couldn't summon it from this distance, he used whatever weapons the enemy left for him.
In the end he broke through the surprised rearguard made up of orc-like beasts. On top of the fact that night had fallen, they shrouded themselves in darkness for protection, to avoid giving enemy arrows a target. He hurried over the corpses but didn't slip or utter a sound and they soon lost sight of him.
Aiphatòn was drawing closer to the single malméner who towered up as rigid as a monument over the auxiliaries. A group of forty lance-bearers was guarding him, his legs soaring into the air behind them like pillars, but the älf wasn't worried about them.
Sure enough, on the monster's right shoulder, Aiphatòn spotted a male figure wearing armour and sitting with his back to him in a saddle contraption with a high, metal-plated backrest. _Just as I thought._
A commotion erupted and started moving towards them from the northeast. Horns were being blown in alarm.
The lance-bearers refocused their attention, looking away from the invisible älf. This made it even easier for him to get close to the brute with the commander on his shoulder.
Aiphatòn saw a ghaist approaching. _Fa'losôi sent it because she understood that only the death of the puppet-master could ward off defeat._ The long groove on the copper helmet revealed that he was dealing with the most dangerous one.
Then Aiphatòn noticed more of the magical creatures, who were so easy to spot with the towering white flags on their backs. He suspected the botoican-woman's aim was to create as big a diversion as possible to get their best warriors where she needed them. On the other hand, it could also mean that—
Ysor'kenôr himself was in front of him.
_The most important playing piece in the game isn't yours yet. The Rhâhoi man needs_ _to wipe out the älfar for me first._ Aiphatòn picked up his pace and cast darkness over the lance-bearers.
He killed one of them with a blow from an armoured glove and stole his weapon, which he immediately hurled at the botoican—but not to kill him. _That should unleash enough terror to provoke him._
The tip flew through the night air and the spear plunged through the reinforced backrest as planned.
The scream that drifted down from the monster's shoulder told Aiphatòn that the blade had bored through as far as the commander. The curse that followed revealed that Ysor'kenôr was still alive. _Excellent. Now he'll drive his troops forward._
But there was no sign from the battlefield that they were redoubling their efforts. The Rhâhoi man didn't seem to want to alter his successful strategy.
The malméner turned around and aimed a kick at Aiphatòn, but he had no difficulty dodging the toes. Two surprised pike-bearers weren't as lucky; they were caught by his foot and flew screaming through the air.
_I'll make you lose your mind with fear, botoican!_ Aiphatòn drew the sword of one of the dead and rushed forwards, the darkness still enveloping him like a protective blanket. _This time I'll force one of your own kind to fulfil my wish!_
He skilfully dodged the indiscriminately kicking feet, came up behind the malméner and severed its heel tendons with powerful blows.
The ligaments snapped with a crack, the brute staggered and uttered muffled cries, then his knees buckled. The lance-bearers ran away to avoid getting buried beneath the falling giant.
But Aiphatòn was right on his heels. He jumped up and cut the tendons in the knee joints too, to stop the malméner getting up again.
The brute fell, breaking his descent with his elbows and emitting such a resounding howl that bystanders covered their ears to protect their eardrums.
Aiphatòn walked around the malméner and looked at the empty seat: either the figure he presumed to be Ysor'kenôr had got himself to safety before the fall or he had gone down with it.
He took a quick look around. _He can't have gone far._
A wind sprang up that pushed the clouds of smoke towards the ground and made his eyes water. Yet Aiphatòn fancied he detected the smell of flowers.
By now the ghaist creatures were being pelted with bulging pig's bladders by their opponents and the smell of petrol was spreading. Flaming arrows flew at them. Ghaist after ghaist turned into a running torch that slowed down the higher the flames leaped around them. Ysor'kenôr knew the magical creatures' vulnerability and was prepared for it.
The ghaist in the copper helmet with the long groove couldn't dodge the pouches either, but he was able to avoid being set on fire.
Aiphatòn saw a shadowy figure flit across the field and disappear among his soldiers' shields. _There you are!_ He raced after the shadow without casting off the darkness. _Do you really feel safe behind the shields?_
A big leap allowed Aiphatòn to soar over them and hit the heavily armed figure right in the back.
The man fell to the ground screaming and rolled over, the heavy, full suit of armour rattling and scraping. The face remained hidden behind the helmet's shut visor.
He stabbed at the älf with his dagger. Meanwhile the wind was getting stronger, little golden tiles dancing wildly in the air with petals and feathers.
Aiphatòn caught the weapon with his armoured hand and crushed the blade effortlessly, dropping it onto the churned-up earth. "If you don't want your death to be called Aiphatòn," he said in a deep voice over the murmur of the breezes chafing at his plates of armour, "keep your guards back." He wrenched the visor open and looked into the face of an unprepossessing man with a dark brown moustache. "Tell me your name!"
So as not to endanger the life of their commander, the guards remained at a distance and even started to retreat slowly.
"Ythan'kenôr," he answered, panting, and immediately he understood. "You're not one of Nhatais' puppets! Let me live and my brother will reward you after the battle."
"I thought _he_ was the last of the Rhâhois?"
The botoican grinned. "So long as our enemies think so, that's all right."
Aiphatòn cursed in the silence. _I'm dealing with very good Tharc players here._ "Is he commanding the troops or are you?"
"We both do," Ythan'kenôr shot back quickly, shouting to be heard over the wind.
"Then I don't need you. One is enough for me. But if it's any consolation to you in death: Fa'losôi Nhatai will follow you." He raised an arm to slay the unremarkable botoican before the distant guards could intervene.
As he did so, the amulet he had found on the deforested land slipped out from underneath his dark clothing.
Ythan'kenôr spotted it and seemed to recognise it. "You've got it?" He had an evil look in his eyes and his left hand jerked upwards to touch it. "I'll show you its power..."
Aiphatòn hammered his fist right into the man's face, shoving the bone at the bridge of his nose up into his brain. Ythan'kenôr uttered an unintelligible sound.
The piece of jewellery glowed and a bright light flashed at the same time.
Aiphatòn felt his plates warming up. The dreaded, painful prickling flooded his entire body; the magic in him was reacting with the energy released—and then it was over.
_Neither pain nor..._ He blinked in surprise at the dead botoican. _What happened?_ He got to his feet and didn't feel any different.
The darkness danced around him protectively; not even the powerful wind could blow it away. There was a jarringly fresh, intense scent on the wind. The swamp, blood and excrement didn't seem to exist anymore. The botoican's guards had bolted, presumably because their mental shackles had fallen away. There was no reason for them to attack the älf and meet with certain death in the attempt.
Aiphatòn turned his attention to the battlefield.
The first enemy units had come to a halt because they were no longer receiving any orders from one of their masters.
The älfar in particular were exploiting the confusion to kill their enemies. Their military fortunes seemed to be on the turn, or at least until the brother got the whole army under his control.
Some Nhatai ghaists had perished in explosions in the distance. Craters had formed and the corpses of the Rhâhoi army were ablaze all around them, while another ghaist blew up in front of the älf's eyes. The fiery shockwave knocked creatures within a radius of thirty paces off their feet.
Dazzled, Aiphatòn had to shut his eyes, bracing himself against the approaching draught of air that descended on him.
Once the glow of the blast had subsided, the wind kept on blowing.
The fallen malméner had a broken, stray spear sticking out of his eye that had found its target by chance. _At least the ghaists are slaughtering more of them._
Aiphatòn held one glove protectively in front of his face. Although it was a clear, starlit night and the moon was a silver glow, a storm seemed to have sprung up, and it was constantly changing direction.
The strong, fresh smells of fruit, green foliage and morning dew were replaced by the fragrance of flowers while light and dark-coloured feathers twirled over the battlefield along with petals. Tiny gold tiles and fine, glittering splinters of glass mingled with them—they hurt on contact with bare skin. A heartbeat later, the smell of iron and earth prevailed, then the air shifted and suddenly smelled of stone and rain. Thin blades of basalt and obsidian clinked as they shattered on Aiphatòn's glove and plates of armour.
The wind intensified and the cuts became more painful.
Blood ran from the many slits where delicate glass had pierced Aiphatòn's skin and sliced it open. _The splinters are going to flay me alive!_ He threw himself onto the ground and tried to work out why this was happening. _A hostile spell that Ythan'kenôr cast with the help of the amulet to rescue his victory?_ He pulled a shield towards him and used it as cover. _But he didn't touch the amulet. Or did he?_
The brewing storm came whistling angrily under the metal-plated wood and tore his protection away.
Aiphatòn screamed as the splinters and tiny blades hit him again. He held both hands in front of his face and crawled forwards until he reached the monstrous corpse of the malméner. He got under it as best he could.
And then finally he realised.
_It's Nodûcor! Fa'losôi removed the mask with the help of the cîani and forced him to summon the winds._
The storm turned into a hurricane, powerful enough to tug at the enormous corpse Aiphatòn had hidden underneath.
The splinters of glass and blades of obsidian and basalt shredded the monster's skin with grating, scraping sounds, blood trickling down onto the älf. The bones crackled as they were ground down until the gusts of wind blew into the cadaver and swept it away with them, making a hollow whistling sound.
Aiphatòn immediately felt the impact of the terrible force that raged and roared from every direction. The wind of mortality swept in from the north, the wind of freedom shot out of the south, the wind of war blew from the west, and the east wind carried inspiration.
_They've all come to speak to Nodûcor, like the legends say._ He felt his skin getting thinner and thinner, the blades penetrating any exposed flesh, and he heard tinkling and rustling as they bounced off his armour.
_I must not die as long as the botoican-woman and the wind-voice are still alive._ Aiphatòn tried to look around and screamed in pain. _The plates are not going to save me._
A figure came walking through the raging storm, enveloped in flickering flames and as erect as if it were made of indestructible stone. The little splinters scraped against the dented copper helmet and poured into the slits like hail, but that didn't bother the warrior.
Indignant, the wind whirred and the flames around the ghaist creature went out.
It turned its head, spotted Aiphatòn and hurried over to throw itself on top of the älf and protect him.
Aiphatòn smelled the petrol, felt the unbearable heat coming off the ghaist and thought he could hear sizzling. But he took the opportunity to huddle beneath his unexpected new shield.
Overcome by the exertion and pain, he fell into a state somewhere between sleep and unconsciousness.
Aiphatòn did not know how long it took for the hurricane to die down and the four winds to withdraw. He didn't wake until the ghaist on top of him stirred and got to its feet.
There was nothing more than a weak gust of wind blowing now and the sun was rising over the plain.
The peaceful silence was incongruous with the damp smell of swampland, mutilated bodies and blood.
Aiphatòn blinked; his eyes were painful and burning. His whole body hurt, as if it were made of raw flesh. He sat up cautiously and clenched his teeth to stop himself screaming.
Before he even looked around, he examined his wounds.
He was barely wearing any clothes anymore. The skin on his arms was already healing underneath an unbroken crust of dirt and blood. The cuts felt like they had closed up and he was itching all over.
He was as pleased as he was astonished by this swift recovery. _My magic has become stronger—because of the amulet? Or is this a feature of the wounds that the winds cause?_
The ghaist was standing next to him and looked like it was waiting.
Aiphatòn lifted his head and surveyed his surroundings through streaming eyes.
There was nothing left of the Nhatai and Rhâhoi armies. Everything had been pulverised and dashed to pieces on the battlefield. The splinters of glass had squeezed through the tiniest holes in their armour and the blades of basalt and obsidian had sliced up everything there was to slice. There weren't even any complete cadavers—there were at most bones polished clean and scattered by the storm.
Aiphatòn stood up and continued to look around, unable to wrap his head around it.
The blood of thousands—as well as flayed skin and slivers of bone, tooth and intestine—had mingled with the churned-up sand, been lifted by the wind and scattered over the town. The coating reminded Aiphatòn of the crust over his wounds.
_The sky has shed crimson rain over the land._
The plain smelled like an abattoir. Weapons and armour were strewn about, the leather torn off the hilts and shafts, the straps shredded; more than a few blades were snapped.
Älfar, orcs, trolls, gnomes, malméners and whatever brutes had served in the armed forces of the warring families were no more.
Although it meant Aiphatòn had almost achieved his goal, he felt afraid of the thin, pale älf he had freed. _Nodûcor must die._ He swallowed. _Nobody is a match for his powers._
Several figures were walking slowly across the plain towards him.
Two copper helmets shone in the light of the rising daystar and next to them he recognised Irïanora, Nodûcor, Fa'losôi and an älf wearing a light blue robe with an elaborate shell embroidered on it, which signified he was a cîanoi from Elhàtor.
Fa'losôi's robe was grimy and tattered. She was holding Aiphatòn's spear, using it as a cane. If he was interpreting the look on her face correctly, she appeared far from pleased.
It took them a while to march through the remains of the warriors. Their trouser legs and the hems of their robes were saturated with moisture; the blood had worked its way up the fabric and penetrated into the seams on the soles of their shoes. Both Irïanora's beautiful dark blue and silver robe and the blonde älf-woman herself were covered in dirt. Only Nodûcor's light, black leather armour looked immaculate.
Aiphatòn didn't notice it until the botoican-woman was standing in front of him. _She has discarded the mind-shackles she usually restrains me with._
He could barely contain his joy. However, surrounded by three ghaist creatures and bearing in mind the unfortunate Tanôtai, he refrained from any attempt to snatch the spear immediately and attack. Instead of setting upon her, he gave a slight, submissive bow.
"Don't you dare congratulate me on my victory," she said sharply.
"So was that not how it was meant to go?" he couldn't help asking.
Fa'losôi rammed the spear blunt-end down into the soft sand and let go of it. "Did I come up with the idea of literally crushing my laboriously assembled army in a storm of flowers, glass, blades and perfumes?" she snarled, wiping away the blood underneath her nose; more blood immediately trickled after it. "The wind-voice shouted too loudly."
Aiphatòn looked at Nodûcor, who suddenly looked harmless without the black half-mask around his chin and mouth; his skin was scarred in some places, grazed in others. _He looks like a scholar, not like someone who gets two-hundred-thousand-strong armies pulverised._ "What happened?"
The wan älf didn't respond.
Fa'losôi let out a nasty laugh. "He can't speak. As soon as he opens his mouth to say anything, what happens is what we experienced last night. If he has to communicate, he'll write it down." She fixed her eyes on Aiphatòn. "I'm surprised. In the best way," she admitted.
"I thought I'd kill Ysor'kenôr for you so that his army would be without a leader," he lied. "But you had the same idea when you sent the ghaists. Did you know there were two of them? He also had a brother who was helping him."
"No. But that's not what I meant." Fa'losôi scrutinised him. "You've been free of my influence for quite some time and yet you stayed and killed one of the Rhâhois." She slowly lowered her symbol-adorned head. "How did you manage to break my control?"
_I'm free? Or is this a test?_ "Kôr'losôi," he answered on an impulse, to buy himself time. "Your cousin wanted to talk me into a pact against you so that I'd kill you. He weakened your influence as often as he could."
Fa'losôi raised her eyebrows. " _That_ explains it! I knew Kôr'losôi was plotting something but I didn't think he was good enough to break your bond with me." She put her hands behind her back, her necklaces and gemstones clinking. "And _what_ did you stay to do, emperor?"
Aiphatòn laughed. "I planned to ask you for the commandership of the älfar." He pointed at the bedraggled-looking Irïanora as an example. "I could have used her. And an army that is well-led can achieve greater victories. _Quicker_ victories with _fewer_ casualties." He looked around pointedly. "You'll have to start over again and I've only got—" he looked at the survivors—"three älfar left."
"I remember what you said about the Tharc game." Fa'losôi smiled. "And you've convinced me: from now on you are to be by my side without my control spell." She nodded to the cîanoi. "Let him see to your wounds quickly and then let's head east. Nodûcor's voice is a little hoarse; that's got to change. He needs to use it more, I think, so that he knows how to say the right words." Fa'losôi gestured to the rune spear invitingly and patronisingly with her right hand. "Take it. It's yours."
Aiphatòn struggled to keep up the pretence of friendliness as he slowly reached out a hand and grasped the shaft. "Ordinary spells don't work on me."
"You're in the wasteland. You ought to have realised that things are different here." Fa'losôi nodded to the cîanoi. "It's possible to understand how magic works and functions and what paths it takes."
_It will roast him alive, just like what almost happened to the healer on board the Mistress of the Sea. Healing me is a suicide mission._
Meanwhile the älf in the pale blue robe was touching Aiphatòn's forearm and murmuring a healing spell; the layer of scabs crumbled off. A prickling sensation wrapped around his wounds and spread through him, soothing and alleviating his pain.
Aiphatòn gazed at the cîanoi in surprise. _This man sets about his work much more carefully._
Then he turned back to Fa'losôi. "What are we going to do in the east?"
"The true Ultai t'Ruy, the Rhâhoi family's capital city, must be there. Given the brothers tricked us, I want to make sure that it's destroyed. _One_ botoican-woman in the wasteland is quite enough." She looked at the soaking wet, filthy hem of her robe, no green or white still visible. "Some new clothes would be..."
_No botoican-woman at all would be even better!_ Aiphatòn thrust the spear, plunging it into Fa'losôi's chest but not killing her with his well-aimed stab. "Keep the ghaist creatures back," he commanded the panting botoican-woman whose legs were giving way. She clung to the shaft—without it she would have fallen to the ground.
Sure enough, the copper helmets didn't move.
Irïanora, Nodûcor and the cîanoi shrank away from him, the sorcerer still murmuring his healing spell because he had not received an order to the contrary from the botoican-woman.
"I have... no power over them anyway," Fa'losôi replied, grinning weakly as her breath rattled. "Are you afraid... that after my death they'll follow any botoican that comes along?" she choked out. "You're so easy to fool," she whispered, and her bald head sank onto her chest with a creaking sound. Her hands slipped away and Fa'losôi slumped forwards.
_Now I'll fulfil the vow I made to Ireheart._ Aiphatòn pulled the spear out of the body that collapsed at his feet and pointed the tip in one fluid movement at the surprised cîanoi.
The blade struck the blue-robed älf in the heart. He collapsed on top of the botoican-woman with a stifled groan and his eyes paled.
Nodûcor watched the dying älf, fascinated and completely calm. It seemed he was completely convinced he would escape death.
"Murder!" Irïanora suddenly screamed at him, outraged. Her mind had been freed from all influence. "Why are you doing this after freeing us from the botoican-woman? Do you want to kill me too?"
"I swore to wipe out the älfar. _That_ is the _real_ reason I left Girdlegard," Aiphatòn explained, turning to the aghast Irïanora. "We must be eradicated." The healing spell was still prickling through his body, but he ignored it.
"Then start with yourself!" The blonde älf-woman stooped down and drew the cîanoi's dagger.
One blow with the blunt end of the spear was enough, the weapon fell out of her hand and lodged in the damp earth.
"We are a cruel tribe. And I've been no better for two hundred cycles. Your towns would have made a nuisance of themselves sooner or later and the generations to come would have regained their old tyrannical ambitions and set themselves up as ruthless rulers." Aiphatòn placed the tip of the spear against the älf-woman's solar plexus. The cîanoi's fresh blood left a dark stain on her blue robe. "Your death..."
"Stop!" Irïanora was breathing fast, her dark-tinted eyes open wide. "Please! Spare me. Together, _we_ could make the älfar tribe rise from the ashes and make it better. You, a shintoìt, and I, a modern älf-woman filled with magic. If you were able to imagine what..."
_The schemer fights to the last._ "With your death and Nodûcor's, I'll have fulfilled my vow," he interrupted her. "Afterwards I'll gladly depart into endingness by my own hand. But _your_ death is called Aiphatòn!"
He stabbed with considerable force so Irïanora wouldn't suffer. But the blonde älf-woman must have been wearing hidden armour under her blue and silver dress—the tip only just went through the material, then stopped.
"Are you sparing me?" Irïanora scoffed. "Would you rather continue your murder spree on Nodûcor and practise until you get it right?"
"No armour will protect you, whether it's made of steel or magic." Aiphatòn deployed his magic, pulling the spear back by half an arm's length and ramming the dazzling runic weapon at her exposed throat. _This time you're passing into endingness._
Irïanora didn't move, standing surprisingly tall as she faced the weapon.
Again, the razor-sharp and usually reliable blade didn't get any further than her dirty skin. No matter how hard Aiphatòn worked his magic, bracing both feet against the ground to force the spear tip into her, nothing happened.
"Put your weapon down," the älf-woman eventually told him in a polite voice. "You can't kill me. Your subconscious is refusing to."
Aiphatòn lowered the spear. _How can this be?_ The prickling in his body intensified and became painful, like on Elhàtor and Dâkiòn. From the spot where the cîanoi had touched him, the pain gnawed its way up his arm into his shoulders. _But the botoican-woman_ , he turned his head to look at her corpse, _is dead_.
"You're so easy to fool," Irïanora repeated the words Fa'losôi had whispered before her death. "And _what_ do you deduce from this?"
"She taught you her power." Aiphatòn would have liked to do something about the burning sensation creeping up his throat and the back of his neck. "You've just proven to me twice over that no älf should remain alive." _What can I do?_ As soon as he used his magic, the pain would get worse. Just the thought of killing the älf-woman made the spear feel as heavy as a thousand stones.
"That would be one explanation." Irïanora smiled indulgently. "The fact you haven't hit upon the other one is a point in my favour."
Nodûcor was still staring at the cîanoi's body, as if the other two älfar didn't exist.
The ghaist with the dented copper helmet walked forwards slowly and stopped next to the älf-woman.
"So that's not a ghaist?" Aiphatòn expected it to remove its headgear and reveal another botoican underneath it.
But it remained still while white smoke gently drifted out of the slits and curled upwards.
"Explain it to me." His vision was blurring.
Irïanora raised her right arm, the index finger pointing at the creature. " _I_ am Fa'losôi Nhatai. The creature you, Kôr'losôi and Saî'losôi thought was a ghaist is actually the puppet-master. And I'm controlling the älf-woman as well as the wind-voice."
Aiphatòn felt nauseous and was overcome with dizziness. "But I... why did you let me kill the botoican-woman?" His eyes were playing new tricks on him. Ávoleï's face suddenly flickered across Irïanora's features as if the young elf-woman was trying to battle the magic from the grave.
"For one thing, she wasn't a true botoican-woman, just a woman who looked like me when I still lived as a human. For another, the collapse of the tower didn't leave her unscathed. She would have died soon anyway. I didn't need her anymore. When I noticed that you were more resistant to my influence spells than all the other älfar, much more resistant even than the elf-women, I wanted to find out how far that freedom went." Irïanora lowered her arm. " _Now_ I know. And I've taken precautions."
The burning sensation had reached the top of Aiphatòn's neck and was creeping into his skull and from there into his brain—gradually it turned into a warm, pleasant feeling. He shuddered.
He found Irïanora increasingly attractive and enchanting. _Why did I not notice she was incomparably beautiful before?_ When he shut his eyelids over his burning eyes and opened them again two heartbeats later, she had come right up to him. "How did you become a ghaist?"
"That's _actually_ Sinthoras and Caphalor's fault. They ensured that the creation of a ghaist went awry on me. My body perished and my soul ended up in this creature along with thousands of others." Irïanora laughed. "My own family threw me into the swamp because they had no use for this apparently faulty being. Eventually I managed to assume control over those raging souls and freed myself. But that's not a story I like to be reminded of." She placed her forearm on his shoulder, her fingers touching the nape of his neck and tenderly caressing it. "Time can be so long and yet it can pass quickly if you celebrate victories."
_Beautiful!_ He looked at her gently curving mouth, listening carefully to the irresistible sound of her beguiling voice. "Allow me to help you celebrate victories," Aiphatòn said longingly. _Everything about her is beautiful._
"So you shall. And to make absolutely certain you do, I've had the cîanoi work a spell that makes you my slave. As long as you live and as long as Irïanora lives, you will not be able to raise your hand against my new self. Soon you will believe it was your own, most heartfelt desire to fulfil my every wish. No matter the cost. Or whoever may die." Irïanora smiled and kissed him lightly on the cheek.
In the same heartbeat, the last sharp pain in his head gave way to a blissful feeling and Aiphatòn basked in it. _Only she can give me peace._ "Whoever may die," he whispered.
Irïanora ran a hand lovingly over his head, through his dark hair. "My best puppet. Effortlessly obedient." She looked at her dirty fingers. "A bath would be lovely."
Aiphatòn breathed in happily. He was content just to gaze at the älf-woman and be near her so that he could carry out her wishes. "A bath?" He looked around. "That won't be easy."
Irïanora couldn't help laughing again. "No, that's not something I'll ask of you."
"What shall we do then?" He looked at Nodûcor. "With him on our side, nothing can resist us."
"We're going east, but you'll have forgotten that at the sight of my enchanting face. We're paying a visit to Ultai t'Ruy." Irïanora let go of him and started to walk away. "And then? The last botoican-woman ought to have a kingdom befitting her status." As she walked, she spun around once and smiled at him, her blue dress flying out a little. "We could have Dâkiòn rebuilt. With my abilities, we'll make ourselves a new army of slaves. What do you think?"
Nodûcor was shuffling along behind them, his gaze remaining fixed on the corpse of the cîanoi, as if he was looking at a dead body for the first time. He didn't seem to care where they were going.
"I look forward to it."
The blonde älf-woman smiled at him, then her gaze wandered down to the middle of his chest. "What have you got there?"
Aiphatòn remembered the amulet. "Oh, I found it where the malméners were. It was lying in the moss." He pulled the chain over his head and held it out to her. "Take it if you like."
Irïanora came closer and examined the piece of jewellery without touching it. "No need. It's been discharged. It was a power repository but now it's merely a nice trinket."
Aiphatòn put the amulet away again and placed his spear on his shoulder, balancing the weapon so that it hovered horizontally, then put one lively foot in front of the other. He was fascinated by Irïanora's charm and could hardly restrain himself.
They were flanked by two ghaist creatures while the third brought up the rear.
Making straight for the east, they walked over the metallic-smelling red sand and the stalks of grass gradually turning brown.
The cool wind blew on them and this time it didn't carry any feathers or glass or basalt blades. Winter was coming faster and it seemed keen to spread ice and snow over the battlefield behind the travellers.
_Samusin, God of Balance, thank you!_ "I would be delighted to lay an enormous kingdom at your feet," Aiphatòn blurted out. "Nobody else deserves to rule over the tribes! Over all the tribes in existence!"
"Oh, you speak the truth, although being in love is making you gush." Irïanora's laugh rang out as clear as a bell. "Let's destroy the town first and renovate Dâkiòn enough for us to spend the winter in a cosy home. We'll see what the coming years have in store."
_It's admittedly not much, what she lets me do, but it's still a start._ "The foundation stone for our kingdom." Aiphatòn exercised great self-control in not reaching for her hand. "Your kingdom, my love." He couldn't imagine anything better than sharing immortality with Irïanora.
_I will fulfil her every wish._ Aiphatòn smiled demonically. _Anything I fail to find in Ishím Voróo, I'll get for her in Girdlegard._
He knew two ways into Girdlegard.
Tark Draan, Human kingdom of Gauragar, Oakenburgh, 5452nd division of unendingness (6491st solar cycle), winter
Carmondai was sitting wrapped in a blanket next to the window. He was on the fourth floor of the town hall tower where he had spent the last few orbits working on new poems.
He was glad to see his surroundings and the woods disappearing more and more beneath the falling snow. _I couldn't have stood the damp, mouldy walls of the dungeon much longer._ Everything reminded him too much of his imprisonment by the Aklán. And yet he was even worse off now than he had been with the triplets.
Oakenburgh stretched out peacefully below him. The people were trudging through the snowdrifts. Huge quantities of firewood and coal were being brought out of the woods on sleds to heat the half-timbered homes.
_Winter is here._ Carmondai opened the window to let the sounds into his room. _And it's magnificent._
The cool westerly wind sent the white splendour swirling in at him, and the high-spirited shouts of children doing battle with snowballs reached his ears. The air smelled of open fires and baking, and sometimes resin, when needles caught fire and released their scent through the chimney.
Carmondai sucked the cold air into his lungs and broke off one of the icicles hanging in a row from the window frame.
He rubbed it over his ravaged cheeks and forehead.
The frozen water cooled his sensitive skin, which still hadn't recovered from the treatment it had received. It hurt to speak and accidentally furrowing his brow meant he immediately had to stifle a scream. The healer who had been so excellent before couldn't give him anything for the pain—or didn't want to.
Once the queen had departed, the people of Oakenburgh's contempt and appetite for murder came to light. The branding and the warning on his forehead prevented any attacks taking the form of punches or knife wounds, but he was spat on, insulted and had excrement and rubbish poured over him.
Since then, Carmondai had preferred to avoid these humiliations by declaring the town hall tower his new quarters. He didn't dare flee so long as he didn't have a safe plan for how to leave Girdlegard. Too many enemies were lurking, from the elves to the zhadár, who all wanted him dead. Perhaps the last älfar were lurking too now, in order to have their revenge on him for preventing the assassination. And besides that, others were trying to get their hands on him alive: dwarves, human kings, scholars. _So_ _this position in Mallenia's shadow is safer._
He felt tired.
Very old and very tired.
_I underestimated Mallenia._ He broke off another icicle to keep cooling his skin; the first one had melted. _Death would have been a relief in comparison to this. That's her form of revenge: calling it a_ _mercy._ He looked around, gathering impressions so that he could commit them to paper straight away.
As he did so, his gaze fell on the window pane where his disfigured face was reflected.
Carmondai swallowed. He was still far from used to this new external appearance of his.
On either side of his face, the Ido coat of arms stretched from his cheekbone to lower jaw, forever designating him a possession of the ruling family.
With a red-hot wire, the following had been etched into his forehead: _Anyone who harms this älf will have the same harm done to them._ His mid-length brown hair was gone, replaced by grey stubble.
_Now I really look old. Or is it the sadness that my divisions of unendingness carved into my face overnight?_ Carmondai touched his hardened features with their bright red wounds. _What have I become?_
_A slave in order to survive_ , was the answer the reflection gave him. The lapdog of a queen who let him live in order to degrade him more deeply than any other punishment could ever have done. The iron had burned his courage and pride out of him.
Furious, he slammed the window shut so that the panes rattled.
A loud, nasty laugh rang out.
"The warning," said a sinister voice behind him, "could have been a bit more clear-cut. You might come across people who think it's worth stabbing you in the arm or leg with a dagger, even though they then have to endure it themselves."
Carmondai didn't need to turn around to know that Carâhnios had slipped unnoticed into the room. "My forehead wasn't big enough."
"But they did shave your head," he said, chuckling. "Lots of things could have been written so that nobody does you any harm at all."
The älf shifted his gaze away from the window pane—which threatened to show him his face again—and turned to the zhadár. "Are you making progress on your hunt?"
Carâhnios bared his black teeth. Darkness swirled around him like heat haze or a sun's corona; he practically radiated shadow. Carmondai understood Mallenia's dislike of the zhadár now. "Unfortunately I haven't achieved any more success since our intervention in Oakenburgh. Either we've already caught them all or they're getting better at hiding from me." He kept one hand concealed behind his back.
"Then I wish you better luck. I can't go with you," he declined the implicit request. "As you can see, Mallenia sees me as her property."
"But you can move freely."
"I can move around Gauragar and Idoslane. But as soon as she returns to Oakenburgh, I'll stay close to her. It is her wish that I do not stray from her side." He pulled the blanket tighter around himself.
That was a lie, but he was desperate to be near her after he recovered to prevent any more assassination attempts on her. The spell bound her life to his.
He may have been in a terrible situation for now, but there was one thing he knew: times changed. _Constantly._ The thought comforted him.
The zhadár guffawed, one hand still behind his back. "They took your dignity and courage away." He was giggling like a lunatic.
"How many times have you taken the remedy?"
"The new one?"
"Yes."
"Three times," he whooped and raised his free hand. The black haze danced around his fingers. "Do you see that?"
"A side-effect, I'd say. You needed a different formula for älfar blood than for elf blood. But I'm not an alchemist." Carmondai reached for paper and ink to draw the effect—and suddenly couldn't see a thing. _What...?_
Two heartbeats later, everything brightened up again.
"Hey, black-eye! That was me!" Carâhnios crowed. "I can plunge a room into darkness just by thinking about it. It even works in the open air, in broad daylight."
"Like Arviû," the älf blurted out, remembering the archer whose älfar power changed after a sudden loss of sight. The zhadár had experienced a similar effect.
"I'm capable of so much and I'm constantly testing out my power." He took a step towards Carmondai. "But I need more blood." He removed his hand from behind his back and in it was one of the familiar bottles.
_He didn't come to take me with him._ Carmondai shrank back, the blanket falling to the floor. Underneath he was wearing a simple woollen robe to beat the winter chill.
He didn't carry a weapon on his person in the tower room—his sword lay on the floor next to the bed and the dagger remained next to the pieces of apple on the table. His injuries may outwardly have healed but his power was still far from restored.
"You said you'd kill me last," he remembered, hoping it would save his life.
"I can't find Aiphatòn anywhere right now. So I'll deal with you first," Carâhnios snarled and immediately laughed at much too high a pitch. He drew his dagger with his free hand. "Don't put up any resistance and this will be quick." His black eyes never left Carmondai. "But if you'd like to give me a laugh, try it. Please."
Without warning, Carmondai tipped the ink out at him—and found himself standing in blackness as if it had been sprayed in his own face.
He soon felt a blow to the backs of his knees and he fell, disoriented, against the table and then onto the wooden floor.
With two powerful blows to the back of the neck, Carâhnios almost knocked him unconscious, all of his limbs suddenly weighing more than an enormous gold block.
"Taken out like a fish on a hook," the zhadár said cheerfully next to him. "Shall I gut you now, little fishy?" He sniggered. "It would be so easy."
Carmondai felt a slight pinch at the neck instead and then the mouth of the bottle was pressed against the wound. He could hear the muffled sound of his blood spraying against the glass in time with his heartbeat. His eyelids closed.
_I'm passing into endingness in such an undignified way_ , he thought as he drifted off, unable to move. How he would have liked to say something impressive. _But what for?_ There was nobody recording his last words for posterity. _What a bad joke on the gods' part._
Before he slipped into unconsciousness fully, he felt a few firm slaps to the cheeks.
The pain in his sensitive, burned skin roused him. Then straight away he had some ice-cold snow thrown into his face, which made him open his eyes wide.
To his surprise he was lying on the bed and could feel a bandage on his neck. _He left me alive?_
Carâhnios was standing in front of him brandishing a bottle with quite a lot of blood sloshing around in it. "Two units. That's enough to start with," he decreed and carefully sealed it with a cork. "Rest up, eat well and you'll be back on your feet in no time, little black-eye fishy." He sniggered. "You thought I'd kill you? Oh, that was amazing, feeling how scared you were."
Carmondai sat up carefully; the melted water was cooling his face as it trickled down. He couldn't speak yet. Dizziness spread over him as soon as he moved too quickly.
"If I don't find any more black-eyes, I'll come visit you often, my inexhaustible source. I know where to find you, don't I? Wherever the little Ido woman is." Carâhnios laughed as he placed the dagger to his own throat and gave himself a little cut—black blood flowed from it. He immediately held a piece of cloth against it. He appeared to have cut the cloth out of the pillow for himself. "There. Now the condition written on your forehead has been met: _anyone who harms this älf will have the same harm done to them._ The queen can't do anything to me."
He left the room without another word.
Weakened, Carmondai hauled himself to his feet and surveyed the mess his brief skirmish with the zhadár had left in its wake. With some difficulty, he went over to the open window to breathe in the fresh air. _He will make good on his threat. And there's nothing I can do about it so long as he has those powers_ _at his fingertips._
He looked outside and saw the groundling riding away on his white pony. He was passing the queen's retinue, who had just arrived in Oakenburgh to check on their valuable slave. _I'll add him to the list of everyone out to get me then._
He looked directly downwards, to where the ground lay a good fifteen paces below.
He could simply lean forwards and fall.
Everything would be forgotten, the pain, the scars, the humiliations and fears.
But a single feeling stopped him.
_Samusin must have something in store for me. Anyone who goes through such dark times will be exalted by him all the more._ Carmondai looked up again and surveyed the woods, darkness and snow descending on them. _What a beautiful contrast._
He went over to the table and tidied up the mess. He took some new ink and began the next drawing and on another page wrote the lines of a poem that had come to him.
Even pain and suffering served as inspiration to an artist.
Sometimes these produced the best pieces of work.
# Epilogue
_A man in love is worse than a grieving man. Because he expects something in return for his actions._
Wise saying of the Älfar
Collected by Carmondai, master of word and image
Tark Draan, Human kingdom of Gauragar, Grey Mountains, 5452nd division of unendingness (6491st/92nd solar cycle), winter
The storm paused for the first time, allowing the two tired travellers of different heights a view of the mountains around them, as if it wanted to reward them for having struggled on to get to this point.
The sun was rising over the vast peaks and broad mountain ridges glittering radiantly with ice and snow.
The brightness was getting unbearable. The unrelenting whiteness intensified the sunlight and forced both humans to squint, having stopped in the middle of nowhere in the Grey Mountains to puff and pant. They did it every ten steps to draw air into their shrivelled-feeling lungs.
And yet they didn't want to take their stunned eyes off it, they wanted to take in the beauty of the sparseness.
The rock appeared to take the shape of various creatures—here a peak looked like a dragon's head, there a gnome seemed to be peeking out of the rock face. The wind blew the snow off the higher slopes, forming white banners that stretched far across the sky as they scattered and dispersed.
"Look! They've hoisted the banners to welcome us, Endô," said the girl, out of breath. Her thick clothing was too big for her; the hems had been shortened using a knife. "I'm sure we're in Tark Draan already."
Endô smiled and placed a hand on her shoulder. His cloaks had also once belonged to a significantly taller creature. The hoods had enough space for two or three heads. "Definitely." He looked around, putting a hand in front of his eyes and peeping through a narrow slit between his fingers to avoid blinding himself permanently.
"Shall we keep going, Uncle?"
"Soon." He took a few steps forwards. Then, to his relief, he noticed the runes that had formed in ice on a precipice. "The next symbol is up there, Sha'taï."
He walked on, panting, and his niece followed.
"Don't forget to close your eyes almost completely. Otherwise you'll go blind," he warned her. Endô took her by the hand and they tramped across hard ice.
This time they got twenty paces before stopping with a groan and taking a break.
Endô didn't know who had carved the älfar runes into the rock but he desperately hoped they were leading him and Sha'taï to a destination that would make a better life possible for them.
He dimly remembered a story he had heard a long time ago, about an älf-woman who had come from Tark Draan, but it seemed too far-fetched to him at the time.
Hadn't she declared herself ruler of Elhàtor? She might as well have been the ruler as any other black-eye. As long as the signs took them to a place where they could live, it was all the same to him.
The symbols had been formed by seeping water that had filled slight indents in the stone and then frozen. Hence the mysterious signposts became visible in the lower-lying regions, only in the winter, and led walkers along a dangerous path.
They had come within a hair's breadth of getting stuck. An entire section of icy pathway must have caved in during the summer and it took them a long time to spot the next rune.
In one chasm they had also found the stiff bodies of monsters who had been stabbed to death. They had taken their frozen provisions and cloaks from them, which meant uncle and niece were better protected from the storms in the mountains.
"We're moving on," he heard Sha'taï saying as she gently dragged him forwards.
She didn't seem to make any allowances for the fact Endô still needed a little longer to regain his strength. "Good, good."
He didn't reveal to her that he had known one of the monsters.
Cushròk was the commander of a notorious band of soldiers deployed when unsavoury things needed doing without the name of the client being made known.
He didn't know what they had been up to in the Grey Mountains.
The wounds didn't match their own weapons so they probably hadn't killed each other. Therefore, there was definitely life among the steep slopes and hidden caves—beyond the odd herd of ibex—and that life was not well disposed towards visitors.
Endô remembered the message that Cushròk had sent him word for word. He had probably sent it to everyone in Ishím Voróo whom he acknowledged had greater power than him.
Endô's mistake had been not to reply. But unlike most of the others who had received a similar letter, he could still beat himself up about his oversight.
_My dear Endô,_
_I'm on the verge of obtaining a magic weapon of obscene power._
You ought to be aware that I'm doing this on the orders of others who know how to handle the weapon.
However, I think it would be fairer if the existence of this weapon became more common knowledge.
I am a soldier and will pledge my word to whoever pays best.
If you want this weapon of destruction to end up in your hands instead of someone else's, possibly an enemy's, send me more than a thousand gold coins of the heaviest kind. I'll bring the weapon to you as soon as I have received the payment—and so long as it amounts to more than the sum I receive from everyone else to whom I'm also sending word.
Regards and prosperity,
_Cushròk_
Since the soldier and his band were lying dead in the icy landscape, it seemed one of the recipients or the original client had taken the message badly. Ignorant people have set out to commit murder and theft for far less than a thousand coins and been known to come back with something more valuable.
As for where the weapon had finally ended up, Endô knew from personal, painful experience.
His lungs felt like they had shrivelled into peas again; black rings spun before his eyes and he had to stop walking. "Wait," he asked Sha'taï.
"Again?" She may have been panting hard, but her youth seemed to make her less susceptible to the altitude and thin air.
What would have happened if he himself had paid Cushròk the most?
Would he be sitting on a comfortable throne in Dâkiòn, ruling over the Majestic? Or would the soldier have kept the weapon for himself after all and used it against all of the tribes?
Endô was panting as he moved off again. His eyes were open just a thin crack to check for the path so he wouldn't veer off and plummet downwards. "I told you to close your eyes!" he barked at his niece.
"But... it's glittering so beautifully," she defended herself, caught in the act.
"You're going to go blind," he said with anxious emphasis, feeling his lips cracking. The dry air and the cold attacked the skin, while the sun gave them severe sunburn.
Endô thought the mountains worse than the most gloomy moorland, the most isolated grassy plain, the most desolate wilderness, or any other area he had visited before.
Sha'taï muttered an unintelligible response.
They continued their trek with its monotonous rhythm in silence: ten paces, stop, ten paces, stop, ten paces—until night started to fall.
Pressed close together, they hunkered down in a narrow niche and prayed for the winter to spare them.
Due to the hardship and the altitude, Endô fell into a sleep that brought little refreshment. He started out of his sleep several times, his hand on his sword.
But there was nobody in the frozen wasteland of rock. Apart from them.
It snowed towards morning.
Thick flakes fell on uncle and niece, shielding them from the bitter, deadly frost with a thick, white coating like a cool cloth.
Sha'taï woke him as the sun rose and shone through the loose, soft white coating that lay on top of them a hand's-width thick.
Endô shared out their provisions—they had to suck on them to thaw them out—and treated himself to a little more rest although the girl was pestering him and seemed oddly restless. "What's wrong? Did you have a nightmare?"
Sha'taï looked nervously at him, as if she had to keep a secret and no longer could. "We're near a valley," she spluttered.
"We're surrounded by them. And by ravines and precipices and..." Endô saw her glowing face. "You snuck away during the night!" The belated worry made him angry at his niece. "What were you thinking? You could have..."
"The moonlight was pleasant and the glittering can't even dazzle you then," she interrupted him slyly. "You were asleep and I thought I was dreaming of juicy apples until I woke up and the smell was still there." Sha'taï pointed north-eastwards. "The path leads to a peak that looks like a crown. Below it is a valley with no snow in it! And there are trees there! I've seen them!" she whooped.
Endô feared the thin air had affected his niece's mind. "It's the depths of winter and we have the gods' mercy to thank that we're still alive..." He suddenly fell silent as she took his hand, opened it and put an apple into it.
"I took this," she admitted happily. "I actually wanted to surprise you and let you find the valley but since you don't believe me: see for yourself."
Endô stared at the apple as if it were the world's greatest treasure. Although his lips cracked even more, he opened his mouth and bit cautiously into the apple.
The fruit was neither frozen nor foul-tasting. The bittersweet juice flooded his mouth. Endô chewed carefully—the taste of the fruit was a revelation on his tongue and palate.
He quickly took another bite, although his open cuts stung. "Is it a magic spell or the work of mountain demons?" he asked with his mouth full. "Are we to be lured into a trap only to end up as their meal?"
"It looked very real." Sha'taï shrugged her shoulders. "I wasn't able to examine it more closely because I've lost my talisman."
"You don't need it. Your powers are strong enough. Why else would you have been entrusted with the mission?" Endô pulled himself together. "So _you_ are leading _me_ now." He smiled and held a hand out to her. "And don't forget about your eyes."
Sha'taï grasped his fingers and pulled him along behind her.
The path went steeply upwards and the travellers had to climb up. The snow had covered the girl's tracks but she made straight for her destination without hesitating.
Endô did her a favour and didn't take any more breaks, even though his heart was beating madly in his chest, the blood was rushing in his ears and the black rings in his vision were no longer going away.
But on the other hand, it smelled of apples and there was the steady sound of a waterfall roaring.
"Here it is!" Sha'taï dragged him forwards.
"You walked this path here and back by yourself?" Endô had made it, coughing and groaning, onto a little platform with steps leading down from it.
When he cast a glance at the valley stretched out in front of them, two miles long and half a mile across, he burst into tears of relief. Even if it were the work of demons, he would still have been glad. He would serve any ghost who ruled over it.
Fruit trees grew on the terraces that had been laid out, the fruit shining rosy-cheeked in the sun; overgrown fields were testament to abandoned grain cultivation. The ruins of stone buildings rose up from the floor of the valley; a fire must have raged through there. Only two structures seemed to have been spared the destruction.
Endô looked at the small lake at the bottom of the waterfall he had heard roaring in the distance. He wondered whether there were any fish in it. His heart raced with joy even more.
A warm gust of wind flowed from the valley into the travellers' faces. The source of the wind appeared to be the numerous holes in the porous rock.
"Saved," he whispered and wiped the tears from his cheeks, the sunburnt skin peeling as he did so. "Let's go and see what the former residents have left for us." He stroked Sha'taï's hair. "If they've got grindstones, I can bake us some bread." He threw the soldiers' provisions over his shoulder in disgust.
His niece let out a loud peal of laughter and raced down the steps.
Endô took a breath in and followed her.
After a few steps he was overcome by dizziness; his heart hurt in his chest, as it had done many times on the journey. The altitude was seriously bothering him, but he just needed to sit down calmly and wait it out.
"Where have you got to?" Sha'taï called to him, having almost reached the bottom.
"I'll be there soon, my dear. I'm going to enjoy the view a little more," Endô replied, slowly kneeling down so that he could sit.
As he moved, the walls and the steps spun, the black rings forming again. He reached his arms out to keep his balance, but his right foot slipped and Endô fell forwards.
The staircase seemed to be getting longer and longer, the edges harder and steeper as he rolled down, his niece's fearful screams in his ears. He couldn't get hold of anything—after every roll, the next somersault followed.
Then Endô saw the blue sky above him and he stretched his arms out to his right and left. His fall finally came to a stop.
Only his head jerked back with one final, severe swinging motion.
Endô's neck broke against the edge of the step with a dry crack.
At the same moment, every thought of the past and future faded because the present had brought him death.
Girdlegard, Human kingdom of Gauragar, Grey Mountains, 6492nd solar cycle, spring
Belogar Strifehammer's bushy brown eyebrows rose very slowly as he looked north from the Jagged Crown and recognised the small valley not far from him and his companions. "By Vraccas!" As the dwarf from the Boulder Heaver clan from the Fifthling tribe shouldered his mace, the coat of chainmail under his thick layer of cloaks clinked softly. "There it is, the secret settlement."
Phenîlas pushed past the upright rocks that had given the peak its name and clapped the dwarf on the back. "An amazing miracle from my goddess and your god," remarked the elf. "My tribe were wrong to keep it to themselves."
"And _my_ tribe should have discovered it," muttered Belogar.
"Actually we did that," piped up Gosalyn Landslip, whose breath had formed ice-crystals under her nose. "But we forgot it rather than keeping it secret. So we're equally to blame." The dwarf-woman squeezed between him and the elf to start the descent. "Let's check what's left. My queen and High King Boïndil are eager for news."
"Wait," came a breathless voice from the Jagged Crown behind them. Rodîr Bannerman appeared, needing to lean on his spear and then against the stone. "I can't go on."
The dwarves and the elf grinned.
"You people just aren't cut out for the mountains." Belogar sounded paternal. "I warned you and your soldiers about coming with us."
"Besides, we chose the easy descent through the mountain," Gosalyn added, laughing. "You only had to walk the last half mile through the snow."
"And I'm very grateful for that," the warrior replied, panting. "But it's pure torture." He looked in the other direction. "My troops will be here very soon."
Belogar pursed his lips, which were surrounded by a sprawling beard. "What wouldn't one do to strengthen the newly won friendship between our peoples?" he teased.
Phenîlas smiled kindly and contemplated the mountains. He adjusted the white fur coat over his light leather armour. "I can see the beauty but I admit I feel better in the Golden Plain. Ice and snow are not for my people, I'm afraid."
"Thanks be to Sitalia," murmured Gosalyn.
The elf laughed sympathetically. "Yes, thanks be to Sitalia. Vraccas knows why _you'd_ be here."
Rodîr approached them. Twenty warrior-women and warriors were coming over the summit, bearing Gauragar's colours on their shields and pennons.
"They look exhausted," Belogar remarked.
"And they've got sunburn," Gosalyn chuckled. "Didn't I say you should make sure their faces were covered?"
"I didn't think it was worth it for half a mile," Rodîr admitted.
"If we had walked faster, you wouldn't look like a virgin who has just been told a dirty joke," Belogar replied and laughed. "Oh, that reminds me, an orc comes up to a dwarf to ask him for directions..."
"Not now, my friend," Phenîlas interrupted him and moved on. "The valley awaits us. Treat us to it there."
"You'd better not." Gosalyn winked at the disappointed dwarf. "Everyone knows it anyway. The pointy-ear is just being polite."
She followed the elf. Rodîr caught up to them while the rest of the human warriors followed shortly afterward.
High King Boïndil had insisted on dispatching a group to visit the legendary settlement where elves and dwarves were reputed to have lived together. There were certainly references to it in the ancient writings of the Fifthlings, but the turmoil of the preceding cycles had caused them to fall into obscurity.
The elves of the Golden Plain also wanted absolute certainty and had invited the humans to share in this flourishing settlement. No tribe ought to have secrets from other tribes anymore, the reasoning went.
Belogar saw it a little differently. There definitely wouldn't be any tunnel tours through the Kingdom of the Fifthlings or sight-seeing of the treasure trove. Friends remained friends, they didn't become family or even a member of the clan.
They assembled on the small ledge with a broad, steep staircase leading down from it, past the terraces of fruit trees and fields of grain. A fire had razed most of the buildings to the ground; just two remained habitable. Insects were buzzing around, the trees were in full bloom.
"I see elven and dwarfish runes on the walls," Phenîlas said and he was moved. "They've been eroded by time and the flames, but I'm reading about friendship and alliance."
"Fantastic," Rodîr gushed. "The warm wind that is protecting the valley from ice and snow is coming out of the holes in the rock!"
"An array of different chimneys coming up from inside the mountain," Belogar realised. "It works the opposite way to the flues we built to bring fresh air into our kingdom." He nodded. "We did a good job."
Phenîlas started to walk on, hesitated, and looked encouragingly at Gosalyn and Rodîr.
They understood his glance and the soles of their shoes lowered onto the first step at the same time. Side by side they strode downwards, Belogar and the warriors following them.
Having reached the ground, Rodîr ordered his battalion to spread out and secure the area.
Belogar laughed at him. "You think there are monsters here?" He loosened the clasp of his cloak and let it slip to the ground. It was too warm.
"Did you believe in the settlement?" the man shot back calmly. "Anything could be hidden out here." He pointed to the small, dark pond with waterlilies dancing on the surface. "A beast could live in there."
"Caution never harmed anyone," Phenîlas conceded.
"So true." The dwarf-woman looked around, one hand resting on the handle of her axe. "It's beautiful here. If I didn't have a home, I'd move."
"Oh, I know what you're thinking," Belogar interjected, "but it's not up to us to decide whether this settlement will ever be inhabited by dwarves and elves..."
"And people," Rodîr chipped in, friendly but firm.
"As far as I'm concerned, it could be inhabited by unicorns and fairies too," Belogar raved. "We've got kings to make that decision, who will wrack their brains about it."
"They certainly will." Rodîr was amused by the dwarf as he leaned on his spear. "Tell me, what made you think of unicorns? That image is practically idyllic."
"Yes. Especially if _he_ is sitting on it," Gosalyn cried, pointing at Belogar and laughing uproariously.
The dwarf rolled his eyes and trudged off. "I'm taking a look around," he growled into his beard. "In case nobody noticed amid their raptures"—he pointed at the fields using his mace—"it's been harvested in places."
Two soldiers suddenly called the commanders over: in one of the houses that was in better condition, they had stumbled across a discovery.
"Didn't I say?" Belogar couldn't help relishing the moment.
"Watch it, you're getting unbearable," Gosalyn muttered as she walked past.
They went inside the hut and saw a dark blonde girl who had lain down to sleep in front of a window the size of a wagon wheel with various symbols painted on it. Her hair was dishevelled and her dark red vest looked threadbare and too small.
The intruders' entrance didn't wake her, her chest slowly rising and falling.
Belogar pointed at several thin flatbreads on the table. "She's a little baker." He tasted some. "Not bad at all. She took salt from the walls..."
Gosalyn grabbed his arm and pulled him back. "I would say she's eleven or twelve cycles."
"She's not an elf-woman." Phenîlas crouched down carefully and examined the sleeping girl, then reached out a hand to shake her awake.
The girl started, scrambling backwards and banging her head on the rune-patterned window, which immediately unleashed a cacophony of metallic noises. Without opening her eyes, she reached out her right hand, groping around, and with the other she whipped out a dagger from under the pillow. The words she uttered were incomprehensible.
"She's blind." Rodîr sounded sympathetic.
"She just has her eyes closed. And she's not from Girdlegard." Belogar's expression darkened. "Nobody speaks that language back home."
"She might be snow-blind. Look at her skin and eyelids. They must have been badly sunburned." Phenîlas looked kindly at the dwarf. "So you've travelled a lot and you know every dialect?"
Belogar huffed. "No."
"What he is trying to say in his bad mood," the dwarf-woman stepped in, "is that she must come from the Outer Lands."
They contemplated the panting, dark blonde girl who was brandishing the dagger to and fro defensively.
"She's got guts." Phenîlas spoke to her in elvish, Rodîr in the language of humans and Gosalyn tried dwarfish.
But the little girl kept shaking her head, answering incomprehensibly, although she did put the weapon away. She had realised they weren't a danger to her.
"We're not educated enough." Rodîr approached her, touching her gingerly on the head and stroking her wild hair soothingly. Then he took his glove off and conveyed by touching her face that he wanted to see her eyes.
"She is from the Outer Lands," Belogar stressed again. "Nothing from there makes it to our homeland."
The girl opened her eyes a crack, exposing inflamed redness. Her eyes started watering immediately and she groaned, holding her hands over them.
"The poor thing. She needs help!" Rodîr got up. "I'm sure the dwarves must be good at treating snow-blindness?"
"Oh yes." Belogar raised his mace. "She'll feel better _after this_."
At the sound of these harsh words, the girl clung to the human warrior's hand for protection. "You seriously want to kill a child?" he asked indignantly.
"A child from the Outer Lands," the dwarf cried, losing his temper. "By Vraccas! What good has come from there in recent cycles? Aiphatòn? The kordrion? The demon? Monsters and älfar?"
" _Tungdil_ came from there," Phenîlas of all people softly replied, and crossed his arms over his white armour. "From the Black Abyss. And he saved you all, as far as I know."
Gosalyn was going to intervene to calm things down, but Belogar dismissed her with a harsh glance. "No, I'm not going to give in. This child will not be taken to the kingdom of the Fifthlings."
Rodîr nodded. "Fine. Then I'll take her to my queen. Our healers will take care of her. We'll see what she can tell us."
"My name is Sha'taï," she said haltingly in a high-pitched voice and cleared her throat. "Do you understand me now? If you do: I had to flee from my family's enemies. The town was destroyed and my uncle brought me..."
"Silence!" Shuddering, Belogar took a step backwards and fear showed on Phenîlas' delicate face. "That was... älfar," he whispered in disgust. "This child speaks älfar!" He snatched up his weapon and made to strike.
Gosalyn stopped him. "No," she screamed. "That's not your decision to make!"
The dwarf wrestled with her and shoved her aside. He knitted his bushy eyebrows. "There's nothing to decide. She's one of them! Or she's a demon. Some kind of new trick!"
"She's not an älf-woman, you can tell at a glance," Phenîlas cut in, his face pale. "She probably comes from an area that belonged to the älfar. As Girdlegard once did."
Belogar spat, not even considering lowering his weapon. He didn't take his eyes off the little girl. "I thought the black-eyes had perished?"
"That remains to be seen." Rodîr pulled the child to her feet and pushed her behind him, the guards coming to his side and forming a rock-solid wall. "It's all the more important that we bring her to Queen Mallenia now. In the interests of all kingdoms and tribes of Girdlegard. The little girl will tell us about the älfar and can warn us if they are going to attack again."
Phenîlas nodded. "I'll guard her. She can't do anything to harm us, my dear dwarf. She's just a child who escaped the älfar and came to this settlement." He placed a hand on his shoulder. "This settlement once represented peace between us."
Belogar was furious but he reluctantly lowered the mace. "You'll have to take the outer path," he thundered. "I'm going to keep my word: this child will not set foot in the kingdom of my tribe. Gosalyn and I will direct you so that you make it to Gauragar safely."
The elf slowly bowed his head. "So be it. The Grey Mountains belong to the Fifthlings." Rodîr wanted to protest but Phenîlas' warning glance made him remain silent. "We'll set out tomorrow morning to have Sha'taï treated and learn more about the Outer Lands. But let's explore the settlement now. That's what we actually came here to do." He went outside with the human warriors.
"I don't have a good feeling about this. High King Ireheart needs to hear about it. About everything. He'll be able to get the lankies and the pointy-ears to see sense." Belogar looked anxiously at Gosalyn. "We've got to find that path from here to the Outer Lands and destroy it."
"Agreed." The dwarf-woman looked out the window at the staircase they had used to get down into the valley. "I'll lead the group by myself. You go straight back to Balyndis. We need more troops for the search and we need our best architects to seal the hole with mountain scree. For good."
Belogar and Gosalyn walked outside and went over to Phenîlas and Rodîr to explain why the dwarf was immediately and unexpectedly going away.
The elf and the human pretended to be sympathetic and wished him a safe journey and all possible aid from the gods so that the path could be found and destroyed. But as they parted, Belogar saw a fine film over the young human warrior's eyes that seemed to disappear the next time he blinked. _That must have been his danger-blindness._
He trudged up the steps, putting his cloaks on again as he did so because ice and snow awaited him.
Halfway up, he turned and surveyed the tranquil valley.
Phenîlas and Rodîr were conferring together a slight distance from the fire that was just being fanned, while Gosalyn was taking a bucket to the waterfall to scoop water out of the pond.
The soldiers from Gauragar were preparing the provisions they had brought with them.
Sha'taï was sitting in their midst, receiving a friendly laugh and encouraging words to show her she didn't need to fear her rescuers. Occasionally someone ran a hand over her dark blonde hair, the way people did with children.
Belogar's mistrust remained undiminished. _I should have killed her._
He hurriedly continued his ascent. Nobody else would ever get into Girdlegard on this path. That much was as good as settled.
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# Afterword and Thanks
With that, they are told for now, the great fortunes and legends of the älfar.
The last älfar have either been wiped out or no longer have their own free will and have become slaves to a stronger power—whatever the shackles that lie on heart and mind.
I admit it wasn't easy for me to take the villains who have style, profound wickedness, cruelty, brilliance and a taste for art, and turn them into a declining, doomed people.
No, it _truly_ wasn't easy.
But history and stories simply don't make any allowances for sensitivities. Anyone who misbehaves for long enough gets the comeuppance they deserve at some point.
The älfar had the misfortune to come across an opponent who was not their equal, but who had the more treacherous tool at their disposal.
It was difficult even for the author to acknowledge that until the bitter end.
Oh well...
People will suppose there might be a reunion between Aiphatòn, Carmondai and possibly an älfar assassin in the fifth Dwarf volume.
But don't worry, it won't be too long.
My thanks once again go to the wonderful test-readers Tanja Karmann, Yvonne Schöneck and Sonja Rüther. They found the demon in the detail.
This time, editor Hanka Jobke had to do battle with the black-eyes and, with her notes and queries, she gave the villains a better send-off. Thank you!
Carsten Polzin should be mentioned for his great care, and once again, Piper Verlag for all of the liberties an author could hope for, from making up the title to the cover design—thanks also to the Guter Punkt Agency who implemented my idea so successfully.
And last but not least, the most enormous THANK YOU to everyone who followed the älfar to the end!
Oh, anyone who wants to know what the frekorian soldiers, ghaists, botoicans, the wind-voice and other topics touched upon are all about is advised to read the _Forgotten Writings_ anthology.
You'll find what you're looking for.
# Dramatis Personae
_**TARK DRAAN**_
**ÄLFAR**
Aiphatòn | emperor of the älfar in Tark Draan and offspring of the Inextinguishables
---|---
Carmondai | master of word and image
Firûsha, Sisaroth and Tirîgon | triplets, joint rulers of the northern älfar
Daitolór | älf-warrior with the rank of a benàmoi
Tanóra | veteran-woman
Vonòria | veteran-woman
Ostòras | älf-warrior
Rhogàta | älf-warrior woman
Votòlor | älf-warrior
**HUMANS**
Mallenia | Queen of Gauragar and Idoslane
---|---
Rodario | King of Urgon
Coïra | maga and Queen of Weyurn
Kerjan Münzler | mayor of Güldenwand
Rodîr Bannerman | warrior
Endô | refugee
Sha'taï | his niece, refugee
Lot-Ionan | magus and one-time foster father to Tungdil Goldhand
**DWARVES**
_**Secondling Kingdom**_
Baromir Goldenstein | messenger
---|---
Boïndil 'Ireheart' Doubleblade | of the clan of the Axe Swingers, King of the Secondlings
_**Thirdling Kingdom**_
Tungdil Goldhand | warrior and scholar
---|---
_**Fifthling Kingdom**_
Belogar Strifehammer | of the clan of the Boulder Heavers
---|---
Gosalyn Landslip | of the clan of the Tunnel Seekers
_**Freelings**_
Carâhnios | the last zhadár
---|---
Beligata Hardblow | a former Thirdling of the clan of the Bloodshedders, now a free dwarf
**ELVES**
Fiëa | elf-leader
---|---
Ilahín | Fiëa's husband
Phenîlas | elf-leader
_**ISHÍM VORÓO**_
**ÄLFAR**
_**Dsôn Elhàtor**_
Modôia | monarchess of Dsôn Elhàtor
---|---
Ôdaiòn | Modôia's son
Leïóva | Modôia's confidante
Ávoleï | Leïóva's daughter and battleship commander
Olòndôras | cîanoi
Khônatá | top cîanai of the fine art
_**Dsôn Dâkiòn**_
Shôtoràs | sovereign of Dsôn Dâkiòn
---|---
Irïanora | Shôtoràs' niece
Saitôra | Irïanora's close friend
Bethòras | chief architect and cartographer
Gathalor and Iophâlor | Irïanora's acquaintances
Pasôlor and Horgôra | confidants of the sovereign
Arthâras | bodyguard
Zelája | maid
Vailóras | warrior and tax collector
Lethòras | top cîanoi
Tanôtai | death-dancer
Anûras | master of the death-dancers
Nodûcor | exiled älf
**OTHERS**
Kôr'losôi | botoican of the Nhatai family
---|---
Saî'losôi | botoican-woman of the Nhatai family
Fa'losôi | top botoican-woman in the Nhatai family
Ysor'kenôr | botoican of the Rhâhoi family
Ythan'kenôr | Ysor'kenôr's brother
Cushròk | commander of a tribe of soldiers for hire
Gricks, Tratshka, Nrashq, Obko | Cushròk's soldiers from the tribe of the Dréki
Joako | pub landlord
**GLOSSARY**
Dsôn Elhàtor | the Magnificent, an älfar town on an island
---|---
Dsôn Dâkiòn | the Majestic, an älfar town on a mountain
Tronjor | river that flows from Dâkiòn to the sea
onwú | sea-faring race of humans, enemies of Elhàtor
shintoìt | designation for a child of the Inextinguishables
zhartài | master assassin who declares älfar targets
zhadár | derived from zhartài, älfar word for the Invisibles
benàmoi | officer rank of älfar
cîanai/cîanoi, cîani (plural) | älfar sorceress/sorcerer
botoican | human with magic powers in Ishím Voróo
Dhaïs Akkoor | old capital of the botoican kingdom
Tr'hoo D'tak | capital of the Nhatai kingdom
Ultai t'Ruy | capital of the Rhâhoi kingdom
malméner | breed of beast comprised of troll, ogre and giant
ghaist | creature comprised of magic and souls bound together in human form; wears a distinctive copper helmet
Children of the Smith | dwarves' term for themselves
# extras
# meet the author
MARKUS HEITZ was born in 1971 in Germany. He studied history, German language and literature, and won the German Fantasy Award in 2003 for his debut novel _Shadows Over Ulldart_. His Dwarves series is a bestseller in Europe. Markus Heitz lives in Zweibrücken.
if you enjoyed
RAGING STORM
look out for
# THE WOLF
Under the Northern Sky: Book One
by
Leo Carew
Beyond the Black River, among the forests and mountains of the north, lives an ancient race of people. Their lives are measured in centuries, not decades; they revel in wilderness and resilience, and they scorn wealth and comfort.
By contrast, those in the south live in the moment, their lives more fleeting. They crave wealth and power; their ambition is limitless, and their cunning unmatched.
When the armies of the south flood across the Black River, the fragile peace between the two races is shattered. On a lightning-struck battlefield, the two sides will fight—for their people, for their land, for their very survival.
# PROLOGUE
It rained as though the world was ending. In a cobbled street made dark by the clouds that covered moon and stars, a hooded figure struggled towards the door of a stone house, dragged back by a bitter wind. The figure leaned forward against the rushing dark, one hand grasping the top of its hood as the wind threatened to unmask it. The roof of the house ahead was unravelling and the air was thick with swirling reed. So great was the pressure the wind exerted on the dwelling that, when the figure reached it and lifted the latch, the door swept inwards and rattled off the stone behind. Within, the darkness was complete. No candles burned, no lamps were lit and there was no natural light on this wild night. Water was pouring somewhere in the dark.
The figure hesitated on the threshold for a moment, casting around. Then it groped inside, forcing the door shut behind. The wind stopped roaring and began to moan instead as it was banished from the room. In the pitch-darkness, the figure lowered its hood.
Footsteps were ringing through the dark.
The figure stood still as light began to erode a corner of the blackness. Into this growing pool of light strode a tall, dark-haired man; his fine features illuminated by a candle which he clutched in a pewter holder. There was a touch of grey at his temples and his eyes were narrowed. He stopped dead at the sight of the figure by the door and dropped his hand to a long dagger at his belt. "Who's that?"
The figure stepped forward into the glow of the candle and resolved itself into the form of a golden-haired woman, hair tied back and gleaming with rain. She smiled and the man's mouth fell open. He stared at her for a moment. "You've been wandering the streets alone?"
"Nobody's out in this," replied the woman. The man took a couple of steps towards her so that the candlelight was able to bring her face into greater resolution. Her clothes were dark with rain, but so fine they obviously belonged to a woman of the highest birth. But here her resemblance to the other noblewomen of the land ended. She was not like them: paled, painted, adorned, frail and delicate. Her beauty was harsher; in the bones of her face, the lines around her eyes and the ease of her stance. She wore no gold or silver and her skin was not chalk-white but browned and lined by the sun.
"Where is His Majesty?" asked the man.
"Sleeping. His physician has administered one of his brews: he won't wake up. He fears the lightning." The golden-haired woman rolled her eyes.
He observed her for a moment. The wind whispered through the cracks in the door, making the candle flicker. "You're mad."
She smiled and raised her eyebrows a little, her eyes slightly narrowed. "That's what the court says about you. 'Be careful of Bellamus of Safinim, Your Majesty. The upstart is not right.'"
Bellamus of Safinim held out an arm and she crossed to him, placing one of her own about his waist and supporting his upon her shoulder. Bellamus looked down at her upturned face, her eyes still narrowed, still smiling, and he kissed her. He raised his hand from her shoulder and inspected a finger and thumb, shining with moisture from her clothes. "You are in need of a fire."
They turned away and into the dark. The candle fought silently with the void, briefly revealing the pool in the centre of the hall into which water fell in sheets from an aperture in the centre of the roof, and then, as they moved on down a corridor, illuminating faded frescoes on the plastered walls. The queen turned her head as they passed to follow one of a boar being skewered by a spear; then another of a bull-necked man in profile, surrounded by leaves and dancing figures. The plaster on which it had been painted had shrunk and cracked and the queen could smell the dust it gave off as it silently disassembled.
At the end of this corridor was a more consistent glow and the two figures emerged into another stone room. This one had a hearth crudely chiselled into a wall, with one wooden chair by the fire that burned within, and another drawn up to a glassless window on the other side of the room.
"You were awake?" asked the queen, glancing at the fire.
"Watching the lightning." Bellamus steered her into the seat by the fire and snuffed out the candle between finger and thumb. He crossed the room to fetch the chair by the window and a blanket that lay next to it, bringing both back to the woman. He gave her the blanket and drew up the chair beside her. "So what did the king say?" he asked.
"He said you're going to war."
Bellamus let out a slow breath. "We're invading?"
She raised her eyebrows a little in response, staring into the hearth.
Bellamus laughed; at first a gentle chuckle, until he lost control of it and it became a full-throated roar of triumph. It carried him onto his feet, and he turned towards the queen to perform a little bow. "Well done, Your Majesty," he said, and he leaned forward to kiss her again, his fingers digging into her shoulders. He broke away but did not resume his seat. "How did you manage that?"
The praise ran off her. "We both managed it. You scared him wicked, the fiery snakes and the flooding put the fear of God into him, and I directed both those fears."
The fiery snakes. The night before, a cool evening with a clear sky, the sound of wails and screams had drawn Queen Aramilla to her window. Looking out, she saw a sky stained unearthly green. As though a veil had descended from the stars, swaying and billowing in a breeze that stirred this apparition alone. It intensified, resembling a giant pot of emerald ink that had been spilled among the stars, flowing in rivers from one horizon to another. Aramilla had watched, entranced and awed, as the city beneath her began to cry. The streets emptied, some people fleeing for their houses; others to the church to pray for deliverance from whatever this omen signified. It had gone on through the night until the clouds preceding the storm rolled in, obscuring the sight.
"They were beautiful," said Bellamus. He sank into his seat again. "They did not look like an ill omen to me, but I'm glad if the king saw things differently."
"Well, they were not an ill omen for you," replied the queen. "They may yet be an ill omen for the king. I made sure he saw it that way, anyway. The flooding, the plague and now the snakes in the sky. He thinks God is furious."
"I am impressed. Was he not worried by launching a campaign so late in the season?"
"He was more worried at the thought of enduring a winter with God's anger unchecked." She placed a hand on his cheek. "But I've sent you to war, my soldier. Don't make me regret it." She sounded a little amused, but he grasped her hand anyway.
"You won't," he said. "I always come back."
"Bring me something back from beyond the Abus?" Her pupils were wide, drinking in the sight of him.
He glanced at her. "What should you like? The Anakim have no treasures. They don't value anything that can't be put to use."
"What do they have?"
"Weapons," said Bellamus. "Bigger and better than anything in the south. I could bring you a splendid axe?"
"Keep thinking," she said, amused. There came a pause. "I'd settle for the antlers of a giant elk."
"A trifle," said Bellamus. "But I intend to present something special to the king. You will not be happy unless you have something equally magnificent."
"What will you give him?"
Bellamus nodded slightly to himself. "The skull of the Black Lord." He still spoke mildly.
She looked at him out of the corner of her eye and then leaned into his chest. "My upstart. I don't envy the Anakim having you as an enemy."
Silence fell for a time. A flash of white light allowed the queen to see this room as it might appear in daylight for the merest instant. Then the darkness swallowed it once more. The queen counted ten heartbeats before a roll of thunder rumbled by and she shivered comfortably. "I wish I could come north. I want to see the Anakim before you wipe them out."
Bellamus had lapsed into thoughtful silence. He stared into the flames, playing vacantly with her hair.
"Have you ever killed one of them?" she asked. "An Anakim?"
"Once or twice," he said. "Never a fully armed and armoured warrior though. I leave those to greater heroes than I. But like all of us, they are considerably less formidable when caught by surprise."
"Is it true about their bone-plates? Or was that just another way to frighten the king?"
Bellamus grinned. "If we are to survive this game, we must stick to lies that won't be uncovered. That one is true. From groin to neck, they are exceedingly difficult to pierce."
"My father scoffed at that. He said it was a rumour of war."
"Earl Seaton is fortunate enough never to have met an Anakim in the flesh. Our borders have been so safe for so long that people have forgotten how severe that threat really is. It is no rumour, my queen."
She squirmed slightly in his arms. "So why disturb them, then?" she pressed him. "I thought they fascinated you. And however uneasy, the peace has held for years. Why risk it all to silence them?"
Bellamus was quiet for a moment and she knew he was wondering how much to reveal. Eventually, he said, "You must pick a side, and then advance it with all your might—must you not? The other side will assuredly do the same. Only by doing it harder will your side triumph."
She thought about that. "I have a side."
"I know who you fight for," he said pointedly.
"The same person you fight for." She smiled up at him. "Me."
if you enjoyed
RAGING STORM
look out for
# THE WINTER ROAD
by
Adrian Selby
_The greatest empire of them all began with a road._
_The Circle—a thousand miles of perilous forests and warring clans. No one has ever tamed such treacherous territory before, but ex-soldier Teyr Amondsen, veteran of a hundred battles, is determined to try._
_With a merchant caravan protected by a crew of skilled mercenaries, Amondsen embarks on a dangerous mission to forge a road across the untamed wilderness that was once her home. But a warlord rises in the wilds of the Circle, uniting its clans and terrorizing its people. Teyr's battles may not be over yet..._
_All roads lead back to war._
# CHAPTER 1
_You will fail, Teyr Amondsen._
My eyes open. The truth wakes me.
_You will fail._
I had slept against a tree to keep the weight off my arm, off my face. My tongue runs over the abscesses in my mouth, the many holes there. My left eye is swollen shut, my cheek broken again, three days ago, falling from a narrow trail after a deer I'd stuck with my only spear.
I close my eyes and listen, desperate to confirm my solitude. A river, quick and throaty over rocks and stones. A grebe's whinnying screech.
I take off one of the boots I'd stolen, see again the face of the man who'd worn them as I strangled him. I feel my toes, my soles, assess the damage. Numb, blisters weeping. My toes are swelling like my fingers, burning like my face. I need a fire, cicely root, fireweed. I have to be grateful my nose was broken clean. A smashed-up nose is a death sentence in the hinterlands. If you can't sniff for plant you're a bag of fresh walking meat. You need plant to heal, plant to kill.
If I keep on after this river I can maybe steal a knife, some plant and warmer clothes. These are Carlessen clan lands, the coast is beyond them. I'm going to live there, get Aude's screaming out of my head, the horns of the whiteboys, the whisperings of the Oskoro who would not, despite a thousand fuck offs and thrown stones in the black forests and blue frozen mountains, let be their debt to me.
The grebe screeches again. Eggs!
I pull on the boot with my right arm, my left strapped against me and healing, itself broken again in my fall.
I pick up my spade and the small sack that I'd put Mosa's shirt in, the spade something of a walking stick to help me along the mossy banks and wretched tracks. Snow was making a last stand among the roots of birch trees, a few weeks yet from thawing out. A few handfuls ease my gums.
The sky is violet and pink ahead of the sun, the woods and banks blue black, snow and earth. I stumble towards the river, a chance to wash my wounds once I've found some nests and broken a few branches for a fire.
The grebes screech at me as I crack their eggs and drink the yolks. I find five in all and they ease my hunger. If a grebe gets close enough I'll eat well. The sun edges over the hills to the east and I am glad to see better, through my one good eye. The river is strong up here, my ears will miss much.
I drop the deerskins I use for a cloak and unbutton my shirt. I didn't have to kill the man I stole that from. I loosen the threads to the discreet pockets that are sewn shut and take a pinch of snuff from one. It's good plant, good for sniffing out what I need. Feels like I've jammed two shards of ice into my nose and I gasp like I'm drowning, cry a bit and then press another pinch to my tongue, pulling the thread on the pocket tight after. Now the scents and smells of the world are as clear to me as my seeing it. For a short while I can sniff plant like a wolf smells prey.
I forget my pains. Now I'm back in woodland I have to find some cicely. The sharp aniseed smell leads me to it, as I'd hoped. I dig some up, chopping around the roots with the spade to protect them. Around me a leaden, tarry smell of birch trees, moss warming on stones, but also wild onion, birch belets. Food for another day or so.
I wash the cicely roots and I'm packing my mouth with them when I hear bells and the throaty grunts of reindeer. Herders. The river had obscured the sounds, and on the bank I have no cover to hide myself in. I cuss and fight to keep some control of myself. No good comes of people out here.
The reindeer come out through the trees and towards the river. Four men, walking. Nokes—by which I mean their skin is clear and free of the colours that mark out soldiers who use the gifts of plant heavily, the strong and dangerous fightbrews. Three have spears, whips for the deer, one bowman. There's a dog led by one of them, gets a nose of me and starts barking to be let free. Man holding him's smoking a pipe, and a golden beard thick and long as a scarf can't hide a smirk as he measures me up. The herd start fanning out on the bank. Forty feet. Thirty feet.
"Hail!" I shout, spitting out my cicely roots to do it. My broken cheek and swelling make it hard for me to form the greeting. I try to stand a bit more upright, to not look like I need the spade to support my weight.
"Hail. Ir vuttu nask mae?" Carlessen lingo. I don't know it.
I shake my head, speaking Abra lingo. "Auksen clan. Have you got woollens to spare? I'm frostbitten." I hold up my good hand, my fingertips silver grey.
He speaks to the others. There's some laughter. I recognise a word amid their own tongue, they're talking about my colour, for I was a soldier once, my skin coloured to an iron rust and grey veins from years of fightbrews. One of them isn't so sure, knowing I must know how to fight, but I reckon the rest of me isn't exactly putting them off thoughts of some games. Colour alone isn't going to settle it. Shit. I reach inside my shirt for some of the small white amony flowers I'd picked in the passes above us to the north.
"No no no. Drop." He gestures for me to drop the spade and the amony. He lets a little of the dog's lead go as well. The bowman unshoulders his bow.
At least the stakes are clear, and I feel calmer for it. He has to be fucked if he thinks I'm going to do a word he says, let alone think his dog could hurt me.
He has nothing that can hurt me, only kill me.
"No, no, no," I says, mimicking him before swallowing a mouthful of the amony and lifting the spade up from the ground to get a grip closer to its middle. I edge back to the river, feeling best I can for some solid flat earth among the pebbles and reeds.
He smiles and nods to the bowman, like this is the way he was hoping it would go, but that isn't true. The bowman looses an arrow. Fool could've stepped forward twenty feet and made sure of me but I throw myself forward. Not quick enough, the amony hadn't got going. Arrow hits my left shoulder. It stops me a moment, the shock of it. He's readying another arrow, so I scream and run at the reindeer that strayed near me, the one with the bell, the one they all follow. It startles and leaps away, heading downstream, the herd give chase.
Time and again I made ready to die these last nine months. I'm ready now, and glad to take some rapists with me. I run forward while they're distracted by how much harder their day is now going to be chasing down the herd. The one with the pipe swears and lets his dog go at me while one of the spears fumbles in his pockets for a whistle to call the herd, running off after them.
Dogs are predictable. It runs up, makes ready to leap and I catch it hard with the spade. It falls, howling, and I get the edge of the spade deep into its neck. I look at the three men left before me.
"Reindeer! You'll lose them, you sad fuckers!" They'll understand "reindeer" at least.
The pipe smoker draws a sword, just as my amony beats its drum. I don't know how much I took but it hits me like a horse just then. I shudder, lose control of myself, my piss running down my legs as my teeth start grinding. I gasp for air, the sun peeling open my eyes, rays bleaching my bones. My new strength is giddying, the amony fills me with fire.
He moves in and swings. He's not very good at this. The flat of my spade sends his thrust past me and I flip it to a reverse grip and drive it hard into his head, opening his mouth both sides back to his ears. I kick him out of my way and run at the bowman behind him. He looses an arrow, and it shears the skin from my skull as it flies past, almost pulling my good eyeball out with it, the blood blinding me instantly. He doesn't know how to fight close, but I'm blind in both eyes now and I'm relying on the sense the amony gives me, half my training done blind all my life for moments like this. I kick him in the gut, drop the spade and put my fist into his head, my hearing, smell exquisite in detail. He falls and I get down on his chest and my good hand seeks his face, shoving it into the earth to stop its writhing, drive my one good thumb through an eye far as it'll go. A shout behind me, I twist to jump clear but the spear goes through me. Out my front it comes, clean out of my guts. I hold the shaft at my belly and spin about, ripping the spear out of his hands, his grip no doubt weakened a moment with the flush of his success. I hear him backing away, jabbering in his lingo "Ildesmur! Ildesmur!" I know this name well enough, he speaks of the ghostly mothers of vengeance, the tale of the War Crows. I scream, a high, foul scritching that sends him running into the trees.
My blood rolls down my belly into my leggings. There's too much of it. Killed by a bunch of fucking nokes. No more than I deserve. I fall to my knees as I realise, fully, that it's over. The river sounds close, an arm's length away maybe. I fall forward, put my arm out, but it gives and I push both the spearhead and the end of the arrow that's in my shoulder back through me a bit. A freezing spike of pain. My senses lighten to wisps, I fall away from the ground, my chest fit to burst, my blood warming my belly and the dirt under me. Why am I angry that it's all over? The sun keeps climbing, the pebbles rattle and hum as the song of the earth runs through me—beating hooves, distant cries, roots of trees stretching and drinking. I hum to quieten the pain. It's my part in the song but I was always part of the song, I just haven't been listening. The birch trees shush me. Snowy peaks crack like thunder in the distance. The sky is blue like his eyes, fathomless.
"I'm coming," I says. He knows I'm coming. I just have to hold out my hand.
BY MARKUS HEITZ
The Dwarves
_The Dwarves_
_The War of the Dwarves_
_The Revenge of the Dwarves_
_The Fate of the Dwarves_
_The Triumph of the Dwarves_
The Legends of the Älfar
_Righteous Fury_
_Devastating Hate_
_Dark Paths_
_Raging Storm_
_Oneiros_
_Aera: The Return of the Ancient Gods_
# Contents
1. Cover
2. Title Page
3. Copyright
4. Dedication
5. Epigraph
6. Prologue
7. Chapter I
8. Chapter II
9. Chapter III
10. Chapter IV
11. Chapter V
12. Chapter VI
13. Chapter VII
14. Chapter VIII
15. Chapter IX
16. Chapter X
17. Chapter XI
18. Chapter XII
19. Chapter XIII
20. Chapter XIV
21. Chapter XV
22. Chapter XVI
23. Epilogue
24. Discover More
25. Afterword and Thanks
26. Dramatis Personae
27. Extras
1. Meet the Author
2. A Preview of "The Wolf"
3. A Preview of "The Winter Road"
28. By Markus Heitz
# Navigation
1. Begin Reading
2. Table of Contents
| {
"redpajama_set_name": "RedPajamaBook"
} | 3,502 |
import logging
import os
_version = os.environ.get('CURRENT_VERSION_ID', '').split('.')[0]
_internal_libs = [
'google.appengine.ext.mapreduce',
'google.appengine._internal.mapreduce'
]
if __name__ in _internal_libs and _version != 'ah-builtin-python-bundle':
msg = ('You should not use the mapreduce library that is bundled with the'
' SDK. Use the one from'
' https://pypi.python.org/pypi/GoogleAppEngineMapReduce instead.')
logging.warn(msg)
| {
"redpajama_set_name": "RedPajamaGithub"
} | 8,199 |
Dragonlance modules and sourcebooks are role-playing game books created for the Dragonlance campaign setting. These books were created for multiple editions of Dungeons & Dragons and for the SAGA System.
Overview
The Dragonlance game project began with Tracy and Laura Hickman, and the idea of a world dominated by dragons. As they drove from Utah to Wisconsin so Tracy could take up a job with TSR in 1981, they discussed this idea. In 1982, Tracy proposed at TSR a series of three modules featuring evil dragons. When this plan reached then head of TSR Gary Gygax, it fitted well with an idea he had considered of doing a series of 12 modules each based on one of the official Monster Manual dragons. The project was then developed, under the code name "Project Overlord" to plan the series. The original group included Tracy Hickman, Harold Johnson, Larry Elmore, Carl Smith and Jeff Grubb. Later in the development process it was decided that a trilogy of fantasy novels would be released with the modules. Originally an external writer was hired, but the design group found themselves more and more disillusioned with his work. At this point it was suggested that Hickman and Margaret Weis, an editor in TSR's book department who had become involved with the project, ought to write the books. They wrote the five chapters over a weekend and were given the job to write the accompanying novels based on that. The first module, Dragons of Despair, was published in March 1984. Then in November 1984, Dragons of Autumn Twilight was published. This novel was written after the completion of the first Dragonlance game modules. Weis and Hickman felt this was constraining and made the novel feel too episodic, so they reversed the process for the next books and completed the novels before the related modules were written. The first Krynn setting guide, Dragonlance Adventures, would follow in 1987.
When AD&D was updated to the 2nd edition in 1989, the Dragonlance campaign setting was updated as well. In 1993, the product line for AD&D was canceled. However, the Dragonlance fiction line "remained wildly successful" and included "some 60 novels and anthologies"; "TSR wanted to bring those fiction fans back into the roleplaying fold if they could, and so a new team was set to work to create a new Dragonlance game". In 1996, Dragonlance was converted to TSR's new SAGA System with the publication of the Dragonlance: Fifth Age roleplaying game. The SAGA System has a more narrative focused gameplay style than AD&D and uses cards to determine the effects of actions. Shannon Appelcline commented that "the non-AD&D game was not to everyone's taste, but it was extensively supported from 1996-2000, with a timeline that pushed considerably into Krynn's future". The majority of the SAGA line was set during 414 AC, however, the final releases of the line were set in 383 AC.
After Wizards of the Coast's acquisition of TSR, the 3rd Edition of Dungeons & Dragons was released in 2000 and Wizards announced that the Dragonlance setting would not be supported. However, Wizards allowed a group of fans to support the line for the 3rd Edition on the internet. Initially, the Dragonlance-L mailing list updated the setting; this mailing list would become known as the Whitestone Council and would maintain The Dragonlance Nexus website. The Whitestone Council was supported by both Tracy Hickman and Margaret Weis. Then in 2002, Margaret Weis's company Sovereign Press acquired the license to publish 3rd Edition Dragonlance material. The official update, Dragonlance Campaign Setting, was published in 2003 for the 3.5 Edition; it moved the timeline to 422 AC and was set six months "after the end of the War of Souls trilogy (2000-2002)". Appelcline highlighted that "the Whitestone Council was asked to review Sovereign's manuscript and in a few cases also got to submit minor bits for the new setting book. The Council would continue to be important to Sovereign following the publication of the Dragonlance Campaign Setting, with a few members contributing increasingly large amounts to later releases". Sovereign Press maintained the Dragonlance line until 2007.
The campaign setting was not supported during the 4th Edition era (2008-2013) of Dungeons & Dragons. In March 2022, Wizards released the PDF Heroes of Krynn which is part of the "Unearthed Arcana" public playtest series for the 5th Edition of Dungeons & Dragons. Polygon commented that this "all but confirmed" the return of the Dragonlance setting. In April 2022, it was announced that the setting will be revisited in December 2022 with a new adventure module for the 5th Edition. This adventure will be set concurrently to the War of the Lance, a fictional conflict in the setting.
Advanced Dungeons & Dragons 1st/2nd Edition
SAGA System
Systemless
Dungeons & Dragons 3rd/3.5 Edition
Dungeons & Dragons 5th Edition
See also
List of Dungeons & Dragons modules
Dragons of Light (anthology by Orson Scott Card)
References
External links
Dragons of Light at a fan made TSR archive
Dragons of Faith at a fan made TSR archive
Modules and sourcebooks
Lists about role-playing games | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 3,038 |
\section{Introduction}
Quantum annealing (QA) \cite{apolloni1989quantum,finnila1994quantum,morita2008mathematical,hauke2020perspectives} is one of the methods to solve combinatorial optimization problems \cite{kadowaki1998quantum,lucas2014ising}.
It is known that the combinatorial optimization problem \cite{schrijver2005history} can be mapped as the problem of finding the ground state of the Ising Hamiltonian \cite{lechner2015quantum}.
QA is used to find the ground state of the Ising Hamiltonian.
In QA, the Hamiltonian is time-dependent; we slowly change the Hamiltonian from the independent spin model with the transverse fields (called the driver Hamiltonian) to the target Ising Hamiltonian (called a problem Hamiltonian).
As long as an adiabatic condition holds \cite{farhi2000quantum,aharonov2008adiabatic,farhi2001quantum,albash2018adiabatic,childs2001robustness}, we can obtain a ground state of the problem Hamiltonian when the initial state is a ground state of the driver Hamiltonian.
D-Wave Systems Inc. has developed a quantum hardware to perform QA using thousands of superconducting flux qubits \cite{mcgeoch2019practical,johnson2011quantum,boixo2014evidence,boixo2013experimental}.
Several other quantum hardware for QA have been proposed and developed\cite{maezawa2019toward,saida2021experimental,saida2022factorization}.
Previous researches mainly focused on the ground-state search for QA.
More recently, there have been studies of excited state
searches in which the excited state of the driver Hamiltonian is
selected as the initial state \cite{seki2021excited,teplukhin2019calculation,teplukhin2020electronic,chen2020demonstration}.
A crucial point of the excited state search is that we need to use non-uniform transverse magnetic fields in the driver Hamiltonian to resolve the degeneracy of the excited state of the driver Hamiltonian.
This procedure allows us to prepare a non-degenerate excited state of the driver Hamiltonian when we start QA.
By changing the Hamiltonian from the driver one to the problem one, we obtain the excited state of the problem Hamiltonian as long as the adiabatic condition is satisfied.
The excited-state search in QA is useful in quantum chemistry\cite{serrano2005quantum}; for example, it is essential to know the photochemical properties of molecules, which requires information not only on the ground state but also on the excited state.
Post-quantum cryptography
has attracted much attention
from many researchers.
RSA (Rivest–Shamir–Adleman) is a widely used public key cryptography with the security based on the difficulty of the prime factorization\cite{rivest1978method}.
Once the fault-tolerant quantum computer is developed, RSA cryptography can be efficiently decrypted by Shor's algorithm \cite{shor1994algorithms}.
Therefore, research on post-quantum cryptography, which is difficult to solve even with a gate-type quantum computer, is underway.
Lattice-based cryptography (LBC) \cite{ajtai1997public} is one of the candidates for post-quantum cryptography \cite{micciancio2009lattice}.
One of the key mathematical problems in LBC is the shortest vector problem (SVP), which is the problem of finding the shortest non-zero vector in a given lattice.
There are
two approaches
to solving lattice problems.
The first approach is to chose input vectors from a distribution on a lattice and iteratively combine the vectors so that output should be probabilistically generated as solutions
\cite{ajtai2001sieve, laarhoven2015sieving, micciancio2010faster, ducas2018shortest}.
The second approach is to
enumerate all vectors in a specific sphere centered at the origin. There is a guarantee that the solution is contained if it is carefully chosen\cite{pohst1981computation, gama2010lattice}.
Although these are classical algorithms, it is known that the SVP can be solved using a gate-type quantum computer. A quantum tree algorithm (based on Grover's algorithm) can solve the SVP \cite{laarhoven2013solving}. However, it still takes an exponentially longer time to solve larger problems.
Recently, a method using quantum annealing was proposed to search for solutions of the SVP. More specifically,
Joseph et al. proposed a heuristic method for finding the solution to the shortest vector problem using ground-state search for QA \cite{joseph2021two}.
The SVP can be mapped onto an Ising Hamiltonian with integer spins, and the first excited state of the Hamiltonian corresponds to the solution.
In their method, after the ground state of the driver Hamiltonian is prepared, the Hamiltonian is changed from the driver Hamiltonian to the problem Hamiltonian over time.
The goal is to obtain the desired first excited state of the problem Hamiltonian via a non-adiabatic transition from the ground state to the first excited state.
However, there is no known method to find a suitable schedule to change the Hamiltonian for obtaining the first excited state in their approach.
If the Hamiltonian is changed slowly, the ground state is obtained.
On the other hand, a rapid change of the Hamiltonian would induce non-adiabatic transitions to not only the first excited state but also to other excited states.
In this paper, we propose to use the excited-state search with QA to find a solution to the SVP.
We adopt the inhomogeneous transverse fields with integer spins as the driver Hamiltonian so that we can prepare the non-degenerate first excited state of the driver Hamiltonian. By changing the Hamiltonian from the driver Hamiltonian to the problem Hamiltonian, we can obtain with finite probability the first excited state of the problem Hamiltonian, which is the solution of the SVP. By increasing the annealing time, the dynamics become more adiabatic, and
the success probability should increase as long as the decoherence is negligible.
We also show that the first excited state of the driver Hamiltonian with integer spins is an entangled state, which is experimentally challenging to prepare.
We show that it is still possible to obtain the first excited state with a high probability in our method by using a specific separable state as the initial state \cite{kitagawa1993squeezed,radcliffe1971some,arecchi1972atomic}.
Moreover, we compare our method based on the excited-state search with the previous approach based on the ground-state search. We show that our method provides higher success probabilities for most of the parameters.
\section{Quantum Annealing (QA)}
\subsection{ground-state search}
In this subsection, we describe QA for the ground-state search.
In QA, quantum fluctuations are used to find a ground state of a given Ising Hamiltonian.
The total Hamiltonian for QA is given as follows:
\begin{eqnarray}
H(t)=\biggl(1-\frac{t}{T}\biggr)H_\mathrm{D}+\biggl(\frac{t}{T}\biggr)H_\mathrm{P},
\end{eqnarray}
\begin{eqnarray}
H_\mathrm{D}=-b_x\sum^{N}_{i=1} \sigma_x^{(i)},
\end{eqnarray}
\begin{eqnarray}
H_\mathrm{P}=\sum^{N}_{i=1} h_{i} \sigma_z^{(i)}
+ \sum^{N}_{i=1} J_{i,j} \sigma_z^{(i)}\sigma_z^{(j)},
\end{eqnarray}
where $H_D$ is the driver Hamiltonian to induce quantum fluctuations, $H_P$ is the problem Hamiltonian whose ground state corresponds to the solution of the combinational optimization problem, $b_x$ denotes the strength of the transverse magnetic field, $h_i$ denotes the longitudinal magnetic field, and $J_{i,j}$ denotes the coupling constant of the Ising interaction.
Also,
$\sigma _x$ and $\sigma _z$
denote the Pauli matrices.
We prepare an initial state as the ground state of the driver Hamiltonian, and let this state evolve by the time-dependent Hamiltonian $H(t)$. As long as the dynamics is adiabatic, we can obtain the ground state of the problem Hamiltonian at $t=T$.
On the other hand, if the dynamics is not slow enough to satisfy the adiabatic condition, non-adiabatic transitions occur, and there will be a finite population in the excited states.
\subsection{Excited state search}
In this section, we describe QA for the excited state search\cite{seki2021excited,teplukhin2019calculation,teplukhin2020electronic,chen2020demonstration}.
We consider the following Hamiltonian
\begin{eqnarray}
H(t)=\biggl(1-\frac{t}{T}\biggr)H_\mathrm{D}^{{(\mathrm{nu})}}+\biggl(\frac{t}{T}\biggr)T_P
\end{eqnarray}
\begin{eqnarray}
H_\mathrm{D}^{(\mathrm{nu)}}=-\sum^{N}_{i=1} b_x^{(i)}\sigma_x^{(i)}
\end{eqnarray}
\begin{eqnarray}
H_\mathrm{P}=\sum^{N}_{i=1} h_{i} \sigma_z(i)
+
\sum^{N}_{i=1} J_{i,j} \sigma_z(i) \sigma_z(j)
\end{eqnarray}
where $b_x^{(i)}$ is the amplitude of the transverse magnetic field at site $i$.
This spatially non-uniform transverse magnetic field can resolve the degeneracy of the first excited state of the driver Hamiltonian.
First, we prepare the first excited state of $H_D$.
Second, we let the system evolve according to the time-dependent Hamiltonian from $t=0$ to $t=T$. After these steps, we can obtain the first excited state of the problem Hamiltonian, as long as the adiabatic condition is satisfied.
\section{The shortest vector problem (SVP)}
We review the shortest vector problem (SVP), which is the mathematical basis for post-quantum cryptography. We consider a set of lattice vectors as defined below:
\begin{eqnarray}
\boldsymbol{L}=\{\sum^{N}_{i=1} {x_{i}\Vec{\boldsymbol{b}}_{i}}\}=\{{\boldsymbol{B}\cdot\boldsymbol{x}:\boldsymbol{x}\in \mathbb{Z}^{N}}\}
\end{eqnarray}
where $\boldsymbol{x}=\{ x_{i} \}_{i=1}^N\in \mathbb{Z}^{N}$ is a set of integers representing the coefficients of the lattice basis vectors, $\boldsymbol{x}$
is a vector of the coefficients,
$\{ \boldsymbol{b}_{i} \}^N_{i=1}$
is a set of linearly independent vectors, and $\boldsymbol{B}=\{\boldsymbol{b}_{1}, \boldsymbol{b}_{2}, \cdots \boldsymbol{b}_{N} \}$ is the lattice basis matrices. Each vector on the lattice is expressed as follows.
\begin{eqnarray}
\boldsymbol{v}=\boldsymbol{B}\cdot\boldsymbol{x}
=x_{1}\boldsymbol{b}_{1}+\cdots +
x_{N}\boldsymbol{b}_{N}\in \boldsymbol{L}
\end{eqnarray}
The SVP aims to find a non-zero vector with the smallest norm on this lattice.
\section{Mapping of SVP}
Let us explain how to map the SVP onto the Ising Hamiltonian \cite{joseph2021two}. The norm of the vector $\boldsymbol{v}$ on the lattice can be written as
\begin{eqnarray}
&&||\boldsymbol{v}||^{2}=\sum^{N}_{i,j=1} x_{i}x_{j}\boldsymbol{b}_{i}\cdot\boldsymbol{b}_{j}\nonumber \\
&=&
\sum^{N}_{i,j=1} x_{i}x_{j} \boldsymbol{G}_{i,j}
\end{eqnarray}
where $\boldsymbol{G}_{i,j}=\boldsymbol{b}_{i}\cdot\boldsymbol{b}_{j}$ is the element of the Gram matrix of the lattice basis vectors.
We consider the search for a solution of the SVP in the range $-k \leq x_i\leq k$ .
Let us consider $2kN$ qubits, and
the Hamiltonian corresponding to the norm can be written as
\begin{eqnarray}
\hat{H}^{(\rm{SVP})}_{\rm{p}}=J\sum^{N}_{i,j=1} \boldsymbol{G}_{i,j}\hat{Q}^{(i)}\hat{Q}^{(j)}\label{hsvp}
,
\end{eqnarray}
where $\hat{Q}^{(i)}$ is a diagonal matrix defined as
$\hat{Q}^{(i)}=\sum^{2k}_{p=1}\hat{\sigma}^{(p,i)}_{z}/2$ ($i=1,2,\cdots, N$),
$J$ denotes a constant factor with a unit of energy,
and $\sigma_z$ denotes a Pauli matrix.
Throughout of this paper, by setting $J=1$, the time and energy are normalized by this value.
To save the computational resources, we consider a subspace spanned by Dicke basis. Then,
the eigenvalue of the operator
$\hat{Q}^{(i)}$ corresponds to the coefficient of the $N$ lattice basis vectors, which takes the integer value
in the range of $-k \leq x_i\leq k$.
The ground state of the Hamiltonian (10) corresponds to the zero vector. Therefore, the first excited state is the solution of the SVP.
\section{Solving SVP using a ground state search using adiabatitic transition with QA}
We briefly explain the previous study \cite{joseph2021two} on finding the solution of the SVP using the ground state search with QA. The driver Hamiltonian is described as
\begin{eqnarray}
\hat{H}^{\rm{SVP}}_{D}=\sum _{i=1}^N B_{x}
\sum^{2k}_{p=1}\hat{\sigma}^{(p,i)}_{x}
,
\end{eqnarray}
where $B_x$ is the strength of the transverse magnetic field and $\hat{\sigma_x}$ denotes the Pauli operator. We adopt $H_P^{(SVP)}$ as the problem Hamiltonian. The total Hamiltonian is given as
\begin{eqnarray}
\hat{H(t)}=\biggl(1-\frac{t}{T}\biggr)\hat{H_D}^{(SVP)}+\biggl(\frac{t}{T}\biggr)\hat{H_P}^{(SVP)}
,
\end{eqnarray}
where $T$ is the annealing time. The QA was originally proposed to find the ground state of the problem Hamiltonian with the adiabatic dynamics. After preparing the ground state of the driver Hamiltonian, we evolve the system according to the total Hamiltonian from $t=0$ to $t=T$. As long as the dynamics is adiabatic, the ground state of the problem Hamiltonian is obtained as a final state. However, since the first excited state of the problem Hamiltonian is the solution of the SVP, we cannot obtain the solution with high probability by using the ground-state search. In the previous approach, non-adiabatic transitions are utilized to excite the system. If one could find suitable scheduling, we may obtain the first excited state with high probability. However, finding an optimal annealing time is
not straightforward
as long as the ground-state search is used.
\section{Solving SVP using excited state search with QA}
In this section, we propose a method for finding a solution to the SVP using the excited-state search with QA.
\subsection{Preparing the first excited state as the initial state}
For the excited-state search, the driver Hamiltonian is given by
\begin{eqnarray}
\hat{H}^{\rm{(SVPE)}}_{D}=\sum _{i=1}^N B_x^{(i)}
\sum^{2k}_{p=1}\hat{\sigma}_x^{(p,i)}
,
\end{eqnarray}
where $\{{B_x}^{(i)}\}_{i=1}^N$ represents the strength of the non-uniform transverse magnetic field.
We set $b_x^{(1)} < b_x^{(2)}=\cdots =b_x^{(N)}$, to resolve the degeneracy of the first excited state of the driver Hamiltonian.
On the other hand, we adopt $H_{P}^{\left(\mathrm{SVP}\right)}$ in Eq.(10) as the problem Hamiltonian. The total Hamiltonian is $H=(1-\frac{t}{T})H_D^{\left(\mathrm{SVPE}\right)}+\frac{t}{T}H_P^{\left(\mathrm{SVP}\right)}$. After we prepare the first excited state of $H_D^{\left(\mathrm{SVPE}\right)}$ as the initial state, we let the system evolve according to $H$ from $t=0$ to $t=T$.
The first excited state of the driver Hamiltonian
is described as
\begin{eqnarray}
|W\rangle _{1-2k} \bigotimes _{j=2k+1}^{2Nk}|-\rangle _j
,
\end{eqnarray}
where
$\bigotimes _{j=l}^{m}|-\rangle _j=|-\rangle _{l}|-\rangle _{l+1}\cdots |-\rangle_{m}$ denotes a separable state, and
$|W\rangle _{1-2k}$ is the entangled state given by.
\begin{eqnarray}
|W\rangle _{1-2k}=\frac{1}{\sqrt{2k}}\sum _{p=1}^{2k} \hat{\sigma}^{(p,1)}_z \bigotimes _{j=1}^{2k}|-\rangle _j.
\end{eqnarray}
Unlike the previous approach of Ref. [34], we change the Hamiltonian in an adiabarically so that we obtain the first excited state of $H_\mathrm{p}^{\left(\mathrm{SVP}\right)}$, which is the solution of the SVP. The adiabatic theorem guarantees that we can obtain the solution with a high probability by taking a sufficiently long time.
\subsection{Using spin coherent state for initial state}
The aforementioned excited state search requires quantum annealing to start from an initial state that contains an entanglement. However, preparing an entangled initial state in the actual QA device is challenging.
In actual experiments, it is desirable to use a separable initial state.
Therefore we consider using the spin-coherent (SC) state as the initial state.
The SC state is described as follows:
\begin{eqnarray}
\ket{\phi}_{1-2k}&=& \bigotimes _{j=1}^{2k}
(\sqrt{\epsilon}|+\rangle _j + \sqrt{1-\epsilon}|-\rangle _j
)
,
\end{eqnarray}
where we set
$\epsilon=\frac{1}{2k-2}$.
The inner product of $\ket{W_{1-2k}}$ and $\ket{\phi_{1-2k}}$ is calculated as
\begin{eqnarray}
{}_{1-2k}\braket{W|\phi}_{1-2k} =\sqrt{k\epsilon(1-\epsilon)^{2k-2}}\\
\fallingdotseq\sqrt{\frac{k}{2k-2}e^{-1}}\\
=\sqrt{\frac{1}{2e}}\approx 0.43\\
(k\gg1)
\end{eqnarray}
This means that the SC state contains the first excited state $\ket{W}_{1-2k}$ with a reasonably high probability.
Therefore, we propose to use the SC state as an initial state for the excited state search to solve the SVP.
We will perform numerical simulations to quantify the performance of the search with the SC state.
\section{Numerical calculation}
In this section, we show numerical results to compare the performance of our scheme with that of the previous scheme [1]. We consider the SVP with $N=2 , i.e.,$ the two-dimensional lattice. The two vectors $\boldsymbol{b_1}$ and $\boldsymbol{b_2}$ are given in the problem. We characterize these vectors
by their norms $\{b_j\}_{j=1}^2$ and the angle $\theta$ between them. By solving the time-dependent Schrödinger equation, we obtain the state after QA.
We define the failure probability as the probability that the measurement result (in computational basis)
for the state after QA gives an incorrect answer for the SVP.
This means that the success probability is defined as a population of the first excited state of the problem Hamiltonian after QA.
We calculate the failure probabilities for the ground-state and excited-state search, respectively.
For the ground-state search, we optimize $B_x$ to minimize the failure probability. On the other hand, for the excited-state search, we optimize $B_x^{(1)}$ to minimize the failure probability while fixing $B_x^{(1)}/B_x^{(2)}$ at a specific value. We set $k=2$, and thus the spin quantum number is 2 in our numerical simulation.
We fix the norm of the vectors to $b_1=b_2$, and change the values of $\theta$ such as $\frac{\pi}{18},\frac{\pi}{9},\frac{\pi}{6}$.
In Fig. 1, we plot the failure probabilities for the ground state and excited-state search against the annealing time $T$, respectively.
These results show that the failure probability for the excited-state search is smaller than that for the ground state search. In the excited state search, the failure probability with $\theta=\frac{\pi}{18}$ is larger than those with $\theta=\frac{\pi}{9},\frac{\pi}{6}$.
This may correspond to the fact that in the SVP, the problem becomes more difficult as the angle $\theta$ becomes smaller. However, the primary advantage of our method is that, even if the problem becomes more difficult, the failure probability can be sufficiently small by taking a reasonably long annealing time $T$, which is guaranteed by the adiabatic theorem.
\begin{figure}[H]
\centering
\includegraphics[width=80mm]{ronbun_kansei_ver1.png}
\caption{Plot of the failure probability of QA for the excited state search, the search with a spin coherent state, the ground state search against an annaling time $T$.
For most of the parameters, the excited state search and the search with the spin coherent state provides a smaller failure probability than the ground state search. We use $k=2$ and $N=2$ and set $b_1=b_2=1$.
We fix
$B_x^{(1)}/B_x^{(2)}=1/2$ for the excited state search and the search with a spin coherent state, while we fix $B_x^{(1)}/B_x^{(2)}=1$ for the ground state search.
Moreover, we optimize the values of $B_x^{(1)}$ to minimize the failure probability.
}\label{thetavsp}
\end{figure}
The failure probability of the search with the SC state is larger than that using the first excited state.
This is because the SC state includes states other than the first excited state.
On the other hand, the search with the SC state
provides a smaller
failure probability
the ground state search when the annealing time $T$ is large, and this shows the practicality of our scheme.
Next, we consider the case where the ratio of the norms of the two vectors is fixed at either 1:1 or 1:2. We then plot how the failure probability changes when the angle between the vectors is changed. In each case, the amplitude of the transverse magnetic field is optimized to minimize the failure probability.
Figure 2 shows that the failure probability is always lower for the excited state search using the first excited state than that for the ground state search.
The search with SC state also shows a smaller failure probability than the ground state search, except for a few exceptional points (where the ratio of vectors is 1:2 and the angle is around $\pi/2$).
The reason why the failure probability of the excited state search is larger at an angle of $\pi/2$ when the ratio of vectors is 1:2 is due to the existence of the symmetry in the Hamiltonian, which causes energy-level crossing in quantum annealing.
This point is explained in detail in the Appendix.
\begin{figure}[H]
\centering
\includegraphics[width=80mm]{ronbun_kansei_ver2.png}
\caption{
Plot of the failure probability of QA
We plot the results for the excited state search (ex), the search with
the spin coherent state (sc), the ground state search (gs), respectively, against the angle $\theta$ where we fix the value of $b_1/b_2$. This graph shows that there is a specific angle at which the probability of failure increases.
We use $k=2$ and $N=2$.
We fix
$B_x^{(1)}/B_x^{(2)}=1/2$ for the excited state search and the search with a spin coherent state, while we fix $B_x^{(1)}/B_x^{(2)}=1$ for the ground state search.
Moreover, we optimize the values of $B_x^{(1)}$ to minimize the failure probability. Also, we fix $T=100$ for the excited state search and the search with a spin coherent state
while we optimize $T$ for the ground state search.
}\label{thetavsp}
\end{figure}
In the case of the excited state search, when the vector ratio is 1:2, the failure probability becomes large around the angle of $\pi/6$.
This is due to the fact that, the energies of the the lowest four excited states of $H_p^{(SVP)}$ are close to each other, as shown in Fig. \ref{thetavsptwo}.
The small energy gap causes non-adiabatic transitions from the first excited state to the other excited states, which increases the failure probability.
Also, when the vector ratio is 1:1, the failure probability is larger around the angle of $\pi/3$.
This is due to the fact that the first excited state of $H^{(\rm{SVP})}_{\rm{p}}$ is 6-fold degenerate
when the vector ratio is 1:1 and the angle is $\pi/3$.
In this case, $(x_{1},x_{2})=(1,0),\ (0,1)\ (1,-1),\ (-1,0),\ (0,-1),\ (-1,1)$ provide the shortest vector.
Therefore, the energy gap between the first excited state and the other excited states becomes smaller at angles around $\pi/3$, resulting in more non-adiabatic transitions.
\begin{figure}[H]
\centering
\includegraphics[width=80mm]{energyspectrum.png}
\caption{We plot the instantaneous eigenenergy of the total Hamiltonian during QA or the vector ratio is 1:2 and the angle
is $\pi/6$.
This graph shows that the energy gaps among the first, second, third, and fourth excited states is very small.
Except the vector ration and the angle these, we use the same parameters as used in
the Fig. \ref{thetavsp}.
}\label{thetavsptwo}
\end{figure}
\section{Possible physical realization }
To implement the excited state search with QA, it is crucial to use a long-lived qubit, because otherwise the excited state would decay into the ground state by the energy relaxation. There was a theoretical proposal to perform QA with capacitively-shunted flux qubits\cite{matsuzaki2020quantum}, which has a long coherence time such as tens of microseconds. Therefore, we expect that our proposed protocol can be demonstrated by the capacitively-shunted flux qubits.
\section{Conclusion}
In conclusion, we propose to use the excited-state search with the QA to solve the SVP.
Importantly, the solution of the SVP is not the ground state but the first excited state of the problem Hamiltonian. So,
unlike the previous approach of solving the SVP by ground-state search using QA, the adiabatic theorem guarantees that our scheme can obtain a solution in our approach
if we take a sufficiently long time.
Our numerical simulations reveal that our scheme provides a smaller failure probability than the previous scheme. Our results show the potential of our scheme to solve the SVP by using a quantum annealer.
However, to satisfy the adiabatic condition with our methods, it may take an exponentially long annealing time with the system size if the energy gap is exponentially small, depending on the problems.
It is essential to classify which problems are difficult to solve due to such an exponentially small energy gap for QA. We leave this point for future work.
\begin{acknowledgments}
K. U. and T. I. contributed to this
work equally.
This work was supported by MEXT's Leading Initiative for Excellent Young Researchers, JST PRESTO (Grant No. JPMJPR1919), Japan. This paper is partly based on the results obtained from the project, JPNP16007, commissioned by the New Energy and Industrial Technology Development Organization (NEDO), Japan.
\end{acknowledgments}
| {
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} | 5,140 |
Haurida distrikt är ett distrikt i Aneby kommun och Jönköpings län.
Distriktet ligger i västra delen av kommunen.
Tidigare administrativ tillhörighet
Distriktet inrättades 2016 och utgörs av socknen Haurida i Aneby kommun.
Området motsvarar den omfattning Haurida församling hade vid årsskiftet 1999/2000.
Referenser
Noter
Indelningar i Aneby kommun
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} | 4,534 |
Q: Known to this context My Java RESTful web service (Spring 3.1.1 and CXF 2.5.2) prints to stdout on every request
SystemId Unknown; Line #-1; Column #-1; class X nor any of its super class is known to this context.
sometimes multiple times. Note that no exception is thrown or that no messages are logged with regards to the error. The class in question is generated by the maven-jaxb2-plugin from an XSD that contains other definitions as well. The element used to define the data type is
<xsd:element name="x">
<xsd:complexType>
<xsd:choice>
<xsd:element name="y" type="y" minOccurs="0" maxOccurs="unbounded"/>
</xsd:choice>
<xsd:attribute name="count" type="xsd:long" use="optional"/>
</xsd:complexType>
</xsd:element>
I have several XSDs that I compile that way, yet class X is the only ever associated with the error message. The generated class has the annotations
@XmlAccessorType(XmlAccessType.FIELD)
@XmlType(name = "", propOrder = {
"y"
})
@XmlRootElement(name = "x")
How do I fix this issue and get rid of the error message?
A: I found the solution to my issue.
Before I unmarshalled my XML, I ran it through an XSL transformation. I gave the processor the wrong destination context. No wonder that the class wasn't known to context!
| {
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\section{Introduction}
The quadratic assignment problem (QAP) is a combinatorial optimization
problem first introduced by Koopmans and Beckman (1957). It
is NP-hard and is considered to be one of the most difficult problems
to be be solved optimally. The problem was defined in the following
context: A set of $N$ facilities are to be located at $N$ locations. The
distance between locations $i$ and $j$ is $D(i,j)$ and the quantity of
materials which flow between locations $i$ and $j$ is $F(i,j)$. The
problem is to assign to each location a single facility so as to minimize
the cost
\begin{equation}C=\sum_{i=1}^N \sum_{j=1}^N F(i,j) D(p_i,p_j).
\end{equation}
where $u=p_i$ represents the assignment of facility $u$ to location
$i$. We will consider symmetric instances of the problem ($
D(i,j)=D(j,i), F(i,j)=F(j,i), D(i,i)=F(i,i)=0$).
There is an extensive literature which addresses the QAP and is
reviewed in Pardalos et al. (1994), Cela (1998), Anstreicher (2003),
and James et al. (2009). With the exception of specially constructed
cases, optimal algorithms have solved only relatively small instances
{$N \le 36$}. Various heuristic approaches have been developed and
applied to problems typically of size $N\approx 100$ or less.
The most successful heuristics to date for large instances are {\it
hybrid heuristics} that combine the {\it robust tabu search}, RTS,
(Taillard (1991)) with other techniques. Here we propose a {\it variable
depth search} heuristic to be used in conjunction with RTS. A variable depth search is a local
search in which the number of moves along a search path is not fixed
but rather is determined by the likelihood that the search path will
be successful in finding an improved solution. If a search path is
not promising, the search path is terminated and another path is
explored. Our {\it variable depth sequential search}, VDSS, is
inspired by the Lin-Kernighan variable depth search for the traveling
salesman problem (TSP) (Lin and Kernighan (1973) and Helsgaun(2000))
\section {Approach}
\label{approach}
It is helpful for this description to think of the
$N$ facilities and the matrix of flows between them in graph theoretic
terms as a graph of $N$ nodes and weighted edges, respectively. Let us
denote
\begin{itemize}
\item{ nodes moved as $u_m, m=0,1,2,\ldots $}
\item{ location to which node $u_m$ is moved as $k_m.$}
\item{ location from which node $u_m$ is moved as $\ell_m.$}
\end{itemize}
The variable depth sequential search algorithm VDSS consists of a sequence
of moves of nodes $u_m$ from locations $\ell_m$ to locations $k_m$,
respectively. The moves are sequential in that node $u_{m+1}$ is the
node located at location $\ell_m$. With each node as a starting node, the
moves are performed as a depth first search to a predefined depth,
$d$. In a given sequence of moves, we do not allow a node to be moved
more than once (see Appendix).
The sequence of moves terminates when either
\begin{itemize}
\item {the sequence can be closed with move $u_z$ which results in
an improved feasible solution by moving the node $u_z$ to
the initial location of node $u_0$ or }
\item {a predefined limit on the number of moves that have been
performed from a given start node is exceeded}.
\end{itemize}
Without any pruning of the search tree, the complexity of the search
would increase as $N^d$ where d is the depth of the search. Therefor, we
prune the search tree as follows: With each move, we associate an
incremental gain $g_m$, the reduction in cost if the move is made. We
also define the cumulative gain $G_m$, the total gain after $m$ moves
\begin{equation}
G_m= g_1 + g_2 + g_3 + \ldots +g_m.
\end{equation}
Before a move is performed, the incremental gain is calculated and
added to the cumulative gain. If the resulting cumulative gain will
be positive, the move is made; if not, the move is not made.
This pruning follows the pruning method introduced by Lin and
Kernighan (1973) for the traveling salesman problem (TSP) in which
edges, instead of nodes, are rewired sequentially. They noted that,
for the TSP, if there is a series of sequential edge rewirings which
result in an improved solution there is a cyclic permutation of the
order of the rewirings for which the cumulative gain is always
positive. Thus only sequences in which the cumulative gain after each move is
positive need be considered. The Lin-Kernighan insight holds for the
TSP because the incremental gains from the rewirings are independent.
For the QAP, however, the insight may not always hold because the
incremental gains for the moves are not independent. As a result, the pruning
may cause us to
\begin{itemize}
\item{miss certain improved solutions which would be found if the pruning were not done or}
\item{proceed in the search but ultimately not find a feasible improvement.}
\end{itemize}
Despite these issues, however, we find that the pruning approach
successfully reduces the complexity of the search while guiding the
search to improved solutions.
\section{Efficient Calculation of Incremental Gain}
\label{efficient}
Let $\Delta_0(u,k)$ be the incremental gain of a move of node $u$ from location $l$
to location $k$ before any moves in a sequence have been performed
\begin{equation}
\Delta_0(u,k)=2 \sum_{v=1,\ne u}^{N}[D(l_v,\ell)-D(\ell_v,k)]F(u,v)
\label{Delta0}
\end{equation}
where $\ell_v$ is the location of node $v$. We can make the heuristic more
efficient by not having to calculate incremental gains using
(\ref{Delta0}) each time they are needed. This was done by Taillard
(1991) for the case of simple swaps. We now describe how this is done
for sequential moves.
Because the incremental gains are not independent, $\Delta_0(u,k)$
will not necessarily be the incremental gain of moving $u$ to location
$k$ if other moves have been performed previously in the sequence. If
other moves have been made, we can calculate, in constant time, the incremental gain of
the $n^{th}$ move in a sequence using
\begin{equation}
g_n(u_n,k_n)= \Delta_0(u_n,k_n) + 2\sum_{m=1}^{n-1} (\delta_m^{\rm curr}-\delta_m^{\rm orig})
\label{Deltan}
\end{equation}
where
\begin{eqnarray}
\delta_m^{\rm curr}=[D(k_m,\ell_n)-D(k_m,k_n)]F(u_n,u_m) \\
\delta_m^{\rm orig}=[D(\ell_m,\ell_n)-D(\ell_m,k_n)]F(u_n,u_m).
\end{eqnarray}
Here $\delta_m^{\rm curr}$ and $\delta_m^{\rm orig}$ are the contributions to
the incremental gain for the edge $(u_m,u_n)$ given the current and
original locations, respectively, of the node $u_m$. Equation
(\ref{Deltan}) takes into account the fact that because of the previous $n-1$
moves the ends of the edges are no longer at the same locations as
they were before the sequence was started. Using (\ref{Deltan})
instead of (\ref{Delta0}) reduces the VDSS time by a factor of $N$.
After a sequence of $n$ moves which results in a feasible improvement,
$\Delta_0$ is updated as follows: Assume the location of node $v$ is
$i$. Then
\begin{eqnarray*}
\Delta_0^{new}(v,j)=\Delta_0(v,j)
+ 2 \sum_{m=1}^n[(D(k_m,i)-D(k_m,j))\\
-(D(\ell_m,i)-D(\ell_m,j))]F(u_m,v),
\end{eqnarray*}
if $v$ is not one of the nodes moved in the sequence. If $v$ is one
of the nodes moved, then $\Delta_0(v,j)$ must be calculated from
(\ref{Delta0}). As with swaps (Taillard (1991)), the overall
evaluation of $\Delta_0$ takes $O(N^2)$ operations. Because there are
relatively few sequences which result in feasible improvements, the
time spent in this calculation is a very small fraction of the total
processing time.
\section{Application of VDSS}
Sections \ref{approach} and \ref{efficient} describe the basic VDSS algorithm. In
practice, in order to minimize the number of operations to find an
improvement, we execute VDSS with increasing maximum
depths ($d_1, d_2$, \ldots). When an improvement is found at one depth, we start the VDSS
algorithm with the new optimal configuration at the smallest
proscribed depth. If an improvement is not found at a given depth,
the algorithm is then executed at the next specified depth. When a
pass is made through all depths with no improvement found, the run terminates.
The code which implements VDSS is available in the Online
Supplement.
\section{Parameter Settings}
For RTS we use Taillard's code (available at
http://mistic.heig-vd.ch/taillard/codes.dir/tabou\_qap.cpp) with the
settings as described in Taillard (1991): number of iterations=$N^2$,
tabu list size between $0.9 N$ and $1.1 N$ and aspiration function
parameter=$2N^2$. We run VDSS at two maximum depths: $d_1=2$ and $d_2=5$.
For any given start node, we limit the number of total moves attempts
to $10^5$. These are the only tunable parameters.
\section{Computational Results}
We study the QAP instances Tai60a, Tai80a, and Tai100a from QAPLIB
(see Burkard et al. (1997)). These instances are the most commonly
used recently for computational testing (James et al. (2009). The
instances are symmetric and the entries of the distance and flow
matrices are randomly and uniformly generated integers between 0 and
99 (Taillard (1991)). Additionally, to test our heuristic on larger
instances we create similar random instances of size $N=200$ and
$N=400$. Files containing these instances and the best known solutions
are included in the Online Supplement.
To compare the efficiency of heuristics, we use a time-to-target plot
(Aiex (2002), Aiex et al. (2002), and Oliveira et al. (2002)). For
any given target solution value and the time to obtain that value, the
time-to-target plot plots the probability that the target cost will be
obtained. As described in Oliveira (2002), a solution target value is
first set. The running time of the algorithm to achieve that cost or
lower is recorded. This is done multiple times and the recorded times
are then sorted. With the $i^{th}$ shortest time we associate a
probability $P_i=(i-1/2)/m$, where $m$ is the number of times recorded.
Figure \ref{ttt} compares time-to-target plots for RTS runs and hybrid
heuristic runs composed of RTS followed by VDSS. A single
hybrid heuristic run consists of first running RTS with a random
starting configuration and then running VDSS with the RTS solution as
input. The instance tested is Tai100a and the target value is 21200000.
We will see below that VDSS used alone is inferior to RTS. However, as
Figure \ref{ttt}illustrates the hybrid solution
of RTS + VDSS provides better performance than RTS alone.
Let the time needed to achieve the target value with $50\%$
probability for a heuristic be $t_{50}$. Then we define the
{\it performance improvement factor} of the hybrid heuristic (RTS + VDSS)
to RTS alone as:
\begin{equation}
I=\frac{t_{50}(RTS)}{t_{50}(RTS+VDSS)}.
\end{equation}
The performance improvement factor for Figure 1 is 2.61.
In Figure. \ref{speedup} we plot the performance improvement factor for the
instances studied versus various target values. Note that for each of
the plots, there is a target value above which the plots are essentially
flat; the performance improvement is constant and less than $1$ here because
RTS alone can reach these targets. Below these {\it improvement thresholds} the performance improvement increases with decreasing target
values. In order to show the plots in a single figure, we plot performance improvement versus
normalized target values
\begin{equation}
\tilde \tau=\frac{\tau-b(N)}{b(N)}
\label{normalizedTarget}
\end{equation}
where $\tau$ is the non-normalized target value and $b(N)$ is a value
which results in the improvement thresholds of the plots being coincident.
Having the improvement thresholds coincident makes comparison of the plots
easier. We note that
\begin{itemize}
\item{for a given instance, the performance improvement factor
increases as the target value is decreased because, as the
target is decreased, RTS alone is less and less likely to reach the
target. Running VDSS following RTS, while adding time to a run,
makes reaching the target more likely.}
\item{as the instance size increases, the performance improvement
increases. Figure \ref{complexity} plots the time per run as a
function of $N$ for RTS, and for VDSS when run following RTS. Note that for RTS the time
scales as $N^x$ where $x\approx 4.1$. This is consistent with the
theoretical estimate that the complexity of RTS is $O(N^4)$ given
that RTS requires $O(N^2)$ operations per iteration and $N^2$
iterations per run. For VDSS the time scales as $N^y$ where
$y\approx 3.5$. This lower order complexity is one reason the
performance improvement of the hybrid algorithm improves as $N$
increases. }
\end{itemize}
In Table \ref{table1} we list the instances tested and the results.
The lowest target value for which we determine the performance
improvement is determined by our ability to perform enough runs which
reach that target value to have meaningful statistics. Below the
target values shown in Table \ref{table1}, the time to perform the
needed number of runs would have been unreasonably long. Performance
improvement results shown in Table \ref{table1} are for these lowest target
values.
In Figure \ref{tttlk} we compare the performance of RTS alone and VDSS
alone. As opposed to the hybrid heuristic RTS+VDSS, VDSS alone has
performance significantly inferior to RTS.
\section{Discussion/Conclusions}
We use the Lin-Kernighan pruning approach to implement an effective
variable depth sequential search which, when used in conjunction with
RTS, provides considerable performance improvement over
RTS alone. RTS efficiently finds a local minima and VDSS explores the
neighborhood around this local minima to improve the solution. Because RTS
is a basic building block in a number of hybrid
heuristics, the combined RTS+VDSS approach described here may provide further performance improvements for those heuristics which use RTS alone.
To the best of our knowledge this is the first use of the Lin-Kernighan
pruning technique for a problem in which the incremental gains for the
sequential moves are not independent. Our results raise the question
of whether variable depth sequential search with Lin-Kernighan pruning can be applied to other
problems in which incremental gains are also not independent and for
that reason the Lin-Kernighan approach may have not been applied to
them. The code which implements VDSS is available in the Online
Supplement and can be used as a model for application to such other problems.
In addition, we introduce two new QAP instances, Pau200a and Pau400a,
available in the Online Supplement. As processing speed increases, we expect
that there will be a need for instances of this size for QAP heuristics.
\section*{Appendix - Moving a node more than once in a sequence}
If a node is not allowed to be moved more than once in a sequence,
there are certain assignments of nodes to locations which cannot be
obtained by a single series of sequential moves starting with a given assignment. For
example, the permutation 2,3,1,5,6,4 cannot be transformed into
1,2,3,4,5,6. The transformation can be obtained with two separate
series of sequential moves each without moving a node more than once, but
if neither of these series of moves results in a positive gain, the
pruning algorithm will not allow these moves to be made. If moving a
node more than once is allowed, any assignment can be obtained. In
practice we have found that there is minimal benefit, if any, to
allowing nodes to be moved more than once and have not allowed it in
our runs.
\section*{Acknowledgment}
We thank the Defense Threat Reduction Agency (DTRA) for support.
\section*{References}
\begin{hangref}
\item Aiex, R.M. 2002. Uma investigacao
experimental da distribuicao de probabilidade de tempo de
solucao em heuristicas GRASP e sua aplicacao
na analise de implementacoes paralelas. PhD thesis,
Department of Computer Science, Catholic University of Rio de
Janeiro, Rio de Janeiro, Brazil.
\item Aiex, R.M., M.G.C. Resende, C.C. Ribeiro. 2002.
Probability distribution of solution time in GRASP: An experimental
investigation. {\it J. Heuristics} {\bf 8} 343-373.
\item Anstreicher, K. 2003. Recent advances in the solution
of quadratic assignment problems. {\it Math. Program.} {\bf 97}, 27-42.
\item Burkard R.E., E. Cela, S. E. Karish, F. Rendl. 1997.
QAPLIB - A Quadratic Assignment Problem Library. {\it J.Global
Optim.} {\bf 10} 391-403; http://www.seas.upenn.edu/qaplib/
\item Cela E. 1998. {\it The Quadratic Assignment Problem: Theory and
Algorithms}. Kluwer, Boston, MA.
\item Helsgaun K. 2000. An Effective Implementation of the
Lin-Kernighan Traveling Salesman Heuristic. {\it Eur. J.
Oper. Res.} {\bf 126} 106-130.
\item James T., C. Rego, F. Glover. 2009. Multistart Tabu Search
and Diversification Strategies for the Quadratic Assignment
Problem. {\it IEEE Tran. on Systems, Man, and Cybernetics
PART A: SYSTEMS AND HUMANS} {\bf 39} 579-596.
\item Koopmans T., M. Beckmann. 1957. Assignment problems
and the location of economic activities. {\it Econometrica} {\bf 25}
53-76.
\item Lin S., B.W. Kernighan. 1973. An effective heuristic algorithm
for the traveling-salesman problem. {\it Operations Research} {\bf 21}
498-516; http://www.cs.bell-labs.com/who/bwk/tsp/index.html.
\item Misevicius, A. 2005. A tabu search algorithm for the
quadratic assignment problem. {\it Comput. Optim. and
Appl.} {\bf 30} 95-111.
\item Misevicius, A. 2008 An implementation of the iterated tabu
search algorithm for the quadratic assignment problem. Working
Paper, Kaunas University of Technology, Kaunas, Lithuania.
\item Oliveira, C.A.S., P.M. Pardalos, G. Mauricio, C. Resende. 2004. GRASP
with Path-Relinking for the Quadratic Assignment Problem.
Ribeiro, C.C. and Martins, S.L. eds., {\it Efficient and Experimental
Algorithms, LNCS} {\bf 3059}, 356-368, Springer-Verlag, Berlin.
\item Pardalos, P.M., F. Rendl, H. Wolkowicz. 1994. The quadratic
assignment problem: A survey and recent developments. Pardalos,
P.M., Wolkowicz, H., eds. {\it Quadratic Assignment and Related
Problems. DIMACS Series on Discrete Mathematics and Theoretical
Computer Science} {\bf 16}, Amer. Math. Soc., Baltimore, MD. 1-42.
\item Taillard, E. 1991. Robust taboo search for the quadratic
assignment problem. {\it Parallel Comput.} {\bf 17} 443-455..
\end{hangref}
\newpage
\begin{table}
\caption{Numerical Results. {\it Improvement threshold} is the approximate target value below which the hybrid solution provides a performance improvement $>1$. {\it Target value} is the target value for which performance improvement is measured. $^a$ Misevicius (2005); $^b$ Misevicius (2008); $^c$ current work. }
\begin{tabular}{| l | r | r | r | r |}
\hline
Problem & Best known & Improvement & Target &Performance \\
& solution & threshold & value &improvement \\
\hline
Tai60a & 7205962$^a$ & 7320000 & 7256000 & 1.30 \\
Tai80a & 13511780$^b$ & 13720000 & 13620000 & 2.52 \\
Tai100a & 21052466$^b$ & 21360000 & 21200000 & 3.07 \\
Pau200a & 89282330$^c$ & 89740000 & 89460000 & 10.94 \\
Pau400a & 366463098$^c$ & 367600000 & 367060000 & 15.15\\
\hline
\end{tabular}
\label{table1}
\end{table}
\newpage
\begin{figure}[tbh]
\centerline{
\epsfxsize=10.0cm
\epsfclipon
\epsfbox{ttt.eps}
}
\caption{Probability of obtaining target solution value of 21220000
versus time for the Tai100a instance. Lower (black) plot is for
RTS only runs; upper (gray) plot is for hybrid heuristic of
RTS and VDSS. The intersection of each plot with the dashed line at
probability $0.5$ is the time $t_{50}$ used for the performance improvement factor calculation}.
\label{ttt}
\end{figure}
\begin{figure}[tbh]
\centerline{
\epsfxsize=10.0cm
\epsfclipon
\epsfbox{speedup.eps}
}
\caption{Performance improvement versus normalized target values (see
(\ref{normalizedTarget}) ) for $N=60$ (squares), $80$ (up-triangles),
$100$ (disks), $200$ (right-triangles) and $400$ (diamonds). Below the normalized target
value of 0.01, the larger the value of $N$ the larger the slopes of
the plots.}
\label{speedup}
\end{figure}
\begin{figure}[tbh]
\centerline{
\epsfxsize=10.0cm
\epsfclipon
\epsfbox{complexity.eps}
}
\caption{Time per run versus $N$ for RTS (black upper plot)
and VDSS (gray lower plot). The slopes on these log-log
plots are the power of $N$ of the computational complexity.}
\label{complexity}
\end{figure}
\begin{figure}[tbh]
\centerline{
\epsfxsize=10.0cm
\epsfclipon
\epsfbox{tttlk.eps}
}
\caption{Probability of obtaining target solution value of 21400000
versus time for the Tai100a instance. Black plot is for RTS-only runs; gray plot is for VDSS-only runs. The RTS plot appears essentially straight but would have a similar shape to the VDSS plot if magnified.
The intersection of each plot with the dashed line at
probability $0.5$ is the time $t_{50}$ used for the performance improvement factor calculation}.
\label{tttlk}
\end{figure}
\end{document}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 5,221 |
{"url":"https:\/\/stackoverflow.com\/questions\/981020\/how-to-force-line-wrapping-in-listings-package\/8264050","text":"# How to force line wrapping in listings package?\n\nI have a problem concerning the listings package in latex. I need to embed a source code of the following XML document http:\/\/www.sparxsystems.com.au\/downloads\/profiles\/EP_Extensions.xml in my master thesis' appendix. The problem is, no matter what options I pass to the package, I don't seem to be able to fit it on the page. The lines in the listing are too long, and the listings package doesn't wrap them, which seems odd... What combination of options will do the trick?\n\nAt the moment I use the following lstset instruction:\n\n``````\\lstset{\nbreakindent=0em,\nlanguage=XML,\nbasicstyle=\\footnotesize,\nnumbers=left,\nnumberstyle=\\footnotesize,\nstepnumber=2,\nnumbersep=5pt,\nbackgroundcolor=\\color{white},\nshowspaces=false,\nshowstringspaces=false,\nshowtabs=false,\nframe=single,\ntabsize=2,\ncaptionpos=b,\nbreaklines=true,\nbreakatwhitespace=true,\nbreakautoindent=true,\nescapeinside={\\%*}{*)},\nlinewidth=\\textwidth\n}\n``````\n\nWhich, with no other options set, and combined with the following command:\n\n``````\\lstinputlisting{EP_Extensions.xml}\n``````\n\nLists the given file's source to the following output:\n\n`breaklines` worked for me, though you do need to set it to true - the default is false:\n\n``````\\lstinputlisting[style=Python,\ncaption=My Class,\nlabel={mine.py},\nbreaklines=true,\n]{..\/python\/mine.py}\n``````\n\nis pretty much what I used\n\nI had the following inclusion: `\\usepackage[none]{hyphenat}` which causes the issue described above. I was using it to fix the problem of latex automatically breaking lines in the middle of a word, which looks really stupid in some circumstances.\n\nAfter much searching for an alternative to this solution I found nothing suitable and settled for properly broken lines but badly placed hyphenation.\n\n\u2022 Thank you! I had the exact same problem, and couldn't figure out why listings wouldn't break my lines even with breaklines=true. You just saved me a lot of head scratching. \u2013\u00a0Zero3 Jan 28 '15 at 16:51\n\u2022 Nice find! I was able to use the `htt` option with monospaced listings - answer. \u2013\u00a0cxw May 15 '18 at 19:21\n\nNot a great answer, but one idea is to word wrap the source code before including it. If you're on linux, the command fold can be used for this. Clearly this works best if the text is in a fixed width font, which i would recommend in any case for code listings.\n\nA followup to Aaron's answer. I was using `basicstyle=\\ttfamily` for my listings. I was therefore able to permit line breaking by changing\n\n``````\\usepackage[none]{hyphenat}\n``````\n\nto\n\n``````\\usepackage[htt]{hyphenat}\n% ^^^\n``````\n\nThe `hyphenat` docs describe that the `htt` option \"enables hyphenation of ... text typeset via either `\\texttt` or `\\ttfamily`.\" In my use case, I didn't see any hyphenation in my listings, but I did get the breaking.","date":"2019-04-19 11:56:42","metadata":"{\"extraction_info\": {\"found_math\": false, \"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\": 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\": 0.8191173076629639, \"perplexity\": 1097.2970951697557}, \"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-2019-18\/segments\/1555578527566.44\/warc\/CC-MAIN-20190419101239-20190419122142-00036.warc.gz\"}"} | null | null |
The Mayor's Food Truck Fiesta is back in Lykes Gaslight Park!
Featuring tasty treats from a variety of local vendors, the Mayor's Food Truck Fiesta occurs the first Wednesday of every month in The Square at Lykes Gaslight Park from 11am to 2pm. Click the link below to see this month's participating food trucks.
To check it out, click here!
Urban Excellence Award Winners Announced!
The Tampa Downtown Partnership announced the 2022 Urban Excellence Award winners last Wednesday at the David A. Straz Center for the Performing Arts. Among the businesses, initiatives, projects, and individuals celebrated this year were Joe Waggoner, CEO of the Tampa Hillsborough Expressway Authority, named the Christine Burdick Downtown Person of the Year, and Kim Puleo winning the People's Choice Award.
To read the full list of winners, click here.
The Gasparilla Festival of the Arts returns to Julian B. Lane Riverfront Park this weekend
For half a century, artists and art lovers from all parts of the country migrated annually to the Raymond James Gasparilla Festival of the Arts, where the country's most accomplished artists and rising stars vie for over $100,000 in prize money.
On March 5-6, 2022, the Festival will showcase artists and their work including ceramic, digital, drawing, fiber, glass, jewelry, mixed media, painting, photography, printmaking, sculpture, watercolor, and wood. This event will also feature the works of local young artists and a weekend full of live entertainment.
St. Paul A.M.E Church served as a hub in Tampa for civil rights activists to meet and organize
The St. Paul African Methodist Episcopal Church in Tampa is an African American landmark. Historic figures like Rev. Dr. Martin Luther King, Thurgood Marshall, Rosa Parks, and more have spoken from the pulpit.
"The St. Paul African Methodist Episcopal Church, or A.M.E Church, was founded in 1870 in Downtown Tampa," Fred Hearns, historian at Tampa Bay History Center, said. "That church drew many of the leading African American citizens for many, many years."
Naked Farmer opens at Water Street Tampa
Naked Farmer opened its third restaurant location at 1001 Water Street this past weekend. The fast-casual restaurant focuses on nutritious foods sourced as locally possible. The new Water Street location was chosen because it was designed to set a higher standard for sustainability and green-living in an urban environment and "aims to change the way we live."
As Tampa's shiny Downtown rises, an old flour mill, and history, disappear
Tampa Bay Times reporter Sue Carlton takes a look at the history of the Ardent Mills flour mill and Tampa's Downtown unique port history. Soon the mill will be torn down to reopen elsewhere, marking an end to Downtown's smokestack era.
Connect with us on social media to get the latest on downtown events!
Monday Morning Memo –Monday Morning Memo is a weekly update of "insider downtown information" regarding developments, transportation, special opportunities and other useful information to help you make the most of downtown. Subscribe to receive this weekly newsletter. | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 2,592 |
Award winning Afrobeats singer Fuse ODG premieres his most anticipated single "Boa Me", which features Grammy Award winning English singer Ed Sheeran & Mugeez of R2Bees. This highlife tune has Ed Sheeran singing in Ghana's Twi language and produced by KillBeatz. Check on it.
Fuse ODG and his New Africa movement took over the whole of London to bring this new amazing high energy banger. "No Daylight" was recorded in Ghana and produced by Killbeatz. Watch below.
Here is visuals to Fuse ODG's new single, "Window Seat". 'Window Seat' is produced by Jnr. Blender and Canadian Duo Banx & Ranx.
UK based Ghanaian artiste, Fuse ODG releases a brand new song titled 'Window Seat'. The new banger was produced by Electro Caribbean Music duo & production team – Banx & Ranx consisting of KNY Factory and Soké. Hit Play! | {
"redpajama_set_name": "RedPajamaC4"
} | 8,060 |
Fiber on one side and copper on the other?
Please find attachment for Apexplus console cable Pin-outs or check page no:165 on ApexPlus user manual Rev 1.0.
Connect Serial/Console cable to Trango Apex at one end and reboot the radio with below Serial/Console port settings on your laptop/computer at other end.
You will be prompted with trango login: prompt. | {
"redpajama_set_name": "RedPajamaC4"
} | 9,610 |
In organic chemistry, the Malaprade reaction or Malaprade oxidation is a glycol cleavage reaction in which a vicinal diol is oxidized by periodic acid or a periodate salt to give the corresponding carbonyl functional groups. The reaction was first reported by in 1928 and also works with β-aminoalcohols.
References
See also
Criegee oxidation
Organic oxidation reactions
Name reactions | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 7,786 |
Has your organisation moved to Office 365 but you are unsure how to get started with SharePoint Online? Our portal is a starting point to get your business quickly utilising some of the core capabilities of SharePoint.
4# Optional onsite training for staff covering how other businesses utilise SharePoint Online in different ways within the market. | {
"redpajama_set_name": "RedPajamaC4"
} | 6,073 |
Q: VBA Code To Display Email Instead Of Automatically Send I currently have a VBA code which selects a custom range and then emails said selected range to a list of E-mails I have in another worksheet. I've attached code, but this code is copied and pasted 8 times (there are 8 blocks)...Idk if that matters but just thought I should give as much information as possible. These are my two problems:
1) How to Display the email window on Outlook instead of automatically send (I've already tried .Item.Display and it does not work, so any alternatives or any other methods please recommend)
2) How to have the selected range keep its format (some of the text is red but once sent in an e-mail is displayed as default text).
Thanks in advance.
For Each aCell In Worksheets("Email List").Range("B3:B" & Cells(Rows.Count, "B").End(xlUp).Row)
If aCell <> "" Then
eTo = eTo & aCell & ";"
End If
Next
eTo = Left(eTo, Len(eTo) - 1)
If IsEmpty(Range("B4")) Then
Else
ActiveSheet.Range("a3", ActiveSheet.Range("e3").End(xlDown)).Select
ActiveWorkbook.EnvelopeVisible = True
With ActiveSheet.MailEnvelope
.Item.To = eTo
.Item.Subject = "Allocations - Barclays" & Format(Date, " mm/dd/yyyy")
.Item.Send
End With
End If
A: I use this and it works - this displays the mail, but can be changed:
With OutMail
.To = mailName ' This is the name of the person to review the documents.
.CC = ""
.BCC = ""
.Subject = "Please review the attached."
.HTMLBody = RangetoHTML(rng)
.Display 'or use .Send
End With
Take a look at http://www.rondebruin.nl/win/s1/outlook/bmail2.htm
This has excellent information on mailing a range with outlook from excel.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 4,535 |
Q: Inviting new friends over Is there a link I can use to gather my friends from Facebook or Google Plus, so I can invite them to join Stack Overflow?
A: Yes:
https://stackoverflow.com/users/signup
But note that there's no privileges gained from inviting, no address book sharing, nor any "social" feature involved.
The focus of the Stack Exchange network is on the content, not users.
It's almost better to use the link https://stackoverflow.com/about, so they arrive straight into the introductory page. As it explains what makes this sites so different from forums and social networks.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 4,704 |
Music|New Year's Eve: A Procrastinator's Guide to Music and Comedy Shows
https://nyti.ms/351gWM2
New Year's Eve: A Procrastinator's Guide to Music and Comedy Shows
You can still grab tickets for the Strokes at Barclays Center, jazz in the Village or comedy in Brooklyn. Here's where to groove, laugh and ring in 2020.
Julian Casablancas and the Strokes will transport fans back to the early 2000s at Barclays Center.Credit...Sipa, via Associated Press
By Jon Pareles, Jon Caramanica, Giovanni Russonello, Elysa Gardner and Sean L. McCarthy
ANNALEIGH ASHFORD AND SETH SIKES Known for paying ebullient homage to timeless luminaries including Judy, Liza and Bernadette, Sikes will hail the new decade with nearly century-old tunes in "Twenty '20s Songs for 2020," set for 7 p.m. and featuring a seven-piece band. At 11 p.m., stargazers can catch latter-day dynamo Ashford, who has twinkled brightly in Broadway roles ranging from Lauren in "Kinky Boots" to Dot in "Sunday in the Park with George" to Sylvia, a dog (with Matthew Broderick playing her human), in "Sylvia." Ashford, who will be joined by Will Van Dyke and the Whiskey 5, promises "a little glam rock, glitter, gay magic and some singalongs." All tickets to her show include a two-course meal, open bar and dessert buffet, with an after-show dance party. Ringside and premium seats entitle each party of two to a half-bottle of champagne and individual dessert platters during the dance party. At Feinstein's/54 Below, Manhattan; 646-476-3551, 54below.com. (Elysa Gardner)
SANDRA BERNHARD AND JUSTIN VIVIAN BOND The clever-as-ever Bond will greet revelers traumatized by recent headlines in "Out With the Old," a program predicated on the notion that "Glamour is resistance!" Accompanying "Auntie Glam," at 7 p.m. are Matt Ray on piano, Nath Ann Carrera on guitar and Claudia Chopek on violin. Fellow iconoclast and nightlife mainstay Bernhard will mark her 10th anniversary offering defiant merriment with "Sandy's Holiday Extravaganza — A Decade of Madness and Mayhem" featuring the Sandyland Squad Band at 9 and 11 p.m. At Joe's Pub, Manhattan; 212-967-7555, joespub.com. (Gardner)
BIRDLAND BIG BAND WITH VERONICA SWIFT The rising young vocalist Veronica Swift was 21 when she came within a hair's breadth of winning the 2015 Thelonious Monk International Jazz Competition. Since then, her startling command and improbably mature delivery have made her a cause célèbre among fans of traditional jazz, and landed her on stages with some of the music's finest improvisers. She's become a frequent presence at Birdland, and for New Year's Eve she will play with the club's resident big band, which is led by the saxophonist David DeJesus. At 8 and 11 p.m., Birdland, Manhattan; 212-581-3080, birdlandjazz.com. (Giovanni Russonello)
CHRIS BOTTI Can you really blame the Blue Note for bringing back Botti — the seraphic, reverb-drenched, synthesized-strings-surfing trumpeter — year after year for a holiday residency? This is his ideal domain. At 7 and 10 p.m., Blue Note, Manhattan; 212-475-8592, bluenote.net. (Russonello)
REGINA CARTER QUINTET An historian of the violin as well as a classically trained virtuoso, Carter is as likely to wail on a jazz standard as she is to dive into early American fiddle repertoire or offer a tribute to the Italian classical violinist Niccolò Paganini. On New Year's Eve she'll perform with a quintet that features Carla Cook on vocals, Nat Adderly Jr. on piano, Chris Lightcap on bass and Alvester Garnett on drums. At 7:30 and 10:30 p.m., Jazz Standard, Manhattan; 212-576-2232, jazzstandard.com. (Russonello)
CITYFOX ODYSSEY For 27 hours, beginning at 9 p.m. on New Year's Eve, you can lose yourself inside the annual Cityfox Odyssey house music extravaganza. The anchor set is by a reunited Sasha & Digweed, who in the 1990s and 2000s were at the forefront of the rise of progressive house. The event also features Hot Since 82, Ida Engberg, Stephan Bodzin, a collaborative set between Âme and Dixon, and many more. At Avant Gardener, Brooklyn; 347-987-3146, avant-gardner.com. (Jon Caramanica)
CLUB CUMMING 2020 NEW YEAR'S EVE BALL The East Village nightspot whose owners include Alan Cumming serves up an "old-school/new school/queer variation" of a year-end gala, with host Shayna Blass and her band joined by the sleek Australian export and cabaret fixture Kim David Smith, the Bowie channeler Michael Tee and "RuPaul's Drag Race" alum Alexis Michelle. Festivities begin at 9 p.m., with DJ Bright Light Bright Light on duty after the ball drops, joined by the Brolesque Boys dance troupe, go-going till 4 a.m. At Club Cumming, Manhattan; 800-838-3006, clubcummingnyc.com. (Gardner)
DISCO BISCUITS If Phish isn't your preferred jam-band scent, perhaps try the Disco Biscuits, whose approach to the form is much more synthetic. Their New Year's Eve performance will be the final show of a four-night stand. At 9 p.m., PlayStation Theater, Manhattan; 212-930-1950, playstationtheater.com. (Caramanica)
NATALIE DOUGLAS With her annual "A Very Natalie New Year," Douglas will once again bring her warm, playful presence and sultry, exuberant singing to old and new songs. She'll be joined this year by Brian Nash, the musical director for Douglas's celebrated tributes to Joni Mitchell, Barbra Streisand, Cher, Shirley Bassey and pop's two great Stevies: Wonder and Nicks. Performances are set for 7:30 and 10:45 p.m. At the Duplex, Manhattan; 212-255-5438, theduplex.com. (Gardner)
GOV'T MULE Warren Haynes, the guitarist, singer and songwriter who leads Gov't Mule, has been a member of both the Dead and the Allman Brothers Band. In Gov't Mule he upholds the Southern rock tradition, slinging muscular guitar riffs and singing about the lessons of a long, hard road; a song by Jimi Hendrix or the Police might easily slip into the set. On Dec. 30 at 7:30 p.m. and Dec. 31 at 9 p.m. at the Beacon Theater, Manhattan; 212-465-6500, msg.com/beacon-theatre. (Jon Pareles)
MACY GRAY She is part soul-music traditionalist, part iconoclast; part pop singer, part rasp. Nothing Gray has done in the past two decades has matched the universal appeal of her debut album, "On How Life Is" (which included the chart-topping smash "I Try"), but she has stayed rather faithful to the sound she sketched out there: a mix of take-no-crap attitude and dreaminess, full of contagious choruses, jazz flourishes and hints of Caribbean rhythm. If you're good with that, her most album, "Ruby," delivers the goods. She will play selections from that record and hits from her back catalog at 7 and 10:15 p.m. At the Iridium, Manhattan; 212-582-2121, theiridium.com. (Russonello)
CARLOS HENRIQUEZ A bassist, Henriquez is one of the youngest and most indispensable members of the Jazz at Lincoln Center Orchestra. He plays with discipline and focus, mixing the rhythmic sophistication of Afro-Caribbean dance music with the swinging power of jazz's big-band tradition. At Dizzy's, Jazz at Lincoln Center's intimate club, he will present an all-star, nine-piece band featuring the trumpeters Michael Rodriguez and Terell Stafford, the tenor saxophonist Melissa Aldana, the trombonist Marshall Gilkes, the flutist and vocalist Jeremy Bosch, the pianist Robert Rodriguez, the drummer Obed Calvaire and the conguero and vocalist Anthony Almonte. At 7:30 and 11 p.m., Dizzy's Club, Manhattan; 212-258-9595, jazz.org/dizzys. (Russonello)
'HOT & FUN NEW YEAR'S EVE' Jenny Gorelick and Zach Teague host this showcase featuring some of the buzziest up-and-coming comedians of 2019 — Mary Beth Barone, Jared Goldstein and Rachel Pegram all made shortlists for industry showcases from Comedy Central, Just for Laughs and the New York Comedy Festival. Also look for a performance from the drag queen Junior Mint. At 7:30 p.m., Union Hall, Brooklyn; 718-638-4400, unionhallny.com. (Sean L. McCarthy)
ETHAN IVERSON TRIO For almost two decades Iverson was the pianist in the Bad Plus, one of jazz's most popular acts — and one of its most heterodox — which played every New Year's Eve at the Village Vanguard. That tradition disappeared when Iverson left the band at the start of 2018, but perhaps he will begin an annual custom of his own around the corner at Zinc Bar. This show is dedicated to the romantic songbook of Burt Bacharach; Marcy Harriell will handle vocals, with Corcoran Holt on bass and Vinnie Sperrazza on drums. At 9 and 11 p.m., Zinc Bar, Manhattan; 212-477-9462, zincjazz.com. (Russonello)
THE JESUS LIZARD AND PROTOMARTYR Two generations of grinding, asymmetrical, abrasively virtuosic post-punk are on this double bill. The Jesus Lizard, formed in 1987 and intermittently reunited since a breakup in 1999, is fronted by David Yow, who snarls, mutters and screams lyrics full of humanity's darker impulses; sooner or later, he usually launches himself into the audience. Protomartyr, formed in 2010, puts Joe Casey's more openly literary, spoke-sung lyrics upfront as the band's riffs blast, writhe, toll or entwine. At 10 p.m., Brooklyn Steel, Brooklyn; 888-929-7849, bowerypresents.com/venues/brooklyn-steel. (Pareles)
DAVID JOHANSEN After years of trotting out his swinging alter ego, Buster Poindexter, Johansen will mark this New Year's Eve by honoring the era that launched his seminal band New York Dolls and other glam and proto-punk players. Hosts for the early '70s-inspired "New York, New NYE 2020" include the photographers Mick Rock and Kristin Gallegos (who won't be snapping pics) and the rock clothing boutique owner Jimmy Webb, with local D.J.s on hand following Johansen's performance. A premium bar is available to all from 9 p.m. to 1 a.m., with hors d'oeuvres, cocktails and bottles of vodka or champagne on offer to seated guests. At the Roxy Hotel, Manhattan; 212-519-6464, roxyhotelnyc.com. (Gardner)
KASKADE This 48-year-old D.J. and producer is a veteran of progressive house music, a style that over the last two decades has come in and out of favor, and then back in again, but hasn't changed much. At 9 p.m., Terminal 5, Manhattan; 212-582-6600, terminal5nyc.com. (Caramanica)
MARILYN MAYE Decades come and go, but Maye's effervescence has proved as enduring as her devout following. The 91-year-old phenom will deliver her "New Year's Eve Extravaganza!" at 7 and 11 p.m. At Birdland Theater, Manhattan; 212-581-3080, birdlandjazz.com. (Gardner)
MURPHY'S LAW The rowdy, riotous and sometimes uproarious side of New York hardcore is best embodied by Murphy's Law, scene survivors since the early 1980s. With Enziguri, the Avoiders, Bowhead and End of Hope. At 7 p.m., Gold Sounds Bar, Brooklyn; 718-618-0686, goldsoundsbar.com. (Caramanica)
SIDNEY MYER As the longtime booking manager of Don't Tell Mama, Myer championed more than a few cabaret darlings; lately his own star has been rising, buoyed by his piquant delivery of tunes and tales drawn from vast experience. Myer will be accompanied by the music director Tracy Stark on piano and Matt Scharfglass on bass, with shows beginning at 8 and 10:30 p.m.; each seating includes a three-course dinner and a half-bottle of prosecco per person. At Pangea, Manhattan; 212-995-0900, pangeanyc.com. (Gardner)
'NEW YEAR'S EVE!' The Stand comedy club relocated in 2019 to a larger spot in Union Square, and celebrates the year's end with shows upstairs and downstairs. Among the performers on the late shows: the SiriusXM stalwart host Ron Bennington, the married couple Rich Vos and Bonnie McFarlane, and Shane Gillis, who you may recall as a new cast member of "Saturday Night Live" for all of one weekend in September. At 6:30, 7, 8:30, 9, 10:30 and 11 p.m., the Stand, Manhattan; 212-677-2600, thestandnyc.com. (McCarthy)
'NEW YEAR'S EVE SPECTACULAR' Carolines on Broadway offers comfort from the cold just a few blocks north of Times Square, while allowing late-show patrons outside sidewalk access for the ball drop. Performers inside include Tyler Fischer, who won the "New York's Funniest" competition this year, alongside some of his fellow finalists: Xazmin Garza, Caitlin Peluffo, and Michael Rowland. The later show also includes a D.J. and dancing after midnight. At 7:30 and 10 p.m., Carolines on Broadway, Manhattan; 212-757-4100, carolines.com. (McCarthy)
'NEW YEAR'S EVE AT THE COMEDY CELLAR' This Greenwich Village mainstay has expanded to multiple rooms to accommodate this decade's comedy boom, with comedians bouncing back and forth from the MacDougal Street and West 3rd Street locations. Among performers on the late shows: Dan Naturman, who'll return to "America's Got Talent" for this January's showcase of "The Champions," Sam Morril, whose voice could be heard telling jokes on the big screen in "Joker," and the longtime Cellar regulars Keith Robinson and Dave Attell. At 8, 8:15, 10:15, 10:30 p.m., Comedy Cellar, Manhattan; 212-254-3480, comedycellar.com. (McCarthy)
'NEW YEAR'S EVE WITH THE GOTHAM ALL-STARS' Ryan Reiss, who provides warm-up for the audiences at "Late Night With Seth Meyers," anchors this lineup of regular in-house talent for the long-running comedy club on 23rd Street. Also featuring Kevin Dombrowski, James Goff, Veronica Mosey, Daniel Tirado and Nathan Macintosh. At 8 and 10:30 p.m., Gotham Comedy Club, Manhattan; 212-367-9000, gothamcomedyclub.com. (McCarthy)
JOHNNY O'NEAL TRIO O'Neal is a masterly performer whose sparkling piano runs and blustery blues singing can tap your nostalgia while keeping you acutely awake to the present. And you'd better be: Whether singing a jazz standard, covering Whitney Houston in a stride-jazz style or improvising a risqué blues, he expects full-blooded participation from the crowd. An avowed pleaser, O'Neal maintains something of an avuncular presence over Mezzrow and its sister club, Smalls, throughout the year. He will ring in the new decade with Mark Lewandowski on bass and Itay Morchi on drums. At 9:30 p.m., Mezzrow, Manhattan; 646-476-4346, mezzrow.com. (Russonello)
PHISH At year's end, Madison Square Garden belongs to Phish for four nights, with hours of whimsical, head-bopping songs and open-ended, light-fingered jams. Yet all that music is nearly overshadowed by a single moment: Phish's annual midnight New Year's stunt. What will it be this year? The shows are sold out, but Phish also offers live webcasts; an elaborate assortment of packages is at phish.com. On Dec. 28-30 at 7:30 p.m. at Madison Square Garden, Manhattan; msg.com. (Pareles)
CHRIS POTTER A tenor saxophonist of unimpeachable command and restless creative instinct, Potter this year released "Circuits," a fine album featuring a new trio with James Francies on keyboards and Eric Harland on drums. To a degree, this new outfit marks a return to the kind of expansive jazz-funk experimentation that Potter first tried out in the mid-2000s, with his quartet Underground. But there's something new going on here, partly thanks to the casual brilliance of Harland's spacious grooves and the acoustic-electric textural play that is Francies's specialty. At 9 and 11 p.m., Village Vanguard, Manhattan; 212-255-4037, villagevanguard.com. (Russonello)
'PREGAME WITH GETHARD AND FRIENDS' That's Chris Gethard, as in the erstwhile host of "The Chris Gethard Show," which began in a basement beneath a Gristedes before reaching TV heights from 2011-2018 on Manhattan cable access, Fusion and later truTV, all via Funny or Die. Gethard, who continues to host the podcast "Beautiful Stories from Anonymous People," will welcome Martin Urbano and Meg Statler, both cast in the newly revamped "National Lampoon Radio Hour." This show has a guaranteed end time of 9 p.m. At 7 p.m., Littlefield, Park Slope, Brooklyn; littlefieldnyc.com. (McCarthy)
PRIESTS This may be the last chance to see Priests, a three-piece indie-rock band from Washington that has focused on the sharpest legacies of post-punk: knotty, kinetic, tightly wound songs that spiral toward Katie Alice Greer's impassioned questions and declarations: "No it's not for anyone/and I can't wait until it's done," she sings in "Nothing Feels Natural." (The band has announced a hiatus after this show.) Also on the bill: the Brooklyn band Russian Baths, which juxtaposes airy melody and churning dissonance, and Anina Ivry-Block from the lo-fi post-punk band Palberta. At 9 p.m., Rough Trade NYC, Brooklyn; 718-388-4111, roughtradenyc.com. (Pareles)
'QED'S NEW YEAR'S EVE SPECTACULAR' Christian Finnegan is not just married to the owner of Astoria's top comedy club; he's also the year-end headliner. You may recognize Finnegan from his recurring appearances providing levity to the news on MSNBC, or from his previous stint as a cast member on VH1's "Best Week Ever." He'll be joined onstage at Q.E.D. by other comedians, including Usama Siddiquee, Sam Morrison, Courtney Fearrington and Lauren Hope Krass. At 8 and 10 p.m., Q.E.D., Astoria, Queens; 347-451-3873, qedastoria.com. (McCarthy)
THE RUB One of the most reliable dance parties in Brooklyn for well over a decade, the Rub returns to the Bell House with guests ItsParlé and Hasan Insane (DJ Ayres and DJ Eleven are its resident D.J.s). Expect the eclectic and the energetic. At 10 p.m., the Bell House, Brooklyn; 718-643-6510, itstherub.com. (Caramanica)
ALEX SENSATION The star D.J. on La Mega 97.9, one of New York's top Spanish-language radio stations, headlines this party at the most prominent Latin-music nightclub in Queens. With DJ Mad, DJ Aneudy, DJ Prostyle and DJ Lobo. At 10 p.m., La Boom, Queens; 718-726-6646, laboomny.com. (Caramanica)
SLAVIC SOUL PARTY! Founded in the early 2000s by a troupe of New York jazz musicians fascinated with the Balkan brass tradition, Slavic Soul Party! has gradually expanded its repertoire, using Barbès — a bar in Park Slope, Brooklyn, with an intimate performance room in the back — as its testing ground. (The nine-piece ensemble holds down a weekly residency there.) Its most recent album was a reworking of Duke Ellington's famous "Far East Suite," recorded at the club. At 10 p.m., Barbès, Brooklyn; 347-422-0248, barbesbrooklyn.com. (Russonello)
SLEIGH BELLS (D.J. SET) The rise of 100 gecs this year triggered at least a little nostalgia for Sleigh Bells, the duo that erupted out of Brooklyn a decade ago with quasi-arty jock jams. "Gonna blast plenty of big, delicious hits, a few deep cuts and whatever else feels right," the band said. At midnight, Brooklyn Bowl, Brooklyn; 718-963-3369, brooklynbowl.com. (Caramanica)
THE STROKES Since their 2001 debut album, the Strokes have been both a throwback and a distillation of leather-jacketed New York City guitar rock, from the Velvets to the New York Dolls to the Ramones to Glenn Branca: lean, driven, jaded but desperately romantic. Pop may have sidelined guitar-driven rock, but live musicianship and tautly structured songs endure. The elaborately casual, downhearted indie-rocker Mac DeMarco and the punky Spanish band Hinds — with the Strokes among their influences — open the show. At 8:30 p.m., Barclays Center, Brooklyn; barclayscenter.com. (Pareles)
KT SULLIVAN AND MARK NADLER Individually and as a duo, Sullivan and Nadler have been charming cabaret audiences for years with their witty, loving showmanship. To ring in the new decade, they've put together a set harking to the Roaring '20s, which according to Nadler will feature tunes by "Gershwin, Porter, Kern, Berlin — all of them rummies. Just to name a few." Back, side, mid-dining and premium dinner seats include a prix fixe four-course dinner and a complimentary glass of champagne at midnight; ringside dinner seating adds an open bar. At Beach Café, Manhattan; 212-988-7299, thebeachcafe.com. (Gardner)
TROMBONE SHORTY & ORLEANS AVENUE/NORTH MISSISSIPPI ALLSTARS Trombone Shorty has been a local hero in New Orleans since his days as a brass-band child prodigy, and his music is infused with the city's heritage, from early jazz to R&B to funk to hip-hop. His band, Orleans Avenue, plays marathon, danceable sets that intersperse his own tunes with anything from "St. James Infirmary" to hip-hop. Luther and Cody Dickinson, who lead the North Mississippi All-Stars, immersed themselves in Mississippi traditions reaching back to Delta blues and rural fife-and-drum music; those backbeats and guitar licks drive their own songs and jams. Devon Gilfillian opens. At 9 p.m., the Capitol Theatre, Port Chester, N.Y.; 914-937-4126; thecapitoltheatre.com. (Pareles)
STEVE TYRELL A prolific interpreter and promoter of American standards — as a singer, producer and, in recent years, radio host — Tyrell has been holding court during the holiday season since the great Bobby Short shuffled off his mortal coil. For his 15th anniversary year, Tyrell will again mix pop standards, from Gershwin to Bacharach, with holiday classics. A black-tie gala, with seating beginning at 8 p.m., provides a four-course prix fixe menu and post-show dancing with the Peter Duchin Orchestra, as well as an autographed copy of one of Tyrell's albums. At Café Carlyle, Manhattan; tickets must be reserved by calling 212-744-1600; cafecarlylenewyork.com. (Gardner)
WAVVES The San Diego band led by Nathan Williams warps the tuneful stomp of California surf-rock with punk distortion, sudden tangents and lyrics that mix slacker nonchalance with acute self-consciousness. It all stays catchy. The show plus an open bar from 8-10 p.m. At Baby's All Right, Brooklyn; 718-599-5800; babysallright.com. (Pareles) | {
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Sir Samuel Alexander Mendes, dit Sam Mendes (prononcé en anglais : ), est un réalisateur, scénariste et producteur de cinéma britannique, né le à Reading (Berkshire).
Sa première réalisation, American Beauty (1999), est récompensée par cinq Oscars du cinéma propulsant Mendes au rang de vedette. Il réalise deux films de la saga autour du personnage de James Bond, Skyfall et Spectre, en 2012 et 2015 respectivement. Fait commandeur de l'ordre de l'Empire britannique par la reine Élisabeth II en 2000 pour services rendus aux arts dramatiques, il est anobli en 2019.
Biographie
Enfance et formations
Samuel Alexander Mendes est le fils d'un Trinidadien du nom de Mendes d'origine portugaise et d'une Britannique Valerie Helene Mendes (Barnett), ses parents divorcent alors qu'il a cinq ans. Son grand-père est l'écrivain Alfred Mendes.
Après ses études secondaires à la Magdalen College School d'Oxford, il s'inscrit à l'université de Cambridge. À Cambridge, il fait partie de la troupe théâtrale de l'université, la Marlowe Society avant de rejoindre le Chichester Festival Theatre, puis la Royal Shakespeare Company où il dirige Troïlus et Cressida avec Ralph Fiennes, et Richard III.
Carrière
En 1992, il devient directeur artistique de la Donmar Warehouse de Londres où il met en scène La Ménagerie de verre de Tennessee Williams et une adaptation scénique de la comédie musicale Cabaret. Il y dirige La Chambre bleue avec Nicole Kidman.
Après cette carrière remarquée au théâtre, il passe derrière la caméra et rencontre dès son premier film un succès international avec American Beauty en 1999, pour lequel il reçoit de nombreuses récompenses dont l'Oscar et le Golden Globe du meilleur réalisateur. En 2006, il met en scène la comédie musicale Cabaret en Europe.
Il dirige pour la première fois son épouse dans son quatrième film, Les Noces rebelles (2008), où Kate Winslet retrouve pour l'occasion ses partenaires de Titanic : Leonardo DiCaprio (meilleur ami de Kate) et Kathy Bates. En 2009, il réalise Away We Go, un film plus « indépendant » que ses précédentes réalisations.
En 2010, il se voit confier la réalisation du des aventures de James Bond, Skyfall. Après un arrêt de la production en raison des problèmes financiers de la Metro-Goldwyn-Mayer qui finance le film, le projet est confirmé et le film sort en 2012. C'est un énorme succès mondial, aussi bien auprès du public, que de la critique. Sam Mendes est alors envisagé pour le film suivant. D'abord hésitant, il annonce finalement qu'il ne rempilera pas, préférant se concentrer sur ses projets théâtraux. En , il est pourtant confirmé comme réalisateur de 007 Spectre, qui sort en France le .
En , il préside le jury international du Festival de Venise. La comédienne anglaise Gemma Arterton en fait notamment partie. Elle et Mendes ont participé à des films James Bond.
Il réalise ensuite 1917, sorti en 2019. Coécrit avec Krysty Wilson-Cairns, le scénario s'inspire en partie des récits de son grand-père paternel, Alfred Mendes. Le film raconte l'histoire de deux jeunes soldats britanniques qui reçoivent l'ordre de délivrer un message annulant une attaque vouée à l'échec peu après la retraite allemande sur la ligne Hindenburg pendant l'opération Alberich en 1917. La réalisation du film donne l'illusion d'un seul long plan-séquence et d'une action en temps réel. Le film reçoit de nombreuses nominations et remporte plusieurs prix, dont deux Golden Globes et trois Oscars.
Il écrit et réalise ensuite le drame romantique Empire of Light, qui sera présenté en avant-première au festival international du film de Toronto 2022.
Vie privée
Sam Mendes a une relation avec l'actrice Rachel Weisz entre 1999 et 2001, future femme de l'acteur Daniel Craig, qu'il dirige en tant que James Bond. Il est marié avec l'actrice britannique Kate Winslet de 2003 à 2010. Leur fils, Joe, naît le . En 2010, le divorce entre Kate Winslet et le réalisateur Sam Mendes est prononcé et engagé à l'amiable en discrétion.
En 2011, il entame une relation avec Rebecca Hall jusqu'en 2013. En , il se marie avec Alison Balsom. En , Balsom donne naissance à leur fille.
Filmographie
Réalisateur
1999 : American Beauty
2002 : Les Sentiers de la perdition
2005 : Jarhead : La Fin de l'innocence
2008 : Les Noces rebelles
2009 : Away We Go
2012 : Skyfall
2015 : 007 Spectre
2019 : 1917
2022 : Empire of Light
Producteur et producteur exécutif
Cinéma
2001 : Les Sentiers de la perdition de lui-même
2006 : Starter for 10 de Tom Vaughan (producteur exécutif)
2007 : Nos souvenirs brûlés (Things We Lost in the Fire) de Susanne Bier
2007 : Les Cerfs-volants de Kaboul (The Kite Runner) de Marc Forster (producteur exécutif)
2008 : Les Noces rebelles de lui-même
2010 : Out of the Ashes de Tim Albone, Lucy Martens et Leslie Knott (documentaire) (producteur exécutif)
2012 : Blood de Nick Murphy (producteur exécutif)
2022 : Ben Stokes : Phoenix from the Ashes de Chris Grubb et Luke Mellows (documentaire) (producteur exécutif)
2023 : Empire of Light de lui-même
Télévision
2007 : Stuart : Une vie à l'envers (Stuart : A Life Backwards) de David Attwood (producteur exécutif)
2012 - 2016 : The Hollow Crown (7 épisodes) (producteur exécutif)
2014 - 2016 : Penny Dreadful (27 épisodes) (producteur exécutif)
2017 - 2019 : Britannia (19 épisodes) (producteur exécutif)
2018 : Informer (10 épisodes) (producteur exécutif)
2020 : Penny Dreadful : City of Angels (10 épisodes) (producteur exécutif)
Scénariste
2019 : 1917
2023 : Empire of Light
Théâtre
Troïlus et Cressida de William Shakespeare
Richard III de William Shakespeare
1989 : La Cerisaie d'Anton Tchekhov
1998 : La Chambre bleue (The Blue Room) de David Hare d'après Arthur Schnitzler
1998 : Cabaret de Joe Masteroff et John Kander co-metteur en scène avec Rob Marshall
2009 : La Cerisaie d'Anton Tchekhov, New York, tournée mondiale
2010 : The Tempest (La Tempête) de William Shakespeare, tournée mondiale
2010 : As You Like It (Comme il vous plaira) de William Shakespeare, tournée mondiale
2011 : Richard III de William Shakespeare avec Kevin Spacey, Old Vic
2012 : Charlie and the Chocolate Factory: the Musical
2019 : The Lehman Trilogy de Stefano Massini
Distinctions
Décorations
Commandeur de l'ordre de l'Empire Britannique (2000)
(2019)
Récompenses
Source :
Los Angeles Film Critics Association Awards 1999 : meilleur réalisateur pour American Beauty
Oscars 2000 : meilleur réalisateur pour American Beauty
Golden Globes 2000 : meilleur réalisateur pour American Beauty
Chicago Film Critics Association Awards 2000 : meilleur réalisateur pour American Beauty
Online Film Critics Society Awards 2000 : meilleur réalisateur pour American Beauty
Rubans d'argent 2000 : meilleur réalisateur d'un film étranger pour American Beauty
Dallas-Fort Worth Film Critics Association Awards 2000 : meilleur réalisateur pour American Beauty
London Film Critics Circle Awards 2000 : meilleur réalisateur pour American Beauty
Southeastern Film Critics Association Awards 2000 : meilleur réalisateur pour American Beauty
Directors Guild of America Awards 2000 : meilleur réalisateur pour American Beauty
Kansas City Film Critics Circle Awards 2000 : meilleur réalisateur pour American Beauty
Florida Film Critics Circle Awards 2000 : meilleur réalisateur pour American Beauty
Bodil 2001 : meilleur film américain pour American Beauty
Lions tchèques 2001 : meilleur film étranger pour American Beauty
Washington D.C. Area Film Critics Association Awards 2002 : meilleur réalisateur pour Les Sentiers de la perdition
ShoWest Convention 2003 : réalisateur de l'année
Directors Guild of Great Britain 2005 : prix honorifique
Hollywood Film Festival 2005 : réalisateur de l'année
Jameson Empire Awards 2013 : meilleur réalisateur pour Skyfall
Golden Globes 2020 : meilleur réalisateur pour 1917
BAFTA 2020 :
Meilleur film pour 1917
Meilleur film britannique
Meilleur réalisateur
Festival international du film de Stockholm 2022 : prix du visionnaire
Nominations
BAFTA Awards 2000 : meilleur réalisateur pour American Beauty
Chlotrudis Awards 2000 : meilleur réalisateur pour American Beauty
Las Vegas Film Critics Society Awards 2000 : meilleur réalisateur pour American Beauty
Satellite Awards 2000 : meilleur réalisateur pour American Beauty
Empire Awards 2001 : meilleur réalisateur britannique et meilleur espoir pour American Beauty
London Film Critics Circle Awards 2003 : meilleur réalisateur pour Les Sentiers de la perdition
Phoenix Film Critics Society Awards 2003 : meilleur réalisateur pour Les Sentiers de la perdition
Golden Globes 2009 : meilleur réalisateur pour Les Noces rebelles
Bodil 2010 : meilleur film américain pour Les Noces rebelles
Oscars 2020 :
Meilleur réalisateur pour 1917
Meilleur scénario original
Bibliographie
The Sam Mendes Handbook - Everything You Need to Know about Sam Mendes, par Emily Smith, éd. Tebbo, 2013,
Sam Mendes at the Donmar: Stepping into Freedom, par Matt Wolf, éd. Limelight Editions, 2004.
Articles et interviews
A Magnificent Road to Ruin in 'The Lehman Trilogy', par Ben Brantley pour le New York Times, 2019,
How Sam became The Man, par Gaby Wood pour The Guardian, 2008,
The Blue Room, par Charles Isherwood pour le magazine Variety, 1998,
Nicole Kidman in the West End – 'she is not just a star: she delivers the goods', par Michael Billington pour The Guardian, 1998.
Box-office
Source : Box Office Mojo
Notes et références
Voir aussi
Liens externes
Naissance à Reading (Royaume-Uni)
Naissance en août 1965
Réalisateur anglais
Scénariste anglais
Réalisateur de James Bond
Metteur en scène britannique
Oscar de la meilleure réalisation
Golden Globe de la meilleure réalisation
Commandeur de l'ordre de l'Empire britannique
Lauréat du Tony Award
Critics' Choice Movie Award de la meilleure réalisation
Étudiant de Peterhouse
Knight Bachelor | {
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{"url":"https:\/\/physics.stackexchange.com\/questions\/86881\/about-the-standard-derivation-of-the-gravitational-redshift","text":"# About the standard derivation of the gravitational redshift\n\nThe objective is to derive the gravitational redshift ONLY from the Einstein's equivalence principle (E.E.P.), without using the whole theory of Relativity.\n\nThis is the standard \"informal\" derivation of the gravitational redshift (For example Carroll in his book follows this way):\n\nConsider an emitter, $E$, e.g. a vibrating atom, at rest at a point near the Earth's surface, say, of gravitational potential $\\phi$. Let it send light, or any other electromagnetic, signals to a receiver $R$ at rest directly above $E$ and distance $h$ from it; the gravitational potential at $R$ is $\\phi+\\Delta\\phi$, where $\\Delta\\phi = gh$, $g$ being the acceleration due to gravity. Let $\\nu_E$ be the frequency of the signal as measured at $E$, and $\\nu_R$ the frequency of the signal received, and measured, at $R$. Then it is used the relativistic Doppler effect, in the case where the receiver is moving with constant relative velocity $V$ respect to the emitter, to show that:\n\n$$\\frac{\\nu_R-\\nu_E}{\\nu_E}=-\\frac{\\Delta\\phi}{c^2}=-\\frac{gh}{c^2}$$\n\nBy the E.E.P. will follow easly the gravitational redshift.\n\nAnd now my trouble:\n\nIn the derivation of the basic formula for the classical Doppler shift (which, it may be recalled, is the first approximation in $\\frac{V}{c}$ of the corresponding special relativistic formula), on which the standard arguent is so decisively based, the emitter and the receiver move with constant velocities relative to an inertial frame and $V$ is the constant velocity of the receiver relative to the emitter and away from it. That is, the velocity of the emitter is the same at the instant of the emission and, likewise, the velocity of the receiver is the same at the instant of the reception. This is not the case when $E$ and $R$ are accelerating relative to an inertial frame.\n\nSo, should I conclude that the above argument is wrong?\n\nI don't have Carroll's book, but I don't recognise the description you give of the derivation of the red shift, and in particular I don't see why the relativistic Doppler shift is relevant. The derivation I'm familiar with is to say that the change in potential energy is $mgd$, where $m$ is the effective mass given by $E = h\\nu = mc^2$. So:\n\n$$h\\nu_e - h\\nu_r = \\frac{h\\nu_e}{c^2} gd$$\n\nand a quick rearrangement gives:\n\n$$\\frac{\\nu_e - \\nu_r}{\\nu_e} = \\frac{gd}{c^2}$$\n\nNo Doppler shift involved.\n\n\u2022 The above derivation uses the fact that the energy of a photon is tied up with its frequency through the Planck's constant. How is this justified within the context of General relativity or even the principle of equivalence? I mean, this derivation explains gravitational red shift in terms of the laws of special relativity and quantum theory - not as a consequence of the principle of equivalence \u2013\u00a0Charuhas Mar 31 '14 at 13:07\n\nthe emitter and the receiver move with constant velocities relative to an inertial frame and $V$ is the constant velocity of the receiver relative to the emitter and away from it.\n\nNo, both the emitter and the receiver are accelerating, and the receiver has gained an extra velocity $\\Delta v$ between the time the photon was emitted and the time it was received.\n\nIn other words, consider an emitter and a receiver, both accelerating with a constant acceleration $g$, and suppose the emitter is a distance $h$ behind the receiver. Also, suppose that $g$ is low enough so that relativistic effects can be ignored.\n\nIf the (trailing) emitter sends out a photon with wavelength $\\lambda_e$, it reaches the (leading) receiver after a time $\\Delta t\\approx h\/c$ (ignoring the little extra distance that the photon has to travel because the receiver has accelerated).\n\nDuring this time, the receiver has gained an extra velocity $\\Delta v=g\\Delta t \\approx gh\/c$. If $\\Delta v$ is small, the standard Newtonian Doppler effect applies, and the wavelength of the received photon has changed as $$\\frac{\\Delta\\lambda}{\\lambda_e} = \\frac{\\Delta v}{c} \\approx \\frac{gh}{c^2},$$ or equivalently, the frequency has changed as $$\\frac{\\Delta\\nu}{\\nu_e} = -\\frac{\\Delta v}{c} \\approx -\\frac{gh}{c^2}.$$ According to the EEP, the acceleration of the emitter and the receiver is equivalent to a gravitational field.","date":"2019-10-16 17:34:45","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\": 0.8812995553016663, \"perplexity\": 109.07386437358579}, \"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-2019-43\/segments\/1570986669057.0\/warc\/CC-MAIN-20191016163146-20191016190646-00355.warc.gz\"}"} | null | null |
Q: how to set an attribute to a selected item of a dropdown list in JQuery? I would like to add an attribute selected="selected" to the selected item in a dropdown list in jQuery. If I change to an other item I like to set selected to that new one etc.
$(document).ready(function() {
$("#to").change(function() {
$("#to option").val('Saab').attr("selected", true);
});
});
<script src="https://ajax.googleapis.com/ajax/libs/jquery/3.2.1/jquery.min.js"></script>
<form action="">
Name: <input type="text" name="user"><br> Car:
<select id="to">
<option>Volvo</option>
<option >Saab</option>
<option>Mercedes</option>
<option>Audi</option>
</select>
</form>
Here' a jsFiddle with the the code
A: From your comment under the question:
I mean set attribute selected="selected" to the selected item in the dropdownlist
To achieve this you can use :selected to retrieve the chosen option element before using attr() to set the attribute on the element. You will also need to use removeAttr() on the other option elements that were previously selected, something like this:
$(document).ready(function() {
$("#to").change(function() {
$('#to option').removeAttr('selected').filter(':selected').attr("selected", true);
});
});
<script src="https://ajax.googleapis.com/ajax/libs/jquery/3.2.1/jquery.min.js">
</script>
<form action="">
Name:
<input type="text" name="user">
<br> Car:
<select id="to">
<option>Volvo</option>
<option>Saab</option>
<option>Mercedes</option>
<option>Audi</option>
</select>
</form>
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 2,935 |
Home > Taxidermy Forms > Lifesize Forms > North American >
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CRB-606
Cottontail Flexiform Running, LT, CM
1 5/8" x 4" x 13 1/2" x 9 1/2"
Cottontail Rabbit Flexiform, Crouching, Slight RT
1 5/8" x 6" x 14 3/8" x 10 1/2"
Cottontail Full Flex® Sitting, LT
Cottontail Rabbit Full Flex® Sitting, Slight LT
JKR-602
by John Schmidt
Jackrabbit Standing, CM
2 1/8" x 6" x 20" x 13 1/2"
Jackrabbit Sitting, CM
2 1/8" x 5 3/8" x 22" x 13"
Jackrabbit Hanging Dead
2 1/8" x 5 3/8" x 22" x 13 1/2" | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 107 |
Australian made using a 175gsm 100% polycotton blend fabric with a high filament fibre, this polo shirt will keep it's fresh new look for longer. The feel of brushed cotton on the inside makes it so comfortable that you will want to wear it everyday. Available in black as part of our core range, so choose one of 12 colours for the insignia. Also gunmetal with a range of 12 colours for the insignia.
Australian made using a 175gsm 100% polycotton blend fabric with a high filament fibre, this men's polo shirt will keep it's fresh new look for longer. The black polo is available in the full range of 12 colours for the insignia. Click here to view our gunmetal polo.
Australian made using a 175gsm 100% polycotton blend fabric with a high filament fibre, this men's polo shirt will keep it's fresh new look for longer. The gunmetal polo is now available in the full range of 12 colours for the insignia. Click here to view our black polo. | {
"redpajama_set_name": "RedPajamaC4"
} | 6,181 |
{"url":"https:\/\/emacs.stackexchange.com\/questions\/45809\/including-standard-boiler-plate-on-opening-a-new-latex-file","text":"# Including standard boiler-plate on opening a new latex file [duplicate]\n\nMost of my \\LaTeX files have the same boiler plate code, so I would like Emacs to automatically insert this boiler-plate whenever I open a fresh, blank \\LaTeX file.\n\nIn particular, I would like to include the following preamble.\n\n \\usepackage{amsthm}\n\\usepackage{amssymb}\n\\usepackage[backend=bibtex, style=numeric, sorting=none]{biblatex}\n\\setlength\\bibitemsep{\\baselineskip}\n\\author{A.U.Thor}\n\\date{}\n\n\\begin{document}\n\\setcounter{tocdepth}{0}\n\n\\nocite{*}\n\\printbibliography\n\\end{document}\n\n\nHow should I modify my .emacs file to do this?\n\nThat page mentions mode Auto Insert, which is part of vanilla Emacs, and it describes libraries header2.el and file-template.el.","date":"2020-01-18 14:00:40","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\": 0.9511483311653137, \"perplexity\": 8942.276579241745}, \"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-2020-05\/segments\/1579250592636.25\/warc\/CC-MAIN-20200118135205-20200118163205-00381.warc.gz\"}"} | null | null |
Q: How to set scrolling or marquee in autocomplete text in android? <AutoCompleteTextView
android:id="@+id/search"
style="@style/EditText"
android:layout_width="0dp"
android:layout_height="match_parent"
android:layout_gravity="center"
android:layout_weight="1"
android:ellipsize="marquee"
android:hint="@string/searchspecial"
android:singleLine="true"
android:imeOptions="flagNoExtractUi"
android:textColor="@color/black" />
This is my autocomplete code but here I used marquee but its not working . Runtime error occurs!
Logcat:
E/AndroidRuntime(29075): android.view.InflateException: Binary XML file line #16: Error inflating class android.widget.AutoCompleteTextView (LOGCAT ERROR)
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 9,677 |
{"url":"http:\/\/tex.stackexchange.com\/questions\/44486\/pixel-perfect-vertical-alignment-of-image-rendered-tex-snippets?answertab=active","text":"Pixel-perfect vertical alignment of image-rendered TeX snippets?\n\nWhat is the most accurate way to automatically calculate the text baseline in an image that has been rendered from a TeX snippet\u2014so that the rendered image can be given proper vertical alignment in a block of text?\n\nMy current approach (which isn\u2019t working in all cases):\n\nHere\u2019s an example of what I\u2019m trying to do. Note that these are screenshots of a web page (HTML\u00a0+ CSS\u00a0+ Latin\u00a0Modern fonts for web) and not of a TeX document. The web page is mostly paragraphs of text, but contains embedded PNG images (rendered TeX snippets) for the formulas involving square roots. Here\u2019s how I want it to look:\n\nBut here\u2019s what I\u2019m getting...\n\nThe second\u2014the smaller\u2014square root formula is aligned correctly, and it was done automatically. I\u2019m calculating the baseline by first rendering a snippet consisting of only a \u201c.\u201d character, and then by measuring the height of the resulting image, after cropping away everything below the \u201c.\u201d, this tells me how much I need to lower the image (using CSS\u2019s vertical-align style) in order to align it with the surrounding text\u2019s baseline. This works well for formulas that aren\u2019t too tall.\n\nWhere it fails is, well, taller formulas, as shown above. In the case of the first\u2014the larger\u2014square root formula, it needs to be lowered less than normal, because it extends higher than normal. My calculations for this are currently wrong, and I\u2019m wondering how I can fix this.\n\nAlternatives?\n\nWhat are some ways of measuring the baseline (in pixels) of a snippet? I can\u2019t really use \\documentclass{standalone} for this because it crops the page as tightly as possible, which produces different image heights for $x$, $X$, and \\sqrt{x}. I\u2019m thinking I may need to render a calibration snippet consisting of two blank lines prior to a lone . (or perhaps a bottom-aligned horizontal rule) instead of just a single . character\u2014but that seems a bit kludgey.\n\nIs there a way to coax TeX into not placing a formula lower on the page when it is taller than standard text? That is, is there some way I can cause a formula at the top of a page to protrude upward into the top margin?\n\nA second problem\n\nI also noticed that I\u2019m seeing sub-pixel alignment problems. Below are screenshots scaled up to 400% actual size: This formula is \u00be pixel too low:\n\nAt first, I thought I was calculating the vertical-align value wrong, so I manually moved it up by one pixel, but then it turns out that it's \u00bc pixel too high\u2014which means the problem lies within the image rather than the alignment value:\n\nI suspect this is fixable by making sure I round the image heights up to the nearest multiple of 4 before I downsample them for embedding in the page. Just wondering if anyone has tackled this problem before, and has any tips. I\u2019m encouraged by these results so far, but doing this correctly turns out to be a lot more subtle than I expected it would be. Na\u00efvely, when I first started this, I hadn\u2019t considered tall formulas or even vertical alignment at all.\n\n-\n\"96 is the screen dpi that modern web browsers assume\" -- is that why it's disastrously broken on 120 dpi\/large font systems? Systems where the user has changed the default font-size to something other than 16px? \u2013\u00a0 user12153 Feb 27 '12 at 20:40\nWhy didn't anybody mention mathjax.org ? \u2013\u00a0 Aur\u00e9lien Ooms Feb 19 at 7:20\n@Aur\u00e9lienOoms \u2014 MathJax is nice, but it solves a different problem. This was about using TeX's rendering engine rather than leaving it up to the browser. In other words, this question is about how to achieve the highest quality alignment from (La)TeX-generated images rather than how to achieve the highest quality typography using built-in fonts. So, by definition, there is no valid answer that would include MathJax, other than simply to mention it as a completely different alternative. \u2013\u00a0 Todd Lehman Feb 19 at 19:01\n\nNote that dvipng can determine the baseline for you, as long as you activate the 'preview' style. Here are the exact steps you need:\n\n1. Put \\usepackage[active,textmath]{preview} in your LaTeX header\n2. Run LaTeX to get a dvi file, (eg myfile.dvi)\nmy ($num,$mod) = @_;\nreturn $num + ($num % $mod == 0? 0 : ($mod - ($num %$mod)));\n}\n\n#------------------------------------------------------------------------------\n#\n# FETCH WIDTH AND HEIGHT FROM PNM FILE\n#\n\nsub pnm_width_height ($) { my ($filename) = @_;\n$filename =~ m\/\\.pnm$\/ or die \"$filename: not .pnm\"; open(PNM, '<',$filename) or die \"$filename: can't read\"; my$line = <PNM>; # Skip first line.\ndo { $line = <PNM> } while$line =~ m\/^#\/; # Read next line, skipping comments\nclose(PNM);\n\nmy ($width,$height) = ($line =~ m\/^(\\d+)\\s+(\\d+)$\/);\ndefined($width) && defined($height)\nor die \"$filename: Couldn't read image size\"; return ($width, $height); } #------------------------------------------------------------------------------ # # COMPILE LATEX SNIPPET INTO HTML # # This routine caches results in the \/tmp directory. Snippets are named and # indexed by their SHA-1 hash. # sub tex_to_html ($$) { my ($tex_template, $tex_snippet) = @_; my$render_antialias_bits = 4;\nmy $render_oversample = 4; my$display_oversample = 4;\nmy $oversample =$render_oversample * $display_oversample; my$render_dpi = 96*1.2 * 72.27\/72 * $oversample; # This is 1850.112 dpi. # --- Generate SHA-1 hash of TeX input for caching. (my$tex_input = $tex_template) =~ s{<SNIPPET>}{$tex_snippet};\nmy $hash = do { use Digest::SHA; uc(Digest::SHA::sha1_hex($tex_input)); };\nmy $file = \"\/tmp\/tex-$hash\";\n\n# --- If the image has already been compiled, then simply return the\n# cached result. Otherwise, continue and create the image.\n\nif (open(HTML, '<', \"$file.html\")) { my$html = do { local $\/; <HTML> }; close(HTML); return$html;\n}\n\n# --- Write TeX source and compile to PDF.\n\nopen(TEX, '>', \"$file.tex\") and print TEX$tex_input and close(TEX)\nor die \"$file.tex: can't write\"; run_command( \"pdflatex\", \"-halt-on-error\", \"-output-directory=\/tmp\", \"-output-format=pdf\", \"$file.tex\",\n\">$file.err 2>&1\" ); # --- Convert PDF to PNM using Ghostscript. run_command( \"gs\", \"-q -dNOPAUSE -dBATCH\", \"-dTextAlphaBits=$render_antialias_bits\",\n\"-dGraphicsAlphaBits=$render_antialias_bits\", \"-r$render_dpi\",\n\"-sDEVICE=pnmraw\",\n\"-sOutputFile=$file.pnm\", \"$file.pdf\"\n);\n\nmy ($img_width,$img_height) = pnm_width_height(\"$file.pnm\"); #print \"# img_width=$img_width\\n\";\n#print \"# img_height=$img_height\\n\"; #print \"# \\n\"; # --- Read dimensions file written by TeX during processing. # # Example of file contents: # snippetdepth = 6.50009pt # snippetheight = 13.53899pt # snippetwidth = 145.4777pt # pagewidth = 153.4777pt # pageheight = 28.03908pt # pagemargin = 4.0pt my$dimensions = {};\ndo {\nopen(DIMENSIONS, '<', \"$file.dimensions\") or die \"$file.dimensions: can't read\";\nwhile (<DIMENSIONS>) {\nif (m\/^(\\S+)\\s+=\\s+(-?[0-9\\.]+)pt$\/) { my ($value, $length) = ($1, $2);$length = $length \/ 72.27 *$render_dpi;\n$dimensions->{$value} = $length; } else { die \"$file.dimensions: invalid line: $_\"; } } close(DIMENSIONS); }; #foreach (keys %$dimensions) { print \"# $_=$dimensions->{$_}px\\n\"; } #print \"# \\n\"; # --- Crop bottom, then measure how much was cropped. run_command(\"pnmcrop -white -bottom$file.pnm >$file.bottomcrop.pnm\"); my ($img_width_bottomcrop, $img_height_bottomcrop) = pnm_width_height(\"$file.bottomcrop.pnm\");\n\nmy $bottomcrop =$img_height - $img_height_bottomcrop; #printf \"# Cropping bottom: %d pixels - %d pixels = %d pixels cropped\\n\", #$img_height, $img_height_bottomcrop,$bottomcrop;\n\n# --- Crop top and sides, then measure how much was cropped from the top.\n\nrun_command(\"pnmcrop -white $file.bottomcrop.pnm >$file.crop.pnm\");\n\nmy ($cropped_img_width,$cropped_img_height) =\npnm_width_height(\"$file.crop.pnm\"); my$topcrop = $img_height_bottomcrop -$cropped_img_height;\n#printf \"# Cropping top: %d pixels - %d pixels = %d pixels cropped\\n\",\n# $img_height_bottomcrop,$cropped_img_height, $topcrop; # --- Pad image with specific values on all four sides, in preparation for # downsampling. # Calculate bottom padding. my$snippet_depth =\nint($dimensions->{snippetdepth} +$dimensions->{pagemargin} + .5)\n- $bottomcrop; my$padded_snippet_depth = round_up($snippet_depth,$oversample);\nmy $increase_snippet_depth =$padded_snippet_depth - $snippet_depth; my$bottom_padding = $increase_snippet_depth; #printf \"# Padding snippet depth: %d pixels + %d pixels = %d pixels\\n\", #$snippet_depth, $increase_snippet_depth,$padded_snippet_depth;\n\nmy $padded_img_height = round_up($cropped_img_height + $bottom_padding,$oversample);\nmy $top_padding =$padded_img_height - ($cropped_img_height +$bottom_padding);\n#printf \"# Padding top: %d pixels + %d pixels = %d pixels\\n\",\n# $cropped_img_height,$top_padding, $padded_img_height; # --- Calculate left and right side padding. Distribute padding evenly. my$padded_img_width = round_up($cropped_img_width,$oversample);\nmy $left_padding = int(($padded_img_width - $cropped_img_width) \/ 2); my$right_padding = ($padded_img_width -$cropped_img_width)\n- $left_padding; #printf \"# Padding left =$left_padding pixels\\n\";\n#printf \"# Padding right = $right_padding pixels\\n\"; # --- Pad the final image. run_command( \"pnmpad\", \"-white\", \"-bottom=$bottom_padding\",\n\"-top=$top_padding\", \"-left=$left_padding\",\n\"-right=$right_padding\", \"$file.crop.pnm\",\n\">$file.pad.pnm\" ); # --- Sanity check of final size. my ($final_pnm_width, $final_pnm_height) = pnm_width_height(\"$file.pad.pnm\");\n$final_pnm_width %$oversample == 0\nor die \"$final_pnm_width is not a multiple of$oversample\";\n$final_pnm_height %$oversample == 0\nor die \"$final_pnm_height is not a multiple of$oversample\";\n\n# --- Convert PNM to PNG.\n\nmy $final_png_width =$final_pnm_width \/ $render_oversample; my$final_png_height = $final_pnm_height \/$render_oversample;\n\nrun_command(\n\"cat $file.pad.pnm\", \"| ppmtopgm\", \"| pamscale -reduce$render_oversample\",\n\"| pnmgamma .3\",\n\"| pnmtopng -compression=9\",\n\"> $file.png\" ); # --- Convert PNG to HTML. my$html_img_width = $final_png_width \/$display_oversample;\nmy $html_img_height =$final_png_height \/ $display_oversample; my$html_img_vertical_align = sprintf(\"%.0f\",\n-$padded_snippet_depth \/$oversample);\n\n(my $html_img_title =$tex_snippet) =~\ns{([&<>'\"])}{sprintf(\"&#%d;\",ord($1))}eg; my$png_data_base64 = do {\nopen(PNG, '<', \"$file.png\") or die \"$file.png: can't open\";\nbinmode PNG;\nmy $png_data = do { local$\/; <PNG> };\nclose(PNG);\nuse MIME::Base64;\nMIME::Base64::encode_base64($png_data); }; #$png_data_base64 =~ s\/\\s+\/\/g;\n\nmy $html = qq{<img\\n} . qq{ width=$html_img_width} .\nqq{ height=html_img_height} . qq{ style=\"vertical-align:{html_img_vertical_align}px;\"} .\nqq{ title=\"$html_img_title\"} . qq{ src=\"data:image\/png;base64,\\n$png_data_base64\" \/>};\n\nopen(HTML, '>', \"$file.html\") and print HTML$html and close(HTML)\nor die \"$file.html: can't write\"; # --- Clean up and return result to caller. run_command( \"rm -f\", \"${file}{.*,}.{tex,aux,dvi,err,log,dimensions,pdf,pnm,png}\"\n);\n\nreturn $html; } #------------------------------------------------------------------------------ # # MAIN CONTROL # binmode(STDIN, \":utf8\"); binmode(STDOUT, \":utf8\"); binmode(STDERR, \":utf8\"); my$tex_template = do { local $\/; <DATA> }; my$input = do { local $\/; <STDIN> }; (my$html = $input) =~ s{\\$(.*?)\\$}{tex_to_html($tex_template,$1)}seg;$html =~ s{([^\\s<>]*<img.*?>[^\\s<>]*)}\n{<span style=\"white-space:nowrap;\">$1<\/span>}sg; print <<EOT; <?xml version=\"1.0\" encoding=\"UTF-8\"?> <!DOCTYPE html PUBLIC \"-\/\/W3C\/\/DTD XHTML 1.0 Strict\/\/EN\" \"http:\/\/www.w3.org\/TR\/xhtml1\/DTD\/xhtml1-strict.dtd\"> <html xmlns=\"http:\/\/www.w3.org\/1999\/xhtml\" xml:lang=\"en\" lang=\"en\"> <head> <meta http-equiv=\"Content-Type\" content=\"text\/html; charset=utf-8\"> <title><\/title> <\/head> <body> <p>$html\n<\/p>\n<\/body>\n<\/html>\nEOT\n\nexit(0);\n\n#------------------------------------------------------------------------------\n#\n# LATEX TEMPLATE\n#\n\n__DATA__\n\\documentclass[10pt]{article}\n\\pagestyle{empty}\n\\setlength{\\topskip}{0pt}\n\\setlength{\\parindent}{0pt}\n\\setlength{\\abovedisplayskip}{0pt}\n\\setlength{\\belowdisplayskip}{0pt}\n\n\\usepackage{geometry}\n\n\\usepackage{amsmath}\n\n\\newsavebox{\\snippetbox}\n\\newlength{\\snippetwidth}\n\\newlength{\\snippetheight}\n\\newlength{\\snippetdepth}\n\\newlength{\\pagewidth}\n\\newlength{\\pageheight}\n\\newlength{\\pagemargin}\n\n\\begin{lrbox}{\\snippetbox}%\n$<SNIPPET>$%\n\\end{lrbox}\n\n\\settowidth{\\snippetwidth}{\\usebox{\\snippetbox}}\n\\settoheight{\\snippetheight}{\\usebox{\\snippetbox}}\n\\settodepth{\\snippetdepth}{\\usebox{\\snippetbox}}\n\n\\setlength\\pagemargin{4pt}\n\n\\setlength\\pagewidth\\snippetwidth\n\n\\setlength\\pageheight\\snippetheight\n\n\\newwrite\\foo\n\\immediate\\openout\\foo=\\jobname.dimensions\n\\immediate\\write\\foo{snippetdepth = \\the\\snippetdepth}\n\\immediate\\write\\foo{snippetheight = \\the\\snippetheight}\n\\immediate\\write\\foo{snippetwidth = \\the\\snippetwidth}\n\\immediate\\write\\foo{pagewidth = \\the\\pagewidth}\n\\immediate\\write\\foo{pageheight = \\the\\pageheight}\n\\immediate\\write\\foo{pagemargin = \\the\\pagemargin}\n\\closeout\\foo\n\n\\geometry{paperwidth=\\pagewidth,paperheight=\\pageheight,margin=\\pagemargin}\n\n\\begin{document}%\n\\usebox{\\snippetbox}%\n\\end{document}\n\n\nUpdate to code: I just added -compression=9 to the pnmtopng command line and added ppmtopgm (convert to grayscale) in the final conversion pipeline. These together reduce the PNG image sizes by 20%. By the way, the average file size of the 24 PNG images in the sample screenshots shown above is 3534.83 bytes. The HTML document is 120,053 bytes. Keep in mind that these PNG images are 4 times larger (in each dimension height and width) than what appears on the screen at the default font size. If display-time oversampling is disabled, then the PNG images average 732.8 bytes each and the HTML document goes down to 29,209 bytes. I\u2019m not particularly worried about HTML and image file sizes anymore like I was in the 1990s, but I thought this was worth noting anyway. (Note: A pnmgamma adjustment of .5 or so should be used instead of .3 if display-time oversampling is diabled.)\n\n-\nBravo! Impressive work. Looks great!! To clarify, this is base64 encoded PNGs embedded in the HTML? (Judging by the code) \u2013\u00a0 MercurialMadnessMan Feb 25 '12 at 7:21\n@MercurialMadnessMan: Yup! it is base64-encoded PNG files embedded directly into the produced HTML document. Thus, the .html file is fully encapulsated, with no external references. \u2013\u00a0 Todd Lehman Feb 25 '12 at 7:43\nIt's written as a pipe: Pipe the input on stdin, then redirect stdout to a file. :) \u2013\u00a0 Todd Lehman Feb 26 '12 at 10:13\nCool stuff! On my ubuntu box i had to modify the script a little bit (here is the diff): 274c274 > \"| pnmtopng -compression=9\", --- < \"| pnmtopng -compression 9\", It seems that my version of pnmtopng doesn't like the equal sign. After fixing this it worked perfectly! \u2013\u00a0 user12149 Feb 27 '12 at 19:07\n@G\u00fcntherHutter: Interesting. That's surprising because the non-= form isn't even mentioned in the user manual. [netpbm.sourceforge.net\/doc\/pnmtopng.html] In any case, I'm glad it worked for you! \u2013\u00a0 Todd Lehman Feb 28 '12 at 4:43\n\nHave a look at the ideas at The baseline problem corrected. They have been incorporated into mathTeX vertical alignment if you want to use mathTeX to create the images.\n\n-\nThis is helping a lot, @stevem \u2014 thanks. I\u2019m about halfway done with implementing the ideas set forth in the Mac OS X TeX Toolbox link you provided. I also figured out some improvements to their techniques; I\u2019ll post a full solution when it\u2019s ready. \u2013\u00a0 Todd Lehman Feb 18 '12 at 8:37\n90% there. Now have an implementation which lines up absolutely perfectly! To do it correctly, though, is rather complicated: Calculations involve the ratio 72.27\/72 and result in a rendering resolution (using GhostScript) of precisely 1850.112 dpi. The image has to be padded with a small margin, then first cropped on the bottom, remeasured, then re-padded on the bottom, and then padded on the top and sides. The top padding is dependent on the bottom padding. A small amount of final subpixel padding is necessary for downsampling on the screen. \u2013\u00a0 Todd Lehman Feb 18 '12 at 11:49","date":"2014-11-29 06:42:21","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 2, \"mathjax_display_tex\": 2, \"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\": 0.8183229565620422, \"perplexity\": 6503.538431494375}, \"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-2014-49\/segments\/1416931013466.18\/warc\/CC-MAIN-20141125155653-00137-ip-10-235-23-156.ec2.internal.warc.gz\"}"} | null | null |
{"url":"http:\/\/mathhelpforum.com\/advanced-statistics\/177845-cumulative-distribution-function.html","text":"# Math Help - Cumulative distribution function\n\n1. ## Cumulative distribution function\n\nWe have cumulative distribution function Fx.\n\nFx = 1\/1000x - 1\/4\n\nHow do we get probability density function (gx) from Fx?\n\nIf we have gx, to get Fx, we need to integrate from 0 to x. Am I right?\n\nSo to get gx from Fx, we need to find the derivative, because it's an opposite operation from integration.\n\n2. Originally Posted by Nforce\nWe have cumulative distribution function Fx.\n\nFx = 1\/1000x - 1\/4\n\nHow do we get probability density function (gx) from Fx?\n\nIf we have gx, to get Fx, we need to integrate from 0 to x. Am I right?\n\nSo to get gx from Fx, we need to find the derivative, because it's an opposite operation from integration.\ng(x) = dF\/dx.\n\nBy the way, your definition of F(x) is very incomplete, you should have included the values of x for which the given rule applies. As it happens, I doubt very much that what you posted defines a valid cdf.\n\n3. yes i have forgot; the interval is [250,1250]\n\nI don't completely understand this:\n\ng(x) = dF\/dx.\n\nWhat is dF in here? Do you mean the derivative? Can you solve for example above.\n\n4. Originally Posted by Nforce\nyes i have forgot; the interval is [250,1250]\n\nI don't completely understand this:\n\ng(x) = dF\/dx.\n\nWhat is dF in here? Do you mean the derivative? Can you solve for example above.\nOf course it's the derivative. What else could it possibly be?\n\nI have no intention of solving it. Surely you know how to find the derivative of a function.\n\n5. ok, thank you.","date":"2014-07-23 11:59:05","metadata":"{\"extraction_info\": {\"found_math\": false, \"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\": 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\": 0.8301250338554382, \"perplexity\": 1071.100460452}, \"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\/1405997877881.80\/warc\/CC-MAIN-20140722025757-00003-ip-10-33-131-23.ec2.internal.warc.gz\"}"} | null | null |
{"url":"https:\/\/answers.ros.org\/answers\/28918\/revisions\/","text":"The approach that I ended up taking was to pre-pend the node's namespace to the filename provided by the private parameter, making use of n_.getNamespace(), and not forcing this into the launchfile.","date":"2022-06-27 01:58:58","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 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\": 0.7856302857398987, \"perplexity\": 2673.692065603695}, \"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\/1656103324665.17\/warc\/CC-MAIN-20220627012807-20220627042807-00146.warc.gz\"}"} | null | null |
{"url":"http:\/\/www.maa.org\/publications\/periodicals\/loci\/joma\/constructing-mathlets-quickly-using-livegraphics3d-parametrized-graphics","text":"# Constructing Mathlets Quickly using LiveGraphics3D - Parametrized Graphics\n\nAuthor(s):\nJonathan Rogness and Martin Kraus\n\nSo far all of our graphics primitives have had fixed, precomputed numbers as coordinates. One of LiveGraphics3D's most powerful features is its ability to display primitives whose coordinates are not fixed, but depend on independent variables which can be adjusted by the user. These objects are referred to as parametrized graphics.\n\nAs a basic example, consider the primitive Point[{x,0,0}] and suppose the initial value of x is 0. LiveGraphics3D would display this as a point at the three-dimensional origin, but you could click on the point and drag it to any location on the x-axis. As the point is dragged, the value of x would be adjusted accordingly. Any other primitives -- points, lines, polygons or text -- whose coordinates depend on x would be redrawn.\n\nNow let's use this idea to continue building our example. First we add a point to our input file as follows.\n\n(* \"mesh\" is the same as in the previous example *)\npoint = {RGBColor[1, 0, 0], PointSize[0.02], Point[{x, y, z}]};\n\nexample = Graphics3D[{mesh, point}, Boxed -> False];\nWriteLiveForm[\"meshPoint.lg3d\", example]\n\n\nBecause the coordinates in Point[{x,y,z}] are not fixed numbers, we need to tell LiveGraphics3D how to compute them at runtime. There is a fundamental difference here between z and the other two variables. x and y are independent variables; after specifying their initial values, we want to be able to change them by moving the point. Conversely, z is a dependent variable whose value should always be calculated using the formula for f(x, y).\n\nThis information is passed to the applet using the INDEPENDENT_VARIABLES and DEPENDENT_VARIABLES parameters. The value for either of these parameters is a list of rules LiveGraphics3D can use to assign values to variables. In the case of independent variables each rule just gives the initial value, which can later be changed by the user. The rules for dependent variables describe how to compute the values using any other previously mentioned variables.\n\nResulting applet:\n\nClick and drag the red point to see how it moves along the surface. The effect of defining z as a dependent variable is quite noticeable in the following sense: if you view the surface from above, the motion of the point is quite natural; motions of the mouse correspond directly to changes in x and y. If you view the surface from the side, however, the point is very tricky to control.\n\nBy now you may have noticed that you can drag the point off of the mesh. This undesirable behavior can be avoided with a feature that is tricky and counter-intuitive, yet highly useful: rules for independent variables can also appear in the value of the DEPENDENT_VARIABLESparameter. This is demonstrated in the following HTML code. We use the same input file as above, together with a new set of rules for dependent variables which restrict the values of x and y so that the point stays on the mesh.\n\nTo understand how this process works, suppose you move the point with the mouse. Internally, LiveGraphics3D will recognize that an independent variable has been changed. Whenever this happens, the rules in the DEPENDENT_VARIABLESparameter will be evaluated in order. Each of the Ifstatements below restricts the value of a variable; for example, the statement x -> If[x < -1, -1, x]sets x=-1if you have dragged it to a value less than -1, and leaves it unchanged otherwise. The new value of z is only computed after the rules for x and y have been processed, ensuring that the point will be on our mesh.\n\nResulting applet:\n\nBefore continuing, we should mention the following issues related to this example.\n\n1. A Point can only be dragged if at least one of its coordinates is an independent variable; if we replaced Point[{x,y,z}] in the input file with Point[{x\/2,y\/2,z}] -- or even Point[{1*x,1*y,z}] -- LiveGraphics3D would not allow us to click on it. (In the latter case, 1*x and 1*y are certainly equivalent to x andy, but LiveGraphics3D is not equipped to make this simplification.)\n2. A Point is the only primitive which can be moved this way. On the next two pages we'll discuss how to make other objects move.\n3. It was not strictly necessary to use the dependent variable z in this example. Replacing Point[{x,y,z}] with Point[{x,y,2*y*Exp[-x^2-y^2]}] would result in the same display, and the rule z -> 2y*Exp[-x^2-y^2] would no longer be needed.\n4. As you examine examples using LiveGraphics3D on the web, it is also worth noting that it is common to combine two Ifstatements such as x -> If[x < -1, -1, x], \u00a0x -> If[x > 3, 3, x] into the more compact form x -> If[x < -1, -1, If[x > 3, 3, x]]. This expression is also equivalent to x -> Max[ -1, Min[x, 3] ].\n\nJonathan Rogness and Martin Kraus, \"Constructing Mathlets Quickly using LiveGraphics3D - Parametrized Graphics,\" Loci (May 2006)\n\n## JOMA\n\nJournal of Online Mathematics and its Applications","date":"2015-02-27 21:19:01","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\": 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\": 0.7300724387168884, \"perplexity\": 802.4364848960097}, \"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-2015-11\/segments\/1424936461416.42\/warc\/CC-MAIN-20150226074101-00198-ip-10-28-5-156.ec2.internal.warc.gz\"}"} | null | null |
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